MoMo v0.1.0 : Artifacts of the Evaluation

NAME TPTP:CSM/THM TPTP RATING DOMAIN DESIGNATION TERMS MODALITIES #PREDICATES/FUNCTIONS MAX FORMULA DEPTH #MODAL OPERATORS SMT-MODEL TPTP-MODEL AXIOMS? ONLY AXIOMS OUTPUT AGMV VERIFICATION RUNTIME [SEC] NOTES GRA076_1.001 CSA 0.50 - - - K system 9 16 28 ( ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false (($x1 $world)) Bool false) (define-fun p1 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p10 ((BOUND_VARIABLE_128381 $world)) Bool false) (define-fun p2 (($x1 $world)) Bool (= (as @$world_0 $world) $x1)) (define-fun p3 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p4 (($x1 $world)) Bool (= (as @$world_0 $world) $x1)) (define-fun p5 (($x1 $world)) Bool false) (define-fun p6 ((_arg_1 $world)) Bool false) (define-fun p8 ((BOUND_VARIABLE_128384 $world)) Bool false) ) tff('k_poly_n.0001', logic, ($modal) == ([($modalities) == ($modal_system_K)])). tff(false_decl, type, false: $o). tff(p1_decl, type, p1: $o). tff(p10_decl, type, p10: $o). tff(p2_decl, type, p2: $o). tff(p3_decl, type, p3: $o). tff(p4_decl, type, p4: $o). tff(p5_decl, type, p5: $o). tff(p6_decl, type, p6: $o). tff(p8_decl, type, p8: $o). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & ~p1 & ~p10 & p2 & ~p3 & p4 & ~p5 & ~p6 & ~p8)) & $in_world(world_1, (~false & p1 & ~p10 & ~p2 & p3 & ~p4 & ~p5 & ~p6 & ~p8)) )). - timeout 3,65 GRA076_1.002 THM 0.00 - - - K system 14 22 58 no countermodel :) no countermodel :) - 30,20 GRA076_1.005 CSA 0.00 - - - K system 27 40 202 task timed out! task timed out! - experiment: run model finder with specification on cardinality of set of possible worlds: listing here as (number worlds, cvc5 output): (1,unsat) (2 task timed out) (3, task timed out) GRA076_1.009 CSA 0.00 - - - K system 45 64 693 task timed out! task timed out! - experiment: run model finder with specification on cardinality of set of possible worlds: listing here as (number worlds, cvc5 output): (1,unsat) (2 task timed out) GRA076_1.013 CSA 0.00 - - - K system 63 88 982 task timed out! task timed out! - experiment: run model finder with specification on cardinality of set of possible worlds: listing here as (number worlds, cvc5 output): (1,unsat) (2 task timed out) GRA076_1.017 CSA 0.00 - - - K system 81 112 1588 task timed out! task timed out! - experiment: run model finder with specification on cardinality of set of possible worlds: listing here as (number worlds, cvc5 output): (1,unsat) (2 task timed out) GRA077_1.010 THM 1.00 - - - K4 system 98 104 1279 task timed out! task timed out! - experiment: run model finder with specification on cardinality of set of possible worlds: listing here as (number worlds, cvc5 output): (1,unsat) (2 task timed out) GRA078_1.002 THM 0.50 - - - D4 system 27 35 315 task timed out! task timed out! - experiment: run model finder with specification on cardinality of set of possible worlds: listing here as (number worlds, cvc5 output, runtime): (1,unsat, 1) (2, unsat, 102) (3, task timed out) GRA078_1.018 THM 1.00 - - - D4 system 171 179 3699 task timed out! task timed out! - GRA079_1.002 THM 1.00 - - - K45 system 39 34 313 task timed out! task timed out! - GRA080_1.006 THM 1.00 - - - S5 system 94 90 944 task timed out! task timed out! - GRA080_1.014 THM 1.00 - - - S5 system 202 186 2636 task timed out! task timed out! - LCL971_1.014 THM 1.00 - - - K system 210 1476 1367 task timed out! task timed out! - LCL972_1.014 THM 1.00 - - - K4 system 420 1480 10817 task timed out! task timed out! - without higher JRE(?) had let error:null LCL973_1.006 THM 1.00 - - - K45 system 126 138 1577 task timed out! task timed out! - LCL974_1.006 THM 1.00 - - - D4 system 85 139 1579 task timed out! task timed out! - experiment: run model finder with specification on cardinality of set of possible worlds: listing here as (number worlds, cvc5 output, runtime): (1,unsat, 2) (2, task timed out) LCL974_1.014 THM 1.00 - - - D4 system 421 1483 17119 task timed out! task timed out! - without higher JRE(?) had let error:null LCL975_1.001 CSA 0.00 - - - S4 system 2 8 2 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p101 (($x1 $world)) Bool true) (define-fun p201 (($x1 $world)) Bool true) ) tff('s4_ph_n.0001', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(p101_decl, type, p101: $o). tff(p201_decl, type, p201: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (p101 & p201)) )). verified; assurance 1,08 LCL975_1.005 CSA 0.67 - - - S4 system 30 82 136 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p101 (($x1 $world)) Bool true) (define-fun p102 (($x1 $world)) Bool false) (define-fun p103 (($x1 $world)) Bool false) (define-fun p104 (($x1 $world)) Bool false) (define-fun p105 (($x1 $world)) Bool false) (define-fun p201 (($x1 $world)) Bool false) (define-fun p202 (($x1 $world)) Bool true) (define-fun p203 (($x1 $world)) Bool false) (define-fun p204 (($x1 $world)) Bool false) (define-fun p205 (($x1 $world)) Bool false) (define-fun p301 (($x1 $world)) Bool false) (define-fun p302 (($x1 $world)) Bool false) (define-fun p303 (($x1 $world)) Bool true) (define-fun p304 (($x1 $world)) Bool false) (define-fun p305 (($x1 $world)) Bool false) (define-fun p401 (($x1 $world)) Bool false) (define-fun p402 (($x1 $world)) Bool false) (define-fun p403 (($x1 $world)) Bool false) (define-fun p404 (($x1 $world)) Bool true) (define-fun p405 (($x1 $world)) Bool false) (define-fun p501 (($x1 $world)) Bool false) (define-fun p502 (($x1 $world)) Bool false) (define-fun p503 (($x1 $world)) Bool false) (define-fun p504 (($x1 $world)) Bool true) (define-fun p505 (($x1 $world)) Bool false) (define-fun p601 (($x1 $world)) Bool false) (define-fun p602 (($x1 $world)) Bool false) (define-fun p603 (($x1 $world)) Bool false) (define-fun p604 (($x1 $world)) Bool false) (define-fun p605 (($x1 $world)) Bool true) ) ...found model! tff('s4_ph_n.0005', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(p101_decl, type, p101: $o). tff(p102_decl, type, p102: $o). tff(p103_decl, type, p103: $o). tff(p104_decl, type, p104: $o). tff(p105_decl, type, p105: $o). tff(p201_decl, type, p201: $o). tff(p202_decl, type, p202: $o). tff(p203_decl, type, p203: $o). tff(p204_decl, type, p204: $o). tff(p205_decl, type, p205: $o). tff(p301_decl, type, p301: $o). tff(p302_decl, type, p302: $o). tff(p303_decl, type, p303: $o). tff(p304_decl, type, p304: $o). tff(p305_decl, type, p305: $o). tff(p401_decl, type, p401: $o). tff(p402_decl, type, p402: $o). tff(p403_decl, type, p403: $o). tff(p404_decl, type, p404: $o). tff(p405_decl, type, p405: $o). tff(p501_decl, type, p501: $o). tff(p502_decl, type, p502: $o). tff(p503_decl, type, p503: $o). tff(p504_decl, type, p504: $o). tff(p505_decl, type, p505: $o). tff(p601_decl, type, p601: $o). tff(p602_decl, type, p602: $o). tff(p603_decl, type, p603: $o). tff(p604_decl, type, p604: $o). tff(p605_decl, type, p605: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (p101 & ~p102 & ~p103 & ~p104 & ~p105 & ~p201 & p202 & ~p203 & ~p204 & ~p205 & ~p301 & ~p302 & p303 & ~p304 & ~p305 & ~p401 & ~p402 & ~p403 & p404 & ~p405 & ~p501 & ~p502 & ~p503 & p504 & ~p505 & ~p601 & ~p602 & ~p603 & ~p604 & p605)) )). timeout 1,72 LCL975_1.009 CSA 1.00 - - - S4 system 90 412 766 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p1001 (($x1 $world)) Bool false) (define-fun p1002 (($x1 $world)) Bool false) (define-fun p1003 (($x1 $world)) Bool false) (define-fun p1004 (($x1 $world)) Bool false) (define-fun p1005 (($x1 $world)) Bool false) (define-fun p1006 (($x1 $world)) Bool false) (define-fun p1007 (($x1 $world)) Bool false) (define-fun p1008 (($x1 $world)) Bool false) (define-fun p1009 (($x1 $world)) Bool true) (define-fun p101 (($x1 $world)) Bool true) (define-fun p102 (($x1 $world)) Bool false) (define-fun p103 (($x1 $world)) Bool false) (define-fun p104 (($x1 $world)) Bool false) (define-fun p105 (($x1 $world)) Bool false) (define-fun p106 (($x1 $world)) Bool false) (define-fun p107 (($x1 $world)) Bool false) (define-fun p108 (($x1 $world)) Bool false) (define-fun p109 (($x1 $world)) Bool false) (define-fun p201 (($x1 $world)) Bool false) (define-fun p202 (($x1 $world)) Bool true) (define-fun p203 (($x1 $world)) Bool false) (define-fun p204 (($x1 $world)) Bool false) (define-fun p205 (($x1 $world)) Bool false) (define-fun p206 (($x1 $world)) Bool false) (define-fun p207 (($x1 $world)) Bool false) (define-fun p208 (($x1 $world)) Bool false) (define-fun p209 (($x1 $world)) Bool false) (define-fun p301 (($x1 $world)) Bool false) (define-fun p302 (($x1 $world)) Bool false) (define-fun p303 (($x1 $world)) Bool true) (define-fun p304 (($x1 $world)) Bool false) (define-fun p305 (($x1 $world)) Bool false) (define-fun p306 (($x1 $world)) Bool false) (define-fun p307 (($x1 $world)) Bool false) (define-fun p308 (($x1 $world)) Bool false) (define-fun p309 (($x1 $world)) Bool false) (define-fun p401 (($x1 $world)) Bool false) (define-fun p402 (($x1 $world)) Bool false) (define-fun p403 (($x1 $world)) Bool false) (define-fun p404 (($x1 $world)) Bool true) (define-fun p405 (($x1 $world)) Bool false) (define-fun p406 (($x1 $world)) Bool false) (define-fun p407 (($x1 $world)) Bool false) (define-fun p408 (($x1 $world)) Bool false) (define-fun p409 (($x1 $world)) Bool false) (define-fun p501 (($x1 $world)) Bool false) (define-fun p502 (($x1 $world)) Bool false) (define-fun p503 (($x1 $world)) Bool false) (define-fun p504 (($x1 $world)) Bool false) (define-fun p505 (($x1 $world)) Bool true) (define-fun p506 (($x1 $world)) Bool false) (define-fun p507 (($x1 $world)) Bool false) (define-fun p508 (($x1 $world)) Bool false) (define-fun p509 (($x1 $world)) Bool false) (define-fun p601 (($x1 $world)) Bool false) (define-fun p602 (($x1 $world)) Bool false) (define-fun p603 (($x1 $world)) Bool false) (define-fun p604 (($x1 $world)) Bool false) (define-fun p605 (($x1 $world)) Bool false) (define-fun p606 (($x1 $world)) Bool true) (define-fun p607 (($x1 $world)) Bool false) (define-fun p608 (($x1 $world)) Bool false) (define-fun p609 (($x1 $world)) Bool false) (define-fun p701 (($x1 $world)) Bool false) (define-fun p702 (($x1 $world)) Bool false) (define-fun p703 (($x1 $world)) Bool false) (define-fun p704 (($x1 $world)) Bool false) (define-fun p705 (($x1 $world)) Bool false) (define-fun p706 (($x1 $world)) Bool false) (define-fun p707 (($x1 $world)) Bool true) (define-fun p708 (($x1 $world)) Bool false) (define-fun p709 (($x1 $world)) Bool false) (define-fun p801 (($x1 $world)) Bool false) (define-fun p802 (($x1 $world)) Bool false) (define-fun p803 (($x1 $world)) Bool false) (define-fun p804 (($x1 $world)) Bool false) (define-fun p805 (($x1 $world)) Bool false) (define-fun p806 (($x1 $world)) Bool false) (define-fun p807 (($x1 $world)) Bool true) (define-fun p808 (($x1 $world)) Bool false) (define-fun p809 (($x1 $world)) Bool false) (define-fun p901 (($x1 $world)) Bool false) (define-fun p902 (($x1 $world)) Bool false) (define-fun p903 (($x1 $world)) Bool false) (define-fun p904 (($x1 $world)) Bool false) (define-fun p905 (($x1 $world)) Bool false) (define-fun p906 (($x1 $world)) Bool false) (define-fun p907 (($x1 $world)) Bool false) (define-fun p908 (($x1 $world)) Bool true) (define-fun p909 (($x1 $world)) Bool false) ) tff('s4_ph_n.0009', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(p1001_decl, type, p1001: $o). tff(p1002_decl, type, p1002: $o). tff(p1003_decl, type, p1003: $o). tff(p1004_decl, type, p1004: $o). tff(p1005_decl, type, p1005: $o). tff(p1006_decl, type, p1006: $o). tff(p1007_decl, type, p1007: $o). tff(p1008_decl, type, p1008: $o). tff(p1009_decl, type, p1009: $o). tff(p101_decl, type, p101: $o). tff(p102_decl, type, p102: $o). tff(p103_decl, type, p103: $o). tff(p104_decl, type, p104: $o). tff(p105_decl, type, p105: $o). tff(p106_decl, type, p106: $o). tff(p107_decl, type, p107: $o). tff(p108_decl, type, p108: $o). tff(p109_decl, type, p109: $o). tff(p201_decl, type, p201: $o). tff(p202_decl, type, p202: $o). tff(p203_decl, type, p203: $o). tff(p204_decl, type, p204: $o). tff(p205_decl, type, p205: $o). tff(p206_decl, type, p206: $o). tff(p207_decl, type, p207: $o). tff(p208_decl, type, p208: $o). tff(p209_decl, type, p209: $o). tff(p301_decl, type, p301: $o). tff(p302_decl, type, p302: $o). tff(p303_decl, type, p303: $o). tff(p304_decl, type, p304: $o). tff(p305_decl, type, p305: $o). tff(p306_decl, type, p306: $o). tff(p307_decl, type, p307: $o). tff(p308_decl, type, p308: $o). tff(p309_decl, type, p309: $o). tff(p401_decl, type, p401: $o). tff(p402_decl, type, p402: $o). tff(p403_decl, type, p403: $o). tff(p404_decl, type, p404: $o). tff(p405_decl, type, p405: $o). tff(p406_decl, type, p406: $o). tff(p407_decl, type, p407: $o). tff(p408_decl, type, p408: $o). tff(p409_decl, type, p409: $o). tff(p501_decl, type, p501: $o). tff(p502_decl, type, p502: $o). tff(p503_decl, type, p503: $o). tff(p504_decl, type, p504: $o). tff(p505_decl, type, p505: $o). tff(p506_decl, type, p506: $o). tff(p507_decl, type, p507: $o). tff(p508_decl, type, p508: $o). tff(p509_decl, type, p509: $o). tff(p601_decl, type, p601: $o). tff(p602_decl, type, p602: $o). tff(p603_decl, type, p603: $o). tff(p604_decl, type, p604: $o). tff(p605_decl, type, p605: $o). tff(p606_decl, type, p606: $o). tff(p607_decl, type, p607: $o). tff(p608_decl, type, p608: $o). tff(p609_decl, type, p609: $o). tff(p701_decl, type, p701: $o). tff(p702_decl, type, p702: $o). tff(p703_decl, type, p703: $o). tff(p704_decl, type, p704: $o). tff(p705_decl, type, p705: $o). tff(p706_decl, type, p706: $o). tff(p707_decl, type, p707: $o). tff(p708_decl, type, p708: $o). tff(p709_decl, type, p709: $o). tff(p801_decl, type, p801: $o). tff(p802_decl, type, p802: $o). tff(p803_decl, type, p803: $o). tff(p804_decl, type, p804: $o). tff(p805_decl, type, p805: $o). tff(p806_decl, type, p806: $o). tff(p807_decl, type, p807: $o). tff(p808_decl, type, p808: $o). tff(p809_decl, type, p809: $o). tff(p901_decl, type, p901: $o). tff(p902_decl, type, p902: $o). tff(p903_decl, type, p903: $o). tff(p904_decl, type, p904: $o). tff(p905_decl, type, p905: $o). tff(p906_decl, type, p906: $o). tff(p907_decl, type, p907: $o). tff(p908_decl, type, p908: $o). tff(p909_decl, type, p909: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~p1001 & ~p1002 & ~p1003 & ~p1004 & ~p1005 & ~p1006 & ~p1007 & ~p1008 & p1009 & p101 & ~p102 & ~p103 & ~p104 & ~p105 & ~p106 & ~p107 & ~p108 & ~p109 & ~p201 & p202 & ~p203 & ~p204 & ~p205 & ~p206 & ~p207 & ~p208 & ~p209 & ~p301 & ~p302 & p303 & ~p304 & ~p305 & ~p306 & ~p307 & ~p308 & ~p309 & ~p401 & ~p402 & ~p403 & p404 & ~p405 & ~p406 & ~p407 & ~p408 & ~p409 & ~p501 & ~p502 & ~p503 & ~p504 & p505 & ~p506 & ~p507 & ~p508 & ~p509 & ~p601 & ~p602 & ~p603 & ~p604 & ~p605 & p606 & ~p607 & ~p608 & ~p609 & ~p701 & ~p702 & ~p703 & ~p704 & ~p705 & ~p706 & p707 & ~p708 & ~p709 & ~p801 & ~p802 & ~p803 & ~p804 & ~p805 & ~p806 & p807 & ~p808 & ~p809 & ~p901 & ~p902 & ~p903 & ~p904 & ~p905 & ~p906 & ~p907 & p908 & ~p909)) )). timeout 8,16 LCL975_1.013 CSA 1.00 - - - S4 system 182 1190 2276 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p1001 (($x1 $world)) Bool false) (define-fun p1002 (($x1 $world)) Bool false) (define-fun p1003 (($x1 $world)) Bool false) (define-fun p1004 (($x1 $world)) Bool false) (define-fun p1005 (($x1 $world)) Bool false) (define-fun p1006 (($x1 $world)) Bool false) (define-fun p1007 (($x1 $world)) Bool false) (define-fun p1008 (($x1 $world)) Bool false) (define-fun p1009 (($x1 $world)) Bool true) (define-fun p101 (($x1 $world)) Bool true) (define-fun p1010 (($x1 $world)) Bool false) (define-fun p1011 (($x1 $world)) Bool false) (define-fun p1012 (($x1 $world)) Bool false) (define-fun p1013 (($x1 $world)) Bool false) (define-fun p102 (($x1 $world)) Bool false) (define-fun p103 (($x1 $world)) Bool false) (define-fun p104 (($x1 $world)) Bool false) (define-fun p105 (($x1 $world)) Bool false) (define-fun p106 (($x1 $world)) Bool false) (define-fun p107 (($x1 $world)) Bool false) (define-fun p108 (($x1 $world)) Bool false) (define-fun p109 (($x1 $world)) Bool false) (define-fun p110 (($x1 $world)) Bool false) (define-fun p1101 (($x1 $world)) Bool false) (define-fun p1102 (($x1 $world)) Bool false) (define-fun p1103 (($x1 $world)) Bool false) (define-fun p1104 (($x1 $world)) Bool false) (define-fun p1105 (($x1 $world)) Bool false) (define-fun p1106 (($x1 $world)) Bool false) (define-fun p1107 (($x1 $world)) Bool false) (define-fun p1108 (($x1 $world)) Bool false) (define-fun p1109 (($x1 $world)) Bool false) (define-fun p111 (($x1 $world)) Bool false) (define-fun p1110 (($x1 $world)) Bool true) (define-fun p1111 (($x1 $world)) Bool false) (define-fun p1112 (($x1 $world)) Bool false) (define-fun p1113 (($x1 $world)) Bool false) (define-fun p112 (($x1 $world)) Bool false) (define-fun p113 (($x1 $world)) Bool false) (define-fun p1201 (($x1 $world)) Bool false) (define-fun p1202 (($x1 $world)) Bool false) (define-fun p1203 (($x1 $world)) Bool false) (define-fun p1204 (($x1 $world)) Bool false) (define-fun p1205 (($x1 $world)) Bool false) (define-fun p1206 (($x1 $world)) Bool false) (define-fun p1207 (($x1 $world)) Bool false) (define-fun p1208 (($x1 $world)) Bool false) (define-fun p1209 (($x1 $world)) Bool false) (define-fun p1210 (($x1 $world)) Bool false) (define-fun p1211 (($x1 $world)) Bool true) (define-fun p1212 (($x1 $world)) Bool false) (define-fun p1213 (($x1 $world)) Bool false) (define-fun p1301 (($x1 $world)) Bool false) (define-fun p1302 (($x1 $world)) Bool false) (define-fun p1303 (($x1 $world)) Bool false) (define-fun p1304 (($x1 $world)) Bool false) (define-fun p1305 (($x1 $world)) Bool false) (define-fun p1306 (($x1 $world)) Bool false) (define-fun p1307 (($x1 $world)) Bool false) (define-fun p1308 (($x1 $world)) Bool false) (define-fun p1309 (($x1 $world)) Bool false) (define-fun p1310 (($x1 $world)) Bool false) (define-fun p1311 (($x1 $world)) Bool false) (define-fun p1312 (($x1 $world)) Bool true) (define-fun p1313 (($x1 $world)) Bool false) (define-fun p1401 (($x1 $world)) Bool false) (define-fun p1402 (($x1 $world)) Bool false) (define-fun p1403 (($x1 $world)) Bool false) (define-fun p1404 (($x1 $world)) Bool false) (define-fun p1405 (($x1 $world)) Bool false) (define-fun p1406 (($x1 $world)) Bool false) (define-fun p1407 (($x1 $world)) Bool false) (define-fun p1408 (($x1 $world)) Bool false) (define-fun p1409 (($x1 $world)) Bool false) (define-fun p1410 (($x1 $world)) Bool false) (define-fun p1411 (($x1 $world)) Bool false) (define-fun p1412 (($x1 $world)) Bool false) (define-fun p1413 (($x1 $world)) Bool true) (define-fun p201 (($x1 $world)) Bool false) (define-fun p202 (($x1 $world)) Bool true) (define-fun p203 (($x1 $world)) Bool false) (define-fun p204 (($x1 $world)) Bool false) (define-fun p205 (($x1 $world)) Bool false) (define-fun p206 (($x1 $world)) Bool false) (define-fun p207 (($x1 $world)) Bool false) (define-fun p208 (($x1 $world)) Bool false) (define-fun p209 (($x1 $world)) Bool false) (define-fun p210 (($x1 $world)) Bool false) (define-fun p211 (($x1 $world)) Bool false) (define-fun p212 (($x1 $world)) Bool false) (define-fun p213 (($x1 $world)) Bool false) (define-fun p301 (($x1 $world)) Bool false) (define-fun p302 (($x1 $world)) Bool false) (define-fun p303 (($x1 $world)) Bool true) (define-fun p304 (($x1 $world)) Bool false) (define-fun p305 (($x1 $world)) Bool false) (define-fun p306 (($x1 $world)) Bool false) (define-fun p307 (($x1 $world)) Bool false) (define-fun p308 (($x1 $world)) Bool false) (define-fun p309 (($x1 $world)) Bool false) (define-fun p310 (($x1 $world)) Bool false) (define-fun p311 (($x1 $world)) Bool false) (define-fun p312 (($x1 $world)) Bool false) (define-fun p313 (($x1 $world)) Bool false) (define-fun p401 (($x1 $world)) Bool false) (define-fun p402 (($x1 $world)) Bool false) (define-fun p403 (($x1 $world)) Bool false) (define-fun p404 (($x1 $world)) Bool true) (define-fun p405 (($x1 $world)) Bool false) (define-fun p406 (($x1 $world)) Bool false) (define-fun p407 (($x1 $world)) Bool false) (define-fun p408 (($x1 $world)) Bool false) (define-fun p409 (($x1 $world)) Bool false) (define-fun p410 (($x1 $world)) Bool false) (define-fun p411 (($x1 $world)) Bool false) (define-fun p412 (($x1 $world)) Bool false) (define-fun p413 (($x1 $world)) Bool false) (define-fun p501 (($x1 $world)) Bool false) (define-fun p502 (($x1 $world)) Bool false) (define-fun p503 (($x1 $world)) Bool false) (define-fun p504 (($x1 $world)) Bool false) (define-fun p505 (($x1 $world)) Bool true) (define-fun p506 (($x1 $world)) Bool false) (define-fun p507 (($x1 $world)) Bool false) (define-fun p508 (($x1 $world)) Bool false) (define-fun p509 (($x1 $world)) Bool false) (define-fun p510 (($x1 $world)) Bool false) (define-fun p511 (($x1 $world)) Bool false) (define-fun p512 (($x1 $world)) Bool false) (define-fun p513 (($x1 $world)) Bool false) (define-fun p601 (($x1 $world)) Bool false) (define-fun p602 (($x1 $world)) Bool false) (define-fun p603 (($x1 $world)) Bool false) (define-fun p604 (($x1 $world)) Bool false) (define-fun p605 (($x1 $world)) Bool false) (define-fun p606 (($x1 $world)) Bool true) (define-fun p607 (($x1 $world)) Bool false) (define-fun p608 (($x1 $world)) Bool false) (define-fun p609 (($x1 $world)) Bool false) (define-fun p610 (($x1 $world)) Bool false) (define-fun p611 (($x1 $world)) Bool false) (define-fun p612 (($x1 $world)) Bool false) (define-fun p613 (($x1 $world)) Bool false) (define-fun p701 (($x1 $world)) Bool false) (define-fun p702 (($x1 $world)) Bool false) (define-fun p703 (($x1 $world)) Bool false) (define-fun p704 (($x1 $world)) Bool false) (define-fun p705 (($x1 $world)) Bool false) (define-fun p706 (($x1 $world)) Bool false) (define-fun p707 (($x1 $world)) Bool true) (define-fun p708 (($x1 $world)) Bool false) (define-fun p709 (($x1 $world)) Bool false) (define-fun p710 (($x1 $world)) Bool false) (define-fun p711 (($x1 $world)) Bool false) (define-fun p712 (($x1 $world)) Bool false) (define-fun p713 (($x1 $world)) Bool false) (define-fun p801 (($x1 $world)) Bool false) (define-fun p802 (($x1 $world)) Bool false) (define-fun p803 (($x1 $world)) Bool false) (define-fun p804 (($x1 $world)) Bool false) (define-fun p805 (($x1 $world)) Bool false) (define-fun p806 (($x1 $world)) Bool false) (define-fun p807 (($x1 $world)) Bool false) (define-fun p808 (($x1 $world)) Bool true) (define-fun p809 (($x1 $world)) Bool false) (define-fun p810 (($x1 $world)) Bool false) (define-fun p811 (($x1 $world)) Bool false) (define-fun p812 (($x1 $world)) Bool false) (define-fun p813 (($x1 $world)) Bool false) (define-fun p901 (($x1 $world)) Bool false) (define-fun p902 (($x1 $world)) Bool false) (define-fun p903 (($x1 $world)) Bool false) (define-fun p904 (($x1 $world)) Bool false) (define-fun p905 (($x1 $world)) Bool false) (define-fun p906 (($x1 $world)) Bool false) (define-fun p907 (($x1 $world)) Bool false) (define-fun p908 (($x1 $world)) Bool false) (define-fun p909 (($x1 $world)) Bool true) (define-fun p910 (($x1 $world)) Bool false) (define-fun p911 (($x1 $world)) Bool false) (define-fun p912 (($x1 $world)) Bool false) (define-fun p913 (($x1 $world)) Bool false) ) tff('s4_ph_n.0013', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(p1001_decl, type, p1001: $o). tff(p1002_decl, type, p1002: $o). tff(p1003_decl, type, p1003: $o). tff(p1004_decl, type, p1004: $o). tff(p1005_decl, type, p1005: $o). tff(p1006_decl, type, p1006: $o). tff(p1007_decl, type, p1007: $o). tff(p1008_decl, type, p1008: $o). tff(p1009_decl, type, p1009: $o). tff(p101_decl, type, p101: $o). tff(p1010_decl, type, p1010: $o). tff(p1011_decl, type, p1011: $o). tff(p1012_decl, type, p1012: $o). tff(p1013_decl, type, p1013: $o). tff(p102_decl, type, p102: $o). tff(p103_decl, type, p103: $o). tff(p104_decl, type, p104: $o). tff(p105_decl, type, p105: $o). tff(p106_decl, type, p106: $o). tff(p107_decl, type, p107: $o). tff(p108_decl, type, p108: $o). tff(p109_decl, type, p109: $o). tff(p110_decl, type, p110: $o). tff(p1101_decl, type, p1101: $o). tff(p1102_decl, type, p1102: $o). tff(p1103_decl, type, p1103: $o). tff(p1104_decl, type, p1104: $o). tff(p1105_decl, type, p1105: $o). tff(p1106_decl, type, p1106: $o). tff(p1107_decl, type, p1107: $o). tff(p1108_decl, type, p1108: $o). tff(p1109_decl, type, p1109: $o). tff(p111_decl, type, p111: $o). tff(p1110_decl, type, p1110: $o). tff(p1111_decl, type, p1111: $o). tff(p1112_decl, type, p1112: $o). tff(p1113_decl, type, p1113: $o). tff(p112_decl, type, p112: $o). tff(p113_decl, type, p113: $o). tff(p1201_decl, type, p1201: $o). tff(p1202_decl, type, p1202: $o). tff(p1203_decl, type, p1203: $o). tff(p1204_decl, type, p1204: $o). tff(p1205_decl, type, p1205: $o). tff(p1206_decl, type, p1206: $o). tff(p1207_decl, type, p1207: $o). tff(p1208_decl, type, p1208: $o). tff(p1209_decl, type, p1209: $o). tff(p1210_decl, type, p1210: $o). tff(p1211_decl, type, p1211: $o). tff(p1212_decl, type, p1212: $o). tff(p1213_decl, type, p1213: $o). tff(p1301_decl, type, p1301: $o). tff(p1302_decl, type, p1302: $o). tff(p1303_decl, type, p1303: $o). tff(p1304_decl, type, p1304: $o). tff(p1305_decl, type, p1305: $o). tff(p1306_decl, type, p1306: $o). tff(p1307_decl, type, p1307: $o). tff(p1308_decl, type, p1308: $o). tff(p1309_decl, type, p1309: $o). tff(p1310_decl, type, p1310: $o). tff(p1311_decl, type, p1311: $o). tff(p1312_decl, type, p1312: $o). tff(p1313_decl, type, p1313: $o). tff(p1401_decl, type, p1401: $o). tff(p1402_decl, type, p1402: $o). tff(p1403_decl, type, p1403: $o). tff(p1404_decl, type, p1404: $o). tff(p1405_decl, type, p1405: $o). tff(p1406_decl, type, p1406: $o). tff(p1407_decl, type, p1407: $o). tff(p1408_decl, type, p1408: $o). tff(p1409_decl, type, p1409: $o). tff(p1410_decl, type, p1410: $o). tff(p1411_decl, type, p1411: $o). tff(p1412_decl, type, p1412: $o). tff(p1413_decl, type, p1413: $o). tff(p201_decl, type, p201: $o). tff(p202_decl, type, p202: $o). tff(p203_decl, type, p203: $o). tff(p204_decl, type, p204: $o). tff(p205_decl, type, p205: $o). tff(p206_decl, type, p206: $o). tff(p207_decl, type, p207: $o). tff(p208_decl, type, p208: $o). tff(p209_decl, type, p209: $o). tff(p210_decl, type, p210: $o). tff(p211_decl, type, p211: $o). tff(p212_decl, type, p212: $o). tff(p213_decl, type, p213: $o). tff(p301_decl, type, p301: $o). tff(p302_decl, type, p302: $o). tff(p303_decl, type, p303: $o). tff(p304_decl, type, p304: $o). tff(p305_decl, type, p305: $o). tff(p306_decl, type, p306: $o). tff(p307_decl, type, p307: $o). tff(p308_decl, type, p308: $o). tff(p309_decl, type, p309: $o). tff(p310_decl, type, p310: $o). tff(p311_decl, type, p311: $o). tff(p312_decl, type, p312: $o). tff(p313_decl, type, p313: $o). tff(p401_decl, type, p401: $o). tff(p402_decl, type, p402: $o). tff(p403_decl, type, p403: $o). tff(p404_decl, type, p404: $o). tff(p405_decl, type, p405: $o). tff(p406_decl, type, p406: $o). tff(p407_decl, type, p407: $o). tff(p408_decl, type, p408: $o). tff(p409_decl, type, p409: $o). tff(p410_decl, type, p410: $o). tff(p411_decl, type, p411: $o). tff(p412_decl, type, p412: $o). tff(p413_decl, type, p413: $o). tff(p501_decl, type, p501: $o). tff(p502_decl, type, p502: $o). tff(p503_decl, type, p503: $o). tff(p504_decl, type, p504: $o). tff(p505_decl, type, p505: $o). tff(p506_decl, type, p506: $o). tff(p507_decl, type, p507: $o). tff(p508_decl, type, p508: $o). tff(p509_decl, type, p509: $o). tff(p510_decl, type, p510: $o). tff(p511_decl, type, p511: $o). tff(p512_decl, type, p512: $o). tff(p513_decl, type, p513: $o). tff(p601_decl, type, p601: $o). tff(p602_decl, type, p602: $o). tff(p603_decl, type, p603: $o). tff(p604_decl, type, p604: $o). tff(p605_decl, type, p605: $o). tff(p606_decl, type, p606: $o). tff(p607_decl, type, p607: $o). tff(p608_decl, type, p608: $o). tff(p609_decl, type, p609: $o). tff(p610_decl, type, p610: $o). tff(p611_decl, type, p611: $o). tff(p612_decl, type, p612: $o). tff(p613_decl, type, p613: $o). tff(p701_decl, type, p701: $o). tff(p702_decl, type, p702: $o). tff(p703_decl, type, p703: $o). tff(p704_decl, type, p704: $o). tff(p705_decl, type, p705: $o). tff(p706_decl, type, p706: $o). tff(p707_decl, type, p707: $o). tff(p708_decl, type, p708: $o). tff(p709_decl, type, p709: $o). tff(p710_decl, type, p710: $o). tff(p711_decl, type, p711: $o). tff(p712_decl, type, p712: $o). tff(p713_decl, type, p713: $o). tff(p801_decl, type, p801: $o). tff(p802_decl, type, p802: $o). tff(p803_decl, type, p803: $o). tff(p804_decl, type, p804: $o). tff(p805_decl, type, p805: $o). tff(p806_decl, type, p806: $o). tff(p807_decl, type, p807: $o). tff(p808_decl, type, p808: $o). tff(p809_decl, type, p809: $o). tff(p810_decl, type, p810: $o). tff(p811_decl, type, p811: $o). tff(p812_decl, type, p812: $o). tff(p813_decl, type, p813: $o). tff(p901_decl, type, p901: $o). tff(p902_decl, type, p902: $o). tff(p903_decl, type, p903: $o). tff(p904_decl, type, p904: $o). tff(p905_decl, type, p905: $o). tff(p906_decl, type, p906: $o). tff(p907_decl, type, p907: $o). tff(p908_decl, type, p908: $o). tff(p909_decl, type, p909: $o). tff(p910_decl, type, p910: $o). tff(p911_decl, type, p911: $o). tff(p912_decl, type, p912: $o). tff(p913_decl, type, p913: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~p1001 & ~p1002 & ~p1003 & ~p1004 & ~p1005 & ~p1006 & ~p1007 & ~p1008 & p1009 & p101 & ~p1010 & ~p1011 & ~p1012 & ~p1013 & ~p102 & ~p103 & ~p104 & ~p105 & ~p106 & ~p107 & ~p108 & ~p109 & ~p110 & ~p1101 & ~p1102 & ~p1103 & ~p1104 & ~p1105 & ~p1106 & ~p1107 & ~p1108 & ~p1109 & ~p111 & p1110 & ~p1111 & ~p1112 & ~p1113 & ~p112 & ~p113 & ~p1201 & ~p1202 & ~p1203 & ~p1204 & ~p1205 & ~p1206 & ~p1207 & ~p1208 & ~p1209 & ~p1210 & p1211 & ~p1212 & ~p1213 & ~p1301 & ~p1302 & ~p1303 & ~p1304 & ~p1305 & ~p1306 & ~p1307 & ~p1308 & ~p1309 & ~p1310 & ~p1311 & p1312 & ~p1313 & ~p1401 & ~p1402 & ~p1403 & ~p1404 & ~p1405 & ~p1406 & ~p1407 & ~p1408 & ~p1409 & ~p1410 & ~p1411 & ~p1412 & p1413 & ~p201 & p202 & ~p203 & ~p204 & ~p205 & ~p206 & ~p207 & ~p208 & ~p209 & ~p210 & ~p211 & ~p212 & ~p213 & ~p301 & ~p302 & p303 & ~p304 & ~p305 & ~p306 & ~p307 & ~p308 & ~p309 & ~p310 & ~p311 & ~p312 & ~p313 & ~p401 & ~p402 & ~p403 & p404 & ~p405 & ~p406 & ~p407 & ~p408 & ~p409 & ~p410 & ~p411 & ~p412 & ~p413 & ~p501 & ~p502 & ~p503 & ~p504 & p505 & ~p506 & ~p507 & ~p508 & ~p509 & ~p510 & ~p511 & ~p512 & ~p513 & ~p601 & ~p602 & ~p603 & ~p604 & ~p605 & p606 & ~p607 & ~p608 & ~p609 & ~p610 & ~p611 & ~p612 & ~p613 & ~p701 & ~p702 & ~p703 & ~p704 & ~p705 & ~p706 & p707 & ~p708 & ~p709 & ~p710 & ~p711 & ~p712 & ~p713 & ~p801 & ~p802 & ~p803 & ~p804 & ~p805 & ~p806 & ~p807 & p808 & ~p809 & ~p810 & ~p811 & ~p812 & ~p813 & ~p901 & ~p902 & ~p903 & ~p904 & ~p905 & ~p906 & ~p907 & ~p908 & p909 & ~p910 & ~p911 & ~p912 & ~p913)) )). timeout 113,18 without higher JRE(?) had let error:null LCL975_1.017 CSA 1.00 - - - S4 system 306 2608 5050 task timed out! task timed out! - without higher JRE(?) had let error:null LCL976_1.002 THM 0.00 - - - S5 system 19 20 96 no countermodel :) no countermodel :) - 1,75 LCL976_1.018 THM 1.00 - - - S5 system 1027 3092 35400 task timed out! task timed out! - without higher JRE(?) had let error:null PLA055_1.010 THM 0.50 - - - K system 7 223 890 task timed out! task timed out! - experiment on constraining world numbers in each run of model finder, note in (number of worlds, cvc5 output): (1, unsat, 1)(2,unsat, 1)(3,unsat, 1)(4,unsat, 3)(5, task timed out)(10,task timed out) PLA056_1.010 THM 1.00 - - - K4 system 12 165 1760 task timed out! task timed out! - PLA057_1.018 THM 1.00 - - - K45 system 18 303 5496 task timed out! task timed out! - PLA058_1.018 THM 1.00 - - - D4 system 13 304 5498 task timed out! task timed out! - PLA059_1.001 CSA 0.00 - - - S4 system 13 43 37 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false ((_arg_1 $world)) Bool false) (define-fun p11 (($x1 $world)) Bool false) (define-fun p12 ((_arg_1 $world)) Bool false) (define-fun p13 (($x1 $world)) Bool false) (define-fun p14 (($x1 $world)) Bool true) (define-fun p15 (($x1 $world)) Bool false) (define-fun p16 (($x1 $world)) Bool true) (define-fun p21 (($x1 $world)) Bool false) (define-fun p22 (($x1 $world)) Bool true) (define-fun p23 (($x1 $world)) Bool false) (define-fun p24 (($x1 $world)) Bool true) (define-fun p25 (($x1 $world)) Bool true) (define-fun p26 (($x1 $world)) Bool true) ) tff('s4_path_n.0001', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(false_decl, type, false: $o). tff(p11_decl, type, p11: $o). tff(p12_decl, type, p12: $o). tff(p13_decl, type, p13: $o). tff(p14_decl, type, p14: $o). tff(p15_decl, type, p15: $o). tff(p16_decl, type, p16: $o). tff(p21_decl, type, p21: $o). tff(p22_decl, type, p22: $o). tff(p23_decl, type, p23: $o). tff(p24_decl, type, p24: $o). tff(p25_decl, type, p25: $o). tff(p26_decl, type, p26: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & ~p11 & ~p12 & ~p13 & p14 & ~p15 & p16 & ~p21 & p22 & ~p23 & p24 & p25 & p26)) )). verified; assurance 1,59 PLA059_1.005 CSA 0.00 - - - S4 system 37 130 317 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false ((_arg_1 $world)) Bool false) (define-fun p11 (($x1 $world)) Bool false) (define-fun p12 (($x1 $world)) Bool false) (define-fun p13 (($x1 $world)) Bool false) (define-fun p14 (($x1 $world)) Bool true) (define-fun p15 (($x1 $world)) Bool false) (define-fun p16 (($x1 $world)) Bool true) (define-fun p21 (($x1 $world)) Bool false) (define-fun p22 (($x1 $world)) Bool true) (define-fun p23 (($x1 $world)) Bool false) (define-fun p24 (($x1 $world)) Bool true) (define-fun p25 (($x1 $world)) Bool false) (define-fun p26 (($x1 $world)) Bool true) (define-fun p31 (($x1 $world)) Bool false) (define-fun p32 (($x1 $world)) Bool true) (define-fun p33 (($x1 $world)) Bool false) (define-fun p34 (($x1 $world)) Bool true) (define-fun p35 (($x1 $world)) Bool false) (define-fun p36 (($x1 $world)) Bool false) (define-fun p41 (($x1 $world)) Bool false) (define-fun p42 (($x1 $world)) Bool true) (define-fun p43 (($x1 $world)) Bool true) (define-fun p44 (($x1 $world)) Bool true) (define-fun p45 (($x1 $world)) Bool false) (define-fun p46 (($x1 $world)) Bool true) (define-fun p51 (($x1 $world)) Bool false) (define-fun p52 (($x1 $world)) Bool true) (define-fun p53 (($x1 $world)) Bool false) (define-fun p54 (($x1 $world)) Bool true) (define-fun p55 (($x1 $world)) Bool false) (define-fun p56 (($x1 $world)) Bool true) (define-fun p61 (($x1 $world)) Bool false) (define-fun p62 (($x1 $world)) Bool true) (define-fun p63 (($x1 $world)) Bool true) (define-fun p64 (($x1 $world)) Bool true) (define-fun p65 (($x1 $world)) Bool false) (define-fun p66 (($x1 $world)) Bool true) ) tff('s4_path_n.0005', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(false_decl, type, false: $o). tff(p11_decl, type, p11: $o). tff(p12_decl, type, p12: $o). tff(p13_decl, type, p13: $o). tff(p14_decl, type, p14: $o). tff(p15_decl, type, p15: $o). tff(p16_decl, type, p16: $o). tff(p21_decl, type, p21: $o). tff(p22_decl, type, p22: $o). tff(p23_decl, type, p23: $o). tff(p24_decl, type, p24: $o). tff(p25_decl, type, p25: $o). tff(p26_decl, type, p26: $o). tff(p31_decl, type, p31: $o). tff(p32_decl, type, p32: $o). tff(p33_decl, type, p33: $o). tff(p34_decl, type, p34: $o). tff(p35_decl, type, p35: $o). tff(p36_decl, type, p36: $o). tff(p41_decl, type, p41: $o). tff(p42_decl, type, p42: $o). tff(p43_decl, type, p43: $o). tff(p44_decl, type, p44: $o). tff(p45_decl, type, p45: $o). tff(p46_decl, type, p46: $o). tff(p51_decl, type, p51: $o). tff(p52_decl, type, p52: $o). tff(p53_decl, type, p53: $o). tff(p54_decl, type, p54: $o). tff(p55_decl, type, p55: $o). tff(p56_decl, type, p56: $o). tff(p61_decl, type, p61: $o). tff(p62_decl, type, p62: $o). tff(p63_decl, type, p63: $o). tff(p64_decl, type, p64: $o). tff(p65_decl, type, p65: $o). tff(p66_decl, type, p66: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & ~p11 & ~p12 & ~p13 & p14 & ~p15 & p16 & ~p21 & p22 & ~p23 & p24 & ~p25 & p26 & ~p31 & p32 & ~p33 & p34 & ~p35 & ~p36 & ~p41 & p42 & p43 & p44 & ~p45 & p46 & ~p51 & p52 & ~p53 & p54 & ~p55 & p56 & ~p61 & p62 & p63 & p64 & ~p65 & p66)) )). timeout 1,8 PLA059_1.009 CSA 0.33 - - - S4 system 61 220 853 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false ((_arg_1 $world)) Bool false) (define-fun p101 (($x1 $world)) Bool true) (define-fun p102 (($x1 $world)) Bool true) (define-fun p103 (($x1 $world)) Bool false) (define-fun p104 (($x1 $world)) Bool true) (define-fun p105 (($x1 $world)) Bool false) (define-fun p106 (($x1 $world)) Bool true) (define-fun p11 (($x1 $world)) Bool false) (define-fun p12 (($x1 $world)) Bool false) (define-fun p13 (($x1 $world)) Bool false) (define-fun p14 (($x1 $world)) Bool true) (define-fun p15 (($x1 $world)) Bool false) (define-fun p16 (($x1 $world)) Bool true) (define-fun p21 (($x1 $world)) Bool false) (define-fun p22 (($x1 $world)) Bool true) (define-fun p23 (($x1 $world)) Bool false) (define-fun p24 (($x1 $world)) Bool true) (define-fun p25 (($x1 $world)) Bool false) (define-fun p26 (($x1 $world)) Bool true) (define-fun p31 (($x1 $world)) Bool false) (define-fun p32 (($x1 $world)) Bool true) (define-fun p33 (($x1 $world)) Bool false) (define-fun p34 (($x1 $world)) Bool true) (define-fun p35 (($x1 $world)) Bool false) (define-fun p36 (($x1 $world)) Bool false) (define-fun p41 (($x1 $world)) Bool false) (define-fun p42 (($x1 $world)) Bool true) (define-fun p43 (($x1 $world)) Bool false) (define-fun p44 (($x1 $world)) Bool true) (define-fun p45 (($x1 $world)) Bool false) (define-fun p46 (($x1 $world)) Bool true) (define-fun p51 (($x1 $world)) Bool false) (define-fun p52 (($x1 $world)) Bool true) (define-fun p53 (($x1 $world)) Bool false) (define-fun p54 (($x1 $world)) Bool false) (define-fun p55 (($x1 $world)) Bool false) (define-fun p56 (($x1 $world)) Bool true) (define-fun p61 (($x1 $world)) Bool true) (define-fun p62 (($x1 $world)) Bool true) (define-fun p63 (($x1 $world)) Bool false) (define-fun p64 (($x1 $world)) Bool true) (define-fun p65 (($x1 $world)) Bool false) (define-fun p66 (($x1 $world)) Bool true) (define-fun p71 (($x1 $world)) Bool false) (define-fun p72 (($x1 $world)) Bool true) (define-fun p73 (($x1 $world)) Bool false) (define-fun p74 (($x1 $world)) Bool true) (define-fun p75 (($x1 $world)) Bool false) (define-fun p76 (($x1 $world)) Bool true) (define-fun p81 (($x1 $world)) Bool true) (define-fun p82 (($x1 $world)) Bool true) (define-fun p83 (($x1 $world)) Bool false) (define-fun p84 (($x1 $world)) Bool true) (define-fun p85 (($x1 $world)) Bool false) (define-fun p86 (($x1 $world)) Bool true) (define-fun p91 (($x1 $world)) Bool false) (define-fun p92 (($x1 $world)) Bool true) (define-fun p93 (($x1 $world)) Bool false) (define-fun p94 (($x1 $world)) Bool true) (define-fun p95 (($x1 $world)) Bool false) (define-fun p96 (($x1 $world)) Bool true) ) tff('s4_path_n.0009', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(false_decl, type, false: $o). tff(p101_decl, type, p101: $o). tff(p102_decl, type, p102: $o). tff(p103_decl, type, p103: $o). tff(p104_decl, type, p104: $o). tff(p105_decl, type, p105: $o). tff(p106_decl, type, p106: $o). tff(p11_decl, type, p11: $o). tff(p12_decl, type, p12: $o). tff(p13_decl, type, p13: $o). tff(p14_decl, type, p14: $o). tff(p15_decl, type, p15: $o). tff(p16_decl, type, p16: $o). tff(p21_decl, type, p21: $o). tff(p22_decl, type, p22: $o). tff(p23_decl, type, p23: $o). tff(p24_decl, type, p24: $o). tff(p25_decl, type, p25: $o). tff(p26_decl, type, p26: $o). tff(p31_decl, type, p31: $o). tff(p32_decl, type, p32: $o). tff(p33_decl, type, p33: $o). tff(p34_decl, type, p34: $o). tff(p35_decl, type, p35: $o). tff(p36_decl, type, p36: $o). tff(p41_decl, type, p41: $o). tff(p42_decl, type, p42: $o). tff(p43_decl, type, p43: $o). tff(p44_decl, type, p44: $o). tff(p45_decl, type, p45: $o). tff(p46_decl, type, p46: $o). tff(p51_decl, type, p51: $o). tff(p52_decl, type, p52: $o). tff(p53_decl, type, p53: $o). tff(p54_decl, type, p54: $o). tff(p55_decl, type, p55: $o). tff(p56_decl, type, p56: $o). tff(p61_decl, type, p61: $o). tff(p62_decl, type, p62: $o). tff(p63_decl, type, p63: $o). tff(p64_decl, type, p64: $o). tff(p65_decl, type, p65: $o). tff(p66_decl, type, p66: $o). tff(p71_decl, type, p71: $o). tff(p72_decl, type, p72: $o). tff(p73_decl, type, p73: $o). tff(p74_decl, type, p74: $o). tff(p75_decl, type, p75: $o). tff(p76_decl, type, p76: $o). tff(p81_decl, type, p81: $o). tff(p82_decl, type, p82: $o). tff(p83_decl, type, p83: $o). tff(p84_decl, type, p84: $o). tff(p85_decl, type, p85: $o). tff(p86_decl, type, p86: $o). tff(p91_decl, type, p91: $o). tff(p92_decl, type, p92: $o). tff(p93_decl, type, p93: $o). tff(p94_decl, type, p94: $o). tff(p95_decl, type, p95: $o). tff(p96_decl, type, p96: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & p101 & p102 & ~p103 & p104 & ~p105 & p106 & ~p11 & ~p12 & ~p13 & p14 & ~p15 & p16 & ~p21 & p22 & ~p23 & p24 & ~p25 & p26 & ~p31 & p32 & ~p33 & p34 & ~p35 & ~p36 & ~p41 & p42 & ~p43 & p44 & ~p45 & p46 & ~p51 & p52 & ~p53 & ~p54 & ~p55 & p56 & p61 & p62 & ~p63 & p64 & ~p65 & p66 & ~p71 & p72 & ~p73 & p74 & ~p75 & p76 & p81 & p82 & ~p83 & p84 & ~p85 & p86 & ~p91 & p92 & ~p93 & p94 & ~p95 & p96)) )). timeout 2,8 PLA059_1.013 CSA 0.33 - - - S4 system 85 310 1645 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false ((_arg_1 $world)) Bool false) (define-fun p101 (($x1 $world)) Bool false) (define-fun p102 (($x1 $world)) Bool true) (define-fun p103 (($x1 $world)) Bool false) (define-fun p104 (($x1 $world)) Bool true) (define-fun p105 (($x1 $world)) Bool true) (define-fun p106 (($x1 $world)) Bool true) (define-fun p11 (($x1 $world)) Bool false) (define-fun p111 (($x1 $world)) Bool false) (define-fun p112 (($x1 $world)) Bool true) (define-fun p113 (($x1 $world)) Bool false) (define-fun p114 (($x1 $world)) Bool true) (define-fun p115 (($x1 $world)) Bool false) (define-fun p116 (($x1 $world)) Bool true) (define-fun p12 (($x1 $world)) Bool false) (define-fun p121 (($x1 $world)) Bool false) (define-fun p122 (($x1 $world)) Bool true) (define-fun p123 (($x1 $world)) Bool false) (define-fun p124 (($x1 $world)) Bool true) (define-fun p125 (($x1 $world)) Bool true) (define-fun p126 (($x1 $world)) Bool true) (define-fun p13 (($x1 $world)) Bool false) (define-fun p131 (($x1 $world)) Bool false) (define-fun p132 (($x1 $world)) Bool true) (define-fun p133 (($x1 $world)) Bool false) (define-fun p134 (($x1 $world)) Bool true) (define-fun p135 (($x1 $world)) Bool false) (define-fun p136 (($x1 $world)) Bool true) (define-fun p14 (($x1 $world)) Bool true) (define-fun p141 (($x1 $world)) Bool false) (define-fun p142 (($x1 $world)) Bool true) (define-fun p143 (($x1 $world)) Bool false) (define-fun p144 (($x1 $world)) Bool true) (define-fun p145 (($x1 $world)) Bool true) (define-fun p146 (($x1 $world)) Bool true) (define-fun p15 (($x1 $world)) Bool false) (define-fun p16 (($x1 $world)) Bool true) (define-fun p21 (($x1 $world)) Bool false) (define-fun p22 (($x1 $world)) Bool true) (define-fun p23 (($x1 $world)) Bool false) (define-fun p24 (($x1 $world)) Bool true) (define-fun p25 (($x1 $world)) Bool false) (define-fun p26 (($x1 $world)) Bool true) (define-fun p31 (($x1 $world)) Bool false) (define-fun p32 (($x1 $world)) Bool true) (define-fun p33 (($x1 $world)) Bool false) (define-fun p34 (($x1 $world)) Bool true) (define-fun p35 (($x1 $world)) Bool false) (define-fun p36 (($x1 $world)) Bool false) (define-fun p41 (($x1 $world)) Bool false) (define-fun p42 (($x1 $world)) Bool true) (define-fun p43 (($x1 $world)) Bool false) (define-fun p44 (($x1 $world)) Bool true) (define-fun p45 (($x1 $world)) Bool false) (define-fun p46 (($x1 $world)) Bool true) (define-fun p51 (($x1 $world)) Bool false) (define-fun p52 (($x1 $world)) Bool true) (define-fun p53 (($x1 $world)) Bool false) (define-fun p54 (($x1 $world)) Bool false) (define-fun p55 (($x1 $world)) Bool false) (define-fun p56 (($x1 $world)) Bool true) (define-fun p61 (($x1 $world)) Bool false) (define-fun p62 (($x1 $world)) Bool true) (define-fun p63 (($x1 $world)) Bool false) (define-fun p64 (($x1 $world)) Bool true) (define-fun p65 (($x1 $world)) Bool false) (define-fun p66 (($x1 $world)) Bool true) (define-fun p71 (($x1 $world)) Bool false) (define-fun p72 (($x1 $world)) Bool false) (define-fun p73 (($x1 $world)) Bool false) (define-fun p74 (($x1 $world)) Bool true) (define-fun p75 (($x1 $world)) Bool false) (define-fun p76 (($x1 $world)) Bool true) (define-fun p81 (($x1 $world)) Bool false) (define-fun p82 (($x1 $world)) Bool true) (define-fun p83 (($x1 $world)) Bool false) (define-fun p84 (($x1 $world)) Bool true) (define-fun p85 (($x1 $world)) Bool true) (define-fun p86 (($x1 $world)) Bool true) (define-fun p91 (($x1 $world)) Bool false) (define-fun p92 (($x1 $world)) Bool true) (define-fun p93 (($x1 $world)) Bool false) (define-fun p94 (($x1 $world)) Bool true) (define-fun p95 (($x1 $world)) Bool false) (define-fun p96 (($x1 $world)) Bool true) ) tff('s4_path_n.0013', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(false_decl, type, false: $o). tff(p101_decl, type, p101: $o). tff(p102_decl, type, p102: $o). tff(p103_decl, type, p103: $o). tff(p104_decl, type, p104: $o). tff(p105_decl, type, p105: $o). tff(p106_decl, type, p106: $o). tff(p11_decl, type, p11: $o). tff(p111_decl, type, p111: $o). tff(p112_decl, type, p112: $o). tff(p113_decl, type, p113: $o). tff(p114_decl, type, p114: $o). tff(p115_decl, type, p115: $o). tff(p116_decl, type, p116: $o). tff(p12_decl, type, p12: $o). tff(p121_decl, type, p121: $o). tff(p122_decl, type, p122: $o). tff(p123_decl, type, p123: $o). tff(p124_decl, type, p124: $o). tff(p125_decl, type, p125: $o). tff(p126_decl, type, p126: $o). tff(p13_decl, type, p13: $o). tff(p131_decl, type, p131: $o). tff(p132_decl, type, p132: $o). tff(p133_decl, type, p133: $o). tff(p134_decl, type, p134: $o). tff(p135_decl, type, p135: $o). tff(p136_decl, type, p136: $o). tff(p14_decl, type, p14: $o). tff(p141_decl, type, p141: $o). tff(p142_decl, type, p142: $o). tff(p143_decl, type, p143: $o). tff(p144_decl, type, p144: $o). tff(p145_decl, type, p145: $o). tff(p146_decl, type, p146: $o). tff(p15_decl, type, p15: $o). tff(p16_decl, type, p16: $o). tff(p21_decl, type, p21: $o). tff(p22_decl, type, p22: $o). tff(p23_decl, type, p23: $o). tff(p24_decl, type, p24: $o). tff(p25_decl, type, p25: $o). tff(p26_decl, type, p26: $o). tff(p31_decl, type, p31: $o). tff(p32_decl, type, p32: $o). tff(p33_decl, type, p33: $o). tff(p34_decl, type, p34: $o). tff(p35_decl, type, p35: $o). tff(p36_decl, type, p36: $o). tff(p41_decl, type, p41: $o). tff(p42_decl, type, p42: $o). tff(p43_decl, type, p43: $o). tff(p44_decl, type, p44: $o). tff(p45_decl, type, p45: $o). tff(p46_decl, type, p46: $o). tff(p51_decl, type, p51: $o). tff(p52_decl, type, p52: $o). tff(p53_decl, type, p53: $o). tff(p54_decl, type, p54: $o). tff(p55_decl, type, p55: $o). tff(p56_decl, type, p56: $o). tff(p61_decl, type, p61: $o). tff(p62_decl, type, p62: $o). tff(p63_decl, type, p63: $o). tff(p64_decl, type, p64: $o). tff(p65_decl, type, p65: $o). tff(p66_decl, type, p66: $o). tff(p71_decl, type, p71: $o). tff(p72_decl, type, p72: $o). tff(p73_decl, type, p73: $o). tff(p74_decl, type, p74: $o). tff(p75_decl, type, p75: $o). tff(p76_decl, type, p76: $o). tff(p81_decl, type, p81: $o). tff(p82_decl, type, p82: $o). tff(p83_decl, type, p83: $o). tff(p84_decl, type, p84: $o). tff(p85_decl, type, p85: $o). tff(p86_decl, type, p86: $o). tff(p91_decl, type, p91: $o). tff(p92_decl, type, p92: $o). tff(p93_decl, type, p93: $o). tff(p94_decl, type, p94: $o). tff(p95_decl, type, p95: $o). tff(p96_decl, type, p96: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & ~p101 & p102 & ~p103 & p104 & p105 & p106 & ~p11 & ~p111 & p112 & ~p113 & p114 & ~p115 & p116 & ~p12 & ~p121 & p122 & ~p123 & p124 & p125 & p126 & ~p13 & ~p131 & p132 & ~p133 & p134 & ~p135 & p136 & p14 & ~p141 & p142 & ~p143 & p144 & p145 & p146 & ~p15 & p16 & ~p21 & p22 & ~p23 & p24 & ~p25 & p26 & ~p31 & p32 & ~p33 & p34 & ~p35 & ~p36 & ~p41 & p42 & ~p43 & p44 & ~p45 & p46 & ~p51 & p52 & ~p53 & ~p54 & ~p55 & p56 & ~p61 & p62 & ~p63 & p64 & ~p65 & p66 & ~p71 & ~p72 & ~p73 & p74 & ~p75 & p76 & ~p81 & p82 & ~p83 & p84 & p85 & p86 & ~p91 & p92 & ~p93 & p94 & ~p95 & p96)) )). timeout 4,51 PLA059_1.014 THM 0.33 - - - S5 system 19 236 3791 task timed out! task timed out! - PLA059_1.017 CSA 1.00 - - - S4 system 109 400 2693 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false ((_arg_1 $world)) Bool false) (define-fun p101 (($x1 $world)) Bool false) (define-fun p102 (($x1 $world)) Bool true) (define-fun p103 (($x1 $world)) Bool true) (define-fun p104 (($x1 $world)) Bool true) (define-fun p105 (($x1 $world)) Bool false) (define-fun p106 (($x1 $world)) Bool true) (define-fun p11 (($x1 $world)) Bool false) (define-fun p111 (($x1 $world)) Bool false) (define-fun p112 (($x1 $world)) Bool true) (define-fun p113 (($x1 $world)) Bool false) (define-fun p114 (($x1 $world)) Bool true) (define-fun p115 (($x1 $world)) Bool false) (define-fun p116 (($x1 $world)) Bool true) (define-fun p12 (($x1 $world)) Bool false) (define-fun p121 (($x1 $world)) Bool false) (define-fun p122 (($x1 $world)) Bool true) (define-fun p123 (($x1 $world)) Bool true) (define-fun p124 (($x1 $world)) Bool true) (define-fun p125 (($x1 $world)) Bool false) (define-fun p126 (($x1 $world)) Bool true) (define-fun p13 (($x1 $world)) Bool false) (define-fun p131 (($x1 $world)) Bool false) (define-fun p132 (($x1 $world)) Bool true) (define-fun p133 (($x1 $world)) Bool false) (define-fun p134 (($x1 $world)) Bool true) (define-fun p135 (($x1 $world)) Bool false) (define-fun p136 (($x1 $world)) Bool true) (define-fun p14 (($x1 $world)) Bool true) (define-fun p141 (($x1 $world)) Bool false) (define-fun p142 (($x1 $world)) Bool true) (define-fun p143 (($x1 $world)) Bool true) (define-fun p144 (($x1 $world)) Bool true) (define-fun p145 (($x1 $world)) Bool false) (define-fun p146 (($x1 $world)) Bool true) (define-fun p15 (($x1 $world)) Bool false) (define-fun p151 (($x1 $world)) Bool false) (define-fun p152 (($x1 $world)) Bool true) (define-fun p153 (($x1 $world)) Bool false) (define-fun p154 (($x1 $world)) Bool true) (define-fun p155 (($x1 $world)) Bool false) (define-fun p156 (($x1 $world)) Bool true) (define-fun p16 (($x1 $world)) Bool true) (define-fun p161 (($x1 $world)) Bool false) (define-fun p162 (($x1 $world)) Bool true) (define-fun p163 (($x1 $world)) Bool true) (define-fun p164 (($x1 $world)) Bool true) (define-fun p165 (($x1 $world)) Bool false) (define-fun p166 (($x1 $world)) Bool true) (define-fun p171 (($x1 $world)) Bool false) (define-fun p172 (($x1 $world)) Bool true) (define-fun p173 (($x1 $world)) Bool false) (define-fun p174 (($x1 $world)) Bool true) (define-fun p175 (($x1 $world)) Bool false) (define-fun p176 (($x1 $world)) Bool true) (define-fun p181 (($x1 $world)) Bool false) (define-fun p182 (($x1 $world)) Bool true) (define-fun p183 (($x1 $world)) Bool true) (define-fun p184 (($x1 $world)) Bool true) (define-fun p185 (($x1 $world)) Bool false) (define-fun p186 (($x1 $world)) Bool true) (define-fun p21 (($x1 $world)) Bool false) (define-fun p22 (($x1 $world)) Bool true) (define-fun p23 (($x1 $world)) Bool false) (define-fun p24 (($x1 $world)) Bool true) (define-fun p25 (($x1 $world)) Bool false) (define-fun p26 (($x1 $world)) Bool true) (define-fun p31 (($x1 $world)) Bool false) (define-fun p32 (($x1 $world)) Bool true) (define-fun p33 (($x1 $world)) Bool false) (define-fun p34 (($x1 $world)) Bool true) (define-fun p35 (($x1 $world)) Bool false) (define-fun p36 (($x1 $world)) Bool false) (define-fun p41 (($x1 $world)) Bool false) (define-fun p42 (($x1 $world)) Bool true) (define-fun p43 (($x1 $world)) Bool false) (define-fun p44 (($x1 $world)) Bool true) (define-fun p45 (($x1 $world)) Bool false) (define-fun p46 (($x1 $world)) Bool true) (define-fun p51 (($x1 $world)) Bool false) (define-fun p52 (($x1 $world)) Bool true) (define-fun p53 (($x1 $world)) Bool false) (define-fun p54 (($x1 $world)) Bool false) (define-fun p55 (($x1 $world)) Bool false) (define-fun p56 (($x1 $world)) Bool true) (define-fun p61 (($x1 $world)) Bool false) (define-fun p62 (($x1 $world)) Bool true) (define-fun p63 (($x1 $world)) Bool false) (define-fun p64 (($x1 $world)) Bool true) (define-fun p65 (($x1 $world)) Bool false) (define-fun p66 (($x1 $world)) Bool true) (define-fun p71 (($x1 $world)) Bool false) (define-fun p72 (($x1 $world)) Bool false) (define-fun p73 (($x1 $world)) Bool false) (define-fun p74 (($x1 $world)) Bool true) (define-fun p75 (($x1 $world)) Bool false) (define-fun p76 (($x1 $world)) Bool true) (define-fun p81 (($x1 $world)) Bool false) (define-fun p82 (($x1 $world)) Bool true) (define-fun p83 (($x1 $world)) Bool false) (define-fun p84 (($x1 $world)) Bool true) (define-fun p85 (($x1 $world)) Bool false) (define-fun p86 (($x1 $world)) Bool true) (define-fun p91 (($x1 $world)) Bool false) (define-fun p92 (($x1 $world)) Bool true) (define-fun p93 (($x1 $world)) Bool false) (define-fun p94 (($x1 $world)) Bool true) (define-fun p95 (($x1 $world)) Bool false) (define-fun p96 (($x1 $world)) Bool false) ) tff('s4_path_n.0017', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(false_decl, type, false: $o). tff(p101_decl, type, p101: $o). tff(p102_decl, type, p102: $o). tff(p103_decl, type, p103: $o). tff(p104_decl, type, p104: $o). tff(p105_decl, type, p105: $o). tff(p106_decl, type, p106: $o). tff(p11_decl, type, p11: $o). tff(p111_decl, type, p111: $o). tff(p112_decl, type, p112: $o). tff(p113_decl, type, p113: $o). tff(p114_decl, type, p114: $o). tff(p115_decl, type, p115: $o). tff(p116_decl, type, p116: $o). tff(p12_decl, type, p12: $o). tff(p121_decl, type, p121: $o). tff(p122_decl, type, p122: $o). tff(p123_decl, type, p123: $o). tff(p124_decl, type, p124: $o). tff(p125_decl, type, p125: $o). tff(p126_decl, type, p126: $o). tff(p13_decl, type, p13: $o). tff(p131_decl, type, p131: $o). tff(p132_decl, type, p132: $o). tff(p133_decl, type, p133: $o). tff(p134_decl, type, p134: $o). tff(p135_decl, type, p135: $o). tff(p136_decl, type, p136: $o). tff(p14_decl, type, p14: $o). tff(p141_decl, type, p141: $o). tff(p142_decl, type, p142: $o). tff(p143_decl, type, p143: $o). tff(p144_decl, type, p144: $o). tff(p145_decl, type, p145: $o). tff(p146_decl, type, p146: $o). tff(p15_decl, type, p15: $o). tff(p151_decl, type, p151: $o). tff(p152_decl, type, p152: $o). tff(p153_decl, type, p153: $o). tff(p154_decl, type, p154: $o). tff(p155_decl, type, p155: $o). tff(p156_decl, type, p156: $o). tff(p16_decl, type, p16: $o). tff(p161_decl, type, p161: $o). tff(p162_decl, type, p162: $o). tff(p163_decl, type, p163: $o). tff(p164_decl, type, p164: $o). tff(p165_decl, type, p165: $o). tff(p166_decl, type, p166: $o). tff(p171_decl, type, p171: $o). tff(p172_decl, type, p172: $o). tff(p173_decl, type, p173: $o). tff(p174_decl, type, p174: $o). tff(p175_decl, type, p175: $o). tff(p176_decl, type, p176: $o). tff(p181_decl, type, p181: $o). tff(p182_decl, type, p182: $o). tff(p183_decl, type, p183: $o). tff(p184_decl, type, p184: $o). tff(p185_decl, type, p185: $o). tff(p186_decl, type, p186: $o). tff(p21_decl, type, p21: $o). tff(p22_decl, type, p22: $o). tff(p23_decl, type, p23: $o). tff(p24_decl, type, p24: $o). tff(p25_decl, type, p25: $o). tff(p26_decl, type, p26: $o). tff(p31_decl, type, p31: $o). tff(p32_decl, type, p32: $o). tff(p33_decl, type, p33: $o). tff(p34_decl, type, p34: $o). tff(p35_decl, type, p35: $o). tff(p36_decl, type, p36: $o). tff(p41_decl, type, p41: $o). tff(p42_decl, type, p42: $o). tff(p43_decl, type, p43: $o). tff(p44_decl, type, p44: $o). tff(p45_decl, type, p45: $o). tff(p46_decl, type, p46: $o). tff(p51_decl, type, p51: $o). tff(p52_decl, type, p52: $o). tff(p53_decl, type, p53: $o). tff(p54_decl, type, p54: $o). tff(p55_decl, type, p55: $o). tff(p56_decl, type, p56: $o). tff(p61_decl, type, p61: $o). tff(p62_decl, type, p62: $o). tff(p63_decl, type, p63: $o). tff(p64_decl, type, p64: $o). tff(p65_decl, type, p65: $o). tff(p66_decl, type, p66: $o). tff(p71_decl, type, p71: $o). tff(p72_decl, type, p72: $o). tff(p73_decl, type, p73: $o). tff(p74_decl, type, p74: $o). tff(p75_decl, type, p75: $o). tff(p76_decl, type, p76: $o). tff(p81_decl, type, p81: $o). tff(p82_decl, type, p82: $o). tff(p83_decl, type, p83: $o). tff(p84_decl, type, p84: $o). tff(p85_decl, type, p85: $o). tff(p86_decl, type, p86: $o). tff(p91_decl, type, p91: $o). tff(p92_decl, type, p92: $o). tff(p93_decl, type, p93: $o). tff(p94_decl, type, p94: $o). tff(p95_decl, type, p95: $o). tff(p96_decl, type, p96: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & ~p101 & p102 & p103 & p104 & ~p105 & p106 & ~p11 & ~p111 & p112 & ~p113 & p114 & ~p115 & p116 & ~p12 & ~p121 & p122 & p123 & p124 & ~p125 & p126 & ~p13 & ~p131 & p132 & ~p133 & p134 & ~p135 & p136 & p14 & ~p141 & p142 & p143 & p144 & ~p145 & p146 & ~p15 & ~p151 & p152 & ~p153 & p154 & ~p155 & p156 & p16 & ~p161 & p162 & p163 & p164 & ~p165 & p166 & ~p171 & p172 & ~p173 & p174 & ~p175 & p176 & ~p181 & p182 & p183 & p184 & ~p185 & p186 & ~p21 & p22 & ~p23 & p24 & ~p25 & p26 & ~p31 & p32 & ~p33 & p34 & ~p35 & ~p36 & ~p41 & p42 & ~p43 & p44 & ~p45 & p46 & ~p51 & p52 & ~p53 & ~p54 & ~p55 & p56 & ~p61 & p62 & ~p63 & p64 & ~p65 & p66 & ~p71 & ~p72 & ~p73 & p74 & ~p75 & p76 & ~p81 & p82 & ~p83 & p84 & ~p85 & p86 & ~p91 & p92 & ~p93 & p94 & ~p95 & ~p96)) )). timeout 7,97 PUZ157_1 CSA ? constant rigid local M system 8 4 3 ( ; cardinality of person is 2 ; rep: (as @person_0 person) ; rep: (as @person_1 person) ; cardinality of product is 1 ; rep: (as @product_0 product) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun alex () person (as @person_0 person)) (define-fun chris () person (as @person_1 person)) (define-fun leo () product (as @product_0 product)) (define-fun work_hard (($x1 $world) ($x2 person) ($x3 product)) Bool true) (define-fun gets_rich (($x1 $world) ($x2 person)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @person_1 person) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @person_0 person) $x2)))) ) tff(semantics, logic, ($alethic_modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_M)])). tff(person_decl, type, person: $tType). tff(product_decl, type, product: $tType). tff(alex_decl, type, alex: person). tff(chris_decl, type, chris: person). tff(leo_decl, type, leo: product). tff(work_hard_decl, type, work_hard: ((person * product) > $o)). tff(gets_rich_decl, type, gets_rich: ((person) > $o)). tff(d_person_decl, type, d_person: $tType). tff(d2person_decl, type, d2person: d_person > person). tff(d_person_0_decl, type, d_person_0: d_person). tff(d_person_1_decl, type, d_person_1: d_person). tff(d_product_decl, type, d_product: $tType). tff(d2product_decl, type, d2product: d_product > product). tff(d_product_0_decl, type, d_product_0: d_product). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(d_person_0, d_person_1) & (! [W: $world]: ($in_world(W, ((! [O: person]: (? [DO: d_person]: O = d2person(DO))) & (! [DO1: d_person, DO2: d_person]: ( (d2person(DO1) = d2person(DO2)) => (DO1 = DO2) )) & (! [DO: d_person]: ( (DO = d_person_0) | (DO = d_person_1) )) & (? [DO: d_person]: (DO = d_person_0)) & (? [DO: d_person]: (DO = d_person_1)))))) & (! [W: $world]: ($in_world(W, ((! [O: product]: (? [DO: d_product]: O = d2product(DO))) & (! [DO1: d_product, DO2: d_product]: ( (d2product(DO1) = d2product(DO2)) => (DO1 = DO2) )) & (! [DO: d_product]: ( (DO = d_product_0) )) & (? [DO: d_product]: (DO = d_product_0)))))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((alex = d2person(d_person_0)) & (chris = d2person(d_person_1)) & (leo = d2product(d_product_0)) & (! [V1: person, V2: product]: work_hard(V1, V2)) & (! [V1: person]: ~(gets_rich(V1))))) & $in_world(world_1, ((alex = d2person(d_person_0)) & (chris = d2person(d_person_1)) & (leo = d2product(d_product_0)) & (! [V1: person, V2: product]: work_hard(V1, V2)) & gets_rich(d2person(d_person_1)) & gets_rich(d2person(d_person_0)))) )). tff(semantics, logic, ($alethic_modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_M)])). tff(person_decl, type, person: $tType). tff(product_decl, type, product: $tType). tff(alex_decl, type, alex: person). tff(chris_decl, type, chris: person). tff(leo_decl, type, leo: product). tff(work_hard_decl, type, work_hard: ((person * product) > $o)). tff(gets_rich_decl, type, gets_rich: ((person) > $o)). tff(d_person_decl, type, d_person: $tType). tff(d2person_decl, type, d2person: d_person > person). tff(d_person_0_decl, type, d_person_0: d_person). tff(d_person_1_decl, type, d_person_1: d_person). tff(d_product_decl, type, d_product: $tType). tff(d2product_decl, type, d2product: d_product > product). tff(d_product_0_decl, type, d_product_0: d_product). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(d_person_0, d_person_1) & (! [W: $world]: ($in_world(W, ((! [O: person]: (? [DO: d_person]: O = d2person(DO))) & (! [DO1: d_person, DO2: d_person]: ( (d2person(DO1) = d2person(DO2)) => (DO1 = DO2) )) & (! [DO: d_person]: ( (DO = d_person_0) | (DO = d_person_1) )) & (? [DO: d_person]: (DO = d_person_0)) & (? [DO: d_person]: (DO = d_person_1)))))) & (! [W: $world]: ($in_world(W, ((! [O: product]: (? [DO: d_product]: O = d2product(DO))) & (! [DO1: d_product, DO2: d_product]: ( (d2product(DO1) = d2product(DO2)) => (DO1 = DO2) )) & (! [DO: d_product]: ( (DO = d_product_0) )) & (? [DO: d_product]: (DO = d_product_0)))))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((alex = d2person(d_person_0)) & (chris = d2person(d_person_1)) & (leo = d2product(d_product_0)) & (! [V1: person, V2: product]: work_hard(V1, V2)) & (! [V1: person]: ~(gets_rich(V1))))) & $in_world(world_1, ((alex = d2person(d_person_0)) & (chris = d2person(d_person_1)) & (leo = d2product(d_product_0)) & (! [V1: person, V2: product]: work_hard(V1, V2)) & gets_rich(d2person(d_person_1)) & gets_rich(d2person(d_person_0)))) )). timeout 0,84 PUZ158_1 CSA ? constant rigid local M system 7 4 3 ( ; cardinality of fruit is 2 ; rep: (as @fruit_0 fruit) ; rep: (as @fruit_1 fruit) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun apple () fruit (as @fruit_0 fruit)) (define-fun banana () fruit (as @fruit_1 fruit)) (define-fun healthy (($x1 $world) ($x2 fruit)) Bool true) (define-fun rotten (($x1 $world) ($x2 fruit)) Bool (and (= (as @$world_0 $world) $x1) (= (as @fruit_1 fruit) $x2))) ) tff(semantics, logic, ($alethic_modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_M)])). tff(fruit_type, type, fruit: $tType). tff(apple_decl, type, apple: fruit). tff(banana_decl, type, banana: fruit). tff(healthy_decl, type, healthy: ((fruit) > $o)). tff(rotten_decl, type, rotten: ((fruit) > $o)). tff(d_fruit_decl, type, d_fruit: $tType). tff(d2fruit_decl, type, d2fruit: d_fruit > fruit). tff(d_fruit_0_decl, type, d_fruit_0: d_fruit). tff(d_fruit_1_decl, type, d_fruit_1: d_fruit). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(d_fruit_0, d_fruit_1) & (! [W: $world]: ($in_world(W, ((! [O: fruit]: (? [DO: d_fruit]: O = d2fruit(DO))) & (! [DO1: d_fruit, DO2: d_fruit]: ( (d2fruit(DO1) = d2fruit(DO2)) => (DO1 = DO2) )) & (! [DO: d_fruit]: ( (DO = d_fruit_0) | (DO = d_fruit_1) )) & (? [DO: d_fruit]: (DO = d_fruit_0)) & (? [DO: d_fruit]: (DO = d_fruit_1)))))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((apple = d2fruit(d_fruit_0)) & (banana = d2fruit(d_fruit_1)) & (! [V1: fruit]: healthy(V1)) & rotten(d2fruit(d_fruit_1)) & (! [V1: fruit]: (~((V1 = d2fruit(d_fruit_1))) => ~rotten(V1))))) & $in_world(world_1, ((apple = d2fruit(d_fruit_0)) & (banana = d2fruit(d_fruit_1)) & (! [V1: fruit]: healthy(V1)) & (! [V1: fruit]: ~(rotten(V1))))) )). tff(semantics, logic, ($alethic_modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_M)])). tff(fruit_type, type, fruit: $tType). tff(apple_decl, type, apple: fruit). tff(banana_decl, type, banana: fruit). tff(healthy_decl, type, healthy: ((fruit) > $o)). tff(rotten_decl, type, rotten: ((fruit) > $o)). tff(d_fruit_decl, type, d_fruit: $tType). tff(d2fruit_decl, type, d2fruit: d_fruit > fruit). tff(d_fruit_0_decl, type, d_fruit_0: d_fruit). tff(d_fruit_1_decl, type, d_fruit_1: d_fruit). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(d_fruit_0, d_fruit_1) & (! [W: $world]: ($in_world(W, ((! [O: fruit]: (? [DO: d_fruit]: O = d2fruit(DO))) & (! [DO1: d_fruit, DO2: d_fruit]: ( (d2fruit(DO1) = d2fruit(DO2)) => (DO1 = DO2) )) & (! [DO: d_fruit]: ( (DO = d_fruit_0) | (DO = d_fruit_1) )) & (? [DO: d_fruit]: (DO = d_fruit_0)) & (? [DO: d_fruit]: (DO = d_fruit_1)))))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((apple = d2fruit(d_fruit_0)) & (banana = d2fruit(d_fruit_1)) & (! [V1: fruit]: healthy(V1)) & rotten(d2fruit(d_fruit_1)) & (! [V1: fruit]: (~((V1 = d2fruit(d_fruit_1))) => ~rotten(V1))))) & $in_world(world_1, ((apple = d2fruit(d_fruit_0)) & (banana = d2fruit(d_fruit_1)) & (! [V1: fruit]: healthy(V1)) & (! [V1: fruit]: ~(rotten(V1))))) )). timeout 2,82 SYN000_6 UNK 1.00 constant rigid local K system 6 4 4 ( ; cardinality of $indiv is 1 ; rep: (as @$indiv_0 $indiv) ; cardinality of new is 1 ; rep: (as @new_0 new) ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun newc () new (as @new_0 new)) (define-fun newf (($x1 new) ($x2 $indiv)) new (as @new_0 new)) (define-fun newp (($x1 $world) ($x2 new) ($x3 $indiv)) Bool true) (define-fun a () $indiv (as @$indiv_0 $indiv)) ) tff(modal_system, logic, ($modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_K)])). tff(new_type, type, new: $tType). tff(newc_decl, type, newc: new). tff(newf_decl, type, newf: ((new * $i) > new)). tff(newp_decl, type, newp: ((new * $i) > $o)). tff(a_decl, type, a: $i). tff(indiv_0_decl, type, indiv_0: $i). tff(d_new_decl, type, d_new: $tType). tff(d2new_decl, type, d2new: d_new > new). tff(d_new_0_decl, type, d_new_0: d_new). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ((! [W: $world]: ($in_world(W, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))))) & (! [W: $world]: ($in_world(W, ((! [O: new]: (? [DO: d_new]: O = d2new(DO))) & (! [DO1: d_new, DO2: d_new]: ( (d2new(DO1) = d2new(DO2)) => (DO1 = DO2) )) & (! [DO: d_new]: ( (DO = d_new_0) )) & (? [DO: d_new]: (DO = d_new_0)))))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((newc = d2new(d_new_0)) & (! [V0: new, V1: $i]: (newf(V0, V1) = d2new(d_new_0))) & (! [V1: new, V2: $i]: newp(V1, V2)) & (a = indiv_0))) )). no conjecture verified; assurance 0,89 SYN000_7 UNK 1.00 - - - - - - - - - no conjecture - - multi modal problem, MoMo doesn't support indexing (currently?) SYO886_1.111 THM 0.00 constant rigid* local* K system 2 4 2 no countermodel :) no countermodel :) - 1,91 SYO886_1.112 THM 0.00 constant rigid* global* K system 2 4 2 no countermodel :) no countermodel :) - 1,75 SYO886_1.121 THM 0.00 constant flexible* local* K system 2 4 2 no countermodel :) no countermodel :) - 1,87 SYO886_1.122 THM 0.00 constant flexible* global* K system 2 4 2 no countermodel :) no countermodel :) - 1,74 SYO886_1.211 CSA 1.00 varying rigid* local* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(k_v_r_l, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_K)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_0, world_0) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 3,46 SYO886_1.212 CSA 1.00 varying rigid* global* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(k_v_r_g, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_0, world_0) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,9 SYO886_1.221 UNK 1.00 varying rigid* local* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(k_v_f_l, logic, ($modal) == ([($domains) == ($varying),($designation) == ($flexible),($terms) == ($local),($modalities) == ($modal_system_K)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_0, world_0) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,05 SYO886_1.222 UNK 1.00 varying flexible* global* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(k_v_f_g, logic, ($modal) == ([($domains) == ($varying),($designation) == ($flexible),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_0, world_0) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,93 SYO886_1.311 CSA 1.00 cumulative rigid* local* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (and (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2))) (not (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2))))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(k_u_r_l, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_K)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & ~$accessible_world(world_0, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0)) | ((W = world_0) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,94 SYO886_1.312 CSA 1.00 cumulative rigid* global* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (and (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2))) (not (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2))))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(k_u_r_g, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & ~$accessible_world(world_0, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0)) | ((W = world_0) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,89 NAME TPTP:CSM/THM TPTP RATING DOMAIN DESIGNATION TERMS MODALITIES #PREDICATES/FUNCTIONS MAX FORMULA DEPTH #MODAL OPERATORS SMT-MODEL TPTP-MODEL AXIOMS? ONLY AXIOMS OUTPUT AGMV VERIFICATION RUNTIME [SEC] NOTES SYO886_1.321 UNK 1.00 cumulative flexible* local* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (and (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2))) (not (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2))))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(k_u_f_l, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($flexible),($terms) == ($local),($modalities) == ($modal_system_K)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & ~$accessible_world(world_0, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0)) | ((W = world_0) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,84 SYO886_1.322 UNK 1.00 cumulative flexible* global* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (and (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2))) (not (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2))))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(k_u_f_g, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($flexible),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & ~$accessible_world(world_0, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0)) | ((W = world_0) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,07 SYO886_1.411 THM 0.00 decreasing rigid* local* K system 2 4 2 no countermodel :) no countermodel :) - 2,03 SYO886_1.412 THM 0.00 decreasing rigid* global* K system 2 4 2 no countermodel :) no countermodel :) - 2 SYO886_1.421 THM 0.00 decreasing flexible* local* K system 2 4 2 no countermodel :) no countermodel :) - 1,92 SYO886_1.422 THM 0.00 decreasing flexible* global* K system 2 4 2 no countermodel :) no countermodel :) - 1,07 SYO886_2.111 THM 0.00 constant rigid* local* D system 2 4 2 no countermodel :) no countermodel :) - 1,33 SYO886_2.112 THM 0.00 constant rigid* global* D system 2 4 2 no countermodel :) no countermodel :) - 0,96 SYO886_2.121 THM 0.00 constant flexible* local* D system 2 4 2 no countermodel :) no countermodel :) - 1,34 SYO886_2.122 THM 0.00 constant flexible* global* D system 2 4 2 no countermodel :) no countermodel :) - 1,03 SYO886_2.211 CSA 0.33 varying rigid* local* D system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(d_v_r_l, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_D)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,16 SYO886_2.212 CSA 1.00 varying rigid* global* D system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(d_v_r_g, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_D)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,05 SYO886_2.221 UNK 1.00 varying rigid* local* D system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(d_v_f_l, logic, ($modal) == ([($domains) == ($varying),($designation) == ($flexible),($terms) == ($local),($modalities) == ($modal_system_D)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). Saved countermodel in SYO886_2.221_model.txt runtime: 8.03875184059143 verified; assurance 1,09 SYO886_2.222 UNK 1.00 varying flexible* global* D system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(d_v_f_g, logic, ($modal) == ([($domains) == ($varying),($designation) == ($flexible),($terms) == ($global),($modalities) == ($modal_system_D)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,07 SYO886_2.311 CSA 0.33 cumulative rigid* local* D system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$world_1 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(d_u_r_l, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_D)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & $accessible_world(world_1, world_0) & $accessible_world(world_0, world_0) & $accessible_world(world_1, world_1) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0)) | ((W = world_0) & (V = world_0)) | ((W = world_1) & (V = world_1))) => ~$accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,95 SYO886_2.312 CSA 1.00 cumulative rigid* global* D system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$world_1 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(d_u_r_g, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_D)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & $accessible_world(world_1, world_0) & $accessible_world(world_0, world_0) & $accessible_world(world_1, world_1) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0)) | ((W = world_0) & (V = world_0)) | ((W = world_1) & (V = world_1))) => ~$accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,06 SYO886_2.321 UNK 1.00 cumulative flexible* local* D system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$world_1 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(d_u_f_l, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($flexible),($terms) == ($local),($modalities) == ($modal_system_D)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & $accessible_world(world_1, world_0) & $accessible_world(world_0, world_0) & $accessible_world(world_1, world_1) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0)) | ((W = world_0) & (V = world_0)) | ((W = world_1) & (V = world_1))) => ~$accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,05 SYO886_2.322 UNK 1.00 cumulative flexible* global* D system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$world_1 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(d_u_f_g, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($flexible),($terms) == ($global),($modalities) == ($modal_system_D)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & $accessible_world(world_1, world_0) & $accessible_world(world_0, world_0) & $accessible_world(world_1, world_1) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0)) | ((W = world_0) & (V = world_0)) | ((W = world_1) & (V = world_1))) => ~$accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,1 SYO886_2.411 THM 0.00 decreasing rigid* local* D system 2 4 2 no countermodel :) no countermodel :) 0,87 SYO886_2.412 THM 0.00 decreasing rigid* global* D system 2 4 2 no countermodel :) no countermodel :) 0,81 SYO886_2.421 THM 0.00 decreasing flexible* local* D system 2 4 2 no countermodel :) no countermodel :) 0,87 SYO886_2.422 THM 0.00 decreasing flexible* global* D system 2 4 2 no countermodel :) no countermodel :) 0,82 SYO886_3.111 THM 0.00 constant rigid* local* M system 2 4 2 no countermodel :) no countermodel :) 0,88 SYO886_3.112 THM 0.00 constant rigid* global* M system 2 4 2 no countermodel :) no countermodel :) 0,85 SYO886_3.121 THM 0.00 constant flexible* local* M system 2 4 2 no countermodel :) no countermodel :) 0,89 SYO886_3.122 THM 0.00 constant flexible* global* M system 2 4 2 no countermodel :) no countermodel :) 0,9 SYO886_3.211 CSA 0.33 varying rigid* local* M system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(m_v_r_l, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_M)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,3 SYO886_3.212 CSA 1.00 varying rigid* global* M system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(m_v_r_g, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_M)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,04 SYO886_3.221 UNK 1.00 varying rigid* local* M system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(m_v_f_l, logic, ($modal) == ([($domains) == ($varying),($designation) == ($flexible),($terms) == ($local),($modalities) == ($modal_system_M)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,02 SYO886_3.222 UNK 1.00 varying flexible* global* M system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(m_v_f_g, logic, ($modal) == ([($domains) == ($varying),($designation) == ($flexible),($terms) == ($global),($modalities) == ($modal_system_M)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,14 SYO886_3.311 CSA 0.33 cumulative rigid* local* M system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(m_u_r_l, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_M)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,09 SYO886_3.312 CSA 1.00 cumulative rigid* global* M system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(m_u_r_g, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_M)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,21 SYO886_3.321 CSA 1.00 cumulative flexible* local* M system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(m_u_f_l, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($flexible),($terms) == ($local),($modalities) == ($modal_system_M)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,84 SYO886_3.322 UNK 1.00 cumulative flexible* global* M system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(m_u_f_g, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($flexible),($terms) == ($global),($modalities) == ($modal_system_M)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,09 SYO886_3.411 THM 0.00 decreasing rigid* local* M system 2 4 2 no countermodel :) no countermodel :) 1,29 SYO886_3.412 THM 0.00 decreasing rigid* global* M system 2 4 2 no countermodel :) no countermodel :) 1,11 SYO886_3.421 THM 0.00 decreasing flexible* local* M system 2 4 2 no countermodel :) no countermodel :) 0,93 SYO886_3.422 THM 0.00 decreasing flexible* global* M system 2 4 2 no countermodel :) no countermodel :) 1,39 SYO886_4.111 THM 0.00 constant rigid* local* S4 system 2 4 2 no countermodel :) no countermodel :) 1,31 SYO886_4.112 THM 0.00 constant rigid* global* S4 system 2 4 2 no countermodel :) no countermodel :) 1,12 SYO886_4.121 THM 0.00 constant flexible* local* S4 system 2 4 2 no countermodel :) no countermodel :) 1,29 SYO886_4.122 THM 0.00 constant flexible* global* S4 system 2 4 2 no countermodel :) no countermodel :) 1,13 NAME TPTP:CSM/THM TPTP RATING DOMAIN DESIGNATION TERMS MODALITIES #PREDICATES/FUNCTIONS MAX FORMULA DEPTH #MODAL OPERATORS SMT-MODEL TPTP-MODEL AXIOMS? ONLY AXIOMS OUTPUT AGMV VERIFICATION RUNTIME [SEC] NOTES SYO886_4.211 CSA 0.33 varying rigid* local* S4 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s4_v_r_l, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_S4)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,07 SYO886_4.212 CSA 1.00 varying rigid* global* S4 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s4_v_r_g, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_S4)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,08 SYO886_4.221 UNK 1.00 varying rigid* local* S4 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s4_v_f_l, logic, ($modal) == ([($domains) == ($varying),($designation) == ($flexible),($terms) == ($local),($modalities) == ($modal_system_S4)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,07 SYO886_4.222 UNK 1.00 varying flexible* global* S4 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s4_v_f_g, logic, ($modal) == ([($domains) == ($varying),($designation) == ($flexible),($terms) == ($global),($modalities) == ($modal_system_S4)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,92 SYO886_4.311 CSA 0.33 cumulative rigid* local* S4 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s4_u_r_l, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_S4)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,11 SYO886_4.312 CSA 1.00 cumulative rigid* global* S4 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s4_u_r_g, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_S4)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,87 SYO886_4.321 UNK 1.00 cumulative flexible* local* S4 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s4_u_f_l, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($flexible),($terms) == ($local),($modalities) == ($modal_system_S4)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,1 SYO886_4.322 UNK 1.00 cumulative flexible* global* S4 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s4_u_f_g, logic, ($modal) == ([($domains) == ($cumulative),($designation) == ($flexible),($terms) == ($global),($modalities) == ($modal_system_S4)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_1, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,84 SYO886_4.411 THM 0.00 decreasing rigid* local* S4 system 2 4 2 no countermodel :) no countermodel :) 1,25 SYO886_4.412 THM 0.00 decreasing rigid* global* S4 system 2 4 2 no countermodel :) no countermodel :) 1,15 SYO886_4.421 THM 0.00 decreasing flexible* local* S4 system 2 4 2 no countermodel :) no countermodel :) 1,17 SYO886_4.422 THM 0.00 decreasing flexible* global* S4 system 2 4 2 no countermodel :) no countermodel :) 1,05 SYO886_5.111 THM 0.00 constant rigid* local* S5 system 2 4 2 no countermodel :) no countermodel :) 0,86 SYO886_5.112 THM 0.00 constant rigid* global* S5 system 2 4 2 no countermodel :) no countermodel :) 0,79 SYO886_5.121 THM 0.00 constant flexible* local* S5 system 2 4 2 no countermodel :) no countermodel :) 0,79 SYO886_5.122 THM 0.00 constant flexible* global* S5 system 2 4 2 no countermodel :) no countermodel :) 0,8 SYO886_5.211 CSA 0.33 varying rigid* local* S5 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s5_v_r_l, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($local),($modalities) == ($modal_system_S5)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,1 SYO886_5.212 THM 1.00 varying rigid* global* S5 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s5_v_r_g, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_S5)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,83 SYO886_5.221 THM 1.00 varying rigid* local* S5 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s5_v_f_l, logic, ($modal) == ([($domains) == ($varying),($designation) == ($flexible),($terms) == ($local),($modalities) == ($modal_system_S5)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 1,08 SYO886_5.222 THM 1.00 varying flexible* global* S5 system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun f (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(s5_v_f_g, logic, ($modal) == ([($domains) == ($varying),($designation) == ($flexible),($terms) == ($global),($modalities) == ($modal_system_S5)])). tff(f_decl, type, f: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) & $in_world(world_1, (f(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~f(V1))))) )). verified; assurance 0,87 SYO886_5.311 THM 0.00 cumulative rigid* local* S5 system 2 4 2 no countermodel :) no countermodel :) 1,56 SYO886_5.312 THM 0.00 cumulative rigid* global* S5 system 2 4 2 no countermodel :) no countermodel :) 1,33 SYO886_5.321 THM 0.00 cumulative flexible* local* S5 system 2 4 2 no countermodel :) no countermodel :) 1,37 SYO886_5.322 THM 0.00 cumulative flexible* global* S5 system 2 4 2 no countermodel :) no countermodel :) 1,34 SYO886_5.411 THM 0.00 decreasing rigid* local* S5 system 2 4 2 no countermodel :) no countermodel :) 1,44 SYO886_5.412 THM 0.00 decreasing rigid* global* S5 system 2 4 2 no countermodel :) no countermodel :) 1,66 SYO886_5.421 THM 0.00 decreasing flexible* local* S5 system 2 4 2 no countermodel :) no countermodel :) 1,76 SYO886_5.422 THM 0.00 decreasing flexible* global* S5 system 2 4 2 no countermodel :) no countermodel :) 1,43 SYO919_1.001 CSA 0.00 - - - S4 system 2 4 0 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false ((_arg_1 $world)) Bool false) (define-fun p1 ((_arg_1 $world)) Bool false) ) tff('s4_md_n.0001', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(false_decl, type, false: $o). tff(p1_decl, type, p1: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & ~p1)) )). verified; assurance 1,02 SYO919_1.005 CSA 0.67 - - - S4 system 2 47 54 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p1 (($x1 $world)) Bool false) (define-fun p2 (($x1 $world)) Bool false) ) tff('s4_md_n.0005', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(p1_decl, type, p1: $o). tff(p2_decl, type, p2: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~p1 & ~p2)) )). verified; assurance 1,05 SYO919_1.009 CSA 0.67 - - - S4 system 2 155 332 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p1 (($x1 $world)) Bool false) (define-fun p2 (($x1 $world)) Bool false) ) tff('s4_md_n.0009', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(p1_decl, type, p1: $o). tff(p2_decl, type, p2: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~p1 & ~p2)) )). timeout 1,69 SYO919_1.013 CSA 1.00 - - - S4 system 2 327 1026 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p1 (($x1 $world)) Bool false) (define-fun p2 (($x1 $world)) Bool false) ) tff('s4_md_n.0013', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(p1_decl, type, p1: $o). tff(p2_decl, type, p2: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~p1 & ~p2)) )). timeout 1,57 SYO919_1.017 CSA 1.00 - - - S4 system 2 563 2328 ( ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p1 (($x1 $world)) Bool false) (define-fun p2 (($x1 $world)) Bool false) ) tff('s4_md_n.0017', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(p1_decl, type, p1: $o). tff(p2_decl, type, p2: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~p1 & ~p2)) )). timeout 12,99 without higher JRE(?) had let error:null SYO920_1.014 THM 0.50 - - - K system 4 58 309 task timed out! task timed out! SYO921_1.006 THM 1.00 - - - K4 system 8 39 344 task timed out! task timed out! SYO922_1.014 THM 0.50 - - - D4 system 9 66 956 task timed out! task timed out! SYO923_1.010 THM 1.00 - - - K45 system 12 53 714 no countermodel :) no countermodel :) 61,79 SYO924_1.002 THM 0.00 - - - S5 system 13 31 235 task timed out! task timed out! experiment on constraining world numbers in each run of model finder, note in (number of worlds, cvc5 output): (1, unsat, 1)(2,unsat, 124) (3, task timed out); it DOES find "no countermodel :)" with longer timeout limit? SYO924_1.018 THM 0.33 - - - S5 system 13 79 1195 task timed out! task timed out! SYO925_1.001 CSA 0.33 - - - S4 system 3 8 5 ( ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false (($x1 $world)) Bool false) (define-fun p1 ((_arg_1 $world)) Bool true) (define-fun p6 (($x1 $world)) Bool (= (as @$world_0 $world) $x1)) ) tff('s4_s5_n.0001', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(false_decl, type, false: $o). tff(p1_decl, type, p1: $o). tff(p6_decl, type, p6: $o). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & p1 & p6)) & $in_world(world_1, (~false & p1 & ~p6)) )). verified; assurance 1,07 SYO925_1.005 CSA 0.00 - - - S4 system 27 58 53 ( ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false (($x1 $world)) Bool false) (define-fun p1 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p10 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p11 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p12 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p13 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p14 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p15 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p16 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p17 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p18 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p19 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p2 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p20 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p21 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p22 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p23 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p24 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p25 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p3 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p30 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p4 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p5 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p6 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p7 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p8 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p9 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) ) tff('s4_s5_n.0005', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(false_decl, type, false: $o). tff(p1_decl, type, p1: $o). tff(p10_decl, type, p10: $o). tff(p11_decl, type, p11: $o). tff(p12_decl, type, p12: $o). tff(p13_decl, type, p13: $o). tff(p14_decl, type, p14: $o). tff(p15_decl, type, p15: $o). tff(p16_decl, type, p16: $o). tff(p17_decl, type, p17: $o). tff(p18_decl, type, p18: $o). tff(p19_decl, type, p19: $o). tff(p2_decl, type, p2: $o). tff(p20_decl, type, p20: $o). tff(p21_decl, type, p21: $o). tff(p22_decl, type, p22: $o). tff(p23_decl, type, p23: $o). tff(p24_decl, type, p24: $o). tff(p25_decl, type, p25: $o). tff(p3_decl, type, p3: $o). tff(p30_decl, type, p30: $o). tff(p4_decl, type, p4: $o). tff(p5_decl, type, p5: $o). tff(p6_decl, type, p6: $o). tff(p7_decl, type, p7: $o). tff(p8_decl, type, p8: $o). tff(p9_decl, type, p9: $o). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & ~p1 & ~p10 & ~p11 & ~p12 & ~p13 & ~p14 & ~p15 & ~p16 & ~p17 & ~p18 & ~p19 & ~p2 & ~p20 & ~p21 & ~p22 & ~p23 & ~p24 & ~p25 & ~p3 & ~p30 & ~p4 & ~p5 & ~p6 & ~p7 & ~p8 & ~p9)) & $in_world(world_1, (~false & p1 & p10 & p11 & p12 & p13 & p14 & p15 & p16 & p17 & p18 & p19 & p2 & p20 & p21 & p22 & p23 & p24 & p25 & p3 & p30 & p4 & p5 & p6 & p7 & p8 & p9)) )). timeout 1,44 SYO925_1.009 CSA 0.33 - - - S4 system 51 106 101 ( ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false (($x1 $world)) Bool false) (define-fun p1 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p10 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p11 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p12 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p13 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p14 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p15 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p16 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p17 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p18 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p19 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p2 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p20 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p21 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p22 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p23 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p24 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p25 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p26 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p27 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p28 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p29 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p3 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p30 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p31 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p32 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p33 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p34 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p35 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p36 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p37 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p38 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p39 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p4 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p40 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p41 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p42 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p43 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p44 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p45 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p46 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p47 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p48 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p49 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p5 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p54 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p6 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p7 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p8 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p9 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) ) tff('s4_s5_n.0009', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(false_decl, type, false: $o). tff(p1_decl, type, p1: $o). tff(p10_decl, type, p10: $o). tff(p11_decl, type, p11: $o). tff(p12_decl, type, p12: $o). tff(p13_decl, type, p13: $o). tff(p14_decl, type, p14: $o). tff(p15_decl, type, p15: $o). tff(p16_decl, type, p16: $o). tff(p17_decl, type, p17: $o). tff(p18_decl, type, p18: $o). tff(p19_decl, type, p19: $o). tff(p2_decl, type, p2: $o). tff(p20_decl, type, p20: $o). tff(p21_decl, type, p21: $o). tff(p22_decl, type, p22: $o). tff(p23_decl, type, p23: $o). tff(p24_decl, type, p24: $o). tff(p25_decl, type, p25: $o). tff(p26_decl, type, p26: $o). tff(p27_decl, type, p27: $o). tff(p28_decl, type, p28: $o). tff(p29_decl, type, p29: $o). tff(p3_decl, type, p3: $o). tff(p30_decl, type, p30: $o). tff(p31_decl, type, p31: $o). tff(p32_decl, type, p32: $o). tff(p33_decl, type, p33: $o). tff(p34_decl, type, p34: $o). tff(p35_decl, type, p35: $o). tff(p36_decl, type, p36: $o). tff(p37_decl, type, p37: $o). tff(p38_decl, type, p38: $o). tff(p39_decl, type, p39: $o). tff(p4_decl, type, p4: $o). tff(p40_decl, type, p40: $o). tff(p41_decl, type, p41: $o). tff(p42_decl, type, p42: $o). tff(p43_decl, type, p43: $o). tff(p44_decl, type, p44: $o). tff(p45_decl, type, p45: $o). tff(p46_decl, type, p46: $o). tff(p47_decl, type, p47: $o). tff(p48_decl, type, p48: $o). tff(p49_decl, type, p49: $o). tff(p5_decl, type, p5: $o). tff(p54_decl, type, p54: $o). tff(p6_decl, type, p6: $o). tff(p7_decl, type, p7: $o). tff(p8_decl, type, p8: $o). tff(p9_decl, type, p9: $o). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & ~p1 & ~p10 & ~p11 & ~p12 & ~p13 & ~p14 & ~p15 & ~p16 & ~p17 & ~p18 & ~p19 & ~p2 & ~p20 & ~p21 & ~p22 & ~p23 & ~p24 & ~p25 & ~p26 & ~p27 & ~p28 & ~p29 & ~p3 & ~p30 & ~p31 & ~p32 & ~p33 & ~p34 & ~p35 & ~p36 & ~p37 & ~p38 & ~p39 & ~p4 & ~p40 & ~p41 & ~p42 & ~p43 & ~p44 & ~p45 & ~p46 & ~p47 & ~p48 & ~p49 & ~p5 & ~p54 & ~p6 & ~p7 & ~p8 & ~p9)) & $in_world(world_1, (~false & p1 & p10 & p11 & p12 & p13 & p14 & p15 & p16 & p17 & p18 & p19 & p2 & p20 & p21 & p22 & p23 & p24 & p25 & p26 & p27 & p28 & p29 & p3 & p30 & p31 & p32 & p33 & p34 & p35 & p36 & p37 & p38 & p39 & p4 & p40 & p41 & p42 & p43 & p44 & p45 & p46 & p47 & p48 & p49 & p5 & p54 & p6 & p7 & p8 & p9)) )). timeout 2,38 NAME TPTP:CSM/THM TPTP RATING DOMAIN DESIGNATION TERMS MODALITIES #PREDICATES/FUNCTIONS MAX FORMULA DEPTH #MODAL OPERATORS SMT-MODEL TPTP-MODEL AXIOMS? ONLY AXIOMS OUTPUT AGMV VERIFICATION RUNTIME [SEC] NOTES SYO925_1.013 CSA 0.33 - - - S4 system 75 154 149 ( ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false (($x1 $world)) Bool false) (define-fun p1 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p10 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p11 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p12 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p13 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p14 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p15 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p16 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p17 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p18 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p19 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p2 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p20 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p21 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p22 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p23 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p24 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p25 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p26 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p27 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p28 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p29 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p3 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p30 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p31 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p32 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p33 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p34 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p35 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p36 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p37 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p38 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p39 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p4 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p40 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p41 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p42 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p43 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p44 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p45 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p46 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p47 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p48 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p49 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p5 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p50 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p51 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p52 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p53 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p54 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p55 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p56 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p57 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p58 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p59 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p6 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p60 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p61 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p62 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p63 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p64 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p65 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p66 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p67 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p68 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p69 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p7 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p70 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p71 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p72 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p73 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p78 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p8 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p9 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) ) tff('s4_s5_n.0013', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(false_decl, type, false: $o). tff(p1_decl, type, p1: $o). tff(p10_decl, type, p10: $o). tff(p11_decl, type, p11: $o). tff(p12_decl, type, p12: $o). tff(p13_decl, type, p13: $o). tff(p14_decl, type, p14: $o). tff(p15_decl, type, p15: $o). tff(p16_decl, type, p16: $o). tff(p17_decl, type, p17: $o). tff(p18_decl, type, p18: $o). tff(p19_decl, type, p19: $o). tff(p2_decl, type, p2: $o). tff(p20_decl, type, p20: $o). tff(p21_decl, type, p21: $o). tff(p22_decl, type, p22: $o). tff(p23_decl, type, p23: $o). tff(p24_decl, type, p24: $o). tff(p25_decl, type, p25: $o). tff(p26_decl, type, p26: $o). tff(p27_decl, type, p27: $o). tff(p28_decl, type, p28: $o). tff(p29_decl, type, p29: $o). tff(p3_decl, type, p3: $o). tff(p30_decl, type, p30: $o). tff(p31_decl, type, p31: $o). tff(p32_decl, type, p32: $o). tff(p33_decl, type, p33: $o). tff(p34_decl, type, p34: $o). tff(p35_decl, type, p35: $o). tff(p36_decl, type, p36: $o). tff(p37_decl, type, p37: $o). tff(p38_decl, type, p38: $o). tff(p39_decl, type, p39: $o). tff(p4_decl, type, p4: $o). tff(p40_decl, type, p40: $o). tff(p41_decl, type, p41: $o). tff(p42_decl, type, p42: $o). tff(p43_decl, type, p43: $o). tff(p44_decl, type, p44: $o). tff(p45_decl, type, p45: $o). tff(p46_decl, type, p46: $o). tff(p47_decl, type, p47: $o). tff(p48_decl, type, p48: $o). tff(p49_decl, type, p49: $o). tff(p5_decl, type, p5: $o). tff(p50_decl, type, p50: $o). tff(p51_decl, type, p51: $o). tff(p52_decl, type, p52: $o). tff(p53_decl, type, p53: $o). tff(p54_decl, type, p54: $o). tff(p55_decl, type, p55: $o). tff(p56_decl, type, p56: $o). tff(p57_decl, type, p57: $o). tff(p58_decl, type, p58: $o). tff(p59_decl, type, p59: $o). tff(p6_decl, type, p6: $o). tff(p60_decl, type, p60: $o). tff(p61_decl, type, p61: $o). tff(p62_decl, type, p62: $o). tff(p63_decl, type, p63: $o). tff(p64_decl, type, p64: $o). tff(p65_decl, type, p65: $o). tff(p66_decl, type, p66: $o). tff(p67_decl, type, p67: $o). tff(p68_decl, type, p68: $o). tff(p69_decl, type, p69: $o). tff(p7_decl, type, p7: $o). tff(p70_decl, type, p70: $o). tff(p71_decl, type, p71: $o). tff(p72_decl, type, p72: $o). tff(p73_decl, type, p73: $o). tff(p78_decl, type, p78: $o). tff(p8_decl, type, p8: $o). tff(p9_decl, type, p9: $o). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & (! [W: $world, V: $world]: $accessible_world(W, V)) )).tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & ~p1 & ~p10 & ~p11 & ~p12 & ~p13 & ~p14 & ~p15 & ~p16 & ~p17 & ~p18 & ~p19 & ~p2 & ~p20 & ~p21 & ~p22 & ~p23 & ~p24 & ~p25 & ~p26 & ~p27 & ~p28 & ~p29 & ~p3 & ~p30 & ~p31 & ~p32 & ~p33 & ~p34 & ~p35 & ~p36 & ~p37 & ~p38 & ~p39 & ~p4 & ~p40 & ~p41 & ~p42 & ~p43 & ~p44 & ~p45 & ~p46 & ~p47 & ~p48 & ~p49 & ~p5 & ~p50 & ~p51 & ~p52 & ~p53 & ~p54 & ~p55 & ~p56 & ~p57 & ~p58 & ~p59 & ~p6 & ~p60 & ~p61 & ~p62 & ~p63 & ~p64 & ~p65 & ~p66 & ~p67 & ~p68 & ~p69 & ~p7 & ~p70 & ~p71 & ~p72 & ~p73 & ~p78 & ~p8 & ~p9)) & $in_world(world_1, (~false & p1 & p10 & p11 & p12 & p13 & p14 & p15 & p16 & p17 & p18 & p19 & p2 & p20 & p21 & p22 & p23 & p24 & p25 & p26 & p27 & p28 & p29 & p3 & p30 & p31 & p32 & p33 & p34 & p35 & p36 & p37 & p38 & p39 & p4 & p40 & p41 & p42 & p43 & p44 & p45 & p46 & p47 & p48 & p49 & p5 & p50 & p51 & p52 & p53 & p54 & p55 & p56 & p57 & p58 & p59 & p6 & p60 & p61 & p62 & p63 & p64 & p65 & p66 & p67 & p68 & p69 & p7 & p70 & p71 & p72 & p73 & p78 & p8 & p9)) )). timeout 3,97 SYO925_1.017 CSA 0.33 - - - S4 system 99 202 197 ( ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun false (($x1 $world)) Bool false) (define-fun p1 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p10 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p102 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p11 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p12 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p13 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p14 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p15 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p16 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p17 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p18 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p19 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p2 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p20 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p21 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p22 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p23 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p24 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p25 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p26 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p27 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p28 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p29 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p3 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p30 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p31 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p32 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p33 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p34 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p35 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p36 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p37 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p38 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p39 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p4 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p40 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p41 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p42 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p43 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p44 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p45 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p46 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p47 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p48 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p49 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p5 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p50 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p51 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p52 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p53 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p54 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p55 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p56 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p57 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p58 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p59 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p6 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p60 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p61 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p62 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p63 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p64 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p65 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p66 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p67 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p68 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p69 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p7 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p70 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p71 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p72 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p73 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p74 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p75 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p76 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p77 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p78 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p79 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p8 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p80 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p81 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p82 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p83 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p84 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p85 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p86 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p87 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p88 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p89 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p9 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p90 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p91 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p92 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p93 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p94 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p95 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p96 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) (define-fun p97 (($x1 $world)) Bool (= (as @$world_1 $world) $x1)) ) tff('s4_s5_n.0017', logic, ($modal) == ([($modalities) == ($modal_system_S4)])). tff(false_decl, type, false: $o). tff(p1_decl, type, p1: $o). tff(p10_decl, type, p10: $o). tff(p102_decl, type, p102: $o). tff(p11_decl, type, p11: $o). tff(p12_decl, type, p12: $o). tff(p13_decl, type, p13: $o). tff(p14_decl, type, p14: $o). tff(p15_decl, type, p15: $o). tff(p16_decl, type, p16: $o). tff(p17_decl, type, p17: $o). tff(p18_decl, type, p18: $o). tff(p19_decl, type, p19: $o). tff(p2_decl, type, p2: $o). tff(p20_decl, type, p20: $o). tff(p21_decl, type, p21: $o). tff(p22_decl, type, p22: $o). tff(p23_decl, type, p23: $o). tff(p24_decl, type, p24: $o). tff(p25_decl, type, p25: $o). tff(p26_decl, type, p26: $o). tff(p27_decl, type, p27: $o). tff(p28_decl, type, p28: $o). tff(p29_decl, type, p29: $o). tff(p3_decl, type, p3: $o). tff(p30_decl, type, p30: $o). tff(p31_decl, type, p31: $o). tff(p32_decl, type, p32: $o). tff(p33_decl, type, p33: $o). tff(p34_decl, type, p34: $o). tff(p35_decl, type, p35: $o). tff(p36_decl, type, p36: $o). tff(p37_decl, type, p37: $o). tff(p38_decl, type, p38: $o). tff(p39_decl, type, p39: $o). tff(p4_decl, type, p4: $o). tff(p40_decl, type, p40: $o). tff(p41_decl, type, p41: $o). tff(p42_decl, type, p42: $o). tff(p43_decl, type, p43: $o). tff(p44_decl, type, p44: $o). tff(p45_decl, type, p45: $o). tff(p46_decl, type, p46: $o). tff(p47_decl, type, p47: $o). tff(p48_decl, type, p48: $o). tff(p49_decl, type, p49: $o). tff(p5_decl, type, p5: $o). tff(p50_decl, type, p50: $o). tff(p51_decl, type, p51: $o). tff(p52_decl, type, p52: $o). tff(p53_decl, type, p53: $o). tff(p54_decl, type, p54: $o). tff(p55_decl, type, p55: $o). tff(p56_decl, type, p56: $o). tff(p57_decl, type, p57: $o). tff(p58_decl, type, p58: $o). tff(p59_decl, type, p59: $o). tff(p6_decl, type, p6: $o). tff(p60_decl, type, p60: $o). tff(p61_decl, type, p61: $o). tff(p62_decl, type, p62: $o). tff(p63_decl, type, p63: $o). tff(p64_decl, type, p64: $o). tff(p65_decl, type, p65: $o). tff(p66_decl, type, p66: $o). tff(p67_decl, type, p67: $o). tff(p68_decl, type, p68: $o). tff(p69_decl, type, p69: $o). tff(p7_decl, type, p7: $o). tff(p70_decl, type, p70: $o). tff(p71_decl, type, p71: $o). tff(p72_decl, type, p72: $o). tff(p73_decl, type, p73: $o). tff(p74_decl, type, p74: $o). tff(p75_decl, type, p75: $o). tff(p76_decl, type, p76: $o). tff(p77_decl, type, p77: $o). tff(p78_decl, type, p78: $o). tff(p79_decl, type, p79: $o). tff(p8_decl, type, p8: $o). tff(p80_decl, type, p80: $o). tff(p81_decl, type, p81: $o). tff(p82_decl, type, p82: $o). tff(p83_decl, type, p83: $o). tff(p84_decl, type, p84: $o). tff(p85_decl, type, p85: $o). tff(p86_decl, type, p86: $o). tff(p87_decl, type, p87: $o). tff(p88_decl, type, p88: $o). tff(p89_decl, type, p89: $o). tff(p9_decl, type, p9: $o). tff(p90_decl, type, p90: $o). tff(p91_decl, type, p91: $o). tff(p92_decl, type, p92: $o). tff(p93_decl, type, p93: $o). tff(p94_decl, type, p94: $o). tff(p95_decl, type, p95: $o). tff(p96_decl, type, p96: $o). tff(p97_decl, type, p97: $o). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~false & ~p1 & ~p10 & ~p102 & ~p11 & ~p12 & ~p13 & ~p14 & ~p15 & ~p16 & ~p17 & ~p18 & ~p19 & ~p2 & ~p20 & ~p21 & ~p22 & ~p23 & ~p24 & ~p25 & ~p26 & ~p27 & ~p28 & ~p29 & ~p3 & ~p30 & ~p31 & ~p32 & ~p33 & ~p34 & ~p35 & ~p36 & ~p37 & ~p38 & ~p39 & ~p4 & ~p40 & ~p41 & ~p42 & ~p43 & ~p44 & ~p45 & ~p46 & ~p47 & ~p48 & ~p49 & ~p5 & ~p50 & ~p51 & ~p52 & ~p53 & ~p54 & ~p55 & ~p56 & ~p57 & ~p58 & ~p59 & ~p6 & ~p60 & ~p61 & ~p62 & ~p63 & ~p64 & ~p65 & ~p66 & ~p67 & ~p68 & ~p69 & ~p7 & ~p70 & ~p71 & ~p72 & ~p73 & ~p74 & ~p75 & ~p76 & ~p77 & ~p78 & ~p79 & ~p8 & ~p80 & ~p81 & ~p82 & ~p83 & ~p84 & ~p85 & ~p86 & ~p87 & ~p88 & ~p89 & ~p9 & ~p90 & ~p91 & ~p92 & ~p93 & ~p94 & ~p95 & ~p96 & ~p97)) & $in_world(world_1, (~false & p1 & p10 & p102 & p11 & p12 & p13 & p14 & p15 & p16 & p17 & p18 & p19 & p2 & p20 & p21 & p22 & p23 & p24 & p25 & p26 & p27 & p28 & p29 & p3 & p30 & p31 & p32 & p33 & p34 & p35 & p36 & p37 & p38 & p39 & p4 & p40 & p41 & p42 & p43 & p44 & p45 & p46 & p47 & p48 & p49 & p5 & p50 & p51 & p52 & p53 & p54 & p55 & p56 & p57 & p58 & p59 & p6 & p60 & p61 & p62 & p63 & p64 & p65 & p66 & p67 & p68 & p69 & p7 & p70 & p71 & p72 & p73 & p74 & p75 & p76 & p77 & p78 & p79 & p8 & p80 & p81 & p82 & p83 & p84 & p85 & p86 & p87 & p88 & p89 & p9 & p90 & p91 & p92 & p93 & p94 & p95 & p96 & p97)) )). - 6,05 SYO935_1 THM ? constant rigid* global* K system 2 5 2 no countermodel :) no countermodel :) - 1,46 SYO936_1 THM ? constant rigid* global* K system 2 5 2 no countermodel :) no countermodel :) - 1,37 SYO937_1 THM ? constant rigid* global* K system 2 5 2 no countermodel :) no countermodel :) - 1,35 SYO938_1 THM ? constant rigid* global* K system 2 5 2 no countermodel :) no countermodel :) - 1,43 SYO939_1 THM ? constant rigid* global* K system 2 5 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(d_indiv_0, d_indiv_1) & (! [W: $world]: ($in_world(W, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (p(indiv_0) & (! [V1: $i]: (~((V1 = indiv_0)) => ~p(V1))))) & $in_world(world_1, (p(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~p(V1))))) )). timeout 1,1 SYO940_1 THM ? constant rigid* global* K system 2 5 2 ( ; cardinality of $indiv is 1 ; rep: (as @$indiv_0 $indiv) ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool false) (define-fun p (($x1 $world) ($x2 $indiv)) Bool true) ) tff(simple_K, logic, ($modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: ~$accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ((! [W: $world]: ($in_world(W, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: p(V1)))) )). verified; assurance 0,79 SYO941_1 THM ? constant rigid* global* K system 2 5 2 ( ; cardinality of $indiv is 1 ; rep: (as @$indiv_0 $indiv) ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool false) (define-fun p (($x1 $world) ($x2 $indiv)) Bool true) ) tff(simple_K, logic, ($modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: ~$accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ((! [W: $world]: ($in_world(W, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: p(V1)))) )). verified; assurance 0,98 SYO942_1 THM ? constant rigid* global* K system 2 5 2 no countermodel :) no countermodel :) - 1,28 SYO943_1 THM ? varying rigid* global* K system 4 6 3 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (and (= (as @$world_0 $world) $x1) (= (as @$world_1 $world) $x2))) (define-fun p (($x1 $world) ($x2 $indiv)) Bool true) (define-fun q (($x1 $world) ($x2 $indiv)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(q_type, type, q: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & $accessible_world(world_0, world_1) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_1))) => ~$accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: p(V1)) & (! [V1: $i]: q(V1)))) & $in_world(world_1, ((! [V1: $i]: p(V1)) & ~q(indiv_0) & (! [V1: $i]: (~((V1 = indiv_0)) => q(V1))))) )). timeout 1,18 SYO944_1 THM ? varying rigid* global* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_0, world_0) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(p(V1))))) & $in_world(world_1, (p(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~p(V1))))) )). verified; assurance 1,15 SYO945_1 THM ? varying rigid* global* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: p(V1)))) & $in_world(world_1, (~p(indiv_0) & (! [V1: $i]: (~((V1 = indiv_0)) => p(V1))))) )). verified; assurance 1,7 SYO946_1 THM ? varying rigid* global* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: p(V1)))) & $in_world(world_1, (~p(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => p(V1))))) )). timeout 1,28 SYO947_1 THM ? varying rigid* global* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (and (= (as @$world_0 $world) $x1) (= (as @$world_1 $world) $x2))) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & $accessible_world(world_0, world_1) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_1))) => ~$accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (p(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~p(V1))))) & $in_world(world_1, (p(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~p(V1))))) )). timeout 1,47 SYO948_1 THM ? varying rigid* global* K system 3 6 3 ( ; cardinality of $indiv is 1 ; rep: (as @$indiv_0 $indiv) ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool false) (define-fun p (($x1 $world) ($x2 $indiv)) Bool true) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool true) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: ~$accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: p(V1)))) )). verified; assurance 1,4 - SYO949_1 THM ? varying rigid* global* K system 3 6 2 ( ; cardinality of $indiv is 1 ; rep: (as @$indiv_0 $indiv) ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool false) (define-fun p (($x1 $world) ($x2 $indiv)) Bool true) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool true) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: ~$accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: p(V1)))) )). timeout 1,44 SYO950_1 THM ? varying rigid* global* K system 2 5 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun r (($x1 $world) ($x2 $indiv) ($x3 $indiv)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2) (= (as @$indiv_0 $indiv) $x3)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(r_type, type, r: (($i * $i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i, V2: $i]: r(V1, V2)))) & $in_world(world_1, (~r(indiv_1, indiv_0) & (! [V1: $i, V2: $i]: (~((V1 = indiv_1) & (V2 = indiv_0)) => r(V1, V2))))) )). timeout 1,44 SYO951_1 THM ? constant rigid* global* K system 3 5 4 no countermodel :) no countermodel :) - 1,4 SYO952_1 THM ? constant rigid* global* K system 3 5 4 no countermodel :) no countermodel :) - 2,27 SYO953_1 THM ? varying rigid* global* K system 2 6 4 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(p(V1))))) & $in_world(world_1, (p(indiv_0) & (! [V1: $i]: (~((V1 = indiv_0)) => ~p(V1))))) )). verified; assurance 2,09 SYO954_1 THM ? varying rigid* global* K system 3 6 4 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (and (= (as @$world_0 $world) $x1) (= (as @$world_1 $world) $x2))) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & $accessible_world(world_0, world_1) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_1))) => ~$accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (p(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~p(V1))))) & $in_world(world_1, (p(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~p(V1))))) )). timeout 2,06 SYO955_1 THM ? varying rigid* global* K system 3 6 4 no countermodel :) no countermodel :) - 1,98 SYO956_1 THM ? varying rigid* global* K system 3 6 4 no countermodel :) no countermodel :) - 2,11 SYO957_1 THM ? varying rigid* global* K system 3 6 4 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_1 $world) $x1) (= (as @$world_1 $world) $x2)))) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & ~$accessible_world(world_1, world_1) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_1))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (p(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~p(V1))))) & $in_world(world_1, ((! [V1: $i]: ~(p(V1))))) )). verified; assurance 1,31 SYO958_1 THM ? varying rigid* global* K system 2 6 4 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_1 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$world_0 $world) $x2))) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_1) & $accessible_world(world_1, world_0) & (! [W: $world, V: $world]: (~(((W = world_1) & (V = world_0))) => ~$accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_1) | (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_1)) & (? [DO: $i ]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (p(indiv_0) & (! [V1: $i]: (~((V1 = indiv_0)) => ~p(V1))))) & $in_world(world_1, (p(indiv_0) & p(indiv_1))) )). verified; assurance 1,42 SYO959_1 THM ? constant rigid* global* K system 3 5 3 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool true) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_0 $world) $x1) (= (as @$indiv_0 $indiv) $x2))) (define-fun q (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(q_type, type, q: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($distinct(d_indiv_0, d_indiv_1) & (! [W: $world]: ($in_world(W, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (p(indiv_0) & (! [V1: $i]: (~((V1 = indiv_0)) => ~p(V1))) & q(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~q(V1))))) )). timeout 1,38 SYO960_1 THM ? constant rigid* global* K system 1 5 0 no countermodel :) no countermodel :) - 1,91 SYO961_1 THM ? constant rigid* global* K system 1 5 0 no countermodel :) no countermodel :) - 1,82 SYO962_1 THM ? constant rigid* global* K system 1 5 0 no countermodel :) no countermodel :) - 0,87 SYO963_1 THM ? constant rigid* global* K system 1 5 0 no countermodel :) no countermodel :) - 0,84 SYO964_1 THM ? varying rigid* global* K system 4 6 6 no countermodel :) no countermodel :) - 0,87 SYO965_1 THM ? varying rigid* global* K system 2 4 2 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_0, world_0) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(p(V1))))) & $in_world(world_1, (p(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~p(V1))))) )). varified, assurance 1,55 SYO966_1 THM ? constant rigid* global* K system 2 4 0 no countermodel :) no countermodel :) - 0,86 SYO967_1 THM ? constant rigid* global* K system 1 4 0 no countermodel :) no countermodel :) - 0,86 SYO968_1 THM ? constant rigid* global* K system 2 4 0 no countermodel :) no countermodel :) - 0,8 SYO969_1 THM ? constant rigid global K system 2 4 0 no countermodel :) no countermodel :) - 0,89 SYO970_1 THM ? constant rigid global K system 2 4 0 no countermodel :) no countermodel :) - 0,86 SYO971_1 THM ? varying rigid* global* T system 3 5 1 no countermodel :) no countermodel :) - 0,81 SYO972_1 THM ? varying rigid* global* K system 4 5 3 no countermodel :) no countermodel :) - 0,84 SYO973_1 THM ? varying rigid* global* D system 4 5 3 no countermodel :) no countermodel :) - 0,85 SYO974_1 THM ? constant rigid global T system 4 6 4 no countermodel :) no countermodel :) - 0,83 SYO975_1 THM ? constant rigid* global* K system 4 5 3 no countermodel :) no countermodel :) - 0,84 SYO976_1 THM ? constant rigid* global* S4 system 2 5 3 no countermodel :) no countermodel :) - 0,86 SYO977_1 THM ? constant rigid* global* S4 system 2 5 3 no countermodel :) no countermodel :) - 0,92 SYO978_1 THM ? constant rigid* global* S5 system 3 5 3 no countermodel :) no countermodel :) - 0,85 SYO979_1 THM ? constant rigid* global* K system 2 4 2 no countermodel :) no countermodel :) - 0,82 SYO980_1 THM ? constant rigid* global* K system 2 4 2 no countermodel :) no countermodel :) - 0,8 SYO981_1 THM ? varying* rigid* global* K system 4 3 1 RuntimeError: Cannot apply equality to functions unless logic is prefixed by HO_. RuntimeError: Cannot apply equality to functions unless logic is prefixed by HO_. - cvc5 error: equality of two boolean constants but it doesn't do (p(world) = q(world)) but (p = q) directly even in let SYO981_1* (see notes) THM ? varying* rigid* global* K system 4 3 1 ( ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world ((_arg_1 $world) (_arg_2 $world)) Bool true) (define-fun x ((_arg_1 $world)) Bool true) (define-fun y ((_arg_1 $world)) Bool (= (as @$world_1 $world) _arg_1)) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(x_decl, type, x: $o). tff(y_decl, type, y: $o). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (x & ~y)) & $in_world(world_1, (x & y)) )). timeout 0,8 see note above + i changed (x = y) to (x <=> y) in the src file. it, then, is CSA but idk if that's REALLY the same? gotta ask SYO982_1 THM ? varying* rigid* global* K system 4 4 1 RuntimeError: Cannot apply equality to functions unless logic is prefixed by HO_. RuntimeError: Cannot apply equality to functions unless logic is prefixed by HO_. - cvc5 error: equality of two boolean constants but it doesn't do (p(world) != q(world)) but (p != q) directly even in let which cvc5 interprets as HOL (equality of functions) SYO982_1* (see notes) THM ? varying* rigid* global* K system 4 4 1 ( ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world ((_arg_1 $world) (_arg_2 $world)) Bool true) (define-fun x ((_arg_1 $world)) Bool true) (define-fun y ((_arg_1 $world)) Bool (= (as @$world_1 $world) _arg_1)) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(x_decl, type, x: $o). tff(y_decl, type, y: $o). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (x & ~y)) & $in_world(world_1, (x & y)) )). timeout 0,85 see note above + i changed (x != y) to ~(x <=> y) in the src file. it, then, is CSA but idk if that's REALLY the same? gotta ask NAME TPTP:CSM/THM TPTP RATING DOMAIN DESIGNATION TERMS MODALITIES #PREDICATES/FUNCTIONS MAX FORMULA DEPTH #MODAL OPERATORS SMT-MODEL TPTP-MODEL AXIOMS? ONLY AXIOMS OUTPUT AGMV VERIFICATION RUNTIME [SEC] NOTES SYO983_1 THM ? varying rigid global K system 4 5 1 ( ; cardinality of $indiv is 1 ; rep: (as @$indiv_0 $indiv) ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world ((BOUND_VARIABLE_460 $world) (BOUND_VARIABLE_461 $world)) Bool false) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool true) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(indiv_0_decl, type, indiv_0: $i). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: ~$accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). timeout previously with bug in TPTP. already fixed within TPTP SYO984_1 THM ? varying rigid global K system 6 6 3 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (and (= (as @$world_0 $world) $x1) (= (as @$world_1 $world) $x2))) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & $accessible_world(world_0, world_1) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_1))) => ~$accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (p(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~p(V1))))) & $in_world(world_1, (p(indiv_0) & (! [V1: $i]: (~((V1 = indiv_0)) => ~p(V1))))) )). timeout previously with bug in TPTP. already fixed within TPTP SYO985_1 THM ? varying rigid* global* K system 4 5 3 no countermodel :) no countermodel :) - 0,92 SYO986_1 THM ? varying rigid* global* K system 3 5 3 ( ; cardinality of $indiv is 2 ; rep: (as @$indiv_0 $indiv) ; rep: (as @$indiv_1 $indiv) ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (not (and (= (as @$world_0 $world) $x1) (= (as @$world_0 $world) $x2)))) (define-fun p (($x1 $world) ($x2 $indiv)) Bool (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2))) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool (or (and (= (as @$world_1 $world) $x1) (= (as @$indiv_0 $indiv) $x2)) (and (= (as @$world_0 $world) $x1) (= (as @$indiv_1 $indiv) $x2)) (and (= (as @$world_1 $world) $x1) (= (as @$indiv_1 $indiv) $x2)))) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(indiv_1_decl, type, indiv_1: $i). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & ~$accessible_world(world_0, world_0) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_0))) => $accessible_world(W,V))))). tff(model_domains, interpretation-domains, ($distinct(indiv_0, indiv_1) & $in_world(world_0, ((! [DO: $i]: ( (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_1)))) & $in_world(world_1, ((! [DO: $i]: ( (DO = indiv_0) | (DO = indiv_1) )) &(? [DO: $i]: (DO = indiv_0)) & (? [DO: $i ]: (DO = indiv_1)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~(p(V1))))) & $in_world(world_1, (p(indiv_1) & (! [V1: $i]: (~((V1 = indiv_1)) => ~p(V1))))) )). verified; assurance 1,28 SYO987_1 THM ? varying rigid global K system 3 4 0 no countermodel :) no countermodel :) - 0,8 SYO988_1 THM ? varying rigid* global* K system 4 6 3 no countermodel :) no countermodel :) - 0,82 SYO989_1 THM ? varying rigid* global* K system 3 4 2 ( ; cardinality of $indiv is 1 ; rep: (as @$indiv_0 $indiv) ; cardinality of $world is 1 ; rep: (as @$world_0 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool false) (define-fun p (($x1 $world) ($x2 $indiv)) Bool true) (define-fun $exists_in_world_$i (($x1 $world) ($x2 $indiv)) Bool true) ) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: ~$accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: p(V1)))) )). verified; assurance 1,06 SYO990_1 THM ? varying rigid* global* K system 3 5 3 no countermodel :) no countermodel :) - 0,81 SYO991_1 THM ? varying rigid* global* K system 4 5 5 no countermodel :) no countermodel :) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(p_type, type, p: (($i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i]: ~p(V1)))) )). - 0,86 SYO992_1 THM ? decreasing rigid* global* K system 2 4 2 no countermodel :) no countermodel :) - 0,82 SYO993_1 THM ? varying rigid* global* K system 4 6 5 no countermodel :) no countermodel :) tff(simple_K, logic, ($modal) == ([($domains) == ($varying),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(r_type, type, r: (($i * $i) > $o)). tff(indiv_0_decl, type, indiv_0: $i). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_domains, interpretation-domains, ($in_world(world_0, ((! [DO: $i]: ( (DO = indiv_0) )) &(? [DO: $i]: (DO = indiv_0)))) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, ((! [V1: $i, V2: $i]: ~r(V1, V2)))) )). - 0,84 SYO994_1 THM ? varying rigid* global* B system 2 9 9 no countermodel :) no countermodel :) - 0,83 SYO995_1 THM ? constant* rigid* global* K system 2 4 3 ( ; cardinality of $world is 2 ; rep: (as @$world_0 $world) ; rep: (as @$world_1 $world) (define-fun $local_world () $world (as @$world_0 $world)) (define-fun $accessible_world (($x1 $world) ($x2 $world)) Bool (and (= (as @$world_0 $world) $x1) (= (as @$world_1 $world) $x2))) (define-fun x (($x1 $world)) Bool false) ) tff(simple_K, logic, ($modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(x_decl, type, x: $o). tff(world_0_decl, type, world_0: $world). tff(world_1_decl, type, world_1: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) | (W = world_1) )) & $distinct(world_0, world_1) & ($local_world = world_0) & $accessible_world(world_0, world_1) & (! [W: $world, V: $world]: (~(((W = world_0) & (V = world_1))) => $accessible_world(W,V))))). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~x)) & $in_world(world_1, (~x)) )). tff(simple_K, logic, ($modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(x_decl, type, x: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (~x)) )). timeout 0,81 SYO996_1 THM ? constant* rigid* global* K system 2 4 3 no countermodel :) no countermodel :) tff(simple_K, logic, ($modal) == ([($domains) == ($constant),($designation) == ($rigid),($terms) == ($global),($modalities) == ($modal_system_K)])). tff(x_decl, type, x: $o). tff(world_0_decl, type, world_0: $world). tff(model_worlds, interpretation-worlds, ((! [W: $world] : ( (W = world_0) )) & ($local_world = world_0) & (! [W: $world, V: $world]: $accessible_world(W, V)) )). tff(model_mapping, interpretation-mappings, ($in_world(world_0, (x)) )). - 0,79