%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL962_16 : TPTP v9.3.1. Released v8.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 12:55:10 PM UTC 2026 % Result : Theorem 6.92s 1.76s % Output : Proof 9.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL962_16 : TPTP v9.3.1. Released v8.2.0. % 0.00/0.03 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.35 % Computer : n017.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 18:45:07 UTC 2026 % 0.09/0.35 % CPUTime : % 0.13/0.37 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.67/0.72 ________ _____ % 0.67/0.72 ___ __ \_________(_)________________________________ % 0.67/0.72 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.67/0.72 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.67/0.72 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.67/0.72 % 0.67/0.72 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.67/0.72 (2023-06-19) % 0.67/0.72 % 0.67/0.72 (c) Philipp Rümmer, 2009-2023 % 0.67/0.72 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.67/0.72 Amanda Stjerna. % 0.67/0.72 Free software under BSD-3-Clause. % 0.67/0.72 % 0.67/0.72 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.67/0.72 % 0.67/0.72 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.67/0.74 Running up to 7 provers in parallel. % 0.67/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.76/1.17 Prover 4: Preprocessing ... % 2.76/1.18 Prover 1: Preprocessing ... % 3.06/1.24 Prover 2: Preprocessing ... % 3.06/1.24 Prover 6: Preprocessing ... % 3.06/1.24 Prover 5: Preprocessing ... % 3.06/1.24 Prover 0: Preprocessing ... % 3.06/1.24 Prover 3: Preprocessing ... % 4.56/1.42 Prover 5: Proving ... % 4.56/1.42 Prover 2: Proving ... % 4.56/1.45 Prover 3: Constructing countermodel ... % 4.56/1.46 Prover 6: Proving ... % 5.35/1.50 Prover 1: Constructing countermodel ... % 5.35/1.50 Prover 4: Constructing countermodel ... % 5.35/1.55 Prover 0: Proving ... % 6.16/1.67 Prover 3: gave up % 6.16/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.92/1.72 Prover 7: Preprocessing ... % 6.92/1.74 Prover 1: gave up % 6.92/1.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.92/1.76 Prover 5: proved (1009ms) % 6.92/1.76 % 6.92/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.92/1.76 % 6.92/1.77 Prover 2: proved (1013ms) % 6.92/1.77 % 6.92/1.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.92/1.77 % 6.92/1.77 Prover 6: stopped % 6.92/1.77 Prover 0: stopped % 6.92/1.77 Prover 7: Warning: ignoring some quantifiers % 6.92/1.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.92/1.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.92/1.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.92/1.77 Prover 7: Constructing countermodel ... % 6.92/1.77 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.92/1.78 Prover 8: Preprocessing ... % 7.73/1.81 Prover 10: Preprocessing ... % 7.73/1.84 Prover 16: Preprocessing ... % 7.73/1.85 Prover 11: Preprocessing ... % 7.73/1.85 Prover 13: Preprocessing ... % 7.73/1.85 Prover 10: Warning: ignoring some quantifiers % 7.73/1.86 Prover 10: Constructing countermodel ... % 7.73/1.88 Prover 13: Warning: ignoring some quantifiers % 7.73/1.88 Prover 7: gave up % 7.73/1.89 Prover 16: Warning: ignoring some quantifiers % 7.73/1.89 Prover 13: Constructing countermodel ... % 7.73/1.89 Prover 16: Constructing countermodel ... % 7.73/1.89 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.73/1.90 Prover 4: Found proof (size 43) % 7.73/1.90 Prover 4: proved (1148ms) % 8.50/1.90 Prover 16: stopped % 8.50/1.91 Prover 13: stopped % 8.50/1.91 Prover 10: stopped % 8.50/1.92 Prover 8: Warning: ignoring some quantifiers % 8.50/1.92 Prover 8: Constructing countermodel ... % 8.50/1.93 Prover 8: stopped % 8.50/1.94 Prover 19: Preprocessing ... % 8.50/1.97 Prover 11: Constructing countermodel ... % 8.50/1.98 Prover 11: stopped % 8.50/2.01 Prover 19: Warning: ignoring some quantifiers % 8.50/2.02 Prover 19: Constructing countermodel ... % 8.50/2.03 Prover 19: stopped % 8.50/2.03 % 8.50/2.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.50/2.03 % 8.50/2.04 % SZS output start Proof for theBenchmark % 8.50/2.04 Assumptions after simplification: % 8.50/2.04 --------------------------------- % 8.50/2.05 % 8.50/2.05 (ab_axiom_1) % 9.33/2.10 $ki_index(#idx(b)) & $ki_index(#idx(a)) & $ki_world($ki_local_world) & ! [v0: % 9.33/2.11 $ki_world] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ (p(v1) = v2) | % 9.33/2.11 ~ (p(v0) = 0) | ~ $ki_world(v1) | ~ $ki_world(v0) | ? [v3: int] : (( ~ % 9.33/2.11 (v3 = 0) & $ki_accessible(#idx(b), v0, v1) = v3) | ( ~ (v3 = 0) & % 9.33/2.11 $ki_accessible(#idx(a), $ki_local_world, v0) = v3))) & ! [v0: % 9.33/2.11 $ki_world] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ (p(v1) = v2) | % 9.33/2.11 ~ ($ki_accessible(#idx(a), $ki_local_world, v0) = 0) | ~ $ki_world(v1) | % 9.33/2.11 ~ $ki_world(v0) | ? [v3: int] : (( ~ (v3 = 0) & p(v0) = v3) | ( ~ (v3 = 0) % 9.33/2.11 & $ki_accessible(#idx(b), v0, v1) = v3))) & ! [v0: $ki_world] : ! [v1: % 9.33/2.11 $ki_world] : ( ~ (p(v0) = 0) | ~ ($ki_accessible(#idx(b), v0, v1) = 0) | ~ % 9.33/2.11 $ki_world(v1) | ~ $ki_world(v0) | ? [v2: int] : ((v2 = 0 & p(v1) = 0) | ( % 9.33/2.11 ~ (v2 = 0) & $ki_accessible(#idx(a), $ki_local_world, v0) = v2))) & ! % 9.33/2.11 [v0: $ki_world] : ! [v1: $ki_world] : ( ~ ($ki_accessible(#idx(b), v0, v1) = % 9.33/2.11 0) | ~ ($ki_accessible(#idx(a), $ki_local_world, v0) = 0) | ~ % 9.33/2.11 $ki_world(v1) | ~ $ki_world(v0) | ? [v2: int] : ((v2 = 0 & p(v1) = 0) | ( % 9.33/2.11 ~ (v2 = 0) & p(v0) = v2))) % 9.33/2.11 % 9.33/2.11 (ab_axiom_2) % 9.33/2.11 $ki_index(#idx(b)) & $ki_index(#idx(a)) & $ki_world($ki_local_world) & ( ! % 9.33/2.11 [v0: $ki_world] : ( ~ ($ki_accessible(#idx(a), $ki_local_world, v0) = 0) | % 9.33/2.11 ~ $ki_world(v0) | ? [v1: $ki_world] : ? [v2: int] : ( ~ (v2 = 0) & p(v1) % 9.33/2.11 = v2 & $ki_accessible(#idx(b), v0, v1) = 0 & $ki_world(v1))) | ( ! [v0: % 9.33/2.11 $ki_world] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | ~ $ki_world(v0) % 9.33/2.11 | ? [v2: int] : ( ~ (v2 = 0) & $ki_accessible(#idx(b), $ki_local_world, % 9.33/2.11 v0) = v2)) & ! [v0: $ki_world] : ( ~ ($ki_accessible(#idx(b), % 9.33/2.11 $ki_local_world, v0) = 0) | ~ $ki_world(v0) | p(v0) = 0))) % 9.33/2.11 % 9.33/2.11 (mrel_reflexive_#idx(b)) % 9.33/2.12 $ki_index(#idx(b)) & ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ % 9.33/2.12 ($ki_accessible(#idx(b), v0, v0) = v1) | ~ $ki_world(v0)) % 9.33/2.12 % 9.33/2.12 (not_a_axiom_1) % 9.33/2.12 $ki_world($ki_local_world) & ? [v0: int] : ( ~ (v0 = 0) & p($ki_local_world) % 9.33/2.12 = v0) % 9.33/2.12 % 9.33/2.12 (verify) % 9.33/2.12 $ki_index(#idx(a)) & $ki_world($ki_local_world) & ? [v0: $ki_world] : (p(v0) % 9.33/2.12 = 0 & $ki_accessible(#idx(a), $ki_local_world, v0) = 0 & $ki_world(v0)) % 9.33/2.12 % 9.33/2.12 (function-axioms) % 9.33/2.12 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $ki_world] : % 9.33/2.12 ! [v3: $ki_world] : ! [v4: $ki_index] : (v1 = v0 | ~ ($ki_accessible(v4, % 9.33/2.12 v3, v2) = v1) | ~ ($ki_accessible(v4, v3, v2) = v0)) & ! [v0: % 9.33/2.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $ki_world] : (v1 = % 9.33/2.12 v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 9.33/2.12 % 9.33/2.12 Further assumptions not needed in the proof: % 9.33/2.12 -------------------------------------------- % 9.33/2.12 mrel_reflexive_#idx(a), mrel_transitive_#idx(a), mrel_transitive_#idx(b) % 9.33/2.12 % 9.33/2.12 Those formulas are unsatisfiable: % 9.33/2.12 --------------------------------- % 9.33/2.12 % 9.33/2.12 Begin of proof % 9.33/2.12 | % 9.33/2.12 | ALPHA: (mrel_reflexive_#idx(b)) implies: % 9.33/2.13 | (1) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ % 9.33/2.13 | ($ki_accessible(#idx(b), v0, v0) = v1) | ~ $ki_world(v0)) % 9.33/2.13 | % 9.33/2.13 | ALPHA: (ab_axiom_1) implies: % 9.33/2.13 | (2) ! [v0: $ki_world] : ! [v1: $ki_world] : ( ~ (p(v0) = 0) | ~ % 9.33/2.13 | ($ki_accessible(#idx(b), v0, v1) = 0) | ~ $ki_world(v1) | ~ % 9.33/2.13 | $ki_world(v0) | ? [v2: int] : ((v2 = 0 & p(v1) = 0) | ( ~ (v2 = 0) & % 9.33/2.13 | $ki_accessible(#idx(a), $ki_local_world, v0) = v2))) % 9.33/2.13 | (3) ! [v0: $ki_world] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ % 9.33/2.13 | (p(v1) = v2) | ~ (p(v0) = 0) | ~ $ki_world(v1) | ~ $ki_world(v0) | % 9.33/2.13 | ? [v3: int] : (( ~ (v3 = 0) & $ki_accessible(#idx(b), v0, v1) = v3) % 9.33/2.13 | | ( ~ (v3 = 0) & $ki_accessible(#idx(a), $ki_local_world, v0) = % 9.33/2.13 | v3))) % 9.33/2.13 | % 9.33/2.13 | ALPHA: (ab_axiom_2) implies: % 9.33/2.14 | (4) ! [v0: $ki_world] : ( ~ ($ki_accessible(#idx(a), $ki_local_world, v0) % 9.33/2.14 | = 0) | ~ $ki_world(v0) | ? [v1: $ki_world] : ? [v2: int] : ( ~ % 9.33/2.14 | (v2 = 0) & p(v1) = v2 & $ki_accessible(#idx(b), v0, v1) = 0 & % 9.33/2.14 | $ki_world(v1))) | ( ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ % 9.33/2.14 | (p(v0) = v1) | ~ $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 9.33/2.14 | $ki_accessible(#idx(b), $ki_local_world, v0) = v2)) & ! [v0: % 9.33/2.14 | $ki_world] : ( ~ ($ki_accessible(#idx(b), $ki_local_world, v0) = 0) % 9.33/2.14 | | ~ $ki_world(v0) | p(v0) = 0)) % 9.33/2.14 | % 9.33/2.14 | ALPHA: (not_a_axiom_1) implies: % 9.33/2.14 | (5) ? [v0: int] : ( ~ (v0 = 0) & p($ki_local_world) = v0) % 9.33/2.14 | % 9.33/2.14 | ALPHA: (verify) implies: % 9.33/2.14 | (6) $ki_world($ki_local_world) % 9.33/2.14 | (7) ? [v0: $ki_world] : (p(v0) = 0 & $ki_accessible(#idx(a), % 9.33/2.14 | $ki_local_world, v0) = 0 & $ki_world(v0)) % 9.33/2.14 | % 9.33/2.14 | ALPHA: (function-axioms) implies: % 9.33/2.14 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.33/2.14 | $ki_world] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 9.33/2.14 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.33/2.14 | $ki_world] : ! [v3: $ki_world] : ! [v4: $ki_index] : (v1 = v0 | ~ % 9.33/2.14 | ($ki_accessible(v4, v3, v2) = v1) | ~ ($ki_accessible(v4, v3, v2) = % 9.33/2.14 | v0)) % 9.33/2.14 | % 9.33/2.14 | DELTA: instantiating (5) with fresh symbol all_13_0 gives: % 9.33/2.14 | (10) ~ (all_13_0 = 0) & p($ki_local_world) = all_13_0 % 9.33/2.14 | % 9.33/2.14 | ALPHA: (10) implies: % 9.33/2.14 | (11) ~ (all_13_0 = 0) % 9.33/2.14 | (12) p($ki_local_world) = all_13_0 % 9.33/2.14 | % 9.33/2.14 | DELTA: instantiating (7) with fresh symbol all_15_0 gives: % 9.33/2.14 | (13) p(all_15_0) = 0 & $ki_accessible(#idx(a), $ki_local_world, all_15_0) = % 9.33/2.14 | 0 & $ki_world(all_15_0) % 9.33/2.14 | % 9.33/2.15 | ALPHA: (13) implies: % 9.33/2.15 | (14) $ki_world(all_15_0) % 9.33/2.15 | (15) $ki_accessible(#idx(a), $ki_local_world, all_15_0) = 0 % 9.33/2.15 | (16) p(all_15_0) = 0 % 9.33/2.15 | % 9.33/2.15 | GROUND_INST: instantiating (3) with all_15_0, $ki_local_world, all_13_0, % 9.33/2.15 | simplifying with (6), (12), (14), (16) gives: % 9.33/2.15 | (17) all_13_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & $ki_accessible(#idx(b), % 9.33/2.15 | all_15_0, $ki_local_world) = v0) | ( ~ (v0 = 0) & % 9.33/2.15 | $ki_accessible(#idx(a), $ki_local_world, all_15_0) = v0)) % 9.33/2.15 | % 9.33/2.15 | BETA: splitting (4) gives: % 9.33/2.15 | % 9.33/2.15 | Case 1: % 9.33/2.15 | | % 9.33/2.15 | | (18) ! [v0: $ki_world] : ( ~ ($ki_accessible(#idx(a), $ki_local_world, % 9.33/2.15 | | v0) = 0) | ~ $ki_world(v0) | ? [v1: $ki_world] : ? [v2: % 9.33/2.15 | | int] : ( ~ (v2 = 0) & p(v1) = v2 & $ki_accessible(#idx(b), v0, % 9.33/2.15 | | v1) = 0 & $ki_world(v1))) % 9.33/2.15 | | % 9.84/2.15 | | GROUND_INST: instantiating (18) with all_15_0, simplifying with (14), (15) % 9.84/2.15 | | gives: % 9.84/2.15 | | (19) ? [v0: $ki_world] : ? [v1: int] : ( ~ (v1 = 0) & p(v0) = v1 & % 9.84/2.15 | | $ki_accessible(#idx(b), all_15_0, v0) = 0 & $ki_world(v0)) % 9.84/2.15 | | % 9.84/2.15 | | DELTA: instantiating (19) with fresh symbols all_24_0, all_24_1 gives: % 9.84/2.15 | | (20) ~ (all_24_0 = 0) & p(all_24_1) = all_24_0 & $ki_accessible(#idx(b), % 9.84/2.15 | | all_15_0, all_24_1) = 0 & $ki_world(all_24_1) % 9.84/2.15 | | % 9.84/2.15 | | ALPHA: (20) implies: % 9.84/2.16 | | (21) ~ (all_24_0 = 0) % 9.84/2.16 | | (22) $ki_world(all_24_1) % 9.84/2.16 | | (23) $ki_accessible(#idx(b), all_15_0, all_24_1) = 0 % 9.84/2.16 | | (24) p(all_24_1) = all_24_0 % 9.84/2.16 | | % 9.84/2.16 | | BETA: splitting (17) gives: % 9.84/2.16 | | % 9.84/2.16 | | Case 1: % 9.84/2.16 | | | % 9.84/2.16 | | | (25) all_13_0 = 0 % 9.84/2.16 | | | % 9.84/2.16 | | | REDUCE: (11), (25) imply: % 9.84/2.16 | | | (26) $false % 9.84/2.16 | | | % 9.84/2.16 | | | CLOSE: (26) is inconsistent. % 9.84/2.16 | | | % 9.84/2.16 | | Case 2: % 9.84/2.16 | | | % 9.84/2.16 | | | % 9.84/2.16 | | | GROUND_INST: instantiating (2) with all_15_0, all_24_1, simplifying with % 9.84/2.16 | | | (14), (16), (22), (23) gives: % 9.84/2.16 | | | (27) ? [v0: int] : ((v0 = 0 & p(all_24_1) = 0) | ( ~ (v0 = 0) & % 9.84/2.16 | | | $ki_accessible(#idx(a), $ki_local_world, all_15_0) = v0)) % 9.84/2.16 | | | % 9.84/2.16 | | | DELTA: instantiating (27) with fresh symbol all_52_0 gives: % 9.84/2.16 | | | (28) (all_52_0 = 0 & p(all_24_1) = 0) | ( ~ (all_52_0 = 0) & % 9.84/2.16 | | | $ki_accessible(#idx(a), $ki_local_world, all_15_0) = all_52_0) % 9.84/2.16 | | | % 9.84/2.16 | | | BETA: splitting (28) gives: % 9.84/2.16 | | | % 9.84/2.16 | | | Case 1: % 9.84/2.16 | | | | % 9.84/2.16 | | | | (29) all_52_0 = 0 & p(all_24_1) = 0 % 9.84/2.16 | | | | % 9.84/2.16 | | | | ALPHA: (29) implies: % 9.84/2.16 | | | | (30) p(all_24_1) = 0 % 9.84/2.16 | | | | % 9.84/2.16 | | | | GROUND_INST: instantiating (8) with all_24_0, 0, all_24_1, simplifying % 9.84/2.16 | | | | with (24), (30) gives: % 9.84/2.16 | | | | (31) all_24_0 = 0 % 9.84/2.16 | | | | % 9.84/2.16 | | | | REDUCE: (21), (31) imply: % 9.84/2.16 | | | | (32) $false % 9.84/2.16 | | | | % 9.84/2.16 | | | | CLOSE: (32) is inconsistent. % 9.84/2.16 | | | | % 9.84/2.16 | | | Case 2: % 9.84/2.16 | | | | % 9.84/2.17 | | | | (33) ~ (all_52_0 = 0) & $ki_accessible(#idx(a), $ki_local_world, % 9.84/2.17 | | | | all_15_0) = all_52_0 % 9.84/2.17 | | | | % 9.84/2.17 | | | | ALPHA: (33) implies: % 9.84/2.17 | | | | (34) ~ (all_52_0 = 0) % 9.84/2.17 | | | | (35) $ki_accessible(#idx(a), $ki_local_world, all_15_0) = all_52_0 % 9.84/2.17 | | | | % 9.84/2.17 | | | | GROUND_INST: instantiating (9) with 0, all_52_0, all_15_0, % 9.84/2.17 | | | | $ki_local_world, #idx(a), simplifying with (15), (35) % 9.84/2.17 | | | | gives: % 9.84/2.17 | | | | (36) all_52_0 = 0 % 9.84/2.17 | | | | % 9.84/2.17 | | | | REDUCE: (34), (36) imply: % 9.84/2.17 | | | | (37) $false % 9.84/2.17 | | | | % 9.84/2.17 | | | | CLOSE: (37) is inconsistent. % 9.84/2.17 | | | | % 9.84/2.17 | | | End of split % 9.84/2.17 | | | % 9.84/2.17 | | End of split % 9.84/2.17 | | % 9.84/2.17 | Case 2: % 9.84/2.17 | | % 9.84/2.17 | | (38) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | ~ % 9.84/2.17 | | $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 9.84/2.17 | | $ki_accessible(#idx(b), $ki_local_world, v0) = v2)) & ! [v0: % 9.84/2.17 | | $ki_world] : ( ~ ($ki_accessible(#idx(b), $ki_local_world, v0) = % 9.84/2.17 | | 0) | ~ $ki_world(v0) | p(v0) = 0) % 9.84/2.17 | | % 9.84/2.17 | | ALPHA: (38) implies: % 9.84/2.17 | | (39) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | ~ % 9.84/2.17 | | $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 9.84/2.17 | | $ki_accessible(#idx(b), $ki_local_world, v0) = v2)) % 9.84/2.17 | | % 9.84/2.17 | | GROUND_INST: instantiating (39) with $ki_local_world, all_13_0, simplifying % 9.84/2.17 | | with (6), (12) gives: % 9.84/2.17 | | (40) all_13_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & $ki_accessible(#idx(b), % 9.84/2.17 | | $ki_local_world, $ki_local_world) = v0) % 9.84/2.17 | | % 9.84/2.17 | | BETA: splitting (40) gives: % 9.84/2.17 | | % 9.84/2.17 | | Case 1: % 9.84/2.17 | | | % 9.84/2.17 | | | (41) all_13_0 = 0 % 9.84/2.17 | | | % 9.84/2.17 | | | REDUCE: (11), (41) imply: % 9.84/2.17 | | | (42) $false % 9.84/2.17 | | | % 9.84/2.17 | | | CLOSE: (42) is inconsistent. % 9.84/2.17 | | | % 9.84/2.17 | | Case 2: % 9.84/2.17 | | | % 9.84/2.17 | | | (43) ? [v0: int] : ( ~ (v0 = 0) & $ki_accessible(#idx(b), % 9.84/2.17 | | | $ki_local_world, $ki_local_world) = v0) % 9.84/2.18 | | | % 9.84/2.18 | | | DELTA: instantiating (43) with fresh symbol all_37_0 gives: % 9.84/2.18 | | | (44) ~ (all_37_0 = 0) & $ki_accessible(#idx(b), $ki_local_world, % 9.84/2.18 | | | $ki_local_world) = all_37_0 % 9.84/2.18 | | | % 9.84/2.18 | | | ALPHA: (44) implies: % 9.84/2.18 | | | (45) ~ (all_37_0 = 0) % 9.84/2.18 | | | (46) $ki_accessible(#idx(b), $ki_local_world, $ki_local_world) = % 9.84/2.18 | | | all_37_0 % 9.84/2.18 | | | % 9.84/2.18 | | | GROUND_INST: instantiating (1) with $ki_local_world, all_37_0, simplifying % 9.84/2.18 | | | with (6), (46) gives: % 9.84/2.18 | | | (47) all_37_0 = 0 % 9.84/2.18 | | | % 9.84/2.18 | | | REDUCE: (45), (47) imply: % 9.84/2.18 | | | (48) $false % 9.84/2.18 | | | % 9.84/2.18 | | | CLOSE: (48) is inconsistent. % 9.84/2.18 | | | % 9.84/2.18 | | End of split % 9.84/2.18 | | % 9.84/2.18 | End of split % 9.84/2.18 | % 9.84/2.18 End of proof % 9.84/2.18 % SZS output end Proof for theBenchmark % 9.84/2.18 % 9.84/2.18 1459ms %------------------------------------------------------------------------------