%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : PLA053_2 : TPTP v8.2.0. Released v8.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n024.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 13:02:56 EDT 2023 % Result : Theorem 8.08s 1.80s % Output : Proof 9.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : PLA053_2 : TPTP v8.2.0. Released v8.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n024.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Aug 27 06:10:08 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.33/1.00 Prover 4: Preprocessing ... % 2.33/1.01 Prover 1: Preprocessing ... % 2.33/1.05 Prover 2: Preprocessing ... % 2.33/1.05 Prover 5: Preprocessing ... % 2.33/1.05 Prover 6: Preprocessing ... % 2.33/1.05 Prover 3: Preprocessing ... % 2.33/1.05 Prover 0: Preprocessing ... % 3.80/1.22 Prover 2: Proving ... % 3.80/1.23 Prover 5: Proving ... % 4.38/1.30 Prover 1: Warning: ignoring some quantifiers % 4.38/1.30 Prover 3: Warning: ignoring some quantifiers % 4.38/1.31 Prover 6: Proving ... % 4.38/1.31 Prover 3: Constructing countermodel ... % 4.38/1.31 Prover 1: Constructing countermodel ... % 5.50/1.46 Prover 4: Warning: ignoring some quantifiers % 5.67/1.48 Prover 4: Constructing countermodel ... % 5.67/1.48 Prover 0: Proving ... % 8.08/1.80 Prover 0: proved (1168ms) % 8.08/1.80 % 8.08/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.08/1.80 % 8.08/1.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.08/1.81 Prover 6: stopped % 8.08/1.81 Prover 5: stopped % 8.08/1.81 Prover 3: stopped % 8.29/1.82 Prover 2: stopped % 8.34/1.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.34/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.34/1.84 Prover 7: Preprocessing ... % 8.34/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.34/1.84 Prover 8: Preprocessing ... % 8.34/1.85 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.34/1.85 Prover 10: Preprocessing ... % 8.34/1.86 Prover 7: Warning: ignoring some quantifiers % 8.34/1.86 Prover 11: Preprocessing ... % 8.34/1.86 Prover 7: Constructing countermodel ... % 8.34/1.87 Prover 4: Found proof (size 37) % 8.34/1.87 Prover 4: proved (1242ms) % 8.34/1.88 Prover 1: stopped % 8.34/1.88 Prover 10: Warning: ignoring some quantifiers % 8.34/1.88 Prover 13: Preprocessing ... % 8.34/1.88 Prover 7: stopped % 8.34/1.88 Prover 10: Constructing countermodel ... % 8.34/1.88 Prover 10: stopped % 8.34/1.88 Prover 11: stopped % 8.34/1.89 Prover 13: Warning: ignoring some quantifiers % 8.34/1.90 Prover 13: Constructing countermodel ... % 8.34/1.90 Prover 13: stopped % 8.34/1.90 Prover 8: Warning: ignoring some quantifiers % 8.34/1.91 Prover 8: Constructing countermodel ... % 8.34/1.92 Prover 8: stopped % 8.34/1.92 % 8.34/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.34/1.92 % 8.34/1.92 % SZS output start Proof for theBenchmark % 8.34/1.93 Assumptions after simplification: % 8.34/1.93 --------------------------------- % 8.34/1.93 % 8.34/1.93 (ax3) % 8.34/1.96 $ki_world($ki_local_world) & ! [v0: $ki_world] : ! [v1: $i] : ( ~ % 8.34/1.96 ($ki_exists_in_world_$i(v0, v1) = 0) | ~ ($ki_accessible($ki_local_world, % 8.34/1.96 v0) = 0) | ~ $ki_world(v0) | ~ $i(v1) | ? [v2: $i] : % 8.34/1.96 ($ki_exists_in_world_$i(v0, v2) = 0 & $i(v2) & ! [v3: $ki_world] : ! [v4: % 8.34/1.96 int] : (v4 = 0 | ~ (defused(v3, v1) = v4) | ~ $ki_world(v3) | ? [v5: % 8.34/1.96 any] : ? [v6: any] : ? [v7: any] : (h(v3, v2) = v7 & bomb(v3, v1) = % 8.34/1.96 v6 & $ki_accessible(v0, v3) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 % 8.34/1.96 = 0)))) & ! [v3: $ki_world] : ( ~ (h(v3, v2) = 0) | ~ % 8.34/1.96 $ki_world(v3) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 8.34/1.96 (defused(v3, v1) = v6 & bomb(v3, v1) = v5 & $ki_accessible(v0, v3) = v4 % 8.34/1.96 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v3: $ki_world] : ( ~ % 8.34/1.96 (bomb(v3, v1) = 0) | ~ $ki_world(v3) | ? [v4: any] : ? [v5: any] : ? % 8.34/1.96 [v6: any] : (defused(v3, v1) = v6 & h(v3, v2) = v5 & $ki_accessible(v0, % 8.34/1.96 v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v3: % 8.34/1.96 $ki_world] : ( ~ ($ki_accessible(v0, v3) = 0) | ~ $ki_world(v3) | ? % 8.34/1.96 [v4: any] : ? [v5: any] : ? [v6: any] : (defused(v3, v1) = v6 & h(v3, % 8.34/1.96 v2) = v5 & bomb(v3, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = % 8.34/1.96 0))))) % 8.34/1.96 % 8.34/1.96 (mrel_reflexive) % 8.34/1.97 ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ ($ki_accessible(v0, v0) = v1) % 8.34/1.97 | ~ $ki_world(v0)) % 8.34/1.97 % 8.34/1.97 (verify) % 9.15/1.97 $ki_world($ki_local_world) & ? [v0: $ki_world] : ? [v1: $i] : ? [v2: any] : % 9.15/1.97 ? [v3: any] : (defused(v0, v1) = v3 & bomb(v0, v1) = v2 & % 9.15/1.97 $ki_exists_in_world_$i(v0, v1) = 0 & $ki_accessible($ki_local_world, v0) = 0 % 9.15/1.97 & $ki_world(v0) & $i(v1) & ! [v4: $i] : ! [v5: MultipleValueBool] : ( ~ % 9.15/1.97 (v3 = 0) | ~ (h(v0, v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & % 9.15/1.97 $ki_exists_in_world_$i(v0, v4) = v6)) & ! [v4: $i] : ! [v5: int] : (v5 % 9.15/1.97 = 0 | ~ (h(v0, v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & % 9.15/1.97 $ki_exists_in_world_$i(v0, v4) = v6)) & ! [v4: $i] : ! [v5: % 9.15/1.97 MultipleValueBool] : (v2 = 0 | ~ (h(v0, v4) = v5) | ~ $i(v4) | ? [v6: % 9.15/1.97 int] : ( ~ (v6 = 0) & $ki_exists_in_world_$i(v0, v4) = v6)) & ! [v4: % 9.15/1.97 $i] : ( ~ (v3 = 0) | ~ ($ki_exists_in_world_$i(v0, v4) = 0) | ~ $i(v4)) % 9.15/1.97 & ! [v4: $i] : (v2 = 0 | ~ ($ki_exists_in_world_$i(v0, v4) = 0) | ~ % 9.15/1.97 $i(v4)) & ! [v4: $i] : ( ~ ($ki_exists_in_world_$i(v0, v4) = 0) | ~ % 9.15/1.97 $i(v4) | h(v0, v4) = 0)) % 9.15/1.97 % 9.15/1.97 (function-axioms) % 9.15/1.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.15/1.97 [v3: $ki_world] : (v1 = v0 | ~ (defused(v3, v2) = v1) | ~ (defused(v3, v2) = % 9.15/1.97 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.15/1.98 $i] : ! [v3: $ki_world] : (v1 = v0 | ~ (h(v3, v2) = v1) | ~ (h(v3, v2) = % 9.15/1.98 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.15/1.98 $i] : ! [v3: $ki_world] : (v1 = v0 | ~ (bomb(v3, v2) = v1) | ~ (bomb(v3, % 9.15/1.98 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 9.15/1.98 ! [v2: $i] : ! [v3: $ki_world] : (v1 = v0 | ~ ($ki_exists_in_world_$i(v3, % 9.15/1.98 v2) = v1) | ~ ($ki_exists_in_world_$i(v3, v2) = v0)) & ! [v0: % 9.15/1.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $ki_world] : ! % 9.15/1.98 [v3: $ki_world] : (v1 = v0 | ~ ($ki_accessible(v3, v2) = v1) | ~ % 9.15/1.98 ($ki_accessible(v3, v2) = v0)) % 9.15/1.98 % 9.15/1.98 Further assumptions not needed in the proof: % 9.15/1.98 -------------------------------------------- % 9.15/1.98 $ki_exists_in_world_$i_const, $ki_exists_in_world_$i_nonempty, ax1, ax2 % 9.15/1.98 % 9.15/1.98 Those formulas are unsatisfiable: % 9.15/1.98 --------------------------------- % 9.15/1.98 % 9.15/1.98 Begin of proof % 9.15/1.98 | % 9.15/1.98 | ALPHA: (ax3) implies: % 9.15/1.98 | (1) ! [v0: $ki_world] : ! [v1: $i] : ( ~ ($ki_exists_in_world_$i(v0, v1) % 9.15/1.98 | = 0) | ~ ($ki_accessible($ki_local_world, v0) = 0) | ~ % 9.15/1.98 | $ki_world(v0) | ~ $i(v1) | ? [v2: $i] : ($ki_exists_in_world_$i(v0, % 9.15/1.98 | v2) = 0 & $i(v2) & ! [v3: $ki_world] : ! [v4: int] : (v4 = 0 | % 9.15/1.98 | ~ (defused(v3, v1) = v4) | ~ $ki_world(v3) | ? [v5: any] : ? % 9.15/1.98 | [v6: any] : ? [v7: any] : (h(v3, v2) = v7 & bomb(v3, v1) = v6 & % 9.15/1.98 | $ki_accessible(v0, v3) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ % 9.15/1.98 | (v5 = 0)))) & ! [v3: $ki_world] : ( ~ (h(v3, v2) = 0) | ~ % 9.15/1.98 | $ki_world(v3) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 9.15/1.98 | (defused(v3, v1) = v6 & bomb(v3, v1) = v5 & $ki_accessible(v0, % 9.15/1.98 | v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v3: % 9.15/1.98 | $ki_world] : ( ~ (bomb(v3, v1) = 0) | ~ $ki_world(v3) | ? [v4: % 9.15/1.98 | any] : ? [v5: any] : ? [v6: any] : (defused(v3, v1) = v6 & % 9.15/1.98 | h(v3, v2) = v5 & $ki_accessible(v0, v3) = v4 & ( ~ (v5 = 0) | % 9.15/1.98 | ~ (v4 = 0) | v6 = 0))) & ! [v3: $ki_world] : ( ~ % 9.15/1.98 | ($ki_accessible(v0, v3) = 0) | ~ $ki_world(v3) | ? [v4: any] : % 9.15/1.98 | ? [v5: any] : ? [v6: any] : (defused(v3, v1) = v6 & h(v3, v2) = % 9.15/1.98 | v5 & bomb(v3, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = % 9.15/1.98 | 0))))) % 9.15/1.98 | % 9.15/1.98 | ALPHA: (verify) implies: % 9.15/1.99 | (2) ? [v0: $ki_world] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 9.15/1.99 | (defused(v0, v1) = v3 & bomb(v0, v1) = v2 & $ki_exists_in_world_$i(v0, % 9.15/1.99 | v1) = 0 & $ki_accessible($ki_local_world, v0) = 0 & $ki_world(v0) & % 9.15/1.99 | $i(v1) & ! [v4: $i] : ! [v5: MultipleValueBool] : ( ~ (v3 = 0) | ~ % 9.15/1.99 | (h(v0, v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & % 9.15/1.99 | $ki_exists_in_world_$i(v0, v4) = v6)) & ! [v4: $i] : ! [v5: % 9.15/1.99 | int] : (v5 = 0 | ~ (h(v0, v4) = v5) | ~ $i(v4) | ? [v6: int] : ( % 9.15/1.99 | ~ (v6 = 0) & $ki_exists_in_world_$i(v0, v4) = v6)) & ! [v4: $i] % 9.15/1.99 | : ! [v5: MultipleValueBool] : (v2 = 0 | ~ (h(v0, v4) = v5) | ~ % 9.15/1.99 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & $ki_exists_in_world_$i(v0, % 9.15/1.99 | v4) = v6)) & ! [v4: $i] : ( ~ (v3 = 0) | ~ % 9.15/1.99 | ($ki_exists_in_world_$i(v0, v4) = 0) | ~ $i(v4)) & ! [v4: $i] : % 9.15/1.99 | (v2 = 0 | ~ ($ki_exists_in_world_$i(v0, v4) = 0) | ~ $i(v4)) & ! % 9.15/1.99 | [v4: $i] : ( ~ ($ki_exists_in_world_$i(v0, v4) = 0) | ~ $i(v4) | % 9.15/1.99 | h(v0, v4) = 0)) % 9.15/1.99 | % 9.15/1.99 | ALPHA: (function-axioms) implies: % 9.15/1.99 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.15/1.99 | ! [v3: $ki_world] : (v1 = v0 | ~ (bomb(v3, v2) = v1) | ~ (bomb(v3, % 9.15/1.99 | v2) = v0)) % 9.15/1.99 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.15/1.99 | ! [v3: $ki_world] : (v1 = v0 | ~ (h(v3, v2) = v1) | ~ (h(v3, v2) = % 9.15/1.99 | v0)) % 9.15/1.99 | % 9.15/1.99 | DELTA: instantiating (2) with fresh symbols all_11_0, all_11_1, all_11_2, % 9.15/1.99 | all_11_3 gives: % 9.15/1.99 | (5) defused(all_11_3, all_11_2) = all_11_0 & bomb(all_11_3, all_11_2) = % 9.15/1.99 | all_11_1 & $ki_exists_in_world_$i(all_11_3, all_11_2) = 0 & % 9.15/1.99 | $ki_accessible($ki_local_world, all_11_3) = 0 & $ki_world(all_11_3) & % 9.15/1.99 | $i(all_11_2) & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (all_11_0 % 9.15/1.99 | = 0) | ~ (h(all_11_3, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 9.15/1.99 | (v2 = 0) & $ki_exists_in_world_$i(all_11_3, v0) = v2)) & ! [v0: % 9.15/1.99 | $i] : ! [v1: int] : (v1 = 0 | ~ (h(all_11_3, v0) = v1) | ~ $i(v0) % 9.15/1.99 | | ? [v2: int] : ( ~ (v2 = 0) & $ki_exists_in_world_$i(all_11_3, v0) % 9.15/1.99 | = v2)) & ! [v0: $i] : ! [v1: MultipleValueBool] : (all_11_1 = 0 | % 9.15/1.99 | ~ (h(all_11_3, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 9.15/1.99 | $ki_exists_in_world_$i(all_11_3, v0) = v2)) & ! [v0: $i] : ( ~ % 9.15/1.99 | (all_11_0 = 0) | ~ ($ki_exists_in_world_$i(all_11_3, v0) = 0) | ~ % 9.15/1.99 | $i(v0)) & ! [v0: $i] : (all_11_1 = 0 | ~ % 9.15/1.99 | ($ki_exists_in_world_$i(all_11_3, v0) = 0) | ~ $i(v0)) & ! [v0: $i] % 9.15/1.99 | : ( ~ ($ki_exists_in_world_$i(all_11_3, v0) = 0) | ~ $i(v0) | % 9.15/1.99 | h(all_11_3, v0) = 0) % 9.15/1.99 | % 9.15/1.99 | ALPHA: (5) implies: % 9.15/1.99 | (6) $i(all_11_2) % 9.15/1.99 | (7) $ki_world(all_11_3) % 9.15/1.99 | (8) $ki_accessible($ki_local_world, all_11_3) = 0 % 9.15/1.99 | (9) $ki_exists_in_world_$i(all_11_3, all_11_2) = 0 % 9.15/1.99 | (10) bomb(all_11_3, all_11_2) = all_11_1 % 9.15/1.99 | (11) defused(all_11_3, all_11_2) = all_11_0 % 9.15/1.99 | (12) ! [v0: $i] : ( ~ ($ki_exists_in_world_$i(all_11_3, v0) = 0) | ~ % 9.15/1.99 | $i(v0) | h(all_11_3, v0) = 0) % 9.15/1.99 | (13) ! [v0: $i] : (all_11_1 = 0 | ~ ($ki_exists_in_world_$i(all_11_3, v0) % 9.15/1.99 | = 0) | ~ $i(v0)) % 9.15/1.99 | (14) ! [v0: $i] : ( ~ (all_11_0 = 0) | ~ % 9.15/2.00 | ($ki_exists_in_world_$i(all_11_3, v0) = 0) | ~ $i(v0)) % 9.15/2.00 | % 9.15/2.00 | GROUND_INST: instantiating (1) with all_11_3, all_11_2, simplifying with (6), % 9.15/2.00 | (7), (8), (9) gives: % 9.15/2.00 | (15) ? [v0: $i] : ($ki_exists_in_world_$i(all_11_3, v0) = 0 & $i(v0) & ! % 9.15/2.00 | [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ (defused(v1, all_11_2) % 9.15/2.00 | = v2) | ~ $ki_world(v1) | ? [v3: any] : ? [v4: any] : ? [v5: % 9.15/2.00 | any] : (h(v1, v0) = v5 & bomb(v1, all_11_2) = v4 & % 9.15/2.00 | $ki_accessible(all_11_3, v1) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | % 9.15/2.00 | ~ (v3 = 0)))) & ! [v1: $ki_world] : ( ~ (h(v1, v0) = 0) | ~ % 9.15/2.00 | $ki_world(v1) | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 9.15/2.00 | (defused(v1, all_11_2) = v4 & bomb(v1, all_11_2) = v3 & % 9.15/2.00 | $ki_accessible(all_11_3, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | % 9.15/2.00 | v4 = 0))) & ! [v1: $ki_world] : ( ~ (bomb(v1, all_11_2) = 0) % 9.15/2.00 | | ~ $ki_world(v1) | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 9.15/2.00 | (defused(v1, all_11_2) = v4 & h(v1, v0) = v3 & % 9.15/2.00 | $ki_accessible(all_11_3, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | % 9.15/2.00 | v4 = 0))) & ! [v1: $ki_world] : ( ~ ($ki_accessible(all_11_3, % 9.15/2.00 | v1) = 0) | ~ $ki_world(v1) | ? [v2: any] : ? [v3: any] : ? % 9.15/2.00 | [v4: any] : (defused(v1, all_11_2) = v4 & h(v1, v0) = v3 & % 9.15/2.00 | bomb(v1, all_11_2) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = % 9.15/2.00 | 0)))) % 9.15/2.00 | % 9.15/2.00 | GROUND_INST: instantiating (14) with all_11_2, simplifying with (6), (9) % 9.15/2.00 | gives: % 9.15/2.00 | (16) ~ (all_11_0 = 0) % 9.15/2.00 | % 9.15/2.00 | GROUND_INST: instantiating (13) with all_11_2, simplifying with (6), (9) % 9.15/2.00 | gives: % 9.15/2.00 | (17) all_11_1 = 0 % 9.15/2.00 | % 9.15/2.00 | DELTA: instantiating (15) with fresh symbol all_25_0 gives: % 9.15/2.00 | (18) $ki_exists_in_world_$i(all_11_3, all_25_0) = 0 & $i(all_25_0) & ! % 9.15/2.00 | [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (defused(v0, all_11_2) = % 9.15/2.00 | v1) | ~ $ki_world(v0) | ? [v2: any] : ? [v3: any] : ? [v4: % 9.15/2.00 | any] : (h(v0, all_25_0) = v4 & bomb(v0, all_11_2) = v3 & % 9.15/2.00 | $ki_accessible(all_11_3, v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | % 9.15/2.00 | ~ (v2 = 0)))) & ! [v0: $ki_world] : ( ~ (h(v0, all_25_0) = 0) | % 9.15/2.00 | ~ $ki_world(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] : % 9.15/2.00 | (defused(v0, all_11_2) = v3 & bomb(v0, all_11_2) = v2 & % 9.15/2.00 | $ki_accessible(all_11_3, v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 9.15/2.00 | v3 = 0))) & ! [v0: $ki_world] : ( ~ (bomb(v0, all_11_2) = 0) | % 9.15/2.00 | ~ $ki_world(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] : % 9.15/2.00 | (defused(v0, all_11_2) = v3 & h(v0, all_25_0) = v2 & % 9.15/2.00 | $ki_accessible(all_11_3, v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 9.15/2.00 | v3 = 0))) & ! [v0: $ki_world] : ( ~ ($ki_accessible(all_11_3, % 9.15/2.00 | v0) = 0) | ~ $ki_world(v0) | ? [v1: any] : ? [v2: any] : ? % 9.15/2.00 | [v3: any] : (defused(v0, all_11_2) = v3 & h(v0, all_25_0) = v2 & % 9.15/2.00 | bomb(v0, all_11_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 9.15/2.00 | % 9.15/2.00 | ALPHA: (18) implies: % 9.15/2.00 | (19) $i(all_25_0) % 9.15/2.00 | (20) $ki_exists_in_world_$i(all_11_3, all_25_0) = 0 % 9.15/2.01 | (21) ! [v0: $ki_world] : ( ~ (bomb(v0, all_11_2) = 0) | ~ $ki_world(v0) | % 9.15/2.01 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (defused(v0, all_11_2) % 9.15/2.01 | = v3 & h(v0, all_25_0) = v2 & $ki_accessible(all_11_3, v0) = v1 & % 9.15/2.01 | ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 9.15/2.01 | (22) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (defused(v0, % 9.15/2.01 | all_11_2) = v1) | ~ $ki_world(v0) | ? [v2: any] : ? [v3: any] % 9.15/2.01 | : ? [v4: any] : (h(v0, all_25_0) = v4 & bomb(v0, all_11_2) = v3 & % 9.15/2.01 | $ki_accessible(all_11_3, v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | % 9.15/2.01 | ~ (v2 = 0)))) % 9.15/2.01 | % 9.15/2.01 | GROUND_INST: instantiating (22) with all_11_3, all_11_0, simplifying with (7), % 9.15/2.01 | (11) gives: % 9.15/2.01 | (23) all_11_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 9.15/2.01 | (h(all_11_3, all_25_0) = v2 & bomb(all_11_3, all_11_2) = v1 & % 9.15/2.01 | $ki_accessible(all_11_3, all_11_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) % 9.15/2.01 | | ~ (v0 = 0))) % 9.15/2.01 | % 9.15/2.01 | REDUCE: (10), (17) imply: % 9.15/2.01 | (24) bomb(all_11_3, all_11_2) = 0 % 9.15/2.01 | % 9.15/2.01 | BETA: splitting (23) gives: % 9.15/2.01 | % 9.15/2.01 | Case 1: % 9.15/2.01 | | % 9.15/2.01 | | (25) all_11_0 = 0 % 9.15/2.01 | | % 9.15/2.01 | | REDUCE: (16), (25) imply: % 9.15/2.01 | | (26) $false % 9.15/2.01 | | % 9.15/2.01 | | CLOSE: (26) is inconsistent. % 9.15/2.01 | | % 9.15/2.01 | Case 2: % 9.15/2.01 | | % 9.15/2.01 | | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : (h(all_11_3, all_25_0) % 9.15/2.01 | | = v2 & bomb(all_11_3, all_11_2) = v1 & $ki_accessible(all_11_3, % 9.15/2.01 | | all_11_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 9.15/2.01 | | % 9.15/2.01 | | DELTA: instantiating (27) with fresh symbols all_35_0, all_35_1, all_35_2 % 9.15/2.01 | | gives: % 9.15/2.01 | | (28) h(all_11_3, all_25_0) = all_35_0 & bomb(all_11_3, all_11_2) = % 9.15/2.01 | | all_35_1 & $ki_accessible(all_11_3, all_11_3) = all_35_2 & ( ~ % 9.15/2.01 | | (all_35_0 = 0) | ~ (all_35_1 = 0) | ~ (all_35_2 = 0)) % 9.15/2.01 | | % 9.15/2.01 | | ALPHA: (28) implies: % 9.15/2.01 | | (29) $ki_accessible(all_11_3, all_11_3) = all_35_2 % 9.15/2.01 | | (30) bomb(all_11_3, all_11_2) = all_35_1 % 9.15/2.01 | | (31) h(all_11_3, all_25_0) = all_35_0 % 9.15/2.01 | | (32) ~ (all_35_0 = 0) | ~ (all_35_1 = 0) | ~ (all_35_2 = 0) % 9.15/2.01 | | % 9.15/2.01 | | GROUND_INST: instantiating (3) with 0, all_35_1, all_11_2, all_11_3, % 9.15/2.01 | | simplifying with (24), (30) gives: % 9.15/2.01 | | (33) all_35_1 = 0 % 9.15/2.01 | | % 9.15/2.01 | | GROUND_INST: instantiating (mrel_reflexive) with all_11_3, all_35_2, % 9.15/2.01 | | simplifying with (7), (29) gives: % 9.15/2.01 | | (34) all_35_2 = 0 % 9.15/2.01 | | % 9.15/2.01 | | GROUND_INST: instantiating (12) with all_25_0, simplifying with (19), (20) % 9.15/2.01 | | gives: % 9.15/2.01 | | (35) h(all_11_3, all_25_0) = 0 % 9.15/2.01 | | % 9.15/2.01 | | GROUND_INST: instantiating (21) with all_11_3, simplifying with (7), (24) % 9.15/2.01 | | gives: % 9.15/2.01 | | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : (defused(all_11_3, % 9.15/2.01 | | all_11_2) = v2 & h(all_11_3, all_25_0) = v1 & % 9.15/2.01 | | $ki_accessible(all_11_3, all_11_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 9.15/2.01 | | 0) | v2 = 0)) % 9.15/2.01 | | % 9.15/2.01 | | DELTA: instantiating (36) with fresh symbols all_47_0, all_47_1, all_47_2 % 9.15/2.01 | | gives: % 9.15/2.02 | | (37) defused(all_11_3, all_11_2) = all_47_0 & h(all_11_3, all_25_0) = % 9.15/2.02 | | all_47_1 & $ki_accessible(all_11_3, all_11_3) = all_47_2 & ( ~ % 9.15/2.02 | | (all_47_1 = 0) | ~ (all_47_2 = 0) | all_47_0 = 0) % 9.15/2.02 | | % 9.15/2.02 | | ALPHA: (37) implies: % 9.15/2.02 | | (38) h(all_11_3, all_25_0) = all_47_1 % 9.15/2.02 | | % 9.15/2.02 | | BETA: splitting (32) gives: % 9.15/2.02 | | % 9.15/2.02 | | Case 1: % 9.15/2.02 | | | % 9.15/2.02 | | | (39) ~ (all_35_0 = 0) % 9.15/2.02 | | | % 9.15/2.02 | | | GROUND_INST: instantiating (4) with all_35_0, all_47_1, all_25_0, % 9.15/2.02 | | | all_11_3, simplifying with (31), (38) gives: % 9.15/2.02 | | | (40) all_47_1 = all_35_0 % 9.15/2.02 | | | % 9.15/2.02 | | | GROUND_INST: instantiating (4) with 0, all_47_1, all_25_0, all_11_3, % 9.15/2.02 | | | simplifying with (35), (38) gives: % 9.15/2.02 | | | (41) all_47_1 = 0 % 9.15/2.02 | | | % 9.15/2.02 | | | COMBINE_EQS: (40), (41) imply: % 9.15/2.02 | | | (42) all_35_0 = 0 % 9.15/2.02 | | | % 9.15/2.02 | | | REDUCE: (39), (42) imply: % 9.15/2.02 | | | (43) $false % 9.15/2.02 | | | % 9.15/2.02 | | | CLOSE: (43) is inconsistent. % 9.15/2.02 | | | % 9.15/2.02 | | Case 2: % 9.15/2.02 | | | % 9.15/2.02 | | | (44) ~ (all_35_1 = 0) | ~ (all_35_2 = 0) % 9.15/2.02 | | | % 9.15/2.02 | | | BETA: splitting (44) gives: % 9.15/2.02 | | | % 9.15/2.02 | | | Case 1: % 9.15/2.02 | | | | % 9.15/2.02 | | | | (45) ~ (all_35_1 = 0) % 9.15/2.02 | | | | % 9.15/2.02 | | | | REDUCE: (33), (45) imply: % 9.15/2.02 | | | | (46) $false % 9.15/2.02 | | | | % 9.15/2.02 | | | | CLOSE: (46) is inconsistent. % 9.15/2.02 | | | | % 9.15/2.02 | | | Case 2: % 9.15/2.02 | | | | % 9.15/2.02 | | | | (47) ~ (all_35_2 = 0) % 9.15/2.02 | | | | % 9.15/2.02 | | | | REDUCE: (34), (47) imply: % 9.15/2.02 | | | | (48) $false % 9.15/2.02 | | | | % 9.15/2.02 | | | | CLOSE: (48) is inconsistent. % 9.15/2.02 | | | | % 9.15/2.02 | | | End of split % 9.15/2.02 | | | % 9.15/2.02 | | End of split % 9.15/2.02 | | % 9.15/2.02 | End of split % 9.15/2.02 | % 9.15/2.02 End of proof % 9.15/2.02 % SZS output end Proof for theBenchmark % 9.15/2.02 % 9.15/2.02 1410ms %------------------------------------------------------------------------------