%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYO889_16 : TPTP v8.2.0. Released v8.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 : Fri Sep 1 04:54:07 EDT 2023 % Result : Theorem 4.22s 1.38s % Output : Proof 6.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO889_16 : TPTP v8.2.0. Released v8.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 07:16:34 EDT 2023 % 0.19/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 2.14/1.00 Prover 4: Preprocessing ... % 2.14/1.00 Prover 1: Preprocessing ... % 2.50/1.04 Prover 5: Preprocessing ... % 2.50/1.04 Prover 3: Preprocessing ... % 2.50/1.04 Prover 0: Preprocessing ... % 2.50/1.04 Prover 6: Preprocessing ... % 2.72/1.05 Prover 2: Preprocessing ... % 3.61/1.18 Prover 2: Proving ... % 3.61/1.18 Prover 5: Proving ... % 3.61/1.20 Prover 1: Warning: ignoring some quantifiers % 3.61/1.21 Prover 6: Proving ... % 3.61/1.22 Prover 1: Constructing countermodel ... % 3.61/1.22 Prover 3: Warning: ignoring some quantifiers % 3.61/1.24 Prover 3: Constructing countermodel ... % 4.22/1.28 Prover 4: Warning: ignoring some quantifiers % 4.22/1.29 Prover 4: Constructing countermodel ... % 4.22/1.30 Prover 0: Proving ... % 4.22/1.38 Prover 2: proved (756ms) % 4.22/1.38 % 4.22/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.22/1.38 % 4.22/1.38 Prover 5: stopped % 4.22/1.38 Prover 0: stopped % 4.22/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.22/1.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.22/1.39 Prover 6: stopped % 4.22/1.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.22/1.39 Prover 3: stopped % 4.22/1.42 Prover 7: Preprocessing ... % 4.22/1.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.22/1.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.22/1.43 Prover 10: Preprocessing ... % 4.22/1.43 Prover 7: Warning: ignoring some quantifiers % 4.22/1.43 Prover 8: Preprocessing ... % 4.22/1.44 Prover 7: Constructing countermodel ... % 4.22/1.45 Prover 10: Warning: ignoring some quantifiers % 4.22/1.46 Prover 10: Constructing countermodel ... % 4.86/1.48 Prover 13: Preprocessing ... % 4.86/1.50 Prover 4: Found proof (size 18) % 5.65/1.50 Prover 4: proved (863ms) % 5.65/1.50 Prover 7: stopped % 5.65/1.50 Prover 11: Preprocessing ... % 5.65/1.50 Prover 10: stopped % 5.65/1.50 Prover 1: stopped % 5.65/1.51 Prover 13: Warning: ignoring some quantifiers % 5.65/1.51 Prover 13: Constructing countermodel ... % 5.65/1.52 Prover 8: Warning: ignoring some quantifiers % 5.65/1.52 Prover 13: stopped % 5.65/1.52 Prover 11: stopped % 5.65/1.52 Prover 8: Constructing countermodel ... % 5.65/1.53 Prover 8: stopped % 5.65/1.53 % 5.65/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.65/1.53 % 5.65/1.53 % SZS output start Proof for theBenchmark % 5.65/1.54 Assumptions after simplification: % 5.65/1.54 --------------------------------- % 5.65/1.54 % 5.65/1.54 (verify) % 5.65/1.57 $ki_world($ki_local_world) & ? [v0: $ki_world] : ? [v1: $i] : % 5.65/1.57 ($ki_exists_in_world_$i(v0, v1) = 0 & $ki_accessible($ki_local_world, v0) = 0 % 5.65/1.57 & $ki_world(v0) & $i(v1) & ! [v2: $ki_world] : ! [v3: $i] : ! [v4: % 5.65/1.57 $ki_world] : ( ~ (b(v4, v3) = 0) | ~ ($ki_exists_in_world_$i(v2, v3) = 0) % 5.65/1.57 | ~ ($ki_accessible($ki_local_world, v2) = 0) | ~ $ki_world(v4) | ~ % 5.65/1.57 $ki_world(v2) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : (a(v4, v3) = v6 % 5.65/1.57 & $ki_accessible(v2, v4) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v2: % 5.65/1.57 $ki_world] : ! [v3: $i] : ! [v4: $ki_world] : ( ~ (a(v4, v3) = 0) | ~ % 5.65/1.57 ($ki_exists_in_world_$i(v2, v3) = 0) | ~ ($ki_accessible($ki_local_world, % 5.65/1.57 v2) = 0) | ~ $ki_world(v4) | ~ $ki_world(v2) | ~ $i(v3) | ? [v5: % 5.65/1.57 any] : ? [v6: any] : (b(v4, v3) = v6 & $ki_accessible(v2, v4) = v5 & ( % 5.65/1.57 ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v2: $ki_world] : ! [v3: $i] : ! % 5.65/1.58 [v4: $ki_world] : ( ~ ($ki_exists_in_world_$i(v2, v3) = 0) | ~ % 5.65/1.58 ($ki_accessible(v2, v4) = 0) | ~ ($ki_accessible($ki_local_world, v2) = % 5.65/1.58 0) | ~ $ki_world(v4) | ~ $ki_world(v2) | ~ $i(v3) | ? [v5: any] : ? % 5.65/1.58 [v6: any] : (b(v4, v3) = v6 & a(v4, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 5.65/1.58 0)))) & ! [v2: $ki_world] : ! [v3: int] : (v3 = 0 | ~ (a(v2, v1) % 5.65/1.58 = v3) | ~ $ki_world(v2) | ? [v4: int] : ( ~ (v4 = 0) & % 5.65/1.58 $ki_accessible(v0, v2) = v4)) & ! [v2: $ki_world] : ! [v3: $i] : ( ~ % 5.65/1.58 ($ki_exists_in_world_$i(v2, v3) = 0) | ~ ($ki_accessible($ki_local_world, % 5.65/1.58 v2) = 0) | ~ $ki_world(v2) | ~ $i(v3) | ? [v4: $ki_world] : (b(v4, % 5.65/1.58 v3) = 0 & $ki_accessible(v2, v4) = 0 & $ki_world(v4))) & ! [v2: % 5.65/1.58 $ki_world] : ( ~ ($ki_accessible(v0, v2) = 0) | ~ $ki_world(v2) | a(v2, % 5.65/1.58 v1) = 0)) % 5.65/1.58 % 5.65/1.58 (function-axioms) % 5.65/1.58 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.65/1.58 [v3: $ki_world] : (v1 = v0 | ~ (b(v3, v2) = v1) | ~ (b(v3, v2) = v0)) & ! % 5.65/1.58 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 5.65/1.58 $ki_world] : (v1 = v0 | ~ (a(v3, v2) = v1) | ~ (a(v3, v2) = v0)) & ! [v0: % 5.65/1.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 5.65/1.58 $ki_world] : (v1 = v0 | ~ ($ki_exists_in_world_$i(v3, v2) = v1) | ~ % 5.65/1.58 ($ki_exists_in_world_$i(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 5.65/1.58 [v1: MultipleValueBool] : ! [v2: $ki_world] : ! [v3: $ki_world] : (v1 = v0 | % 5.65/1.58 ~ ($ki_accessible(v3, v2) = v1) | ~ ($ki_accessible(v3, v2) = v0)) % 5.65/1.58 % 5.65/1.58 Further assumptions not needed in the proof: % 5.65/1.58 -------------------------------------------- % 5.65/1.58 $ki_exists_in_world_$i_cumul, $ki_exists_in_world_$i_nonempty, mrel_reflexive, % 5.65/1.58 mrel_transitive % 5.65/1.58 % 5.65/1.58 Those formulas are unsatisfiable: % 5.65/1.58 --------------------------------- % 5.65/1.58 % 5.65/1.58 Begin of proof % 6.10/1.58 | % 6.10/1.58 | ALPHA: (verify) implies: % 6.10/1.59 | (1) ? [v0: $ki_world] : ? [v1: $i] : ($ki_exists_in_world_$i(v0, v1) = 0 % 6.10/1.59 | & $ki_accessible($ki_local_world, v0) = 0 & $ki_world(v0) & $i(v1) & % 6.10/1.59 | ! [v2: $ki_world] : ! [v3: $i] : ! [v4: $ki_world] : ( ~ (b(v4, v3) % 6.10/1.59 | = 0) | ~ ($ki_exists_in_world_$i(v2, v3) = 0) | ~ % 6.10/1.59 | ($ki_accessible($ki_local_world, v2) = 0) | ~ $ki_world(v4) | ~ % 6.10/1.59 | $ki_world(v2) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : (a(v4, % 6.10/1.59 | v3) = v6 & $ki_accessible(v2, v4) = v5 & ( ~ (v6 = 0) | ~ (v5 % 6.10/1.59 | = 0)))) & ! [v2: $ki_world] : ! [v3: $i] : ! [v4: % 6.10/1.59 | $ki_world] : ( ~ (a(v4, v3) = 0) | ~ ($ki_exists_in_world_$i(v2, % 6.10/1.59 | v3) = 0) | ~ ($ki_accessible($ki_local_world, v2) = 0) | ~ % 6.10/1.59 | $ki_world(v4) | ~ $ki_world(v2) | ~ $i(v3) | ? [v5: any] : ? % 6.10/1.59 | [v6: any] : (b(v4, v3) = v6 & $ki_accessible(v2, v4) = v5 & ( ~ (v6 % 6.10/1.59 | = 0) | ~ (v5 = 0)))) & ! [v2: $ki_world] : ! [v3: $i] : ! % 6.10/1.59 | [v4: $ki_world] : ( ~ ($ki_exists_in_world_$i(v2, v3) = 0) | ~ % 6.10/1.59 | ($ki_accessible(v2, v4) = 0) | ~ ($ki_accessible($ki_local_world, % 6.10/1.59 | v2) = 0) | ~ $ki_world(v4) | ~ $ki_world(v2) | ~ $i(v3) | ? % 6.10/1.59 | [v5: any] : ? [v6: any] : (b(v4, v3) = v6 & a(v4, v3) = v5 & ( ~ % 6.10/1.59 | (v6 = 0) | ~ (v5 = 0)))) & ! [v2: $ki_world] : ! [v3: int] : % 6.10/1.59 | (v3 = 0 | ~ (a(v2, v1) = v3) | ~ $ki_world(v2) | ? [v4: int] : ( ~ % 6.10/1.59 | (v4 = 0) & $ki_accessible(v0, v2) = v4)) & ! [v2: $ki_world] : % 6.10/1.59 | ! [v3: $i] : ( ~ ($ki_exists_in_world_$i(v2, v3) = 0) | ~ % 6.10/1.59 | ($ki_accessible($ki_local_world, v2) = 0) | ~ $ki_world(v2) | ~ % 6.10/1.59 | $i(v3) | ? [v4: $ki_world] : (b(v4, v3) = 0 & $ki_accessible(v2, % 6.10/1.59 | v4) = 0 & $ki_world(v4))) & ! [v2: $ki_world] : ( ~ % 6.10/1.59 | ($ki_accessible(v0, v2) = 0) | ~ $ki_world(v2) | a(v2, v1) = 0)) % 6.10/1.59 | % 6.10/1.59 | ALPHA: (function-axioms) implies: % 6.10/1.60 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 6.10/1.60 | $ki_world] : ! [v3: $ki_world] : (v1 = v0 | ~ ($ki_accessible(v3, % 6.10/1.60 | v2) = v1) | ~ ($ki_accessible(v3, v2) = v0)) % 6.10/1.60 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.10/1.60 | ! [v3: $ki_world] : (v1 = v0 | ~ (a(v3, v2) = v1) | ~ (a(v3, v2) = % 6.10/1.60 | v0)) % 6.10/1.60 | % 6.10/1.60 | DELTA: instantiating (1) with fresh symbols all_10_0, all_10_1 gives: % 6.10/1.60 | (4) $ki_exists_in_world_$i(all_10_1, all_10_0) = 0 & % 6.10/1.60 | $ki_accessible($ki_local_world, all_10_1) = 0 & $ki_world(all_10_1) & % 6.10/1.60 | $i(all_10_0) & ! [v0: $ki_world] : ! [v1: $i] : ! [v2: $ki_world] : % 6.10/1.60 | ( ~ (b(v2, v1) = 0) | ~ ($ki_exists_in_world_$i(v0, v1) = 0) | ~ % 6.10/1.60 | ($ki_accessible($ki_local_world, v0) = 0) | ~ $ki_world(v2) | ~ % 6.10/1.60 | $ki_world(v0) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (a(v2, v1) % 6.10/1.60 | = v4 & $ki_accessible(v0, v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 6.10/1.60 | & ! [v0: $ki_world] : ! [v1: $i] : ! [v2: $ki_world] : ( ~ (a(v2, % 6.10/1.60 | v1) = 0) | ~ ($ki_exists_in_world_$i(v0, v1) = 0) | ~ % 6.10/1.60 | ($ki_accessible($ki_local_world, v0) = 0) | ~ $ki_world(v2) | ~ % 6.10/1.60 | $ki_world(v0) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (b(v2, v1) % 6.10/1.60 | = v4 & $ki_accessible(v0, v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 6.10/1.60 | & ! [v0: $ki_world] : ! [v1: $i] : ! [v2: $ki_world] : ( ~ % 6.10/1.60 | ($ki_exists_in_world_$i(v0, v1) = 0) | ~ ($ki_accessible(v0, v2) = % 6.10/1.60 | 0) | ~ ($ki_accessible($ki_local_world, v0) = 0) | ~ % 6.10/1.60 | $ki_world(v2) | ~ $ki_world(v0) | ~ $i(v1) | ? [v3: any] : ? [v4: % 6.10/1.60 | any] : (b(v2, v1) = v4 & a(v2, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 6.10/1.60 | 0)))) & ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (a(v0, % 6.10/1.60 | all_10_0) = v1) | ~ $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) % 6.10/1.60 | & $ki_accessible(all_10_1, v0) = v2)) & ! [v0: $ki_world] : ! % 6.10/1.60 | [v1: $i] : ( ~ ($ki_exists_in_world_$i(v0, v1) = 0) | ~ % 6.10/1.60 | ($ki_accessible($ki_local_world, v0) = 0) | ~ $ki_world(v0) | ~ % 6.10/1.60 | $i(v1) | ? [v2: $ki_world] : (b(v2, v1) = 0 & $ki_accessible(v0, v2) % 6.10/1.60 | = 0 & $ki_world(v2))) & ! [v0: $ki_world] : ( ~ % 6.10/1.60 | ($ki_accessible(all_10_1, v0) = 0) | ~ $ki_world(v0) | a(v0, % 6.10/1.60 | all_10_0) = 0) % 6.10/1.60 | % 6.10/1.60 | ALPHA: (4) implies: % 6.10/1.61 | (5) $i(all_10_0) % 6.10/1.61 | (6) $ki_world(all_10_1) % 6.10/1.61 | (7) $ki_accessible($ki_local_world, all_10_1) = 0 % 6.10/1.61 | (8) $ki_exists_in_world_$i(all_10_1, all_10_0) = 0 % 6.10/1.61 | (9) ! [v0: $ki_world] : ( ~ ($ki_accessible(all_10_1, v0) = 0) | ~ % 6.10/1.61 | $ki_world(v0) | a(v0, all_10_0) = 0) % 6.10/1.61 | (10) ! [v0: $ki_world] : ! [v1: $i] : ( ~ ($ki_exists_in_world_$i(v0, v1) % 6.10/1.61 | = 0) | ~ ($ki_accessible($ki_local_world, v0) = 0) | ~ % 6.10/1.61 | $ki_world(v0) | ~ $i(v1) | ? [v2: $ki_world] : (b(v2, v1) = 0 & % 6.10/1.61 | $ki_accessible(v0, v2) = 0 & $ki_world(v2))) % 6.10/1.61 | (11) ! [v0: $ki_world] : ! [v1: $i] : ! [v2: $ki_world] : ( ~ (b(v2, v1) % 6.10/1.61 | = 0) | ~ ($ki_exists_in_world_$i(v0, v1) = 0) | ~ % 6.10/1.61 | ($ki_accessible($ki_local_world, v0) = 0) | ~ $ki_world(v2) | ~ % 6.10/1.61 | $ki_world(v0) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (a(v2, v1) % 6.10/1.61 | = v4 & $ki_accessible(v0, v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 6.10/1.61 | % 6.10/1.61 | GROUND_INST: instantiating (10) with all_10_1, all_10_0, simplifying with (5), % 6.10/1.61 | (6), (7), (8) gives: % 6.10/1.61 | (12) ? [v0: $ki_world] : (b(v0, all_10_0) = 0 & $ki_accessible(all_10_1, % 6.10/1.61 | v0) = 0 & $ki_world(v0)) % 6.10/1.61 | % 6.10/1.61 | DELTA: instantiating (12) with fresh symbol all_18_0 gives: % 6.10/1.61 | (13) b(all_18_0, all_10_0) = 0 & $ki_accessible(all_10_1, all_18_0) = 0 & % 6.10/1.61 | $ki_world(all_18_0) % 6.10/1.61 | % 6.10/1.61 | ALPHA: (13) implies: % 6.10/1.61 | (14) $ki_world(all_18_0) % 6.10/1.61 | (15) $ki_accessible(all_10_1, all_18_0) = 0 % 6.10/1.61 | (16) b(all_18_0, all_10_0) = 0 % 6.10/1.61 | % 6.10/1.61 | GROUND_INST: instantiating (9) with all_18_0, simplifying with (14), (15) % 6.10/1.61 | gives: % 6.10/1.61 | (17) a(all_18_0, all_10_0) = 0 % 6.10/1.61 | % 6.10/1.61 | GROUND_INST: instantiating (11) with all_10_1, all_10_0, all_18_0, simplifying % 6.10/1.61 | with (5), (6), (7), (8), (14), (16) gives: % 6.10/1.61 | (18) ? [v0: any] : ? [v1: any] : (a(all_18_0, all_10_0) = v1 & % 6.10/1.62 | $ki_accessible(all_10_1, all_18_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 6.10/1.62 | 0))) % 6.10/1.62 | % 6.10/1.62 | DELTA: instantiating (18) with fresh symbols all_28_0, all_28_1 gives: % 6.10/1.62 | (19) a(all_18_0, all_10_0) = all_28_0 & $ki_accessible(all_10_1, all_18_0) % 6.10/1.62 | = all_28_1 & ( ~ (all_28_0 = 0) | ~ (all_28_1 = 0)) % 6.10/1.62 | % 6.10/1.62 | ALPHA: (19) implies: % 6.10/1.62 | (20) $ki_accessible(all_10_1, all_18_0) = all_28_1 % 6.10/1.62 | (21) a(all_18_0, all_10_0) = all_28_0 % 6.10/1.62 | (22) ~ (all_28_0 = 0) | ~ (all_28_1 = 0) % 6.10/1.62 | % 6.10/1.62 | GROUND_INST: instantiating (2) with 0, all_28_1, all_18_0, all_10_1, % 6.10/1.62 | simplifying with (15), (20) gives: % 6.10/1.62 | (23) all_28_1 = 0 % 6.10/1.62 | % 6.10/1.62 | GROUND_INST: instantiating (3) with 0, all_28_0, all_10_0, all_18_0, % 6.10/1.62 | simplifying with (17), (21) gives: % 6.10/1.62 | (24) all_28_0 = 0 % 6.10/1.62 | % 6.10/1.62 | BETA: splitting (22) gives: % 6.10/1.62 | % 6.10/1.62 | Case 1: % 6.10/1.62 | | % 6.10/1.62 | | (25) ~ (all_28_0 = 0) % 6.10/1.62 | | % 6.10/1.62 | | REDUCE: (24), (25) imply: % 6.10/1.62 | | (26) $false % 6.10/1.62 | | % 6.10/1.62 | | CLOSE: (26) is inconsistent. % 6.10/1.62 | | % 6.10/1.62 | Case 2: % 6.10/1.62 | | % 6.10/1.62 | | (27) ~ (all_28_1 = 0) % 6.10/1.62 | | % 6.10/1.62 | | REDUCE: (23), (27) imply: % 6.10/1.62 | | (28) $false % 6.10/1.62 | | % 6.10/1.62 | | CLOSE: (28) is inconsistent. % 6.10/1.62 | | % 6.10/1.62 | End of split % 6.10/1.62 | % 6.10/1.62 End of proof % 6.10/1.62 % SZS output end Proof for theBenchmark % 6.10/1.62 % 6.10/1.62 1018ms %------------------------------------------------------------------------------