%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEV517+1 : TPTP v8.1.2. Released v7.3.0. % 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 19:37:03 EDT 2023 % Result : Theorem 10.85s 2.21s % Output : Proof 12.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEV517+1 : TPTP v8.1.2. Released v7.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n024.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Aug 24 02:25:54 EDT 2023 % 0.12/0.34 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 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 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 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 % 3.16/1.09 Prover 1: Preprocessing ... % 3.16/1.09 Prover 4: Preprocessing ... % 3.16/1.12 Prover 3: Preprocessing ... % 3.16/1.12 Prover 6: Preprocessing ... % 3.41/1.12 Prover 2: Preprocessing ... % 3.41/1.12 Prover 0: Preprocessing ... % 3.41/1.12 Prover 5: Preprocessing ... % 7.17/1.65 Prover 5: Proving ... % 7.17/1.67 Prover 1: Warning: ignoring some quantifiers % 7.43/1.68 Prover 2: Proving ... % 7.43/1.70 Prover 3: Warning: ignoring some quantifiers % 7.43/1.70 Prover 6: Proving ... % 7.43/1.70 Prover 1: Constructing countermodel ... % 7.43/1.73 Prover 3: Constructing countermodel ... % 8.76/1.92 Prover 3: gave up % 8.76/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.76/1.93 Prover 4: Warning: ignoring some quantifiers % 8.76/1.96 Prover 1: gave up % 8.76/1.97 Prover 4: Constructing countermodel ... % 8.76/1.97 Prover 0: Proving ... % 8.76/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.76/1.98 Prover 7: Preprocessing ... % 9.74/2.01 Prover 8: Preprocessing ... % 10.51/2.12 Prover 7: Warning: ignoring some quantifiers % 10.51/2.15 Prover 7: Constructing countermodel ... % 10.85/2.21 Prover 0: proved (1583ms) % 10.85/2.21 % 10.85/2.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.85/2.21 % 10.85/2.22 Prover 6: stopped % 10.85/2.22 Prover 5: stopped % 10.85/2.22 Prover 8: Warning: ignoring some quantifiers % 10.85/2.22 Prover 2: stopped % 10.85/2.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.85/2.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.85/2.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.85/2.22 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.85/2.24 Prover 8: Constructing countermodel ... % 11.45/2.26 Prover 10: Preprocessing ... % 11.45/2.26 Prover 16: Preprocessing ... % 11.76/2.28 Prover 13: Preprocessing ... % 11.76/2.28 Prover 11: Preprocessing ... % 12.14/2.34 Prover 16: Warning: ignoring some quantifiers % 12.27/2.35 Prover 4: Found proof (size 32) % 12.27/2.35 Prover 4: proved (1716ms) % 12.27/2.35 Prover 7: stopped % 12.27/2.35 Prover 16: Constructing countermodel ... % 12.27/2.35 Prover 13: stopped % 12.27/2.35 Prover 8: stopped % 12.27/2.36 Prover 16: stopped % 12.27/2.37 Prover 10: Warning: ignoring some quantifiers % 12.27/2.38 Prover 10: Constructing countermodel ... % 12.27/2.39 Prover 11: stopped % 12.27/2.39 Prover 10: stopped % 12.27/2.39 % 12.27/2.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.27/2.39 % 12.27/2.40 % SZS output start Proof for theBenchmark % 12.27/2.40 Assumptions after simplification: % 12.27/2.40 --------------------------------- % 12.27/2.40 % 12.27/2.40 (diff_elem_in_partition) % 12.62/2.43 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 12.62/2.43 $i] : ? [v6: $i] : (partition(v3, v1) = 0 & singleton(v2) = v5 & % 12.62/2.43 difference(v3, v5) = v6 & difference(v1, v2) = v4 & member(v0, v4) = 0 & % 12.62/2.43 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] : % 12.62/2.43 ( ~ (member(v7, v6) = 0) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & % 12.62/2.43 member(v0, v7) = v8)) & ! [v7: $i] : ( ~ (member(v0, v7) = 0) | ~ % 12.62/2.43 $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & member(v7, v6) = v8))) % 12.62/2.43 % 12.62/2.43 (difference) % 12.62/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 12.62/2.43 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 12.62/2.43 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v5 & % 12.62/2.43 member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] % 12.62/2.43 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, % 12.62/2.43 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 12.62/2.43 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 12.62/2.43 % 12.62/2.43 (partition) % 12.62/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2 % 12.62/2.44 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v3) = 0) | ~ (member(v3, v0) % 12.62/2.44 = 0) | ~ (member(v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 12.62/2.44 $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & member(v4, v2) = v5)) & % 12.62/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2 % 12.62/2.44 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v0) % 12.62/2.44 = 0) | ~ (member(v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 12.62/2.44 $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & member(v4, v3) = v5)) & % 12.62/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.62/2.44 (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 12.62/2.44 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: % 12.62/2.44 $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (partition(v0, v1) = v2) | % 12.62/2.44 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ? [v6: % 12.62/2.44 int] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : ? [v10: $i] : ? [v11: % 12.62/2.44 int] : ? [v12: $i] : ? [v13: int] : ? [v14: int] : ($i(v12) & $i(v10) & % 12.62/2.44 $i(v7) & $i(v4) & $i(v3) & ((v13 = 0 & ~ (v14 = 0) & subset(v12, v1) = % 12.62/2.44 v14 & member(v12, v0) = 0) | (v11 = 0 & member(v10, v1) = 0 & ! [v15: % 12.62/2.44 $i] : ( ~ (member(v15, v0) = 0) | ~ $i(v15) | ? [v16: int] : ( ~ % 12.62/2.44 (v16 = 0) & member(v10, v15) = v16)) & ! [v15: $i] : ( ~ % 12.62/2.44 (member(v10, v15) = 0) | ~ $i(v15) | ? [v16: int] : ( ~ (v16 = 0) % 12.62/2.44 & member(v15, v0) = v16))) | (v9 = 0 & v8 = 0 & v6 = 0 & v5 = 0 & % 12.62/2.44 ~ (v4 = v3) & member(v7, v4) = 0 & member(v7, v3) = 0 & member(v4, v0) % 12.62/2.44 = 0 & member(v3, v0) = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 12.62/2.44 : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ~ $i(v2) | ~ % 12.62/2.44 $i(v1) | ~ $i(v0) | ? [v3: $i] : (member(v3, v0) = 0 & member(v2, v3) = 0 % 12.62/2.44 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (partition(v0, % 12.62/2.44 v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 12.62/2.44 subset(v2, v1) = 0) % 12.62/2.44 % 12.62/2.44 (singleton) % 12.62/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | % 12.62/2.44 ~ (member(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 12.62/2.44 $i] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0) | ~ % 12.62/2.44 $i(v1) | ~ $i(v0)) % 12.62/2.44 % 12.62/2.44 (function-axioms) % 12.62/2.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 12.62/2.45 | ~ (insertIntoMember(v4, v3, v2) = v1) | ~ (insertIntoMember(v4, v3, v2) % 12.62/2.45 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 12.62/2.45 $i] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ % 12.62/2.45 (equivalence_class(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.62/2.45 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 12.62/2.45 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: % 12.62/2.45 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.62/2.45 : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! % 12.62/2.45 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.62/2.45 $i] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = % 12.62/2.45 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.62/2.45 $i] : ! [v3: $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ % 12.62/2.45 (partition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.62/2.45 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, % 12.62/2.45 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 12.62/2.45 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 12.62/2.45 (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 12.62/2.45 ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) % 12.62/2.45 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 12.62/2.45 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 12.62/2.45 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) % 12.62/2.45 | ~ (intersection(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.62/2.45 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.62/2.45 (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0: % 12.62/2.45 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.62/2.45 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 12.62/2.45 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.62/2.45 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: % 12.62/2.45 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (unaryUnion(v2) = v1) | ~ % 12.62/2.45 (unaryUnion(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.62/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (non_overlapping(v2) = v1) % 12.62/2.45 | ~ (non_overlapping(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 12.62/2.45 (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0: $i] : ! % 12.62/2.45 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & % 12.62/2.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | % 12.62/2.45 ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 12.62/2.45 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 12.62/2.45 % 12.62/2.45 Further assumptions not needed in the proof: % 12.62/2.45 -------------------------------------------- % 12.62/2.45 d4_tarski, disjoint, empty_set, equal_set, equivalence, equivalence_class, % 12.62/2.45 insertIntoMember, intersection, non_overlapping, power_set, pre_order, product, % 12.62/2.45 subset, sum, union, unordered_pair % 12.62/2.45 % 12.62/2.45 Those formulas are unsatisfiable: % 12.62/2.45 --------------------------------- % 12.62/2.45 % 12.62/2.45 Begin of proof % 12.62/2.45 | % 12.62/2.45 | ALPHA: (difference) implies: % 12.62/2.45 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 12.62/2.45 | (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ % 12.62/2.45 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, v2) = 0 % 12.62/2.45 | & member(v0, v1) = v4)) % 12.62/2.45 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 12.62/2.45 | (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ % 12.62/2.45 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 12.62/2.45 | (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 12.62/2.45 | % 12.62/2.45 | ALPHA: (singleton) implies: % 12.62/2.46 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1) % 12.62/2.46 | = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 12.62/2.46 | % 12.62/2.46 | ALPHA: (partition) implies: % 12.62/2.46 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (partition(v0, v1) = 0) | % 12.83/2.46 | ~ (member(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 12.83/2.46 | $i] : (member(v3, v0) = 0 & member(v2, v3) = 0 & $i(v3))) % 12.83/2.46 | % 12.83/2.46 | ALPHA: (function-axioms) implies: % 12.83/2.46 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.83/2.46 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 12.83/2.46 | = v0)) % 12.83/2.46 | % 12.83/2.46 | DELTA: instantiating (diff_elem_in_partition) with fresh symbols all_23_0, % 12.83/2.46 | all_23_1, all_23_2, all_23_3, all_23_4, all_23_5, all_23_6 gives: % 12.83/2.46 | (6) partition(all_23_3, all_23_5) = 0 & singleton(all_23_4) = all_23_1 & % 12.83/2.46 | difference(all_23_3, all_23_1) = all_23_0 & difference(all_23_5, % 12.83/2.46 | all_23_4) = all_23_2 & member(all_23_6, all_23_2) = 0 & $i(all_23_0) % 12.83/2.46 | & $i(all_23_1) & $i(all_23_2) & $i(all_23_3) & $i(all_23_4) & % 12.83/2.46 | $i(all_23_5) & $i(all_23_6) & ! [v0: $i] : ( ~ (member(v0, all_23_0) = % 12.83/2.46 | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(all_23_6, v0) % 12.83/2.46 | = v1)) & ! [v0: $i] : ( ~ (member(all_23_6, v0) = 0) | ~ $i(v0) | % 12.83/2.46 | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_23_0) = v1)) % 12.83/2.46 | % 12.83/2.46 | ALPHA: (6) implies: % 12.83/2.46 | (7) $i(all_23_6) % 12.83/2.46 | (8) $i(all_23_5) % 12.83/2.46 | (9) $i(all_23_4) % 12.83/2.46 | (10) $i(all_23_3) % 12.83/2.46 | (11) $i(all_23_1) % 12.83/2.46 | (12) member(all_23_6, all_23_2) = 0 % 12.83/2.46 | (13) difference(all_23_5, all_23_4) = all_23_2 % 12.83/2.46 | (14) difference(all_23_3, all_23_1) = all_23_0 % 12.83/2.46 | (15) singleton(all_23_4) = all_23_1 % 12.83/2.46 | (16) partition(all_23_3, all_23_5) = 0 % 12.83/2.46 | (17) ! [v0: $i] : ( ~ (member(all_23_6, v0) = 0) | ~ $i(v0) | ? [v1: % 12.83/2.46 | int] : ( ~ (v1 = 0) & member(v0, all_23_0) = v1)) % 12.83/2.46 | % 12.83/2.46 | GROUND_INST: instantiating (1) with all_23_6, all_23_4, all_23_5, all_23_2, % 12.83/2.46 | simplifying with (7), (8), (9), (12), (13) gives: % 12.83/2.46 | (18) ? [v0: int] : ( ~ (v0 = 0) & member(all_23_6, all_23_4) = v0 & % 12.83/2.46 | member(all_23_6, all_23_5) = 0) % 12.83/2.46 | % 12.83/2.46 | DELTA: instantiating (18) with fresh symbol all_35_0 gives: % 12.83/2.47 | (19) ~ (all_35_0 = 0) & member(all_23_6, all_23_4) = all_35_0 & % 12.83/2.47 | member(all_23_6, all_23_5) = 0 % 12.83/2.47 | % 12.83/2.47 | ALPHA: (19) implies: % 12.83/2.47 | (20) ~ (all_35_0 = 0) % 12.83/2.47 | (21) member(all_23_6, all_23_5) = 0 % 12.83/2.47 | (22) member(all_23_6, all_23_4) = all_35_0 % 12.83/2.47 | % 12.83/2.47 | GROUND_INST: instantiating (4) with all_23_3, all_23_5, all_23_6, simplifying % 12.83/2.47 | with (7), (8), (10), (16), (21) gives: % 12.83/2.47 | (23) ? [v0: $i] : (member(v0, all_23_3) = 0 & member(all_23_6, v0) = 0 & % 12.83/2.47 | $i(v0)) % 12.83/2.47 | % 12.83/2.47 | DELTA: instantiating (23) with fresh symbol all_44_0 gives: % 12.83/2.47 | (24) member(all_44_0, all_23_3) = 0 & member(all_23_6, all_44_0) = 0 & % 12.83/2.47 | $i(all_44_0) % 12.83/2.47 | % 12.83/2.47 | ALPHA: (24) implies: % 12.83/2.47 | (25) $i(all_44_0) % 12.83/2.47 | (26) member(all_23_6, all_44_0) = 0 % 12.83/2.47 | (27) member(all_44_0, all_23_3) = 0 % 12.83/2.47 | % 12.83/2.47 | GROUND_INST: instantiating (17) with all_44_0, simplifying with (25), (26) % 12.83/2.47 | gives: % 12.83/2.47 | (28) ? [v0: int] : ( ~ (v0 = 0) & member(all_44_0, all_23_0) = v0) % 12.83/2.47 | % 12.83/2.47 | DELTA: instantiating (28) with fresh symbol all_58_0 gives: % 12.83/2.47 | (29) ~ (all_58_0 = 0) & member(all_44_0, all_23_0) = all_58_0 % 12.83/2.47 | % 12.83/2.47 | ALPHA: (29) implies: % 12.83/2.47 | (30) ~ (all_58_0 = 0) % 12.83/2.47 | (31) member(all_44_0, all_23_0) = all_58_0 % 12.83/2.47 | % 12.83/2.47 | GROUND_INST: instantiating (2) with all_44_0, all_23_1, all_23_3, all_23_0, % 12.83/2.47 | all_58_0, simplifying with (10), (11), (14), (25), (31) gives: % 12.83/2.47 | (32) all_58_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_44_0, % 12.83/2.47 | all_23_1) = v1 & member(all_44_0, all_23_3) = v0 & ( ~ (v0 = 0) | % 12.83/2.47 | v1 = 0)) % 12.83/2.47 | % 12.83/2.47 | BETA: splitting (32) gives: % 12.83/2.47 | % 12.83/2.47 | Case 1: % 12.83/2.47 | | % 12.83/2.47 | | (33) all_58_0 = 0 % 12.83/2.47 | | % 12.83/2.47 | | REDUCE: (30), (33) imply: % 12.83/2.47 | | (34) $false % 12.83/2.47 | | % 12.83/2.47 | | CLOSE: (34) is inconsistent. % 12.83/2.47 | | % 12.83/2.47 | Case 2: % 12.83/2.47 | | % 12.83/2.47 | | (35) ? [v0: any] : ? [v1: any] : (member(all_44_0, all_23_1) = v1 & % 12.83/2.47 | | member(all_44_0, all_23_3) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 12.83/2.47 | | % 12.83/2.47 | | DELTA: instantiating (35) with fresh symbols all_85_0, all_85_1 gives: % 12.83/2.47 | | (36) member(all_44_0, all_23_1) = all_85_0 & member(all_44_0, all_23_3) = % 12.83/2.47 | | all_85_1 & ( ~ (all_85_1 = 0) | all_85_0 = 0) % 12.83/2.47 | | % 12.83/2.47 | | ALPHA: (36) implies: % 12.83/2.47 | | (37) member(all_44_0, all_23_3) = all_85_1 % 12.83/2.47 | | (38) member(all_44_0, all_23_1) = all_85_0 % 12.83/2.47 | | (39) ~ (all_85_1 = 0) | all_85_0 = 0 % 12.83/2.47 | | % 12.83/2.48 | | GROUND_INST: instantiating (5) with 0, all_85_1, all_23_3, all_44_0, % 12.83/2.48 | | simplifying with (27), (37) gives: % 12.83/2.48 | | (40) all_85_1 = 0 % 12.83/2.48 | | % 12.83/2.48 | | BETA: splitting (39) gives: % 12.83/2.48 | | % 12.83/2.48 | | Case 1: % 12.83/2.48 | | | % 12.83/2.48 | | | (41) ~ (all_85_1 = 0) % 12.83/2.48 | | | % 12.83/2.48 | | | REDUCE: (40), (41) imply: % 12.83/2.48 | | | (42) $false % 12.83/2.48 | | | % 12.83/2.48 | | | CLOSE: (42) is inconsistent. % 12.83/2.48 | | | % 12.83/2.48 | | Case 2: % 12.83/2.48 | | | % 12.83/2.48 | | | (43) all_85_0 = 0 % 12.83/2.48 | | | % 12.83/2.48 | | | REDUCE: (38), (43) imply: % 12.83/2.48 | | | (44) member(all_44_0, all_23_1) = 0 % 12.83/2.48 | | | % 12.83/2.48 | | | GROUND_INST: instantiating (3) with all_44_0, all_23_4, all_23_1, % 12.83/2.48 | | | simplifying with (9), (15), (25), (44) gives: % 12.83/2.48 | | | (45) all_44_0 = all_23_4 % 12.83/2.48 | | | % 12.83/2.48 | | | REDUCE: (26), (45) imply: % 12.83/2.48 | | | (46) member(all_23_6, all_23_4) = 0 % 12.83/2.48 | | | % 12.83/2.48 | | | GROUND_INST: instantiating (5) with all_35_0, 0, all_23_4, all_23_6, % 12.83/2.48 | | | simplifying with (22), (46) gives: % 12.83/2.48 | | | (47) all_35_0 = 0 % 12.83/2.48 | | | % 12.83/2.48 | | | REDUCE: (20), (47) imply: % 12.83/2.48 | | | (48) $false % 12.83/2.48 | | | % 12.83/2.48 | | | CLOSE: (48) is inconsistent. % 12.83/2.48 | | | % 12.83/2.48 | | End of split % 12.83/2.48 | | % 12.83/2.48 | End of split % 12.83/2.48 | % 12.83/2.48 End of proof % 12.83/2.48 % SZS output end Proof for theBenchmark % 12.83/2.48 % 12.83/2.48 1868ms %------------------------------------------------------------------------------