%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET906+1 : TPTP v8.1.2. Released v3.2.0. % 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 : Thu Aug 31 15:26:58 EDT 2023 % Result : Theorem 6.92s 1.73s % Output : Proof 8.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET906+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n027.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sat Aug 26 14:38:35 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.16/1.03 Prover 1: Preprocessing ... % 2.16/1.03 Prover 4: Preprocessing ... % 2.16/1.07 Prover 0: Preprocessing ... % 2.16/1.07 Prover 5: Preprocessing ... % 2.16/1.07 Prover 3: Preprocessing ... % 2.16/1.07 Prover 6: Preprocessing ... % 2.16/1.07 Prover 2: Preprocessing ... % 4.69/1.41 Prover 1: Warning: ignoring some quantifiers % 4.69/1.41 Prover 3: Warning: ignoring some quantifiers % 4.69/1.44 Prover 5: Proving ... % 4.69/1.44 Prover 6: Proving ... % 4.69/1.44 Prover 1: Constructing countermodel ... % 4.69/1.44 Prover 3: Constructing countermodel ... % 4.69/1.44 Prover 4: Warning: ignoring some quantifiers % 4.69/1.46 Prover 4: Constructing countermodel ... % 4.69/1.47 Prover 2: Proving ... % 4.69/1.50 Prover 0: Proving ... % 6.92/1.72 Prover 2: proved (1090ms) % 6.92/1.72 % 6.92/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.92/1.73 % 6.92/1.73 Prover 6: stopped % 6.92/1.73 Prover 5: stopped % 6.92/1.74 Prover 3: stopped % 6.92/1.74 Prover 0: stopped % 6.92/1.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.92/1.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.92/1.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.92/1.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.92/1.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.92/1.75 Prover 7: Preprocessing ... % 6.92/1.77 Prover 10: Preprocessing ... % 6.92/1.78 Prover 8: Preprocessing ... % 6.92/1.78 Prover 13: Preprocessing ... % 7.38/1.79 Prover 11: Preprocessing ... % 7.38/1.80 Prover 4: Found proof (size 30) % 7.38/1.80 Prover 4: proved (1157ms) % 7.38/1.80 Prover 1: stopped % 7.38/1.81 Prover 10: stopped % 7.38/1.82 Prover 13: stopped % 7.38/1.82 Prover 11: stopped % 7.38/1.83 Prover 7: Warning: ignoring some quantifiers % 7.38/1.83 Prover 7: Constructing countermodel ... % 7.38/1.84 Prover 7: stopped % 7.90/1.87 Prover 8: Warning: ignoring some quantifiers % 7.95/1.88 Prover 8: Constructing countermodel ... % 7.95/1.89 Prover 8: stopped % 7.95/1.89 % 7.95/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.95/1.89 % 7.95/1.89 % SZS output start Proof for theBenchmark % 7.95/1.90 Assumptions after simplification: % 7.95/1.90 --------------------------------- % 7.95/1.90 % 7.95/1.90 (commutativity_k2_tarski) % 8.17/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | % 8.17/1.94 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i] % 8.17/1.94 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | % 8.17/1.94 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 8.17/1.94 % 8.17/1.94 (commutativity_k2_xboole_0) % 8.17/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 8.17/1.94 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 8.17/1.94 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 8.17/1.94 | (set_union2(v1, v0) = v2 & $i(v2))) % 8.17/1.94 % 8.17/1.94 (d2_tarski) % 8.17/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | % 8.17/1.95 ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 8.17/1.95 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 8.17/1.95 ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = % 8.17/1.95 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 8.17/1.95 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ % 8.17/1.95 (in(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! % 8.17/1.95 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = % 8.17/1.95 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : % 8.17/1.95 (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & % 8.17/1.95 (v5 = 0 | v4 = v2 | v4 = v1))) % 8.17/1.95 % 8.17/1.95 (d2_xboole_0) % 8.17/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.17/1.96 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ % 8.17/1.96 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) % 8.17/1.96 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : ! % 8.17/1.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 8.17/1.96 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 8.17/1.96 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & % 8.17/1.96 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 8.17/1.96 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) = % 8.17/1.96 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 8.17/1.96 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 % 8.17/1.96 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.17/1.96 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | % 8.17/1.96 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 8.17/1.96 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = % 8.17/1.96 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 8.17/1.96 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | % 8.17/1.96 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, % 8.17/1.96 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & % 8.17/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) % 8.17/1.96 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.17/1.96 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 & % 8.17/1.96 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.17/1.96 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.17/1.96 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, % 8.17/1.96 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( % 8.17/1.96 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) % 8.17/1.96 % 8.17/1.96 (d3_tarski) % 8.17/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.17/1.96 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.17/1.96 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 8.17/1.96 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 8.17/1.96 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 8.17/1.96 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 8.17/1.96 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 8.17/1.96 $i(v0) | in(v2, v1) = 0) % 8.17/1.96 % 8.17/1.96 (t47_zfmisc_1) % 8.17/1.97 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.17/1.97 int] : ( ~ (v5 = 0) & subset(v4, v2) = 0 & set_union2(v3, v2) = v4 & % 8.17/1.97 unordered_pair(v0, v1) = v3 & in(v0, v2) = v5 & $i(v4) & $i(v3) & $i(v2) & % 8.17/1.97 $i(v1) & $i(v0)) % 8.17/1.97 % 8.17/1.97 (function-axioms) % 8.17/1.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.17/1.97 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 8.17/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.17/1.97 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 8.17/1.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 8.17/1.97 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.17/1.97 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, % 8.17/1.97 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.17/1.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 8.17/1.97 (empty(v2) = v0)) % 8.17/1.97 % 8.17/1.97 Further assumptions not needed in the proof: % 8.17/1.97 -------------------------------------------- % 8.17/1.97 antisymmetry_r2_hidden, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 8.17/1.97 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski % 8.17/1.97 % 8.17/1.97 Those formulas are unsatisfiable: % 8.17/1.97 --------------------------------- % 8.17/1.97 % 8.17/1.97 Begin of proof % 8.17/1.97 | % 8.17/1.97 | ALPHA: (commutativity_k2_tarski) implies: % 8.17/1.97 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 8.17/1.97 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & % 8.17/1.97 | $i(v2))) % 8.17/1.97 | % 8.17/1.97 | ALPHA: (commutativity_k2_xboole_0) implies: % 8.17/1.97 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 8.17/1.97 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 8.17/1.97 | % 8.17/1.97 | ALPHA: (d2_tarski) implies: % 8.17/1.97 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.17/1.97 | (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3) | ~ $i(v2) | ~ % 8.17/1.97 | $i(v1) | ~ $i(v0)) % 8.17/1.97 | % 8.17/1.97 | ALPHA: (d2_xboole_0) implies: % 8.17/1.98 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 8.17/1.98 | ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 8.17/1.98 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 8.17/1.98 | (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 % 8.17/1.98 | = 0))))) % 8.17/1.98 | % 8.17/1.98 | ALPHA: (d3_tarski) implies: % 8.17/1.98 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.17/1.98 | (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 8.17/1.98 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 8.17/1.98 | % 8.17/1.98 | ALPHA: (function-axioms) implies: % 8.17/1.98 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.17/1.98 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 8.17/1.98 | % 8.17/1.98 | DELTA: instantiating (t47_zfmisc_1) with fresh symbols all_17_0, all_17_1, % 8.17/1.98 | all_17_2, all_17_3, all_17_4, all_17_5 gives: % 8.17/1.98 | (7) ~ (all_17_0 = 0) & subset(all_17_1, all_17_3) = 0 & % 8.17/1.98 | set_union2(all_17_2, all_17_3) = all_17_1 & unordered_pair(all_17_5, % 8.17/1.98 | all_17_4) = all_17_2 & in(all_17_5, all_17_3) = all_17_0 & % 8.17/1.98 | $i(all_17_1) & $i(all_17_2) & $i(all_17_3) & $i(all_17_4) & % 8.17/1.98 | $i(all_17_5) % 8.17/1.98 | % 8.17/1.98 | ALPHA: (7) implies: % 8.17/1.98 | (8) ~ (all_17_0 = 0) % 8.17/1.98 | (9) $i(all_17_5) % 8.17/1.98 | (10) $i(all_17_4) % 8.17/1.98 | (11) $i(all_17_3) % 8.17/1.98 | (12) $i(all_17_1) % 8.17/1.98 | (13) in(all_17_5, all_17_3) = all_17_0 % 8.17/1.98 | (14) unordered_pair(all_17_5, all_17_4) = all_17_2 % 8.17/1.98 | (15) set_union2(all_17_2, all_17_3) = all_17_1 % 8.17/1.98 | (16) subset(all_17_1, all_17_3) = 0 % 8.17/1.98 | % 8.17/1.98 | GROUND_INST: instantiating (1) with all_17_4, all_17_5, all_17_2, simplifying % 8.17/1.98 | with (9), (10), (14) gives: % 8.17/1.98 | (17) unordered_pair(all_17_4, all_17_5) = all_17_2 & $i(all_17_2) % 8.17/1.98 | % 8.17/1.98 | ALPHA: (17) implies: % 8.17/1.98 | (18) $i(all_17_2) % 8.17/1.98 | (19) unordered_pair(all_17_4, all_17_5) = all_17_2 % 8.17/1.98 | % 8.17/1.98 | GROUND_INST: instantiating (4) with all_17_2, all_17_3, all_17_1, all_17_5, % 8.17/1.98 | all_17_0, simplifying with (9), (11), (12), (13), (15), (18) % 8.17/1.99 | gives: % 8.17/1.99 | (20) ? [v0: any] : ? [v1: any] : (in(all_17_5, all_17_1) = v1 & % 8.17/1.99 | in(all_17_5, all_17_2) = v0 & (v1 = 0 | ( ~ (v0 = 0) & ~ (all_17_0 % 8.17/1.99 | = 0)))) % 8.17/1.99 | % 8.17/1.99 | GROUND_INST: instantiating (2) with all_17_3, all_17_2, all_17_1, simplifying % 8.17/1.99 | with (11), (15), (18) gives: % 8.17/1.99 | (21) set_union2(all_17_3, all_17_2) = all_17_1 & $i(all_17_1) % 8.17/1.99 | % 8.17/1.99 | GROUND_INST: instantiating (5) with all_17_1, all_17_3, all_17_5, all_17_0, % 8.17/1.99 | simplifying with (9), (11), (12), (13), (16) gives: % 8.17/1.99 | (22) all_17_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_17_5, all_17_1) = % 8.17/1.99 | v0) % 8.17/1.99 | % 8.17/1.99 | DELTA: instantiating (20) with fresh symbols all_33_0, all_33_1 gives: % 8.17/1.99 | (23) in(all_17_5, all_17_1) = all_33_0 & in(all_17_5, all_17_2) = all_33_1 % 8.17/1.99 | & (all_33_0 = 0 | ( ~ (all_33_1 = 0) & ~ (all_17_0 = 0))) % 8.17/1.99 | % 8.17/1.99 | ALPHA: (23) implies: % 8.17/1.99 | (24) in(all_17_5, all_17_2) = all_33_1 % 8.17/1.99 | (25) in(all_17_5, all_17_1) = all_33_0 % 8.17/1.99 | (26) all_33_0 = 0 | ( ~ (all_33_1 = 0) & ~ (all_17_0 = 0)) % 8.17/1.99 | % 8.17/1.99 | BETA: splitting (22) gives: % 8.17/1.99 | % 8.17/1.99 | Case 1: % 8.17/1.99 | | % 8.17/1.99 | | (27) all_17_0 = 0 % 8.17/1.99 | | % 8.17/1.99 | | REDUCE: (8), (27) imply: % 8.17/1.99 | | (28) $false % 8.17/1.99 | | % 8.17/1.99 | | CLOSE: (28) is inconsistent. % 8.17/1.99 | | % 8.17/1.99 | Case 2: % 8.17/1.99 | | % 8.17/1.99 | | (29) ? [v0: int] : ( ~ (v0 = 0) & in(all_17_5, all_17_1) = v0) % 8.17/1.99 | | % 8.17/1.99 | | DELTA: instantiating (29) with fresh symbol all_39_0 gives: % 8.17/1.99 | | (30) ~ (all_39_0 = 0) & in(all_17_5, all_17_1) = all_39_0 % 8.17/1.99 | | % 8.17/1.99 | | ALPHA: (30) implies: % 8.17/1.99 | | (31) ~ (all_39_0 = 0) % 8.17/1.99 | | (32) in(all_17_5, all_17_1) = all_39_0 % 8.17/1.99 | | % 8.17/1.99 | | GROUND_INST: instantiating (6) with all_33_0, all_39_0, all_17_1, all_17_5, % 8.17/1.99 | | simplifying with (25), (32) gives: % 8.17/1.99 | | (33) all_39_0 = all_33_0 % 8.17/1.99 | | % 8.17/1.99 | | REDUCE: (31), (33) imply: % 8.17/1.99 | | (34) ~ (all_33_0 = 0) % 8.17/1.99 | | % 8.17/1.99 | | BETA: splitting (26) gives: % 8.17/1.99 | | % 8.17/1.99 | | Case 1: % 8.17/1.99 | | | % 8.17/1.99 | | | (35) all_33_0 = 0 % 8.17/1.99 | | | % 8.17/1.99 | | | REDUCE: (34), (35) imply: % 8.17/1.99 | | | (36) $false % 8.17/1.99 | | | % 8.17/1.99 | | | CLOSE: (36) is inconsistent. % 8.17/1.99 | | | % 8.17/1.99 | | Case 2: % 8.17/1.99 | | | % 8.17/1.99 | | | (37) ~ (all_33_1 = 0) & ~ (all_17_0 = 0) % 8.17/1.99 | | | % 8.17/1.99 | | | ALPHA: (37) implies: % 8.17/2.00 | | | (38) ~ (all_33_1 = 0) % 8.17/2.00 | | | % 8.17/2.00 | | | GROUND_INST: instantiating (3) with all_17_4, all_17_5, all_17_2, % 8.17/2.00 | | | all_33_1, simplifying with (9), (10), (18), (19), (24) gives: % 8.17/2.00 | | | (39) all_33_1 = 0 % 8.17/2.00 | | | % 8.17/2.00 | | | REDUCE: (38), (39) imply: % 8.17/2.00 | | | (40) $false % 8.17/2.00 | | | % 8.17/2.00 | | | CLOSE: (40) is inconsistent. % 8.17/2.00 | | | % 8.17/2.00 | | End of split % 8.17/2.00 | | % 8.17/2.00 | End of split % 8.17/2.00 | % 8.17/2.00 End of proof % 8.17/2.00 % SZS output end Proof for theBenchmark % 8.17/2.00 % 8.17/2.00 1384ms %------------------------------------------------------------------------------