%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET944+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 : n023.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 15:27:09 EDT 2023 % Result : Theorem 7.05s 1.67s % Output : Proof 8.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.01/0.12 % Problem : SET944+1 : TPTP v8.1.2. Released v3.2.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n023.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 % 0.19/0.34 % CPULimit : 300 % 0.19/0.34 % WCLimit : 300 % 0.19/0.34 % DateTime : Sat Aug 26 10:56:41 EDT 2023 % 0.19/0.34 % CPUTime : % 0.58/0.61 ________ _____ % 0.58/0.61 ___ __ \_________(_)________________________________ % 0.58/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.58/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.58/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.58/0.61 % 0.58/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.58/0.61 (2023-06-19) % 0.58/0.61 % 0.58/0.61 (c) Philipp Rümmer, 2009-2023 % 0.58/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.58/0.61 Amanda Stjerna. % 0.58/0.61 Free software under BSD-3-Clause. % 0.58/0.61 % 0.58/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.58/0.61 % 0.58/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.58/0.62 Running up to 7 provers in parallel. % 0.71/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.11/0.97 Prover 4: Preprocessing ... % 2.11/0.97 Prover 1: Preprocessing ... % 2.52/1.02 Prover 6: Preprocessing ... % 2.52/1.02 Prover 3: Preprocessing ... % 2.52/1.02 Prover 0: Preprocessing ... % 2.52/1.02 Prover 5: Preprocessing ... % 2.52/1.02 Prover 2: Preprocessing ... % 4.20/1.25 Prover 1: Warning: ignoring some quantifiers % 4.20/1.26 Prover 5: Proving ... % 4.20/1.26 Prover 6: Proving ... % 4.20/1.27 Prover 3: Warning: ignoring some quantifiers % 4.20/1.28 Prover 1: Constructing countermodel ... % 4.20/1.28 Prover 2: Proving ... % 4.20/1.28 Prover 3: Constructing countermodel ... % 4.70/1.30 Prover 4: Warning: ignoring some quantifiers % 4.70/1.32 Prover 4: Constructing countermodel ... % 4.70/1.34 Prover 0: Proving ... % 7.05/1.66 Prover 0: proved (1032ms) % 7.05/1.66 % 7.05/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.05/1.67 % 7.05/1.67 Prover 3: stopped % 7.05/1.67 Prover 2: stopped % 7.05/1.67 Prover 6: stopped % 7.05/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.05/1.67 Prover 5: stopped % 7.55/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.55/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.55/1.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.55/1.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.55/1.69 Prover 8: Preprocessing ... % 7.55/1.69 Prover 7: Preprocessing ... % 7.55/1.70 Prover 13: Preprocessing ... % 7.55/1.70 Prover 10: Preprocessing ... % 7.55/1.71 Prover 11: Preprocessing ... % 7.55/1.74 Prover 10: Warning: ignoring some quantifiers % 7.55/1.75 Prover 10: Constructing countermodel ... % 7.55/1.76 Prover 13: Warning: ignoring some quantifiers % 7.55/1.76 Prover 8: Warning: ignoring some quantifiers % 7.55/1.77 Prover 13: Constructing countermodel ... % 7.55/1.77 Prover 4: Found proof (size 59) % 7.55/1.77 Prover 4: proved (1135ms) % 7.55/1.77 Prover 10: stopped % 7.55/1.77 Prover 13: stopped % 8.26/1.77 Prover 1: stopped % 8.26/1.77 Prover 8: Constructing countermodel ... % 8.26/1.77 Prover 8: stopped % 8.26/1.78 Prover 7: Warning: ignoring some quantifiers % 8.26/1.78 Prover 11: stopped % 8.26/1.78 Prover 7: Constructing countermodel ... % 8.26/1.79 Prover 7: stopped % 8.26/1.79 % 8.26/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.26/1.79 % 8.38/1.80 % SZS output start Proof for theBenchmark % 8.38/1.80 Assumptions after simplification: % 8.38/1.80 --------------------------------- % 8.38/1.80 % 8.38/1.80 (commutativity_k3_xboole_0) % 8.53/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2) % 8.53/1.83 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & ! % 8.53/1.83 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 8.53/1.83 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 8.53/1.83 % 8.53/1.83 (d3_tarski) % 8.53/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.53/1.84 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.53/1.84 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 8.53/1.84 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 8.53/1.84 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 8.53/1.84 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 8.53/1.84 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 8.53/1.84 $i(v0) | in(v2, v1) = 0) % 8.53/1.84 % 8.53/1.84 (d3_xboole_0) % 8.53/1.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.53/1.85 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | % 8.53/1.85 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) % 8.53/1.85 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 8.53/1.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 8.53/1.85 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 8.53/1.85 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 8.53/1.85 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 8.53/1.85 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 8.53/1.85 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ % 8.53/1.85 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 8.53/1.86 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 8.53/1.86 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 8.53/1.86 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 8.53/1.86 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 8.53/1.86 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | % 8.53/1.86 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 8.53/1.86 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] % 8.53/1.86 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = % 8.53/1.86 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 8.53/1.86 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 % 8.53/1.86 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.53/1.86 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 8.53/1.86 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 8.53/1.86 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) % 8.53/1.86 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) % 8.53/1.86 % 8.53/1.86 (d4_tarski) % 8.53/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 % 8.53/1.87 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ~ % 8.53/1.87 $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 8.53/1.87 in(v2, v4) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] % 8.53/1.87 : ! [v4: $i] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ % 8.53/1.87 (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 8.53/1.87 int] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 8.53/1.87 [v2: $i] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) % 8.53/1.87 | ~ $i(v0) | ? [v3: $i] : (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3))) & ? % 8.53/1.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (union(v1) = v2) | ~ % 8.53/1.87 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] % 8.53/1.87 : ? [v7: int] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ( ! % 8.53/1.87 [v8: $i] : ( ~ (in(v8, v1) = 0) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 = % 8.53/1.87 0) & in(v3, v8) = v9)) & ! [v8: $i] : ( ~ (in(v3, v8) = 0) | ~ % 8.53/1.87 $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & in(v8, v1) = v9)))) & (v4 = 0 % 8.53/1.87 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0)))) % 8.53/1.87 % 8.53/1.87 (t97_zfmisc_1) % 8.53/1.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.53/1.87 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & union(v2) = v3 & union(v1) % 8.53/1.87 = v5 & union(v0) = v4 & subset(v3, v6) = v7 & set_intersection2(v4, v5) = v6 % 8.53/1.87 & set_intersection2(v0, v1) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 8.53/1.87 $i(v2) & $i(v1) & $i(v0)) % 8.53/1.87 % 8.53/1.87 (function-axioms) % 8.53/1.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.53/1.87 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 8.53/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.53/1.87 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 8.53/1.87 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 8.53/1.87 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 8.53/1.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.53/1.87 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 8.53/1.87 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 8.53/1.87 % 8.53/1.87 Further assumptions not needed in the proof: % 8.53/1.87 -------------------------------------------- % 8.53/1.87 antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, % 8.53/1.87 reflexivity_r1_tarski % 8.53/1.87 % 8.53/1.87 Those formulas are unsatisfiable: % 8.53/1.87 --------------------------------- % 8.53/1.87 % 8.53/1.87 Begin of proof % 8.53/1.88 | % 8.53/1.88 | ALPHA: (commutativity_k3_xboole_0) implies: % 8.53/1.88 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, % 8.53/1.88 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = % 8.53/1.88 | v2 & $i(v2))) % 8.53/1.88 | % 8.53/1.88 | ALPHA: (d3_tarski) implies: % 8.53/1.88 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.53/1.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.53/1.88 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 8.53/1.88 | % 8.53/1.88 | ALPHA: (d3_xboole_0) implies: % 8.53/1.88 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.53/1.88 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | % 8.53/1.88 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) % 8.53/1.88 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 8.53/1.88 | (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | % 8.53/1.88 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 8.53/1.88 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 8.53/1.88 | 0)))) % 8.53/1.88 | % 8.53/1.88 | ALPHA: (d4_tarski) implies: % 8.53/1.88 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0) = v1) | ~ % 8.53/1.88 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 8.53/1.88 | (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3))) % 8.53/1.88 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : % 8.53/1.88 | (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = % 8.53/1.88 | v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] % 8.53/1.88 | : ( ~ (v5 = 0) & in(v4, v0) = v5)) % 8.53/1.88 | % 8.53/1.88 | ALPHA: (function-axioms) implies: % 8.53/1.89 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.53/1.89 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 8.53/1.89 | % 8.53/1.89 | DELTA: instantiating (t97_zfmisc_1) with fresh symbols all_14_0, all_14_1, % 8.53/1.89 | all_14_2, all_14_3, all_14_4, all_14_5, all_14_6, all_14_7 gives: % 8.53/1.89 | (8) ~ (all_14_0 = 0) & union(all_14_5) = all_14_4 & union(all_14_6) = % 8.53/1.89 | all_14_2 & union(all_14_7) = all_14_3 & subset(all_14_4, all_14_1) = % 8.53/1.89 | all_14_0 & set_intersection2(all_14_3, all_14_2) = all_14_1 & % 8.53/1.89 | set_intersection2(all_14_7, all_14_6) = all_14_5 & $i(all_14_1) & % 8.53/1.89 | $i(all_14_2) & $i(all_14_3) & $i(all_14_4) & $i(all_14_5) & % 8.53/1.89 | $i(all_14_6) & $i(all_14_7) % 8.53/1.89 | % 8.53/1.89 | ALPHA: (8) implies: % 8.53/1.89 | (9) ~ (all_14_0 = 0) % 8.53/1.89 | (10) $i(all_14_7) % 8.53/1.89 | (11) $i(all_14_6) % 8.53/1.89 | (12) $i(all_14_4) % 8.53/1.89 | (13) $i(all_14_3) % 8.53/1.89 | (14) $i(all_14_2) % 8.53/1.89 | (15) set_intersection2(all_14_7, all_14_6) = all_14_5 % 8.53/1.89 | (16) set_intersection2(all_14_3, all_14_2) = all_14_1 % 8.53/1.89 | (17) subset(all_14_4, all_14_1) = all_14_0 % 8.53/1.89 | (18) union(all_14_7) = all_14_3 % 8.53/1.89 | (19) union(all_14_6) = all_14_2 % 8.53/1.89 | (20) union(all_14_5) = all_14_4 % 8.53/1.89 | % 8.53/1.89 | GROUND_INST: instantiating (1) with all_14_6, all_14_7, all_14_5, simplifying % 8.53/1.89 | with (10), (11), (15) gives: % 8.53/1.89 | (21) set_intersection2(all_14_6, all_14_7) = all_14_5 & $i(all_14_5) % 8.53/1.89 | % 8.53/1.89 | ALPHA: (21) implies: % 8.53/1.89 | (22) $i(all_14_5) % 8.53/1.89 | % 8.53/1.89 | GROUND_INST: instantiating (1) with all_14_2, all_14_3, all_14_1, simplifying % 8.53/1.89 | with (13), (14), (16) gives: % 8.53/1.89 | (23) set_intersection2(all_14_2, all_14_3) = all_14_1 & $i(all_14_1) % 8.53/1.89 | % 8.53/1.89 | ALPHA: (23) implies: % 8.53/1.89 | (24) $i(all_14_1) % 8.53/1.89 | (25) set_intersection2(all_14_2, all_14_3) = all_14_1 % 8.53/1.89 | % 8.53/1.89 | GROUND_INST: instantiating (2) with all_14_4, all_14_1, all_14_0, simplifying % 8.53/1.89 | with (12), (17), (24) gives: % 8.53/1.90 | (26) all_14_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 8.53/1.90 | all_14_1) = v1 & in(v0, all_14_4) = 0 & $i(v0)) % 8.53/1.90 | % 8.53/1.90 | BETA: splitting (26) gives: % 8.53/1.90 | % 8.53/1.90 | Case 1: % 8.53/1.90 | | % 8.53/1.90 | | (27) all_14_0 = 0 % 8.53/1.90 | | % 8.53/1.90 | | REDUCE: (9), (27) imply: % 8.53/1.90 | | (28) $false % 8.89/1.90 | | % 8.89/1.90 | | CLOSE: (28) is inconsistent. % 8.89/1.90 | | % 8.89/1.90 | Case 2: % 8.89/1.90 | | % 8.89/1.90 | | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_14_1) = v1 & % 8.89/1.90 | | in(v0, all_14_4) = 0 & $i(v0)) % 8.89/1.90 | | % 8.89/1.90 | | DELTA: instantiating (29) with fresh symbols all_30_0, all_30_1 gives: % 8.89/1.90 | | (30) ~ (all_30_0 = 0) & in(all_30_1, all_14_1) = all_30_0 & in(all_30_1, % 8.89/1.90 | | all_14_4) = 0 & $i(all_30_1) % 8.89/1.90 | | % 8.89/1.90 | | ALPHA: (30) implies: % 8.89/1.90 | | (31) ~ (all_30_0 = 0) % 8.89/1.90 | | (32) $i(all_30_1) % 8.89/1.90 | | (33) in(all_30_1, all_14_4) = 0 % 8.89/1.90 | | (34) in(all_30_1, all_14_1) = all_30_0 % 8.89/1.90 | | % 8.89/1.90 | | GROUND_INST: instantiating (5) with all_14_5, all_14_4, all_30_1, % 8.89/1.90 | | simplifying with (12), (20), (22), (32), (33) gives: % 8.89/1.90 | | (35) ? [v0: $i] : (in(v0, all_14_5) = 0 & in(all_30_1, v0) = 0 & $i(v0)) % 8.89/1.90 | | % 8.89/1.90 | | GROUND_INST: instantiating (4) with all_14_3, all_14_2, all_14_1, all_30_1, % 8.89/1.90 | | all_30_0, simplifying with (13), (14), (16), (24), (32), (34) % 8.89/1.90 | | gives: % 8.89/1.90 | | (36) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_30_1, all_14_2) % 8.89/1.90 | | = v1 & in(all_30_1, all_14_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.89/1.90 | | % 8.89/1.90 | | GROUND_INST: instantiating (4) with all_14_2, all_14_3, all_14_1, all_30_1, % 8.89/1.90 | | all_30_0, simplifying with (13), (14), (24), (25), (32), (34) % 8.89/1.90 | | gives: % 8.89/1.91 | | (37) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_30_1, all_14_2) % 8.89/1.91 | | = v0 & in(all_30_1, all_14_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.89/1.91 | | % 8.89/1.91 | | DELTA: instantiating (35) with fresh symbol all_39_0 gives: % 8.89/1.91 | | (38) in(all_39_0, all_14_5) = 0 & in(all_30_1, all_39_0) = 0 & % 8.89/1.91 | | $i(all_39_0) % 8.89/1.91 | | % 8.89/1.91 | | ALPHA: (38) implies: % 8.89/1.91 | | (39) $i(all_39_0) % 8.89/1.91 | | (40) in(all_30_1, all_39_0) = 0 % 8.89/1.91 | | (41) in(all_39_0, all_14_5) = 0 % 8.89/1.91 | | % 8.89/1.91 | | BETA: splitting (36) gives: % 8.89/1.91 | | % 8.89/1.91 | | Case 1: % 8.89/1.91 | | | % 8.89/1.91 | | | (42) all_30_0 = 0 % 8.89/1.91 | | | % 8.89/1.91 | | | REDUCE: (31), (42) imply: % 8.89/1.91 | | | (43) $false % 8.89/1.91 | | | % 8.89/1.91 | | | CLOSE: (43) is inconsistent. % 8.89/1.91 | | | % 8.89/1.91 | | Case 2: % 8.89/1.91 | | | % 8.89/1.91 | | | (44) ? [v0: any] : ? [v1: any] : (in(all_30_1, all_14_2) = v1 & % 8.89/1.91 | | | in(all_30_1, all_14_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.89/1.91 | | | % 8.89/1.91 | | | DELTA: instantiating (44) with fresh symbols all_45_0, all_45_1 gives: % 8.89/1.91 | | | (45) in(all_30_1, all_14_2) = all_45_0 & in(all_30_1, all_14_3) = % 8.89/1.91 | | | all_45_1 & ( ~ (all_45_0 = 0) | ~ (all_45_1 = 0)) % 8.89/1.91 | | | % 8.89/1.91 | | | ALPHA: (45) implies: % 8.89/1.91 | | | (46) in(all_30_1, all_14_3) = all_45_1 % 8.89/1.91 | | | (47) in(all_30_1, all_14_2) = all_45_0 % 8.89/1.91 | | | (48) ~ (all_45_0 = 0) | ~ (all_45_1 = 0) % 8.89/1.91 | | | % 8.89/1.91 | | | BETA: splitting (37) gives: % 8.89/1.91 | | | % 8.89/1.91 | | | Case 1: % 8.89/1.91 | | | | % 8.89/1.91 | | | | (49) all_30_0 = 0 % 8.89/1.91 | | | | % 8.89/1.91 | | | | REDUCE: (31), (49) imply: % 8.89/1.91 | | | | (50) $false % 8.89/1.91 | | | | % 8.89/1.91 | | | | CLOSE: (50) is inconsistent. % 8.89/1.91 | | | | % 8.89/1.91 | | | Case 2: % 8.89/1.91 | | | | % 8.89/1.91 | | | | (51) ? [v0: any] : ? [v1: any] : (in(all_30_1, all_14_2) = v0 & % 8.89/1.91 | | | | in(all_30_1, all_14_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.89/1.91 | | | | % 8.89/1.91 | | | | DELTA: instantiating (51) with fresh symbols all_50_0, all_50_1 gives: % 8.89/1.91 | | | | (52) in(all_30_1, all_14_2) = all_50_1 & in(all_30_1, all_14_3) = % 8.89/1.91 | | | | all_50_0 & ( ~ (all_50_0 = 0) | ~ (all_50_1 = 0)) % 8.89/1.91 | | | | % 8.89/1.91 | | | | ALPHA: (52) implies: % 8.89/1.91 | | | | (53) in(all_30_1, all_14_3) = all_50_0 % 8.89/1.91 | | | | (54) in(all_30_1, all_14_2) = all_50_1 % 8.89/1.91 | | | | % 8.89/1.91 | | | | GROUND_INST: instantiating (7) with all_45_1, all_50_0, all_14_3, % 8.89/1.91 | | | | all_30_1, simplifying with (46), (53) gives: % 8.89/1.91 | | | | (55) all_50_0 = all_45_1 % 8.89/1.91 | | | | % 8.89/1.92 | | | | GROUND_INST: instantiating (7) with all_45_0, all_50_1, all_14_2, % 8.89/1.92 | | | | all_30_1, simplifying with (47), (54) gives: % 8.89/1.92 | | | | (56) all_50_1 = all_45_0 % 8.89/1.92 | | | | % 8.89/1.92 | | | | GROUND_INST: instantiating (6) with all_14_6, all_14_2, all_30_1, % 8.89/1.92 | | | | all_45_0, all_39_0, simplifying with (11), (14), (19), % 8.89/1.92 | | | | (32), (39), (40), (47) gives: % 8.89/1.92 | | | | (57) all_45_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0, % 8.89/1.92 | | | | all_14_6) = v0) % 8.89/1.92 | | | | % 8.89/1.92 | | | | GROUND_INST: instantiating (6) with all_14_7, all_14_3, all_30_1, % 8.89/1.92 | | | | all_45_1, all_39_0, simplifying with (10), (13), (18), % 8.89/1.92 | | | | (32), (39), (40), (46) gives: % 8.89/1.92 | | | | (58) all_45_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0, % 8.89/1.92 | | | | all_14_7) = v0) % 8.89/1.92 | | | | % 8.89/1.92 | | | | GROUND_INST: instantiating (3) with all_14_7, all_14_6, all_14_5, % 8.89/1.92 | | | | all_39_0, simplifying with (10), (11), (15), (22), (39), % 8.89/1.92 | | | | (41) gives: % 8.89/1.92 | | | | (59) in(all_39_0, all_14_6) = 0 & in(all_39_0, all_14_7) = 0 % 8.89/1.92 | | | | % 8.89/1.92 | | | | ALPHA: (59) implies: % 8.89/1.92 | | | | (60) in(all_39_0, all_14_7) = 0 % 8.89/1.92 | | | | (61) in(all_39_0, all_14_6) = 0 % 8.89/1.92 | | | | % 8.89/1.92 | | | | BETA: splitting (58) gives: % 8.89/1.92 | | | | % 8.89/1.92 | | | | Case 1: % 8.89/1.92 | | | | | % 8.89/1.92 | | | | | (62) all_45_1 = 0 % 8.89/1.92 | | | | | % 8.89/1.92 | | | | | BETA: splitting (57) gives: % 8.89/1.92 | | | | | % 8.89/1.92 | | | | | Case 1: % 8.89/1.92 | | | | | | % 8.89/1.92 | | | | | | (63) all_45_0 = 0 % 8.89/1.92 | | | | | | % 8.89/1.92 | | | | | | BETA: splitting (48) gives: % 8.89/1.92 | | | | | | % 8.89/1.92 | | | | | | Case 1: % 8.89/1.92 | | | | | | | % 8.89/1.92 | | | | | | | (64) ~ (all_45_0 = 0) % 8.89/1.92 | | | | | | | % 8.89/1.92 | | | | | | | REDUCE: (63), (64) imply: % 8.89/1.92 | | | | | | | (65) $false % 8.89/1.92 | | | | | | | % 8.89/1.92 | | | | | | | CLOSE: (65) is inconsistent. % 8.89/1.92 | | | | | | | % 8.89/1.92 | | | | | | Case 2: % 8.89/1.92 | | | | | | | % 8.89/1.92 | | | | | | | (66) ~ (all_45_1 = 0) % 8.89/1.92 | | | | | | | % 8.89/1.92 | | | | | | | REDUCE: (62), (66) imply: % 8.89/1.92 | | | | | | | (67) $false % 8.89/1.92 | | | | | | | % 8.89/1.92 | | | | | | | CLOSE: (67) is inconsistent. % 8.89/1.92 | | | | | | | % 8.89/1.92 | | | | | | End of split % 8.89/1.92 | | | | | | % 8.89/1.92 | | | | | Case 2: % 8.89/1.92 | | | | | | % 8.89/1.92 | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0, all_14_6) = v0) % 8.89/1.92 | | | | | | % 8.89/1.92 | | | | | | DELTA: instantiating (68) with fresh symbol all_74_0 gives: % 8.89/1.92 | | | | | | (69) ~ (all_74_0 = 0) & in(all_39_0, all_14_6) = all_74_0 % 8.89/1.92 | | | | | | % 8.89/1.92 | | | | | | ALPHA: (69) implies: % 8.89/1.92 | | | | | | (70) ~ (all_74_0 = 0) % 8.89/1.92 | | | | | | (71) in(all_39_0, all_14_6) = all_74_0 % 8.89/1.92 | | | | | | % 8.89/1.92 | | | | | | GROUND_INST: instantiating (7) with 0, all_74_0, all_14_6, all_39_0, % 8.89/1.92 | | | | | | simplifying with (61), (71) gives: % 8.89/1.92 | | | | | | (72) all_74_0 = 0 % 8.89/1.92 | | | | | | % 8.89/1.92 | | | | | | REDUCE: (70), (72) imply: % 8.89/1.92 | | | | | | (73) $false % 8.89/1.92 | | | | | | % 8.89/1.92 | | | | | | CLOSE: (73) is inconsistent. % 8.89/1.93 | | | | | | % 8.89/1.93 | | | | | End of split % 8.89/1.93 | | | | | % 8.89/1.93 | | | | Case 2: % 8.89/1.93 | | | | | % 8.89/1.93 | | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0, all_14_7) = v0) % 8.89/1.93 | | | | | % 8.89/1.93 | | | | | DELTA: instantiating (74) with fresh symbol all_70_0 gives: % 8.89/1.93 | | | | | (75) ~ (all_70_0 = 0) & in(all_39_0, all_14_7) = all_70_0 % 8.89/1.93 | | | | | % 8.89/1.93 | | | | | ALPHA: (75) implies: % 8.89/1.93 | | | | | (76) ~ (all_70_0 = 0) % 8.89/1.93 | | | | | (77) in(all_39_0, all_14_7) = all_70_0 % 8.89/1.93 | | | | | % 8.89/1.93 | | | | | GROUND_INST: instantiating (7) with 0, all_70_0, all_14_7, all_39_0, % 8.89/1.93 | | | | | simplifying with (60), (77) gives: % 8.89/1.93 | | | | | (78) all_70_0 = 0 % 8.89/1.93 | | | | | % 8.89/1.93 | | | | | REDUCE: (76), (78) imply: % 8.89/1.93 | | | | | (79) $false % 8.89/1.93 | | | | | % 8.89/1.93 | | | | | CLOSE: (79) is inconsistent. % 8.89/1.93 | | | | | % 8.89/1.93 | | | | End of split % 8.89/1.93 | | | | % 8.89/1.93 | | | End of split % 8.89/1.93 | | | % 8.89/1.93 | | End of split % 8.89/1.93 | | % 8.89/1.93 | End of split % 8.89/1.93 | % 8.89/1.93 End of proof % 8.89/1.93 % SZS output end Proof for theBenchmark % 8.89/1.93 % 8.89/1.93 1317ms %------------------------------------------------------------------------------