%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET597+3 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.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 15:25:30 EDT 2023 % Result : Theorem 7.13s 1.74s % Output : Proof 9.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET597+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n013.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 12:49:32 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.28/1.04 Prover 1: Preprocessing ... % 2.28/1.04 Prover 4: Preprocessing ... % 2.28/1.09 Prover 3: Preprocessing ... % 2.28/1.09 Prover 2: Preprocessing ... % 2.28/1.09 Prover 6: Preprocessing ... % 2.28/1.09 Prover 5: Preprocessing ... % 2.28/1.09 Prover 0: Preprocessing ... % 4.07/1.36 Prover 5: Proving ... % 4.07/1.38 Prover 2: Proving ... % 4.07/1.38 Prover 3: Warning: ignoring some quantifiers % 4.07/1.38 Prover 6: Proving ... % 4.07/1.39 Prover 3: Constructing countermodel ... % 4.07/1.41 Prover 1: Warning: ignoring some quantifiers % 4.07/1.41 Prover 4: Warning: ignoring some quantifiers % 4.07/1.42 Prover 0: Proving ... % 4.07/1.42 Prover 1: Constructing countermodel ... % 4.07/1.42 Prover 4: Constructing countermodel ... % 6.59/1.68 Prover 3: gave up % 6.59/1.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.74/1.71 Prover 7: Preprocessing ... % 7.13/1.74 Prover 0: proved (1090ms) % 7.13/1.74 % 7.13/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.13/1.74 % 7.13/1.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.13/1.74 Prover 5: stopped % 7.13/1.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.13/1.74 Prover 2: stopped % 7.13/1.75 Prover 6: stopped % 7.13/1.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.13/1.76 Prover 10: Preprocessing ... % 7.13/1.76 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.13/1.77 Prover 8: Preprocessing ... % 7.13/1.77 Prover 11: Preprocessing ... % 7.13/1.78 Prover 7: Warning: ignoring some quantifiers % 7.13/1.78 Prover 7: Constructing countermodel ... % 7.13/1.79 Prover 13: Preprocessing ... % 7.71/1.85 Prover 1: gave up % 7.71/1.85 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.71/1.85 Prover 10: Warning: ignoring some quantifiers % 7.71/1.86 Prover 10: Constructing countermodel ... % 7.71/1.87 Prover 16: Preprocessing ... % 8.22/1.89 Prover 13: Warning: ignoring some quantifiers % 8.22/1.90 Prover 8: Warning: ignoring some quantifiers % 8.22/1.90 Prover 13: Constructing countermodel ... % 8.22/1.91 Prover 4: Found proof (size 85) % 8.22/1.91 Prover 4: proved (1260ms) % 8.22/1.91 Prover 7: stopped % 8.22/1.91 Prover 10: stopped % 8.22/1.91 Prover 8: Constructing countermodel ... % 8.22/1.91 Prover 8: stopped % 8.22/1.92 Prover 13: stopped % 8.22/1.93 Prover 16: Warning: ignoring some quantifiers % 8.22/1.94 Prover 16: Constructing countermodel ... % 8.22/1.94 Prover 16: stopped % 8.22/1.95 Prover 11: Warning: ignoring some quantifiers % 8.22/1.96 Prover 11: Constructing countermodel ... % 8.78/1.96 Prover 11: stopped % 8.78/1.96 % 8.78/1.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.78/1.96 % 8.78/1.97 % SZS output start Proof for theBenchmark % 8.78/1.98 Assumptions after simplification: % 8.78/1.98 --------------------------------- % 8.78/1.98 % 8.78/1.98 (commutativity_of_union) % 8.78/2.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~ $i(v1) % 8.78/2.00 | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : % 8.78/2.00 ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (union(v1, v0) % 8.78/2.00 = v2 & $i(v2))) % 8.78/2.00 % 8.78/2.00 (equal_defn) % 8.78/2.01 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~ $i(v1) | % 8.78/2.01 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0: $i] % 8.78/2.01 : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 8.78/2.01 ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i] : ! [v1: % 8.78/2.01 int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0)) % 8.78/2.01 % 8.78/2.01 (prove_th56) % 8.78/2.02 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 8.78/2.02 any] : ? [v6: $i] : ? [v7: int] : ? [v8: int] : ? [v9: int] : (union(v1, % 8.78/2.02 v2) = v3 & subset(v2, v0) = v5 & subset(v1, v0) = v4 & $i(v6) & $i(v3) & % 8.78/2.02 $i(v2) & $i(v1) & $i(v0) & ((v5 = 0 & v4 = 0 & ~ (v3 = v0) & ! [v10: $i] : % 8.78/2.02 ! [v11: int] : (v11 = 0 | ~ (subset(v0, v10) = v11) | ~ $i(v10) | ? % 8.78/2.02 [v12: any] : ? [v13: any] : (subset(v2, v10) = v13 & subset(v1, v10) % 8.78/2.02 = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10: $i] : ( ~ % 8.78/2.02 (subset(v2, v10) = 0) | ~ $i(v10) | ? [v11: any] : ? [v12: any] : % 8.78/2.02 (subset(v1, v10) = v11 & subset(v0, v10) = v12 & ( ~ (v11 = 0) | v12 = % 8.78/2.02 0))) & ! [v10: $i] : ( ~ (subset(v1, v10) = 0) | ~ $i(v10) | ? % 8.78/2.02 [v11: any] : ? [v12: any] : (subset(v2, v10) = v11 & subset(v0, v10) % 8.78/2.02 = v12 & ( ~ (v11 = 0) | v12 = 0)))) | (v3 = v0 & ( ~ (v5 = 0) | ~ % 8.78/2.02 (v4 = 0) | (v8 = 0 & v7 = 0 & ~ (v9 = 0) & subset(v2, v6) = 0 & % 8.78/2.02 subset(v1, v6) = 0 & subset(v0, v6) = v9))))) % 8.78/2.02 % 8.78/2.02 (subset_of_union) % 8.78/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) % 8.78/2.02 | ~ $i(v0) | subset(v0, v2) = 0) % 8.78/2.02 % 8.78/2.02 (union_subset) % 8.78/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.78/2.02 | ~ (union(v0, v2) = v3) | ~ (subset(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) % 8.78/2.02 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (subset(v2, v1) = v6 & % 8.78/2.02 subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 8.78/2.02 % 8.78/2.02 (function-axioms) % 8.78/2.02 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.78/2.02 [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & % 8.78/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.78/2.02 (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 8.78/2.02 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.78/2.02 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 8.78/2.02 % 8.78/2.02 Further assumptions not needed in the proof: % 8.78/2.02 -------------------------------------------- % 8.78/2.02 equal_member_defn, reflexivity_of_subset, subset_defn, union_defn % 8.78/2.02 % 8.78/2.02 Those formulas are unsatisfiable: % 8.78/2.02 --------------------------------- % 8.78/2.02 % 8.78/2.02 Begin of proof % 8.78/2.02 | % 8.78/2.02 | ALPHA: (equal_defn) implies: % 8.78/2.03 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~ % 8.78/2.03 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = % 8.78/2.03 | v2)) % 8.78/2.03 | % 8.78/2.03 | ALPHA: (commutativity_of_union) implies: % 8.78/2.03 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~ % 8.78/2.03 | $i(v1) | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2))) % 8.78/2.03 | % 8.78/2.03 | ALPHA: (function-axioms) implies: % 8.78/2.03 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.78/2.03 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 8.78/2.03 | = v0)) % 8.78/2.03 | % 8.78/2.03 | DELTA: instantiating (prove_th56) with fresh symbols all_11_0, all_11_1, % 8.78/2.03 | all_11_2, all_11_3, all_11_4, all_11_5, all_11_6, all_11_7, all_11_8, % 8.78/2.03 | all_11_9 gives: % 8.78/2.03 | (4) union(all_11_8, all_11_7) = all_11_6 & subset(all_11_7, all_11_9) = % 8.78/2.03 | all_11_4 & subset(all_11_8, all_11_9) = all_11_5 & $i(all_11_3) & % 8.78/2.03 | $i(all_11_6) & $i(all_11_7) & $i(all_11_8) & $i(all_11_9) & ((all_11_4 % 8.78/2.03 | = 0 & all_11_5 = 0 & ~ (all_11_6 = all_11_9) & ! [v0: $i] : ! % 8.78/2.03 | [v1: int] : (v1 = 0 | ~ (subset(all_11_9, v0) = v1) | ~ $i(v0) | % 8.78/2.03 | ? [v2: any] : ? [v3: any] : (subset(all_11_7, v0) = v3 & % 8.78/2.03 | subset(all_11_8, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! % 8.78/2.03 | [v0: $i] : ( ~ (subset(all_11_7, v0) = 0) | ~ $i(v0) | ? [v1: % 8.78/2.03 | any] : ? [v2: any] : (subset(all_11_8, v0) = v1 & % 8.78/2.03 | subset(all_11_9, v0) = v2 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0: % 8.78/2.03 | $i] : ( ~ (subset(all_11_8, v0) = 0) | ~ $i(v0) | ? [v1: any] : % 8.78/2.03 | ? [v2: any] : (subset(all_11_7, v0) = v1 & subset(all_11_9, v0) % 8.78/2.03 | = v2 & ( ~ (v1 = 0) | v2 = 0)))) | (all_11_6 = all_11_9 & ( ~ % 8.78/2.03 | (all_11_4 = 0) | ~ (all_11_5 = 0) | (all_11_1 = 0 & all_11_2 = 0 % 8.78/2.03 | & ~ (all_11_0 = 0) & subset(all_11_7, all_11_3) = 0 & % 8.78/2.03 | subset(all_11_8, all_11_3) = 0 & subset(all_11_9, all_11_3) = % 8.78/2.03 | all_11_0)))) % 8.78/2.03 | % 8.78/2.03 | ALPHA: (4) implies: % 8.78/2.04 | (5) $i(all_11_9) % 8.78/2.04 | (6) $i(all_11_8) % 8.78/2.04 | (7) $i(all_11_7) % 8.78/2.04 | (8) $i(all_11_3) % 8.78/2.04 | (9) subset(all_11_8, all_11_9) = all_11_5 % 8.78/2.04 | (10) subset(all_11_7, all_11_9) = all_11_4 % 8.78/2.04 | (11) union(all_11_8, all_11_7) = all_11_6 % 8.78/2.04 | (12) (all_11_4 = 0 & all_11_5 = 0 & ~ (all_11_6 = all_11_9) & ! [v0: $i] % 8.78/2.04 | : ! [v1: int] : (v1 = 0 | ~ (subset(all_11_9, v0) = v1) | ~ % 8.78/2.04 | $i(v0) | ? [v2: any] : ? [v3: any] : (subset(all_11_7, v0) = v3 % 8.78/2.04 | & subset(all_11_8, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! % 8.78/2.04 | [v0: $i] : ( ~ (subset(all_11_7, v0) = 0) | ~ $i(v0) | ? [v1: any] % 8.78/2.04 | : ? [v2: any] : (subset(all_11_8, v0) = v1 & subset(all_11_9, v0) % 8.78/2.04 | = v2 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0: $i] : ( ~ % 8.78/2.04 | (subset(all_11_8, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 8.78/2.04 | any] : (subset(all_11_7, v0) = v1 & subset(all_11_9, v0) = v2 & % 8.78/2.04 | ( ~ (v1 = 0) | v2 = 0)))) | (all_11_6 = all_11_9 & ( ~ (all_11_4 % 8.78/2.04 | = 0) | ~ (all_11_5 = 0) | (all_11_1 = 0 & all_11_2 = 0 & ~ % 8.78/2.04 | (all_11_0 = 0) & subset(all_11_7, all_11_3) = 0 & % 8.78/2.04 | subset(all_11_8, all_11_3) = 0 & subset(all_11_9, all_11_3) = % 8.78/2.04 | all_11_0))) % 8.78/2.04 | % 8.78/2.04 | GROUND_INST: instantiating (2) with all_11_7, all_11_8, all_11_6, simplifying % 8.78/2.04 | with (6), (7), (11) gives: % 8.78/2.04 | (13) union(all_11_7, all_11_8) = all_11_6 & $i(all_11_6) % 8.78/2.04 | % 8.78/2.04 | ALPHA: (13) implies: % 8.78/2.04 | (14) $i(all_11_6) % 8.78/2.04 | (15) union(all_11_7, all_11_8) = all_11_6 % 8.78/2.04 | % 8.78/2.04 | GROUND_INST: instantiating (subset_of_union) with all_11_8, all_11_7, % 8.78/2.04 | all_11_6, simplifying with (6), (7), (11) gives: % 8.78/2.04 | (16) subset(all_11_8, all_11_6) = 0 % 8.78/2.04 | % 8.78/2.04 | GROUND_INST: instantiating (subset_of_union) with all_11_7, all_11_8, % 8.78/2.04 | all_11_6, simplifying with (6), (7), (15) gives: % 8.78/2.04 | (17) subset(all_11_7, all_11_6) = 0 % 8.78/2.04 | % 8.78/2.04 | BETA: splitting (12) gives: % 8.78/2.04 | % 8.78/2.04 | Case 1: % 8.78/2.04 | | % 8.78/2.05 | | (18) all_11_4 = 0 & all_11_5 = 0 & ~ (all_11_6 = all_11_9) & ! [v0: $i] % 8.78/2.05 | | : ! [v1: int] : (v1 = 0 | ~ (subset(all_11_9, v0) = v1) | ~ % 8.78/2.05 | | $i(v0) | ? [v2: any] : ? [v3: any] : (subset(all_11_7, v0) = v3 % 8.78/2.05 | | & subset(all_11_8, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! % 8.78/2.05 | | [v0: $i] : ( ~ (subset(all_11_7, v0) = 0) | ~ $i(v0) | ? [v1: any] % 8.78/2.05 | | : ? [v2: any] : (subset(all_11_8, v0) = v1 & subset(all_11_9, v0) % 8.78/2.05 | | = v2 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0: $i] : ( ~ % 8.78/2.05 | | (subset(all_11_8, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 8.78/2.05 | | any] : (subset(all_11_7, v0) = v1 & subset(all_11_9, v0) = v2 & % 8.78/2.05 | | ( ~ (v1 = 0) | v2 = 0))) % 8.78/2.05 | | % 8.78/2.05 | | ALPHA: (18) implies: % 8.78/2.05 | | (19) all_11_5 = 0 % 8.78/2.05 | | (20) all_11_4 = 0 % 8.78/2.05 | | (21) ~ (all_11_6 = all_11_9) % 8.78/2.05 | | (22) ! [v0: $i] : ( ~ (subset(all_11_8, v0) = 0) | ~ $i(v0) | ? [v1: % 8.78/2.05 | | any] : ? [v2: any] : (subset(all_11_7, v0) = v1 & % 8.78/2.05 | | subset(all_11_9, v0) = v2 & ( ~ (v1 = 0) | v2 = 0))) % 8.78/2.05 | | (23) ! [v0: $i] : ( ~ (subset(all_11_7, v0) = 0) | ~ $i(v0) | ? [v1: % 8.78/2.05 | | any] : ? [v2: any] : (subset(all_11_8, v0) = v1 & % 8.78/2.05 | | subset(all_11_9, v0) = v2 & ( ~ (v1 = 0) | v2 = 0))) % 8.78/2.05 | | % 8.78/2.05 | | GROUND_INST: instantiating (22) with all_11_6, simplifying with (14), (16) % 8.78/2.05 | | gives: % 8.78/2.05 | | (24) ? [v0: any] : ? [v1: any] : (subset(all_11_7, all_11_6) = v0 & % 8.78/2.05 | | subset(all_11_9, all_11_6) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 8.78/2.05 | | % 8.78/2.05 | | GROUND_INST: instantiating (23) with all_11_6, simplifying with (14), (17) % 8.78/2.05 | | gives: % 8.78/2.05 | | (25) ? [v0: any] : ? [v1: any] : (subset(all_11_8, all_11_6) = v0 & % 8.78/2.05 | | subset(all_11_9, all_11_6) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 8.78/2.05 | | % 8.78/2.05 | | DELTA: instantiating (25) with fresh symbols all_33_0, all_33_1 gives: % 8.78/2.05 | | (26) subset(all_11_8, all_11_6) = all_33_1 & subset(all_11_9, all_11_6) = % 8.78/2.05 | | all_33_0 & ( ~ (all_33_1 = 0) | all_33_0 = 0) % 8.78/2.05 | | % 8.78/2.05 | | ALPHA: (26) implies: % 8.78/2.05 | | (27) subset(all_11_9, all_11_6) = all_33_0 % 8.78/2.05 | | (28) subset(all_11_8, all_11_6) = all_33_1 % 8.78/2.05 | | (29) ~ (all_33_1 = 0) | all_33_0 = 0 % 8.78/2.05 | | % 8.78/2.05 | | DELTA: instantiating (24) with fresh symbols all_35_0, all_35_1 gives: % 8.78/2.05 | | (30) subset(all_11_7, all_11_6) = all_35_1 & subset(all_11_9, all_11_6) = % 8.78/2.05 | | all_35_0 & ( ~ (all_35_1 = 0) | all_35_0 = 0) % 8.78/2.05 | | % 8.78/2.05 | | ALPHA: (30) implies: % 8.78/2.05 | | (31) subset(all_11_9, all_11_6) = all_35_0 % 8.78/2.05 | | % 8.78/2.05 | | REDUCE: (10), (20) imply: % 8.78/2.05 | | (32) subset(all_11_7, all_11_9) = 0 % 8.78/2.05 | | % 8.78/2.05 | | REDUCE: (9), (19) imply: % 8.78/2.05 | | (33) subset(all_11_8, all_11_9) = 0 % 8.78/2.05 | | % 8.78/2.05 | | GROUND_INST: instantiating (3) with all_33_0, all_35_0, all_11_6, all_11_9, % 8.78/2.05 | | simplifying with (27), (31) gives: % 8.78/2.05 | | (34) all_35_0 = all_33_0 % 8.78/2.05 | | % 8.78/2.06 | | GROUND_INST: instantiating (3) with 0, all_33_1, all_11_6, all_11_8, % 8.78/2.06 | | simplifying with (16), (28) gives: % 8.78/2.06 | | (35) all_33_1 = 0 % 8.78/2.06 | | % 8.78/2.06 | | BETA: splitting (29) gives: % 8.78/2.06 | | % 8.78/2.06 | | Case 1: % 8.78/2.06 | | | % 8.78/2.06 | | | (36) ~ (all_33_1 = 0) % 8.78/2.06 | | | % 8.78/2.06 | | | REDUCE: (35), (36) imply: % 8.78/2.06 | | | (37) $false % 8.78/2.06 | | | % 8.78/2.06 | | | CLOSE: (37) is inconsistent. % 8.78/2.06 | | | % 8.78/2.06 | | Case 2: % 8.78/2.06 | | | % 8.78/2.06 | | | (38) all_33_0 = 0 % 8.78/2.06 | | | % 8.78/2.06 | | | REDUCE: (27), (38) imply: % 8.78/2.06 | | | (39) subset(all_11_9, all_11_6) = 0 % 8.78/2.06 | | | % 8.78/2.06 | | | GROUND_INST: instantiating (1) with all_11_6, all_11_9, simplifying with % 8.78/2.06 | | | (5), (14), (39) gives: % 8.78/2.06 | | | (40) all_11_6 = all_11_9 | ? [v0: int] : ( ~ (v0 = 0) & % 8.78/2.06 | | | subset(all_11_6, all_11_9) = v0) % 8.78/2.06 | | | % 8.78/2.06 | | | GROUND_INST: instantiating (22) with all_11_9, simplifying with (5), (33) % 8.78/2.06 | | | gives: % 8.78/2.06 | | | (41) ? [v0: any] : ? [v1: any] : (subset(all_11_7, all_11_9) = v0 & % 8.78/2.06 | | | subset(all_11_9, all_11_9) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 8.78/2.06 | | | % 8.78/2.06 | | | GROUND_INST: instantiating (23) with all_11_9, simplifying with (5), (32) % 8.78/2.06 | | | gives: % 8.78/2.06 | | | (42) ? [v0: any] : ? [v1: any] : (subset(all_11_8, all_11_9) = v0 & % 8.78/2.06 | | | subset(all_11_9, all_11_9) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 8.78/2.06 | | | % 8.78/2.06 | | | DELTA: instantiating (42) with fresh symbols all_50_0, all_50_1 gives: % 8.78/2.06 | | | (43) subset(all_11_8, all_11_9) = all_50_1 & subset(all_11_9, all_11_9) % 8.78/2.06 | | | = all_50_0 & ( ~ (all_50_1 = 0) | all_50_0 = 0) % 8.78/2.06 | | | % 8.78/2.06 | | | ALPHA: (43) implies: % 8.78/2.06 | | | (44) subset(all_11_8, all_11_9) = all_50_1 % 8.78/2.06 | | | % 8.78/2.06 | | | DELTA: instantiating (41) with fresh symbols all_52_0, all_52_1 gives: % 8.78/2.06 | | | (45) subset(all_11_7, all_11_9) = all_52_1 & subset(all_11_9, all_11_9) % 8.78/2.06 | | | = all_52_0 & ( ~ (all_52_1 = 0) | all_52_0 = 0) % 8.78/2.06 | | | % 8.78/2.06 | | | ALPHA: (45) implies: % 8.78/2.06 | | | (46) subset(all_11_7, all_11_9) = all_52_1 % 8.78/2.06 | | | % 8.78/2.06 | | | BETA: splitting (40) gives: % 8.78/2.06 | | | % 8.78/2.06 | | | Case 1: % 8.78/2.06 | | | | % 8.78/2.06 | | | | (47) all_11_6 = all_11_9 % 8.78/2.06 | | | | % 8.78/2.06 | | | | REDUCE: (21), (47) imply: % 8.78/2.06 | | | | (48) $false % 8.78/2.06 | | | | % 8.78/2.06 | | | | CLOSE: (48) is inconsistent. % 8.78/2.06 | | | | % 8.78/2.06 | | | Case 2: % 8.78/2.06 | | | | % 8.78/2.06 | | | | (49) ? [v0: int] : ( ~ (v0 = 0) & subset(all_11_6, all_11_9) = v0) % 8.78/2.06 | | | | % 8.78/2.06 | | | | DELTA: instantiating (49) with fresh symbol all_58_0 gives: % 8.78/2.06 | | | | (50) ~ (all_58_0 = 0) & subset(all_11_6, all_11_9) = all_58_0 % 8.78/2.06 | | | | % 8.78/2.06 | | | | ALPHA: (50) implies: % 8.78/2.06 | | | | (51) ~ (all_58_0 = 0) % 8.78/2.06 | | | | (52) subset(all_11_6, all_11_9) = all_58_0 % 8.78/2.06 | | | | % 8.78/2.06 | | | | GROUND_INST: instantiating (3) with 0, all_50_1, all_11_9, all_11_8, % 8.78/2.06 | | | | simplifying with (33), (44) gives: % 8.78/2.06 | | | | (53) all_50_1 = 0 % 8.78/2.07 | | | | % 8.78/2.07 | | | | GROUND_INST: instantiating (3) with 0, all_52_1, all_11_9, all_11_7, % 8.78/2.07 | | | | simplifying with (32), (46) gives: % 8.78/2.07 | | | | (54) all_52_1 = 0 % 8.78/2.07 | | | | % 8.78/2.07 | | | | GROUND_INST: instantiating (union_subset) with all_11_8, all_11_9, % 8.78/2.07 | | | | all_11_7, all_11_6, all_58_0, simplifying with (5), (6), % 8.78/2.07 | | | | (7), (11), (52) gives: % 8.78/2.07 | | | | (55) all_58_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_11_7, % 8.78/2.07 | | | | all_11_9) = v1 & subset(all_11_8, all_11_9) = v0 & ( ~ (v1 = % 8.78/2.07 | | | | 0) | ~ (v0 = 0))) % 8.78/2.07 | | | | % 8.78/2.07 | | | | BETA: splitting (55) gives: % 8.78/2.07 | | | | % 8.78/2.07 | | | | Case 1: % 8.78/2.07 | | | | | % 8.78/2.07 | | | | | (56) all_58_0 = 0 % 8.78/2.07 | | | | | % 8.78/2.07 | | | | | REDUCE: (51), (56) imply: % 8.78/2.07 | | | | | (57) $false % 8.78/2.07 | | | | | % 8.78/2.07 | | | | | CLOSE: (57) is inconsistent. % 8.78/2.07 | | | | | % 8.78/2.07 | | | | Case 2: % 8.78/2.07 | | | | | % 8.78/2.07 | | | | | (58) ? [v0: any] : ? [v1: any] : (subset(all_11_7, all_11_9) = v1 % 8.78/2.07 | | | | | & subset(all_11_8, all_11_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 8.78/2.07 | | | | | 0))) % 8.78/2.07 | | | | | % 8.78/2.07 | | | | | DELTA: instantiating (58) with fresh symbols all_79_0, all_79_1 gives: % 8.78/2.07 | | | | | (59) subset(all_11_7, all_11_9) = all_79_0 & subset(all_11_8, % 8.78/2.07 | | | | | all_11_9) = all_79_1 & ( ~ (all_79_0 = 0) | ~ (all_79_1 = % 8.78/2.07 | | | | | 0)) % 8.78/2.07 | | | | | % 8.78/2.07 | | | | | ALPHA: (59) implies: % 8.78/2.07 | | | | | (60) subset(all_11_8, all_11_9) = all_79_1 % 8.78/2.07 | | | | | (61) subset(all_11_7, all_11_9) = all_79_0 % 8.78/2.07 | | | | | (62) ~ (all_79_0 = 0) | ~ (all_79_1 = 0) % 8.78/2.07 | | | | | % 8.78/2.07 | | | | | GROUND_INST: instantiating (3) with 0, all_79_1, all_11_9, all_11_8, % 8.78/2.07 | | | | | simplifying with (33), (60) gives: % 8.78/2.07 | | | | | (63) all_79_1 = 0 % 8.78/2.07 | | | | | % 8.78/2.07 | | | | | GROUND_INST: instantiating (3) with 0, all_79_0, all_11_9, all_11_7, % 8.78/2.07 | | | | | simplifying with (32), (61) gives: % 8.78/2.07 | | | | | (64) all_79_0 = 0 % 8.78/2.07 | | | | | % 8.78/2.07 | | | | | BETA: splitting (62) gives: % 8.78/2.07 | | | | | % 8.78/2.07 | | | | | Case 1: % 8.78/2.07 | | | | | | % 8.78/2.07 | | | | | | (65) ~ (all_79_0 = 0) % 8.78/2.07 | | | | | | % 8.78/2.07 | | | | | | REDUCE: (64), (65) imply: % 8.78/2.07 | | | | | | (66) $false % 8.78/2.07 | | | | | | % 8.78/2.07 | | | | | | CLOSE: (66) is inconsistent. % 8.78/2.07 | | | | | | % 8.78/2.07 | | | | | Case 2: % 8.78/2.07 | | | | | | % 8.78/2.07 | | | | | | (67) ~ (all_79_1 = 0) % 8.78/2.07 | | | | | | % 8.78/2.07 | | | | | | REDUCE: (63), (67) imply: % 8.78/2.07 | | | | | | (68) $false % 8.78/2.07 | | | | | | % 8.78/2.07 | | | | | | CLOSE: (68) is inconsistent. % 8.78/2.07 | | | | | | % 8.78/2.07 | | | | | End of split % 8.78/2.07 | | | | | % 8.78/2.07 | | | | End of split % 8.78/2.07 | | | | % 8.78/2.07 | | | End of split % 8.78/2.07 | | | % 8.78/2.07 | | End of split % 8.78/2.07 | | % 8.78/2.07 | Case 2: % 8.78/2.07 | | % 8.78/2.07 | | (69) all_11_6 = all_11_9 & ( ~ (all_11_4 = 0) | ~ (all_11_5 = 0) | % 8.78/2.07 | | (all_11_1 = 0 & all_11_2 = 0 & ~ (all_11_0 = 0) & % 8.78/2.07 | | subset(all_11_7, all_11_3) = 0 & subset(all_11_8, all_11_3) = 0 % 8.78/2.07 | | & subset(all_11_9, all_11_3) = all_11_0)) % 8.78/2.07 | | % 8.78/2.07 | | ALPHA: (69) implies: % 8.78/2.07 | | (70) all_11_6 = all_11_9 % 8.78/2.07 | | (71) ~ (all_11_4 = 0) | ~ (all_11_5 = 0) | (all_11_1 = 0 & all_11_2 = 0 % 8.78/2.07 | | & ~ (all_11_0 = 0) & subset(all_11_7, all_11_3) = 0 & % 8.78/2.07 | | subset(all_11_8, all_11_3) = 0 & subset(all_11_9, all_11_3) = % 8.78/2.07 | | all_11_0) % 8.78/2.07 | | % 8.78/2.07 | | REDUCE: (15), (70) imply: % 8.78/2.07 | | (72) union(all_11_7, all_11_8) = all_11_9 % 8.78/2.07 | | % 8.78/2.07 | | REDUCE: (17), (70) imply: % 8.78/2.07 | | (73) subset(all_11_7, all_11_9) = 0 % 8.78/2.07 | | % 8.78/2.08 | | REDUCE: (16), (70) imply: % 8.78/2.08 | | (74) subset(all_11_8, all_11_9) = 0 % 8.78/2.08 | | % 8.78/2.08 | | GROUND_INST: instantiating (3) with all_11_5, 0, all_11_9, all_11_8, % 8.78/2.08 | | simplifying with (9), (74) gives: % 8.78/2.08 | | (75) all_11_5 = 0 % 8.78/2.08 | | % 8.78/2.08 | | GROUND_INST: instantiating (3) with all_11_4, 0, all_11_9, all_11_7, % 8.78/2.08 | | simplifying with (10), (73) gives: % 8.78/2.08 | | (76) all_11_4 = 0 % 8.78/2.08 | | % 8.78/2.08 | | BETA: splitting (71) gives: % 8.78/2.08 | | % 8.78/2.08 | | Case 1: % 8.78/2.08 | | | % 8.78/2.08 | | | (77) ~ (all_11_4 = 0) % 8.78/2.08 | | | % 8.78/2.08 | | | REDUCE: (76), (77) imply: % 8.78/2.08 | | | (78) $false % 8.78/2.08 | | | % 8.78/2.08 | | | CLOSE: (78) is inconsistent. % 8.78/2.08 | | | % 8.78/2.08 | | Case 2: % 8.78/2.08 | | | % 8.78/2.08 | | | (79) ~ (all_11_5 = 0) | (all_11_1 = 0 & all_11_2 = 0 & ~ (all_11_0 = % 8.78/2.08 | | | 0) & subset(all_11_7, all_11_3) = 0 & subset(all_11_8, % 8.78/2.08 | | | all_11_3) = 0 & subset(all_11_9, all_11_3) = all_11_0) % 8.78/2.08 | | | % 8.78/2.08 | | | BETA: splitting (79) gives: % 8.78/2.08 | | | % 8.78/2.08 | | | Case 1: % 8.78/2.08 | | | | % 8.78/2.08 | | | | (80) ~ (all_11_5 = 0) % 8.78/2.08 | | | | % 8.78/2.08 | | | | REDUCE: (75), (80) imply: % 8.78/2.08 | | | | (81) $false % 8.78/2.08 | | | | % 8.78/2.08 | | | | CLOSE: (81) is inconsistent. % 8.78/2.08 | | | | % 8.78/2.08 | | | Case 2: % 8.78/2.08 | | | | % 8.78/2.08 | | | | (82) all_11_1 = 0 & all_11_2 = 0 & ~ (all_11_0 = 0) & % 8.78/2.08 | | | | subset(all_11_7, all_11_3) = 0 & subset(all_11_8, all_11_3) = 0 % 8.78/2.08 | | | | & subset(all_11_9, all_11_3) = all_11_0 % 8.78/2.08 | | | | % 8.78/2.08 | | | | ALPHA: (82) implies: % 8.78/2.08 | | | | (83) ~ (all_11_0 = 0) % 8.78/2.08 | | | | (84) subset(all_11_9, all_11_3) = all_11_0 % 8.78/2.08 | | | | (85) subset(all_11_8, all_11_3) = 0 % 8.78/2.08 | | | | (86) subset(all_11_7, all_11_3) = 0 % 8.78/2.08 | | | | % 8.78/2.08 | | | | GROUND_INST: instantiating (union_subset) with all_11_7, all_11_3, % 8.78/2.08 | | | | all_11_8, all_11_9, all_11_0, simplifying with (6), (7), % 8.78/2.08 | | | | (8), (72), (84) gives: % 8.78/2.08 | | | | (87) all_11_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_11_7, % 8.78/2.08 | | | | all_11_3) = v0 & subset(all_11_8, all_11_3) = v1 & ( ~ (v1 = % 8.78/2.08 | | | | 0) | ~ (v0 = 0))) % 8.78/2.08 | | | | % 8.78/2.08 | | | | BETA: splitting (87) gives: % 8.78/2.08 | | | | % 8.78/2.08 | | | | Case 1: % 8.78/2.08 | | | | | % 8.78/2.08 | | | | | (88) all_11_0 = 0 % 8.78/2.08 | | | | | % 8.78/2.08 | | | | | REDUCE: (83), (88) imply: % 8.78/2.08 | | | | | (89) $false % 8.78/2.08 | | | | | % 8.78/2.08 | | | | | CLOSE: (89) is inconsistent. % 8.78/2.08 | | | | | % 8.78/2.08 | | | | Case 2: % 8.78/2.08 | | | | | % 8.78/2.08 | | | | | (90) ? [v0: any] : ? [v1: any] : (subset(all_11_7, all_11_3) = v0 % 8.78/2.08 | | | | | & subset(all_11_8, all_11_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 8.78/2.08 | | | | | 0))) % 8.78/2.08 | | | | | % 8.78/2.08 | | | | | DELTA: instantiating (90) with fresh symbols all_55_0, all_55_1 gives: % 8.78/2.08 | | | | | (91) subset(all_11_7, all_11_3) = all_55_1 & subset(all_11_8, % 8.78/2.08 | | | | | all_11_3) = all_55_0 & ( ~ (all_55_0 = 0) | ~ (all_55_1 = % 8.78/2.08 | | | | | 0)) % 9.13/2.08 | | | | | % 9.13/2.08 | | | | | ALPHA: (91) implies: % 9.13/2.08 | | | | | (92) subset(all_11_8, all_11_3) = all_55_0 % 9.13/2.08 | | | | | (93) subset(all_11_7, all_11_3) = all_55_1 % 9.13/2.08 | | | | | (94) ~ (all_55_0 = 0) | ~ (all_55_1 = 0) % 9.13/2.08 | | | | | % 9.13/2.09 | | | | | GROUND_INST: instantiating (3) with 0, all_55_0, all_11_3, all_11_8, % 9.13/2.09 | | | | | simplifying with (85), (92) gives: % 9.13/2.09 | | | | | (95) all_55_0 = 0 % 9.13/2.09 | | | | | % 9.13/2.09 | | | | | GROUND_INST: instantiating (3) with 0, all_55_1, all_11_3, all_11_7, % 9.13/2.09 | | | | | simplifying with (86), (93) gives: % 9.13/2.09 | | | | | (96) all_55_1 = 0 % 9.13/2.09 | | | | | % 9.13/2.09 | | | | | BETA: splitting (94) gives: % 9.13/2.09 | | | | | % 9.13/2.09 | | | | | Case 1: % 9.13/2.09 | | | | | | % 9.13/2.09 | | | | | | (97) ~ (all_55_0 = 0) % 9.13/2.09 | | | | | | % 9.13/2.09 | | | | | | REDUCE: (95), (97) imply: % 9.13/2.09 | | | | | | (98) $false % 9.13/2.09 | | | | | | % 9.13/2.09 | | | | | | CLOSE: (98) is inconsistent. % 9.13/2.09 | | | | | | % 9.13/2.09 | | | | | Case 2: % 9.13/2.09 | | | | | | % 9.13/2.09 | | | | | | (99) ~ (all_55_1 = 0) % 9.13/2.09 | | | | | | % 9.13/2.09 | | | | | | REDUCE: (96), (99) imply: % 9.13/2.09 | | | | | | (100) $false % 9.13/2.09 | | | | | | % 9.13/2.09 | | | | | | CLOSE: (100) is inconsistent. % 9.13/2.09 | | | | | | % 9.13/2.09 | | | | | End of split % 9.13/2.09 | | | | | % 9.13/2.09 | | | | End of split % 9.13/2.09 | | | | % 9.13/2.09 | | | End of split % 9.13/2.09 | | | % 9.13/2.09 | | End of split % 9.13/2.09 | | % 9.13/2.09 | End of split % 9.13/2.09 | % 9.13/2.09 End of proof % 9.13/2.09 % SZS output end Proof for theBenchmark % 9.13/2.09 % 9.13/2.09 1461ms %------------------------------------------------------------------------------