%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU159+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.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 17:42:53 EDT 2023 % Result : Theorem 5.57s 1.53s % Output : Proof 6.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU159+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n019.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Wed Aug 23 13:06:44 EDT 2023 % 0.13/0.35 % 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 % 2.21/1.01 Prover 1: Preprocessing ... % 2.21/1.01 Prover 4: Preprocessing ... % 2.21/1.06 Prover 3: Preprocessing ... % 2.21/1.06 Prover 0: Preprocessing ... % 2.21/1.06 Prover 2: Preprocessing ... % 2.21/1.06 Prover 6: Preprocessing ... % 2.21/1.06 Prover 5: Preprocessing ... % 3.79/1.23 Prover 5: Proving ... % 3.79/1.23 Prover 6: Proving ... % 3.80/1.24 Prover 1: Warning: ignoring some quantifiers % 3.80/1.24 Prover 3: Warning: ignoring some quantifiers % 3.80/1.24 Prover 4: Warning: ignoring some quantifiers % 3.80/1.25 Prover 3: Constructing countermodel ... % 3.80/1.25 Prover 1: Constructing countermodel ... % 3.80/1.25 Prover 4: Constructing countermodel ... % 3.80/1.25 Prover 0: Proving ... % 3.80/1.26 Prover 2: Proving ... % 4.83/1.45 Prover 1: gave up % 4.83/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.83/1.47 Prover 3: gave up % 4.83/1.49 Prover 7: Preprocessing ... % 4.83/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.57/1.50 Prover 8: Preprocessing ... % 5.57/1.52 Prover 7: Warning: ignoring some quantifiers % 5.57/1.53 Prover 0: proved (904ms) % 5.57/1.53 % 5.57/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.57/1.53 % 5.57/1.54 Prover 2: stopped % 5.57/1.54 Prover 5: stopped % 5.57/1.54 Prover 7: Constructing countermodel ... % 5.57/1.54 Prover 6: stopped % 5.57/1.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.57/1.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.57/1.54 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 5.57/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.57/1.56 Prover 13: Preprocessing ... % 5.57/1.56 Prover 16: Preprocessing ... % 5.57/1.56 Prover 10: Preprocessing ... % 5.57/1.58 Prover 8: Warning: ignoring some quantifiers % 5.57/1.58 Prover 11: Preprocessing ... % 5.57/1.59 Prover 8: Constructing countermodel ... % 6.36/1.60 Prover 13: Warning: ignoring some quantifiers % 6.36/1.61 Prover 16: Warning: ignoring some quantifiers % 6.36/1.61 Prover 4: Found proof (size 51) % 6.36/1.61 Prover 4: proved (979ms) % 6.36/1.61 Prover 10: Warning: ignoring some quantifiers % 6.36/1.61 Prover 16: Constructing countermodel ... % 6.36/1.61 Prover 13: Constructing countermodel ... % 6.36/1.62 Prover 16: stopped % 6.36/1.62 Prover 13: stopped % 6.36/1.62 Prover 7: stopped % 6.36/1.62 Prover 8: stopped % 6.36/1.62 Prover 10: Constructing countermodel ... % 6.36/1.62 Prover 10: stopped % 6.36/1.64 Prover 11: Warning: ignoring some quantifiers % 6.36/1.64 Prover 11: Constructing countermodel ... % 6.36/1.65 Prover 11: stopped % 6.36/1.65 % 6.36/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.36/1.65 % 6.36/1.66 % SZS output start Proof for theBenchmark % 6.36/1.66 Assumptions after simplification: % 6.36/1.66 --------------------------------- % 6.36/1.66 % 6.36/1.66 (commutativity_k2_tarski) % 6.36/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | % 6.36/1.69 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i] % 6.36/1.69 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | % 6.36/1.69 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 6.36/1.69 % 6.36/1.69 (d2_tarski) % 6.36/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | % 6.36/1.69 ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 6.36/1.69 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 6.36/1.69 ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = % 6.36/1.69 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 6.36/1.70 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ % 6.36/1.70 (in(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! % 6.36/1.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = % 6.36/1.70 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : % 6.36/1.70 (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & % 6.36/1.70 (v5 = 0 | v4 = v2 | v4 = v1))) % 6.36/1.70 % 6.36/1.70 (d3_tarski) % 6.87/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 6.87/1.70 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 6.87/1.70 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 6.87/1.70 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 6.87/1.70 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 6.87/1.70 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 6.87/1.70 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 6.87/1.70 $i(v0) | in(v2, v1) = 0) % 6.87/1.70 % 6.87/1.70 (t38_zfmisc_1) % 6.87/1.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 6.87/1.70 any] : ? [v6: any] : (subset(v3, v2) = v4 & unordered_pair(v0, v1) = v3 & % 6.87/1.70 in(v1, v2) = v6 & in(v0, v2) = v5 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 % 6.87/1.70 = 0 & v5 = 0 & ~ (v4 = 0)) | (v4 = 0 & ( ~ (v6 = 0) | ~ (v5 = 0))))) % 6.87/1.70 % 6.87/1.70 (function-axioms) % 6.87/1.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 6.87/1.71 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 6.87/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.87/1.71 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 6.87/1.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 6.87/1.71 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 6.87/1.71 % 6.87/1.71 Further assumptions not needed in the proof: % 6.87/1.71 -------------------------------------------- % 6.87/1.71 antisymmetry_r2_hidden, dt_k2_tarski, reflexivity_r1_tarski % 6.87/1.71 % 6.87/1.71 Those formulas are unsatisfiable: % 6.87/1.71 --------------------------------- % 6.87/1.71 % 6.87/1.71 Begin of proof % 6.87/1.71 | % 6.87/1.71 | ALPHA: (commutativity_k2_tarski) implies: % 6.87/1.71 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 6.87/1.71 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & % 6.87/1.71 | $i(v2))) % 6.87/1.71 | % 6.87/1.71 | ALPHA: (d2_tarski) implies: % 6.87/1.71 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 6.87/1.71 | (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ $i(v2) | ~ % 6.87/1.71 | $i(v1) | ~ $i(v0)) % 6.87/1.71 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 6.87/1.71 | (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3) | ~ $i(v2) | ~ % 6.87/1.71 | $i(v1) | ~ $i(v0)) % 6.87/1.72 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = % 6.87/1.72 | v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ % 6.87/1.72 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 6.87/1.72 | % 6.87/1.72 | ALPHA: (d3_tarski) implies: % 6.87/1.72 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 6.87/1.72 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 6.87/1.72 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 6.87/1.72 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 6.87/1.72 | (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 6.87/1.72 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 6.87/1.72 | % 6.87/1.72 | ALPHA: (function-axioms) implies: % 6.87/1.72 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.87/1.72 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 6.87/1.72 | % 6.87/1.72 | DELTA: instantiating (t38_zfmisc_1) with fresh symbols all_10_0, all_10_1, % 6.87/1.72 | all_10_2, all_10_3, all_10_4, all_10_5, all_10_6 gives: % 6.87/1.72 | (8) subset(all_10_3, all_10_4) = all_10_2 & unordered_pair(all_10_6, % 6.87/1.72 | all_10_5) = all_10_3 & in(all_10_5, all_10_4) = all_10_0 & % 6.87/1.72 | in(all_10_6, all_10_4) = all_10_1 & $i(all_10_3) & $i(all_10_4) & % 6.87/1.72 | $i(all_10_5) & $i(all_10_6) & ((all_10_0 = 0 & all_10_1 = 0 & ~ % 6.87/1.72 | (all_10_2 = 0)) | (all_10_2 = 0 & ( ~ (all_10_0 = 0) | ~ (all_10_1 % 6.87/1.72 | = 0)))) % 6.87/1.72 | % 6.87/1.72 | ALPHA: (8) implies: % 6.87/1.72 | (9) $i(all_10_6) % 6.87/1.72 | (10) $i(all_10_5) % 6.87/1.72 | (11) $i(all_10_4) % 6.87/1.72 | (12) in(all_10_6, all_10_4) = all_10_1 % 6.87/1.72 | (13) in(all_10_5, all_10_4) = all_10_0 % 6.87/1.72 | (14) unordered_pair(all_10_6, all_10_5) = all_10_3 % 6.87/1.72 | (15) subset(all_10_3, all_10_4) = all_10_2 % 6.87/1.72 | (16) (all_10_0 = 0 & all_10_1 = 0 & ~ (all_10_2 = 0)) | (all_10_2 = 0 & ( % 6.87/1.72 | ~ (all_10_0 = 0) | ~ (all_10_1 = 0))) % 6.87/1.72 | % 6.87/1.73 | GROUND_INST: instantiating (1) with all_10_5, all_10_6, all_10_3, simplifying % 6.87/1.73 | with (9), (10), (14) gives: % 6.87/1.73 | (17) unordered_pair(all_10_5, all_10_6) = all_10_3 & $i(all_10_3) % 6.87/1.73 | % 6.87/1.73 | ALPHA: (17) implies: % 6.87/1.73 | (18) $i(all_10_3) % 6.87/1.73 | % 6.87/1.73 | GROUND_INST: instantiating (5) with all_10_3, all_10_4, all_10_2, simplifying % 6.87/1.73 | with (11), (15), (18) gives: % 6.87/1.73 | (19) all_10_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 6.87/1.73 | all_10_3) = 0 & in(v0, all_10_4) = v1 & $i(v0)) % 6.87/1.73 | % 6.87/1.73 | BETA: splitting (16) gives: % 6.87/1.73 | % 6.87/1.73 | Case 1: % 6.87/1.73 | | % 6.87/1.73 | | (20) all_10_0 = 0 & all_10_1 = 0 & ~ (all_10_2 = 0) % 6.87/1.73 | | % 6.87/1.73 | | ALPHA: (20) implies: % 6.87/1.73 | | (21) all_10_1 = 0 % 6.87/1.73 | | (22) all_10_0 = 0 % 6.87/1.73 | | (23) ~ (all_10_2 = 0) % 6.87/1.73 | | % 6.87/1.73 | | REDUCE: (13), (22) imply: % 6.87/1.73 | | (24) in(all_10_5, all_10_4) = 0 % 6.87/1.73 | | % 6.87/1.73 | | REDUCE: (12), (21) imply: % 6.87/1.73 | | (25) in(all_10_6, all_10_4) = 0 % 6.87/1.73 | | % 6.87/1.73 | | BETA: splitting (19) gives: % 6.87/1.73 | | % 6.87/1.73 | | Case 1: % 6.87/1.73 | | | % 6.87/1.73 | | | (26) all_10_2 = 0 % 6.87/1.73 | | | % 6.87/1.73 | | | REDUCE: (23), (26) imply: % 6.87/1.73 | | | (27) $false % 6.87/1.73 | | | % 6.87/1.73 | | | CLOSE: (27) is inconsistent. % 6.87/1.73 | | | % 6.87/1.73 | | Case 2: % 6.87/1.73 | | | % 6.87/1.73 | | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_10_3) = 0 & % 6.87/1.73 | | | in(v0, all_10_4) = v1 & $i(v0)) % 6.87/1.73 | | | % 6.87/1.73 | | | DELTA: instantiating (28) with fresh symbols all_29_0, all_29_1 gives: % 6.87/1.73 | | | (29) ~ (all_29_0 = 0) & in(all_29_1, all_10_3) = 0 & in(all_29_1, % 6.87/1.73 | | | all_10_4) = all_29_0 & $i(all_29_1) % 6.87/1.73 | | | % 6.87/1.73 | | | ALPHA: (29) implies: % 6.87/1.73 | | | (30) ~ (all_29_0 = 0) % 6.87/1.73 | | | (31) $i(all_29_1) % 6.87/1.73 | | | (32) in(all_29_1, all_10_4) = all_29_0 % 6.87/1.73 | | | (33) in(all_29_1, all_10_3) = 0 % 6.87/1.73 | | | % 6.87/1.74 | | | GROUND_INST: instantiating (4) with all_10_6, all_10_5, all_10_3, % 6.87/1.74 | | | all_29_1, simplifying with (9), (10), (14), (18), (31), (33) % 6.87/1.74 | | | gives: % 6.87/1.74 | | | (34) all_29_1 = all_10_5 | all_29_1 = all_10_6 % 6.87/1.74 | | | % 6.87/1.74 | | | BETA: splitting (34) gives: % 6.87/1.74 | | | % 6.87/1.74 | | | Case 1: % 6.87/1.74 | | | | % 6.87/1.74 | | | | (35) all_29_1 = all_10_5 % 6.87/1.74 | | | | % 6.87/1.74 | | | | REDUCE: (32), (35) imply: % 6.87/1.74 | | | | (36) in(all_10_5, all_10_4) = all_29_0 % 6.87/1.74 | | | | % 6.87/1.74 | | | | GROUND_INST: instantiating (7) with 0, all_29_0, all_10_4, all_10_5, % 6.87/1.74 | | | | simplifying with (24), (36) gives: % 6.87/1.74 | | | | (37) all_29_0 = 0 % 6.87/1.74 | | | | % 6.87/1.74 | | | | REDUCE: (30), (37) imply: % 6.87/1.74 | | | | (38) $false % 6.87/1.74 | | | | % 6.87/1.74 | | | | CLOSE: (38) is inconsistent. % 6.87/1.74 | | | | % 6.87/1.74 | | | Case 2: % 6.87/1.74 | | | | % 6.87/1.74 | | | | (39) all_29_1 = all_10_6 % 6.87/1.74 | | | | % 6.87/1.74 | | | | REDUCE: (32), (39) imply: % 6.87/1.74 | | | | (40) in(all_10_6, all_10_4) = all_29_0 % 6.87/1.74 | | | | % 6.87/1.74 | | | | GROUND_INST: instantiating (7) with 0, all_29_0, all_10_4, all_10_6, % 6.87/1.74 | | | | simplifying with (25), (40) gives: % 6.87/1.74 | | | | (41) all_29_0 = 0 % 6.87/1.74 | | | | % 6.87/1.74 | | | | REDUCE: (30), (41) imply: % 6.87/1.74 | | | | (42) $false % 6.87/1.74 | | | | % 6.87/1.74 | | | | CLOSE: (42) is inconsistent. % 6.87/1.74 | | | | % 6.87/1.74 | | | End of split % 6.87/1.74 | | | % 6.87/1.74 | | End of split % 6.87/1.74 | | % 6.87/1.74 | Case 2: % 6.87/1.74 | | % 6.87/1.74 | | (43) all_10_2 = 0 & ( ~ (all_10_0 = 0) | ~ (all_10_1 = 0)) % 6.87/1.74 | | % 6.87/1.74 | | ALPHA: (43) implies: % 6.87/1.74 | | (44) all_10_2 = 0 % 6.87/1.74 | | (45) ~ (all_10_0 = 0) | ~ (all_10_1 = 0) % 6.87/1.74 | | % 6.87/1.74 | | REDUCE: (15), (44) imply: % 6.87/1.74 | | (46) subset(all_10_3, all_10_4) = 0 % 6.87/1.74 | | % 6.87/1.74 | | GROUND_INST: instantiating (6) with all_10_3, all_10_4, all_10_5, all_10_0, % 6.87/1.74 | | simplifying with (10), (11), (13), (18), (46) gives: % 6.87/1.74 | | (47) all_10_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_10_5, all_10_3) % 6.87/1.74 | | = v0) % 6.87/1.74 | | % 6.87/1.74 | | GROUND_INST: instantiating (6) with all_10_3, all_10_4, all_10_6, all_10_1, % 6.87/1.74 | | simplifying with (9), (11), (12), (18), (46) gives: % 6.87/1.74 | | (48) all_10_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_10_6, all_10_3) % 6.87/1.74 | | = v0) % 6.87/1.74 | | % 6.87/1.74 | | BETA: splitting (45) gives: % 6.87/1.74 | | % 6.87/1.74 | | Case 1: % 6.87/1.74 | | | % 6.87/1.74 | | | (49) ~ (all_10_0 = 0) % 6.87/1.74 | | | % 6.87/1.74 | | | BETA: splitting (47) gives: % 6.87/1.74 | | | % 6.87/1.74 | | | Case 1: % 6.87/1.74 | | | | % 6.87/1.74 | | | | (50) all_10_0 = 0 % 6.87/1.74 | | | | % 6.87/1.74 | | | | REDUCE: (49), (50) imply: % 6.87/1.74 | | | | (51) $false % 6.87/1.74 | | | | % 6.87/1.74 | | | | CLOSE: (51) is inconsistent. % 6.87/1.74 | | | | % 6.87/1.74 | | | Case 2: % 6.87/1.74 | | | | % 6.87/1.74 | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & in(all_10_5, all_10_3) = v0) % 6.87/1.74 | | | | % 6.87/1.74 | | | | DELTA: instantiating (52) with fresh symbol all_50_0 gives: % 6.87/1.74 | | | | (53) ~ (all_50_0 = 0) & in(all_10_5, all_10_3) = all_50_0 % 6.87/1.74 | | | | % 6.87/1.74 | | | | ALPHA: (53) implies: % 6.87/1.74 | | | | (54) ~ (all_50_0 = 0) % 6.87/1.75 | | | | (55) in(all_10_5, all_10_3) = all_50_0 % 6.87/1.75 | | | | % 6.87/1.75 | | | | GROUND_INST: instantiating (3) with all_10_6, all_10_5, all_10_3, % 6.87/1.75 | | | | all_50_0, simplifying with (9), (10), (14), (18), (55) % 6.87/1.75 | | | | gives: % 6.87/1.75 | | | | (56) all_50_0 = 0 % 6.87/1.75 | | | | % 6.87/1.75 | | | | REDUCE: (54), (56) imply: % 6.87/1.75 | | | | (57) $false % 6.87/1.75 | | | | % 6.87/1.75 | | | | CLOSE: (57) is inconsistent. % 6.87/1.75 | | | | % 6.87/1.75 | | | End of split % 6.87/1.75 | | | % 6.87/1.75 | | Case 2: % 6.87/1.75 | | | % 6.87/1.75 | | | (58) ~ (all_10_1 = 0) % 6.87/1.75 | | | % 6.87/1.75 | | | BETA: splitting (48) gives: % 6.87/1.75 | | | % 6.87/1.75 | | | Case 1: % 6.87/1.75 | | | | % 6.87/1.75 | | | | (59) all_10_1 = 0 % 6.87/1.75 | | | | % 6.87/1.75 | | | | REDUCE: (58), (59) imply: % 6.87/1.75 | | | | (60) $false % 6.87/1.75 | | | | % 6.87/1.75 | | | | CLOSE: (60) is inconsistent. % 6.87/1.75 | | | | % 6.87/1.75 | | | Case 2: % 6.87/1.75 | | | | % 6.87/1.75 | | | | (61) ? [v0: int] : ( ~ (v0 = 0) & in(all_10_6, all_10_3) = v0) % 6.87/1.75 | | | | % 6.87/1.75 | | | | DELTA: instantiating (61) with fresh symbol all_50_0 gives: % 6.87/1.75 | | | | (62) ~ (all_50_0 = 0) & in(all_10_6, all_10_3) = all_50_0 % 6.87/1.75 | | | | % 6.87/1.75 | | | | ALPHA: (62) implies: % 6.87/1.75 | | | | (63) ~ (all_50_0 = 0) % 6.87/1.75 | | | | (64) in(all_10_6, all_10_3) = all_50_0 % 6.87/1.75 | | | | % 6.87/1.75 | | | | GROUND_INST: instantiating (2) with all_10_6, all_10_5, all_10_3, % 6.87/1.75 | | | | all_50_0, simplifying with (9), (10), (14), (18), (64) % 6.87/1.75 | | | | gives: % 6.87/1.75 | | | | (65) all_50_0 = 0 % 6.87/1.75 | | | | % 6.87/1.75 | | | | REDUCE: (63), (65) imply: % 6.87/1.75 | | | | (66) $false % 6.87/1.75 | | | | % 6.87/1.75 | | | | CLOSE: (66) is inconsistent. % 6.87/1.75 | | | | % 6.87/1.75 | | | End of split % 6.87/1.75 | | | % 6.87/1.75 | | End of split % 6.87/1.75 | | % 6.87/1.75 | End of split % 6.87/1.75 | % 6.87/1.75 End of proof % 6.87/1.75 % SZS output end Proof for theBenchmark % 6.87/1.75 % 6.87/1.75 1140ms %------------------------------------------------------------------------------