%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU156+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 : n008.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 17:42:51 EDT 2023 % Result : Theorem 8.31s 1.87s % Output : Proof 21.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU156+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n008.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 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 19:58:47 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.12/1.02 Prover 4: Preprocessing ... % 2.12/1.02 Prover 1: Preprocessing ... % 2.12/1.06 Prover 5: Preprocessing ... % 2.12/1.06 Prover 6: Preprocessing ... % 2.12/1.06 Prover 2: Preprocessing ... % 2.12/1.06 Prover 3: Preprocessing ... % 2.12/1.06 Prover 0: Preprocessing ... % 3.53/1.23 Prover 1: Warning: ignoring some quantifiers % 3.53/1.24 Prover 5: Proving ... % 3.53/1.24 Prover 3: Warning: ignoring some quantifiers % 3.53/1.24 Prover 6: Proving ... % 3.53/1.25 Prover 1: Constructing countermodel ... % 3.53/1.25 Prover 3: Constructing countermodel ... % 3.53/1.26 Prover 4: Constructing countermodel ... % 3.53/1.27 Prover 0: Proving ... % 3.53/1.28 Prover 2: Proving ... % 3.53/1.39 Prover 3: gave up % 3.53/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.53/1.40 Prover 6: gave up % 3.53/1.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.53/1.42 Prover 1: gave up % 3.53/1.43 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 3.53/1.44 Prover 7: Preprocessing ... % 3.53/1.45 Prover 9: Preprocessing ... % 3.53/1.45 Prover 8: Preprocessing ... % 4.62/1.50 Prover 7: Warning: ignoring some quantifiers % 4.62/1.51 Prover 7: Constructing countermodel ... % 4.62/1.52 Prover 8: Warning: ignoring some quantifiers % 4.62/1.53 Prover 8: Constructing countermodel ... % 4.62/1.55 Prover 9: Warning: ignoring some quantifiers % 4.62/1.55 Prover 9: Constructing countermodel ... % 6.79/1.67 Prover 8: gave up % 6.79/1.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.03/1.72 Prover 10: Preprocessing ... % 7.30/1.76 Prover 10: Warning: ignoring some quantifiers % 7.30/1.76 Prover 10: Constructing countermodel ... % 7.30/1.80 Prover 10: gave up % 7.30/1.80 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.81/1.81 Prover 11: Preprocessing ... % 7.81/1.86 Prover 5: proved (1214ms) % 8.31/1.87 % 8.31/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.31/1.87 % 8.31/1.87 Prover 9: stopped % 8.31/1.87 Prover 2: stopped % 8.31/1.87 Prover 0: stopped % 8.31/1.88 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.31/1.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.31/1.88 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.31/1.88 Prover 16: Preprocessing ... % 8.31/1.88 Prover 13: Preprocessing ... % 8.31/1.89 Prover 19: Preprocessing ... % 8.31/1.89 Prover 11: Constructing countermodel ... % 8.31/1.93 Prover 16: Warning: ignoring some quantifiers % 8.31/1.93 Prover 16: Constructing countermodel ... % 8.31/1.94 Prover 19: Warning: ignoring some quantifiers % 8.31/1.95 Prover 19: Constructing countermodel ... % 8.31/1.95 Prover 13: Warning: ignoring some quantifiers % 8.31/1.95 Prover 13: Constructing countermodel ... % 9.21/2.00 Prover 13: gave up % 9.21/2.01 Prover 19: gave up % 9.48/2.12 Prover 16: gave up % 20.99/3.86 Prover 4: Found proof (size 109) % 20.99/3.86 Prover 4: proved (3220ms) % 20.99/3.86 Prover 7: stopped % 20.99/3.86 Prover 11: stopped % 20.99/3.86 % 20.99/3.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.99/3.86 % 20.99/3.89 % SZS output start Proof for theBenchmark % 20.99/3.89 Assumptions after simplification: % 20.99/3.89 --------------------------------- % 20.99/3.90 % 20.99/3.90 (commutativity_k2_tarski) % 21.42/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | % 21.42/3.93 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i] % 21.42/3.93 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | % 21.42/3.93 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 21.42/3.93 % 21.42/3.93 (d5_tarski) % 21.42/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 21.42/3.93 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (singleton(v0) = v4 & % 21.42/3.93 unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3 & $i(v4) & % 21.42/3.93 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 21.42/3.93 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 21.42/3.93 [v4: $i] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & % 21.42/3.93 unordered_pair(v2, v4) = v3 & $i(v4) & $i(v3))) % 21.42/3.93 % 21.42/3.93 (t10_zfmisc_1) % 21.42/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 % 21.42/3.94 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = % 21.42/3.94 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 21.42/3.94 % 21.42/3.94 (t33_zfmisc_1) % 21.42/3.94 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 21.42/3.94 (ordered_pair(v2, v3) = v4 & ordered_pair(v0, v1) = v4 & $i(v4) & $i(v3) & % 21.42/3.94 $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = v1) | ~ (v2 = v0))) % 21.42/3.94 % 21.42/3.94 (t69_enumset1) % 21.42/3.94 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 21.42/3.94 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.42/3.94 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1))) % 21.42/3.94 % 21.42/3.94 (t8_zfmisc_1) % 21.42/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.42/3.94 (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ % 21.42/3.94 $i(v1) | ~ $i(v0)) % 21.42/3.94 % 21.42/3.94 (t9_zfmisc_1) % 21.42/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 21.42/3.94 (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ % 21.42/3.94 $i(v1) | ~ $i(v0)) % 21.42/3.94 % 21.42/3.94 (function-axioms) % 21.42/3.95 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 21.42/3.95 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 21.42/3.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.42/3.95 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 21.42/3.95 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, % 21.42/3.95 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 21.42/3.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 21.42/3.95 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 21.42/3.95 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 21.42/3.95 % 21.42/3.95 Further assumptions not needed in the proof: % 21.42/3.95 -------------------------------------------- % 21.42/3.95 dt_k1_tarski, dt_k2_tarski, dt_k4_tarski, fc1_zfmisc_1, rc1_xboole_0, % 21.42/3.95 rc2_xboole_0, reflexivity_r1_tarski, t6_zfmisc_1 % 21.42/3.95 % 21.42/3.95 Those formulas are unsatisfiable: % 21.42/3.95 --------------------------------- % 21.42/3.95 % 21.42/3.95 Begin of proof % 21.42/3.95 | % 21.42/3.95 | ALPHA: (commutativity_k2_tarski) implies: % 21.42/3.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 21.42/3.95 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & % 21.42/3.95 | $i(v2))) % 21.42/3.95 | % 21.42/3.95 | ALPHA: (d5_tarski) implies: % 21.42/3.95 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 21.42/3.95 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 21.42/3.95 | (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & unordered_pair(v2, % 21.42/3.95 | v4) = v3 & $i(v4) & $i(v3))) % 21.42/3.95 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 21.42/3.95 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 21.42/3.95 | (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & % 21.42/3.95 | unordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) & $i(v2))) % 21.42/3.95 | % 21.42/3.95 | ALPHA: (t69_enumset1) implies: % 21.42/3.96 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 21.42/3.96 | (unordered_pair(v0, v0) = v1 & $i(v1))) % 21.42/3.96 | % 21.42/3.96 | ALPHA: (function-axioms) implies: % 21.42/3.96 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 21.42/3.96 | = v1) | ~ (singleton(v2) = v0)) % 21.42/3.96 | % 21.42/3.96 | DELTA: instantiating (t33_zfmisc_1) with fresh symbols all_16_0, all_16_1, % 21.42/3.96 | all_16_2, all_16_3, all_16_4 gives: % 21.42/3.96 | (6) ordered_pair(all_16_2, all_16_1) = all_16_0 & ordered_pair(all_16_4, % 21.42/3.96 | all_16_3) = all_16_0 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & % 21.42/3.96 | $i(all_16_3) & $i(all_16_4) & ( ~ (all_16_1 = all_16_3) | ~ (all_16_2 % 21.42/3.96 | = all_16_4)) % 21.42/3.96 | % 21.42/3.96 | ALPHA: (6) implies: % 21.42/3.96 | (7) $i(all_16_4) % 21.42/3.96 | (8) $i(all_16_3) % 21.42/3.96 | (9) $i(all_16_2) % 21.42/3.96 | (10) $i(all_16_1) % 21.42/3.96 | (11) ordered_pair(all_16_4, all_16_3) = all_16_0 % 21.42/3.96 | (12) ordered_pair(all_16_2, all_16_1) = all_16_0 % 21.42/3.96 | (13) ~ (all_16_1 = all_16_3) | ~ (all_16_2 = all_16_4) % 21.42/3.96 | % 21.42/3.96 | GROUND_INST: instantiating (3) with all_16_4, all_16_3, all_16_0, simplifying % 21.42/3.96 | with (7), (8), (11) gives: % 21.42/3.96 | (14) ? [v0: $i] : ? [v1: $i] : (singleton(all_16_4) = v1 & % 21.42/3.96 | unordered_pair(v0, v1) = all_16_0 & unordered_pair(all_16_4, % 21.42/3.96 | all_16_3) = v0 & $i(v1) & $i(v0) & $i(all_16_0)) % 21.42/3.96 | % 21.42/3.96 | GROUND_INST: instantiating (3) with all_16_2, all_16_1, all_16_0, simplifying % 21.42/3.96 | with (9), (10), (12) gives: % 21.42/3.96 | (15) ? [v0: $i] : ? [v1: $i] : (singleton(all_16_2) = v1 & % 21.42/3.96 | unordered_pair(v0, v1) = all_16_0 & unordered_pair(all_16_2, % 21.42/3.96 | all_16_1) = v0 & $i(v1) & $i(v0) & $i(all_16_0)) % 21.42/3.96 | % 21.42/3.96 | DELTA: instantiating (14) with fresh symbols all_25_0, all_25_1 gives: % 21.42/3.96 | (16) singleton(all_16_4) = all_25_0 & unordered_pair(all_25_1, all_25_0) = % 21.42/3.96 | all_16_0 & unordered_pair(all_16_4, all_16_3) = all_25_1 & % 21.42/3.96 | $i(all_25_0) & $i(all_25_1) & $i(all_16_0) % 21.42/3.96 | % 21.42/3.96 | ALPHA: (16) implies: % 21.42/3.97 | (17) $i(all_25_0) % 21.42/3.97 | (18) unordered_pair(all_16_4, all_16_3) = all_25_1 % 21.42/3.97 | (19) unordered_pair(all_25_1, all_25_0) = all_16_0 % 21.42/3.97 | (20) singleton(all_16_4) = all_25_0 % 21.42/3.97 | % 21.42/3.97 | DELTA: instantiating (15) with fresh symbols all_27_0, all_27_1 gives: % 21.42/3.97 | (21) singleton(all_16_2) = all_27_0 & unordered_pair(all_27_1, all_27_0) = % 21.42/3.97 | all_16_0 & unordered_pair(all_16_2, all_16_1) = all_27_1 & % 21.42/3.97 | $i(all_27_0) & $i(all_27_1) & $i(all_16_0) % 21.42/3.97 | % 21.42/3.97 | ALPHA: (21) implies: % 21.42/3.97 | (22) $i(all_27_0) % 21.42/3.97 | (23) unordered_pair(all_16_2, all_16_1) = all_27_1 % 21.42/3.97 | (24) unordered_pair(all_27_1, all_27_0) = all_16_0 % 21.42/3.97 | (25) singleton(all_16_2) = all_27_0 % 21.42/3.97 | % 21.42/3.97 | GROUND_INST: instantiating (1) with all_16_3, all_16_4, all_25_1, simplifying % 21.42/3.97 | with (7), (8), (18) gives: % 21.42/3.97 | (26) unordered_pair(all_16_3, all_16_4) = all_25_1 & $i(all_25_1) % 21.42/3.97 | % 21.42/3.97 | ALPHA: (26) implies: % 21.42/3.97 | (27) $i(all_25_1) % 21.42/3.97 | (28) unordered_pair(all_16_3, all_16_4) = all_25_1 % 21.42/3.97 | % 21.42/3.97 | GROUND_INST: instantiating (1) with all_16_1, all_16_2, all_27_1, simplifying % 21.42/3.97 | with (9), (10), (23) gives: % 21.42/3.97 | (29) unordered_pair(all_16_1, all_16_2) = all_27_1 & $i(all_27_1) % 21.42/3.97 | % 21.42/3.97 | ALPHA: (29) implies: % 21.42/3.97 | (30) $i(all_27_1) % 21.42/3.97 | (31) unordered_pair(all_16_1, all_16_2) = all_27_1 % 21.42/3.97 | % 21.42/3.97 | GROUND_INST: instantiating (1) with all_25_0, all_25_1, all_16_0, simplifying % 21.42/3.97 | with (17), (19), (27) gives: % 21.42/3.97 | (32) unordered_pair(all_25_0, all_25_1) = all_16_0 & $i(all_16_0) % 21.42/3.97 | % 21.42/3.97 | ALPHA: (32) implies: % 21.42/3.97 | (33) unordered_pair(all_25_0, all_25_1) = all_16_0 % 21.42/3.97 | % 21.42/3.97 | GROUND_INST: instantiating (1) with all_27_0, all_27_1, all_16_0, simplifying % 21.42/3.97 | with (22), (24), (30) gives: % 21.42/3.97 | (34) unordered_pair(all_27_0, all_27_1) = all_16_0 & $i(all_16_0) % 21.42/3.97 | % 21.42/3.97 | ALPHA: (34) implies: % 21.42/3.97 | (35) unordered_pair(all_27_0, all_27_1) = all_16_0 % 21.42/3.97 | % 21.42/3.97 | GROUND_INST: instantiating (4) with all_16_4, all_25_0, simplifying with (7), % 21.42/3.97 | (20) gives: % 21.42/3.97 | (36) unordered_pair(all_16_4, all_16_4) = all_25_0 & $i(all_25_0) % 21.42/3.97 | % 21.42/3.97 | ALPHA: (36) implies: % 21.42/3.97 | (37) unordered_pair(all_16_4, all_16_4) = all_25_0 % 21.42/3.97 | % 21.42/3.97 | GROUND_INST: instantiating (4) with all_16_2, all_27_0, simplifying with (9), % 21.42/3.97 | (25) gives: % 21.42/3.97 | (38) unordered_pair(all_16_2, all_16_2) = all_27_0 & $i(all_27_0) % 21.42/3.97 | % 21.42/3.97 | ALPHA: (38) implies: % 21.42/3.97 | (39) unordered_pair(all_16_2, all_16_2) = all_27_0 % 21.42/3.97 | % 21.42/3.97 | GROUND_INST: instantiating (2) with all_16_4, all_16_4, all_25_0, simplifying % 21.42/3.97 | with (7), (37) gives: % 21.42/3.97 | (40) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_16_4, all_16_4) = v0 & % 21.42/3.97 | singleton(all_16_4) = v1 & unordered_pair(all_25_0, v1) = v0 & % 21.42/3.97 | $i(v1) & $i(v0)) % 21.42/3.97 | % 21.42/3.97 | GROUND_INST: instantiating (2) with all_16_2, all_16_2, all_27_0, simplifying % 21.42/3.97 | with (9), (39) gives: % 21.42/3.97 | (41) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_16_2, all_16_2) = v0 & % 21.42/3.97 | singleton(all_16_2) = v1 & unordered_pair(all_27_0, v1) = v0 & % 21.42/3.97 | $i(v1) & $i(v0)) % 21.42/3.97 | % 21.42/3.98 | GROUND_INST: instantiating (t10_zfmisc_1) with all_27_1, all_27_0, all_25_0, % 21.42/3.98 | all_25_1, all_16_0, simplifying with (17), (22), (24), (27), % 21.42/3.98 | (30), (33) gives: % 21.42/3.98 | (42) all_27_1 = all_25_0 | all_27_1 = all_25_1 % 21.42/3.98 | % 21.42/3.98 | GROUND_INST: instantiating (t10_zfmisc_1) with all_25_1, all_25_0, all_27_0, % 21.42/3.98 | all_27_1, all_16_0, simplifying with (17), (19), (22), (27), % 21.42/3.98 | (30), (35) gives: % 21.42/3.98 | (43) all_27_0 = all_25_1 | all_27_1 = all_25_1 % 21.42/3.98 | % 21.42/3.98 | GROUND_INST: instantiating (t10_zfmisc_1) with all_25_0, all_25_1, all_27_0, % 21.42/3.98 | all_27_1, all_16_0, simplifying with (17), (22), (27), (30), % 21.42/3.98 | (33), (35) gives: % 21.42/3.98 | (44) all_27_0 = all_25_0 | all_27_1 = all_25_0 % 21.42/3.98 | % 21.42/3.98 | GROUND_INST: instantiating (t10_zfmisc_1) with all_27_0, all_27_1, all_25_0, % 21.42/3.98 | all_25_1, all_16_0, simplifying with (17), (22), (27), (30), % 21.42/3.98 | (33), (35) gives: % 21.42/3.98 | (45) all_27_0 = all_25_0 | all_27_0 = all_25_1 % 21.42/3.98 | % 21.42/3.98 | DELTA: instantiating (41) with fresh symbols all_53_0, all_53_1 gives: % 21.67/3.98 | (46) ordered_pair(all_16_2, all_16_2) = all_53_1 & singleton(all_16_2) = % 21.67/3.98 | all_53_0 & unordered_pair(all_27_0, all_53_0) = all_53_1 & % 21.67/3.98 | $i(all_53_0) & $i(all_53_1) % 21.67/3.98 | % 21.67/3.98 | ALPHA: (46) implies: % 21.67/3.98 | (47) singleton(all_16_2) = all_53_0 % 21.67/3.98 | % 21.67/3.98 | DELTA: instantiating (40) with fresh symbols all_57_0, all_57_1 gives: % 21.67/3.98 | (48) ordered_pair(all_16_4, all_16_4) = all_57_1 & singleton(all_16_4) = % 21.67/3.98 | all_57_0 & unordered_pair(all_25_0, all_57_0) = all_57_1 & % 21.67/3.98 | $i(all_57_0) & $i(all_57_1) % 21.67/3.98 | % 21.67/3.98 | ALPHA: (48) implies: % 21.67/3.98 | (49) singleton(all_16_4) = all_57_0 % 21.67/3.98 | % 21.67/3.98 | GROUND_INST: instantiating (5) with all_25_0, all_57_0, all_16_4, simplifying % 21.67/3.98 | with (20), (49) gives: % 21.67/3.98 | (50) all_57_0 = all_25_0 % 21.67/3.98 | % 21.67/3.98 | GROUND_INST: instantiating (5) with all_27_0, all_53_0, all_16_2, simplifying % 21.67/3.98 | with (25), (47) gives: % 21.67/3.98 | (51) all_53_0 = all_27_0 % 21.67/3.98 | % 21.67/3.98 | BETA: splitting (13) gives: % 21.67/3.98 | % 21.67/3.98 | Case 1: % 21.67/3.98 | | % 21.67/3.98 | | (52) ~ (all_16_1 = all_16_3) % 21.67/3.98 | | % 21.67/3.98 | | BETA: splitting (42) gives: % 21.67/3.98 | | % 21.67/3.98 | | Case 1: % 21.67/3.98 | | | % 21.67/3.98 | | | (53) all_27_1 = all_25_0 % 21.67/3.98 | | | % 21.67/3.98 | | | REDUCE: (31), (53) imply: % 21.67/3.98 | | | (54) unordered_pair(all_16_1, all_16_2) = all_25_0 % 21.67/3.98 | | | % 21.67/3.98 | | | BETA: splitting (43) gives: % 21.67/3.98 | | | % 21.67/3.98 | | | Case 1: % 21.67/3.98 | | | | % 21.67/3.98 | | | | (55) all_27_0 = all_25_1 % 21.67/3.98 | | | | % 21.67/3.98 | | | | REDUCE: (25), (55) imply: % 21.67/3.98 | | | | (56) singleton(all_16_2) = all_25_1 % 21.67/3.98 | | | | % 21.67/3.98 | | | | GROUND_INST: instantiating (t9_zfmisc_1) with all_16_4, all_16_1, % 21.67/3.98 | | | | all_16_2, all_25_0, simplifying with (7), (9), (10), (20), % 21.67/3.98 | | | | (54) gives: % 21.67/3.98 | | | | (57) all_16_1 = all_16_2 % 21.67/3.98 | | | | % 21.67/3.98 | | | | GROUND_INST: instantiating (t8_zfmisc_1) with all_16_4, all_16_1, % 21.67/3.98 | | | | all_16_2, all_25_0, simplifying with (7), (9), (10), (20), % 21.67/3.98 | | | | (54) gives: % 21.67/3.98 | | | | (58) all_16_1 = all_16_4 % 21.67/3.98 | | | | % 21.67/3.99 | | | | GROUND_INST: instantiating (t8_zfmisc_1) with all_16_2, all_16_3, % 21.67/3.99 | | | | all_16_4, all_25_1, simplifying with (7), (8), (9), (28), % 21.67/3.99 | | | | (56) gives: % 21.67/3.99 | | | | (59) all_16_2 = all_16_3 % 21.67/3.99 | | | | % 21.67/3.99 | | | | COMBINE_EQS: (57), (58) imply: % 21.67/3.99 | | | | (60) all_16_2 = all_16_4 % 21.67/3.99 | | | | % 21.67/3.99 | | | | SIMP: (60) implies: % 21.67/3.99 | | | | (61) all_16_2 = all_16_4 % 21.67/3.99 | | | | % 21.67/3.99 | | | | COMBINE_EQS: (59), (61) imply: % 21.67/3.99 | | | | (62) all_16_3 = all_16_4 % 21.67/3.99 | | | | % 21.67/3.99 | | | | SIMP: (62) implies: % 21.67/3.99 | | | | (63) all_16_3 = all_16_4 % 21.67/3.99 | | | | % 21.67/3.99 | | | | REDUCE: (52), (58), (63) imply: % 21.67/3.99 | | | | (64) $false % 21.67/3.99 | | | | % 21.67/3.99 | | | | CLOSE: (64) is inconsistent. % 21.67/3.99 | | | | % 21.67/3.99 | | | Case 2: % 21.67/3.99 | | | | % 21.67/3.99 | | | | (65) all_27_1 = all_25_1 % 21.67/3.99 | | | | (66) ~ (all_27_0 = all_25_1) % 21.67/3.99 | | | | % 21.67/3.99 | | | | COMBINE_EQS: (53), (65) imply: % 21.67/3.99 | | | | (67) all_25_0 = all_25_1 % 21.67/3.99 | | | | % 21.67/3.99 | | | | REF_CLOSE: (45), (66), (67) are inconsistent by sub-proof #1. % 21.67/3.99 | | | | % 21.67/3.99 | | | End of split % 21.67/3.99 | | | % 21.67/3.99 | | Case 2: % 21.67/3.99 | | | % 21.67/3.99 | | | (68) all_27_1 = all_25_1 % 21.67/3.99 | | | (69) ~ (all_27_1 = all_25_0) % 21.67/3.99 | | | % 21.67/3.99 | | | REDUCE: (68), (69) imply: % 21.67/3.99 | | | (70) ~ (all_25_0 = all_25_1) % 21.67/3.99 | | | % 21.67/3.99 | | | SIMP: (70) implies: % 21.67/3.99 | | | (71) ~ (all_25_0 = all_25_1) % 21.67/3.99 | | | % 21.67/3.99 | | | REDUCE: (31), (68) imply: % 21.67/3.99 | | | (72) unordered_pair(all_16_1, all_16_2) = all_25_1 % 21.67/3.99 | | | % 21.67/3.99 | | | BETA: splitting (44) gives: % 21.67/3.99 | | | % 21.67/3.99 | | | Case 1: % 21.67/3.99 | | | | % 21.67/3.99 | | | | (73) all_27_0 = all_25_0 % 21.67/3.99 | | | | % 21.67/3.99 | | | | REDUCE: (25), (73) imply: % 21.67/3.99 | | | | (74) singleton(all_16_2) = all_25_0 % 21.67/3.99 | | | | % 21.67/3.99 | | | | GROUND_INST: instantiating (t10_zfmisc_1) with all_16_3, all_16_4, % 21.67/3.99 | | | | all_16_1, all_16_2, all_25_1, simplifying with (7), (8), % 21.67/3.99 | | | | (9), (10), (28), (72) gives: % 21.67/3.99 | | | | (75) all_16_1 = all_16_3 | all_16_2 = all_16_3 % 21.67/3.99 | | | | % 21.67/3.99 | | | | GROUND_INST: instantiating (t10_zfmisc_1) with all_16_1, all_16_2, % 21.67/3.99 | | | | all_16_4, all_16_3, all_25_1, simplifying with (7), (8), % 21.67/3.99 | | | | (9), (10), (18), (72) gives: % 21.67/3.99 | | | | (76) all_16_1 = all_16_3 | all_16_1 = all_16_4 % 21.67/3.99 | | | | % 21.67/3.99 | | | | GROUND_INST: instantiating (t8_zfmisc_1) with all_16_2, all_16_4, % 21.67/3.99 | | | | all_16_4, all_25_0, simplifying with (7), (9), (37), (74) % 21.67/3.99 | | | | gives: % 21.67/3.99 | | | | (77) all_16_2 = all_16_4 % 21.67/3.99 | | | | % 21.67/3.99 | | | | BETA: splitting (75) gives: % 21.67/3.99 | | | | % 21.67/3.99 | | | | Case 1: % 21.67/3.99 | | | | | % 21.67/3.99 | | | | | (78) all_16_1 = all_16_3 % 21.67/3.99 | | | | | % 21.67/3.99 | | | | | REDUCE: (52), (78) imply: % 21.67/3.99 | | | | | (79) $false % 21.67/3.99 | | | | | % 21.67/3.99 | | | | | CLOSE: (79) is inconsistent. % 21.67/3.99 | | | | | % 21.67/3.99 | | | | Case 2: % 21.67/3.99 | | | | | % 21.67/3.99 | | | | | (80) all_16_2 = all_16_3 % 21.67/3.99 | | | | | % 21.67/3.99 | | | | | COMBINE_EQS: (77), (80) imply: % 21.67/3.99 | | | | | (81) all_16_3 = all_16_4 % 21.67/3.99 | | | | | % 21.67/3.99 | | | | | SIMP: (81) implies: % 21.67/3.99 | | | | | (82) all_16_3 = all_16_4 % 21.67/3.99 | | | | | % 21.67/3.99 | | | | | REDUCE: (52), (82) imply: % 21.67/3.99 | | | | | (83) ~ (all_16_1 = all_16_4) % 21.67/3.99 | | | | | % 21.67/3.99 | | | | | BETA: splitting (76) gives: % 21.67/3.99 | | | | | % 21.67/3.99 | | | | | Case 1: % 21.67/3.99 | | | | | | % 21.67/3.99 | | | | | | (84) all_16_1 = all_16_3 % 21.67/3.99 | | | | | | % 21.67/3.99 | | | | | | COMBINE_EQS: (82), (84) imply: % 21.67/3.99 | | | | | | (85) all_16_1 = all_16_4 % 21.67/3.99 | | | | | | % 21.67/3.99 | | | | | | REDUCE: (83), (85) imply: % 21.67/3.99 | | | | | | (86) $false % 21.67/3.99 | | | | | | % 21.67/3.99 | | | | | | CLOSE: (86) is inconsistent. % 21.67/3.99 | | | | | | % 21.67/3.99 | | | | | Case 2: % 21.67/3.99 | | | | | | % 21.67/3.99 | | | | | | (87) all_16_1 = all_16_4 % 21.67/3.99 | | | | | | % 21.67/3.99 | | | | | | REDUCE: (83), (87) imply: % 21.67/3.99 | | | | | | (88) $false % 21.67/3.99 | | | | | | % 21.67/3.99 | | | | | | CLOSE: (88) is inconsistent. % 21.67/3.99 | | | | | | % 21.67/3.99 | | | | | End of split % 21.67/3.99 | | | | | % 21.67/3.99 | | | | End of split % 21.67/3.99 | | | | % 21.67/3.99 | | | Case 2: % 21.67/3.99 | | | | % 21.67/3.99 | | | | (89) all_27_1 = all_25_0 % 21.67/3.99 | | | | % 21.67/4.00 | | | | COMBINE_EQS: (68), (89) imply: % 21.67/4.00 | | | | (90) all_25_0 = all_25_1 % 21.67/4.00 | | | | % 21.67/4.00 | | | | SIMP: (90) implies: % 21.67/4.00 | | | | (91) all_25_0 = all_25_1 % 21.67/4.00 | | | | % 21.67/4.00 | | | | REDUCE: (71), (91) imply: % 21.67/4.00 | | | | (92) $false % 21.67/4.00 | | | | % 21.67/4.00 | | | | CLOSE: (92) is inconsistent. % 21.67/4.00 | | | | % 21.67/4.00 | | | End of split % 21.67/4.00 | | | % 21.67/4.00 | | End of split % 21.67/4.00 | | % 21.67/4.00 | Case 2: % 21.67/4.00 | | % 21.67/4.00 | | (93) all_16_1 = all_16_3 % 21.67/4.00 | | (94) ~ (all_16_2 = all_16_4) % 21.67/4.00 | | % 21.67/4.00 | | BETA: splitting (42) gives: % 21.67/4.00 | | % 21.67/4.00 | | Case 1: % 21.67/4.00 | | | % 21.67/4.00 | | | (95) all_27_1 = all_25_0 % 21.67/4.00 | | | % 21.67/4.00 | | | BETA: splitting (43) gives: % 21.67/4.00 | | | % 21.67/4.00 | | | Case 1: % 21.67/4.00 | | | | % 21.67/4.00 | | | | (96) all_27_0 = all_25_1 % 21.67/4.00 | | | | % 21.67/4.00 | | | | REDUCE: (25), (96) imply: % 21.67/4.00 | | | | (97) singleton(all_16_2) = all_25_1 % 21.67/4.00 | | | | % 21.67/4.00 | | | | GROUND_INST: instantiating (t8_zfmisc_1) with all_16_2, all_16_4, % 21.67/4.00 | | | | all_16_3, all_25_1, simplifying with (7), (8), (9), (18), % 21.67/4.00 | | | | (97) gives: % 21.67/4.00 | | | | (98) all_16_2 = all_16_4 % 21.67/4.00 | | | | % 21.67/4.00 | | | | REDUCE: (94), (98) imply: % 21.67/4.00 | | | | (99) $false % 21.67/4.00 | | | | % 21.67/4.00 | | | | CLOSE: (99) is inconsistent. % 21.67/4.00 | | | | % 21.67/4.00 | | | Case 2: % 21.67/4.00 | | | | % 21.67/4.00 | | | | (100) all_27_1 = all_25_1 % 21.67/4.00 | | | | (101) ~ (all_27_0 = all_25_1) % 21.67/4.00 | | | | % 21.67/4.00 | | | | COMBINE_EQS: (95), (100) imply: % 21.67/4.00 | | | | (102) all_25_0 = all_25_1 % 21.67/4.00 | | | | % 21.67/4.00 | | | | REF_CLOSE: (45), (101), (102) are inconsistent by sub-proof #1. % 21.67/4.00 | | | | % 21.67/4.00 | | | End of split % 21.67/4.00 | | | % 21.67/4.00 | | Case 2: % 21.67/4.00 | | | % 21.67/4.00 | | | (103) all_27_1 = all_25_1 % 21.67/4.00 | | | (104) ~ (all_27_1 = all_25_0) % 21.67/4.00 | | | % 21.67/4.00 | | | REDUCE: (103), (104) imply: % 21.67/4.00 | | | (105) ~ (all_25_0 = all_25_1) % 21.67/4.00 | | | % 21.67/4.00 | | | SIMP: (105) implies: % 21.67/4.00 | | | (106) ~ (all_25_0 = all_25_1) % 21.67/4.00 | | | % 21.67/4.00 | | | BETA: splitting (44) gives: % 21.67/4.00 | | | % 21.67/4.00 | | | Case 1: % 21.67/4.00 | | | | % 21.67/4.00 | | | | (107) all_27_0 = all_25_0 % 21.67/4.00 | | | | % 21.67/4.00 | | | | REDUCE: (25), (107) imply: % 21.67/4.00 | | | | (108) singleton(all_16_2) = all_25_0 % 21.67/4.00 | | | | % 21.67/4.00 | | | | GROUND_INST: instantiating (t8_zfmisc_1) with all_16_2, all_16_4, % 21.67/4.00 | | | | all_16_4, all_25_0, simplifying with (7), (9), (37), (108) % 21.67/4.00 | | | | gives: % 21.67/4.00 | | | | (109) all_16_2 = all_16_4 % 21.67/4.00 | | | | % 21.67/4.00 | | | | REDUCE: (94), (109) imply: % 21.67/4.00 | | | | (110) $false % 21.67/4.00 | | | | % 21.67/4.00 | | | | CLOSE: (110) is inconsistent. % 21.67/4.00 | | | | % 21.67/4.00 | | | Case 2: % 21.67/4.00 | | | | % 21.67/4.00 | | | | (111) all_27_1 = all_25_0 % 21.67/4.00 | | | | % 21.67/4.00 | | | | COMBINE_EQS: (103), (111) imply: % 21.67/4.00 | | | | (112) all_25_0 = all_25_1 % 21.67/4.00 | | | | % 21.67/4.00 | | | | SIMP: (112) implies: % 21.67/4.00 | | | | (113) all_25_0 = all_25_1 % 21.67/4.00 | | | | % 21.67/4.00 | | | | REDUCE: (106), (113) imply: % 21.67/4.00 | | | | (114) $false % 21.67/4.00 | | | | % 21.67/4.00 | | | | CLOSE: (114) is inconsistent. % 21.67/4.00 | | | | % 21.67/4.00 | | | End of split % 21.67/4.00 | | | % 21.67/4.00 | | End of split % 21.67/4.00 | | % 21.67/4.00 | End of split % 21.67/4.00 | % 21.67/4.00 End of proof % 21.67/4.00 % 21.67/4.00 Sub-proof #1 shows that the following formulas are inconsistent: % 21.67/4.00 ---------------------------------------------------------------- % 21.67/4.00 (1) all_27_0 = all_25_0 | all_27_0 = all_25_1 % 21.67/4.00 (2) all_25_0 = all_25_1 % 21.67/4.00 (3) ~ (all_27_0 = all_25_1) % 21.67/4.00 % 21.67/4.00 Begin of proof % 21.67/4.00 | % 21.67/4.00 | BETA: splitting (1) gives: % 21.67/4.00 | % 21.67/4.00 | Case 1: % 21.67/4.00 | | % 21.67/4.00 | | (4) all_27_0 = all_25_0 % 21.67/4.00 | | % 21.67/4.00 | | COMBINE_EQS: (2), (4) imply: % 21.67/4.00 | | (5) all_27_0 = all_25_1 % 21.67/4.00 | | % 21.67/4.00 | | REDUCE: (3), (5) imply: % 21.67/4.00 | | (6) $false % 21.67/4.00 | | % 21.67/4.00 | | CLOSE: (6) is inconsistent. % 21.67/4.00 | | % 21.67/4.00 | Case 2: % 21.67/4.00 | | % 21.67/4.00 | | (7) all_27_0 = all_25_1 % 21.67/4.00 | | % 21.67/4.00 | | REDUCE: (3), (7) imply: % 21.67/4.00 | | (8) $false % 21.67/4.00 | | % 21.67/4.00 | | CLOSE: (8) is inconsistent. % 21.67/4.00 | | % 21.67/4.00 | End of split % 21.67/4.00 | % 21.67/4.00 End of proof % 21.67/4.00 % SZS output end Proof for theBenchmark % 21.67/4.01 % 21.67/4.01 3388ms %------------------------------------------------------------------------------