%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET901+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 : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 15:26:57 EDT 2023 % Result : Theorem 4.49s 1.31s % Output : Proof 6.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET901+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.34 % Computer : n020.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Sat Aug 26 12:30:29 EDT 2023 % 0.15/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.99/0.96 Prover 4: Preprocessing ... % 1.99/0.96 Prover 1: Preprocessing ... % 2.35/1.00 Prover 0: Preprocessing ... % 2.35/1.00 Prover 5: Preprocessing ... % 2.35/1.00 Prover 6: Preprocessing ... % 2.35/1.00 Prover 2: Preprocessing ... % 2.35/1.00 Prover 3: Preprocessing ... % 3.18/1.14 Prover 1: Warning: ignoring some quantifiers % 3.47/1.16 Prover 4: Constructing countermodel ... % 3.47/1.16 Prover 1: Constructing countermodel ... % 3.47/1.16 Prover 3: Warning: ignoring some quantifiers % 3.47/1.17 Prover 3: Constructing countermodel ... % 3.47/1.18 Prover 6: Proving ... % 3.47/1.19 Prover 5: Proving ... % 3.47/1.20 Prover 2: Proving ... % 3.47/1.20 Prover 0: Proving ... % 4.49/1.31 Prover 3: proved (683ms) % 4.49/1.31 % 4.49/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.49/1.31 % 4.49/1.31 Prover 6: stopped % 4.49/1.31 Prover 5: stopped % 4.49/1.31 Prover 0: stopped % 4.49/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.49/1.32 Prover 2: stopped % 4.49/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.49/1.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.49/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.49/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.49/1.34 Prover 7: Preprocessing ... % 4.49/1.34 Prover 11: Preprocessing ... % 4.49/1.34 Prover 8: Preprocessing ... % 4.96/1.35 Prover 10: Preprocessing ... % 4.96/1.35 Prover 13: Preprocessing ... % 4.96/1.39 Prover 7: Warning: ignoring some quantifiers % 4.96/1.39 Prover 7: Constructing countermodel ... % 4.96/1.41 Prover 13: Warning: ignoring some quantifiers % 4.96/1.41 Prover 13: Constructing countermodel ... % 4.96/1.41 Prover 10: Warning: ignoring some quantifiers % 4.96/1.42 Prover 8: Warning: ignoring some quantifiers % 4.96/1.43 Prover 10: Constructing countermodel ... % 4.96/1.43 Prover 8: Constructing countermodel ... % 4.96/1.44 Prover 1: Found proof (size 51) % 4.96/1.44 Prover 1: proved (815ms) % 4.96/1.44 Prover 7: stopped % 4.96/1.44 Prover 8: stopped % 4.96/1.44 Prover 4: stopped % 4.96/1.44 Prover 10: stopped % 4.96/1.44 Prover 13: stopped % 4.96/1.45 Prover 11: Constructing countermodel ... % 4.96/1.45 Prover 11: stopped % 4.96/1.45 % 4.96/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.96/1.45 % 4.96/1.46 % SZS output start Proof for theBenchmark % 4.96/1.46 Assumptions after simplification: % 4.96/1.46 --------------------------------- % 4.96/1.46 % 4.96/1.46 (l46_zfmisc_1) % 5.73/1.50 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 5.73/1.50 [v4: int] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (unordered_pair(v1, v2) = % 5.73/1.50 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v3 = v0) & ~ (v0 = % 5.73/1.50 empty_set) & ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v0) & ~ (v5 = v0) & % 5.73/1.50 singleton(v2) = v6 & singleton(v1) = v5 & $i(v6) & $i(v5)))) & ! [v0: % 5.73/1.50 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v0 = empty_set | % 5.73/1.50 ~ (subset(v0, v3) = 0) | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ % 5.73/1.50 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (singleton(v2) = v5 & % 5.73/1.50 singleton(v1) = v4 & $i(v5) & $i(v4) & (v5 = v0 | v4 = v0))) % 5.73/1.50 % 5.73/1.50 (t42_zfmisc_1) % 5.73/1.50 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 5.73/1.50 [v4: any] : ? [v5: $i] : ? [v6: $i] : (singleton(v2) = v6 & singleton(v1) = % 5.73/1.50 v5 & subset(v0, v3) = v4 & unordered_pair(v1, v2) = v3 & $i(v6) & $i(v5) & % 5.73/1.50 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v6 = v0) & ~ (v5 = v0) & % 5.73/1.50 ~ (v3 = v0) & ~ (v0 = empty_set)) | ( ~ (v4 = 0) & (v6 = v0 | v5 = v0 % 5.73/1.50 | v3 = v0 | v0 = empty_set)))) % 5.73/1.50 % 5.73/1.50 (function-axioms) % 5.73/1.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.73/1.51 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 5.73/1.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.73/1.51 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 5.73/1.51 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 5.73/1.51 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 5.73/1.51 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 5.73/1.51 (empty(v2) = v0)) % 5.73/1.51 % 5.73/1.51 Further assumptions not needed in the proof: % 5.73/1.51 -------------------------------------------- % 5.73/1.51 commutativity_k2_tarski, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0, % 5.73/1.51 reflexivity_r1_tarski % 5.73/1.51 % 5.73/1.51 Those formulas are unsatisfiable: % 5.73/1.51 --------------------------------- % 5.73/1.51 % 5.73/1.51 Begin of proof % 5.73/1.51 | % 5.73/1.51 | ALPHA: (l46_zfmisc_1) implies: % 5.73/1.51 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v0 = % 5.73/1.51 | empty_set | ~ (subset(v0, v3) = 0) | ~ (unordered_pair(v1, v2) = % 5.73/1.51 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] % 5.73/1.51 | : (singleton(v2) = v5 & singleton(v1) = v4 & $i(v5) & $i(v4) & (v5 = % 5.73/1.51 | v0 | v4 = v0))) % 5.73/1.52 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 5.73/1.52 | (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (unordered_pair(v1, v2) = v3) | % 5.73/1.52 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v3 = v0) & ~ (v0 = % 5.73/1.52 | empty_set) & ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v0) & ~ (v5 = % 5.73/1.52 | v0) & singleton(v2) = v6 & singleton(v1) = v5 & $i(v6) & % 5.73/1.52 | $i(v5)))) % 5.73/1.52 | % 5.73/1.52 | ALPHA: (t42_zfmisc_1) implies: % 5.73/1.52 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : % 5.73/1.52 | ? [v5: $i] : ? [v6: $i] : (singleton(v2) = v6 & singleton(v1) = v5 & % 5.73/1.52 | subset(v0, v3) = v4 & unordered_pair(v1, v2) = v3 & $i(v6) & $i(v5) & % 5.73/1.52 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v6 = v0) & ~ (v5 % 5.73/1.52 | = v0) & ~ (v3 = v0) & ~ (v0 = empty_set)) | ( ~ (v4 = 0) & % 5.73/1.52 | (v6 = v0 | v5 = v0 | v3 = v0 | v0 = empty_set)))) % 5.73/1.52 | % 5.73/1.52 | ALPHA: (function-axioms) implies: % 5.73/1.52 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 5.73/1.52 | = v1) | ~ (singleton(v2) = v0)) % 5.73/1.52 | % 6.01/1.52 | DELTA: instantiating (3) with fresh symbols all_12_0, all_12_1, all_12_2, % 6.01/1.52 | all_12_3, all_12_4, all_12_5, all_12_6 gives: % 6.01/1.52 | (5) singleton(all_12_4) = all_12_0 & singleton(all_12_5) = all_12_1 & % 6.01/1.52 | subset(all_12_6, all_12_3) = all_12_2 & unordered_pair(all_12_5, % 6.01/1.52 | all_12_4) = all_12_3 & $i(all_12_0) & $i(all_12_1) & $i(all_12_3) & % 6.01/1.52 | $i(all_12_4) & $i(all_12_5) & $i(all_12_6) & ((all_12_2 = 0 & ~ % 6.01/1.53 | (all_12_0 = all_12_6) & ~ (all_12_1 = all_12_6) & ~ (all_12_3 = % 6.01/1.53 | all_12_6) & ~ (all_12_6 = empty_set)) | ( ~ (all_12_2 = 0) & % 6.01/1.53 | (all_12_0 = all_12_6 | all_12_1 = all_12_6 | all_12_3 = all_12_6 | % 6.01/1.53 | all_12_6 = empty_set))) % 6.01/1.53 | % 6.01/1.53 | ALPHA: (5) implies: % 6.01/1.53 | (6) $i(all_12_6) % 6.01/1.53 | (7) $i(all_12_5) % 6.01/1.53 | (8) $i(all_12_4) % 6.01/1.53 | (9) unordered_pair(all_12_5, all_12_4) = all_12_3 % 6.01/1.53 | (10) subset(all_12_6, all_12_3) = all_12_2 % 6.01/1.53 | (11) singleton(all_12_5) = all_12_1 % 6.01/1.53 | (12) singleton(all_12_4) = all_12_0 % 6.01/1.53 | (13) (all_12_2 = 0 & ~ (all_12_0 = all_12_6) & ~ (all_12_1 = all_12_6) & % 6.01/1.53 | ~ (all_12_3 = all_12_6) & ~ (all_12_6 = empty_set)) | ( ~ (all_12_2 % 6.01/1.53 | = 0) & (all_12_0 = all_12_6 | all_12_1 = all_12_6 | all_12_3 = % 6.01/1.53 | all_12_6 | all_12_6 = empty_set)) % 6.01/1.53 | % 6.01/1.53 | GROUND_INST: instantiating (2) with all_12_6, all_12_5, all_12_4, all_12_3, % 6.01/1.53 | all_12_2, simplifying with (6), (7), (8), (9), (10) gives: % 6.01/1.53 | (14) all_12_2 = 0 | ( ~ (all_12_3 = all_12_6) & ~ (all_12_6 = empty_set) & % 6.01/1.53 | ? [v0: any] : ? [v1: any] : ( ~ (v1 = all_12_6) & ~ (v0 = % 6.01/1.53 | all_12_6) & singleton(all_12_4) = v1 & singleton(all_12_5) = v0 % 6.01/1.53 | & $i(v1) & $i(v0))) % 6.01/1.53 | % 6.01/1.53 | BETA: splitting (13) gives: % 6.01/1.53 | % 6.01/1.53 | Case 1: % 6.01/1.53 | | % 6.01/1.53 | | (15) all_12_2 = 0 & ~ (all_12_0 = all_12_6) & ~ (all_12_1 = all_12_6) & % 6.01/1.53 | | ~ (all_12_3 = all_12_6) & ~ (all_12_6 = empty_set) % 6.01/1.53 | | % 6.01/1.53 | | ALPHA: (15) implies: % 6.01/1.53 | | (16) all_12_2 = 0 % 6.01/1.53 | | (17) ~ (all_12_6 = empty_set) % 6.01/1.53 | | (18) ~ (all_12_3 = all_12_6) % 6.01/1.53 | | (19) ~ (all_12_1 = all_12_6) % 6.01/1.53 | | (20) ~ (all_12_0 = all_12_6) % 6.01/1.53 | | % 6.01/1.53 | | REDUCE: (10), (16) imply: % 6.01/1.54 | | (21) subset(all_12_6, all_12_3) = 0 % 6.01/1.54 | | % 6.01/1.54 | | GROUND_INST: instantiating (1) with all_12_6, all_12_5, all_12_4, all_12_3, % 6.01/1.54 | | simplifying with (6), (7), (8), (9), (21) gives: % 6.01/1.54 | | (22) all_12_3 = all_12_6 | all_12_6 = empty_set | ? [v0: $i] : ? [v1: % 6.01/1.54 | | $i] : (singleton(all_12_4) = v1 & singleton(all_12_5) = v0 & % 6.01/1.54 | | $i(v1) & $i(v0) & (v1 = all_12_6 | v0 = all_12_6)) % 6.01/1.54 | | % 6.01/1.54 | | BETA: splitting (22) gives: % 6.01/1.54 | | % 6.01/1.54 | | Case 1: % 6.01/1.54 | | | % 6.01/1.54 | | | (23) all_12_6 = empty_set % 6.01/1.54 | | | % 6.01/1.54 | | | REDUCE: (17), (23) imply: % 6.01/1.54 | | | (24) $false % 6.01/1.54 | | | % 6.01/1.54 | | | CLOSE: (24) is inconsistent. % 6.01/1.54 | | | % 6.01/1.54 | | Case 2: % 6.01/1.54 | | | % 6.01/1.54 | | | (25) all_12_3 = all_12_6 | ? [v0: $i] : ? [v1: $i] : % 6.01/1.54 | | | (singleton(all_12_4) = v1 & singleton(all_12_5) = v0 & $i(v1) & % 6.01/1.54 | | | $i(v0) & (v1 = all_12_6 | v0 = all_12_6)) % 6.01/1.54 | | | % 6.01/1.54 | | | BETA: splitting (25) gives: % 6.01/1.54 | | | % 6.01/1.54 | | | Case 1: % 6.01/1.54 | | | | % 6.01/1.54 | | | | (26) all_12_3 = all_12_6 % 6.01/1.54 | | | | % 6.01/1.54 | | | | REDUCE: (18), (26) imply: % 6.01/1.54 | | | | (27) $false % 6.01/1.54 | | | | % 6.01/1.54 | | | | CLOSE: (27) is inconsistent. % 6.01/1.54 | | | | % 6.01/1.54 | | | Case 2: % 6.01/1.54 | | | | % 6.01/1.54 | | | | (28) ? [v0: $i] : ? [v1: $i] : (singleton(all_12_4) = v1 & % 6.01/1.54 | | | | singleton(all_12_5) = v0 & $i(v1) & $i(v0) & (v1 = all_12_6 | % 6.01/1.54 | | | | v0 = all_12_6)) % 6.01/1.54 | | | | % 6.01/1.54 | | | | DELTA: instantiating (28) with fresh symbols all_38_0, all_38_1 gives: % 6.01/1.54 | | | | (29) singleton(all_12_4) = all_38_0 & singleton(all_12_5) = all_38_1 % 6.01/1.54 | | | | & $i(all_38_0) & $i(all_38_1) & (all_38_0 = all_12_6 | all_38_1 % 6.01/1.54 | | | | = all_12_6) % 6.01/1.54 | | | | % 6.01/1.54 | | | | ALPHA: (29) implies: % 6.01/1.54 | | | | (30) singleton(all_12_5) = all_38_1 % 6.01/1.54 | | | | (31) singleton(all_12_4) = all_38_0 % 6.01/1.54 | | | | (32) all_38_0 = all_12_6 | all_38_1 = all_12_6 % 6.01/1.54 | | | | % 6.01/1.54 | | | | GROUND_INST: instantiating (4) with all_12_1, all_38_1, all_12_5, % 6.01/1.54 | | | | simplifying with (11), (30) gives: % 6.01/1.54 | | | | (33) all_38_1 = all_12_1 % 6.01/1.54 | | | | % 6.01/1.54 | | | | GROUND_INST: instantiating (4) with all_12_0, all_38_0, all_12_4, % 6.01/1.54 | | | | simplifying with (12), (31) gives: % 6.01/1.54 | | | | (34) all_38_0 = all_12_0 % 6.01/1.54 | | | | % 6.01/1.54 | | | | BETA: splitting (32) gives: % 6.01/1.54 | | | | % 6.01/1.54 | | | | Case 1: % 6.01/1.54 | | | | | % 6.01/1.54 | | | | | (35) all_38_0 = all_12_6 % 6.01/1.54 | | | | | % 6.01/1.54 | | | | | COMBINE_EQS: (34), (35) imply: % 6.01/1.54 | | | | | (36) all_12_0 = all_12_6 % 6.01/1.54 | | | | | % 6.01/1.54 | | | | | REDUCE: (20), (36) imply: % 6.01/1.54 | | | | | (37) $false % 6.01/1.54 | | | | | % 6.01/1.54 | | | | | CLOSE: (37) is inconsistent. % 6.01/1.54 | | | | | % 6.01/1.54 | | | | Case 2: % 6.01/1.54 | | | | | % 6.01/1.54 | | | | | (38) all_38_1 = all_12_6 % 6.01/1.54 | | | | | % 6.01/1.55 | | | | | COMBINE_EQS: (33), (38) imply: % 6.01/1.55 | | | | | (39) all_12_1 = all_12_6 % 6.01/1.55 | | | | | % 6.01/1.55 | | | | | SIMP: (39) implies: % 6.01/1.55 | | | | | (40) all_12_1 = all_12_6 % 6.01/1.55 | | | | | % 6.01/1.55 | | | | | REDUCE: (19), (40) imply: % 6.01/1.55 | | | | | (41) $false % 6.01/1.55 | | | | | % 6.01/1.55 | | | | | CLOSE: (41) is inconsistent. % 6.01/1.55 | | | | | % 6.01/1.55 | | | | End of split % 6.01/1.55 | | | | % 6.01/1.55 | | | End of split % 6.01/1.55 | | | % 6.01/1.55 | | End of split % 6.01/1.55 | | % 6.01/1.55 | Case 2: % 6.01/1.55 | | % 6.01/1.55 | | (42) ~ (all_12_2 = 0) & (all_12_0 = all_12_6 | all_12_1 = all_12_6 | % 6.01/1.55 | | all_12_3 = all_12_6 | all_12_6 = empty_set) % 6.01/1.55 | | % 6.01/1.55 | | ALPHA: (42) implies: % 6.01/1.55 | | (43) ~ (all_12_2 = 0) % 6.01/1.55 | | (44) all_12_0 = all_12_6 | all_12_1 = all_12_6 | all_12_3 = all_12_6 | % 6.01/1.55 | | all_12_6 = empty_set % 6.01/1.55 | | % 6.01/1.55 | | BETA: splitting (14) gives: % 6.01/1.55 | | % 6.01/1.55 | | Case 1: % 6.01/1.55 | | | % 6.01/1.55 | | | (45) all_12_2 = 0 % 6.01/1.55 | | | % 6.01/1.55 | | | REDUCE: (43), (45) imply: % 6.01/1.55 | | | (46) $false % 6.01/1.55 | | | % 6.01/1.55 | | | CLOSE: (46) is inconsistent. % 6.01/1.55 | | | % 6.01/1.55 | | Case 2: % 6.01/1.55 | | | % 6.01/1.55 | | | (47) ~ (all_12_3 = all_12_6) & ~ (all_12_6 = empty_set) & ? [v0: % 6.01/1.55 | | | any] : ? [v1: any] : ( ~ (v1 = all_12_6) & ~ (v0 = all_12_6) & % 6.01/1.55 | | | singleton(all_12_4) = v1 & singleton(all_12_5) = v0 & $i(v1) & % 6.01/1.55 | | | $i(v0)) % 6.01/1.55 | | | % 6.01/1.55 | | | ALPHA: (47) implies: % 6.01/1.55 | | | (48) ~ (all_12_6 = empty_set) % 6.01/1.55 | | | (49) ~ (all_12_3 = all_12_6) % 6.01/1.55 | | | (50) ? [v0: any] : ? [v1: any] : ( ~ (v1 = all_12_6) & ~ (v0 = % 6.01/1.55 | | | all_12_6) & singleton(all_12_4) = v1 & singleton(all_12_5) = % 6.01/1.55 | | | v0 & $i(v1) & $i(v0)) % 6.01/1.55 | | | % 6.01/1.55 | | | DELTA: instantiating (50) with fresh symbols all_31_0, all_31_1 gives: % 6.01/1.55 | | | (51) ~ (all_31_0 = all_12_6) & ~ (all_31_1 = all_12_6) & % 6.01/1.55 | | | singleton(all_12_4) = all_31_0 & singleton(all_12_5) = all_31_1 & % 6.01/1.55 | | | $i(all_31_0) & $i(all_31_1) % 6.01/1.55 | | | % 6.01/1.55 | | | ALPHA: (51) implies: % 6.01/1.55 | | | (52) ~ (all_31_1 = all_12_6) % 6.01/1.55 | | | (53) ~ (all_31_0 = all_12_6) % 6.01/1.55 | | | (54) singleton(all_12_5) = all_31_1 % 6.01/1.55 | | | (55) singleton(all_12_4) = all_31_0 % 6.01/1.55 | | | % 6.01/1.55 | | | GROUND_INST: instantiating (4) with all_12_1, all_31_1, all_12_5, % 6.01/1.55 | | | simplifying with (11), (54) gives: % 6.01/1.55 | | | (56) all_31_1 = all_12_1 % 6.01/1.55 | | | % 6.01/1.55 | | | GROUND_INST: instantiating (4) with all_12_0, all_31_0, all_12_4, % 6.01/1.55 | | | simplifying with (12), (55) gives: % 6.01/1.55 | | | (57) all_31_0 = all_12_0 % 6.01/1.55 | | | % 6.01/1.55 | | | REDUCE: (53), (57) imply: % 6.01/1.55 | | | (58) ~ (all_12_0 = all_12_6) % 6.01/1.55 | | | % 6.01/1.55 | | | REDUCE: (52), (56) imply: % 6.01/1.55 | | | (59) ~ (all_12_1 = all_12_6) % 6.01/1.55 | | | % 6.01/1.55 | | | BETA: splitting (44) gives: % 6.01/1.55 | | | % 6.01/1.55 | | | Case 1: % 6.01/1.55 | | | | % 6.01/1.55 | | | | (60) all_12_6 = empty_set % 6.01/1.55 | | | | % 6.01/1.55 | | | | REDUCE: (48), (60) imply: % 6.01/1.55 | | | | (61) $false % 6.01/1.55 | | | | % 6.01/1.55 | | | | CLOSE: (61) is inconsistent. % 6.01/1.55 | | | | % 6.01/1.56 | | | Case 2: % 6.01/1.56 | | | | % 6.01/1.56 | | | | (62) all_12_0 = all_12_6 | all_12_1 = all_12_6 | all_12_3 = all_12_6 % 6.01/1.56 | | | | % 6.01/1.56 | | | | BETA: splitting (62) gives: % 6.01/1.56 | | | | % 6.01/1.56 | | | | Case 1: % 6.01/1.56 | | | | | % 6.01/1.56 | | | | | (63) all_12_0 = all_12_6 % 6.01/1.56 | | | | | % 6.01/1.56 | | | | | REDUCE: (58), (63) imply: % 6.01/1.56 | | | | | (64) $false % 6.01/1.56 | | | | | % 6.01/1.56 | | | | | CLOSE: (64) is inconsistent. % 6.01/1.56 | | | | | % 6.01/1.56 | | | | Case 2: % 6.01/1.56 | | | | | % 6.01/1.56 | | | | | (65) all_12_1 = all_12_6 | all_12_3 = all_12_6 % 6.01/1.56 | | | | | % 6.01/1.56 | | | | | BETA: splitting (65) gives: % 6.01/1.56 | | | | | % 6.01/1.56 | | | | | Case 1: % 6.01/1.56 | | | | | | % 6.01/1.56 | | | | | | (66) all_12_1 = all_12_6 % 6.01/1.56 | | | | | | % 6.01/1.56 | | | | | | REDUCE: (59), (66) imply: % 6.01/1.56 | | | | | | (67) $false % 6.01/1.56 | | | | | | % 6.01/1.56 | | | | | | CLOSE: (67) is inconsistent. % 6.01/1.56 | | | | | | % 6.01/1.56 | | | | | Case 2: % 6.01/1.56 | | | | | | % 6.01/1.56 | | | | | | (68) all_12_3 = all_12_6 % 6.01/1.56 | | | | | | % 6.01/1.56 | | | | | | REDUCE: (49), (68) imply: % 6.01/1.56 | | | | | | (69) $false % 6.01/1.56 | | | | | | % 6.01/1.56 | | | | | | CLOSE: (69) is inconsistent. % 6.01/1.56 | | | | | | % 6.01/1.56 | | | | | End of split % 6.01/1.56 | | | | | % 6.01/1.56 | | | | End of split % 6.01/1.56 | | | | % 6.01/1.56 | | | End of split % 6.01/1.56 | | | % 6.01/1.56 | | End of split % 6.01/1.56 | | % 6.01/1.56 | End of split % 6.01/1.56 | % 6.01/1.56 End of proof % 6.01/1.56 % SZS output end Proof for theBenchmark % 6.01/1.56 % 6.01/1.56 952ms %------------------------------------------------------------------------------