%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET887+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 : n017.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 15:26:55 EDT 2023 % Result : Theorem 6.99s 1.66s % Output : Proof 9.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET887+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n017.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 12:34:11 EDT 2023 % 0.12/0.34 % 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 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.32/1.00 Prover 1: Preprocessing ... % 2.32/1.01 Prover 4: Preprocessing ... % 2.57/1.05 Prover 0: Preprocessing ... % 2.57/1.05 Prover 2: Preprocessing ... % 2.57/1.05 Prover 3: Preprocessing ... % 2.57/1.05 Prover 6: Preprocessing ... % 2.57/1.05 Prover 5: Preprocessing ... % 4.23/1.36 Prover 4: Warning: ignoring some quantifiers % 4.23/1.36 Prover 1: Warning: ignoring some quantifiers % 4.73/1.37 Prover 3: Warning: ignoring some quantifiers % 4.73/1.37 Prover 6: Proving ... % 4.73/1.38 Prover 5: Proving ... % 4.73/1.38 Prover 2: Proving ... % 4.73/1.38 Prover 4: Constructing countermodel ... % 4.73/1.38 Prover 0: Proving ... % 4.73/1.39 Prover 1: Constructing countermodel ... % 4.73/1.39 Prover 3: Constructing countermodel ... % 6.97/1.66 Prover 2: proved (1038ms) % 6.99/1.66 % 6.99/1.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.99/1.66 % 6.99/1.67 Prover 3: stopped % 6.99/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.99/1.67 Prover 0: stopped % 6.99/1.67 Prover 6: stopped % 6.99/1.67 Prover 5: stopped % 6.99/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.99/1.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.99/1.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.99/1.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.99/1.70 Prover 11: Preprocessing ... % 6.99/1.70 Prover 7: Preprocessing ... % 7.25/1.70 Prover 8: Preprocessing ... % 7.25/1.71 Prover 10: Preprocessing ... % 7.25/1.71 Prover 13: Preprocessing ... % 7.50/1.75 Prover 7: Warning: ignoring some quantifiers % 7.50/1.75 Prover 10: Warning: ignoring some quantifiers % 7.50/1.75 Prover 7: Constructing countermodel ... % 7.50/1.76 Prover 13: Warning: ignoring some quantifiers % 7.50/1.76 Prover 10: Constructing countermodel ... % 7.50/1.76 Prover 13: Constructing countermodel ... % 7.50/1.77 Prover 8: Warning: ignoring some quantifiers % 7.50/1.77 Prover 8: Constructing countermodel ... % 7.50/1.79 Prover 11: Warning: ignoring some quantifiers % 7.50/1.80 Prover 11: Constructing countermodel ... % 8.22/1.84 Prover 10: gave up % 8.22/1.85 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.22/1.87 Prover 1: gave up % 8.22/1.89 Prover 16: Preprocessing ... % 8.22/1.89 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.22/1.91 Prover 19: Preprocessing ... % 8.22/1.93 Prover 16: Warning: ignoring some quantifiers % 8.22/1.94 Prover 16: Constructing countermodel ... % 8.87/1.97 Prover 7: Found proof (size 38) % 8.87/1.97 Prover 7: proved (303ms) % 8.87/1.97 Prover 16: stopped % 8.87/1.97 Prover 13: stopped % 8.87/1.97 Prover 8: stopped % 8.87/1.97 Prover 4: stopped % 8.87/1.97 Prover 11: stopped % 8.87/1.99 Prover 19: Warning: ignoring some quantifiers % 8.87/2.00 Prover 19: Constructing countermodel ... % 8.87/2.01 Prover 19: stopped % 8.87/2.01 % 8.87/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.87/2.01 % 8.87/2.02 % SZS output start Proof for theBenchmark % 8.87/2.02 Assumptions after simplification: % 8.87/2.02 --------------------------------- % 8.87/2.02 % 8.87/2.02 (commutativity_k2_tarski) % 9.49/2.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | % 9.49/2.05 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i] % 9.49/2.05 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | % 9.49/2.05 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 9.49/2.05 % 9.49/2.05 (d1_xboole_0) % 9.49/2.05 $i(empty_set) & ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) & ? [v0: $i] % 9.49/2.05 : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0))) % 9.49/2.05 % 9.49/2.05 (d2_tarski) % 9.49/2.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | % 9.49/2.06 ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 9.49/2.06 $i(v0) | ~ in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 9.49/2.06 $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 9.49/2.06 ~ $i(v0) | ? [v4: $i] : ($i(v4) & (v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ % 9.49/2.06 in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0: $i] : ! [v1: % 9.49/2.06 $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ % 9.49/2.06 $i(v1) | ~ $i(v0) | in(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 9.49/2.06 ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, % 9.49/2.06 v2)) % 9.49/2.06 % 9.49/2.06 (l46_zfmisc_1) % 9.49/2.07 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = % 9.49/2.07 v0 | v0 = empty_set | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ % 9.49/2.07 $i(v1) | ~ $i(v0) | ~ subset(v0, v3) | ? [v4: $i] : ? [v5: $i] : ((v5 = % 9.49/2.07 v0 & singleton(v2) = v0) | (v4 = v0 & singleton(v1) = v0))) & ? [v0: % 9.49/2.07 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (unordered_pair(v1, v2) % 9.49/2.07 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | subset(v0, v3) | ? [v4: $i] : % 9.49/2.07 ? [v5: $i] : ( ~ (v5 = v0) & ~ (v4 = v0) & singleton(v2) = v5 & % 9.49/2.07 singleton(v1) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! % 9.49/2.07 [v2: $i] : ( ~ (unordered_pair(v1, v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ % 9.49/2.07 $i(v0) | subset(v0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 9.49/2.07 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | subset(empty_set, % 9.49/2.07 v2)) % 9.49/2.07 % 9.49/2.07 (t10_zfmisc_1) % 9.49/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 % 9.49/2.07 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = % 9.49/2.07 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 9.49/2.07 % 9.49/2.07 (t28_zfmisc_1) % 9.49/2.07 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 9.49/2.07 $i] : ( ~ (v3 = v0) & ~ (v2 = v0) & unordered_pair(v2, v3) = v5 & % 9.49/2.07 unordered_pair(v0, v1) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 9.49/2.07 $i(v0) & subset(v4, v5)) % 9.49/2.07 % 9.49/2.07 (t8_zfmisc_1) % 9.49/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.49/2.07 (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ % 9.49/2.07 $i(v1) | ~ $i(v0)) % 9.49/2.07 % 9.49/2.07 Further assumptions not needed in the proof: % 9.49/2.07 -------------------------------------------- % 9.49/2.07 antisymmetry_r2_hidden, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0, % 9.49/2.07 reflexivity_r1_tarski % 9.49/2.07 % 9.49/2.07 Those formulas are unsatisfiable: % 9.49/2.07 --------------------------------- % 9.49/2.07 % 9.49/2.07 Begin of proof % 9.49/2.07 | % 9.49/2.07 | ALPHA: (commutativity_k2_tarski) implies: % 9.49/2.08 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 9.49/2.08 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & % 9.49/2.08 | $i(v2))) % 9.49/2.08 | % 9.49/2.08 | ALPHA: (d1_xboole_0) implies: % 9.49/2.08 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) % 9.49/2.08 | % 9.49/2.08 | ALPHA: (d2_tarski) implies: % 9.49/2.08 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 9.49/2.08 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, v2)) % 9.49/2.08 | % 9.49/2.08 | ALPHA: (l46_zfmisc_1) implies: % 9.49/2.08 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v0 = % 9.49/2.08 | empty_set | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 9.49/2.08 | | ~ $i(v0) | ~ subset(v0, v3) | ? [v4: $i] : ? [v5: $i] : ((v5 = % 9.49/2.08 | v0 & singleton(v2) = v0) | (v4 = v0 & singleton(v1) = v0))) % 9.49/2.08 | % 9.49/2.08 | DELTA: instantiating (t28_zfmisc_1) with fresh symbols all_19_0, all_19_1, % 9.49/2.08 | all_19_2, all_19_3, all_19_4, all_19_5 gives: % 9.49/2.08 | (5) ~ (all_19_2 = all_19_5) & ~ (all_19_3 = all_19_5) & % 9.49/2.08 | unordered_pair(all_19_3, all_19_2) = all_19_0 & % 9.49/2.08 | unordered_pair(all_19_5, all_19_4) = all_19_1 & $i(all_19_0) & % 9.49/2.08 | $i(all_19_1) & $i(all_19_2) & $i(all_19_3) & $i(all_19_4) & % 9.49/2.08 | $i(all_19_5) & subset(all_19_1, all_19_0) % 9.49/2.08 | % 9.49/2.08 | ALPHA: (5) implies: % 9.49/2.08 | (6) ~ (all_19_3 = all_19_5) % 9.49/2.08 | (7) ~ (all_19_2 = all_19_5) % 9.49/2.08 | (8) subset(all_19_1, all_19_0) % 9.49/2.08 | (9) $i(all_19_5) % 9.49/2.08 | (10) $i(all_19_4) % 9.49/2.08 | (11) $i(all_19_3) % 9.49/2.08 | (12) $i(all_19_2) % 9.49/2.08 | (13) unordered_pair(all_19_5, all_19_4) = all_19_1 % 9.49/2.08 | (14) unordered_pair(all_19_3, all_19_2) = all_19_0 % 9.49/2.08 | % 9.49/2.08 | GROUND_INST: instantiating (1) with all_19_4, all_19_5, all_19_1, simplifying % 9.49/2.08 | with (9), (10), (13) gives: % 9.49/2.08 | (15) unordered_pair(all_19_4, all_19_5) = all_19_1 & $i(all_19_1) % 9.49/2.08 | % 9.49/2.08 | ALPHA: (15) implies: % 9.49/2.08 | (16) $i(all_19_1) % 9.49/2.08 | % 9.49/2.08 | GROUND_INST: instantiating (3) with all_19_5, all_19_4, all_19_1, simplifying % 9.49/2.08 | with (9), (10), (13), (16) gives: % 9.49/2.09 | (17) in(all_19_5, all_19_1) % 9.49/2.09 | % 9.49/2.09 | GROUND_INST: instantiating (t10_zfmisc_1) with all_19_5, all_19_4, all_19_3, % 9.49/2.09 | all_19_2, all_19_1, simplifying with (9), (10), (11), (12), (13) % 9.49/2.09 | gives: % 9.49/2.09 | (18) all_19_2 = all_19_5 | all_19_3 = all_19_5 | ~ % 9.49/2.09 | (unordered_pair(all_19_3, all_19_2) = all_19_1) % 9.49/2.09 | % 9.49/2.09 | GROUND_INST: instantiating (4) with all_19_1, all_19_3, all_19_2, all_19_0, % 9.49/2.09 | simplifying with (8), (11), (12), (14), (16) gives: % 9.49/2.09 | (19) all_19_0 = all_19_1 | all_19_1 = empty_set | ? [v0: int] : ? [v1: % 9.49/2.09 | int] : ((v1 = all_19_1 & singleton(all_19_2) = all_19_1) | (v0 = % 9.49/2.09 | all_19_1 & singleton(all_19_3) = all_19_1)) % 9.49/2.09 | % 9.49/2.09 | BETA: splitting (18) gives: % 9.49/2.09 | % 9.49/2.09 | Case 1: % 9.49/2.09 | | % 9.49/2.09 | | (20) ~ (unordered_pair(all_19_3, all_19_2) = all_19_1) % 9.49/2.09 | | % 9.49/2.09 | | PRED_UNIFY: (14), (20) imply: % 9.49/2.09 | | (21) ~ (all_19_0 = all_19_1) % 9.49/2.09 | | % 9.49/2.09 | | GROUND_INST: instantiating (2) with all_19_5, simplifying with (9) gives: % 9.49/2.09 | | (22) ~ in(all_19_5, empty_set) % 9.49/2.09 | | % 9.49/2.09 | | PRED_UNIFY: (17), (22) imply: % 9.49/2.09 | | (23) ~ (all_19_1 = empty_set) % 9.49/2.09 | | % 9.49/2.09 | | BETA: splitting (19) gives: % 9.49/2.09 | | % 9.49/2.09 | | Case 1: % 9.49/2.09 | | | % 9.49/2.09 | | | (24) all_19_1 = empty_set % 9.49/2.09 | | | % 9.49/2.09 | | | REDUCE: (23), (24) imply: % 9.49/2.09 | | | (25) $false % 9.49/2.09 | | | % 9.49/2.09 | | | CLOSE: (25) is inconsistent. % 9.49/2.09 | | | % 9.49/2.09 | | Case 2: % 9.49/2.09 | | | % 9.49/2.09 | | | (26) all_19_0 = all_19_1 | ? [v0: int] : ? [v1: int] : ((v1 = % 9.49/2.09 | | | all_19_1 & singleton(all_19_2) = all_19_1) | (v0 = all_19_1 & % 9.49/2.09 | | | singleton(all_19_3) = all_19_1)) % 9.49/2.09 | | | % 9.49/2.09 | | | BETA: splitting (26) gives: % 9.49/2.09 | | | % 9.49/2.09 | | | Case 1: % 9.49/2.09 | | | | % 9.49/2.09 | | | | (27) all_19_0 = all_19_1 % 9.49/2.09 | | | | % 9.49/2.09 | | | | REDUCE: (21), (27) imply: % 9.49/2.09 | | | | (28) $false % 9.49/2.09 | | | | % 9.49/2.09 | | | | CLOSE: (28) is inconsistent. % 9.49/2.09 | | | | % 9.49/2.09 | | | Case 2: % 9.49/2.09 | | | | % 9.49/2.09 | | | | (29) ? [v0: int] : ? [v1: int] : ((v1 = all_19_1 & % 9.49/2.09 | | | | singleton(all_19_2) = all_19_1) | (v0 = all_19_1 & % 9.49/2.09 | | | | singleton(all_19_3) = all_19_1)) % 9.49/2.09 | | | | % 9.49/2.09 | | | | DELTA: instantiating (29) with fresh symbols all_62_0, all_62_1 gives: % 9.49/2.10 | | | | (30) (all_62_0 = all_19_1 & singleton(all_19_2) = all_19_1) | % 9.49/2.10 | | | | (all_62_1 = all_19_1 & singleton(all_19_3) = all_19_1) % 9.49/2.10 | | | | % 9.49/2.10 | | | | BETA: splitting (30) gives: % 9.49/2.10 | | | | % 9.49/2.10 | | | | Case 1: % 9.49/2.10 | | | | | % 9.49/2.10 | | | | | (31) all_62_0 = all_19_1 & singleton(all_19_2) = all_19_1 % 9.49/2.10 | | | | | % 9.49/2.10 | | | | | ALPHA: (31) implies: % 9.49/2.10 | | | | | (32) singleton(all_19_2) = all_19_1 % 9.49/2.10 | | | | | % 9.49/2.10 | | | | | GROUND_INST: instantiating (t8_zfmisc_1) with all_19_2, all_19_5, % 9.49/2.10 | | | | | all_19_4, all_19_1, simplifying with (9), (10), (12), % 9.49/2.10 | | | | | (13), (32) gives: % 9.49/2.10 | | | | | (33) all_19_2 = all_19_5 % 9.49/2.10 | | | | | % 9.49/2.10 | | | | | REDUCE: (7), (33) imply: % 9.49/2.10 | | | | | (34) $false % 9.49/2.10 | | | | | % 9.49/2.10 | | | | | CLOSE: (34) is inconsistent. % 9.49/2.10 | | | | | % 9.49/2.10 | | | | Case 2: % 9.49/2.10 | | | | | % 9.49/2.10 | | | | | (35) all_62_1 = all_19_1 & singleton(all_19_3) = all_19_1 % 9.49/2.10 | | | | | % 9.49/2.10 | | | | | ALPHA: (35) implies: % 9.49/2.10 | | | | | (36) singleton(all_19_3) = all_19_1 % 9.49/2.10 | | | | | % 9.49/2.10 | | | | | GROUND_INST: instantiating (t8_zfmisc_1) with all_19_3, all_19_5, % 9.49/2.10 | | | | | all_19_4, all_19_1, simplifying with (9), (10), (11), % 9.49/2.10 | | | | | (13), (36) gives: % 9.49/2.10 | | | | | (37) all_19_3 = all_19_5 % 9.49/2.10 | | | | | % 9.49/2.10 | | | | | REDUCE: (6), (37) imply: % 9.49/2.10 | | | | | (38) $false % 9.49/2.10 | | | | | % 9.49/2.10 | | | | | CLOSE: (38) is inconsistent. % 9.49/2.10 | | | | | % 9.49/2.10 | | | | End of split % 9.49/2.10 | | | | % 9.49/2.10 | | | End of split % 9.49/2.10 | | | % 9.49/2.10 | | End of split % 9.49/2.10 | | % 9.49/2.10 | Case 2: % 9.49/2.10 | | % 9.49/2.10 | | (39) all_19_2 = all_19_5 | all_19_3 = all_19_5 % 9.49/2.10 | | % 9.49/2.10 | | BETA: splitting (39) gives: % 9.49/2.10 | | % 9.49/2.10 | | Case 1: % 9.49/2.10 | | | % 9.49/2.10 | | | (40) all_19_2 = all_19_5 % 9.49/2.10 | | | % 9.86/2.10 | | | REDUCE: (7), (40) imply: % 9.86/2.10 | | | (41) $false % 9.86/2.10 | | | % 9.86/2.10 | | | CLOSE: (41) is inconsistent. % 9.86/2.10 | | | % 9.86/2.10 | | Case 2: % 9.86/2.10 | | | % 9.86/2.10 | | | (42) all_19_3 = all_19_5 % 9.86/2.10 | | | % 9.86/2.10 | | | REDUCE: (6), (42) imply: % 9.86/2.10 | | | (43) $false % 9.86/2.10 | | | % 9.86/2.10 | | | CLOSE: (43) is inconsistent. % 9.86/2.10 | | | % 9.86/2.10 | | End of split % 9.86/2.10 | | % 9.86/2.10 | End of split % 9.86/2.10 | % 9.86/2.10 End of proof % 9.86/2.10 % SZS output end Proof for theBenchmark % 9.86/2.10 % 9.86/2.10 1504ms %------------------------------------------------------------------------------