%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU151+3 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.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 17:42:49 EDT 2023 % Result : Theorem 5.68s 1.61s % Output : Proof 8.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU151+3 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.32 % Computer : n004.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Wed Aug 23 18:57:53 EDT 2023 % 0.11/0.32 % CPUTime : % 0.15/0.58 ________ _____ % 0.15/0.58 ___ __ \_________(_)________________________________ % 0.15/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.58 % 0.15/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.58 (2023-06-19) % 0.15/0.58 % 0.15/0.58 (c) Philipp Rümmer, 2009-2023 % 0.15/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.59 Amanda Stjerna. % 0.15/0.59 Free software under BSD-3-Clause. % 0.15/0.59 % 0.15/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.59 % 0.15/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.15/0.60 Running up to 7 provers in parallel. % 0.15/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.15/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.15/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.15/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.15/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.15/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.15/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.92/0.98 Prover 1: Preprocessing ... % 1.92/0.98 Prover 4: Preprocessing ... % 1.92/1.03 Prover 6: Preprocessing ... % 1.92/1.03 Prover 2: Preprocessing ... % 1.92/1.03 Prover 3: Preprocessing ... % 1.92/1.03 Prover 5: Preprocessing ... % 1.92/1.03 Prover 0: Preprocessing ... % 3.36/1.24 Prover 1: Warning: ignoring some quantifiers % 3.36/1.25 Prover 6: Proving ... % 3.36/1.25 Prover 4: Warning: ignoring some quantifiers % 3.36/1.25 Prover 5: Proving ... % 3.36/1.25 Prover 3: Warning: ignoring some quantifiers % 3.36/1.25 Prover 1: Constructing countermodel ... % 3.36/1.26 Prover 3: Constructing countermodel ... % 3.36/1.26 Prover 4: Constructing countermodel ... % 3.36/1.27 Prover 0: Proving ... % 3.71/1.29 Prover 2: Proving ... % 5.68/1.61 Prover 2: proved (975ms) % 5.68/1.61 % 5.68/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.68/1.61 % 5.68/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.68/1.61 Prover 3: stopped % 5.68/1.61 Prover 6: stopped % 5.68/1.61 Prover 0: stopped % 5.68/1.61 Prover 5: stopped % 5.68/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.68/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.68/1.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.68/1.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.68/1.63 Prover 7: Preprocessing ... % 6.14/1.64 Prover 10: Preprocessing ... % 6.14/1.65 Prover 8: Preprocessing ... % 6.14/1.65 Prover 11: Preprocessing ... % 6.14/1.66 Prover 13: Preprocessing ... % 6.41/1.68 Prover 10: Warning: ignoring some quantifiers % 6.41/1.69 Prover 10: Constructing countermodel ... % 6.41/1.71 Prover 7: Warning: ignoring some quantifiers % 6.41/1.71 Prover 7: Constructing countermodel ... % 6.41/1.71 Prover 11: Warning: ignoring some quantifiers % 6.41/1.72 Prover 11: Constructing countermodel ... % 6.41/1.72 Prover 8: Warning: ignoring some quantifiers % 6.41/1.72 Prover 13: Warning: ignoring some quantifiers % 6.41/1.73 Prover 8: Constructing countermodel ... % 6.41/1.73 Prover 13: Constructing countermodel ... % 7.07/1.79 Prover 1: gave up % 7.07/1.79 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.07/1.79 Prover 4: gave up % 7.07/1.80 Prover 11: gave up % 7.07/1.80 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.50/1.82 Prover 10: Found proof (size 29) % 7.50/1.82 Prover 10: proved (210ms) % 7.50/1.82 Prover 13: stopped % 7.50/1.82 Prover 8: stopped % 7.50/1.83 Prover 7: stopped % 7.50/1.83 Prover 16: Preprocessing ... % 7.50/1.83 Prover 19: Preprocessing ... % 7.72/1.87 Prover 16: Warning: ignoring some quantifiers % 7.72/1.87 Prover 16: Constructing countermodel ... % 7.72/1.87 Prover 16: stopped % 7.72/1.88 Prover 19: Warning: ignoring some quantifiers % 7.72/1.89 Prover 19: Constructing countermodel ... % 7.72/1.89 Prover 19: stopped % 7.72/1.89 % 7.72/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.72/1.89 % 7.72/1.90 % SZS output start Proof for theBenchmark % 7.72/1.91 Assumptions after simplification: % 7.72/1.91 --------------------------------- % 7.72/1.91 % 7.72/1.91 (commutativity_k2_tarski) % 8.11/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | % 8.11/1.94 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 8.11/1.94 % 8.11/1.94 (d2_tarski) % 8.11/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | % 8.11/1.95 ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.11/1.95 $i(v0) | ~ in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.11/1.95 $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 8.11/1.95 ~ $i(v0) | ? [v4: $i] : ($i(v4) & (v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ % 8.11/1.95 in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0: $i] : ! [v1: % 8.11/1.95 $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ % 8.11/1.95 $i(v1) | ~ $i(v0) | in(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 8.11/1.95 ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, % 8.11/1.95 v2)) % 8.11/1.95 % 8.11/1.95 (t10_zfmisc_1) % 8.11/1.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v3 % 8.11/1.95 = v0) & ~ (v2 = v0) & unordered_pair(v2, v3) = v4 & unordered_pair(v0, % 8.11/1.95 v1) = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.11/1.95 % 8.11/1.95 Further assumptions not needed in the proof: % 8.11/1.95 -------------------------------------------- % 8.11/1.95 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0 % 8.11/1.95 % 8.11/1.95 Those formulas are unsatisfiable: % 8.11/1.95 --------------------------------- % 8.11/1.95 % 8.11/1.95 Begin of proof % 8.11/1.96 | % 8.11/1.96 | ALPHA: (d2_tarski) implies: % 8.11/1.96 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 8.11/1.96 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, v2)) % 8.11/1.96 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 8.11/1.96 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v1, v2)) % 8.11/1.97 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = % 8.11/1.97 | v0 | ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 8.11/1.97 | $i(v1) | ~ $i(v0) | ~ in(v3, v2)) % 8.11/1.97 | % 8.11/1.97 | DELTA: instantiating (t10_zfmisc_1) with fresh symbols all_10_0, all_10_1, % 8.11/1.97 | all_10_2, all_10_3, all_10_4 gives: % 8.11/1.97 | (4) ~ (all_10_1 = all_10_4) & ~ (all_10_2 = all_10_4) & % 8.11/1.97 | unordered_pair(all_10_2, all_10_1) = all_10_0 & % 8.11/1.97 | unordered_pair(all_10_4, all_10_3) = all_10_0 & $i(all_10_0) & % 8.11/1.97 | $i(all_10_1) & $i(all_10_2) & $i(all_10_3) & $i(all_10_4) % 8.11/1.97 | % 8.11/1.97 | ALPHA: (4) implies: % 8.11/1.97 | (5) ~ (all_10_2 = all_10_4) % 8.11/1.97 | (6) ~ (all_10_1 = all_10_4) % 8.11/1.97 | (7) $i(all_10_4) % 8.11/1.97 | (8) $i(all_10_3) % 8.30/1.97 | (9) $i(all_10_2) % 8.30/1.97 | (10) $i(all_10_1) % 8.30/1.97 | (11) $i(all_10_0) % 8.30/1.97 | (12) unordered_pair(all_10_4, all_10_3) = all_10_0 % 8.30/1.97 | (13) unordered_pair(all_10_2, all_10_1) = all_10_0 % 8.30/1.97 | % 8.30/1.98 | GROUND_INST: instantiating (1) with all_10_4, all_10_3, all_10_0, simplifying % 8.30/1.98 | with (7), (8), (11), (12) gives: % 8.30/1.98 | (14) in(all_10_4, all_10_0) % 8.30/1.98 | % 8.30/1.98 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_10_4, all_10_3, % 8.30/1.98 | all_10_0, simplifying with (7), (8), (12) gives: % 8.30/1.98 | (15) unordered_pair(all_10_3, all_10_4) = all_10_0 & $i(all_10_0) % 8.30/1.98 | % 8.30/1.98 | ALPHA: (15) implies: % 8.30/1.98 | (16) unordered_pair(all_10_3, all_10_4) = all_10_0 % 8.30/1.98 | % 8.30/1.98 | GROUND_INST: instantiating (2) with all_10_2, all_10_1, all_10_0, simplifying % 8.30/1.98 | with (9), (10), (11), (13) gives: % 8.30/1.98 | (17) in(all_10_1, all_10_0) % 8.30/1.98 | % 8.30/1.98 | GROUND_INST: instantiating (1) with all_10_2, all_10_1, all_10_0, simplifying % 8.30/1.98 | with (9), (10), (11), (13) gives: % 8.30/1.98 | (18) in(all_10_2, all_10_0) % 8.30/1.98 | % 8.30/1.98 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_10_2, all_10_1, % 8.30/1.98 | all_10_0, simplifying with (9), (10), (13) gives: % 8.30/1.98 | (19) unordered_pair(all_10_1, all_10_2) = all_10_0 & $i(all_10_0) % 8.30/1.98 | % 8.30/1.98 | ALPHA: (19) implies: % 8.30/1.98 | (20) unordered_pair(all_10_1, all_10_2) = all_10_0 % 8.30/1.98 | % 8.30/1.99 | GROUND_INST: instantiating (3) with all_10_3, all_10_4, all_10_0, all_10_1, % 8.30/1.99 | simplifying with (7), (8), (10), (11), (16), (17) gives: % 8.30/1.99 | (21) all_10_1 = all_10_3 | all_10_1 = all_10_4 % 8.30/1.99 | % 8.30/1.99 | GROUND_INST: instantiating (3) with all_10_3, all_10_4, all_10_0, all_10_2, % 8.30/1.99 | simplifying with (7), (8), (9), (11), (16), (18) gives: % 8.30/1.99 | (22) all_10_2 = all_10_3 | all_10_2 = all_10_4 % 8.30/1.99 | % 8.30/1.99 | GROUND_INST: instantiating (3) with all_10_1, all_10_2, all_10_0, all_10_4, % 8.30/1.99 | simplifying with (7), (9), (10), (11), (14), (20) gives: % 8.30/1.99 | (23) all_10_1 = all_10_4 | all_10_2 = all_10_4 % 8.30/1.99 | % 8.30/1.99 | BETA: splitting (21) gives: % 8.30/1.99 | % 8.30/1.99 | Case 1: % 8.30/1.99 | | % 8.30/1.99 | | (24) all_10_1 = all_10_3 % 8.30/1.99 | | % 8.30/1.99 | | BETA: splitting (22) gives: % 8.30/1.99 | | % 8.30/1.99 | | Case 1: % 8.30/1.99 | | | % 8.30/1.99 | | | (25) all_10_2 = all_10_3 % 8.30/1.99 | | | % 8.30/1.99 | | | REDUCE: (5), (25) imply: % 8.30/1.99 | | | (26) ~ (all_10_3 = all_10_4) % 8.30/1.99 | | | % 8.30/1.99 | | | BETA: splitting (23) gives: % 8.30/1.99 | | | % 8.30/1.99 | | | Case 1: % 8.30/1.99 | | | | % 8.30/1.99 | | | | (27) all_10_1 = all_10_4 % 8.30/1.99 | | | | % 8.30/1.99 | | | | COMBINE_EQS: (24), (27) imply: % 8.30/1.99 | | | | (28) all_10_3 = all_10_4 % 8.30/1.99 | | | | % 8.30/1.99 | | | | REDUCE: (26), (28) imply: % 8.30/1.99 | | | | (29) $false % 8.30/1.99 | | | | % 8.30/1.99 | | | | CLOSE: (29) is inconsistent. % 8.30/1.99 | | | | % 8.30/1.99 | | | Case 2: % 8.30/1.99 | | | | % 8.30/1.99 | | | | (30) all_10_2 = all_10_4 % 8.30/1.99 | | | | % 8.30/1.99 | | | | COMBINE_EQS: (25), (30) imply: % 8.30/2.00 | | | | (31) all_10_3 = all_10_4 % 8.30/2.00 | | | | % 8.30/2.00 | | | | SIMP: (31) implies: % 8.30/2.00 | | | | (32) all_10_3 = all_10_4 % 8.30/2.00 | | | | % 8.30/2.00 | | | | REDUCE: (26), (32) imply: % 8.30/2.00 | | | | (33) $false % 8.30/2.00 | | | | % 8.30/2.00 | | | | CLOSE: (33) is inconsistent. % 8.30/2.00 | | | | % 8.30/2.00 | | | End of split % 8.30/2.00 | | | % 8.30/2.00 | | Case 2: % 8.30/2.00 | | | % 8.30/2.00 | | | (34) all_10_2 = all_10_4 % 8.30/2.00 | | | % 8.30/2.00 | | | REDUCE: (5), (34) imply: % 8.30/2.00 | | | (35) $false % 8.30/2.00 | | | % 8.30/2.00 | | | CLOSE: (35) is inconsistent. % 8.30/2.00 | | | % 8.30/2.00 | | End of split % 8.30/2.00 | | % 8.30/2.00 | Case 2: % 8.30/2.00 | | % 8.30/2.00 | | (36) all_10_1 = all_10_4 % 8.30/2.00 | | % 8.30/2.00 | | REDUCE: (6), (36) imply: % 8.30/2.00 | | (37) $false % 8.30/2.00 | | % 8.30/2.00 | | CLOSE: (37) is inconsistent. % 8.30/2.00 | | % 8.30/2.00 | End of split % 8.30/2.00 | % 8.30/2.00 End of proof % 8.30/2.00 % SZS output end Proof for theBenchmark % 8.30/2.00 % 8.30/2.00 1413ms %------------------------------------------------------------------------------