%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET886+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 : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 15:26:55 EDT 2023 % Result : Theorem 3.95s 1.25s % Output : Proof 3.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET886+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 16:14:43 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.56 ________ _____ % 0.19/0.56 ___ __ \_________(_)________________________________ % 0.19/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.56 % 0.19/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.56 (2023-06-19) % 0.19/0.56 % 0.19/0.56 (c) Philipp Rümmer, 2009-2023 % 0.19/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.56 Amanda Stjerna. % 0.19/0.56 Free software under BSD-3-Clause. % 0.19/0.56 % 0.19/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.56 % 0.19/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.57 Running up to 7 provers in parallel. % 0.19/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.85/0.96 Prover 4: Preprocessing ... % 1.85/0.96 Prover 1: Preprocessing ... % 1.85/1.00 Prover 2: Preprocessing ... % 1.85/1.00 Prover 0: Preprocessing ... % 1.85/1.00 Prover 6: Preprocessing ... % 1.85/1.00 Prover 3: Preprocessing ... % 1.85/1.00 Prover 5: Preprocessing ... % 3.02/1.11 Prover 1: Warning: ignoring some quantifiers % 3.02/1.11 Prover 6: Proving ... % 3.02/1.12 Prover 3: Warning: ignoring some quantifiers % 3.02/1.12 Prover 1: Constructing countermodel ... % 3.02/1.12 Prover 3: Constructing countermodel ... % 3.02/1.13 Prover 5: Proving ... % 3.02/1.13 Prover 4: Constructing countermodel ... % 3.02/1.13 Prover 0: Proving ... % 3.02/1.14 Prover 2: Proving ... % 3.95/1.25 Prover 3: proved (666ms) % 3.95/1.25 % 3.95/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.95/1.25 % 3.95/1.25 Prover 6: stopped % 3.95/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.95/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.95/1.26 Prover 5: proved (673ms) % 3.95/1.26 % 3.95/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.95/1.26 % 3.95/1.26 Prover 2: proved (681ms) % 3.95/1.26 % 3.95/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.95/1.26 % 3.95/1.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.95/1.26 Prover 0: proved (682ms) % 3.95/1.26 % 3.95/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.95/1.26 % 3.95/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.95/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.95/1.27 Prover 7: Preprocessing ... % 3.95/1.27 Prover 1: Found proof (size 16) % 3.95/1.27 Prover 1: proved (691ms) % 3.95/1.27 Prover 10: Preprocessing ... % 3.95/1.28 Prover 4: stopped % 3.95/1.28 Prover 13: Preprocessing ... % 3.95/1.28 Prover 11: Preprocessing ... % 3.95/1.28 Prover 8: Preprocessing ... % 3.95/1.30 Prover 11: stopped % 3.95/1.31 Prover 7: Warning: ignoring some quantifiers % 3.95/1.31 Prover 7: Constructing countermodel ... % 3.95/1.32 Prover 10: Warning: ignoring some quantifiers % 3.95/1.32 Prover 8: Warning: ignoring some quantifiers % 3.95/1.32 Prover 7: stopped % 3.95/1.32 Prover 10: Constructing countermodel ... % 3.95/1.32 Prover 13: Warning: ignoring some quantifiers % 3.95/1.32 Prover 10: stopped % 3.95/1.32 Prover 8: Constructing countermodel ... % 3.95/1.33 Prover 13: Constructing countermodel ... % 3.95/1.33 Prover 8: stopped % 3.95/1.33 Prover 13: stopped % 3.95/1.33 % 3.95/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.95/1.33 % 3.95/1.33 % SZS output start Proof for theBenchmark % 3.95/1.34 Assumptions after simplification: % 3.95/1.34 --------------------------------- % 3.95/1.34 % 3.95/1.34 (commutativity_k2_tarski) % 3.95/1.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | % 3.95/1.37 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 3.95/1.37 % 3.95/1.37 (t26_zfmisc_1) % 3.95/1.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 % 3.95/1.37 | ~ (singleton(v2) = v4) | ~ (subset(v3, v4) = 0) | ~ (unordered_pair(v0, % 3.95/1.37 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 3.95/1.37 % 3.95/1.37 (t27_zfmisc_1) % 3.95/1.37 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 % 3.95/1.37 = v3) & singleton(v2) = v4 & subset(v3, v4) = 0 & unordered_pair(v0, v1) = % 3.95/1.37 v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 3.95/1.37 % 3.95/1.37 (t69_enumset1) % 3.95/1.38 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 3.95/1.38 (unordered_pair(v0, v0) = v1 & $i(v1))) % 3.95/1.38 % 3.95/1.38 (function-axioms) % 3.95/1.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 3.95/1.38 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 3.95/1.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 3.95/1.38 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 3.95/1.38 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 3.95/1.38 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 3.95/1.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 3.95/1.38 (empty(v2) = v0)) % 3.95/1.38 % 3.95/1.38 Further assumptions not needed in the proof: % 3.95/1.38 -------------------------------------------- % 3.95/1.38 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski % 3.95/1.38 % 3.95/1.38 Those formulas are unsatisfiable: % 3.95/1.38 --------------------------------- % 3.95/1.38 % 3.95/1.38 Begin of proof % 3.95/1.38 | % 3.95/1.38 | ALPHA: (function-axioms) implies: % 3.95/1.38 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 3.95/1.38 | (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 3.95/1.38 | % 3.95/1.38 | DELTA: instantiating (t27_zfmisc_1) with fresh symbols all_12_0, all_12_1, % 3.95/1.39 | all_12_2, all_12_3, all_12_4 gives: % 3.95/1.39 | (2) ~ (all_12_0 = all_12_1) & singleton(all_12_2) = all_12_0 & % 3.95/1.39 | subset(all_12_1, all_12_0) = 0 & unordered_pair(all_12_4, all_12_3) = % 3.95/1.39 | all_12_1 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & $i(all_12_3) & % 3.95/1.39 | $i(all_12_4) % 3.95/1.39 | % 3.95/1.39 | ALPHA: (2) implies: % 3.95/1.39 | (3) ~ (all_12_0 = all_12_1) % 3.95/1.39 | (4) $i(all_12_4) % 3.95/1.39 | (5) $i(all_12_3) % 3.95/1.39 | (6) $i(all_12_2) % 3.95/1.39 | (7) unordered_pair(all_12_4, all_12_3) = all_12_1 % 3.95/1.39 | (8) subset(all_12_1, all_12_0) = 0 % 3.95/1.39 | (9) singleton(all_12_2) = all_12_0 % 3.95/1.39 | % 3.95/1.39 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_12_4, all_12_3, % 3.95/1.39 | all_12_1, simplifying with (4), (5), (7) gives: % 3.95/1.39 | (10) unordered_pair(all_12_3, all_12_4) = all_12_1 & $i(all_12_1) % 3.95/1.39 | % 3.95/1.39 | ALPHA: (10) implies: % 3.95/1.39 | (11) unordered_pair(all_12_3, all_12_4) = all_12_1 % 3.95/1.39 | % 3.95/1.39 | GROUND_INST: instantiating (t26_zfmisc_1) with all_12_4, all_12_3, all_12_2, % 3.95/1.39 | all_12_1, all_12_0, simplifying with (4), (5), (6), (7), (8), (9) % 3.95/1.39 | gives: % 3.95/1.39 | (12) all_12_2 = all_12_4 % 3.95/1.39 | % 3.95/1.39 | GROUND_INST: instantiating (t69_enumset1) with all_12_2, all_12_0, simplifying % 3.95/1.39 | with (6), (9) gives: % 3.95/1.39 | (13) unordered_pair(all_12_2, all_12_2) = all_12_0 & $i(all_12_0) % 3.95/1.39 | % 3.95/1.39 | ALPHA: (13) implies: % 3.95/1.39 | (14) unordered_pair(all_12_2, all_12_2) = all_12_0 % 3.95/1.39 | % 3.95/1.39 | REDUCE: (9), (12) imply: % 3.95/1.39 | (15) singleton(all_12_4) = all_12_0 % 3.95/1.39 | % 3.95/1.39 | REDUCE: (12), (14) imply: % 3.95/1.40 | (16) unordered_pair(all_12_4, all_12_4) = all_12_0 % 3.95/1.40 | % 3.95/1.40 | GROUND_INST: instantiating (t26_zfmisc_1) with all_12_3, all_12_4, all_12_4, % 3.95/1.40 | all_12_1, all_12_0, simplifying with (4), (5), (8), (11), (15) % 3.95/1.40 | gives: % 3.95/1.40 | (17) all_12_3 = all_12_4 % 3.95/1.40 | % 3.95/1.40 | REDUCE: (7), (17) imply: % 3.95/1.40 | (18) unordered_pair(all_12_4, all_12_4) = all_12_1 % 3.95/1.40 | % 3.95/1.40 | GROUND_INST: instantiating (1) with all_12_0, all_12_1, all_12_4, all_12_4, % 3.95/1.40 | simplifying with (16), (18) gives: % 3.95/1.40 | (19) all_12_0 = all_12_1 % 3.95/1.40 | % 3.95/1.40 | REDUCE: (3), (19) imply: % 3.95/1.40 | (20) $false % 3.95/1.40 | % 3.95/1.40 | CLOSE: (20) is inconsistent. % 3.95/1.40 | % 3.95/1.40 End of proof % 3.95/1.40 % SZS output end Proof for theBenchmark % 3.95/1.40 % 3.95/1.40 839ms %------------------------------------------------------------------------------