%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET940+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 : n009.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 15:27:08 EDT 2023 % Result : Theorem 3.93s 1.29s % Output : Proof 5.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET940+1 : TPTP v8.1.2. Released v3.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n009.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 12:45:50 EDT 2023 % 0.13/0.35 % CPUTime : % 0.62/0.62 ________ _____ % 0.62/0.62 ___ __ \_________(_)________________________________ % 0.62/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.62/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.62/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.62/0.62 % 0.62/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.62/0.62 (2023-06-19) % 0.62/0.62 % 0.62/0.62 (c) Philipp Rümmer, 2009-2023 % 0.62/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.62/0.62 Amanda Stjerna. % 0.62/0.62 Free software under BSD-3-Clause. % 0.62/0.62 % 0.62/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.62/0.62 % 0.62/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.63 Running up to 7 provers in parallel. % 0.66/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.84/0.98 Prover 4: Preprocessing ... % 1.84/0.98 Prover 1: Preprocessing ... % 2.41/1.03 Prover 5: Preprocessing ... % 2.41/1.03 Prover 6: Preprocessing ... % 2.41/1.03 Prover 3: Preprocessing ... % 2.41/1.03 Prover 2: Preprocessing ... % 2.41/1.03 Prover 0: Preprocessing ... % 2.89/1.16 Prover 1: Warning: ignoring some quantifiers % 2.89/1.16 Prover 3: Warning: ignoring some quantifiers % 3.51/1.18 Prover 3: Constructing countermodel ... % 3.51/1.18 Prover 1: Constructing countermodel ... % 3.51/1.18 Prover 6: Proving ... % 3.51/1.18 Prover 4: Constructing countermodel ... % 3.51/1.18 Prover 5: Proving ... % 3.58/1.19 Prover 0: Proving ... % 3.58/1.20 Prover 2: Proving ... % 3.93/1.29 Prover 3: proved (641ms) % 3.93/1.29 % 3.93/1.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.93/1.29 % 3.93/1.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.93/1.29 Prover 5: stopped % 3.93/1.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.93/1.29 Prover 2: stopped % 3.93/1.30 Prover 0: stopped % 3.93/1.30 Prover 6: stopped % 3.93/1.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.93/1.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.93/1.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.93/1.31 Prover 7: Preprocessing ... % 4.52/1.32 Prover 10: Preprocessing ... % 4.52/1.32 Prover 13: Preprocessing ... % 4.52/1.33 Prover 8: Preprocessing ... % 4.52/1.33 Prover 11: Preprocessing ... % 4.52/1.36 Prover 10: Constructing countermodel ... % 4.52/1.36 Prover 1: Found proof (size 12) % 4.52/1.36 Prover 1: proved (724ms) % 4.52/1.36 Prover 4: Found proof (size 12) % 4.52/1.36 Prover 4: proved (721ms) % 4.52/1.37 Prover 10: stopped % 4.52/1.37 Prover 8: Warning: ignoring some quantifiers % 5.01/1.38 Prover 8: Constructing countermodel ... % 5.01/1.38 Prover 13: Warning: ignoring some quantifiers % 5.01/1.38 Prover 7: Constructing countermodel ... % 5.01/1.38 Prover 8: stopped % 5.01/1.38 Prover 7: stopped % 5.01/1.38 Prover 13: Constructing countermodel ... % 5.01/1.39 Prover 13: stopped % 5.01/1.39 Prover 11: Constructing countermodel ... % 5.01/1.40 Prover 11: stopped % 5.01/1.40 % 5.01/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.01/1.40 % 5.01/1.40 % SZS output start Proof for theBenchmark % 5.01/1.40 Assumptions after simplification: % 5.01/1.40 --------------------------------- % 5.01/1.40 % 5.01/1.40 (l52_zfmisc_1) % 5.01/1.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | % 5.01/1.43 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (union(v2) = v3 & set_union2(v0, v1) = % 5.01/1.43 v3 & $i(v3))) % 5.01/1.43 % 5.01/1.43 (t93_zfmisc_1) % 5.01/1.44 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 % 5.01/1.44 = v3) & union(v2) = v3 & unordered_pair(v0, v1) = v2 & set_union2(v0, v1) % 5.01/1.44 = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.01/1.44 % 5.01/1.44 (function-axioms) % 5.01/1.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.01/1.44 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 5.01/1.44 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.01/1.44 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 5.01/1.44 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 5.01/1.44 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 5.01/1.44 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 5.01/1.44 % 5.01/1.44 Further assumptions not needed in the proof: % 5.01/1.44 -------------------------------------------- % 5.01/1.44 commutativity_k2_tarski, commutativity_k2_xboole_0, fc2_xboole_0, fc3_xboole_0, % 5.01/1.44 idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0 % 5.01/1.44 % 5.01/1.44 Those formulas are unsatisfiable: % 5.01/1.44 --------------------------------- % 5.01/1.44 % 5.01/1.44 Begin of proof % 5.01/1.44 | % 5.01/1.44 | ALPHA: (function-axioms) implies: % 5.01/1.44 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = % 5.01/1.44 | v1) | ~ (union(v2) = v0)) % 5.01/1.45 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.01/1.45 | (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 5.01/1.45 | % 5.01/1.45 | DELTA: instantiating (t93_zfmisc_1) with fresh symbols all_14_0, all_14_1, % 5.01/1.45 | all_14_2, all_14_3, all_14_4 gives: % 5.01/1.45 | (3) ~ (all_14_0 = all_14_1) & union(all_14_2) = all_14_1 & % 5.01/1.45 | unordered_pair(all_14_4, all_14_3) = all_14_2 & set_union2(all_14_4, % 5.01/1.45 | all_14_3) = all_14_0 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & % 5.01/1.45 | $i(all_14_3) & $i(all_14_4) % 5.01/1.45 | % 5.01/1.45 | ALPHA: (3) implies: % 5.01/1.45 | (4) ~ (all_14_0 = all_14_1) % 5.01/1.45 | (5) $i(all_14_4) % 5.01/1.45 | (6) $i(all_14_3) % 5.01/1.45 | (7) set_union2(all_14_4, all_14_3) = all_14_0 % 5.01/1.45 | (8) unordered_pair(all_14_4, all_14_3) = all_14_2 % 5.01/1.45 | (9) union(all_14_2) = all_14_1 % 5.01/1.45 | % 5.01/1.45 | GROUND_INST: instantiating (l52_zfmisc_1) with all_14_4, all_14_3, all_14_2, % 5.01/1.45 | simplifying with (5), (6), (8) gives: % 5.01/1.45 | (10) ? [v0: $i] : (union(all_14_2) = v0 & set_union2(all_14_4, all_14_3) = % 5.01/1.45 | v0 & $i(v0)) % 5.01/1.45 | % 5.01/1.45 | DELTA: instantiating (10) with fresh symbol all_22_0 gives: % 5.01/1.45 | (11) union(all_14_2) = all_22_0 & set_union2(all_14_4, all_14_3) = all_22_0 % 5.01/1.46 | & $i(all_22_0) % 5.01/1.46 | % 5.01/1.46 | ALPHA: (11) implies: % 5.01/1.46 | (12) set_union2(all_14_4, all_14_3) = all_22_0 % 5.01/1.46 | (13) union(all_14_2) = all_22_0 % 5.01/1.46 | % 5.01/1.46 | GROUND_INST: instantiating (2) with all_14_0, all_22_0, all_14_3, all_14_4, % 5.01/1.46 | simplifying with (7), (12) gives: % 5.01/1.46 | (14) all_22_0 = all_14_0 % 5.01/1.46 | % 5.01/1.46 | GROUND_INST: instantiating (1) with all_14_1, all_22_0, all_14_2, simplifying % 5.01/1.46 | with (9), (13) gives: % 5.01/1.46 | (15) all_22_0 = all_14_1 % 5.01/1.46 | % 5.01/1.46 | COMBINE_EQS: (14), (15) imply: % 5.01/1.46 | (16) all_14_0 = all_14_1 % 5.01/1.46 | % 5.01/1.46 | SIMP: (16) implies: % 5.01/1.46 | (17) all_14_0 = all_14_1 % 5.01/1.46 | % 5.01/1.46 | REDUCE: (4), (17) imply: % 5.01/1.46 | (18) $false % 5.01/1.46 | % 5.01/1.46 | CLOSE: (18) is inconsistent. % 5.01/1.46 | % 5.01/1.46 End of proof % 5.01/1.46 % SZS output end Proof for theBenchmark % 5.01/1.46 % 5.01/1.46 837ms %------------------------------------------------------------------------------