%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET917+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 : n027.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 15:27:02 EDT 2023 % Result : Theorem 3.85s 1.39s % Output : Proof 5.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET917+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n027.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 12:36:19 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.67 ________ _____ % 0.21/0.67 ___ __ \_________(_)________________________________ % 0.21/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.67 % 0.21/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.67 (2023-06-19) % 0.21/0.67 % 0.21/0.67 (c) Philipp Rümmer, 2009-2023 % 0.21/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.67 Amanda Stjerna. % 0.21/0.67 Free software under BSD-3-Clause. % 0.21/0.67 % 0.21/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.67 % 0.21/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.69 Running up to 7 provers in parallel. % 0.21/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.94/1.08 Prover 1: Preprocessing ... % 1.94/1.08 Prover 4: Preprocessing ... % 2.51/1.12 Prover 3: Preprocessing ... % 2.51/1.12 Prover 0: Preprocessing ... % 2.51/1.12 Prover 5: Preprocessing ... % 2.51/1.12 Prover 2: Preprocessing ... % 2.51/1.12 Prover 6: Preprocessing ... % 3.02/1.25 Prover 1: Warning: ignoring some quantifiers % 3.02/1.26 Prover 6: Proving ... % 3.02/1.26 Prover 1: Constructing countermodel ... % 3.02/1.27 Prover 5: Proving ... % 3.02/1.27 Prover 3: Warning: ignoring some quantifiers % 3.02/1.27 Prover 2: Proving ... % 3.72/1.28 Prover 3: Constructing countermodel ... % 3.85/1.30 Prover 4: Constructing countermodel ... % 3.85/1.30 Prover 0: Proving ... % 3.85/1.39 Prover 3: proved (690ms) % 3.85/1.39 % 3.85/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.85/1.39 % 3.85/1.40 Prover 2: stopped % 3.85/1.40 Prover 0: stopped % 3.85/1.40 Prover 6: stopped % 3.85/1.42 Prover 5: stopped % 3.85/1.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.85/1.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.85/1.44 Prover 8: Preprocessing ... % 3.85/1.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.85/1.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.85/1.44 Prover 10: Preprocessing ... % 4.75/1.44 Prover 1: Found proof (size 18) % 4.75/1.44 Prover 11: Preprocessing ... % 4.75/1.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.75/1.44 Prover 7: Preprocessing ... % 4.75/1.45 Prover 1: proved (754ms) % 4.75/1.45 Prover 13: Preprocessing ... % 4.75/1.45 Prover 4: stopped % 4.92/1.45 Prover 11: stopped % 4.92/1.46 Prover 10: Warning: ignoring some quantifiers % 4.92/1.46 Prover 13: stopped % 4.92/1.47 Prover 10: Constructing countermodel ... % 4.92/1.47 Prover 7: Warning: ignoring some quantifiers % 4.92/1.47 Prover 10: stopped % 4.92/1.47 Prover 7: Constructing countermodel ... % 4.92/1.47 Prover 7: stopped % 4.92/1.47 Prover 8: Warning: ignoring some quantifiers % 4.92/1.48 Prover 8: Constructing countermodel ... % 4.92/1.49 Prover 8: stopped % 4.92/1.49 % 4.92/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.92/1.49 % 4.92/1.49 % SZS output start Proof for theBenchmark % 4.92/1.49 Assumptions after simplification: % 4.92/1.49 --------------------------------- % 4.92/1.49 % 4.92/1.49 (commutativity_k3_xboole_0) % 4.92/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 4.92/1.52 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 4.92/1.52 % 4.92/1.52 (l28_zfmisc_1) % 4.92/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.92/1.52 (singleton(v0) = v2) | ~ (disjoint(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | % 4.92/1.52 in(v0, v1) = 0) % 4.92/1.52 % 4.92/1.52 (l32_zfmisc_1) % 4.92/1.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 4.92/1.53 (singleton(v0) = v2) | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v1) | ~ % 4.92/1.53 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 4.92/1.53 % 4.92/1.53 (t58_zfmisc_1) % 5.38/1.53 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] : ( ~ (v4 % 5.38/1.53 = v2) & ~ (v3 = 0) & singleton(v0) = v2 & disjoint(v2, v1) = v3 & % 5.38/1.53 set_intersection2(v2, v1) = v4 & $i(v4) & $i(v2) & $i(v1) & $i(v0)) % 5.38/1.53 % 5.38/1.53 (function-axioms) % 5.38/1.53 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.38/1.53 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 5.38/1.53 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.38/1.53 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 5.38/1.53 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 5.38/1.53 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 5.38/1.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 5.38/1.53 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 5.38/1.54 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 5.38/1.54 % 5.38/1.54 Further assumptions not needed in the proof: % 5.38/1.54 -------------------------------------------- % 5.38/1.54 antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, % 5.38/1.54 symmetry_r1_xboole_0 % 5.38/1.54 % 5.38/1.54 Those formulas are unsatisfiable: % 5.38/1.54 --------------------------------- % 5.38/1.54 % 5.38/1.54 Begin of proof % 5.38/1.54 | % 5.38/1.54 | ALPHA: (function-axioms) implies: % 5.38/1.54 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.38/1.54 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 5.38/1.54 | % 5.38/1.54 | DELTA: instantiating (t58_zfmisc_1) with fresh symbols all_14_0, all_14_1, % 5.38/1.54 | all_14_2, all_14_3, all_14_4 gives: % 5.38/1.54 | (2) ~ (all_14_0 = all_14_2) & ~ (all_14_1 = 0) & singleton(all_14_4) = % 5.38/1.54 | all_14_2 & disjoint(all_14_2, all_14_3) = all_14_1 & % 5.38/1.54 | set_intersection2(all_14_2, all_14_3) = all_14_0 & $i(all_14_0) & % 5.38/1.54 | $i(all_14_2) & $i(all_14_3) & $i(all_14_4) % 5.38/1.54 | % 5.38/1.54 | ALPHA: (2) implies: % 5.38/1.54 | (3) ~ (all_14_1 = 0) % 5.38/1.54 | (4) ~ (all_14_0 = all_14_2) % 5.38/1.54 | (5) $i(all_14_4) % 5.38/1.54 | (6) $i(all_14_3) % 5.38/1.54 | (7) $i(all_14_2) % 5.38/1.54 | (8) set_intersection2(all_14_2, all_14_3) = all_14_0 % 5.38/1.54 | (9) disjoint(all_14_2, all_14_3) = all_14_1 % 5.38/1.54 | (10) singleton(all_14_4) = all_14_2 % 5.38/1.54 | % 5.38/1.55 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_14_2, % 5.38/1.55 | all_14_3, all_14_0, simplifying with (6), (7), (8) gives: % 5.38/1.55 | (11) set_intersection2(all_14_3, all_14_2) = all_14_0 & $i(all_14_0) % 5.38/1.55 | % 5.38/1.55 | ALPHA: (11) implies: % 5.38/1.55 | (12) set_intersection2(all_14_3, all_14_2) = all_14_0 % 5.38/1.55 | % 5.38/1.55 | GROUND_INST: instantiating (l28_zfmisc_1) with all_14_4, all_14_3, all_14_2, % 5.38/1.55 | all_14_1, simplifying with (5), (6), (9), (10) gives: % 5.38/1.55 | (13) all_14_1 = 0 | in(all_14_4, all_14_3) = 0 % 5.38/1.55 | % 5.38/1.55 | BETA: splitting (13) gives: % 5.38/1.55 | % 5.38/1.55 | Case 1: % 5.38/1.55 | | % 5.38/1.55 | | (14) in(all_14_4, all_14_3) = 0 % 5.38/1.55 | | % 5.38/1.55 | | GROUND_INST: instantiating (l32_zfmisc_1) with all_14_4, all_14_3, all_14_2, % 5.38/1.55 | | all_14_0, simplifying with (5), (6), (10), (12) gives: % 5.38/1.55 | | (15) all_14_0 = all_14_2 | ? [v0: int] : ( ~ (v0 = 0) & in(all_14_4, % 5.38/1.55 | | all_14_3) = v0) % 5.38/1.55 | | % 5.38/1.55 | | BETA: splitting (15) gives: % 5.38/1.55 | | % 5.38/1.55 | | Case 1: % 5.38/1.55 | | | % 5.38/1.55 | | | (16) all_14_0 = all_14_2 % 5.38/1.55 | | | % 5.38/1.55 | | | REDUCE: (4), (16) imply: % 5.38/1.55 | | | (17) $false % 5.38/1.55 | | | % 5.38/1.55 | | | CLOSE: (17) is inconsistent. % 5.38/1.55 | | | % 5.38/1.55 | | Case 2: % 5.38/1.55 | | | % 5.38/1.55 | | | (18) ? [v0: int] : ( ~ (v0 = 0) & in(all_14_4, all_14_3) = v0) % 5.38/1.55 | | | % 5.38/1.55 | | | DELTA: instantiating (18) with fresh symbol all_37_0 gives: % 5.38/1.55 | | | (19) ~ (all_37_0 = 0) & in(all_14_4, all_14_3) = all_37_0 % 5.38/1.55 | | | % 5.38/1.55 | | | ALPHA: (19) implies: % 5.38/1.55 | | | (20) ~ (all_37_0 = 0) % 5.38/1.55 | | | (21) in(all_14_4, all_14_3) = all_37_0 % 5.38/1.55 | | | % 5.38/1.55 | | | GROUND_INST: instantiating (1) with 0, all_37_0, all_14_3, all_14_4, % 5.38/1.55 | | | simplifying with (14), (21) gives: % 5.38/1.55 | | | (22) all_37_0 = 0 % 5.38/1.55 | | | % 5.38/1.55 | | | REDUCE: (20), (22) imply: % 5.38/1.55 | | | (23) $false % 5.38/1.55 | | | % 5.38/1.55 | | | CLOSE: (23) is inconsistent. % 5.38/1.55 | | | % 5.38/1.55 | | End of split % 5.38/1.55 | | % 5.38/1.55 | Case 2: % 5.38/1.55 | | % 5.38/1.55 | | (24) all_14_1 = 0 % 5.38/1.55 | | % 5.38/1.55 | | REDUCE: (3), (24) imply: % 5.38/1.55 | | (25) $false % 5.38/1.55 | | % 5.38/1.55 | | CLOSE: (25) is inconsistent. % 5.38/1.55 | | % 5.38/1.55 | End of split % 5.38/1.55 | % 5.38/1.55 End of proof % 5.38/1.55 % SZS output end Proof for theBenchmark % 5.38/1.55 % 5.38/1.55 880ms %------------------------------------------------------------------------------