%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET877+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 15:26:52 EDT 2023 % Result : Theorem 4.75s 1.38s % Output : Proof 5.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET877+1 : TPTP v8.1.2. Released v3.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n017.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 13:07:56 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.16/1.02 Prover 4: Preprocessing ... % 2.16/1.02 Prover 1: Preprocessing ... % 2.55/1.07 Prover 5: Preprocessing ... % 2.55/1.07 Prover 6: Preprocessing ... % 2.55/1.07 Prover 3: Preprocessing ... % 2.55/1.07 Prover 2: Preprocessing ... % 2.55/1.07 Prover 0: Preprocessing ... % 3.47/1.21 Prover 1: Warning: ignoring some quantifiers % 3.47/1.23 Prover 6: Proving ... % 3.47/1.23 Prover 3: Warning: ignoring some quantifiers % 3.47/1.23 Prover 0: Proving ... % 3.47/1.23 Prover 1: Constructing countermodel ... % 3.47/1.23 Prover 4: Warning: ignoring some quantifiers % 3.47/1.24 Prover 3: Constructing countermodel ... % 3.47/1.24 Prover 5: Proving ... % 3.47/1.24 Prover 4: Constructing countermodel ... % 3.47/1.28 Prover 2: Proving ... % 4.75/1.38 Prover 3: proved (748ms) % 4.75/1.38 % 4.75/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.75/1.38 % 4.75/1.38 Prover 0: stopped % 4.75/1.38 Prover 6: stopped % 4.75/1.40 Prover 2: stopped % 4.75/1.40 Prover 5: stopped % 4.75/1.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.75/1.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.75/1.40 Prover 7: Preprocessing ... % 4.75/1.40 Prover 4: Found proof (size 10) % 4.75/1.40 Prover 4: proved (768ms) % 4.75/1.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.75/1.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.75/1.40 Prover 8: Preprocessing ... % 4.75/1.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.75/1.40 Prover 1: stopped % 4.75/1.41 Prover 7: stopped % 4.75/1.42 Prover 11: Preprocessing ... % 4.75/1.42 Prover 10: Preprocessing ... % 4.75/1.42 Prover 13: Preprocessing ... % 4.75/1.43 Prover 10: stopped % 4.75/1.43 Prover 11: stopped % 4.75/1.44 Prover 13: stopped % 4.75/1.45 Prover 8: Warning: ignoring some quantifiers % 4.75/1.45 Prover 8: Constructing countermodel ... % 4.75/1.46 Prover 8: stopped % 4.75/1.46 % 4.75/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.75/1.46 % 4.75/1.46 % SZS output start Proof for theBenchmark % 5.37/1.46 Assumptions after simplification: % 5.37/1.46 --------------------------------- % 5.37/1.46 % 5.37/1.46 (commutativity_k3_xboole_0) % 5.49/1.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2) % 5.49/1.50 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & ! % 5.49/1.50 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 5.49/1.50 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 5.49/1.50 % 5.49/1.50 (d1_tarski) % 5.49/1.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 5.49/1.50 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 5.49/1.50 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = % 5.49/1.50 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 5.49/1.50 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 5.49/1.50 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = % 5.49/1.50 0 | v3 = v1))) % 5.49/1.50 % 5.49/1.50 (l30_zfmisc_1) % 5.49/1.51 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, v0) = v2) | ~ % 5.49/1.51 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & % 5.49/1.51 singleton(v1) = v3 & set_intersection2(v0, v3) = v4 & $i(v4) & $i(v3))) & % 5.49/1.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v1) = v2) | ~ % 5.49/1.51 (set_intersection2(v0, v2) = v2) | ~ $i(v1) | ~ $i(v0) | in(v1, v0) = 0) % 5.49/1.51 % 5.49/1.51 (t18_zfmisc_1) % 5.49/1.51 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = v0) & % 5.49/1.51 singleton(v1) = v3 & singleton(v0) = v2 & set_intersection2(v2, v3) = v2 & % 5.49/1.51 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.49/1.51 % 5.49/1.51 Further assumptions not needed in the proof: % 5.49/1.51 -------------------------------------------- % 5.49/1.51 antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0 % 5.49/1.51 % 5.49/1.51 Those formulas are unsatisfiable: % 5.49/1.51 --------------------------------- % 5.49/1.51 % 5.49/1.51 Begin of proof % 5.49/1.51 | % 5.49/1.51 | ALPHA: (commutativity_k3_xboole_0) implies: % 5.49/1.51 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, % 5.49/1.51 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = % 5.49/1.51 | v2 & $i(v2))) % 5.49/1.51 | % 5.49/1.51 | ALPHA: (d1_tarski) implies: % 5.49/1.51 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 5.49/1.51 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 5.49/1.51 | % 5.49/1.51 | ALPHA: (l30_zfmisc_1) implies: % 5.49/1.52 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v1) = v2) | ~ % 5.49/1.52 | (set_intersection2(v0, v2) = v2) | ~ $i(v1) | ~ $i(v0) | in(v1, v0) % 5.49/1.52 | = 0) % 5.49/1.52 | % 5.49/1.52 | DELTA: instantiating (t18_zfmisc_1) with fresh symbols all_12_0, all_12_1, % 5.49/1.52 | all_12_2, all_12_3 gives: % 5.49/1.52 | (4) ~ (all_12_2 = all_12_3) & singleton(all_12_2) = all_12_0 & % 5.49/1.52 | singleton(all_12_3) = all_12_1 & set_intersection2(all_12_1, all_12_0) % 5.49/1.52 | = all_12_1 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & $i(all_12_3) % 5.49/1.52 | % 5.49/1.52 | ALPHA: (4) implies: % 5.49/1.52 | (5) ~ (all_12_2 = all_12_3) % 5.49/1.52 | (6) $i(all_12_3) % 5.49/1.52 | (7) $i(all_12_2) % 5.49/1.52 | (8) $i(all_12_1) % 5.49/1.52 | (9) $i(all_12_0) % 5.49/1.52 | (10) set_intersection2(all_12_1, all_12_0) = all_12_1 % 5.49/1.52 | (11) singleton(all_12_3) = all_12_1 % 5.49/1.52 | (12) singleton(all_12_2) = all_12_0 % 5.49/1.52 | % 5.49/1.52 | GROUND_INST: instantiating (1) with all_12_0, all_12_1, all_12_1, simplifying % 5.49/1.52 | with (8), (9), (10) gives: % 5.49/1.52 | (13) set_intersection2(all_12_0, all_12_1) = all_12_1 % 5.49/1.52 | % 5.66/1.52 | GROUND_INST: instantiating (3) with all_12_0, all_12_3, all_12_1, simplifying % 5.66/1.52 | with (6), (9), (11), (13) gives: % 5.66/1.52 | (14) in(all_12_3, all_12_0) = 0 % 5.66/1.52 | % 5.66/1.53 | GROUND_INST: instantiating (2) with all_12_2, all_12_0, all_12_3, simplifying % 5.66/1.53 | with (6), (7), (9), (12), (14) gives: % 5.66/1.53 | (15) all_12_2 = all_12_3 % 5.66/1.53 | % 5.66/1.53 | REDUCE: (5), (15) imply: % 5.66/1.53 | (16) $false % 5.66/1.53 | % 5.66/1.53 | CLOSE: (16) is inconsistent. % 5.66/1.53 | % 5.66/1.53 End of proof % 5.66/1.53 % SZS output end Proof for theBenchmark % 5.66/1.53 % 5.66/1.53 917ms %------------------------------------------------------------------------------