%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET908+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 : n022.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 15:26:59 EDT 2023 % Result : Theorem 6.12s 1.67s % Output : Proof 8.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET908+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n022.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 13:32:40 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 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 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 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 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 % 2.10/1.02 Prover 1: Preprocessing ... % 2.10/1.02 Prover 4: Preprocessing ... % 2.10/1.07 Prover 3: Preprocessing ... % 2.10/1.07 Prover 0: Preprocessing ... % 2.10/1.07 Prover 6: Preprocessing ... % 2.10/1.07 Prover 2: Preprocessing ... % 2.10/1.07 Prover 5: Preprocessing ... % 4.13/1.38 Prover 4: Warning: ignoring some quantifiers % 4.13/1.38 Prover 1: Warning: ignoring some quantifiers % 4.13/1.39 Prover 3: Warning: ignoring some quantifiers % 4.13/1.41 Prover 2: Proving ... % 4.13/1.41 Prover 6: Proving ... % 4.13/1.41 Prover 3: Constructing countermodel ... % 4.13/1.41 Prover 1: Constructing countermodel ... % 4.13/1.41 Prover 4: Constructing countermodel ... % 4.13/1.42 Prover 5: Proving ... % 4.13/1.43 Prover 0: Proving ... % 6.12/1.67 Prover 2: proved (1034ms) % 6.12/1.67 % 6.12/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.12/1.67 % 6.12/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.12/1.67 Prover 0: stopped % 6.12/1.67 Prover 5: stopped % 6.12/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.12/1.68 Prover 6: stopped % 6.12/1.70 Prover 3: stopped % 6.85/1.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.85/1.71 Prover 8: Preprocessing ... % 6.85/1.71 Prover 7: Preprocessing ... % 6.85/1.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.85/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.85/1.71 Prover 10: Preprocessing ... % 6.85/1.72 Prover 11: Preprocessing ... % 6.85/1.74 Prover 13: Preprocessing ... % 6.85/1.75 Prover 7: Warning: ignoring some quantifiers % 6.85/1.75 Prover 10: Warning: ignoring some quantifiers % 6.85/1.76 Prover 7: Constructing countermodel ... % 6.85/1.77 Prover 10: Constructing countermodel ... % 6.85/1.77 Prover 4: gave up % 6.85/1.77 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.85/1.78 Prover 8: Warning: ignoring some quantifiers % 6.85/1.79 Prover 8: Constructing countermodel ... % 6.85/1.79 Prover 16: Preprocessing ... % 7.55/1.84 Prover 13: Warning: ignoring some quantifiers % 7.55/1.84 Prover 13: Constructing countermodel ... % 7.55/1.85 Prover 10: Found proof (size 12) % 7.55/1.85 Prover 10: proved (164ms) % 7.55/1.85 Prover 8: stopped % 7.55/1.85 Prover 1: stopped % 7.55/1.85 Prover 7: stopped % 7.55/1.85 Prover 13: stopped % 7.55/1.86 Prover 16: Warning: ignoring some quantifiers % 7.55/1.87 Prover 16: Constructing countermodel ... % 7.55/1.87 Prover 11: Warning: ignoring some quantifiers % 7.55/1.87 Prover 16: stopped % 7.55/1.88 Prover 11: Constructing countermodel ... % 7.55/1.88 Prover 11: stopped % 7.55/1.89 % 7.55/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.55/1.89 % 8.16/1.89 % SZS output start Proof for theBenchmark % 8.16/1.89 Assumptions after simplification: % 8.16/1.89 --------------------------------- % 8.16/1.89 % 8.16/1.89 (commutativity_k2_xboole_0) % 8.24/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ % 8.24/1.92 $i(v1) | ~ $i(v0) | (set_union2(v1, v0) = v2 & $i(v2))) % 8.24/1.92 % 8.24/1.92 (d1_tarski) % 8.24/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 8.24/1.92 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1: % 8.24/1.92 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ % 8.24/1.92 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | % 8.24/1.92 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | % 8.24/1.92 ~ $i(v1) | ~ $i(v0) | in(v0, v1)) % 8.24/1.92 % 8.24/1.92 (d1_xboole_0) % 8.24/1.92 $i(empty_set) & ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) & ? [v0: $i] % 8.24/1.92 : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0))) % 8.24/1.92 % 8.24/1.92 (d2_xboole_0) % 8.24/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, % 8.24/1.93 v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, % 8.24/1.93 v2) | in(v3, v1) | in(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 8.24/1.93 ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 8.24/1.93 $i(v1) | ~ $i(v0) | ~ in(v3, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i] % 8.24/1.93 : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ % 8.24/1.93 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2)) & ? [v0: $i] : % 8.24/1.93 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_union2(v1, v2) = % 8.24/1.93 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ($i(v4) & ( ~ % 8.24/1.93 in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) % 8.24/1.93 | in(v4, v0)))) % 8.24/1.93 % 8.24/1.93 (t49_zfmisc_1) % 8.24/1.93 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(v0) = v2 % 8.24/1.93 & set_union2(v2, v1) = empty_set & $i(v2) & $i(v1) & $i(v0)) % 8.24/1.93 % 8.24/1.93 Further assumptions not needed in the proof: % 8.24/1.93 -------------------------------------------- % 8.24/1.93 antisymmetry_r2_hidden, fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, % 8.24/1.93 idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0 % 8.24/1.93 % 8.24/1.93 Those formulas are unsatisfiable: % 8.24/1.93 --------------------------------- % 8.24/1.93 % 8.24/1.93 Begin of proof % 8.24/1.93 | % 8.24/1.93 | ALPHA: (d1_tarski) implies: % 8.24/1.94 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ % 8.24/1.94 | $i(v0) | in(v0, v1)) % 8.24/1.94 | % 8.24/1.94 | ALPHA: (d1_xboole_0) implies: % 8.24/1.94 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) % 8.24/1.94 | % 8.24/1.94 | ALPHA: (d2_xboole_0) implies: % 8.24/1.94 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.24/1.94 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.24/1.94 | $i(v0) | ~ in(v3, v1) | in(v3, v2)) % 8.24/1.94 | % 8.24/1.94 | ALPHA: (t49_zfmisc_1) implies: % 8.24/1.94 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(v0) = v2 & % 8.24/1.94 | set_union2(v2, v1) = empty_set & $i(v2) & $i(v1) & $i(v0)) % 8.24/1.94 | % 8.24/1.94 | DELTA: instantiating (4) with fresh symbols all_17_0, all_17_1, all_17_2 % 8.24/1.94 | gives: % 8.24/1.94 | (5) singleton(all_17_2) = all_17_0 & set_union2(all_17_0, all_17_1) = % 8.24/1.94 | empty_set & $i(all_17_0) & $i(all_17_1) & $i(all_17_2) % 8.24/1.94 | % 8.24/1.94 | ALPHA: (5) implies: % 8.24/1.94 | (6) $i(all_17_2) % 8.24/1.94 | (7) $i(all_17_1) % 8.24/1.94 | (8) $i(all_17_0) % 8.24/1.94 | (9) set_union2(all_17_0, all_17_1) = empty_set % 8.24/1.94 | (10) singleton(all_17_2) = all_17_0 % 8.24/1.94 | % 8.24/1.94 | GROUND_INST: instantiating (commutativity_k2_xboole_0) with all_17_0, % 8.24/1.94 | all_17_1, empty_set, simplifying with (7), (8), (9) gives: % 8.24/1.94 | (11) set_union2(all_17_1, all_17_0) = empty_set & $i(empty_set) % 8.24/1.94 | % 8.24/1.94 | ALPHA: (11) implies: % 8.24/1.94 | (12) $i(empty_set) % 8.24/1.95 | (13) set_union2(all_17_1, all_17_0) = empty_set % 8.24/1.95 | % 8.24/1.95 | GROUND_INST: instantiating (1) with all_17_2, all_17_0, simplifying with (6), % 8.24/1.95 | (8), (10) gives: % 8.24/1.95 | (14) in(all_17_2, all_17_0) % 8.24/1.95 | % 8.24/1.95 | GROUND_INST: instantiating (3) with all_17_1, all_17_0, empty_set, all_17_2, % 8.24/1.95 | simplifying with (6), (7), (8), (12), (13), (14) gives: % 8.24/1.95 | (15) in(all_17_2, empty_set) % 8.24/1.95 | % 8.24/1.95 | GROUND_INST: instantiating (2) with all_17_2, simplifying with (6), (15) % 8.24/1.95 | gives: % 8.24/1.95 | (16) $false % 8.24/1.95 | % 8.24/1.95 | CLOSE: (16) is inconsistent. % 8.24/1.95 | % 8.24/1.95 End of proof % 8.24/1.95 % SZS output end Proof for theBenchmark % 8.24/1.95 % 8.24/1.95 1338ms %------------------------------------------------------------------------------