%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET909+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 15:26:59 EDT 2023 % Result : Theorem 6.15s 1.61s % Output : Proof 8.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET909+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 : n019.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 13:05:58 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 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 % 1.81/1.00 Prover 4: Preprocessing ... % 1.81/1.00 Prover 1: Preprocessing ... % 2.37/1.04 Prover 6: Preprocessing ... % 2.37/1.04 Prover 2: Preprocessing ... % 2.37/1.04 Prover 3: Preprocessing ... % 2.37/1.04 Prover 0: Preprocessing ... % 2.37/1.04 Prover 5: Preprocessing ... % 4.46/1.34 Prover 1: Warning: ignoring some quantifiers % 4.46/1.35 Prover 3: Warning: ignoring some quantifiers % 4.46/1.36 Prover 4: Warning: ignoring some quantifiers % 4.46/1.36 Prover 3: Constructing countermodel ... % 4.46/1.36 Prover 1: Constructing countermodel ... % 4.46/1.37 Prover 4: Constructing countermodel ... % 4.46/1.38 Prover 6: Proving ... % 4.46/1.38 Prover 5: Proving ... % 4.46/1.38 Prover 2: Proving ... % 4.95/1.40 Prover 0: Proving ... % 6.15/1.61 Prover 2: proved (975ms) % 6.15/1.61 % 6.15/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.15/1.61 % 6.59/1.62 Prover 6: stopped % 6.59/1.62 Prover 5: stopped % 6.59/1.63 Prover 0: stopped % 6.59/1.63 Prover 3: stopped % 6.59/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.59/1.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.59/1.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.59/1.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.59/1.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.79/1.65 Prover 8: Preprocessing ... % 6.79/1.65 Prover 10: Preprocessing ... % 6.79/1.65 Prover 13: Preprocessing ... % 6.79/1.66 Prover 11: Preprocessing ... % 6.79/1.67 Prover 7: Preprocessing ... % 6.79/1.72 Prover 10: Warning: ignoring some quantifiers % 7.30/1.73 Prover 7: Warning: ignoring some quantifiers % 7.30/1.73 Prover 8: Warning: ignoring some quantifiers % 7.30/1.73 Prover 10: Constructing countermodel ... % 7.30/1.74 Prover 7: Constructing countermodel ... % 7.30/1.74 Prover 8: Constructing countermodel ... % 7.30/1.74 Prover 13: Warning: ignoring some quantifiers % 7.30/1.77 Prover 13: Constructing countermodel ... % 7.66/1.80 Prover 11: Warning: ignoring some quantifiers % 7.66/1.81 Prover 11: Constructing countermodel ... % 7.66/1.83 Prover 10: Found proof (size 14) % 7.66/1.83 Prover 10: proved (205ms) % 7.66/1.84 Prover 7: stopped % 7.66/1.84 Prover 1: stopped % 7.66/1.84 Prover 11: stopped % 7.66/1.84 Prover 13: stopped % 7.66/1.84 Prover 8: stopped % 7.66/1.84 Prover 4: stopped % 7.66/1.84 % 7.66/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.66/1.84 % 7.66/1.84 % SZS output start Proof for theBenchmark % 7.66/1.85 Assumptions after simplification: % 7.66/1.85 --------------------------------- % 7.66/1.85 % 8.21/1.85 (commutativity_k2_tarski) % 8.21/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | % 8.21/1.87 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 8.21/1.87 % 8.21/1.87 (commutativity_k2_xboole_0) % 8.35/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ % 8.35/1.87 $i(v1) | ~ $i(v0) | (set_union2(v1, v0) = v2 & $i(v2))) % 8.35/1.87 % 8.35/1.87 (d1_xboole_0) % 8.35/1.88 $i(empty_set) & ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) & ? [v0: $i] % 8.35/1.88 : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0))) % 8.35/1.88 % 8.35/1.88 (d2_tarski) % 8.35/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | % 8.35/1.88 ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.35/1.88 $i(v0) | ~ in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.35/1.88 $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 8.35/1.88 ~ $i(v0) | ? [v4: $i] : ($i(v4) & (v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ % 8.35/1.88 in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0: $i] : ! [v1: % 8.35/1.88 $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ % 8.35/1.88 $i(v1) | ~ $i(v0) | in(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 8.35/1.88 ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, % 8.35/1.88 v2)) % 8.35/1.88 % 8.35/1.88 (d2_xboole_0) % 8.35/1.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, % 8.35/1.89 v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, % 8.35/1.89 v2) | in(v3, v1) | in(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 8.35/1.89 ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 8.35/1.89 $i(v1) | ~ $i(v0) | ~ in(v3, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i] % 8.35/1.89 : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ % 8.35/1.89 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2)) & ? [v0: $i] : % 8.35/1.89 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_union2(v1, v2) = % 8.35/1.89 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ($i(v4) & ( ~ % 8.35/1.89 in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) % 8.35/1.89 | in(v4, v0)))) % 8.35/1.89 % 8.35/1.89 (t50_zfmisc_1) % 8.35/1.89 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 8.35/1.89 (set_union2(v3, v2) = empty_set & unordered_pair(v0, v1) = v3 & $i(v3) & % 8.35/1.89 $i(v2) & $i(v1) & $i(v0)) % 8.35/1.89 % 8.35/1.89 Further assumptions not needed in the proof: % 8.35/1.89 -------------------------------------------- % 8.35/1.89 antisymmetry_r2_hidden, fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, % 8.35/1.89 idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0 % 8.35/1.89 % 8.35/1.89 Those formulas are unsatisfiable: % 8.35/1.89 --------------------------------- % 8.35/1.89 % 8.35/1.89 Begin of proof % 8.35/1.89 | % 8.35/1.90 | ALPHA: (d1_xboole_0) implies: % 8.35/1.90 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) % 8.35/1.90 | % 8.35/1.90 | ALPHA: (d2_tarski) implies: % 8.35/1.90 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 8.35/1.90 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v1, v2)) % 8.35/1.90 | % 8.35/1.90 | ALPHA: (d2_xboole_0) implies: % 8.35/1.90 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.35/1.90 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.35/1.90 | $i(v0) | ~ in(v3, v1) | in(v3, v2)) % 8.35/1.90 | % 8.35/1.90 | ALPHA: (t50_zfmisc_1) implies: % 8.35/1.90 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (set_union2(v3, % 8.35/1.90 | v2) = empty_set & unordered_pair(v0, v1) = v3 & $i(v3) & $i(v2) & % 8.35/1.90 | $i(v1) & $i(v0)) % 8.35/1.90 | % 8.35/1.90 | DELTA: instantiating (4) with fresh symbols all_18_0, all_18_1, all_18_2, % 8.35/1.90 | all_18_3 gives: % 8.35/1.90 | (5) set_union2(all_18_0, all_18_1) = empty_set & unordered_pair(all_18_3, % 8.35/1.90 | all_18_2) = all_18_0 & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) & % 8.35/1.90 | $i(all_18_3) % 8.35/1.90 | % 8.35/1.90 | ALPHA: (5) implies: % 8.35/1.90 | (6) $i(all_18_3) % 8.35/1.90 | (7) $i(all_18_2) % 8.35/1.90 | (8) $i(all_18_1) % 8.35/1.90 | (9) $i(all_18_0) % 8.35/1.90 | (10) unordered_pair(all_18_3, all_18_2) = all_18_0 % 8.35/1.90 | (11) set_union2(all_18_0, all_18_1) = empty_set % 8.35/1.90 | % 8.35/1.90 | GROUND_INST: instantiating (2) with all_18_3, all_18_2, all_18_0, simplifying % 8.35/1.90 | with (6), (7), (9), (10) gives: % 8.35/1.90 | (12) in(all_18_2, all_18_0) % 8.35/1.90 | % 8.35/1.90 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_18_3, all_18_2, % 8.35/1.90 | all_18_0, simplifying with (6), (7), (10) gives: % 8.35/1.90 | (13) unordered_pair(all_18_2, all_18_3) = all_18_0 & $i(all_18_0) % 8.35/1.90 | % 8.35/1.91 | GROUND_INST: instantiating (commutativity_k2_xboole_0) with all_18_0, % 8.35/1.91 | all_18_1, empty_set, simplifying with (8), (9), (11) gives: % 8.35/1.91 | (14) set_union2(all_18_1, all_18_0) = empty_set & $i(empty_set) % 8.35/1.91 | % 8.35/1.91 | ALPHA: (14) implies: % 8.35/1.91 | (15) $i(empty_set) % 8.35/1.91 | (16) set_union2(all_18_1, all_18_0) = empty_set % 8.35/1.91 | % 8.35/1.91 | GROUND_INST: instantiating (3) with all_18_1, all_18_0, empty_set, all_18_2, % 8.35/1.91 | simplifying with (7), (8), (9), (12), (15), (16) gives: % 8.35/1.91 | (17) in(all_18_2, empty_set) % 8.35/1.91 | % 8.35/1.91 | GROUND_INST: instantiating (1) with all_18_2, simplifying with (7), (17) % 8.35/1.91 | gives: % 8.35/1.91 | (18) $false % 8.35/1.91 | % 8.35/1.91 | CLOSE: (18) is inconsistent. % 8.35/1.91 | % 8.35/1.91 End of proof % 8.35/1.91 % SZS output end Proof for theBenchmark % 8.35/1.91 % 8.35/1.91 1291ms %------------------------------------------------------------------------------