%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU112+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 17:42:33 EDT 2023 % Result : Theorem 8.94s 1.94s % Output : Proof 11.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU112+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n019.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Aug 24 00:50:14 EDT 2023 % 0.14/0.35 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 2.90/1.10 Prover 4: Preprocessing ... % 2.90/1.10 Prover 1: Preprocessing ... % 3.23/1.14 Prover 5: Preprocessing ... % 3.23/1.14 Prover 6: Preprocessing ... % 3.23/1.15 Prover 0: Preprocessing ... % 3.23/1.15 Prover 2: Preprocessing ... % 3.23/1.15 Prover 3: Preprocessing ... % 5.83/1.57 Prover 5: Proving ... % 6.43/1.59 Prover 1: Warning: ignoring some quantifiers % 6.61/1.61 Prover 2: Proving ... % 6.72/1.62 Prover 1: Constructing countermodel ... % 6.72/1.64 Prover 6: Proving ... % 6.72/1.65 Prover 3: Warning: ignoring some quantifiers % 6.72/1.67 Prover 4: Warning: ignoring some quantifiers % 6.72/1.67 Prover 3: Constructing countermodel ... % 6.72/1.70 Prover 4: Constructing countermodel ... % 7.43/1.74 Prover 0: Proving ... % 8.94/1.93 Prover 5: proved (1292ms) % 8.94/1.93 % 8.94/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.94/1.94 % 8.94/1.95 Prover 3: stopped % 8.94/1.95 Prover 6: stopped % 8.94/1.95 Prover 2: stopped % 8.94/1.95 Prover 0: stopped % 8.94/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.94/1.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.94/1.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.94/1.95 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.94/1.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.57/2.02 Prover 10: Preprocessing ... % 9.57/2.02 Prover 13: Preprocessing ... % 9.57/2.03 Prover 8: Preprocessing ... % 9.57/2.03 Prover 11: Preprocessing ... % 9.57/2.03 Prover 7: Preprocessing ... % 9.57/2.10 Prover 10: Warning: ignoring some quantifiers % 9.57/2.11 Prover 7: Warning: ignoring some quantifiers % 9.57/2.12 Prover 7: Constructing countermodel ... % 9.57/2.13 Prover 13: Warning: ignoring some quantifiers % 9.57/2.13 Prover 10: Constructing countermodel ... % 9.57/2.14 Prover 13: Constructing countermodel ... % 9.57/2.20 Prover 8: Warning: ignoring some quantifiers % 9.57/2.23 Prover 8: Constructing countermodel ... % 11.01/2.25 Prover 13: Found proof (size 11) % 11.01/2.25 Prover 13: proved (295ms) % 11.01/2.25 Prover 7: stopped % 11.01/2.25 Prover 4: stopped % 11.01/2.25 Prover 10: Found proof (size 10) % 11.01/2.25 Prover 10: proved (297ms) % 11.01/2.25 Prover 8: stopped % 11.01/2.25 Prover 1: stopped % 11.01/2.27 Prover 11: Warning: ignoring some quantifiers % 11.01/2.28 Prover 11: Constructing countermodel ... % 11.01/2.29 Prover 11: stopped % 11.01/2.29 % 11.01/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.01/2.29 % 11.01/2.29 % SZS output start Proof for theBenchmark % 11.01/2.29 Assumptions after simplification: % 11.01/2.29 --------------------------------- % 11.01/2.29 % 11.01/2.29 (commutativity_k2_xboole_0) % 11.01/2.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ % 11.01/2.32 $i(v1) | ~ $i(v0) | (set_union2(v1, v0) = v2 & $i(v2))) % 11.01/2.32 % 11.01/2.32 (t23_finsub_1) % 11.01/2.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 11.01/2.32 (finite_subsets(v1) = v3) | ~ (finite_subsets(v0) = v2) | ~ $i(v1) | ~ % 11.01/2.32 $i(v0) | ~ subset(v0, v1) | subset(v2, v3)) % 11.01/2.32 % 11.01/2.32 (t25_finsub_1) % 11.01/2.32 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 11.01/2.32 $i] : ? [v6: $i] : (set_union2(v2, v3) = v4 & set_union2(v0, v1) = v5 & % 11.01/2.32 finite_subsets(v5) = v6 & finite_subsets(v1) = v3 & finite_subsets(v0) = v2 % 11.01/2.32 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 11.01/2.32 subset(v4, v6)) % 11.01/2.32 % 11.01/2.32 (t7_xboole_1) % 11.01/2.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ % 11.01/2.32 $i(v1) | ~ $i(v0) | subset(v0, v2)) & ? [v0: $i] : ? [v1: $i] : ( ~ % 11.01/2.32 $i(v1) | ~ $i(v0) | ? [v2: $i] : (set_union2(v0, v1) = v2 & $i(v2) & % 11.01/2.32 subset(v0, v2))) % 11.01/2.32 % 11.01/2.33 (t8_xboole_1) % 11.01/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, % 11.01/2.33 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ subset(v2, v1) | ~ % 11.01/2.33 subset(v0, v1) | subset(v3, v1)) % 11.01/2.33 % 11.01/2.33 Further assumptions not needed in the proof: % 11.01/2.33 -------------------------------------------- % 11.01/2.33 antisymmetry_r2_hidden, cc1_finset_1, cc1_finsub_1, cc2_finset_1, cc2_finsub_1, % 11.01/2.33 cc3_finsub_1, dt_k5_finsub_1, existence_m1_subset_1, fc1_finsub_1, fc1_subset_1, % 11.01/2.33 fc1_xboole_0, fc2_finsub_1, fc2_xboole_0, fc3_xboole_0, fc9_finset_1, % 11.01/2.33 idempotence_k2_xboole_0, rc1_finset_1, rc1_finsub_1, rc1_subset_1, rc1_xboole_0, % 11.01/2.33 rc2_finset_1, rc2_subset_1, rc2_xboole_0, rc3_finset_1, rc4_finset_1, % 11.01/2.33 reflexivity_r1_tarski, t1_boole, t1_subset, t2_subset, t3_subset, t4_subset, % 11.01/2.33 t5_subset, t6_boole, t7_boole, t8_boole % 11.01/2.33 % 11.01/2.33 Those formulas are unsatisfiable: % 11.01/2.33 --------------------------------- % 11.01/2.33 % 11.01/2.33 Begin of proof % 11.68/2.33 | % 11.68/2.33 | ALPHA: (t7_xboole_1) implies: % 11.68/2.33 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) % 11.68/2.33 | | ~ $i(v1) | ~ $i(v0) | subset(v0, v2)) % 11.68/2.33 | % 11.68/2.33 | DELTA: instantiating (t25_finsub_1) with fresh symbols all_49_0, all_49_1, % 11.68/2.33 | all_49_2, all_49_3, all_49_4, all_49_5, all_49_6 gives: % 11.68/2.33 | (2) set_union2(all_49_4, all_49_3) = all_49_2 & set_union2(all_49_6, % 11.68/2.33 | all_49_5) = all_49_1 & finite_subsets(all_49_1) = all_49_0 & % 11.68/2.33 | finite_subsets(all_49_5) = all_49_3 & finite_subsets(all_49_6) = % 11.68/2.33 | all_49_4 & $i(all_49_0) & $i(all_49_1) & $i(all_49_2) & $i(all_49_3) & % 11.68/2.33 | $i(all_49_4) & $i(all_49_5) & $i(all_49_6) & ~ subset(all_49_2, % 11.68/2.33 | all_49_0) % 11.68/2.33 | % 11.68/2.33 | ALPHA: (2) implies: % 11.71/2.33 | (3) ~ subset(all_49_2, all_49_0) % 11.71/2.33 | (4) $i(all_49_6) % 11.71/2.33 | (5) $i(all_49_5) % 11.71/2.33 | (6) $i(all_49_4) % 11.71/2.33 | (7) $i(all_49_3) % 11.71/2.33 | (8) $i(all_49_0) % 11.71/2.33 | (9) finite_subsets(all_49_6) = all_49_4 % 11.71/2.33 | (10) finite_subsets(all_49_5) = all_49_3 % 11.71/2.33 | (11) finite_subsets(all_49_1) = all_49_0 % 11.71/2.33 | (12) set_union2(all_49_6, all_49_5) = all_49_1 % 11.71/2.33 | (13) set_union2(all_49_4, all_49_3) = all_49_2 % 11.71/2.33 | % 11.71/2.34 | GROUND_INST: instantiating (1) with all_49_6, all_49_5, all_49_1, simplifying % 11.71/2.34 | with (4), (5), (12) gives: % 11.71/2.34 | (14) subset(all_49_6, all_49_1) % 11.71/2.34 | % 11.71/2.34 | GROUND_INST: instantiating (commutativity_k2_xboole_0) with all_49_6, % 11.71/2.34 | all_49_5, all_49_1, simplifying with (4), (5), (12) gives: % 11.71/2.34 | (15) set_union2(all_49_5, all_49_6) = all_49_1 & $i(all_49_1) % 11.71/2.34 | % 11.71/2.34 | ALPHA: (15) implies: % 11.71/2.34 | (16) $i(all_49_1) % 11.71/2.34 | (17) set_union2(all_49_5, all_49_6) = all_49_1 % 11.71/2.34 | % 11.71/2.34 | GROUND_INST: instantiating (t23_finsub_1) with all_49_6, all_49_1, all_49_4, % 11.71/2.34 | all_49_0, simplifying with (4), (9), (11), (14), (16) gives: % 11.71/2.34 | (18) subset(all_49_4, all_49_0) % 11.71/2.34 | % 11.71/2.34 | GROUND_INST: instantiating (1) with all_49_5, all_49_6, all_49_1, simplifying % 11.71/2.34 | with (4), (5), (17) gives: % 11.71/2.34 | (19) subset(all_49_5, all_49_1) % 11.71/2.34 | % 11.71/2.34 | GROUND_INST: instantiating (t23_finsub_1) with all_49_5, all_49_1, all_49_3, % 11.71/2.34 | all_49_0, simplifying with (5), (10), (11), (16), (19) gives: % 11.71/2.34 | (20) subset(all_49_3, all_49_0) % 11.71/2.34 | % 11.71/2.34 | GROUND_INST: instantiating (t8_xboole_1) with all_49_4, all_49_0, all_49_3, % 11.71/2.34 | all_49_2, simplifying with (3), (6), (7), (8), (13), (18), (20) % 11.71/2.34 | gives: % 11.71/2.34 | (21) $false % 11.71/2.34 | % 11.71/2.34 | CLOSE: (21) is inconsistent. % 11.71/2.34 | % 11.71/2.34 End of proof % 11.71/2.34 % SZS output end Proof for theBenchmark % 11.71/2.34 % 11.71/2.34 1730ms %------------------------------------------------------------------------------