%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU172+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n003.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 17:43:02 EDT 2023 % Result : Theorem 6.50s 1.65s % Output : Proof 9.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU172+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n003.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Aug 23 19:57:22 EDT 2023 % 0.17/0.35 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.87/0.99 Prover 1: Preprocessing ... % 1.87/0.99 Prover 4: Preprocessing ... % 2.51/1.03 Prover 6: Preprocessing ... % 2.51/1.03 Prover 3: Preprocessing ... % 2.51/1.03 Prover 0: Preprocessing ... % 2.51/1.03 Prover 2: Preprocessing ... % 2.51/1.04 Prover 5: Preprocessing ... % 4.55/1.38 Prover 1: Warning: ignoring some quantifiers % 4.55/1.40 Prover 4: Warning: ignoring some quantifiers % 4.55/1.40 Prover 3: Warning: ignoring some quantifiers % 5.08/1.41 Prover 6: Proving ... % 5.08/1.41 Prover 2: Proving ... % 5.08/1.41 Prover 3: Constructing countermodel ... % 5.08/1.41 Prover 1: Constructing countermodel ... % 5.08/1.42 Prover 5: Proving ... % 5.08/1.42 Prover 4: Constructing countermodel ... % 5.08/1.45 Prover 0: Proving ... % 6.50/1.63 Prover 5: proved (1002ms) % 6.50/1.64 % 6.50/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.50/1.65 % 6.50/1.65 Prover 6: stopped % 6.50/1.65 Prover 0: stopped % 6.50/1.65 Prover 2: stopped % 6.50/1.67 Prover 3: stopped % 6.50/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.50/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.50/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.50/1.67 Prover 8: Preprocessing ... % 6.50/1.67 Prover 10: Preprocessing ... % 6.50/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.50/1.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.50/1.70 Prover 7: Preprocessing ... % 6.50/1.71 Prover 11: Preprocessing ... % 7.19/1.71 Prover 13: Preprocessing ... % 7.19/1.78 Prover 10: Warning: ignoring some quantifiers % 7.19/1.79 Prover 10: Constructing countermodel ... % 7.83/1.81 Prover 7: Warning: ignoring some quantifiers % 7.83/1.81 Prover 8: Warning: ignoring some quantifiers % 7.83/1.82 Prover 7: Constructing countermodel ... % 7.83/1.82 Prover 8: Constructing countermodel ... % 7.83/1.82 Prover 13: Warning: ignoring some quantifiers % 7.83/1.84 Prover 13: Constructing countermodel ... % 7.83/1.85 Prover 11: Warning: ignoring some quantifiers % 7.83/1.86 Prover 11: Constructing countermodel ... % 8.55/1.91 Prover 10: Found proof (size 21) % 8.55/1.91 Prover 10: proved (260ms) % 8.55/1.91 Prover 8: stopped % 8.55/1.91 Prover 4: stopped % 8.55/1.91 Prover 13: stopped % 8.55/1.92 Prover 1: stopped % 8.55/1.92 Prover 11: stopped % 8.55/1.92 Prover 7: stopped % 8.55/1.92 % 8.55/1.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.55/1.92 % 8.55/1.92 % SZS output start Proof for theBenchmark % 8.55/1.93 Assumptions after simplification: % 8.55/1.93 --------------------------------- % 8.55/1.93 % 8.55/1.93 (d4_xboole_0) % 8.55/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.55/1.96 (set_difference(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.55/1.96 $i(v0) | ~ in(v3, v2) | ~ in(v3, v1)) & ! [v0: $i] : ! [v1: $i] : ! % 8.55/1.96 [v2: $i] : ! [v3: $i] : ( ~ (set_difference(v0, v1) = v2) | ~ $i(v3) | ~ % 8.55/1.96 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v2) | in(v3, v0)) & ! [v0: $i] : % 8.55/1.96 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_difference(v0, v1) = v2) | % 8.55/1.96 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2) | % 8.55/1.96 in(v3, v1)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = % 8.55/1.96 v0 | ~ (set_difference(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 8.55/1.96 ? [v4: $i] : ($i(v4) & ( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & % 8.55/1.96 (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) % 8.55/1.96 % 8.55/1.96 (d5_subset_1) % 8.55/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 8.55/1.96 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ((v4 = v2 & % 8.55/1.96 set_difference(v0, v1) = v2 & $i(v2)) | (powerset(v0) = v3 & $i(v3) & ~ % 8.55/1.96 element(v1, v3)))) % 8.55/1.96 % 8.55/1.96 (dt_k3_subset_1) % 8.55/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 8.55/1.96 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (powerset(v0) = v3 & $i(v3) & ( ~ % 8.55/1.96 element(v1, v3) | element(v2, v3)))) % 8.55/1.96 % 8.55/1.96 (t54_subset_1) % 8.55/1.96 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 8.55/1.96 (subset_complement(v0, v2) = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & $i(v2) % 8.55/1.96 & $i(v1) & $i(v0) & in(v1, v4) & in(v1, v2) & element(v2, v3)) % 8.55/1.96 % 8.55/1.96 (function-axioms) % 8.55/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.55/1.97 (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! % 8.55/1.97 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.55/1.97 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 8.55/1.97 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 8.55/1.97 (powerset(v2) = v0)) % 8.55/1.97 % 8.55/1.97 Further assumptions not needed in the proof: % 8.55/1.97 -------------------------------------------- % 8.55/1.97 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k4_xboole_0, % 8.55/1.97 dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, % 8.55/1.97 involutiveness_k3_subset_1, rc1_subset_1, rc1_xboole_0, rc2_subset_1, % 8.55/1.97 rc2_xboole_0, t3_boole, t4_boole, t6_boole, t7_boole, t8_boole % 8.55/1.97 % 8.55/1.97 Those formulas are unsatisfiable: % 8.55/1.97 --------------------------------- % 8.55/1.97 % 8.55/1.97 Begin of proof % 8.55/1.97 | % 8.55/1.97 | ALPHA: (d4_xboole_0) implies: % 8.55/1.97 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.55/1.97 | (set_difference(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 8.55/1.97 | ~ $i(v0) | ~ in(v3, v2) | ~ in(v3, v1)) % 8.55/1.97 | % 8.55/1.97 | ALPHA: (function-axioms) implies: % 8.55/1.97 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = % 8.55/1.97 | v1) | ~ (powerset(v2) = v0)) % 8.55/1.97 | % 8.55/1.97 | DELTA: instantiating (t54_subset_1) with fresh symbols all_22_0, all_22_1, % 8.55/1.97 | all_22_2, all_22_3, all_22_4 gives: % 8.55/1.97 | (3) subset_complement(all_22_4, all_22_2) = all_22_0 & powerset(all_22_4) = % 8.55/1.97 | all_22_1 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & $i(all_22_3) & % 8.55/1.97 | $i(all_22_4) & in(all_22_3, all_22_0) & in(all_22_3, all_22_2) & % 8.55/1.97 | element(all_22_2, all_22_1) % 8.55/1.97 | % 8.55/1.97 | ALPHA: (3) implies: % 8.55/1.97 | (4) element(all_22_2, all_22_1) % 8.55/1.97 | (5) in(all_22_3, all_22_2) % 8.55/1.97 | (6) in(all_22_3, all_22_0) % 8.55/1.97 | (7) $i(all_22_4) % 8.55/1.97 | (8) $i(all_22_3) % 8.55/1.97 | (9) $i(all_22_2) % 8.55/1.97 | (10) powerset(all_22_4) = all_22_1 % 8.55/1.97 | (11) subset_complement(all_22_4, all_22_2) = all_22_0 % 8.55/1.97 | % 8.55/1.98 | GROUND_INST: instantiating (d5_subset_1) with all_22_4, all_22_2, all_22_0, % 8.55/1.98 | simplifying with (7), (9), (11) gives: % 8.55/1.98 | (12) ? [v0: $i] : ? [v1: int] : ((v1 = all_22_0 & % 8.55/1.98 | set_difference(all_22_4, all_22_2) = all_22_0 & $i(all_22_0)) | % 8.55/1.98 | (powerset(all_22_4) = v0 & $i(v0) & ~ element(all_22_2, v0))) % 8.55/1.98 | % 8.55/1.98 | GROUND_INST: instantiating (dt_k3_subset_1) with all_22_4, all_22_2, all_22_0, % 8.55/1.98 | simplifying with (7), (9), (11) gives: % 8.55/1.98 | (13) ? [v0: $i] : (powerset(all_22_4) = v0 & $i(v0) & ( ~ % 8.55/1.98 | element(all_22_2, v0) | element(all_22_0, v0))) % 8.55/1.98 | % 8.55/1.98 | DELTA: instantiating (13) with fresh symbol all_34_0 gives: % 8.55/1.98 | (14) powerset(all_22_4) = all_34_0 & $i(all_34_0) & ( ~ element(all_22_2, % 8.55/1.98 | all_34_0) | element(all_22_0, all_34_0)) % 8.55/1.98 | % 8.55/1.98 | ALPHA: (14) implies: % 8.55/1.98 | (15) powerset(all_22_4) = all_34_0 % 8.55/1.98 | % 8.55/1.98 | DELTA: instantiating (12) with fresh symbols all_36_0, all_36_1 gives: % 8.55/1.98 | (16) (all_36_0 = all_22_0 & set_difference(all_22_4, all_22_2) = all_22_0 & % 8.55/1.98 | $i(all_22_0)) | (powerset(all_22_4) = all_36_1 & $i(all_36_1) & ~ % 8.55/1.98 | element(all_22_2, all_36_1)) % 8.55/1.98 | % 8.55/1.98 | GROUND_INST: instantiating (2) with all_22_1, all_34_0, all_22_4, simplifying % 8.55/1.98 | with (10), (15) gives: % 8.55/1.98 | (17) all_34_0 = all_22_1 % 8.55/1.98 | % 8.55/1.98 | BETA: splitting (16) gives: % 8.55/1.98 | % 8.55/1.98 | Case 1: % 8.55/1.98 | | % 8.55/1.98 | | (18) all_36_0 = all_22_0 & set_difference(all_22_4, all_22_2) = all_22_0 % 8.55/1.98 | | & $i(all_22_0) % 8.55/1.98 | | % 8.55/1.98 | | ALPHA: (18) implies: % 8.55/1.98 | | (19) $i(all_22_0) % 8.55/1.98 | | (20) set_difference(all_22_4, all_22_2) = all_22_0 % 8.55/1.98 | | % 8.55/1.98 | | GROUND_INST: instantiating (1) with all_22_4, all_22_2, all_22_0, all_22_3, % 8.55/1.98 | | simplifying with (5), (6), (7), (8), (9), (19), (20) gives: % 8.55/1.98 | | (21) $false % 9.10/1.98 | | % 9.10/1.98 | | CLOSE: (21) is inconsistent. % 9.10/1.98 | | % 9.10/1.98 | Case 2: % 9.10/1.98 | | % 9.10/1.98 | | (22) powerset(all_22_4) = all_36_1 & $i(all_36_1) & ~ element(all_22_2, % 9.10/1.98 | | all_36_1) % 9.10/1.98 | | % 9.10/1.98 | | ALPHA: (22) implies: % 9.10/1.99 | | (23) ~ element(all_22_2, all_36_1) % 9.10/1.99 | | (24) powerset(all_22_4) = all_36_1 % 9.10/1.99 | | % 9.10/1.99 | | GROUND_INST: instantiating (2) with all_22_1, all_36_1, all_22_4, % 9.10/1.99 | | simplifying with (10), (24) gives: % 9.10/1.99 | | (25) all_36_1 = all_22_1 % 9.10/1.99 | | % 9.10/1.99 | | REDUCE: (23), (25) imply: % 9.10/1.99 | | (26) ~ element(all_22_2, all_22_1) % 9.10/1.99 | | % 9.10/1.99 | | PRED_UNIFY: (4), (26) imply: % 9.10/1.99 | | (27) $false % 9.10/1.99 | | % 9.10/1.99 | | CLOSE: (27) is inconsistent. % 9.10/1.99 | | % 9.10/1.99 | End of split % 9.10/1.99 | % 9.10/1.99 End of proof % 9.10/1.99 % SZS output end Proof for theBenchmark % 9.10/1.99 % 9.10/1.99 1384ms %------------------------------------------------------------------------------