%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU354+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 : n028.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 17:44:15 EDT 2023 % Result : Theorem 10.07s 2.16s % Output : Proof 13.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU354+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n028.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % 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 : Wed Aug 23 12:59:18 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.67 ________ _____ % 0.20/0.67 ___ __ \_________(_)________________________________ % 0.20/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.67 % 0.20/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.67 (2023-06-19) % 0.20/0.67 % 0.20/0.67 (c) Philipp Rümmer, 2009-2023 % 0.20/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.67 Amanda Stjerna. % 0.20/0.67 Free software under BSD-3-Clause. % 0.20/0.67 % 0.20/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.67 % 0.20/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.68 Running up to 7 provers in parallel. % 0.20/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.14/1.17 Prover 4: Preprocessing ... % 3.14/1.18 Prover 1: Preprocessing ... % 3.37/1.22 Prover 6: Preprocessing ... % 3.37/1.22 Prover 3: Preprocessing ... % 3.37/1.22 Prover 2: Preprocessing ... % 3.37/1.22 Prover 0: Preprocessing ... % 3.37/1.22 Prover 5: Preprocessing ... % 6.50/1.68 Prover 1: Warning: ignoring some quantifiers % 7.12/1.73 Prover 3: Warning: ignoring some quantifiers % 7.12/1.74 Prover 1: Constructing countermodel ... % 7.12/1.75 Prover 2: Proving ... % 7.12/1.75 Prover 5: Proving ... % 7.12/1.75 Prover 6: Proving ... % 7.12/1.75 Prover 3: Constructing countermodel ... % 8.22/1.93 Prover 4: Warning: ignoring some quantifiers % 8.22/1.99 Prover 4: Constructing countermodel ... % 9.40/2.08 Prover 0: Proving ... % 10.07/2.16 Prover 5: proved (1462ms) % 10.07/2.16 % 10.07/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.07/2.16 % 10.07/2.16 Prover 3: stopped % 10.07/2.16 Prover 2: stopped % 10.07/2.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.07/2.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.07/2.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.07/2.16 Prover 6: stopped % 10.07/2.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.07/2.17 Prover 0: stopped % 10.07/2.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.44/2.23 Prover 13: Preprocessing ... % 10.44/2.24 Prover 10: Preprocessing ... % 10.92/2.25 Prover 7: Preprocessing ... % 11.02/2.26 Prover 11: Preprocessing ... % 11.02/2.27 Prover 8: Preprocessing ... % 11.42/2.33 Prover 13: Warning: ignoring some quantifiers % 11.42/2.34 Prover 10: Warning: ignoring some quantifiers % 11.72/2.35 Prover 13: Constructing countermodel ... % 11.72/2.36 Prover 7: Warning: ignoring some quantifiers % 11.72/2.38 Prover 7: Constructing countermodel ... % 11.72/2.38 Prover 10: Constructing countermodel ... % 11.72/2.40 Prover 8: Warning: ignoring some quantifiers % 11.72/2.43 Prover 8: Constructing countermodel ... % 12.40/2.48 Prover 13: Found proof (size 20) % 12.40/2.48 Prover 13: proved (311ms) % 12.40/2.48 Prover 8: stopped % 12.40/2.48 Prover 10: stopped % 12.40/2.48 Prover 4: stopped % 12.40/2.48 Prover 1: stopped % 12.40/2.48 Prover 7: stopped % 13.05/2.57 Prover 11: Warning: ignoring some quantifiers % 13.05/2.58 Prover 11: Constructing countermodel ... % 13.05/2.60 Prover 11: stopped % 13.05/2.60 % 13.05/2.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.05/2.60 % 13.05/2.60 % SZS output start Proof for theBenchmark % 13.05/2.61 Assumptions after simplification: % 13.05/2.61 --------------------------------- % 13.05/2.61 % 13.05/2.61 (d2_tex_2) % 13.05/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (union(v0) = v2) | ~ % 13.05/2.64 $i(v1) | ~ $i(v0) | ~ element(v1, v0) | proper_element(v1, v0)) & ! [v0: % 13.05/2.64 $i] : ! [v1: $i] : ( ~ (union(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ % 13.05/2.64 proper_element(v1, v0) | ~ element(v1, v0)) % 13.05/2.64 % 13.05/2.64 (rc2_tex_2) % 13.05/2.64 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 13.05/2.64 : ($i(v2) & element(v2, v1) & ~ proper_element(v2, v1))) % 13.05/2.64 % 13.05/2.64 (t5_tex_2) % 13.05/2.64 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (powerset(v0) = v2 & $i(v2) & $i(v1) % 13.05/2.64 & $i(v0) & element(v1, v2) & ((v1 = v0 & proper_element(v0, v2)) | ( ~ (v1 = % 13.05/2.64 v0) & ~ proper_element(v1, v2)))) % 13.05/2.64 % 13.05/2.64 (t99_zfmisc_1) % 13.05/2.64 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | union(v1) = % 13.05/2.64 v0) % 13.05/2.64 % 13.05/2.64 Further assumptions not needed in the proof: % 13.05/2.64 -------------------------------------------- % 13.05/2.64 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered, % 13.05/2.64 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered, % 13.05/2.64 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered, % 13.05/2.64 cc3_membered, cc4_membered, dt_k1_pcomps_1, dt_k1_xboole_0, dt_k1_zfmisc_1, % 13.05/2.64 dt_k3_tarski, dt_k5_setfam_1, dt_m1_subset_1, existence_m1_subset_1, % 13.05/2.64 fc1_subset_1, fc6_membered, rc1_membered, rc1_subset_1, rc2_subset_1, % 13.05/2.64 redefinition_k1_pcomps_1, redefinition_k5_setfam_1, reflexivity_r1_tarski, % 13.05/2.64 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, % 13.05/2.64 t8_boole % 13.05/2.64 % 13.05/2.64 Those formulas are unsatisfiable: % 13.05/2.64 --------------------------------- % 13.05/2.64 % 13.05/2.64 Begin of proof % 13.05/2.64 | % 13.05/2.65 | ALPHA: (d2_tex_2) implies: % 13.05/2.65 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (union(v0) = % 13.05/2.65 | v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v1, v0) | % 13.05/2.65 | proper_element(v1, v0)) % 13.05/2.65 | % 13.05/2.65 | DELTA: instantiating (t5_tex_2) with fresh symbols all_43_0, all_43_1, % 13.05/2.65 | all_43_2 gives: % 13.05/2.65 | (2) powerset(all_43_2) = all_43_0 & $i(all_43_0) & $i(all_43_1) & % 13.05/2.65 | $i(all_43_2) & element(all_43_1, all_43_0) & ((all_43_1 = all_43_2 & % 13.05/2.65 | proper_element(all_43_2, all_43_0)) | ( ~ (all_43_1 = all_43_2) & % 13.05/2.65 | ~ proper_element(all_43_1, all_43_0))) % 13.05/2.65 | % 13.05/2.65 | ALPHA: (2) implies: % 13.05/2.65 | (3) element(all_43_1, all_43_0) % 13.05/2.65 | (4) $i(all_43_2) % 13.05/2.65 | (5) $i(all_43_1) % 13.05/2.65 | (6) $i(all_43_0) % 13.05/2.65 | (7) powerset(all_43_2) = all_43_0 % 13.05/2.65 | (8) (all_43_1 = all_43_2 & proper_element(all_43_2, all_43_0)) | ( ~ % 13.05/2.65 | (all_43_1 = all_43_2) & ~ proper_element(all_43_1, all_43_0)) % 13.05/2.65 | % 13.05/2.65 | GROUND_INST: instantiating (t99_zfmisc_1) with all_43_2, all_43_0, simplifying % 13.05/2.65 | with (4), (7) gives: % 13.05/2.66 | (9) union(all_43_0) = all_43_2 % 13.05/2.66 | % 13.05/2.66 | GROUND_INST: instantiating (rc2_tex_2) with all_43_2, all_43_0, simplifying % 13.05/2.66 | with (4), (7) gives: % 13.32/2.66 | (10) ? [v0: $i] : ($i(v0) & element(v0, all_43_0) & ~ proper_element(v0, % 13.32/2.66 | all_43_0)) % 13.32/2.66 | % 13.32/2.66 | DELTA: instantiating (10) with fresh symbol all_52_0 gives: % 13.32/2.66 | (11) $i(all_52_0) & element(all_52_0, all_43_0) & ~ % 13.32/2.66 | proper_element(all_52_0, all_43_0) % 13.32/2.66 | % 13.32/2.66 | ALPHA: (11) implies: % 13.32/2.66 | (12) ~ proper_element(all_52_0, all_43_0) % 13.32/2.66 | (13) element(all_52_0, all_43_0) % 13.32/2.66 | (14) $i(all_52_0) % 13.32/2.66 | % 13.32/2.66 | GROUND_INST: instantiating (1) with all_43_0, all_43_1, all_43_2, simplifying % 13.32/2.66 | with (3), (5), (6), (9) gives: % 13.32/2.66 | (15) all_43_1 = all_43_2 | proper_element(all_43_1, all_43_0) % 13.32/2.66 | % 13.32/2.66 | GROUND_INST: instantiating (1) with all_43_0, all_52_0, all_43_2, simplifying % 13.32/2.66 | with (6), (9), (12), (13), (14) gives: % 13.32/2.66 | (16) all_52_0 = all_43_2 % 13.32/2.66 | % 13.32/2.66 | REDUCE: (12), (16) imply: % 13.32/2.66 | (17) ~ proper_element(all_43_2, all_43_0) % 13.32/2.66 | % 13.32/2.66 | BETA: splitting (8) gives: % 13.32/2.66 | % 13.32/2.66 | Case 1: % 13.32/2.66 | | % 13.32/2.66 | | (18) all_43_1 = all_43_2 & proper_element(all_43_2, all_43_0) % 13.32/2.66 | | % 13.32/2.66 | | ALPHA: (18) implies: % 13.32/2.66 | | (19) proper_element(all_43_2, all_43_0) % 13.32/2.66 | | % 13.32/2.66 | | PRED_UNIFY: (17), (19) imply: % 13.32/2.66 | | (20) $false % 13.32/2.66 | | % 13.32/2.66 | | CLOSE: (20) is inconsistent. % 13.32/2.66 | | % 13.32/2.66 | Case 2: % 13.32/2.66 | | % 13.32/2.67 | | (21) ~ (all_43_1 = all_43_2) & ~ proper_element(all_43_1, all_43_0) % 13.32/2.67 | | % 13.32/2.67 | | ALPHA: (21) implies: % 13.32/2.67 | | (22) ~ (all_43_1 = all_43_2) % 13.32/2.67 | | (23) ~ proper_element(all_43_1, all_43_0) % 13.32/2.67 | | % 13.32/2.67 | | BETA: splitting (15) gives: % 13.32/2.67 | | % 13.32/2.67 | | Case 1: % 13.32/2.67 | | | % 13.32/2.67 | | | (24) proper_element(all_43_1, all_43_0) % 13.32/2.67 | | | % 13.32/2.67 | | | PRED_UNIFY: (23), (24) imply: % 13.32/2.67 | | | (25) $false % 13.32/2.67 | | | % 13.32/2.67 | | | CLOSE: (25) is inconsistent. % 13.32/2.67 | | | % 13.32/2.67 | | Case 2: % 13.32/2.67 | | | % 13.32/2.67 | | | (26) all_43_1 = all_43_2 % 13.32/2.67 | | | % 13.32/2.67 | | | REDUCE: (22), (26) imply: % 13.32/2.67 | | | (27) $false % 13.32/2.67 | | | % 13.32/2.67 | | | CLOSE: (27) is inconsistent. % 13.32/2.67 | | | % 13.32/2.67 | | End of split % 13.32/2.67 | | % 13.32/2.67 | End of split % 13.32/2.67 | % 13.32/2.67 End of proof % 13.32/2.67 % SZS output end Proof for theBenchmark % 13.32/2.67 % 13.32/2.67 2001ms %------------------------------------------------------------------------------