%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU096+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 : n008.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 17:42:30 EDT 2023 % Result : Theorem 15.26s 2.85s % Output : Proof 17.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU096+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n008.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 % 0.14/0.34 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Wed Aug 23 18:07:18 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.59 ________ _____ % 0.21/0.59 ___ __ \_________(_)________________________________ % 0.21/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.59 % 0.21/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.59 (2023-06-19) % 0.21/0.59 % 0.21/0.59 (c) Philipp Rümmer, 2009-2023 % 0.21/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.59 Amanda Stjerna. % 0.21/0.59 Free software under BSD-3-Clause. % 0.21/0.59 % 0.21/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.59 % 0.21/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.39/1.17 Prover 1: Preprocessing ... % 3.39/1.17 Prover 4: Preprocessing ... % 3.39/1.21 Prover 0: Preprocessing ... % 3.39/1.21 Prover 2: Preprocessing ... % 3.39/1.21 Prover 6: Preprocessing ... % 3.39/1.21 Prover 3: Preprocessing ... % 3.39/1.21 Prover 5: Preprocessing ... % 6.82/1.67 Prover 2: Proving ... % 6.82/1.68 Prover 5: Proving ... % 7.01/1.72 Prover 1: Warning: ignoring some quantifiers % 7.41/1.76 Prover 1: Constructing countermodel ... % 7.41/1.79 Prover 3: Warning: ignoring some quantifiers % 7.96/1.82 Prover 3: Constructing countermodel ... % 7.96/1.84 Prover 6: Proving ... % 8.39/1.95 Prover 4: Warning: ignoring some quantifiers % 9.23/1.99 Prover 4: Constructing countermodel ... % 9.23/2.02 Prover 0: Proving ... % 12.43/2.42 Prover 3: gave up % 12.43/2.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.95/2.49 Prover 7: Preprocessing ... % 13.93/2.61 Prover 7: Warning: ignoring some quantifiers % 13.93/2.62 Prover 7: Constructing countermodel ... % 15.26/2.85 Prover 2: proved (2233ms) % 15.26/2.85 % 15.26/2.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.26/2.85 % 15.26/2.85 Prover 5: stopped % 15.26/2.85 Prover 6: stopped % 15.82/2.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.82/2.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.82/2.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.82/2.86 Prover 0: stopped % 15.82/2.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.82/2.95 Prover 11: Preprocessing ... % 15.82/2.95 Prover 8: Preprocessing ... % 15.82/2.96 Prover 13: Preprocessing ... % 15.82/2.96 Prover 10: Preprocessing ... % 15.82/2.96 Prover 7: Found proof (size 14) % 15.82/2.96 Prover 7: proved (533ms) % 15.82/2.96 Prover 1: stopped % 15.82/2.96 Prover 4: stopped % 15.82/2.98 Prover 10: stopped % 15.82/3.00 Prover 13: stopped % 15.82/3.01 Prover 11: stopped % 16.28/3.04 Prover 8: Warning: ignoring some quantifiers % 17.03/3.05 Prover 8: Constructing countermodel ... % 17.03/3.06 Prover 8: stopped % 17.03/3.06 % 17.03/3.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.03/3.06 % 17.03/3.06 % SZS output start Proof for theBenchmark % 17.12/3.07 Assumptions after simplification: % 17.12/3.07 --------------------------------- % 17.12/3.07 % 17.12/3.07 (t147_funct_1) % 17.12/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_inverse_image(v1, v0) % 17.12/3.09 = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ? % 17.12/3.09 [v3: $i] : ? [v4: $i] : ((v4 = v0 & relation_image(v1, v2) = v0) | % 17.12/3.09 (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3)))) % 17.12/3.09 % 17.12/3.09 (t17_finset_1) % 17.12/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_image(v1, v0) = v2) | % 17.12/3.09 ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ~ finite(v0) | % 17.12/3.09 finite(v2)) % 17.12/3.09 % 17.12/3.09 (t27_finset_1) % 17.12/3.09 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 17.12/3.09 (relation_inverse_image(v1, v0) = v3 & relation_rng(v1) = v2 & $i(v3) & $i(v2) % 17.12/3.09 & $i(v1) & $i(v0) & subset(v0, v2) & relation(v1) & function(v1) & % 17.12/3.09 finite(v3) & ~ finite(v0)) % 17.12/3.09 % 17.12/3.09 (function-axioms) % 17.12/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.12/3.10 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = % 17.12/3.10 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 17.12/3.10 ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! % 17.12/3.10 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | % 17.12/3.10 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 17.12/3.10 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 17.12/3.10 % 17.12/3.10 Further assumptions not needed in the proof: % 17.12/3.10 -------------------------------------------- % 17.12/3.10 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1, % 17.12/3.10 cc1_relat_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1, % 17.12/3.10 cc4_arytm_3, existence_m1_subset_1, fc12_relat_1, fc13_finset_1, fc1_subset_1, % 17.12/3.10 fc1_xboole_0, fc2_ordinal1, fc4_relat_1, fc6_funct_1, fc6_relat_1, fc8_arytm_3, % 17.12/3.10 fc8_relat_1, rc1_arytm_3, rc1_finset_1, rc1_funcop_1, rc1_funct_1, rc1_ordinal1, % 17.12/3.10 rc1_ordinal2, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_arytm_3, % 17.12/3.10 rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_ordinal2, rc2_relat_1, % 17.12/3.10 rc2_subset_1, rc2_xboole_0, rc3_arytm_3, rc3_finset_1, rc3_funct_1, % 17.12/3.10 rc3_ordinal1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc5_funct_1, % 17.12/3.10 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, % 17.12/3.10 t6_boole, t7_boole, t8_boole % 17.12/3.10 % 17.12/3.10 Those formulas are unsatisfiable: % 17.12/3.10 --------------------------------- % 17.12/3.10 % 17.12/3.10 Begin of proof % 17.12/3.10 | % 17.12/3.10 | ALPHA: (function-axioms) implies: % 17.12/3.10 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.12/3.10 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 17.12/3.10 | % 17.12/3.10 | DELTA: instantiating (t27_finset_1) with fresh symbols all_79_0, all_79_1, % 17.12/3.10 | all_79_2, all_79_3 gives: % 17.12/3.10 | (2) relation_inverse_image(all_79_2, all_79_3) = all_79_0 & % 17.12/3.10 | relation_rng(all_79_2) = all_79_1 & $i(all_79_0) & $i(all_79_1) & % 17.12/3.10 | $i(all_79_2) & $i(all_79_3) & subset(all_79_3, all_79_1) & % 17.12/3.10 | relation(all_79_2) & function(all_79_2) & finite(all_79_0) & ~ % 17.12/3.10 | finite(all_79_3) % 17.12/3.10 | % 17.12/3.10 | ALPHA: (2) implies: % 17.12/3.10 | (3) ~ finite(all_79_3) % 17.12/3.10 | (4) finite(all_79_0) % 17.12/3.10 | (5) function(all_79_2) % 17.12/3.10 | (6) relation(all_79_2) % 17.12/3.10 | (7) subset(all_79_3, all_79_1) % 17.12/3.10 | (8) $i(all_79_3) % 17.12/3.10 | (9) $i(all_79_2) % 17.12/3.10 | (10) $i(all_79_0) % 17.12/3.10 | (11) relation_rng(all_79_2) = all_79_1 % 17.12/3.10 | (12) relation_inverse_image(all_79_2, all_79_3) = all_79_0 % 17.12/3.10 | % 17.12/3.10 | GROUND_INST: instantiating (t147_funct_1) with all_79_3, all_79_2, all_79_0, % 17.12/3.10 | simplifying with (5), (6), (8), (9), (12) gives: % 17.12/3.10 | (13) ? [v0: $i] : ? [v1: int] : ((v1 = all_79_3 & % 17.12/3.10 | relation_image(all_79_2, all_79_0) = all_79_3) | % 17.12/3.10 | (relation_rng(all_79_2) = v0 & $i(v0) & ~ subset(all_79_3, v0))) % 17.12/3.10 | % 17.12/3.10 | DELTA: instantiating (13) with fresh symbols all_91_0, all_91_1 gives: % 17.12/3.10 | (14) (all_91_0 = all_79_3 & relation_image(all_79_2, all_79_0) = all_79_3) % 17.12/3.10 | | (relation_rng(all_79_2) = all_91_1 & $i(all_91_1) & ~ % 17.12/3.10 | subset(all_79_3, all_91_1)) % 17.12/3.10 | % 17.12/3.10 | BETA: splitting (14) gives: % 17.12/3.10 | % 17.12/3.10 | Case 1: % 17.12/3.10 | | % 17.12/3.10 | | (15) all_91_0 = all_79_3 & relation_image(all_79_2, all_79_0) = all_79_3 % 17.12/3.10 | | % 17.12/3.10 | | ALPHA: (15) implies: % 17.12/3.11 | | (16) relation_image(all_79_2, all_79_0) = all_79_3 % 17.12/3.11 | | % 17.12/3.11 | | GROUND_INST: instantiating (t17_finset_1) with all_79_0, all_79_2, all_79_3, % 17.12/3.11 | | simplifying with (3), (4), (5), (6), (9), (10), (16) gives: % 17.12/3.11 | | (17) $false % 17.12/3.11 | | % 17.12/3.11 | | CLOSE: (17) is inconsistent. % 17.12/3.11 | | % 17.12/3.11 | Case 2: % 17.12/3.11 | | % 17.12/3.11 | | (18) relation_rng(all_79_2) = all_91_1 & $i(all_91_1) & ~ % 17.12/3.11 | | subset(all_79_3, all_91_1) % 17.12/3.11 | | % 17.12/3.11 | | ALPHA: (18) implies: % 17.12/3.11 | | (19) ~ subset(all_79_3, all_91_1) % 17.12/3.11 | | (20) relation_rng(all_79_2) = all_91_1 % 17.12/3.11 | | % 17.12/3.11 | | GROUND_INST: instantiating (1) with all_79_1, all_91_1, all_79_2, % 17.12/3.11 | | simplifying with (11), (20) gives: % 17.12/3.11 | | (21) all_91_1 = all_79_1 % 17.12/3.11 | | % 17.12/3.11 | | PRED_UNIFY: (7), (19) imply: % 17.12/3.11 | | (22) ~ (all_91_1 = all_79_1) % 17.12/3.11 | | % 17.12/3.11 | | REDUCE: (21), (22) imply: % 17.12/3.11 | | (23) $false % 17.12/3.11 | | % 17.12/3.11 | | CLOSE: (23) is inconsistent. % 17.12/3.11 | | % 17.12/3.11 | End of split % 17.12/3.11 | % 17.12/3.11 End of proof % 17.12/3.11 % SZS output end Proof for theBenchmark % 17.12/3.11 % 17.12/3.11 2514ms %------------------------------------------------------------------------------