%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET991+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 : n016.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 15:27:18 EDT 2023 % Result : Theorem 7.76s 1.87s % Output : Proof 12.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET991+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n016.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 16:00:57 EDT 2023 % 0.12/0.34 % CPUTime : % 0.18/0.61 ________ _____ % 0.18/0.61 ___ __ \_________(_)________________________________ % 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.61 % 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.61 (2023-06-19) % 0.18/0.61 % 0.18/0.61 (c) Philipp Rümmer, 2009-2023 % 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.61 Amanda Stjerna. % 0.18/0.61 Free software under BSD-3-Clause. % 0.18/0.61 % 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.61 % 0.18/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.62 Running up to 7 provers in parallel. % 0.18/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.45/1.07 Prover 4: Preprocessing ... % 2.45/1.07 Prover 1: Preprocessing ... % 2.45/1.11 Prover 2: Preprocessing ... % 2.45/1.11 Prover 6: Preprocessing ... % 2.45/1.11 Prover 5: Preprocessing ... % 2.45/1.11 Prover 0: Preprocessing ... % 2.45/1.12 Prover 3: Preprocessing ... % 5.62/1.54 Prover 1: Warning: ignoring some quantifiers % 5.62/1.55 Prover 3: Warning: ignoring some quantifiers % 5.62/1.57 Prover 6: Proving ... % 5.62/1.57 Prover 1: Constructing countermodel ... % 5.62/1.58 Prover 3: Constructing countermodel ... % 5.62/1.58 Prover 2: Proving ... % 5.62/1.58 Prover 5: Proving ... % 6.97/1.69 Prover 4: Warning: ignoring some quantifiers % 7.08/1.74 Prover 0: Proving ... % 7.08/1.77 Prover 4: Constructing countermodel ... % 7.76/1.87 Prover 3: proved (1233ms) % 7.76/1.87 % 7.76/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.76/1.87 % 7.76/1.87 Prover 0: stopped % 7.76/1.87 Prover 6: stopped % 7.76/1.87 Prover 5: stopped % 7.76/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.76/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.76/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.76/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.76/1.88 Prover 2: stopped % 8.37/1.91 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.37/1.93 Prover 10: Preprocessing ... % 8.37/1.95 Prover 8: Preprocessing ... % 8.37/1.99 Prover 7: Preprocessing ... % 8.98/1.99 Prover 13: Preprocessing ... % 8.98/1.99 Prover 11: Preprocessing ... % 9.00/2.14 Prover 7: Warning: ignoring some quantifiers % 9.00/2.14 Prover 10: Warning: ignoring some quantifiers % 9.00/2.15 Prover 10: Constructing countermodel ... % 9.15/2.16 Prover 7: Constructing countermodel ... % 10.05/2.19 Prover 8: Warning: ignoring some quantifiers % 10.05/2.21 Prover 8: Constructing countermodel ... % 10.05/2.22 Prover 13: Warning: ignoring some quantifiers % 10.05/2.25 Prover 13: Constructing countermodel ... % 11.48/2.36 Prover 10: Found proof (size 12) % 11.48/2.36 Prover 10: proved (482ms) % 11.48/2.36 Prover 8: stopped % 11.48/2.36 Prover 1: stopped % 11.48/2.36 Prover 13: stopped % 11.48/2.36 Prover 7: stopped % 11.48/2.36 Prover 4: stopped % 11.79/2.41 Prover 11: Warning: ignoring some quantifiers % 11.79/2.42 Prover 11: Constructing countermodel ... % 11.79/2.43 Prover 11: stopped % 11.79/2.43 % 11.79/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.79/2.43 % 11.79/2.43 % SZS output start Proof for theBenchmark % 11.79/2.44 Assumptions after simplification: % 11.79/2.44 --------------------------------- % 11.79/2.44 % 11.79/2.44 (d5_funct_1) % 12.07/2.47 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 12.07/2.47 function(v0) | ~ relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & % 12.07/2.47 $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (apply(v0, v4) = v3) | ~ $i(v4) % 12.07/2.47 | ~ $i(v3) | ~ $i(v1) | ~ in(v4, v2) | in(v3, v1)) & ! [v3: $i] : ( % 12.07/2.47 ~ $i(v3) | ~ $i(v1) | ~ in(v3, v1) | ? [v4: $i] : (apply(v0, v4) = v3 % 12.07/2.47 & $i(v4) & in(v4, v2))) & ? [v3: $i] : (v3 = v1 | ~ $i(v3) | ? [v4: % 12.07/2.47 $i] : ? [v5: $i] : ? [v6: $i] : ($i(v5) & $i(v4) & ( ~ in(v4, v3) | % 12.07/2.47 ! [v7: $i] : ( ~ (apply(v0, v7) = v4) | ~ $i(v7) | ~ in(v7, v2))) % 12.07/2.47 & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) % 12.07/2.47 % 12.07/2.47 (t12_funct_1) % 12.07/2.47 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.07/2.47 (apply(v1, v0) = v3 & relation_rng(v1) = v4 & relation_dom(v1) = v2 & $i(v4) & % 12.07/2.47 $i(v3) & $i(v2) & $i(v1) & $i(v0) & in(v0, v2) & function(v1) & relation(v1) % 12.07/2.47 & ~ in(v3, v4)) % 12.07/2.47 % 12.07/2.47 (function-axioms) % 12.07/2.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.07/2.47 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 12.07/2.47 : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = % 12.07/2.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 12.07/2.47 (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] : ! % 12.07/2.47 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 12.07/2.47 = v0)) % 12.07/2.47 % 12.07/2.47 Further assumptions not needed in the proof: % 12.07/2.47 -------------------------------------------- % 12.07/2.47 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, existence_m1_subset_1, % 12.07/2.47 fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, fc5_relat_1, fc6_relat_1, % 12.07/2.47 fc7_relat_1, fc8_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, % 12.07/2.47 rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_relat_1, reflexivity_r1_tarski, % 12.07/2.47 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, % 12.07/2.47 t8_boole % 12.07/2.47 % 12.07/2.47 Those formulas are unsatisfiable: % 12.07/2.47 --------------------------------- % 12.07/2.47 % 12.07/2.47 Begin of proof % 12.07/2.48 | % 12.07/2.48 | ALPHA: (function-axioms) implies: % 12.07/2.48 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 12.07/2.48 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 12.07/2.48 | % 12.07/2.48 | DELTA: instantiating (t12_funct_1) with fresh symbols all_37_0, all_37_1, % 12.07/2.48 | all_37_2, all_37_3, all_37_4 gives: % 12.07/2.48 | (2) apply(all_37_3, all_37_4) = all_37_1 & relation_rng(all_37_3) = % 12.07/2.48 | all_37_0 & relation_dom(all_37_3) = all_37_2 & $i(all_37_0) & % 12.07/2.48 | $i(all_37_1) & $i(all_37_2) & $i(all_37_3) & $i(all_37_4) & % 12.07/2.48 | in(all_37_4, all_37_2) & function(all_37_3) & relation(all_37_3) & ~ % 12.07/2.48 | in(all_37_1, all_37_0) % 12.07/2.48 | % 12.07/2.48 | ALPHA: (2) implies: % 12.07/2.48 | (3) ~ in(all_37_1, all_37_0) % 12.07/2.48 | (4) relation(all_37_3) % 12.07/2.48 | (5) function(all_37_3) % 12.07/2.48 | (6) in(all_37_4, all_37_2) % 12.07/2.48 | (7) $i(all_37_4) % 12.07/2.48 | (8) $i(all_37_3) % 12.07/2.48 | (9) $i(all_37_1) % 12.07/2.48 | (10) $i(all_37_0) % 12.07/2.48 | (11) relation_dom(all_37_3) = all_37_2 % 12.07/2.48 | (12) relation_rng(all_37_3) = all_37_0 % 12.07/2.48 | (13) apply(all_37_3, all_37_4) = all_37_1 % 12.07/2.48 | % 12.07/2.48 | GROUND_INST: instantiating (d5_funct_1) with all_37_3, all_37_0, simplifying % 12.07/2.48 | with (4), (5), (8), (12) gives: % 12.07/2.49 | (14) ? [v0: $i] : (relation_dom(all_37_3) = v0 & $i(v0) & ! [v1: $i] : ! % 12.07/2.49 | [v2: $i] : ( ~ (apply(all_37_3, v2) = v1) | ~ $i(v2) | ~ $i(v1) | % 12.07/2.49 | ~ $i(all_37_0) | ~ in(v2, v0) | in(v1, all_37_0)) & ! [v1: $i] : % 12.07/2.49 | ( ~ $i(v1) | ~ $i(all_37_0) | ~ in(v1, all_37_0) | ? [v2: $i] : % 12.07/2.49 | (apply(all_37_3, v2) = v1 & $i(v2) & in(v2, v0))) & ? [v1: any] : % 12.07/2.49 | (v1 = all_37_0 | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 12.07/2.49 | : ($i(v3) & $i(v2) & ( ~ in(v2, v1) | ! [v5: $i] : ( ~ % 12.07/2.49 | (apply(all_37_3, v5) = v2) | ~ $i(v5) | ~ in(v5, v0))) & % 12.07/2.49 | (in(v2, v1) | (v4 = v2 & apply(all_37_3, v3) = v2 & in(v3, % 12.07/2.49 | v0)))))) % 12.07/2.49 | % 12.07/2.49 | DELTA: instantiating (14) with fresh symbol all_45_0 gives: % 12.07/2.49 | (15) relation_dom(all_37_3) = all_45_0 & $i(all_45_0) & ! [v0: $i] : ! % 12.07/2.49 | [v1: $i] : ( ~ (apply(all_37_3, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 12.07/2.49 | $i(all_37_0) | ~ in(v1, all_45_0) | in(v0, all_37_0)) & ! [v0: $i] % 12.07/2.49 | : ( ~ $i(v0) | ~ $i(all_37_0) | ~ in(v0, all_37_0) | ? [v1: $i] : % 12.07/2.49 | (apply(all_37_3, v1) = v0 & $i(v1) & in(v1, all_45_0))) & ? [v0: % 12.07/2.49 | any] : (v0 = all_37_0 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? % 12.07/2.49 | [v3: $i] : ($i(v2) & $i(v1) & ( ~ in(v1, v0) | ! [v4: $i] : ( ~ % 12.07/2.49 | (apply(all_37_3, v4) = v1) | ~ $i(v4) | ~ in(v4, all_45_0))) % 12.07/2.49 | & (in(v1, v0) | (v3 = v1 & apply(all_37_3, v2) = v1 & in(v2, % 12.07/2.49 | all_45_0))))) % 12.07/2.49 | % 12.07/2.49 | ALPHA: (15) implies: % 12.07/2.49 | (16) relation_dom(all_37_3) = all_45_0 % 12.07/2.49 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_37_3, v1) = v0) | ~ $i(v1) % 12.07/2.49 | | ~ $i(v0) | ~ $i(all_37_0) | ~ in(v1, all_45_0) | in(v0, % 12.07/2.49 | all_37_0)) % 12.07/2.49 | % 12.07/2.49 | GROUND_INST: instantiating (1) with all_37_2, all_45_0, all_37_3, simplifying % 12.07/2.49 | with (11), (16) gives: % 12.07/2.49 | (18) all_45_0 = all_37_2 % 12.07/2.49 | % 12.07/2.49 | GROUND_INST: instantiating (17) with all_37_1, all_37_4, simplifying with (3), % 12.07/2.49 | (7), (9), (10), (13) gives: % 12.07/2.49 | (19) ~ in(all_37_4, all_45_0) % 12.07/2.49 | % 12.07/2.49 | REDUCE: (18), (19) imply: % 12.07/2.49 | (20) ~ in(all_37_4, all_37_2) % 12.07/2.49 | % 12.07/2.49 | PRED_UNIFY: (6), (20) imply: % 12.07/2.49 | (21) $false % 12.07/2.49 | % 12.07/2.49 | CLOSE: (21) is inconsistent. % 12.07/2.49 | % 12.07/2.49 End of proof % 12.07/2.49 % SZS output end Proof for theBenchmark % 12.07/2.49 % 12.07/2.49 1882ms %------------------------------------------------------------------------------