%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 12:54:11 PM UTC 2026 % Result : Theorem 15.08s 2.72s % Output : Proof 18.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.36 % Computer : n017.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Fri Sep 4 20:35:21 UTC 2026 % 0.10/0.36 % CPUTime : % 0.10/0.38 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.71/0.70 ________ _____ % 0.71/0.70 ___ __ \_________(_)________________________________ % 0.71/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.71/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.71/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.71/0.70 % 0.71/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.71/0.70 (2023-06-19) % 0.71/0.70 % 0.71/0.70 (c) Philipp Rümmer, 2009-2023 % 0.71/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.71/0.70 Amanda Stjerna. % 0.71/0.70 Free software under BSD-3-Clause. % 0.71/0.70 % 0.71/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.71/0.70 % 0.71/0.70 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.72 Running up to 7 provers in parallel. % 0.71/0.73 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.73 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.73 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.73 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.73 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.73 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.73 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.14/1.35 Prover 1: Preprocessing ... % 4.14/1.35 Prover 4: Preprocessing ... % 4.14/1.38 Prover 6: Preprocessing ... % 4.14/1.38 Prover 2: Preprocessing ... % 4.14/1.38 Prover 5: Preprocessing ... % 4.14/1.39 Prover 0: Preprocessing ... % 4.14/1.39 Prover 3: Preprocessing ... % 11.98/2.40 Prover 1: Constructing countermodel ... % 12.73/2.47 Prover 6: Constructing countermodel ... % 13.53/2.51 Prover 5: Proving ... % 13.53/2.53 Prover 0: Proving ... % 13.53/2.55 Prover 4: Constructing countermodel ... % 13.53/2.60 Prover 3: Constructing countermodel ... % 14.34/2.68 Prover 2: Proving ... % 15.08/2.71 Prover 5: proved (1978ms) % 15.08/2.71 % 15.08/2.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.08/2.72 % 15.08/2.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.08/2.73 Prover 6: stopped % 15.08/2.73 Prover 2: stopped % 15.08/2.73 Prover 3: stopped % 15.08/2.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.08/2.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.08/2.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.08/2.74 Prover 0: stopped % 15.08/2.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.08/2.78 Prover 7: Preprocessing ... % 15.87/2.83 Prover 1: Found proof (size 19) % 15.87/2.83 Prover 1: proved (2102ms) % 15.87/2.83 Prover 4: stopped % 15.87/2.86 Prover 8: Preprocessing ... % 15.87/2.87 Prover 7: stopped % 16.63/2.90 Prover 13: Preprocessing ... % 16.63/2.91 Prover 10: Preprocessing ... % 16.63/2.92 Prover 11: Preprocessing ... % 16.63/3.00 Prover 10: stopped % 16.63/3.04 Prover 13: stopped % 17.76/3.07 Prover 11: stopped % 17.76/3.14 Prover 8: Warning: ignoring some quantifiers % 18.28/3.15 Prover 8: Constructing countermodel ... % 18.28/3.16 Prover 8: stopped % 18.28/3.17 % 18.28/3.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.28/3.17 % 18.28/3.18 % SZS output start Proof for theBenchmark % 18.28/3.19 Assumptions after simplification: % 18.28/3.19 --------------------------------- % 18.28/3.19 % 18.28/3.19 (cn1) % 18.49/3.26 (cn1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 18.49/3.26 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (implies(v4, v5) = v6) | ~ % 18.49/3.26 (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = % 18.49/3.26 v5) | ~ (implies(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.49/3.26 is_a_theorem(v7) = 0)) | ( ~ cn1 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 18.49/3.26 : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 18.49/3.26 [v8: int] : ( ~ (v8 = 0) & implies(v4, v5) = v6 & implies(v3, v6) = v7 & % 18.49/3.26 implies(v1, v2) = v4 & implies(v0, v2) = v5 & implies(v0, v1) = v3 & % 18.49/3.26 is_a_theorem(v7) = v8 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 18.49/3.26 $i(v2) & $i(v1) & $i(v0))) % 18.49/3.26 % 18.49/3.26 (hilbert_implies_3) % 18.49/3.26 implies_3 % 18.49/3.26 % 18.49/3.26 (implies_3) % 18.49/3.27 (implies_3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 18.49/3.27 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (implies(v4, v5) = v6) % 18.49/3.27 | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, % 18.49/3.27 v2) = v5) | ~ (implies(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 18.49/3.27 $i(v0) | is_a_theorem(v7) = 0)) | ( ~ implies_3 & ? [v0: $i] : ? [v1: % 18.49/3.27 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 18.49/3.27 : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & implies(v4, v5) = v6 & % 18.49/3.27 implies(v3, v6) = v7 & implies(v1, v2) = v4 & implies(v0, v2) = v5 & % 18.49/3.27 implies(v0, v1) = v3 & is_a_theorem(v7) = v8 & $i(v7) & $i(v6) & $i(v5) & % 18.49/3.27 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))) % 18.49/3.27 % 18.49/3.27 (luka_cn1) % 18.49/3.27 ~ cn1 % 18.49/3.27 % 18.49/3.27 (function-axioms) % 18.49/3.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3, % 18.49/3.28 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.49/3.28 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = % 18.49/3.28 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 18.49/3.28 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 18.49/3.28 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ % 18.49/3.28 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 18.49/3.28 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 18.49/3.28 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_a_theorem(v2) = v1) % 18.49/3.28 | ~ (is_a_theorem(v2) = v0)) % 18.49/3.28 % 18.49/3.28 Further assumptions not needed in the proof: % 18.49/3.28 -------------------------------------------- % 18.49/3.28 and_1, and_2, and_3, cn2, cn3, equivalence_1, equivalence_2, equivalence_3, % 18.49/3.28 hilbert_and_1, hilbert_and_2, hilbert_and_3, hilbert_equivalence_1, % 18.49/3.28 hilbert_equivalence_2, hilbert_equivalence_3, hilbert_implies_1, % 18.49/3.28 hilbert_implies_2, hilbert_modus_ponens, hilbert_modus_tollens, % 18.49/3.28 hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or, hilbert_or_1, % 18.49/3.28 hilbert_or_2, hilbert_or_3, implies_1, implies_2, kn1, kn2, kn3, luka_op_equiv, % 18.49/3.28 luka_op_implies, luka_op_or, modus_ponens, modus_tollens, op_and, op_equiv, % 18.49/3.28 op_implies_and, op_implies_or, op_or, or_1, or_2, or_3, r1, r2, r3, r4, r5, % 18.49/3.28 substitution_of_equivalents, use_substitution_of_equivalents % 18.49/3.28 % 18.49/3.28 Those formulas are unsatisfiable: % 18.49/3.28 --------------------------------- % 18.49/3.28 % 18.49/3.28 Begin of proof % 18.49/3.28 | % 18.49/3.29 | ALPHA: (function-axioms) implies: % 18.49/3.29 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 18.49/3.29 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) % 18.49/3.29 | % 18.49/3.29 | BETA: splitting (implies_3) gives: % 18.49/3.29 | % 18.49/3.29 | Case 1: % 18.49/3.29 | | % 18.49/3.29 | | (2) implies_3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 18.49/3.29 | | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 18.49/3.29 | | (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ % 18.49/3.29 | | (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~ % 18.49/3.29 | | (implies(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.49/3.29 | | is_a_theorem(v7) = 0) % 18.49/3.29 | | % 18.49/3.29 | | ALPHA: (2) implies: % 18.49/3.29 | | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 18.49/3.29 | | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (implies(v4, v5) = v6) % 18.49/3.29 | | | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ % 18.49/3.29 | | (implies(v0, v2) = v5) | ~ (implies(v0, v1) = v3) | ~ $i(v2) | ~ % 18.49/3.29 | | $i(v1) | ~ $i(v0) | is_a_theorem(v7) = 0) % 18.49/3.29 | | % 18.49/3.29 | | BETA: splitting (cn1) gives: % 18.49/3.29 | | % 18.49/3.29 | | Case 1: % 18.49/3.29 | | | % 18.95/3.30 | | | (4) cn1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 18.95/3.30 | | | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 18.95/3.30 | | | (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ % 18.95/3.30 | | | (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~ % 18.95/3.30 | | | (implies(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.95/3.30 | | | is_a_theorem(v7) = 0) % 18.95/3.30 | | | % 18.95/3.30 | | | ALPHA: (4) implies: % 18.95/3.30 | | | (5) cn1 % 18.95/3.30 | | | % 18.95/3.30 | | | PRED_UNIFY: (5), (luka_cn1) imply: % 18.95/3.30 | | | (6) $false % 18.95/3.30 | | | % 18.95/3.30 | | | CLOSE: (6) is inconsistent. % 18.95/3.30 | | | % 18.95/3.30 | | Case 2: % 18.95/3.30 | | | % 18.95/3.30 | | | (7) ~ cn1 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 18.95/3.30 | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 18.95/3.30 | | | ( ~ (v8 = 0) & implies(v4, v5) = v6 & implies(v3, v6) = v7 & % 18.95/3.30 | | | implies(v1, v2) = v4 & implies(v0, v2) = v5 & implies(v0, v1) = % 18.95/3.30 | | | v3 & is_a_theorem(v7) = v8 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 18.95/3.30 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 18.95/3.31 | | | % 18.95/3.31 | | | ALPHA: (7) implies: % 18.95/3.31 | | | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 18.95/3.31 | | | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 % 18.95/3.31 | | | = 0) & implies(v4, v5) = v6 & implies(v3, v6) = v7 & % 18.95/3.31 | | | implies(v1, v2) = v4 & implies(v0, v2) = v5 & implies(v0, v1) = % 18.95/3.31 | | | v3 & is_a_theorem(v7) = v8 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 18.95/3.31 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 18.95/3.31 | | | % 18.95/3.31 | | | DELTA: instantiating (8) with fresh symbols all_80_0, all_80_1, all_80_2, % 18.95/3.31 | | | all_80_3, all_80_4, all_80_5, all_80_6, all_80_7, all_80_8 gives: % 18.95/3.31 | | | (9) ~ (all_80_0 = 0) & implies(all_80_4, all_80_3) = all_80_2 & % 18.95/3.31 | | | implies(all_80_5, all_80_2) = all_80_1 & implies(all_80_7, % 18.95/3.31 | | | all_80_6) = all_80_4 & implies(all_80_8, all_80_6) = all_80_3 & % 18.95/3.31 | | | implies(all_80_8, all_80_7) = all_80_5 & is_a_theorem(all_80_1) = % 18.95/3.31 | | | all_80_0 & $i(all_80_1) & $i(all_80_2) & $i(all_80_3) & % 18.95/3.31 | | | $i(all_80_4) & $i(all_80_5) & $i(all_80_6) & $i(all_80_7) & % 18.95/3.31 | | | $i(all_80_8) % 18.95/3.31 | | | % 18.95/3.31 | | | ALPHA: (9) implies: % 18.95/3.31 | | | (10) ~ (all_80_0 = 0) % 18.95/3.31 | | | (11) $i(all_80_8) % 18.95/3.32 | | | (12) $i(all_80_7) % 18.95/3.32 | | | (13) $i(all_80_6) % 18.95/3.32 | | | (14) is_a_theorem(all_80_1) = all_80_0 % 18.95/3.32 | | | (15) implies(all_80_8, all_80_7) = all_80_5 % 18.95/3.32 | | | (16) implies(all_80_8, all_80_6) = all_80_3 % 18.95/3.32 | | | (17) implies(all_80_7, all_80_6) = all_80_4 % 18.95/3.32 | | | (18) implies(all_80_5, all_80_2) = all_80_1 % 18.95/3.32 | | | (19) implies(all_80_4, all_80_3) = all_80_2 % 18.95/3.32 | | | % 18.95/3.32 | | | GROUND_INST: instantiating (3) with all_80_8, all_80_7, all_80_6, % 18.95/3.32 | | | all_80_5, all_80_4, all_80_3, all_80_2, all_80_1, simplifying % 18.95/3.32 | | | with (11), (12), (13), (15), (16), (17), (18), (19) gives: % 18.95/3.32 | | | (20) is_a_theorem(all_80_1) = 0 % 18.95/3.32 | | | % 18.95/3.32 | | | GROUND_INST: instantiating (1) with all_80_0, 0, all_80_1, simplifying % 18.95/3.32 | | | with (14), (20) gives: % 18.95/3.32 | | | (21) all_80_0 = 0 % 18.95/3.32 | | | % 18.95/3.32 | | | REDUCE: (10), (21) imply: % 18.95/3.32 | | | (22) $false % 18.95/3.32 | | | % 18.95/3.32 | | | CLOSE: (22) is inconsistent. % 18.95/3.32 | | | % 18.95/3.32 | | End of split % 18.95/3.32 | | % 18.95/3.32 | Case 2: % 18.95/3.32 | | % 18.95/3.33 | | (23) ~ implies_3 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 18.95/3.33 | | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 18.95/3.33 | | int] : ( ~ (v8 = 0) & implies(v4, v5) = v6 & implies(v3, v6) = v7 % 18.95/3.33 | | & implies(v1, v2) = v4 & implies(v0, v2) = v5 & implies(v0, v1) = % 18.95/3.33 | | v3 & is_a_theorem(v7) = v8 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 18.95/3.33 | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 18.95/3.33 | | % 18.95/3.33 | | ALPHA: (23) implies: % 18.95/3.33 | | (24) ~ implies_3 % 18.95/3.33 | | % 18.95/3.33 | | PRED_UNIFY: (24), (hilbert_implies_3) imply: % 18.95/3.33 | | (25) $false % 18.95/3.33 | | % 18.95/3.33 | | CLOSE: (25) is inconsistent. % 18.95/3.33 | | % 18.95/3.33 | End of split % 18.95/3.33 | % 18.95/3.33 End of proof % 18.95/3.33 % SZS output end Proof for theBenchmark % 18.95/3.33 % 18.95/3.33 2630ms %------------------------------------------------------------------------------