%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL459+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 : n003.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 12:54:12 PM UTC 2026 % Result : Theorem 20.14s 3.51s % Output : Proof 38.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL459+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.38 % Computer : n003.cluster.edu % 0.11/0.38 % Model : x86_64 x86_64 % 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.38 % Memory : 8046.5625MB % 0.11/0.38 % OS : Linux 6.8.0-71-generic % 0.11/0.38 % CPULimit : 300 % 0.11/0.38 % WCLimit : 300 % 0.11/0.38 % DateTime : Fri Sep 4 14:31:19 UTC 2026 % 0.11/0.38 % CPUTime : % 0.11/0.40 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. % 0.63/0.73 ________ _____ % 0.63/0.73 ___ __ \_________(_)________________________________ % 0.63/0.73 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.63/0.73 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.63/0.73 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.63/0.73 % 0.63/0.73 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.63/0.73 (2023-06-19) % 0.63/0.73 % 0.63/0.73 (c) Philipp Rümmer, 2009-2023 % 0.63/0.73 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.63/0.73 Amanda Stjerna. % 0.63/0.73 Free software under BSD-3-Clause. % 0.63/0.73 % 0.63/0.73 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.63/0.73 % 0.63/0.73 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.63/0.75 Running up to 7 provers in parallel. % 0.63/0.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.63/0.77 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.63/0.77 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.63/0.77 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.63/0.77 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.63/0.77 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.63/0.77 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.38/1.51 Prover 1: Preprocessing ... % 4.38/1.53 Prover 2: Preprocessing ... % 4.38/1.53 Prover 3: Preprocessing ... % 4.38/1.53 Prover 5: Preprocessing ... % 4.38/1.53 Prover 6: Preprocessing ... % 4.38/1.53 Prover 0: Preprocessing ... % 4.38/1.54 Prover 4: Preprocessing ... % 12.28/2.52 Prover 5: Proving ... % 12.28/2.54 Prover 1: Constructing countermodel ... % 12.28/2.57 Prover 6: Constructing countermodel ... % 13.02/2.60 Prover 3: Constructing countermodel ... % 13.02/2.61 Prover 4: Constructing countermodel ... % 13.02/2.64 Prover 0: Proving ... % 13.80/2.74 Prover 2: Proving ... % 20.14/3.50 Prover 0: proved (2738ms) % 20.14/3.51 % 20.14/3.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.14/3.51 % 20.14/3.51 Prover 1: gave up % 20.14/3.52 Prover 6: stopped % 20.14/3.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.14/3.52 Prover 3: stopped % 20.14/3.52 Prover 2: stopped % 20.14/3.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.14/3.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.14/3.53 Prover 5: stopped % 20.14/3.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.14/3.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.14/3.54 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 20.91/3.62 Prover 13: Preprocessing ... % 20.91/3.64 Prover 16: Preprocessing ... % 20.91/3.65 Prover 8: Preprocessing ... % 20.91/3.67 Prover 10: Preprocessing ... % 20.91/3.68 Prover 7: Preprocessing ... % 21.71/3.71 Prover 11: Preprocessing ... % 22.50/3.89 Prover 13: Constructing countermodel ... % 23.30/3.97 Prover 8: Warning: ignoring some quantifiers % 23.30/3.98 Prover 8: Constructing countermodel ... % 23.30/4.01 Prover 16: Warning: ignoring some quantifiers % 24.32/4.05 Prover 10: Constructing countermodel ... % 24.32/4.05 Prover 16: Constructing countermodel ... % 24.32/4.05 Prover 11: Constructing countermodel ... % 24.32/4.11 Prover 7: Constructing countermodel ... % 26.47/4.38 Prover 8: gave up % 26.47/4.38 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 27.24/4.49 Prover 13: gave up % 28.00/4.54 Prover 19: Preprocessing ... % 28.80/4.61 Prover 10: gave up % 29.58/4.76 Prover 19: Constructing countermodel ... % 31.11/5.03 Prover 19: gave up % 37.71/5.84 Prover 7: Found proof (size 50) % 37.71/5.84 Prover 7: proved (2324ms) % 37.71/5.84 Prover 11: stopped % 37.71/5.84 Prover 4: stopped % 37.71/5.85 Prover 16: stopped % 37.71/5.85 % 37.71/5.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 37.71/5.85 % 37.71/5.87 % SZS output start Proof for theBenchmark % 37.71/5.88 Assumptions after simplification: % 37.71/5.88 --------------------------------- % 37.71/5.88 % 37.71/5.88 (and_3) % 38.29/5.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v1) % 38.29/5.95 & $i(v0) & ((and(v0, v1) = v2 & implies(v1, v2) = v3 & implies(v0, v3) = v4 % 38.29/5.96 & $i(v4) & $i(v3) & $i(v2) & ~ and_3 & ~ is_a_theorem(v4)) | (and_3 & % 38.29/5.96 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (and(v5, v6) = v7) | ~ % 38.29/5.96 $i(v6) | ~ $i(v5) | ? [v8: $i] : ? [v9: $i] : (implies(v6, v7) = v8 % 38.29/5.96 & implies(v5, v8) = v9 & $i(v9) & $i(v8) & is_a_theorem(v9)))))) % 38.29/5.96 % 38.29/5.96 (hilbert_and_3) % 38.29/5.96 and_3 % 38.29/5.96 % 38.29/5.96 (hilbert_implies_2) % 38.29/5.96 implies_2 % 38.29/5.96 % 38.29/5.96 (hilbert_modus_ponens) % 38.29/5.96 modus_ponens % 38.29/5.96 % 38.29/5.96 (implies_2) % 38.29/5.97 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v1) % 38.29/5.97 & $i(v0) & ((implies(v3, v2) = v4 & implies(v0, v2) = v3 & implies(v0, v1) = % 38.29/5.97 v2 & $i(v4) & $i(v3) & $i(v2) & ~ implies_2 & ~ is_a_theorem(v4)) | % 38.29/5.97 (implies_2 & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (implies(v5, % 38.29/5.97 v6) = v7) | ~ $i(v6) | ~ $i(v5) | ? [v8: $i] : ? [v9: $i] : % 38.29/5.97 (implies(v8, v7) = v9 & implies(v5, v7) = v8 & $i(v9) & $i(v8) & % 38.29/5.97 is_a_theorem(v9)))))) % 38.29/5.97 % 38.29/5.97 (kn1) % 38.29/5.97 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v0) & ((and(v0, v0) = v1 & % 38.29/5.97 implies(v0, v1) = v2 & $i(v2) & $i(v1) & ~ kn1 & ~ is_a_theorem(v2)) | % 38.29/5.97 (kn1 & ! [v3: $i] : ! [v4: $i] : ( ~ (and(v3, v3) = v4) | ~ $i(v3) | ? % 38.29/5.97 [v5: $i] : (implies(v3, v4) = v5 & $i(v5) & is_a_theorem(v5)))))) % 38.29/5.97 % 38.29/5.97 (modus_ponens) % 38.29/5.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v1) & $i(v0) & ((implies(v0, v1) % 38.29/5.98 = v2 & $i(v2) & is_a_theorem(v2) & is_a_theorem(v0) & ~ % 38.29/5.98 is_a_theorem(v1) & ~ modus_ponens) | (modus_ponens & ! [v3: $i] : ! % 38.29/5.98 [v4: $i] : ! [v5: $i] : ( ~ (implies(v3, v4) = v5) | ~ $i(v4) | ~ % 38.29/5.98 $i(v3) | ~ is_a_theorem(v5) | ~ is_a_theorem(v3) | % 38.29/5.98 is_a_theorem(v4))))) % 38.29/5.98 % 38.29/5.98 (rosser_kn1) % 38.29/5.98 ~ kn1 % 38.29/5.98 % 38.29/5.98 (function-axioms) % 38.29/5.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3, % 38.29/5.98 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 38.29/5.98 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = % 38.29/5.98 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 38.29/5.98 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 38.29/5.98 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ % 38.29/5.98 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 38.29/5.98 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) % 38.29/5.98 % 38.29/5.98 Further assumptions not needed in the proof: % 38.29/5.98 -------------------------------------------- % 38.29/5.98 and_1, and_2, cn1, cn2, cn3, equivalence_1, equivalence_2, equivalence_3, % 38.29/5.98 hilbert_and_1, hilbert_and_2, hilbert_equivalence_1, hilbert_equivalence_2, % 38.29/5.98 hilbert_equivalence_3, hilbert_implies_1, hilbert_implies_3, % 38.29/5.98 hilbert_modus_tollens, hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or, % 38.29/5.98 hilbert_or_1, hilbert_or_2, hilbert_or_3, implies_1, implies_3, kn2, kn3, % 38.29/5.98 modus_tollens, op_and, op_equiv, op_implies_and, op_implies_or, op_or, or_1, % 38.29/5.98 or_2, or_3, r1, r2, r3, r4, r5, rosser_op_equiv, rosser_op_implies_and, % 38.29/5.98 rosser_op_or, substitution_of_equivalents, use_substitution_of_equivalents % 38.29/5.98 % 38.29/5.98 Those formulas are unsatisfiable: % 38.29/5.98 --------------------------------- % 38.29/5.98 % 38.29/5.98 Begin of proof % 38.29/5.98 | % 38.29/5.99 | ALPHA: (function-axioms) implies: % 38.29/5.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.29/5.99 | (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0)) % 38.29/5.99 | % 38.29/5.99 | DELTA: instantiating (kn1) with fresh symbols all_6_0, all_6_1, all_6_2 gives: % 38.29/5.99 | (2) $i(all_6_2) & ((and(all_6_2, all_6_2) = all_6_1 & implies(all_6_2, % 38.29/5.99 | all_6_1) = all_6_0 & $i(all_6_0) & $i(all_6_1) & ~ kn1 & ~ % 38.29/5.99 | is_a_theorem(all_6_0)) | (kn1 & ! [v0: $i] : ! [v1: $i] : ( ~ % 38.29/5.99 | (and(v0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : (implies(v0, v1) = % 38.29/5.99 | v2 & $i(v2) & is_a_theorem(v2))))) % 38.29/5.99 | % 38.29/5.99 | ALPHA: (2) implies: % 38.29/5.99 | (3) $i(all_6_2) % 38.29/5.99 | (4) (and(all_6_2, all_6_2) = all_6_1 & implies(all_6_2, all_6_1) = all_6_0 % 38.29/5.99 | & $i(all_6_0) & $i(all_6_1) & ~ kn1 & ~ is_a_theorem(all_6_0)) | % 38.29/5.99 | (kn1 & ! [v0: $i] : ! [v1: $i] : ( ~ (and(v0, v0) = v1) | ~ $i(v0) | % 38.29/5.99 | ? [v2: $i] : (implies(v0, v1) = v2 & $i(v2) & is_a_theorem(v2)))) % 38.29/5.99 | % 38.29/5.99 | DELTA: instantiating (modus_ponens) with fresh symbols all_12_0, all_12_1, % 38.29/5.99 | all_12_2 gives: % 38.29/6.00 | (5) $i(all_12_1) & $i(all_12_2) & ((implies(all_12_2, all_12_1) = all_12_0 % 38.29/6.00 | & $i(all_12_0) & is_a_theorem(all_12_0) & is_a_theorem(all_12_2) & % 38.29/6.00 | ~ is_a_theorem(all_12_1) & ~ modus_ponens) | (modus_ponens & ! % 38.29/6.00 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | % 38.29/6.00 | ~ $i(v1) | ~ $i(v0) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) % 38.29/6.00 | | is_a_theorem(v1)))) % 38.29/6.00 | % 38.29/6.00 | ALPHA: (5) implies: % 38.29/6.00 | (6) (implies(all_12_2, all_12_1) = all_12_0 & $i(all_12_0) & % 38.29/6.00 | is_a_theorem(all_12_0) & is_a_theorem(all_12_2) & ~ % 38.29/6.00 | is_a_theorem(all_12_1) & ~ modus_ponens) | (modus_ponens & ! [v0: % 38.29/6.00 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ % 38.29/6.00 | $i(v1) | ~ $i(v0) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | % 38.29/6.00 | is_a_theorem(v1))) % 38.29/6.00 | % 38.29/6.00 | DELTA: instantiating (and_3) with fresh symbols all_30_0, all_30_1, all_30_2, % 38.29/6.00 | all_30_3, all_30_4 gives: % 38.29/6.00 | (7) $i(all_30_3) & $i(all_30_4) & ((and(all_30_4, all_30_3) = all_30_2 & % 38.29/6.00 | implies(all_30_3, all_30_2) = all_30_1 & implies(all_30_4, % 38.29/6.00 | all_30_1) = all_30_0 & $i(all_30_0) & $i(all_30_1) & $i(all_30_2) % 38.29/6.00 | & ~ and_3 & ~ is_a_theorem(all_30_0)) | (and_3 & ! [v0: $i] : ! % 38.29/6.00 | [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = v2) | ~ $i(v1) | ~ % 38.29/6.00 | $i(v0) | ? [v3: $i] : ? [v4: $i] : (implies(v1, v2) = v3 & % 38.29/6.00 | implies(v0, v3) = v4 & $i(v4) & $i(v3) & is_a_theorem(v4))))) % 38.29/6.00 | % 38.29/6.00 | ALPHA: (7) implies: % 38.29/6.01 | (8) (and(all_30_4, all_30_3) = all_30_2 & implies(all_30_3, all_30_2) = % 38.29/6.01 | all_30_1 & implies(all_30_4, all_30_1) = all_30_0 & $i(all_30_0) & % 38.29/6.01 | $i(all_30_1) & $i(all_30_2) & ~ and_3 & ~ is_a_theorem(all_30_0)) | % 38.29/6.01 | (and_3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = % 38.29/6.01 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 38.29/6.01 | (implies(v1, v2) = v3 & implies(v0, v3) = v4 & $i(v4) & $i(v3) & % 38.29/6.01 | is_a_theorem(v4)))) % 38.29/6.01 | % 38.29/6.01 | DELTA: instantiating (implies_2) with fresh symbols all_32_0, all_32_1, % 38.29/6.01 | all_32_2, all_32_3, all_32_4 gives: % 38.29/6.01 | (9) $i(all_32_3) & $i(all_32_4) & ((implies(all_32_1, all_32_2) = all_32_0 % 38.29/6.01 | & implies(all_32_4, all_32_2) = all_32_1 & implies(all_32_4, % 38.29/6.01 | all_32_3) = all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) % 38.29/6.01 | & ~ implies_2 & ~ is_a_theorem(all_32_0)) | (implies_2 & ! [v0: % 38.29/6.01 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ % 38.29/6.01 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (implies(v3, v2) % 38.29/6.01 | = v4 & implies(v0, v2) = v3 & $i(v4) & $i(v3) & % 38.29/6.01 | is_a_theorem(v4))))) % 38.29/6.01 | % 38.29/6.01 | ALPHA: (9) implies: % 38.29/6.01 | (10) (implies(all_32_1, all_32_2) = all_32_0 & implies(all_32_4, all_32_2) % 38.29/6.01 | = all_32_1 & implies(all_32_4, all_32_3) = all_32_2 & $i(all_32_0) & % 38.29/6.01 | $i(all_32_1) & $i(all_32_2) & ~ implies_2 & ~ % 38.29/6.01 | is_a_theorem(all_32_0)) | (implies_2 & ! [v0: $i] : ! [v1: $i] : % 38.29/6.01 | ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.29/6.01 | [v3: $i] : ? [v4: $i] : (implies(v3, v2) = v4 & implies(v0, v2) = % 38.29/6.01 | v3 & $i(v4) & $i(v3) & is_a_theorem(v4)))) % 38.29/6.01 | % 38.29/6.01 | BETA: splitting (4) gives: % 38.29/6.01 | % 38.29/6.01 | Case 1: % 38.29/6.01 | | % 38.29/6.02 | | (11) and(all_6_2, all_6_2) = all_6_1 & implies(all_6_2, all_6_1) = % 38.29/6.02 | | all_6_0 & $i(all_6_0) & $i(all_6_1) & ~ kn1 & ~ % 38.29/6.02 | | is_a_theorem(all_6_0) % 38.29/6.02 | | % 38.29/6.02 | | ALPHA: (11) implies: % 38.29/6.02 | | (12) ~ is_a_theorem(all_6_0) % 38.29/6.02 | | (13) $i(all_6_1) % 38.29/6.02 | | (14) implies(all_6_2, all_6_1) = all_6_0 % 38.29/6.02 | | (15) and(all_6_2, all_6_2) = all_6_1 % 38.29/6.02 | | % 38.29/6.02 | | BETA: splitting (6) gives: % 38.29/6.02 | | % 38.29/6.02 | | Case 1: % 38.29/6.02 | | | % 38.29/6.02 | | | (16) implies(all_12_2, all_12_1) = all_12_0 & $i(all_12_0) & % 38.29/6.02 | | | is_a_theorem(all_12_0) & is_a_theorem(all_12_2) & ~ % 38.29/6.02 | | | is_a_theorem(all_12_1) & ~ modus_ponens % 38.29/6.02 | | | % 38.29/6.02 | | | ALPHA: (16) implies: % 38.29/6.02 | | | (17) ~ modus_ponens % 38.29/6.02 | | | % 38.29/6.02 | | | PRED_UNIFY: (17), (hilbert_modus_ponens) imply: % 38.29/6.02 | | | (18) $false % 38.29/6.02 | | | % 38.29/6.02 | | | CLOSE: (18) is inconsistent. % 38.29/6.02 | | | % 38.29/6.02 | | Case 2: % 38.29/6.02 | | | % 38.29/6.02 | | | (19) modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 38.29/6.02 | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 38.29/6.02 | | | is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1)) % 38.29/6.02 | | | % 38.29/6.02 | | | ALPHA: (19) implies: % 38.29/6.02 | | | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = % 38.29/6.02 | | | v2) | ~ $i(v1) | ~ $i(v0) | ~ is_a_theorem(v2) | ~ % 38.29/6.02 | | | is_a_theorem(v0) | is_a_theorem(v1)) % 38.29/6.02 | | | % 38.29/6.02 | | | BETA: splitting (8) gives: % 38.29/6.03 | | | % 38.29/6.03 | | | Case 1: % 38.29/6.03 | | | | % 38.29/6.03 | | | | (21) and(all_30_4, all_30_3) = all_30_2 & implies(all_30_3, all_30_2) % 38.29/6.03 | | | | = all_30_1 & implies(all_30_4, all_30_1) = all_30_0 & % 38.29/6.03 | | | | $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & ~ and_3 & ~ % 38.29/6.03 | | | | is_a_theorem(all_30_0) % 38.29/6.03 | | | | % 38.29/6.03 | | | | ALPHA: (21) implies: % 38.29/6.03 | | | | (22) ~ and_3 % 38.29/6.03 | | | | % 38.29/6.03 | | | | PRED_UNIFY: (22), (hilbert_and_3) imply: % 38.29/6.03 | | | | (23) $false % 38.29/6.03 | | | | % 38.29/6.03 | | | | CLOSE: (23) is inconsistent. % 38.29/6.03 | | | | % 38.29/6.03 | | | Case 2: % 38.29/6.03 | | | | % 38.29/6.03 | | | | (24) and_3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, % 38.29/6.03 | | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 38.29/6.03 | | | | $i] : (implies(v1, v2) = v3 & implies(v0, v3) = v4 & $i(v4) % 38.29/6.03 | | | | & $i(v3) & is_a_theorem(v4))) % 38.29/6.03 | | | | % 38.29/6.03 | | | | ALPHA: (24) implies: % 38.29/6.03 | | | | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = v2) % 38.29/6.03 | | | | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 38.29/6.03 | | | | (implies(v1, v2) = v3 & implies(v0, v3) = v4 & $i(v4) & $i(v3) % 38.29/6.03 | | | | & is_a_theorem(v4))) % 38.29/6.03 | | | | % 38.29/6.03 | | | | BETA: splitting (10) gives: % 38.29/6.03 | | | | % 38.29/6.03 | | | | Case 1: % 38.29/6.03 | | | | | % 38.95/6.03 | | | | | (26) implies(all_32_1, all_32_2) = all_32_0 & implies(all_32_4, % 38.95/6.03 | | | | | all_32_2) = all_32_1 & implies(all_32_4, all_32_3) = % 38.95/6.03 | | | | | all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & ~ % 38.95/6.03 | | | | | implies_2 & ~ is_a_theorem(all_32_0) % 38.95/6.03 | | | | | % 38.95/6.03 | | | | | ALPHA: (26) implies: % 38.95/6.03 | | | | | (27) ~ implies_2 % 38.95/6.03 | | | | | % 38.95/6.03 | | | | | PRED_UNIFY: (27), (hilbert_implies_2) imply: % 38.95/6.03 | | | | | (28) $false % 38.95/6.03 | | | | | % 38.95/6.03 | | | | | CLOSE: (28) is inconsistent. % 38.95/6.03 | | | | | % 38.95/6.03 | | | | Case 2: % 38.95/6.03 | | | | | % 38.95/6.03 | | | | | (29) implies_2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 38.95/6.03 | | | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 38.95/6.03 | | | | | : ? [v4: $i] : (implies(v3, v2) = v4 & implies(v0, v2) = v3 % 38.95/6.03 | | | | | & $i(v4) & $i(v3) & is_a_theorem(v4))) % 38.95/6.04 | | | | | % 38.95/6.04 | | | | | ALPHA: (29) implies: % 38.95/6.04 | | | | | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) % 38.95/6.04 | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] % 38.95/6.04 | | | | | : (implies(v3, v2) = v4 & implies(v0, v2) = v3 & $i(v4) & % 38.95/6.04 | | | | | $i(v3) & is_a_theorem(v4))) % 38.95/6.04 | | | | | % 38.95/6.04 | | | | | GROUND_INST: instantiating (30) with all_6_2, all_6_1, all_6_0, % 38.95/6.04 | | | | | simplifying with (3), (13), (14) gives: % 38.95/6.04 | | | | | (31) ? [v0: $i] : ? [v1: $i] : (implies(v0, all_6_0) = v1 & % 38.95/6.04 | | | | | implies(all_6_2, all_6_0) = v0 & $i(v1) & $i(v0) & % 38.95/6.04 | | | | | is_a_theorem(v1)) % 38.95/6.04 | | | | | % 38.95/6.04 | | | | | GROUND_INST: instantiating (25) with all_6_2, all_6_2, all_6_1, % 38.95/6.04 | | | | | simplifying with (3), (15) gives: % 38.95/6.04 | | | | | (32) ? [v0: $i] : ? [v1: $i] : (implies(all_6_2, v0) = v1 & % 38.95/6.04 | | | | | implies(all_6_2, all_6_1) = v0 & $i(v1) & $i(v0) & % 38.95/6.04 | | | | | is_a_theorem(v1)) % 38.95/6.04 | | | | | % 38.95/6.04 | | | | | DELTA: instantiating (31) with fresh symbols all_146_0, all_146_1 % 38.95/6.04 | | | | | gives: % 38.95/6.04 | | | | | (33) implies(all_146_1, all_6_0) = all_146_0 & implies(all_6_2, % 38.95/6.04 | | | | | all_6_0) = all_146_1 & $i(all_146_0) & $i(all_146_1) & % 38.95/6.04 | | | | | is_a_theorem(all_146_0) % 38.95/6.04 | | | | | % 38.95/6.04 | | | | | ALPHA: (33) implies: % 38.95/6.05 | | | | | (34) is_a_theorem(all_146_0) % 38.95/6.05 | | | | | (35) implies(all_6_2, all_6_0) = all_146_1 % 38.95/6.05 | | | | | (36) implies(all_146_1, all_6_0) = all_146_0 % 38.95/6.05 | | | | | % 38.95/6.05 | | | | | DELTA: instantiating (32) with fresh symbols all_150_0, all_150_1 % 38.95/6.05 | | | | | gives: % 38.95/6.05 | | | | | (37) implies(all_6_2, all_150_1) = all_150_0 & implies(all_6_2, % 38.95/6.05 | | | | | all_6_1) = all_150_1 & $i(all_150_0) & $i(all_150_1) & % 38.95/6.05 | | | | | is_a_theorem(all_150_0) % 38.95/6.05 | | | | | % 38.95/6.05 | | | | | ALPHA: (37) implies: % 38.95/6.05 | | | | | (38) is_a_theorem(all_150_0) % 38.95/6.05 | | | | | (39) $i(all_150_1) % 38.95/6.05 | | | | | (40) $i(all_150_0) % 38.95/6.05 | | | | | (41) implies(all_6_2, all_6_1) = all_150_1 % 38.95/6.05 | | | | | (42) implies(all_6_2, all_150_1) = all_150_0 % 38.95/6.05 | | | | | % 38.95/6.05 | | | | | GROUND_INST: instantiating (1) with all_6_0, all_150_1, all_6_1, % 38.95/6.05 | | | | | all_6_2, simplifying with (14), (41) gives: % 38.95/6.05 | | | | | (43) all_150_1 = all_6_0 % 38.95/6.05 | | | | | % 38.95/6.05 | | | | | GROUND_INST: instantiating (1) with all_146_1, all_150_0, all_6_0, % 38.95/6.05 | | | | | all_6_2, simplifying with (35) gives: % 38.95/6.05 | | | | | (44) all_150_0 = all_146_1 | ~ (implies(all_6_2, all_6_0) = % 38.95/6.05 | | | | | all_150_0) % 38.95/6.05 | | | | | % 38.95/6.05 | | | | | REDUCE: (42), (43) imply: % 38.95/6.05 | | | | | (45) implies(all_6_2, all_6_0) = all_150_0 % 38.95/6.05 | | | | | % 38.95/6.05 | | | | | REDUCE: (39), (43) imply: % 38.95/6.05 | | | | | (46) $i(all_6_0) % 38.95/6.05 | | | | | % 38.95/6.05 | | | | | BETA: splitting (44) gives: % 38.95/6.05 | | | | | % 38.95/6.05 | | | | | Case 1: % 38.95/6.05 | | | | | | % 38.95/6.05 | | | | | | (47) ~ (implies(all_6_2, all_6_0) = all_150_0) % 38.95/6.05 | | | | | | % 38.95/6.05 | | | | | | PRED_UNIFY: (45), (47) imply: % 38.95/6.05 | | | | | | (48) $false % 38.95/6.05 | | | | | | % 38.95/6.05 | | | | | | CLOSE: (48) is inconsistent. % 38.95/6.05 | | | | | | % 38.95/6.05 | | | | | Case 2: % 38.95/6.05 | | | | | | % 38.95/6.05 | | | | | | (49) all_150_0 = all_146_1 % 38.95/6.05 | | | | | | % 38.95/6.06 | | | | | | REDUCE: (40), (49) imply: % 38.95/6.06 | | | | | | (50) $i(all_146_1) % 38.95/6.06 | | | | | | % 38.95/6.06 | | | | | | REDUCE: (38), (49) imply: % 38.95/6.06 | | | | | | (51) is_a_theorem(all_146_1) % 38.95/6.06 | | | | | | % 38.95/6.06 | | | | | | GROUND_INST: instantiating (20) with all_146_1, all_6_0, all_146_0, % 38.95/6.06 | | | | | | simplifying with (12), (34), (36), (46), (50), (51) % 38.95/6.06 | | | | | | gives: % 38.95/6.06 | | | | | | (52) $false % 38.95/6.06 | | | | | | % 38.95/6.06 | | | | | | CLOSE: (52) is inconsistent. % 38.95/6.06 | | | | | | % 38.95/6.06 | | | | | End of split % 38.95/6.06 | | | | | % 38.95/6.06 | | | | End of split % 38.95/6.06 | | | | % 38.95/6.06 | | | End of split % 38.95/6.06 | | | % 38.95/6.06 | | End of split % 38.95/6.06 | | % 38.95/6.06 | Case 2: % 38.95/6.06 | | % 38.95/6.06 | | (53) kn1 & ! [v0: $i] : ! [v1: $i] : ( ~ (and(v0, v0) = v1) | ~ $i(v0) % 38.95/6.06 | | | ? [v2: $i] : (implies(v0, v1) = v2 & $i(v2) & % 38.95/6.06 | | is_a_theorem(v2))) % 38.95/6.06 | | % 38.95/6.06 | | ALPHA: (53) implies: % 38.95/6.06 | | (54) kn1 % 38.95/6.06 | | % 38.95/6.06 | | PRED_UNIFY: (54), (rosser_kn1) imply: % 38.95/6.06 | | (55) $false % 38.95/6.06 | | % 38.95/6.06 | | CLOSE: (55) is inconsistent. % 38.95/6.06 | | % 38.95/6.06 | End of split % 38.95/6.06 | % 38.95/6.06 End of proof % 38.95/6.06 % SZS output end Proof for theBenchmark % 38.95/6.06 % 38.95/6.06 5326ms %------------------------------------------------------------------------------