%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL540+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 : n001.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 12:54:18 PM UTC 2026 % Result : Theorem 20.80s 3.46s % Output : Proof 53.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL540+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 : n001.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 16:07:59 UTC 2026 % 0.10/0.36 % CPUTime : % 0.13/0.37 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. % 0.55/0.69 ________ _____ % 0.55/0.69 ___ __ \_________(_)________________________________ % 0.55/0.69 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.55/0.69 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.55/0.69 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.55/0.69 % 0.55/0.69 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.55/0.69 (2023-06-19) % 0.55/0.69 % 0.55/0.69 (c) Philipp Rümmer, 2009-2023 % 0.55/0.69 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.55/0.69 Amanda Stjerna. % 0.55/0.69 Free software under BSD-3-Clause. % 0.55/0.69 % 0.55/0.69 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.55/0.69 % 0.55/0.69 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.71 Running up to 7 provers in parallel. % 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 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 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 % 4.99/1.49 Prover 1: Preprocessing ... % 5.78/1.50 Prover 4: Preprocessing ... % 5.78/1.53 Prover 6: Preprocessing ... % 5.78/1.53 Prover 2: Preprocessing ... % 5.78/1.53 Prover 3: Preprocessing ... % 5.78/1.53 Prover 0: Preprocessing ... % 5.78/1.53 Prover 5: Preprocessing ... % 16.87/2.96 Prover 6: Constructing countermodel ... % 16.87/2.97 Prover 5: Proving ... % 16.87/3.03 Prover 1: Constructing countermodel ... % 18.01/3.07 Prover 3: Constructing countermodel ... % 18.01/3.13 Prover 4: Constructing countermodel ... % 18.77/3.18 Prover 0: Proving ... % 19.23/3.21 Prover 2: Proving ... % 20.80/3.46 Prover 3: proved (2732ms) % 20.80/3.46 % 20.80/3.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.80/3.46 % 20.80/3.47 Prover 6: stopped % 20.80/3.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.80/3.47 Prover 0: stopped % 20.80/3.47 Prover 5: stopped % 20.80/3.48 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.80/3.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.80/3.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 21.59/3.53 Prover 2: stopped % 21.59/3.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 22.41/3.62 Prover 7: Preprocessing ... % 22.41/3.69 Prover 8: Preprocessing ... % 23.22/3.71 Prover 10: Preprocessing ... % 23.22/3.74 Prover 11: Preprocessing ... % 23.22/3.77 Prover 13: Preprocessing ... % 24.79/3.93 Prover 8: Warning: ignoring some quantifiers % 24.79/3.98 Prover 8: Constructing countermodel ... % 26.03/4.11 Prover 7: Constructing countermodel ... % 26.03/4.15 Prover 10: Constructing countermodel ... % 26.03/4.16 Prover 13: Constructing countermodel ... % 28.76/4.42 Prover 11: Constructing countermodel ... % 51.62/7.36 Prover 7: Found proof (size 38) % 51.62/7.36 Prover 7: proved (3895ms) % 51.62/7.37 Prover 10: stopped % 51.62/7.37 Prover 8: stopped % 51.62/7.38 Prover 4: stopped % 51.62/7.38 Prover 11: stopped % 52.35/7.40 Prover 1: stopped % 52.77/7.54 Prover 13: stopped % 52.77/7.54 % 52.77/7.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 52.77/7.54 % 52.77/7.55 % SZS output start Proof for theBenchmark % 52.77/7.56 Assumptions after simplification: % 52.77/7.56 --------------------------------- % 52.77/7.56 % 52.77/7.56 (adjunction) % 53.18/7.62 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v1) & $i(v0) & ((and(v0, v1) = % 53.18/7.62 v2 & $i(v2) & is_a_theorem(v1) & is_a_theorem(v0) & ~ adjunction & ~ % 53.18/7.62 is_a_theorem(v2)) | (adjunction & ! [v3: $i] : ! [v4: $i] : ! [v5: % 53.18/7.62 $i] : ( ~ (and(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 53.18/7.62 is_a_theorem(v4) | ~ is_a_theorem(v3) | is_a_theorem(v5))))) % 53.18/7.62 % 53.18/7.62 (and_3) % 53.18/7.63 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v1) % 53.18/7.63 & $i(v0) & ((and(v0, v1) = v2 & implies(v1, v2) = v3 & implies(v0, v3) = v4 % 53.18/7.63 & $i(v4) & $i(v3) & $i(v2) & ~ and_3 & ~ is_a_theorem(v4)) | (and_3 & % 53.18/7.63 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (and(v5, v6) = v7) | ~ % 53.18/7.63 $i(v6) | ~ $i(v5) | ? [v8: $i] : ? [v9: $i] : (implies(v6, v7) = v8 % 53.18/7.63 & implies(v5, v8) = v9 & $i(v9) & $i(v8) & is_a_theorem(v9)))))) % 53.18/7.63 % 53.18/7.63 (hilbert_and_3) % 53.18/7.63 and_3 % 53.18/7.63 % 53.18/7.63 (hilbert_modus_ponens) % 53.18/7.63 modus_ponens % 53.18/7.63 % 53.18/7.63 (hilbert_modus_tollens) % 53.18/7.63 modus_tollens % 53.18/7.63 % 53.18/7.63 (modus_ponens) % 53.18/7.64 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v1) & $i(v0) & ((implies(v0, v1) % 53.18/7.64 = v2 & $i(v2) & is_a_theorem(v2) & is_a_theorem(v0) & ~ % 53.18/7.64 is_a_theorem(v1) & ~ modus_ponens) | (modus_ponens & ! [v3: $i] : ! % 53.18/7.64 [v4: $i] : ! [v5: $i] : ( ~ (implies(v3, v4) = v5) | ~ $i(v4) | ~ % 53.18/7.64 $i(v3) | ~ is_a_theorem(v5) | ~ is_a_theorem(v3) | % 53.18/7.64 is_a_theorem(v4))))) % 53.18/7.64 % 53.18/7.64 (modus_tollens) % 53.18/7.65 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 53.18/7.65 $i] : ? [v6: $i] : ($i(v1) & $i(v0) & ((not(v1) = v2 & not(v0) = v3 & % 53.18/7.65 implies(v4, v5) = v6 & implies(v2, v3) = v4 & implies(v0, v1) = v5 & % 53.18/7.65 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ~ modus_tollens & ~ % 53.18/7.65 is_a_theorem(v6)) | (modus_tollens & ! [v7: $i] : ! [v8: $i] : ! [v9: % 53.18/7.65 $i] : ! [v10: $i] : ! [v11: $i] : ( ~ (not(v8) = v9) | ~ (not(v7) = % 53.18/7.65 v10) | ~ (implies(v9, v10) = v11) | ~ $i(v8) | ~ $i(v7) | ? % 53.18/7.65 [v12: $i] : ? [v13: $i] : (implies(v11, v12) = v13 & implies(v7, v8) % 53.18/7.65 = v12 & $i(v13) & $i(v12) & is_a_theorem(v13))) & ! [v7: $i] : ! % 53.18/7.65 [v8: $i] : ! [v9: $i] : ( ~ (implies(v7, v8) = v9) | ~ $i(v8) | ~ % 53.18/7.65 $i(v7) | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : % 53.18/7.65 (not(v8) = v10 & not(v7) = v11 & implies(v12, v9) = v13 & implies(v10, % 53.18/7.65 v11) = v12 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & % 53.18/7.65 is_a_theorem(v13)))))) % 53.18/7.65 % 53.18/7.65 (s1_0_adjunction) % 53.18/7.65 ~ adjunction % 53.18/7.65 % 53.18/7.65 Further assumptions not needed in the proof: % 53.18/7.65 -------------------------------------------- % 53.18/7.65 and_1, and_2, axiom_4, axiom_5, axiom_B, axiom_K, axiom_M, axiom_m1, axiom_m10, % 53.18/7.65 axiom_m2, axiom_m3, axiom_m4, axiom_m5, axiom_m6, axiom_m7, axiom_m8, axiom_m9, % 53.18/7.65 axiom_s1, axiom_s2, axiom_s3, axiom_s4, cn1, cn2, cn3, equivalence_1, % 53.18/7.65 equivalence_2, equivalence_3, hilbert_and_1, hilbert_and_2, % 53.18/7.65 hilbert_equivalence_1, hilbert_equivalence_2, hilbert_equivalence_3, % 53.18/7.65 hilbert_implies_1, hilbert_implies_2, hilbert_implies_3, hilbert_op_equiv, % 53.18/7.65 hilbert_op_implies_and, hilbert_op_or, hilbert_or_1, hilbert_or_2, hilbert_or_3, % 53.18/7.65 implies_1, implies_2, implies_3, km4b_axiom_4, km4b_axiom_B, km4b_axiom_K, % 53.18/7.65 km4b_axiom_M, km4b_necessitation, km4b_op_possibly, kn1, kn2, kn3, % 53.18/7.65 modus_ponens_strict_implies, necessitation, op_and, op_equiv, op_implies_and, % 53.18/7.65 op_implies_or, op_necessarily, op_or, op_possibly, op_strict_equiv, % 53.18/7.65 op_strict_implies, or_1, or_2, or_3, r1, r2, r3, r4, r5, s1_0_op_equiv, % 53.18/7.65 s1_0_op_implies, s1_0_op_or, s1_0_op_possibly, s1_0_op_strict_equiv, % 53.18/7.65 s1_0_op_strict_implies, substitution_of_equivalents, substitution_strict_equiv, % 53.18/7.65 use_substitution_of_equivalents % 53.18/7.65 % 53.18/7.65 Those formulas are unsatisfiable: % 53.18/7.65 --------------------------------- % 53.18/7.65 % 53.18/7.65 Begin of proof % 53.18/7.66 | % 53.18/7.66 | DELTA: instantiating (modus_ponens) with fresh symbols all_26_0, all_26_1, % 53.18/7.66 | all_26_2 gives: % 53.18/7.66 | (1) $i(all_26_1) & $i(all_26_2) & ((implies(all_26_2, all_26_1) = all_26_0 % 53.18/7.66 | & $i(all_26_0) & is_a_theorem(all_26_0) & is_a_theorem(all_26_2) & % 53.18/7.66 | ~ is_a_theorem(all_26_1) & ~ modus_ponens) | (modus_ponens & ! % 53.18/7.66 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | % 53.18/7.66 | ~ $i(v1) | ~ $i(v0) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) % 53.18/7.66 | | is_a_theorem(v1)))) % 53.18/7.66 | % 53.18/7.66 | ALPHA: (1) implies: % 53.18/7.67 | (2) (implies(all_26_2, all_26_1) = all_26_0 & $i(all_26_0) & % 53.18/7.67 | is_a_theorem(all_26_0) & is_a_theorem(all_26_2) & ~ % 53.18/7.67 | is_a_theorem(all_26_1) & ~ modus_ponens) | (modus_ponens & ! [v0: % 53.18/7.67 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ % 53.18/7.67 | $i(v1) | ~ $i(v0) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | % 53.18/7.67 | is_a_theorem(v1))) % 53.18/7.67 | % 53.18/7.67 | DELTA: instantiating (adjunction) with fresh symbols all_30_0, all_30_1, % 53.18/7.67 | all_30_2 gives: % 53.18/7.67 | (3) $i(all_30_1) & $i(all_30_2) & ((and(all_30_2, all_30_1) = all_30_0 & % 53.18/7.67 | $i(all_30_0) & is_a_theorem(all_30_1) & is_a_theorem(all_30_2) & ~ % 53.18/7.67 | adjunction & ~ is_a_theorem(all_30_0)) | (adjunction & ! [v0: $i] % 53.18/7.67 | : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = v2) | ~ $i(v1) | % 53.18/7.67 | ~ $i(v0) | ~ is_a_theorem(v1) | ~ is_a_theorem(v0) | % 53.18/7.67 | is_a_theorem(v2)))) % 53.18/7.67 | % 53.18/7.67 | ALPHA: (3) implies: % 53.18/7.67 | (4) $i(all_30_2) % 53.18/7.67 | (5) $i(all_30_1) % 53.18/7.67 | (6) (and(all_30_2, all_30_1) = all_30_0 & $i(all_30_0) & % 53.18/7.67 | is_a_theorem(all_30_1) & is_a_theorem(all_30_2) & ~ adjunction & ~ % 53.18/7.67 | is_a_theorem(all_30_0)) | (adjunction & ! [v0: $i] : ! [v1: $i] : % 53.18/7.67 | ! [v2: $i] : ( ~ (and(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 53.18/7.67 | is_a_theorem(v1) | ~ is_a_theorem(v0) | is_a_theorem(v2))) % 53.18/7.67 | % 53.18/7.67 | DELTA: instantiating (and_3) with fresh symbols all_62_0, all_62_1, all_62_2, % 53.18/7.67 | all_62_3, all_62_4 gives: % 53.18/7.68 | (7) $i(all_62_3) & $i(all_62_4) & ((and(all_62_4, all_62_3) = all_62_2 & % 53.18/7.68 | implies(all_62_3, all_62_2) = all_62_1 & implies(all_62_4, % 53.18/7.68 | all_62_1) = all_62_0 & $i(all_62_0) & $i(all_62_1) & $i(all_62_2) % 53.18/7.68 | & ~ and_3 & ~ is_a_theorem(all_62_0)) | (and_3 & ! [v0: $i] : ! % 53.18/7.68 | [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = v2) | ~ $i(v1) | ~ % 53.18/7.68 | $i(v0) | ? [v3: $i] : ? [v4: $i] : (implies(v1, v2) = v3 & % 53.18/7.68 | implies(v0, v3) = v4 & $i(v4) & $i(v3) & is_a_theorem(v4))))) % 53.18/7.68 | % 53.18/7.68 | ALPHA: (7) implies: % 53.18/7.68 | (8) (and(all_62_4, all_62_3) = all_62_2 & implies(all_62_3, all_62_2) = % 53.18/7.68 | all_62_1 & implies(all_62_4, all_62_1) = all_62_0 & $i(all_62_0) & % 53.18/7.68 | $i(all_62_1) & $i(all_62_2) & ~ and_3 & ~ is_a_theorem(all_62_0)) | % 53.18/7.68 | (and_3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = % 53.18/7.68 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 53.18/7.68 | (implies(v1, v2) = v3 & implies(v0, v3) = v4 & $i(v4) & $i(v3) & % 53.18/7.68 | is_a_theorem(v4)))) % 53.18/7.68 | % 53.18/7.68 | DELTA: instantiating (modus_tollens) with fresh symbols all_86_0, all_86_1, % 53.18/7.68 | all_86_2, all_86_3, all_86_4, all_86_5, all_86_6 gives: % 53.18/7.69 | (9) $i(all_86_5) & $i(all_86_6) & ((not(all_86_5) = all_86_4 & % 53.18/7.69 | not(all_86_6) = all_86_3 & implies(all_86_2, all_86_1) = all_86_0 & % 53.18/7.69 | implies(all_86_4, all_86_3) = all_86_2 & implies(all_86_6, % 53.18/7.69 | all_86_5) = all_86_1 & $i(all_86_0) & $i(all_86_1) & $i(all_86_2) % 53.18/7.69 | & $i(all_86_3) & $i(all_86_4) & ~ modus_tollens & ~ % 53.18/7.69 | is_a_theorem(all_86_0)) | (modus_tollens & ! [v0: $i] : ! [v1: % 53.18/7.69 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (not(v1) = % 53.18/7.69 | v2) | ~ (not(v0) = v3) | ~ (implies(v2, v3) = v4) | ~ $i(v1) % 53.18/7.69 | | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (implies(v4, v5) = v6 & % 53.18/7.69 | implies(v0, v1) = v5 & $i(v6) & $i(v5) & is_a_theorem(v6))) & % 53.18/7.69 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) % 53.18/7.69 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 53.18/7.69 | : ? [v6: $i] : (not(v1) = v3 & not(v0) = v4 & implies(v5, v2) = % 53.18/7.69 | v6 & implies(v3, v4) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 53.18/7.69 | is_a_theorem(v6))))) % 53.18/7.69 | % 53.18/7.69 | ALPHA: (9) implies: % 53.68/7.70 | (10) (not(all_86_5) = all_86_4 & not(all_86_6) = all_86_3 & % 53.68/7.70 | implies(all_86_2, all_86_1) = all_86_0 & implies(all_86_4, all_86_3) % 53.68/7.70 | = all_86_2 & implies(all_86_6, all_86_5) = all_86_1 & $i(all_86_0) & % 53.68/7.70 | $i(all_86_1) & $i(all_86_2) & $i(all_86_3) & $i(all_86_4) & ~ % 53.68/7.70 | modus_tollens & ~ is_a_theorem(all_86_0)) | (modus_tollens & ! % 53.68/7.70 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 53.68/7.70 | ~ (not(v1) = v2) | ~ (not(v0) = v3) | ~ (implies(v2, v3) = v4) | % 53.68/7.70 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (implies(v4, % 53.68/7.70 | v5) = v6 & implies(v0, v1) = v5 & $i(v6) & $i(v5) & % 53.68/7.70 | is_a_theorem(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( % 53.68/7.70 | ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 53.68/7.70 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (not(v1) = v3 & not(v0) = % 53.68/7.70 | v4 & implies(v5, v2) = v6 & implies(v3, v4) = v5 & $i(v6) & % 53.68/7.70 | $i(v5) & $i(v4) & $i(v3) & is_a_theorem(v6)))) % 53.68/7.70 | % 53.68/7.70 | BETA: splitting (6) gives: % 53.68/7.70 | % 53.68/7.70 | Case 1: % 53.68/7.70 | | % 53.68/7.70 | | (11) and(all_30_2, all_30_1) = all_30_0 & $i(all_30_0) & % 53.68/7.70 | | is_a_theorem(all_30_1) & is_a_theorem(all_30_2) & ~ adjunction & ~ % 53.68/7.70 | | is_a_theorem(all_30_0) % 53.68/7.70 | | % 53.68/7.70 | | ALPHA: (11) implies: % 53.68/7.70 | | (12) ~ is_a_theorem(all_30_0) % 53.68/7.70 | | (13) is_a_theorem(all_30_2) % 53.68/7.70 | | (14) is_a_theorem(all_30_1) % 53.68/7.70 | | (15) $i(all_30_0) % 53.68/7.70 | | (16) and(all_30_2, all_30_1) = all_30_0 % 53.68/7.70 | | % 53.68/7.70 | | BETA: splitting (2) gives: % 53.68/7.70 | | % 53.68/7.70 | | Case 1: % 53.68/7.70 | | | % 53.68/7.70 | | | (17) implies(all_26_2, all_26_1) = all_26_0 & $i(all_26_0) & % 53.68/7.70 | | | is_a_theorem(all_26_0) & is_a_theorem(all_26_2) & ~ % 53.68/7.70 | | | is_a_theorem(all_26_1) & ~ modus_ponens % 53.68/7.70 | | | % 53.68/7.70 | | | ALPHA: (17) implies: % 53.68/7.70 | | | (18) ~ modus_ponens % 53.68/7.70 | | | % 53.68/7.70 | | | PRED_UNIFY: (18), (hilbert_modus_ponens) imply: % 53.68/7.70 | | | (19) $false % 53.68/7.71 | | | % 53.68/7.71 | | | CLOSE: (19) is inconsistent. % 53.68/7.71 | | | % 53.68/7.71 | | Case 2: % 53.68/7.71 | | | % 53.68/7.71 | | | (20) modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 53.68/7.71 | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 53.68/7.71 | | | is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1)) % 53.68/7.71 | | | % 53.68/7.71 | | | ALPHA: (20) implies: % 53.68/7.71 | | | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = % 53.68/7.71 | | | v2) | ~ $i(v1) | ~ $i(v0) | ~ is_a_theorem(v2) | ~ % 53.68/7.71 | | | is_a_theorem(v0) | is_a_theorem(v1)) % 53.68/7.71 | | | % 53.68/7.71 | | | BETA: splitting (8) gives: % 53.68/7.71 | | | % 53.68/7.71 | | | Case 1: % 53.68/7.71 | | | | % 53.68/7.71 | | | | (22) and(all_62_4, all_62_3) = all_62_2 & implies(all_62_3, all_62_2) % 53.68/7.71 | | | | = all_62_1 & implies(all_62_4, all_62_1) = all_62_0 & % 53.68/7.71 | | | | $i(all_62_0) & $i(all_62_1) & $i(all_62_2) & ~ and_3 & ~ % 53.68/7.71 | | | | is_a_theorem(all_62_0) % 53.68/7.71 | | | | % 53.68/7.71 | | | | ALPHA: (22) implies: % 53.68/7.71 | | | | (23) ~ and_3 % 53.68/7.71 | | | | % 53.68/7.71 | | | | PRED_UNIFY: (23), (hilbert_and_3) imply: % 53.68/7.71 | | | | (24) $false % 53.68/7.71 | | | | % 53.68/7.71 | | | | CLOSE: (24) is inconsistent. % 53.68/7.71 | | | | % 53.68/7.71 | | | Case 2: % 53.68/7.71 | | | | % 53.68/7.72 | | | | (25) and_3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, % 53.68/7.72 | | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 53.68/7.72 | | | | $i] : (implies(v1, v2) = v3 & implies(v0, v3) = v4 & $i(v4) % 53.68/7.72 | | | | & $i(v3) & is_a_theorem(v4))) % 53.68/7.72 | | | | % 53.68/7.72 | | | | ALPHA: (25) implies: % 53.68/7.72 | | | | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = v2) % 53.68/7.72 | | | | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 53.68/7.72 | | | | (implies(v1, v2) = v3 & implies(v0, v3) = v4 & $i(v4) & $i(v3) % 53.68/7.72 | | | | & is_a_theorem(v4))) % 53.68/7.72 | | | | % 53.68/7.72 | | | | BETA: splitting (10) gives: % 53.68/7.72 | | | | % 53.68/7.72 | | | | Case 1: % 53.68/7.72 | | | | | % 53.68/7.72 | | | | | (27) not(all_86_5) = all_86_4 & not(all_86_6) = all_86_3 & % 53.68/7.72 | | | | | implies(all_86_2, all_86_1) = all_86_0 & implies(all_86_4, % 53.68/7.72 | | | | | all_86_3) = all_86_2 & implies(all_86_6, all_86_5) = % 53.68/7.72 | | | | | all_86_1 & $i(all_86_0) & $i(all_86_1) & $i(all_86_2) & % 53.68/7.72 | | | | | $i(all_86_3) & $i(all_86_4) & ~ modus_tollens & ~ % 53.68/7.72 | | | | | is_a_theorem(all_86_0) % 53.68/7.72 | | | | | % 53.68/7.72 | | | | | ALPHA: (27) implies: % 53.68/7.72 | | | | | (28) ~ modus_tollens % 53.68/7.72 | | | | | % 53.68/7.72 | | | | | PRED_UNIFY: (28), (hilbert_modus_tollens) imply: % 53.68/7.72 | | | | | (29) $false % 53.68/7.72 | | | | | % 53.68/7.72 | | | | | CLOSE: (29) is inconsistent. % 53.68/7.72 | | | | | % 53.68/7.72 | | | | Case 2: % 53.68/7.72 | | | | | % 53.68/7.72 | | | | | % 53.68/7.72 | | | | | GROUND_INST: instantiating (26) with all_30_2, all_30_1, all_30_0, % 53.68/7.72 | | | | | simplifying with (4), (5), (16) gives: % 53.68/7.72 | | | | | (30) ? [v0: $i] : ? [v1: $i] : (implies(all_30_1, all_30_0) = v0 % 53.68/7.72 | | | | | & implies(all_30_2, v0) = v1 & $i(v1) & $i(v0) & % 53.68/7.72 | | | | | is_a_theorem(v1)) % 53.68/7.72 | | | | | % 53.68/7.73 | | | | | DELTA: instantiating (30) with fresh symbols all_224_0, all_224_1 % 53.68/7.73 | | | | | gives: % 53.68/7.73 | | | | | (31) implies(all_30_1, all_30_0) = all_224_1 & implies(all_30_2, % 53.68/7.73 | | | | | all_224_1) = all_224_0 & $i(all_224_0) & $i(all_224_1) & % 53.68/7.73 | | | | | is_a_theorem(all_224_0) % 53.68/7.73 | | | | | % 53.68/7.73 | | | | | ALPHA: (31) implies: % 53.68/7.73 | | | | | (32) is_a_theorem(all_224_0) % 53.68/7.73 | | | | | (33) $i(all_224_1) % 53.68/7.73 | | | | | (34) implies(all_30_2, all_224_1) = all_224_0 % 53.68/7.73 | | | | | (35) implies(all_30_1, all_30_0) = all_224_1 % 53.68/7.73 | | | | | % 53.68/7.73 | | | | | GROUND_INST: instantiating (21) with all_30_2, all_224_1, all_224_0, % 53.68/7.73 | | | | | simplifying with (4), (13), (32), (33), (34) gives: % 53.68/7.73 | | | | | (36) is_a_theorem(all_224_1) % 53.68/7.73 | | | | | % 53.68/7.73 | | | | | GROUND_INST: instantiating (21) with all_30_1, all_30_0, all_224_1, % 53.68/7.73 | | | | | simplifying with (5), (12), (14), (15), (35) gives: % 53.68/7.73 | | | | | (37) ~ is_a_theorem(all_224_1) % 53.68/7.73 | | | | | % 53.68/7.73 | | | | | PRED_UNIFY: (36), (37) imply: % 53.68/7.73 | | | | | (38) $false % 53.68/7.73 | | | | | % 53.68/7.73 | | | | | CLOSE: (38) is inconsistent. % 53.68/7.73 | | | | | % 53.68/7.73 | | | | End of split % 53.68/7.73 | | | | % 53.68/7.73 | | | End of split % 53.68/7.73 | | | % 53.68/7.73 | | End of split % 53.68/7.73 | | % 53.68/7.73 | Case 2: % 53.68/7.73 | | % 53.68/7.74 | | (39) adjunction & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, % 53.68/7.74 | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ is_a_theorem(v1) | ~ % 53.68/7.74 | | is_a_theorem(v0) | is_a_theorem(v2)) % 53.68/7.74 | | % 53.68/7.74 | | ALPHA: (39) implies: % 53.68/7.74 | | (40) adjunction % 53.68/7.74 | | % 53.68/7.74 | | PRED_UNIFY: (40), (s1_0_adjunction) imply: % 53.68/7.74 | | (41) $false % 53.68/7.74 | | % 53.68/7.74 | | CLOSE: (41) is inconsistent. % 53.68/7.74 | | % 53.68/7.74 | End of split % 53.68/7.74 | % 53.68/7.74 End of proof % 53.68/7.74 % SZS output end Proof for theBenchmark % 53.68/7.74 % 53.68/7.74 7042ms %------------------------------------------------------------------------------