%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL527+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 : n020.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 12:54:17 PM UTC 2026 % Result : Theorem 22.18s 3.72s % Output : Proof 56.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL527+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.03 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.35 % Computer : n020.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Sun Sep 6 00:38:12 UTC 2026 % 0.08/0.35 % 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. % 0.68/0.71 ________ _____ % 0.68/0.71 ___ __ \_________(_)________________________________ % 0.68/0.71 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.68/0.71 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.68/0.71 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.68/0.71 % 0.68/0.71 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.68/0.71 (2023-06-19) % 0.68/0.71 % 0.68/0.71 (c) Philipp Rümmer, 2009-2023 % 0.68/0.71 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.68/0.71 Amanda Stjerna. % 0.68/0.71 Free software under BSD-3-Clause. % 0.68/0.71 % 0.68/0.71 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.68/0.71 % 0.68/0.71 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.73 Running up to 7 provers in parallel. % 0.68/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.68/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.68/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.68/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.68/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.68/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.68/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.83/1.57 Prover 2: Preprocessing ... % 5.66/1.62 Prover 4: Preprocessing ... % 5.66/1.63 Prover 5: Preprocessing ... % 5.66/1.64 Prover 1: Preprocessing ... % 5.66/1.64 Prover 6: Preprocessing ... % 5.66/1.65 Prover 0: Preprocessing ... % 5.66/1.67 Prover 3: Preprocessing ... % 15.85/3.05 Prover 5: Proving ... % 17.10/3.07 Prover 4: Constructing countermodel ... % 17.10/3.10 Prover 6: Constructing countermodel ... % 18.22/3.21 Prover 1: Constructing countermodel ... % 18.22/3.23 Prover 3: Constructing countermodel ... % 18.22/3.27 Prover 0: Proving ... % 18.98/3.38 Prover 2: Proving ... % 22.18/3.71 Prover 3: proved (2967ms) % 22.18/3.71 % 22.18/3.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.18/3.72 % 22.18/3.72 Prover 6: stopped % 22.18/3.72 Prover 0: stopped % 22.18/3.72 Prover 5: stopped % 22.18/3.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.18/3.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 22.18/3.73 Prover 2: stopped % 22.18/3.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.18/3.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 22.18/3.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 22.94/3.88 Prover 8: Preprocessing ... % 22.94/3.88 Prover 10: Preprocessing ... % 23.76/3.96 Prover 7: Preprocessing ... % 23.76/4.00 Prover 11: Preprocessing ... % 24.93/4.05 Prover 13: Preprocessing ... % 27.66/4.45 Prover 10: Constructing countermodel ... % 27.66/4.45 Prover 8: Warning: ignoring some quantifiers % 28.44/4.53 Prover 8: Constructing countermodel ... % 29.27/4.65 Prover 13: Constructing countermodel ... % 29.98/4.76 Prover 11: Constructing countermodel ... % 30.76/4.81 Prover 7: Constructing countermodel ... % 54.29/7.88 Prover 7: Found proof (size 38) % 54.29/7.89 Prover 7: proved (4165ms) % 54.29/7.89 Prover 1: stopped % 54.29/7.90 Prover 8: stopped % 55.07/7.90 Prover 11: stopped % 55.07/7.90 Prover 4: stopped % 55.07/7.90 Prover 13: stopped % 55.07/7.97 Prover 10: stopped % 55.07/7.97 % 55.07/7.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 55.07/7.97 % 55.07/7.98 % SZS output start Proof for theBenchmark % 55.07/7.99 Assumptions after simplification: % 55.07/7.99 --------------------------------- % 55.07/7.99 % 55.07/7.99 (adjunction) % 55.49/8.05 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v1) & $i(v0) & ((and(v0, v1) = % 55.49/8.05 v2 & $i(v2) & is_a_theorem(v1) & is_a_theorem(v0) & ~ adjunction & ~ % 55.49/8.05 is_a_theorem(v2)) | (adjunction & ! [v3: $i] : ! [v4: $i] : ! [v5: % 55.49/8.05 $i] : ( ~ (and(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 55.49/8.05 is_a_theorem(v4) | ~ is_a_theorem(v3) | is_a_theorem(v5))))) % 55.49/8.05 % 55.49/8.05 (and_3) % 55.49/8.06 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v1) % 55.49/8.06 & $i(v0) & ((and(v0, v1) = v2 & implies(v1, v2) = v3 & implies(v0, v3) = v4 % 55.49/8.06 & $i(v4) & $i(v3) & $i(v2) & ~ and_3 & ~ is_a_theorem(v4)) | (and_3 & % 55.49/8.06 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (and(v5, v6) = v7) | ~ % 55.49/8.06 $i(v6) | ~ $i(v5) | ? [v8: $i] : ? [v9: $i] : (implies(v6, v7) = v8 % 55.49/8.06 & implies(v5, v8) = v9 & $i(v9) & $i(v8) & is_a_theorem(v9)))))) % 55.49/8.06 % 55.49/8.06 (equivalence_3) % 55.49/8.08 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 55.49/8.08 $i] : ? [v6: $i] : ($i(v1) & $i(v0) & ((equiv(v0, v1) = v4 & implies(v3, % 55.49/8.08 v4) = v5 & implies(v2, v5) = v6 & implies(v1, v0) = v3 & implies(v0, % 55.49/8.08 v1) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ~ % 55.49/8.08 equivalence_3 & ~ is_a_theorem(v6)) | (equivalence_3 & ! [v7: $i] : ! % 55.49/8.08 [v8: $i] : ! [v9: $i] : ( ~ (equiv(v7, v8) = v9) | ~ $i(v8) | ~ % 55.49/8.08 $i(v7) | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : % 55.49/8.08 (implies(v11, v9) = v12 & implies(v10, v12) = v13 & implies(v8, v7) = % 55.49/8.08 v11 & implies(v7, v8) = v10 & $i(v13) & $i(v12) & $i(v11) & $i(v10) % 55.49/8.08 & is_a_theorem(v13))) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( % 55.49/8.08 ~ (implies(v8, v7) = v9) | ~ $i(v8) | ~ $i(v7) | ? [v10: $i] : ? % 55.49/8.08 [v11: $i] : ? [v12: $i] : ? [v13: $i] : (equiv(v7, v8) = v11 & % 55.49/8.08 implies(v10, v12) = v13 & implies(v9, v11) = v12 & implies(v7, v8) = % 55.49/8.08 v10 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & is_a_theorem(v13))) & % 55.49/8.08 ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (implies(v7, v8) = v9) | ~ % 55.49/8.08 $i(v8) | ~ $i(v7) | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 55.49/8.08 [v13: $i] : (equiv(v7, v8) = v11 & implies(v10, v11) = v12 & % 55.49/8.08 implies(v9, v12) = v13 & implies(v8, v7) = v10 & $i(v13) & $i(v12) & % 55.49/8.08 $i(v11) & $i(v10) & is_a_theorem(v13)))))) % 55.49/8.08 % 55.49/8.08 (hilbert_and_3) % 55.49/8.08 and_3 % 55.49/8.08 % 55.49/8.08 (hilbert_equivalence_3) % 55.49/8.08 equivalence_3 % 55.49/8.08 % 55.49/8.08 (hilbert_modus_ponens) % 55.49/8.08 modus_ponens % 55.49/8.08 % 55.49/8.08 (modus_ponens) % 55.49/8.09 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v1) & $i(v0) & ((implies(v0, v1) % 55.49/8.09 = v2 & $i(v2) & is_a_theorem(v2) & is_a_theorem(v0) & ~ % 55.49/8.09 is_a_theorem(v1) & ~ modus_ponens) | (modus_ponens & ! [v3: $i] : ! % 55.49/8.09 [v4: $i] : ! [v5: $i] : ( ~ (implies(v3, v4) = v5) | ~ $i(v4) | ~ % 55.49/8.09 $i(v3) | ~ is_a_theorem(v5) | ~ is_a_theorem(v3) | % 55.49/8.09 is_a_theorem(v4))))) % 55.49/8.09 % 55.49/8.09 (s1_0_adjunction) % 55.49/8.09 ~ adjunction % 55.49/8.09 % 55.49/8.09 Further assumptions not needed in the proof: % 55.49/8.09 -------------------------------------------- % 55.49/8.09 and_1, and_2, axiom_4, axiom_5, axiom_B, axiom_K, axiom_M, axiom_m1, axiom_m10, % 55.49/8.09 axiom_m2, axiom_m3, axiom_m4, axiom_m5, axiom_m6, axiom_m7, axiom_m8, axiom_m9, % 55.49/8.09 axiom_s1, axiom_s2, axiom_s3, axiom_s4, cn1, cn2, cn3, equivalence_1, % 55.49/8.09 equivalence_2, hilbert_and_1, hilbert_and_2, hilbert_equivalence_1, % 55.49/8.09 hilbert_equivalence_2, hilbert_implies_1, hilbert_implies_2, hilbert_implies_3, % 55.49/8.09 hilbert_modus_tollens, hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or, % 55.49/8.09 hilbert_or_1, hilbert_or_2, hilbert_or_3, implies_1, implies_2, implies_3, % 55.49/8.09 km5_axiom_5, km5_axiom_K, km5_axiom_M, km5_necessitation, km5_op_possibly, kn1, % 55.49/8.09 kn2, kn3, modus_ponens_strict_implies, modus_tollens, necessitation, op_and, % 55.49/8.09 op_equiv, op_implies_and, op_implies_or, op_necessarily, op_or, op_possibly, % 55.49/8.09 op_strict_equiv, op_strict_implies, or_1, or_2, or_3, r1, r2, r3, r4, r5, % 55.49/8.09 s1_0_op_equiv, s1_0_op_implies, s1_0_op_or, s1_0_op_possibly, % 55.49/8.09 s1_0_op_strict_equiv, s1_0_op_strict_implies, substitution_of_equivalents, % 55.49/8.09 substitution_strict_equiv, use_substitution_of_equivalents % 55.49/8.09 % 55.49/8.09 Those formulas are unsatisfiable: % 55.49/8.09 --------------------------------- % 55.49/8.09 % 55.49/8.09 Begin of proof % 55.49/8.09 | % 55.49/8.09 | DELTA: instantiating (modus_ponens) with fresh symbols all_24_0, all_24_1, % 55.49/8.09 | all_24_2 gives: % 55.49/8.10 | (1) $i(all_24_1) & $i(all_24_2) & ((implies(all_24_2, all_24_1) = all_24_0 % 55.49/8.10 | & $i(all_24_0) & is_a_theorem(all_24_0) & is_a_theorem(all_24_2) & % 55.49/8.10 | ~ is_a_theorem(all_24_1) & ~ modus_ponens) | (modus_ponens & ! % 55.49/8.10 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | % 55.49/8.10 | ~ $i(v1) | ~ $i(v0) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) % 55.49/8.10 | | is_a_theorem(v1)))) % 55.49/8.10 | % 55.49/8.10 | ALPHA: (1) implies: % 55.49/8.10 | (2) (implies(all_24_2, all_24_1) = all_24_0 & $i(all_24_0) & % 55.49/8.10 | is_a_theorem(all_24_0) & is_a_theorem(all_24_2) & ~ % 55.49/8.10 | is_a_theorem(all_24_1) & ~ modus_ponens) | (modus_ponens & ! [v0: % 55.49/8.10 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ % 55.49/8.10 | $i(v1) | ~ $i(v0) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | % 55.49/8.10 | is_a_theorem(v1))) % 55.49/8.10 | % 55.49/8.10 | DELTA: instantiating (adjunction) with fresh symbols all_28_0, all_28_1, % 55.49/8.10 | all_28_2 gives: % 55.49/8.10 | (3) $i(all_28_1) & $i(all_28_2) & ((and(all_28_2, all_28_1) = all_28_0 & % 55.49/8.10 | $i(all_28_0) & is_a_theorem(all_28_1) & is_a_theorem(all_28_2) & ~ % 55.49/8.10 | adjunction & ~ is_a_theorem(all_28_0)) | (adjunction & ! [v0: $i] % 55.49/8.10 | : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = v2) | ~ $i(v1) | % 55.49/8.10 | ~ $i(v0) | ~ is_a_theorem(v1) | ~ is_a_theorem(v0) | % 55.49/8.10 | is_a_theorem(v2)))) % 55.49/8.10 | % 55.49/8.10 | ALPHA: (3) implies: % 55.49/8.11 | (4) $i(all_28_2) % 55.49/8.11 | (5) $i(all_28_1) % 55.49/8.11 | (6) (and(all_28_2, all_28_1) = all_28_0 & $i(all_28_0) & % 55.49/8.11 | is_a_theorem(all_28_1) & is_a_theorem(all_28_2) & ~ adjunction & ~ % 55.49/8.11 | is_a_theorem(all_28_0)) | (adjunction & ! [v0: $i] : ! [v1: $i] : % 55.49/8.11 | ! [v2: $i] : ( ~ (and(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 55.49/8.11 | is_a_theorem(v1) | ~ is_a_theorem(v0) | is_a_theorem(v2))) % 55.49/8.11 | % 55.49/8.11 | DELTA: instantiating (and_3) with fresh symbols all_62_0, all_62_1, all_62_2, % 55.49/8.11 | all_62_3, all_62_4 gives: % 55.49/8.11 | (7) $i(all_62_3) & $i(all_62_4) & ((and(all_62_4, all_62_3) = all_62_2 & % 55.49/8.11 | implies(all_62_3, all_62_2) = all_62_1 & implies(all_62_4, % 55.49/8.11 | all_62_1) = all_62_0 & $i(all_62_0) & $i(all_62_1) & $i(all_62_2) % 55.49/8.11 | & ~ and_3 & ~ is_a_theorem(all_62_0)) | (and_3 & ! [v0: $i] : ! % 55.49/8.11 | [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = v2) | ~ $i(v1) | ~ % 55.49/8.11 | $i(v0) | ? [v3: $i] : ? [v4: $i] : (implies(v1, v2) = v3 & % 55.49/8.11 | implies(v0, v3) = v4 & $i(v4) & $i(v3) & is_a_theorem(v4))))) % 55.49/8.11 | % 55.49/8.11 | ALPHA: (7) implies: % 55.49/8.12 | (8) (and(all_62_4, all_62_3) = all_62_2 & implies(all_62_3, all_62_2) = % 55.49/8.12 | all_62_1 & implies(all_62_4, all_62_1) = all_62_0 & $i(all_62_0) & % 55.49/8.12 | $i(all_62_1) & $i(all_62_2) & ~ and_3 & ~ is_a_theorem(all_62_0)) | % 55.49/8.12 | (and_3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = % 55.49/8.12 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 55.49/8.12 | (implies(v1, v2) = v3 & implies(v0, v3) = v4 & $i(v4) & $i(v3) & % 55.49/8.12 | is_a_theorem(v4)))) % 55.49/8.12 | % 55.49/8.12 | DELTA: instantiating (equivalence_3) with fresh symbols all_100_0, all_100_1, % 55.49/8.12 | all_100_2, all_100_3, all_100_4, all_100_5, all_100_6 gives: % 55.49/8.13 | (9) $i(all_100_5) & $i(all_100_6) & ((equiv(all_100_6, all_100_5) = % 55.49/8.13 | all_100_2 & implies(all_100_3, all_100_2) = all_100_1 & % 55.49/8.13 | implies(all_100_4, all_100_1) = all_100_0 & implies(all_100_5, % 55.49/8.13 | all_100_6) = all_100_3 & implies(all_100_6, all_100_5) = % 55.49/8.13 | all_100_4 & $i(all_100_0) & $i(all_100_1) & $i(all_100_2) & % 55.49/8.13 | $i(all_100_3) & $i(all_100_4) & ~ equivalence_3 & ~ % 55.49/8.13 | is_a_theorem(all_100_0)) | (equivalence_3 & ! [v0: $i] : ! [v1: % 55.49/8.13 | $i] : ! [v2: $i] : ( ~ (equiv(v0, v1) = v2) | ~ $i(v1) | ~ % 55.49/8.13 | $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 55.49/8.13 | (implies(v4, v2) = v5 & implies(v3, v5) = v6 & implies(v1, v0) = % 55.49/8.13 | v4 & implies(v0, v1) = v3 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 55.49/8.13 | is_a_theorem(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 55.49/8.13 | ( ~ (implies(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 55.49/8.13 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (equiv(v0, v1) = v4 & % 55.49/8.13 | implies(v3, v5) = v6 & implies(v2, v4) = v5 & implies(v0, v1) = % 55.49/8.13 | v3 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & is_a_theorem(v6))) & % 55.49/8.13 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) % 55.49/8.13 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 55.49/8.13 | : ? [v6: $i] : (equiv(v0, v1) = v4 & implies(v3, v4) = v5 & % 55.49/8.13 | implies(v2, v5) = v6 & implies(v1, v0) = v3 & $i(v6) & $i(v5) & % 55.49/8.13 | $i(v4) & $i(v3) & is_a_theorem(v6))))) % 55.49/8.13 | % 55.49/8.13 | ALPHA: (9) implies: % 55.49/8.14 | (10) (equiv(all_100_6, all_100_5) = all_100_2 & implies(all_100_3, % 55.49/8.14 | all_100_2) = all_100_1 & implies(all_100_4, all_100_1) = all_100_0 % 55.49/8.14 | & implies(all_100_5, all_100_6) = all_100_3 & implies(all_100_6, % 55.49/8.14 | all_100_5) = all_100_4 & $i(all_100_0) & $i(all_100_1) & % 55.49/8.14 | $i(all_100_2) & $i(all_100_3) & $i(all_100_4) & ~ equivalence_3 & % 55.49/8.14 | ~ is_a_theorem(all_100_0)) | (equivalence_3 & ! [v0: $i] : ! [v1: % 55.49/8.14 | $i] : ! [v2: $i] : ( ~ (equiv(v0, v1) = v2) | ~ $i(v1) | ~ % 55.49/8.14 | $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 55.49/8.14 | (implies(v4, v2) = v5 & implies(v3, v5) = v6 & implies(v1, v0) = % 55.49/8.14 | v4 & implies(v0, v1) = v3 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 55.49/8.14 | is_a_theorem(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( % 55.49/8.14 | ~ (implies(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 55.49/8.14 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (equiv(v0, v1) = v4 & % 55.49/8.14 | implies(v3, v5) = v6 & implies(v2, v4) = v5 & implies(v0, v1) = % 55.49/8.14 | v3 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & is_a_theorem(v6))) & ! % 55.49/8.14 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | % 55.49/8.14 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 55.49/8.14 | ? [v6: $i] : (equiv(v0, v1) = v4 & implies(v3, v4) = v5 & % 55.49/8.14 | implies(v2, v5) = v6 & implies(v1, v0) = v3 & $i(v6) & $i(v5) & % 55.49/8.14 | $i(v4) & $i(v3) & is_a_theorem(v6)))) % 55.49/8.14 | % 55.49/8.14 | BETA: splitting (6) gives: % 55.49/8.14 | % 55.49/8.14 | Case 1: % 55.49/8.14 | | % 55.49/8.14 | | (11) and(all_28_2, all_28_1) = all_28_0 & $i(all_28_0) & % 55.49/8.14 | | is_a_theorem(all_28_1) & is_a_theorem(all_28_2) & ~ adjunction & ~ % 55.49/8.14 | | is_a_theorem(all_28_0) % 55.49/8.14 | | % 55.49/8.14 | | ALPHA: (11) implies: % 55.49/8.14 | | (12) ~ is_a_theorem(all_28_0) % 55.49/8.14 | | (13) is_a_theorem(all_28_2) % 55.49/8.14 | | (14) is_a_theorem(all_28_1) % 55.49/8.14 | | (15) $i(all_28_0) % 55.49/8.14 | | (16) and(all_28_2, all_28_1) = all_28_0 % 55.49/8.14 | | % 55.49/8.14 | | BETA: splitting (2) gives: % 55.49/8.14 | | % 55.49/8.14 | | Case 1: % 55.49/8.14 | | | % 55.49/8.14 | | | (17) implies(all_24_2, all_24_1) = all_24_0 & $i(all_24_0) & % 55.49/8.14 | | | is_a_theorem(all_24_0) & is_a_theorem(all_24_2) & ~ % 55.49/8.14 | | | is_a_theorem(all_24_1) & ~ modus_ponens % 55.49/8.14 | | | % 55.49/8.14 | | | ALPHA: (17) implies: % 55.49/8.14 | | | (18) ~ modus_ponens % 55.49/8.14 | | | % 55.49/8.14 | | | PRED_UNIFY: (18), (hilbert_modus_ponens) imply: % 55.49/8.14 | | | (19) $false % 56.21/8.14 | | | % 56.21/8.14 | | | CLOSE: (19) is inconsistent. % 56.21/8.14 | | | % 56.21/8.14 | | Case 2: % 56.21/8.14 | | | % 56.21/8.15 | | | (20) modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 56.21/8.15 | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 56.21/8.15 | | | is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1)) % 56.21/8.15 | | | % 56.21/8.15 | | | ALPHA: (20) implies: % 56.21/8.15 | | | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = % 56.21/8.15 | | | v2) | ~ $i(v1) | ~ $i(v0) | ~ is_a_theorem(v2) | ~ % 56.21/8.15 | | | is_a_theorem(v0) | is_a_theorem(v1)) % 56.21/8.15 | | | % 56.21/8.15 | | | BETA: splitting (8) gives: % 56.21/8.15 | | | % 56.21/8.15 | | | Case 1: % 56.21/8.15 | | | | % 56.21/8.15 | | | | (22) and(all_62_4, all_62_3) = all_62_2 & implies(all_62_3, all_62_2) % 56.21/8.15 | | | | = all_62_1 & implies(all_62_4, all_62_1) = all_62_0 & % 56.21/8.15 | | | | $i(all_62_0) & $i(all_62_1) & $i(all_62_2) & ~ and_3 & ~ % 56.21/8.15 | | | | is_a_theorem(all_62_0) % 56.21/8.15 | | | | % 56.21/8.15 | | | | ALPHA: (22) implies: % 56.21/8.15 | | | | (23) ~ and_3 % 56.21/8.15 | | | | % 56.21/8.15 | | | | PRED_UNIFY: (23), (hilbert_and_3) imply: % 56.21/8.15 | | | | (24) $false % 56.21/8.15 | | | | % 56.21/8.15 | | | | CLOSE: (24) is inconsistent. % 56.21/8.15 | | | | % 56.21/8.15 | | | Case 2: % 56.21/8.15 | | | | % 56.21/8.15 | | | | (25) and_3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, % 56.21/8.15 | | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 56.21/8.15 | | | | $i] : (implies(v1, v2) = v3 & implies(v0, v3) = v4 & $i(v4) % 56.21/8.15 | | | | & $i(v3) & is_a_theorem(v4))) % 56.21/8.15 | | | | % 56.21/8.15 | | | | ALPHA: (25) implies: % 56.21/8.16 | | | | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = v2) % 56.21/8.16 | | | | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 56.21/8.16 | | | | (implies(v1, v2) = v3 & implies(v0, v3) = v4 & $i(v4) & $i(v3) % 56.21/8.16 | | | | & is_a_theorem(v4))) % 56.21/8.16 | | | | % 56.21/8.16 | | | | BETA: splitting (10) gives: % 56.21/8.16 | | | | % 56.21/8.16 | | | | Case 1: % 56.21/8.16 | | | | | % 56.21/8.16 | | | | | (27) equiv(all_100_6, all_100_5) = all_100_2 & implies(all_100_3, % 56.21/8.16 | | | | | all_100_2) = all_100_1 & implies(all_100_4, all_100_1) = % 56.21/8.16 | | | | | all_100_0 & implies(all_100_5, all_100_6) = all_100_3 & % 56.21/8.16 | | | | | implies(all_100_6, all_100_5) = all_100_4 & $i(all_100_0) & % 56.21/8.16 | | | | | $i(all_100_1) & $i(all_100_2) & $i(all_100_3) & $i(all_100_4) % 56.21/8.16 | | | | | & ~ equivalence_3 & ~ is_a_theorem(all_100_0) % 56.21/8.16 | | | | | % 56.21/8.16 | | | | | ALPHA: (27) implies: % 56.21/8.16 | | | | | (28) ~ equivalence_3 % 56.21/8.16 | | | | | % 56.21/8.16 | | | | | PRED_UNIFY: (28), (hilbert_equivalence_3) imply: % 56.21/8.16 | | | | | (29) $false % 56.21/8.16 | | | | | % 56.21/8.16 | | | | | CLOSE: (29) is inconsistent. % 56.21/8.16 | | | | | % 56.21/8.16 | | | | Case 2: % 56.21/8.16 | | | | | % 56.21/8.16 | | | | | % 56.21/8.16 | | | | | GROUND_INST: instantiating (26) with all_28_2, all_28_1, all_28_0, % 56.21/8.16 | | | | | simplifying with (4), (5), (16) gives: % 56.21/8.16 | | | | | (30) ? [v0: $i] : ? [v1: $i] : (implies(all_28_1, all_28_0) = v0 % 56.21/8.16 | | | | | & implies(all_28_2, v0) = v1 & $i(v1) & $i(v0) & % 56.21/8.16 | | | | | is_a_theorem(v1)) % 56.21/8.16 | | | | | % 56.21/8.16 | | | | | DELTA: instantiating (30) with fresh symbols all_220_0, all_220_1 % 56.21/8.16 | | | | | gives: % 56.21/8.17 | | | | | (31) implies(all_28_1, all_28_0) = all_220_1 & implies(all_28_2, % 56.21/8.17 | | | | | all_220_1) = all_220_0 & $i(all_220_0) & $i(all_220_1) & % 56.21/8.17 | | | | | is_a_theorem(all_220_0) % 56.21/8.17 | | | | | % 56.21/8.17 | | | | | ALPHA: (31) implies: % 56.21/8.17 | | | | | (32) is_a_theorem(all_220_0) % 56.21/8.17 | | | | | (33) $i(all_220_1) % 56.21/8.17 | | | | | (34) implies(all_28_2, all_220_1) = all_220_0 % 56.21/8.17 | | | | | (35) implies(all_28_1, all_28_0) = all_220_1 % 56.21/8.17 | | | | | % 56.21/8.17 | | | | | GROUND_INST: instantiating (21) with all_28_2, all_220_1, all_220_0, % 56.21/8.17 | | | | | simplifying with (4), (13), (32), (33), (34) gives: % 56.21/8.17 | | | | | (36) is_a_theorem(all_220_1) % 56.21/8.17 | | | | | % 56.21/8.17 | | | | | GROUND_INST: instantiating (21) with all_28_1, all_28_0, all_220_1, % 56.21/8.17 | | | | | simplifying with (5), (12), (14), (15), (35) gives: % 56.21/8.17 | | | | | (37) ~ is_a_theorem(all_220_1) % 56.21/8.17 | | | | | % 56.21/8.17 | | | | | PRED_UNIFY: (36), (37) imply: % 56.21/8.17 | | | | | (38) $false % 56.21/8.17 | | | | | % 56.21/8.17 | | | | | CLOSE: (38) is inconsistent. % 56.21/8.17 | | | | | % 56.21/8.17 | | | | End of split % 56.21/8.17 | | | | % 56.21/8.17 | | | End of split % 56.21/8.17 | | | % 56.21/8.17 | | End of split % 56.21/8.17 | | % 56.21/8.17 | Case 2: % 56.21/8.17 | | % 56.21/8.17 | | (39) adjunction & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, % 56.21/8.17 | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ is_a_theorem(v1) | ~ % 56.21/8.17 | | is_a_theorem(v0) | is_a_theorem(v2)) % 56.21/8.17 | | % 56.21/8.17 | | ALPHA: (39) implies: % 56.21/8.17 | | (40) adjunction % 56.21/8.17 | | % 56.21/8.17 | | PRED_UNIFY: (40), (s1_0_adjunction) imply: % 56.21/8.17 | | (41) $false % 56.21/8.17 | | % 56.21/8.17 | | CLOSE: (41) is inconsistent. % 56.21/8.17 | | % 56.21/8.17 | End of split % 56.21/8.17 | % 56.21/8.17 End of proof % 56.21/8.17 % SZS output end Proof for theBenchmark % 56.21/8.17 % 56.21/8.17 7463ms %------------------------------------------------------------------------------