%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL525+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 : n028.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 20.55s 3.41s % Output : Proof 62.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL525+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 : n028.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 : Sat Sep 5 13:12:59 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. % 0.71/0.71 ________ _____ % 0.71/0.72 ___ __ \_________(_)________________________________ % 0.71/0.72 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.71/0.72 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.71/0.72 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.71/0.72 % 0.71/0.72 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.71/0.72 (2023-06-19) % 0.71/0.72 % 0.71/0.72 (c) Philipp Rümmer, 2009-2023 % 0.71/0.72 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.71/0.72 Amanda Stjerna. % 0.71/0.72 Free software under BSD-3-Clause. % 0.71/0.72 % 0.71/0.72 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.71/0.72 % 0.71/0.72 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.74 Running up to 7 provers in parallel. % 0.71/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.83/1.48 Prover 5: Preprocessing ... % 4.83/1.48 Prover 2: Preprocessing ... % 4.83/1.48 Prover 0: Preprocessing ... % 5.61/1.50 Prover 1: Preprocessing ... % 5.61/1.53 Prover 3: Preprocessing ... % 5.61/1.53 Prover 6: Preprocessing ... % 5.61/1.55 Prover 4: Preprocessing ... % 15.09/2.75 Prover 6: Constructing countermodel ... % 15.89/2.85 Prover 5: Proving ... % 16.69/2.91 Prover 1: Constructing countermodel ... % 16.69/3.05 Prover 3: Constructing countermodel ... % 17.92/3.11 Prover 4: Constructing countermodel ... % 18.77/3.19 Prover 0: Proving ... % 19.01/3.21 Prover 2: Proving ... % 20.55/3.40 Prover 3: proved (2650ms) % 20.55/3.41 % 20.55/3.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.55/3.41 % 20.55/3.41 Prover 0: stopped % 20.55/3.41 Prover 6: stopped % 20.55/3.42 Prover 5: stopped % 20.55/3.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.55/3.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.55/3.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.55/3.42 Prover 2: stopped % 20.55/3.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.55/3.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.34/3.53 Prover 11: Preprocessing ... % 22.18/3.60 Prover 10: Preprocessing ... % 22.18/3.66 Prover 13: Preprocessing ... % 22.18/3.66 Prover 8: Preprocessing ... % 22.18/3.69 Prover 7: Preprocessing ... % 25.81/4.08 Prover 13: Constructing countermodel ... % 25.81/4.10 Prover 10: Constructing countermodel ... % 25.81/4.10 Prover 7: Constructing countermodel ... % 26.66/4.19 Prover 8: Warning: ignoring some quantifiers % 26.88/4.21 Prover 8: Constructing countermodel ... % 28.46/4.41 Prover 11: Constructing countermodel ... % 59.63/8.46 Prover 8: Found proof (size 75) % 59.63/8.47 Prover 8: proved (5043ms) % 59.63/8.48 Prover 7: stopped % 59.63/8.48 Prover 4: stopped % 59.63/8.48 Prover 11: stopped % 59.63/8.49 Prover 13: stopped % 59.63/8.49 Prover 1: stopped % 61.56/8.98 Prover 10: stopped % 61.56/8.98 % 61.56/8.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 61.56/8.98 % 61.56/8.99 % SZS output start Proof for theBenchmark % 61.56/9.00 Assumptions after simplification: % 61.56/9.00 --------------------------------- % 61.56/9.00 % 61.56/9.00 (axiom_M) % 61.89/9.05 (axiom_M & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (necessarily(v0) = % 61.89/9.05 v1) | ~ (implies(v1, v0) = v2) | ~ $i(v0) | is_a_theorem(v2) = 0)) | ( % 61.89/9.05 ~ axiom_M & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 % 61.89/9.05 = 0) & necessarily(v0) = v1 & implies(v1, v0) = v2 & is_a_theorem(v2) = % 61.89/9.05 v3 & $i(v2) & $i(v1) & $i(v0))) % 61.89/9.05 % 61.89/9.06 (hilbert_modus_ponens) % 61.89/9.06 modus_ponens % 61.89/9.06 % 61.89/9.06 (hilbert_or_2) % 61.89/9.06 or_2 % 61.89/9.06 % 61.89/9.06 (km5_axiom_M) % 61.89/9.06 axiom_M % 61.89/9.06 % 61.89/9.06 (modus_ponens) % 61.89/9.06 (modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 61.89/9.06 (is_a_theorem(v1) = v2) | ~ (is_a_theorem(v0) = 0) | ~ $i(v1) | ~ % 61.89/9.06 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & implies(v0, v1) = v3 % 61.89/9.06 & is_a_theorem(v3) = v4 & $i(v3)))) | ( ~ modus_ponens & ? [v0: $i] : % 61.89/9.06 ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & implies(v0, v1) = % 61.89/9.06 v2 & is_a_theorem(v2) = 0 & is_a_theorem(v1) = v3 & is_a_theorem(v0) = 0 & % 61.89/9.06 $i(v2) & $i(v1) & $i(v0))) % 61.89/9.06 % 61.89/9.06 (modus_ponens_strict_implies) % 61.89/9.07 (modus_ponens_strict_implies & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 61.89/9.07 (strict_implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? % 61.89/9.07 [v4: any] : ? [v5: any] : (is_a_theorem(v2) = v4 & is_a_theorem(v1) = v5 % 61.89/9.07 & is_a_theorem(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))) | ( ~ % 61.89/9.07 modus_ponens_strict_implies & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 61.89/9.07 [v3: int] : ( ~ (v3 = 0) & strict_implies(v0, v1) = v2 & is_a_theorem(v2) = % 61.89/9.07 0 & is_a_theorem(v1) = v3 & is_a_theorem(v0) = 0 & $i(v2) & $i(v1) & % 61.89/9.07 $i(v0))) % 61.89/9.07 % 61.89/9.07 (op_strict_implies) % 61.89/9.07 ~ op_strict_implies | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 61.89/9.07 (strict_implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 61.89/9.07 (necessarily(v3) = v2 & implies(v0, v1) = v3 & $i(v3) & $i(v2))) % 61.89/9.07 % 61.89/9.07 (or_2) % 61.89/9.08 (or_2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (or(v0, % 61.89/9.08 v1) = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~ $i(v0) | % 61.89/9.08 is_a_theorem(v3) = 0)) | ( ~ or_2 & ? [v0: $i] : ? [v1: $i] : ? [v2: % 61.89/9.08 $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & % 61.89/9.08 implies(v1, v2) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & % 61.89/9.08 $i(v0))) % 61.89/9.08 % 61.89/9.08 (r2) % 61.89/9.08 (r2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (or(v0, v1) % 61.89/9.08 = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~ $i(v0) | % 61.89/9.08 is_a_theorem(v3) = 0)) | ( ~ r2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 61.89/9.08 : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v1, % 61.89/9.09 v2) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))) % 61.89/9.09 % 61.89/9.09 (s1_0_modus_ponens_strict_implies) % 61.89/9.09 ~ modus_ponens_strict_implies % 61.89/9.09 % 61.89/9.09 (s1_0_op_strict_implies) % 61.89/9.09 op_strict_implies % 61.89/9.09 % 61.89/9.09 (function-axioms) % 61.89/9.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 61.89/9.10 (strict_equiv(v3, v2) = v1) | ~ (strict_equiv(v3, v2) = v0)) & ! [v0: $i] % 61.89/9.10 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (strict_implies(v3, % 61.89/9.10 v2) = v1) | ~ (strict_implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 61.89/9.10 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3, v2) = v1) | ~ % 61.89/9.10 (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 61.89/9.10 (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = v0)) & ! [v0: $i] : ! % 61.89/9.10 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (equiv(v3, v2) = v1) | ~ % 61.89/9.10 (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 61.89/9.10 $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0)) & ! % 61.89/9.10 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (possibly(v2) = v1) | ~ % 61.89/9.10 (possibly(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 61.89/9.10 ~ (necessarily(v2) = v1) | ~ (necessarily(v2) = v0)) & ! [v0: $i] : ! % 61.89/9.10 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & % 61.89/9.10 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 61.89/9.10 v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) & ? [v0: $i] % 61.89/9.10 : ? [v1: $i] : ? [v2: $i] : (strict_equiv(v1, v0) = v2 & $i(v2)) & ? [v0: % 61.89/9.10 $i] : ? [v1: $i] : ? [v2: $i] : (strict_implies(v1, v0) = v2 & $i(v2)) & % 61.89/9.10 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (or(v1, v0) = v2 & $i(v2)) & ? [v0: % 61.89/9.10 $i] : ? [v1: $i] : ? [v2: $i] : (and(v1, v0) = v2 & $i(v2)) & ? [v0: $i] % 61.89/9.10 : ? [v1: $i] : ? [v2: $i] : (equiv(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? % 61.89/9.10 [v1: $i] : ? [v2: $i] : (implies(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? % 61.89/9.10 [v1: MultipleValueBool] : (is_a_theorem(v0) = v1) & ? [v0: $i] : ? [v1: $i] % 61.89/9.10 : (possibly(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (necessarily(v0) % 61.89/9.10 = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (not(v0) = v1 & $i(v1)) % 61.89/9.10 % 61.89/9.11 Further assumptions not needed in the proof: % 61.89/9.11 -------------------------------------------- % 61.89/9.11 adjunction, and_1, and_2, and_3, axiom_4, axiom_5, axiom_B, axiom_K, axiom_m1, % 61.89/9.11 axiom_m10, axiom_m2, axiom_m3, axiom_m4, axiom_m5, axiom_m6, axiom_m7, axiom_m8, % 61.89/9.11 axiom_m9, axiom_s1, axiom_s2, axiom_s3, axiom_s4, cn1, cn2, cn3, equivalence_1, % 61.89/9.11 equivalence_2, equivalence_3, hilbert_and_1, hilbert_and_2, hilbert_and_3, % 61.89/9.11 hilbert_equivalence_1, hilbert_equivalence_2, hilbert_equivalence_3, % 61.89/9.11 hilbert_implies_1, hilbert_implies_2, hilbert_implies_3, hilbert_modus_tollens, % 61.89/9.11 hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or, hilbert_or_1, % 61.89/9.11 hilbert_or_3, implies_1, implies_2, implies_3, km5_axiom_5, km5_axiom_K, % 61.89/9.11 km5_necessitation, km5_op_possibly, kn1, kn2, kn3, modus_tollens, necessitation, % 61.89/9.11 op_and, op_equiv, op_implies_and, op_implies_or, op_necessarily, op_or, % 61.89/9.11 op_possibly, op_strict_equiv, or_1, or_3, r1, r3, r4, r5, s1_0_op_equiv, % 61.89/9.11 s1_0_op_implies, s1_0_op_or, s1_0_op_possibly, s1_0_op_strict_equiv, % 61.89/9.11 substitution_of_equivalents, substitution_strict_equiv, % 61.89/9.11 use_substitution_of_equivalents % 61.89/9.11 % 61.89/9.11 Those formulas are unsatisfiable: % 61.89/9.11 --------------------------------- % 61.89/9.11 % 61.89/9.11 Begin of proof % 61.89/9.11 | % 61.89/9.11 | ALPHA: (function-axioms) implies: % 61.89/9.11 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 61.89/9.11 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) % 61.89/9.11 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 61.89/9.11 | (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0)) % 61.89/9.11 | % 61.89/9.11 | BETA: splitting (op_strict_implies) gives: % 61.89/9.11 | % 61.89/9.11 | Case 1: % 61.89/9.11 | | % 61.89/9.11 | | (3) ~ op_strict_implies % 61.89/9.11 | | % 61.89/9.11 | | PRED_UNIFY: (3), (s1_0_op_strict_implies) imply: % 61.89/9.11 | | (4) $false % 61.89/9.12 | | % 61.89/9.12 | | CLOSE: (4) is inconsistent. % 61.89/9.12 | | % 61.89/9.12 | Case 2: % 61.89/9.12 | | % 61.89/9.12 | | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (strict_implies(v0, v1) % 61.89/9.12 | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (necessarily(v3) = % 61.89/9.12 | | v2 & implies(v0, v1) = v3 & $i(v3) & $i(v2))) % 61.89/9.12 | | % 61.89/9.12 | | BETA: splitting (modus_ponens) gives: % 61.89/9.12 | | % 61.89/9.12 | | Case 1: % 61.89/9.12 | | | % 61.89/9.12 | | | (6) modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 61.89/9.12 | | | ~ (is_a_theorem(v1) = v2) | ~ (is_a_theorem(v0) = 0) | ~ % 61.89/9.12 | | | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 61.89/9.12 | | | implies(v0, v1) = v3 & is_a_theorem(v3) = v4 & $i(v3))) % 61.89/9.12 | | | % 61.89/9.12 | | | ALPHA: (6) implies: % 61.89/9.12 | | | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 61.89/9.12 | | | (is_a_theorem(v1) = v2) | ~ (is_a_theorem(v0) = 0) | ~ $i(v1) | % 61.89/9.12 | | | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 61.89/9.12 | | | implies(v0, v1) = v3 & is_a_theorem(v3) = v4 & $i(v3))) % 61.89/9.12 | | | % 61.89/9.12 | | | BETA: splitting (axiom_M) gives: % 61.89/9.12 | | | % 61.89/9.12 | | | Case 1: % 61.89/9.12 | | | | % 61.89/9.12 | | | | (8) axiom_M & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 61.89/9.12 | | | | (necessarily(v0) = v1) | ~ (implies(v1, v0) = v2) | ~ $i(v0) % 61.89/9.12 | | | | | is_a_theorem(v2) = 0) % 61.89/9.12 | | | | % 61.89/9.12 | | | | ALPHA: (8) implies: % 61.89/9.13 | | | | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (necessarily(v0) = % 61.89/9.13 | | | | v1) | ~ (implies(v1, v0) = v2) | ~ $i(v0) | % 61.89/9.13 | | | | is_a_theorem(v2) = 0) % 61.89/9.13 | | | | % 61.89/9.13 | | | | BETA: splitting (or_2) gives: % 61.89/9.13 | | | | % 61.89/9.13 | | | | Case 1: % 61.89/9.13 | | | | | % 61.89/9.13 | | | | | (10) or_2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 61.89/9.13 | | | | | ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) % 61.89/9.13 | | | | | | ~ $i(v0) | is_a_theorem(v3) = 0) % 61.89/9.13 | | | | | % 61.89/9.13 | | | | | ALPHA: (10) implies: % 61.89/9.13 | | | | | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 62.38/9.13 | | | | | (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | % 62.38/9.13 | | | | | ~ $i(v0) | is_a_theorem(v3) = 0) % 62.38/9.13 | | | | | % 62.38/9.13 | | | | | BETA: splitting (modus_ponens_strict_implies) gives: % 62.38/9.13 | | | | | % 62.38/9.13 | | | | | Case 1: % 62.38/9.13 | | | | | | % 62.38/9.13 | | | | | | (12) modus_ponens_strict_implies & ! [v0: $i] : ! [v1: $i] : ! % 62.38/9.13 | | | | | | [v2: $i] : ( ~ (strict_implies(v0, v1) = v2) | ~ $i(v1) | % 62.38/9.13 | | | | | | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 62.38/9.13 | | | | | | (is_a_theorem(v2) = v4 & is_a_theorem(v1) = v5 & % 62.38/9.13 | | | | | | is_a_theorem(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 % 62.38/9.13 | | | | | | = 0))) % 62.38/9.13 | | | | | | % 62.38/9.13 | | | | | | ALPHA: (12) implies: % 62.38/9.13 | | | | | | (13) modus_ponens_strict_implies % 62.38/9.13 | | | | | | % 62.38/9.13 | | | | | | PRED_UNIFY: (13), (s1_0_modus_ponens_strict_implies) imply: % 62.38/9.13 | | | | | | (14) $false % 62.38/9.13 | | | | | | % 62.38/9.13 | | | | | | CLOSE: (14) is inconsistent. % 62.38/9.13 | | | | | | % 62.38/9.13 | | | | | Case 2: % 62.38/9.13 | | | | | | % 62.38/9.13 | | | | | | (15) ~ modus_ponens_strict_implies & ? [v0: $i] : ? [v1: $i] : % 62.38/9.13 | | | | | | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 62.38/9.13 | | | | | | strict_implies(v0, v1) = v2 & is_a_theorem(v2) = 0 & % 62.38/9.13 | | | | | | is_a_theorem(v1) = v3 & is_a_theorem(v0) = 0 & $i(v2) & % 62.38/9.13 | | | | | | $i(v1) & $i(v0)) % 62.38/9.13 | | | | | | % 62.38/9.13 | | | | | | ALPHA: (15) implies: % 62.38/9.14 | | | | | | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ % 62.38/9.14 | | | | | | (v3 = 0) & strict_implies(v0, v1) = v2 & is_a_theorem(v2) % 62.38/9.14 | | | | | | = 0 & is_a_theorem(v1) = v3 & is_a_theorem(v0) = 0 & % 62.38/9.14 | | | | | | $i(v2) & $i(v1) & $i(v0)) % 62.38/9.14 | | | | | | % 62.38/9.14 | | | | | | DELTA: instantiating (16) with fresh symbols all_128_0, all_128_1, % 62.38/9.14 | | | | | | all_128_2, all_128_3 gives: % 62.38/9.14 | | | | | | (17) ~ (all_128_0 = 0) & strict_implies(all_128_3, all_128_2) = % 62.38/9.14 | | | | | | all_128_1 & is_a_theorem(all_128_1) = 0 & % 62.38/9.14 | | | | | | is_a_theorem(all_128_2) = all_128_0 & % 62.38/9.14 | | | | | | is_a_theorem(all_128_3) = 0 & $i(all_128_1) & $i(all_128_2) % 62.38/9.14 | | | | | | & $i(all_128_3) % 62.38/9.14 | | | | | | % 62.38/9.14 | | | | | | ALPHA: (17) implies: % 62.38/9.14 | | | | | | (18) ~ (all_128_0 = 0) % 62.38/9.14 | | | | | | (19) $i(all_128_3) % 62.38/9.14 | | | | | | (20) $i(all_128_2) % 62.38/9.14 | | | | | | (21) $i(all_128_1) % 62.38/9.14 | | | | | | (22) is_a_theorem(all_128_3) = 0 % 62.38/9.14 | | | | | | (23) is_a_theorem(all_128_2) = all_128_0 % 62.38/9.14 | | | | | | (24) is_a_theorem(all_128_1) = 0 % 62.38/9.14 | | | | | | (25) strict_implies(all_128_3, all_128_2) = all_128_1 % 62.38/9.14 | | | | | | % 62.38/9.14 | | | | | | GROUND_INST: instantiating (7) with all_128_3, all_128_2, all_128_0, % 62.38/9.14 | | | | | | simplifying with (19), (20), (22), (23) gives: % 62.38/9.14 | | | | | | (26) all_128_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 62.38/9.14 | | | | | | implies(all_128_3, all_128_2) = v0 & is_a_theorem(v0) = v1 % 62.38/9.14 | | | | | | & $i(v0)) % 62.38/9.14 | | | | | | % 62.38/9.15 | | | | | | GROUND_INST: instantiating (7) with all_128_1, all_128_2, all_128_0, % 62.38/9.15 | | | | | | simplifying with (20), (21), (23), (24) gives: % 62.38/9.15 | | | | | | (27) all_128_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 62.38/9.15 | | | | | | implies(all_128_1, all_128_2) = v0 & is_a_theorem(v0) = v1 % 62.38/9.15 | | | | | | & $i(v0)) % 62.38/9.15 | | | | | | % 62.38/9.15 | | | | | | GROUND_INST: instantiating (5) with all_128_3, all_128_2, all_128_1, % 62.38/9.15 | | | | | | simplifying with (19), (20), (25) gives: % 62.38/9.15 | | | | | | (28) ? [v0: $i] : (necessarily(v0) = all_128_1 & % 62.38/9.15 | | | | | | implies(all_128_3, all_128_2) = v0 & $i(v0) & % 62.38/9.15 | | | | | | $i(all_128_1)) % 62.38/9.15 | | | | | | % 62.38/9.15 | | | | | | DELTA: instantiating (28) with fresh symbol all_135_0 gives: % 62.38/9.15 | | | | | | (29) necessarily(all_135_0) = all_128_1 & implies(all_128_3, % 62.38/9.15 | | | | | | all_128_2) = all_135_0 & $i(all_135_0) & $i(all_128_1) % 62.38/9.15 | | | | | | % 62.38/9.15 | | | | | | ALPHA: (29) implies: % 62.38/9.15 | | | | | | (30) implies(all_128_3, all_128_2) = all_135_0 % 62.38/9.15 | | | | | | (31) necessarily(all_135_0) = all_128_1 % 62.38/9.15 | | | | | | % 62.38/9.15 | | | | | | BETA: splitting (26) gives: % 62.38/9.15 | | | | | | % 62.38/9.15 | | | | | | Case 1: % 62.38/9.15 | | | | | | | % 62.38/9.15 | | | | | | | (32) all_128_0 = 0 % 62.38/9.15 | | | | | | | % 62.38/9.15 | | | | | | | REDUCE: (18), (32) imply: % 62.38/9.15 | | | | | | | (33) $false % 62.38/9.15 | | | | | | | % 62.38/9.15 | | | | | | | CLOSE: (33) is inconsistent. % 62.38/9.15 | | | | | | | % 62.38/9.15 | | | | | | Case 2: % 62.38/9.15 | | | | | | | % 62.38/9.15 | | | | | | | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 62.38/9.15 | | | | | | | implies(all_128_3, all_128_2) = v0 & is_a_theorem(v0) = % 62.38/9.15 | | | | | | | v1 & $i(v0)) % 62.38/9.15 | | | | | | | % 62.38/9.15 | | | | | | | DELTA: instantiating (34) with fresh symbols all_141_0, all_141_1 % 62.38/9.15 | | | | | | | gives: % 62.38/9.15 | | | | | | | (35) ~ (all_141_0 = 0) & implies(all_128_3, all_128_2) = % 62.38/9.15 | | | | | | | all_141_1 & is_a_theorem(all_141_1) = all_141_0 & % 62.38/9.15 | | | | | | | $i(all_141_1) % 62.38/9.15 | | | | | | | % 62.38/9.15 | | | | | | | ALPHA: (35) implies: % 62.38/9.15 | | | | | | | (36) ~ (all_141_0 = 0) % 62.38/9.15 | | | | | | | (37) $i(all_141_1) % 62.38/9.15 | | | | | | | (38) is_a_theorem(all_141_1) = all_141_0 % 62.38/9.15 | | | | | | | (39) implies(all_128_3, all_128_2) = all_141_1 % 62.38/9.15 | | | | | | | % 62.38/9.15 | | | | | | | BETA: splitting (27) gives: % 62.38/9.15 | | | | | | | % 62.38/9.15 | | | | | | | Case 1: % 62.38/9.15 | | | | | | | | % 62.38/9.15 | | | | | | | | (40) all_128_0 = 0 % 62.38/9.15 | | | | | | | | % 62.38/9.15 | | | | | | | | REDUCE: (18), (40) imply: % 62.38/9.15 | | | | | | | | (41) $false % 62.38/9.15 | | | | | | | | % 62.38/9.15 | | | | | | | | CLOSE: (41) is inconsistent. % 62.38/9.15 | | | | | | | | % 62.38/9.15 | | | | | | | Case 2: % 62.38/9.15 | | | | | | | | % 62.38/9.16 | | | | | | | | (42) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 62.38/9.16 | | | | | | | | implies(all_128_1, all_128_2) = v0 & is_a_theorem(v0) % 62.38/9.16 | | | | | | | | = v1 & $i(v0)) % 62.38/9.16 | | | | | | | | % 62.38/9.16 | | | | | | | | DELTA: instantiating (42) with fresh symbols all_146_0, % 62.38/9.16 | | | | | | | | all_146_1 gives: % 62.38/9.16 | | | | | | | | (43) ~ (all_146_0 = 0) & implies(all_128_1, all_128_2) = % 62.38/9.16 | | | | | | | | all_146_1 & is_a_theorem(all_146_1) = all_146_0 & % 62.38/9.16 | | | | | | | | $i(all_146_1) % 62.38/9.16 | | | | | | | | % 62.38/9.16 | | | | | | | | ALPHA: (43) implies: % 62.38/9.16 | | | | | | | | (44) ~ (all_146_0 = 0) % 62.38/9.16 | | | | | | | | (45) $i(all_146_1) % 62.38/9.16 | | | | | | | | (46) is_a_theorem(all_146_1) = all_146_0 % 62.38/9.16 | | | | | | | | % 62.38/9.16 | | | | | | | | GROUND_INST: instantiating (2) with all_135_0, all_141_1, % 62.38/9.16 | | | | | | | | all_128_2, all_128_3, simplifying with (30), (39) % 62.38/9.16 | | | | | | | | gives: % 62.38/9.16 | | | | | | | | (47) all_141_1 = all_135_0 % 62.38/9.16 | | | | | | | | % 62.38/9.16 | | | | | | | | REDUCE: (38), (47) imply: % 62.38/9.16 | | | | | | | | (48) is_a_theorem(all_135_0) = all_141_0 % 62.38/9.16 | | | | | | | | % 62.38/9.16 | | | | | | | | REDUCE: (37), (47) imply: % 62.38/9.16 | | | | | | | | (49) $i(all_135_0) % 62.38/9.16 | | | | | | | | % 62.38/9.16 | | | | | | | | BETA: splitting (r2) gives: % 62.38/9.16 | | | | | | | | % 62.38/9.16 | | | | | | | | Case 1: % 62.38/9.16 | | | | | | | | | % 62.38/9.16 | | | | | | | | | % 62.38/9.16 | | | | | | | | | GROUND_INST: instantiating (7) with all_128_1, all_135_0, % 62.38/9.16 | | | | | | | | | all_141_0, simplifying with (21), (24), (48), (49) % 62.38/9.16 | | | | | | | | | gives: % 62.38/9.16 | | | | | | | | | (50) all_141_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = % 62.38/9.16 | | | | | | | | | 0) & implies(all_128_1, all_135_0) = v0 & % 62.38/9.16 | | | | | | | | | is_a_theorem(v0) = v1 & $i(v0)) % 62.38/9.16 | | | | | | | | | % 62.38/9.16 | | | | | | | | | GROUND_INST: instantiating (7) with all_128_1, all_146_1, % 62.38/9.16 | | | | | | | | | all_146_0, simplifying with (21), (24), (45), (46) % 62.38/9.16 | | | | | | | | | gives: % 62.38/9.16 | | | | | | | | | (51) all_146_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = % 62.38/9.16 | | | | | | | | | 0) & implies(all_128_1, all_146_1) = v0 & % 62.38/9.16 | | | | | | | | | is_a_theorem(v0) = v1 & $i(v0)) % 62.38/9.16 | | | | | | | | | % 62.38/9.16 | | | | | | | | | BETA: splitting (50) gives: % 62.38/9.16 | | | | | | | | | % 62.38/9.16 | | | | | | | | | Case 1: % 62.38/9.16 | | | | | | | | | | % 62.38/9.16 | | | | | | | | | | (52) all_141_0 = 0 % 62.38/9.16 | | | | | | | | | | % 62.38/9.16 | | | | | | | | | | REDUCE: (36), (52) imply: % 62.38/9.16 | | | | | | | | | | (53) $false % 62.38/9.16 | | | | | | | | | | % 62.38/9.16 | | | | | | | | | | CLOSE: (53) is inconsistent. % 62.38/9.16 | | | | | | | | | | % 62.38/9.16 | | | | | | | | | Case 2: % 62.38/9.16 | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | (54) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 62.38/9.17 | | | | | | | | | | implies(all_128_1, all_135_0) = v0 & % 62.38/9.17 | | | | | | | | | | is_a_theorem(v0) = v1 & $i(v0)) % 62.38/9.17 | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | DELTA: instantiating (54) with fresh symbols all_521_0, % 62.38/9.17 | | | | | | | | | | all_521_1 gives: % 62.38/9.17 | | | | | | | | | | (55) ~ (all_521_0 = 0) & implies(all_128_1, all_135_0) = % 62.38/9.17 | | | | | | | | | | all_521_1 & is_a_theorem(all_521_1) = all_521_0 & % 62.38/9.17 | | | | | | | | | | $i(all_521_1) % 62.38/9.17 | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | ALPHA: (55) implies: % 62.38/9.17 | | | | | | | | | | (56) ~ (all_521_0 = 0) % 62.38/9.17 | | | | | | | | | | (57) is_a_theorem(all_521_1) = all_521_0 % 62.38/9.17 | | | | | | | | | | (58) implies(all_128_1, all_135_0) = all_521_1 % 62.38/9.17 | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | BETA: splitting (51) gives: % 62.38/9.17 | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | Case 1: % 62.38/9.17 | | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | | (59) all_146_0 = 0 % 62.38/9.17 | | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | | REDUCE: (44), (59) imply: % 62.38/9.17 | | | | | | | | | | | (60) $false % 62.38/9.17 | | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | | CLOSE: (60) is inconsistent. % 62.38/9.17 | | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | Case 2: % 62.38/9.17 | | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | | GROUND_INST: instantiating (9) with all_135_0, all_128_1, % 62.38/9.17 | | | | | | | | | | | all_521_1, simplifying with (31), (49), (58) % 62.38/9.17 | | | | | | | | | | | gives: % 62.38/9.17 | | | | | | | | | | | (61) is_a_theorem(all_521_1) = 0 % 62.38/9.17 | | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_521_0, 0, all_521_1, % 62.38/9.17 | | | | | | | | | | | simplifying with (57), (61) gives: % 62.38/9.17 | | | | | | | | | | | (62) all_521_0 = 0 % 62.38/9.17 | | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | | REDUCE: (56), (62) imply: % 62.38/9.17 | | | | | | | | | | | (63) $false % 62.38/9.17 | | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | | CLOSE: (63) is inconsistent. % 62.38/9.17 | | | | | | | | | | | % 62.38/9.17 | | | | | | | | | | End of split % 62.38/9.17 | | | | | | | | | | % 62.38/9.17 | | | | | | | | | End of split % 62.38/9.17 | | | | | | | | | % 62.38/9.17 | | | | | | | | Case 2: % 62.38/9.17 | | | | | | | | | % 62.38/9.17 | | | | | | | | | (64) ~ r2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 62.38/9.17 | | | | | | | | | [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = % 62.38/9.17 | | | | | | | | | v2 & implies(v1, v2) = v3 & is_a_theorem(v3) = v4 & % 62.38/9.17 | | | | | | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 62.38/9.17 | | | | | | | | | % 62.38/9.17 | | | | | | | | | ALPHA: (64) implies: % 62.38/9.17 | | | | | | | | | (65) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 62.38/9.17 | | | | | | | | | : ? [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & % 62.38/9.17 | | | | | | | | | implies(v1, v2) = v3 & is_a_theorem(v3) = v4 & % 62.38/9.17 | | | | | | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 62.38/9.17 | | | | | | | | | % 62.38/9.17 | | | | | | | | | DELTA: instantiating (65) with fresh symbols all_292_0, % 62.38/9.17 | | | | | | | | | all_292_1, all_292_2, all_292_3, all_292_4 gives: % 62.38/9.18 | | | | | | | | | (66) ~ (all_292_0 = 0) & or(all_292_4, all_292_3) = % 62.38/9.18 | | | | | | | | | all_292_2 & implies(all_292_3, all_292_2) = all_292_1 % 62.38/9.18 | | | | | | | | | & is_a_theorem(all_292_1) = all_292_0 & $i(all_292_1) % 62.38/9.18 | | | | | | | | | & $i(all_292_2) & $i(all_292_3) & $i(all_292_4) % 62.38/9.18 | | | | | | | | | % 62.38/9.18 | | | | | | | | | ALPHA: (66) implies: % 62.38/9.18 | | | | | | | | | (67) ~ (all_292_0 = 0) % 62.38/9.18 | | | | | | | | | (68) $i(all_292_4) % 62.38/9.18 | | | | | | | | | (69) $i(all_292_3) % 62.38/9.18 | | | | | | | | | (70) is_a_theorem(all_292_1) = all_292_0 % 62.38/9.18 | | | | | | | | | (71) implies(all_292_3, all_292_2) = all_292_1 % 62.38/9.18 | | | | | | | | | (72) or(all_292_4, all_292_3) = all_292_2 % 62.38/9.18 | | | | | | | | | % 62.38/9.18 | | | | | | | | | GROUND_INST: instantiating (11) with all_292_4, all_292_3, % 62.38/9.18 | | | | | | | | | all_292_2, all_292_1, simplifying with (68), (69), % 62.38/9.18 | | | | | | | | | (71), (72) gives: % 62.38/9.18 | | | | | | | | | (73) is_a_theorem(all_292_1) = 0 % 62.38/9.18 | | | | | | | | | % 62.38/9.18 | | | | | | | | | GROUND_INST: instantiating (1) with all_292_0, 0, all_292_1, % 62.38/9.18 | | | | | | | | | simplifying with (70), (73) gives: % 62.38/9.18 | | | | | | | | | (74) all_292_0 = 0 % 62.38/9.18 | | | | | | | | | % 62.38/9.18 | | | | | | | | | REDUCE: (67), (74) imply: % 62.38/9.18 | | | | | | | | | (75) $false % 62.38/9.18 | | | | | | | | | % 62.38/9.18 | | | | | | | | | CLOSE: (75) is inconsistent. % 62.38/9.18 | | | | | | | | | % 62.38/9.18 | | | | | | | | End of split % 62.38/9.18 | | | | | | | | % 62.38/9.18 | | | | | | | End of split % 62.38/9.18 | | | | | | | % 62.38/9.18 | | | | | | End of split % 62.38/9.18 | | | | | | % 62.38/9.18 | | | | | End of split % 62.38/9.18 | | | | | % 62.38/9.18 | | | | Case 2: % 62.38/9.18 | | | | | % 62.38/9.18 | | | | | (76) ~ or_2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 62.38/9.18 | | | | | $i] : ? [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & % 62.38/9.18 | | | | | implies(v1, v2) = v3 & is_a_theorem(v3) = v4 & $i(v3) & % 62.38/9.18 | | | | | $i(v2) & $i(v1) & $i(v0)) % 62.38/9.18 | | | | | % 62.38/9.18 | | | | | ALPHA: (76) implies: % 62.38/9.18 | | | | | (77) ~ or_2 % 62.38/9.18 | | | | | % 62.38/9.18 | | | | | PRED_UNIFY: (77), (hilbert_or_2) imply: % 62.38/9.18 | | | | | (78) $false % 62.38/9.18 | | | | | % 62.38/9.18 | | | | | CLOSE: (78) is inconsistent. % 62.38/9.18 | | | | | % 62.38/9.18 | | | | End of split % 62.38/9.18 | | | | % 62.38/9.18 | | | Case 2: % 62.38/9.18 | | | | % 62.38/9.18 | | | | (79) ~ axiom_M & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 62.38/9.18 | | | | int] : ( ~ (v3 = 0) & necessarily(v0) = v1 & implies(v1, v0) = % 62.38/9.18 | | | | v2 & is_a_theorem(v2) = v3 & $i(v2) & $i(v1) & $i(v0)) % 62.38/9.18 | | | | % 62.38/9.18 | | | | ALPHA: (79) implies: % 62.38/9.18 | | | | (80) ~ axiom_M % 62.38/9.18 | | | | % 62.38/9.18 | | | | PRED_UNIFY: (80), (km5_axiom_M) imply: % 62.38/9.18 | | | | (81) $false % 62.38/9.18 | | | | % 62.38/9.18 | | | | CLOSE: (81) is inconsistent. % 62.38/9.18 | | | | % 62.38/9.18 | | | End of split % 62.38/9.18 | | | % 62.38/9.18 | | Case 2: % 62.38/9.18 | | | % 62.38/9.19 | | | (82) ~ modus_ponens & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 62.38/9.19 | | | [v3: int] : ( ~ (v3 = 0) & implies(v0, v1) = v2 & is_a_theorem(v2) % 62.38/9.19 | | | = 0 & is_a_theorem(v1) = v3 & is_a_theorem(v0) = 0 & $i(v2) & % 62.38/9.19 | | | $i(v1) & $i(v0)) % 62.38/9.19 | | | % 62.38/9.19 | | | ALPHA: (82) implies: % 62.38/9.19 | | | (83) ~ modus_ponens % 62.38/9.19 | | | % 62.38/9.19 | | | PRED_UNIFY: (83), (hilbert_modus_ponens) imply: % 62.38/9.19 | | | (84) $false % 62.38/9.19 | | | % 62.38/9.19 | | | CLOSE: (84) is inconsistent. % 62.38/9.19 | | | % 62.38/9.19 | | End of split % 62.38/9.19 | | % 62.38/9.19 | End of split % 62.38/9.19 | % 62.38/9.19 End of proof % 62.38/9.19 % SZS output end Proof for theBenchmark % 62.38/9.19 % 62.38/9.19 8470ms %------------------------------------------------------------------------------