%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL536+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 : n018.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 18.86s 3.25s % Output : Proof 46.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL536+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.36 % Computer : n018.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 02:51:48 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.38 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. % 0.69/0.71 ________ _____ % 0.69/0.71 ___ __ \_________(_)________________________________ % 0.69/0.71 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.69/0.71 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.69/0.71 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.69/0.71 % 0.69/0.71 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.69/0.71 (2023-06-19) % 0.69/0.71 % 0.69/0.71 (c) Philipp Rümmer, 2009-2023 % 0.69/0.71 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.69/0.71 Amanda Stjerna. % 0.69/0.71 Free software under BSD-3-Clause. % 0.69/0.71 % 0.69/0.72 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.69/0.72 % 0.69/0.72 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.74 Running up to 7 provers in parallel. % 0.69/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.69/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.69/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.69/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.69/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.69/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.69/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.64/1.56 Prover 4: Preprocessing ... % 5.64/1.56 Prover 1: Preprocessing ... % 5.64/1.57 Prover 2: Preprocessing ... % 5.64/1.57 Prover 0: Preprocessing ... % 5.64/1.57 Prover 5: Preprocessing ... % 5.64/1.59 Prover 3: Preprocessing ... % 6.36/1.60 Prover 6: Preprocessing ... % 16.56/2.95 Prover 3: Constructing countermodel ... % 16.56/3.02 Prover 5: Proving ... % 16.56/3.05 Prover 1: Constructing countermodel ... % 17.84/3.13 Prover 4: Constructing countermodel ... % 17.84/3.15 Prover 6: Constructing countermodel ... % 18.86/3.24 Prover 3: proved (2496ms) % 18.86/3.24 % 18.86/3.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.86/3.25 % 18.86/3.26 Prover 6: stopped % 18.86/3.26 Prover 0: Proving ... % 18.86/3.26 Prover 0: stopped % 18.86/3.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 18.86/3.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 18.86/3.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.86/3.28 Prover 5: stopped % 18.86/3.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.45/3.44 Prover 8: Preprocessing ... % 21.23/3.51 Prover 7: Preprocessing ... % 21.23/3.51 Prover 2: Proving ... % 21.23/3.54 Prover 2: stopped % 21.23/3.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.23/3.56 Prover 10: Preprocessing ... % 22.07/3.66 Prover 11: Preprocessing ... % 22.82/3.78 Prover 8: Warning: ignoring some quantifiers % 22.82/3.79 Prover 13: Preprocessing ... % 23.61/3.84 Prover 8: Constructing countermodel ... % 24.40/4.00 Prover 7: Constructing countermodel ... % 27.52/4.39 Prover 10: Constructing countermodel ... % 29.05/4.53 Prover 13: Constructing countermodel ... % 29.85/4.60 Prover 11: Constructing countermodel ... % 43.95/6.44 Prover 1: Found proof (size 58) % 43.95/6.44 Prover 1: proved (5692ms) % 43.95/6.44 Prover 7: stopped % 43.95/6.44 Prover 11: stopped % 43.95/6.44 Prover 8: stopped % 43.95/6.45 Prover 4: stopped % 43.95/6.46 Prover 13: stopped % 45.36/6.70 Prover 10: stopped % 45.36/6.70 % 45.36/6.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 45.36/6.70 % 45.36/6.71 % SZS output start Proof for theBenchmark % 45.36/6.72 Assumptions after simplification: % 45.36/6.72 --------------------------------- % 45.36/6.72 % 45.36/6.72 (and_1) % 45.36/6.78 (and_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (and(v0, % 45.36/6.78 v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 45.36/6.78 is_a_theorem(v3) = 0)) | ( ~ and_1 & ? [v0: $i] : ? [v1: $i] : ? [v2: % 45.36/6.78 $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & % 45.36/6.78 implies(v2, v0) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & % 45.36/6.78 $i(v0))) % 45.36/6.78 % 45.36/6.78 (axiom_5) % 45.36/6.79 (axiom_5 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 45.36/6.79 (possibly(v0) = v1) | ~ (necessarily(v1) = v2) | ~ (implies(v1, v2) = % 45.36/6.79 v3) | ~ $i(v0) | is_a_theorem(v3) = 0)) | ( ~ axiom_5 & ? [v0: $i] : % 45.36/6.79 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 45.36/6.79 possibly(v0) = v1 & necessarily(v1) = v2 & implies(v1, v2) = v3 & % 45.36/6.79 is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))) % 45.36/6.79 % 45.36/6.79 (axiom_m10) % 45.36/6.79 (axiom_m10 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 45.36/6.79 (possibly(v0) = v1) | ~ (strict_implies(v1, v2) = v3) | ~ % 45.36/6.79 (necessarily(v1) = v2) | ~ $i(v0) | is_a_theorem(v3) = 0)) | ( ~ % 45.36/6.79 axiom_m10 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 45.36/6.79 int] : ( ~ (v4 = 0) & possibly(v0) = v1 & strict_implies(v1, v2) = v3 & % 45.36/6.79 necessarily(v1) = v2 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & % 45.36/6.79 $i(v0))) % 45.36/6.79 % 45.36/6.79 (hilbert_and_1) % 45.36/6.79 and_1 % 45.36/6.79 % 45.36/6.79 (km5_axiom_5) % 45.36/6.79 axiom_5 % 45.36/6.79 % 45.36/6.79 (km5_necessitation) % 45.36/6.80 necessitation % 45.36/6.80 % 45.36/6.80 (kn2) % 45.82/6.80 (kn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (and(v0, % 45.82/6.80 v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 45.82/6.80 is_a_theorem(v3) = 0)) | ( ~ kn2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 45.82/6.80 : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, % 45.82/6.80 v0) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))) % 45.82/6.80 % 45.82/6.80 (necessitation) % 45.82/6.81 (necessitation & ! [v0: $i] : ! [v1: $i] : ( ~ (necessarily(v0) = v1) | ~ % 45.82/6.81 $i(v0) | ? [v2: any] : ? [v3: any] : (is_a_theorem(v1) = v3 & % 45.82/6.81 is_a_theorem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))) | ( ~ necessitation & % 45.82/6.81 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & necessarily(v0) = % 45.82/6.81 v1 & is_a_theorem(v1) = v2 & is_a_theorem(v0) = 0 & $i(v1) & $i(v0))) % 45.82/6.81 % 45.82/6.81 (op_strict_implies) % 45.82/6.81 ~ op_strict_implies | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 45.82/6.81 (strict_implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 45.82/6.81 (necessarily(v3) = v2 & implies(v0, v1) = v3 & $i(v3) & $i(v2))) % 45.82/6.81 % 45.82/6.81 (s1_0_m10_axiom_m10) % 45.82/6.81 ~ axiom_m10 % 45.82/6.81 % 45.82/6.81 (s1_0_op_strict_implies) % 45.82/6.81 op_strict_implies % 45.82/6.81 % 45.82/6.81 (function-axioms) % 45.82/6.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 45.82/6.82 (strict_equiv(v3, v2) = v1) | ~ (strict_equiv(v3, v2) = v0)) & ! [v0: $i] % 45.82/6.82 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (strict_implies(v3, % 45.82/6.82 v2) = v1) | ~ (strict_implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 45.82/6.82 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3, v2) = v1) | ~ % 45.82/6.82 (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 45.82/6.82 (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = v0)) & ! [v0: $i] : ! % 45.82/6.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (equiv(v3, v2) = v1) | ~ % 45.82/6.82 (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 45.82/6.82 $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0)) & ! % 45.82/6.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (possibly(v2) = v1) | ~ % 45.82/6.82 (possibly(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 45.82/6.82 ~ (necessarily(v2) = v1) | ~ (necessarily(v2) = v0)) & ! [v0: $i] : ! % 45.82/6.82 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & % 45.82/6.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 45.82/6.82 v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) % 45.82/6.82 % 45.82/6.82 Further assumptions not needed in the proof: % 45.82/6.82 -------------------------------------------- % 45.82/6.82 adjunction, and_2, and_3, axiom_4, axiom_B, axiom_K, axiom_M, axiom_m1, % 45.82/6.82 axiom_m2, axiom_m3, axiom_m4, axiom_m5, axiom_m6, axiom_m7, axiom_m8, axiom_m9, % 45.82/6.82 axiom_s1, axiom_s2, axiom_s3, axiom_s4, cn1, cn2, cn3, equivalence_1, % 45.82/6.82 equivalence_2, equivalence_3, hilbert_and_2, hilbert_and_3, % 45.82/6.82 hilbert_equivalence_1, hilbert_equivalence_2, hilbert_equivalence_3, % 45.82/6.82 hilbert_implies_1, hilbert_implies_2, hilbert_implies_3, hilbert_modus_ponens, % 45.82/6.82 hilbert_modus_tollens, hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or, % 45.82/6.82 hilbert_or_1, hilbert_or_2, hilbert_or_3, implies_1, implies_2, implies_3, % 45.82/6.82 km5_axiom_K, km5_axiom_M, km5_op_possibly, kn1, kn3, modus_ponens, % 45.82/6.82 modus_ponens_strict_implies, modus_tollens, op_and, op_equiv, op_implies_and, % 45.82/6.82 op_implies_or, op_necessarily, op_or, op_possibly, op_strict_equiv, or_1, or_2, % 45.82/6.82 or_3, r1, r2, r3, r4, r5, s1_0_op_equiv, s1_0_op_implies, s1_0_op_or, % 45.82/6.82 s1_0_op_possibly, s1_0_op_strict_equiv, substitution_of_equivalents, % 45.82/6.82 substitution_strict_equiv, use_substitution_of_equivalents % 45.82/6.82 % 45.82/6.82 Those formulas are unsatisfiable: % 45.82/6.82 --------------------------------- % 45.82/6.82 % 45.82/6.82 Begin of proof % 45.82/6.82 | % 45.82/6.83 | ALPHA: (function-axioms) implies: % 45.82/6.83 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 45.82/6.83 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) % 45.82/6.83 | % 45.82/6.83 | BETA: splitting (op_strict_implies) gives: % 45.82/6.83 | % 45.82/6.83 | Case 1: % 45.82/6.83 | | % 45.82/6.83 | | (2) ~ op_strict_implies % 45.82/6.83 | | % 45.82/6.83 | | PRED_UNIFY: (2), (s1_0_op_strict_implies) imply: % 45.82/6.83 | | (3) $false % 45.82/6.83 | | % 45.82/6.83 | | CLOSE: (3) is inconsistent. % 45.82/6.83 | | % 45.82/6.83 | Case 2: % 45.82/6.83 | | % 45.82/6.83 | | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (strict_implies(v0, v1) % 45.82/6.83 | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (necessarily(v3) = % 45.82/6.83 | | v2 & implies(v0, v1) = v3 & $i(v3) & $i(v2))) % 45.82/6.83 | | % 45.82/6.83 | | BETA: splitting (and_1) gives: % 45.82/6.83 | | % 45.82/6.83 | | Case 1: % 45.82/6.83 | | | % 45.82/6.83 | | | (5) and_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 45.82/6.83 | | | (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ % 45.82/6.84 | | | $i(v0) | is_a_theorem(v3) = 0) % 45.82/6.84 | | | % 45.82/6.84 | | | ALPHA: (5) implies: % 45.82/6.84 | | | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 45.82/6.84 | | | (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ % 45.82/6.84 | | | $i(v0) | is_a_theorem(v3) = 0) % 45.82/6.84 | | | % 45.82/6.84 | | | BETA: splitting (necessitation) gives: % 45.82/6.84 | | | % 45.82/6.84 | | | Case 1: % 45.82/6.84 | | | | % 45.82/6.84 | | | | (7) necessitation & ! [v0: $i] : ! [v1: $i] : ( ~ (necessarily(v0) % 45.82/6.84 | | | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 45.82/6.84 | | | | (is_a_theorem(v1) = v3 & is_a_theorem(v0) = v2 & ( ~ (v2 = 0) | % 45.82/6.84 | | | | v3 = 0))) % 45.82/6.84 | | | | % 45.82/6.84 | | | | ALPHA: (7) implies: % 45.82/6.84 | | | | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (necessarily(v0) = v1) | ~ % 45.82/6.84 | | | | $i(v0) | ? [v2: any] : ? [v3: any] : (is_a_theorem(v1) = v3 & % 45.82/6.84 | | | | is_a_theorem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 45.82/6.84 | | | | % 45.82/6.84 | | | | BETA: splitting (axiom_5) gives: % 45.82/6.84 | | | | % 45.82/6.84 | | | | Case 1: % 45.82/6.84 | | | | | % 45.82/6.84 | | | | | (9) axiom_5 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 45.82/6.84 | | | | | : ( ~ (possibly(v0) = v1) | ~ (necessarily(v1) = v2) | ~ % 45.82/6.84 | | | | | (implies(v1, v2) = v3) | ~ $i(v0) | is_a_theorem(v3) = 0) % 45.82/6.84 | | | | | % 45.82/6.84 | | | | | ALPHA: (9) implies: % 45.82/6.85 | | | | | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 45.82/6.85 | | | | | (possibly(v0) = v1) | ~ (necessarily(v1) = v2) | ~ % 45.82/6.85 | | | | | (implies(v1, v2) = v3) | ~ $i(v0) | is_a_theorem(v3) = 0) % 45.82/6.85 | | | | | % 45.82/6.85 | | | | | BETA: splitting (axiom_m10) gives: % 45.82/6.85 | | | | | % 45.82/6.85 | | | | | Case 1: % 45.82/6.85 | | | | | | % 45.82/6.85 | | | | | | (11) axiom_m10 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 45.82/6.85 | | | | | | [v3: $i] : ( ~ (possibly(v0) = v1) | ~ (strict_implies(v1, % 45.82/6.85 | | | | | | v2) = v3) | ~ (necessarily(v1) = v2) | ~ $i(v0) | % 45.82/6.85 | | | | | | is_a_theorem(v3) = 0) % 45.82/6.85 | | | | | | % 45.82/6.85 | | | | | | ALPHA: (11) implies: % 45.82/6.85 | | | | | | (12) axiom_m10 % 45.82/6.85 | | | | | | % 45.82/6.85 | | | | | | PRED_UNIFY: (12), (s1_0_m10_axiom_m10) imply: % 45.82/6.85 | | | | | | (13) $false % 45.82/6.85 | | | | | | % 45.82/6.85 | | | | | | CLOSE: (13) is inconsistent. % 45.82/6.85 | | | | | | % 45.82/6.85 | | | | | Case 2: % 45.82/6.85 | | | | | | % 45.82/6.85 | | | | | | (14) ~ axiom_m10 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 45.82/6.85 | | | | | | [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & possibly(v0) = v1 & % 45.82/6.85 | | | | | | strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & % 45.82/6.85 | | | | | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 45.82/6.85 | | | | | | % 45.82/6.85 | | | | | | ALPHA: (14) implies: % 45.82/6.85 | | | | | | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 45.82/6.85 | | | | | | [v4: int] : ( ~ (v4 = 0) & possibly(v0) = v1 & % 45.82/6.85 | | | | | | strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & % 45.82/6.85 | | | | | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 45.82/6.85 | | | | | | % 45.82/6.85 | | | | | | DELTA: instantiating (15) with fresh symbols all_108_0, all_108_1, % 45.82/6.85 | | | | | | all_108_2, all_108_3, all_108_4 gives: % 45.82/6.86 | | | | | | (16) ~ (all_108_0 = 0) & possibly(all_108_4) = all_108_3 & % 45.82/6.86 | | | | | | strict_implies(all_108_3, all_108_2) = all_108_1 & % 45.82/6.86 | | | | | | necessarily(all_108_3) = all_108_2 & is_a_theorem(all_108_1) % 45.82/6.86 | | | | | | = all_108_0 & $i(all_108_1) & $i(all_108_2) & $i(all_108_3) % 45.82/6.86 | | | | | | & $i(all_108_4) % 45.82/6.86 | | | | | | % 45.82/6.86 | | | | | | ALPHA: (16) implies: % 45.82/6.86 | | | | | | (17) ~ (all_108_0 = 0) % 45.82/6.86 | | | | | | (18) $i(all_108_4) % 45.82/6.86 | | | | | | (19) $i(all_108_3) % 45.82/6.86 | | | | | | (20) $i(all_108_2) % 45.82/6.86 | | | | | | (21) is_a_theorem(all_108_1) = all_108_0 % 45.82/6.86 | | | | | | (22) necessarily(all_108_3) = all_108_2 % 45.82/6.86 | | | | | | (23) strict_implies(all_108_3, all_108_2) = all_108_1 % 45.82/6.86 | | | | | | (24) possibly(all_108_4) = all_108_3 % 45.82/6.86 | | | | | | % 45.82/6.86 | | | | | | GROUND_INST: instantiating (4) with all_108_3, all_108_2, all_108_1, % 45.82/6.86 | | | | | | simplifying with (19), (20), (23) gives: % 45.82/6.86 | | | | | | (25) ? [v0: $i] : (necessarily(v0) = all_108_1 & % 45.82/6.86 | | | | | | implies(all_108_3, all_108_2) = v0 & $i(v0) & % 45.82/6.86 | | | | | | $i(all_108_1)) % 45.82/6.86 | | | | | | % 45.82/6.86 | | | | | | DELTA: instantiating (25) with fresh symbol all_115_0 gives: % 45.82/6.86 | | | | | | (26) necessarily(all_115_0) = all_108_1 & implies(all_108_3, % 45.82/6.86 | | | | | | all_108_2) = all_115_0 & $i(all_115_0) & $i(all_108_1) % 45.82/6.86 | | | | | | % 45.82/6.86 | | | | | | ALPHA: (26) implies: % 45.82/6.86 | | | | | | (27) $i(all_115_0) % 45.82/6.86 | | | | | | (28) implies(all_108_3, all_108_2) = all_115_0 % 45.82/6.87 | | | | | | (29) necessarily(all_115_0) = all_108_1 % 45.82/6.87 | | | | | | % 45.82/6.87 | | | | | | BETA: splitting (kn2) gives: % 45.82/6.87 | | | | | | % 45.82/6.87 | | | | | | Case 1: % 45.82/6.87 | | | | | | | % 45.82/6.87 | | | | | | | % 45.82/6.87 | | | | | | | GROUND_INST: instantiating (10) with all_108_4, all_108_3, % 45.82/6.87 | | | | | | | all_108_2, all_115_0, simplifying with (18), (22), % 45.82/6.87 | | | | | | | (24), (28) gives: % 45.82/6.87 | | | | | | | (30) is_a_theorem(all_115_0) = 0 % 45.82/6.87 | | | | | | | % 45.82/6.87 | | | | | | | GROUND_INST: instantiating (8) with all_115_0, all_108_1, % 45.82/6.87 | | | | | | | simplifying with (27), (29) gives: % 45.82/6.87 | | | | | | | (31) ? [v0: any] : ? [v1: any] : (is_a_theorem(all_115_0) = % 45.82/6.87 | | | | | | | v0 & is_a_theorem(all_108_1) = v1 & ( ~ (v0 = 0) | v1 = % 45.82/6.87 | | | | | | | 0)) % 45.82/6.87 | | | | | | | % 45.82/6.87 | | | | | | | DELTA: instantiating (31) with fresh symbols all_372_0, all_372_1 % 45.82/6.87 | | | | | | | gives: % 45.82/6.87 | | | | | | | (32) is_a_theorem(all_115_0) = all_372_1 & % 45.82/6.87 | | | | | | | is_a_theorem(all_108_1) = all_372_0 & ( ~ (all_372_1 = 0) % 45.82/6.87 | | | | | | | | all_372_0 = 0) % 45.82/6.87 | | | | | | | % 45.82/6.87 | | | | | | | ALPHA: (32) implies: % 45.82/6.87 | | | | | | | (33) is_a_theorem(all_108_1) = all_372_0 % 45.82/6.87 | | | | | | | (34) is_a_theorem(all_115_0) = all_372_1 % 45.82/6.87 | | | | | | | (35) ~ (all_372_1 = 0) | all_372_0 = 0 % 45.82/6.87 | | | | | | | % 45.82/6.87 | | | | | | | GROUND_INST: instantiating (1) with all_108_0, all_372_0, % 45.82/6.87 | | | | | | | all_108_1, simplifying with (21), (33) gives: % 45.82/6.87 | | | | | | | (36) all_372_0 = all_108_0 % 45.82/6.87 | | | | | | | % 45.82/6.87 | | | | | | | GROUND_INST: instantiating (1) with 0, all_372_1, all_115_0, % 45.82/6.87 | | | | | | | simplifying with (30), (34) gives: % 45.82/6.87 | | | | | | | (37) all_372_1 = 0 % 45.82/6.87 | | | | | | | % 45.82/6.87 | | | | | | | BETA: splitting (35) gives: % 45.82/6.87 | | | | | | | % 45.82/6.87 | | | | | | | Case 1: % 45.82/6.87 | | | | | | | | % 45.82/6.87 | | | | | | | | (38) ~ (all_372_1 = 0) % 45.82/6.87 | | | | | | | | % 45.82/6.87 | | | | | | | | REDUCE: (37), (38) imply: % 45.82/6.87 | | | | | | | | (39) $false % 45.82/6.87 | | | | | | | | % 45.82/6.87 | | | | | | | | CLOSE: (39) is inconsistent. % 45.82/6.87 | | | | | | | | % 45.82/6.87 | | | | | | | Case 2: % 45.82/6.87 | | | | | | | | % 45.82/6.87 | | | | | | | | (40) all_372_0 = 0 % 45.82/6.87 | | | | | | | | % 45.82/6.87 | | | | | | | | COMBINE_EQS: (36), (40) imply: % 45.82/6.87 | | | | | | | | (41) all_108_0 = 0 % 45.82/6.87 | | | | | | | | % 45.82/6.88 | | | | | | | | SIMP: (41) implies: % 45.82/6.88 | | | | | | | | (42) all_108_0 = 0 % 45.82/6.88 | | | | | | | | % 45.82/6.88 | | | | | | | | REDUCE: (17), (42) imply: % 45.82/6.88 | | | | | | | | (43) $false % 45.82/6.88 | | | | | | | | % 45.82/6.88 | | | | | | | | CLOSE: (43) is inconsistent. % 45.82/6.88 | | | | | | | | % 45.82/6.88 | | | | | | | End of split % 45.82/6.88 | | | | | | | % 45.82/6.88 | | | | | | Case 2: % 45.82/6.88 | | | | | | | % 45.82/6.88 | | | | | | | (44) ~ kn2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 45.82/6.88 | | | | | | | $i] : ? [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & % 45.82/6.88 | | | | | | | implies(v2, v0) = v3 & is_a_theorem(v3) = v4 & $i(v3) & % 45.82/6.88 | | | | | | | $i(v2) & $i(v1) & $i(v0)) % 45.82/6.88 | | | | | | | % 45.82/6.88 | | | | | | | ALPHA: (44) implies: % 45.82/6.88 | | | | | | | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 45.82/6.88 | | | | | | | [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, % 45.82/6.88 | | | | | | | v0) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & % 45.82/6.88 | | | | | | | $i(v1) & $i(v0)) % 45.82/6.88 | | | | | | | % 45.82/6.88 | | | | | | | DELTA: instantiating (45) with fresh symbols all_146_0, all_146_1, % 45.82/6.88 | | | | | | | all_146_2, all_146_3, all_146_4 gives: % 45.82/6.88 | | | | | | | (46) ~ (all_146_0 = 0) & and(all_146_4, all_146_3) = all_146_2 % 45.82/6.88 | | | | | | | & implies(all_146_2, all_146_4) = all_146_1 & % 45.82/6.88 | | | | | | | is_a_theorem(all_146_1) = all_146_0 & $i(all_146_1) & % 45.82/6.88 | | | | | | | $i(all_146_2) & $i(all_146_3) & $i(all_146_4) % 45.82/6.88 | | | | | | | % 45.82/6.88 | | | | | | | ALPHA: (46) implies: % 45.82/6.89 | | | | | | | (47) ~ (all_146_0 = 0) % 45.82/6.89 | | | | | | | (48) $i(all_146_4) % 45.82/6.89 | | | | | | | (49) $i(all_146_3) % 45.82/6.89 | | | | | | | (50) is_a_theorem(all_146_1) = all_146_0 % 45.82/6.89 | | | | | | | (51) implies(all_146_2, all_146_4) = all_146_1 % 45.82/6.89 | | | | | | | (52) and(all_146_4, all_146_3) = all_146_2 % 45.82/6.89 | | | | | | | % 45.82/6.89 | | | | | | | GROUND_INST: instantiating (6) with all_146_4, all_146_3, % 45.82/6.89 | | | | | | | all_146_2, all_146_1, simplifying with (48), (49), % 45.82/6.89 | | | | | | | (51), (52) gives: % 45.82/6.89 | | | | | | | (53) is_a_theorem(all_146_1) = 0 % 45.82/6.89 | | | | | | | % 45.82/6.89 | | | | | | | GROUND_INST: instantiating (1) with all_146_0, 0, all_146_1, % 45.82/6.89 | | | | | | | simplifying with (50), (53) gives: % 45.82/6.89 | | | | | | | (54) all_146_0 = 0 % 45.82/6.89 | | | | | | | % 45.82/6.89 | | | | | | | REDUCE: (47), (54) imply: % 45.82/6.89 | | | | | | | (55) $false % 45.82/6.89 | | | | | | | % 45.82/6.89 | | | | | | | CLOSE: (55) is inconsistent. % 45.82/6.89 | | | | | | | % 45.82/6.89 | | | | | | End of split % 45.82/6.89 | | | | | | % 45.82/6.89 | | | | | End of split % 45.82/6.89 | | | | | % 45.82/6.89 | | | | Case 2: % 45.82/6.89 | | | | | % 45.82/6.89 | | | | | (56) ~ axiom_5 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 45.82/6.89 | | | | | $i] : ? [v4: int] : ( ~ (v4 = 0) & possibly(v0) = v1 & % 45.82/6.89 | | | | | necessarily(v1) = v2 & implies(v1, v2) = v3 & % 45.82/6.89 | | | | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 45.82/6.89 | | | | | % 45.82/6.89 | | | | | ALPHA: (56) implies: % 45.82/6.89 | | | | | (57) ~ axiom_5 % 45.82/6.89 | | | | | % 45.82/6.89 | | | | | PRED_UNIFY: (57), (km5_axiom_5) imply: % 45.82/6.89 | | | | | (58) $false % 45.82/6.89 | | | | | % 45.82/6.89 | | | | | CLOSE: (58) is inconsistent. % 45.82/6.89 | | | | | % 45.82/6.89 | | | | End of split % 45.82/6.89 | | | | % 45.82/6.89 | | | Case 2: % 45.82/6.89 | | | | % 45.82/6.90 | | | | (59) ~ necessitation & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( % 45.82/6.90 | | | | ~ (v2 = 0) & necessarily(v0) = v1 & is_a_theorem(v1) = v2 & % 45.82/6.90 | | | | is_a_theorem(v0) = 0 & $i(v1) & $i(v0)) % 45.82/6.90 | | | | % 45.82/6.90 | | | | ALPHA: (59) implies: % 46.31/6.90 | | | | (60) ~ necessitation % 46.31/6.90 | | | | % 46.31/6.90 | | | | PRED_UNIFY: (60), (km5_necessitation) imply: % 46.31/6.90 | | | | (61) $false % 46.31/6.90 | | | | % 46.31/6.90 | | | | CLOSE: (61) is inconsistent. % 46.31/6.90 | | | | % 46.31/6.90 | | | End of split % 46.31/6.90 | | | % 46.31/6.90 | | Case 2: % 46.31/6.90 | | | % 46.31/6.90 | | | (62) ~ and_1 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 46.31/6.90 | | | ? [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, v0) = % 46.31/6.90 | | | v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 46.31/6.90 | | | % 46.31/6.90 | | | ALPHA: (62) implies: % 46.31/6.90 | | | (63) ~ and_1 % 46.31/6.90 | | | % 46.31/6.90 | | | PRED_UNIFY: (63), (hilbert_and_1) imply: % 46.31/6.90 | | | (64) $false % 46.31/6.90 | | | % 46.31/6.90 | | | CLOSE: (64) is inconsistent. % 46.31/6.90 | | | % 46.31/6.90 | | End of split % 46.31/6.90 | | % 46.31/6.90 | End of split % 46.31/6.90 | % 46.31/6.90 End of proof % 46.31/6.90 % SZS output end Proof for theBenchmark % 46.31/6.90 % 46.31/6.90 6184ms %------------------------------------------------------------------------------