%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL469+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 : n029.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 12:54:13 PM UTC 2026 % Result : Theorem 14.39s 2.65s % Output : Proof 52.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL469+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.03 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.34 % Computer : n029.cluster.edu % 0.09/0.34 % Model : x86_64 x86_64 % 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.34 % Memory : 8046.5625MB % 0.09/0.34 % OS : Linux 6.8.0-71-generic % 0.09/0.34 % CPULimit : 300 % 0.09/0.34 % WCLimit : 300 % 0.09/0.34 % DateTime : Fri Sep 4 18:45:54 UTC 2026 % 0.09/0.35 % CPUTime : % 0.12/0.36 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. % 0.29/0.54 ________ _____ % 0.29/0.54 ___ __ \_________(_)________________________________ % 0.29/0.54 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.29/0.54 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.29/0.54 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.29/0.54 % 0.29/0.54 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.29/0.54 (2023-06-19) % 0.29/0.54 % 0.29/0.54 (c) Philipp Rümmer, 2009-2023 % 0.29/0.54 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.29/0.54 Amanda Stjerna. % 0.29/0.54 Free software under BSD-3-Clause. % 0.29/0.54 % 0.29/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.29/0.54 % 0.29/0.55 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.29/0.56 Running up to 7 provers in parallel. % 0.57/0.57 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.57/0.57 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.57/0.57 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.57/0.57 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.57/0.57 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.57/0.57 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.57/0.57 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.25/1.30 Prover 4: Preprocessing ... % 4.25/1.30 Prover 1: Preprocessing ... % 4.25/1.32 Prover 0: Preprocessing ... % 4.25/1.32 Prover 3: Preprocessing ... % 4.25/1.32 Prover 6: Preprocessing ... % 4.25/1.32 Prover 2: Preprocessing ... % 4.25/1.32 Prover 5: Preprocessing ... % 9.99/2.13 Prover 5: Proving ... % 12.04/2.32 Prover 6: Constructing countermodel ... % 12.04/2.35 Prover 3: Constructing countermodel ... % 12.04/2.37 Prover 1: Constructing countermodel ... % 12.84/2.40 Prover 0: Proving ... % 12.84/2.43 Prover 4: Constructing countermodel ... % 14.39/2.61 Prover 2: Proving ... % 14.39/2.64 Prover 5: proved (2073ms) % 14.39/2.64 % 14.39/2.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.39/2.65 % 14.39/2.65 Prover 0: stopped % 14.39/2.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.39/2.66 Prover 3: stopped % 14.39/2.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.39/2.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.39/2.66 Prover 6: stopped % 14.39/2.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.39/2.67 Prover 2: stopped % 14.39/2.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.19/2.76 Prover 13: Preprocessing ... % 15.19/2.79 Prover 11: Preprocessing ... % 15.99/2.83 Prover 8: Preprocessing ... % 15.99/2.85 Prover 7: Preprocessing ... % 15.99/2.86 Prover 10: Preprocessing ... % 18.68/3.17 Prover 13: Constructing countermodel ... % 18.68/3.19 Prover 8: Warning: ignoring some quantifiers % 19.12/3.20 Prover 7: Constructing countermodel ... % 19.12/3.23 Prover 8: Constructing countermodel ... % 19.12/3.24 Prover 10: Constructing countermodel ... % 19.90/3.36 Prover 11: Constructing countermodel ... % 23.09/3.75 Prover 1: gave up % 23.09/3.75 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 23.88/3.83 Prover 16: Preprocessing ... % 23.88/3.86 Prover 13: gave up % 23.88/3.87 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 24.68/3.92 Prover 19: Preprocessing ... % 24.68/4.03 Prover 16: Warning: ignoring some quantifiers % 24.68/4.05 Prover 16: Constructing countermodel ... % 24.68/4.05 Prover 19: Constructing countermodel ... % 25.98/4.07 Prover 8: gave up % 27.02/4.27 Prover 19: gave up % 27.80/4.37 Prover 10: gave up % 43.71/6.59 Prover 16: gave up % 51.12/7.70 Prover 11: Found proof (size 102) % 51.12/7.70 Prover 11: proved (5032ms) % 51.12/7.70 Prover 7: stopped % 51.12/7.70 Prover 4: stopped % 51.12/7.70 % 51.12/7.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 51.12/7.70 % 51.12/7.72 % SZS output start Proof for theBenchmark % 51.12/7.72 Assumptions after simplification: % 51.12/7.72 --------------------------------- % 51.12/7.72 % 51.12/7.72 (cn2) % 51.12/7.77 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 51.12/7.77 int] : ($i(v1) & $i(v0) & (( ~ (v5 = 0) & not(v0) = v2 & implies(v2, v1) = % 51.12/7.77 v3 & implies(v0, v3) = v4 & is_a_theorem(v4) = v5 & $i(v4) & $i(v3) & % 51.12/7.77 $i(v2) & ~ cn2) | (cn2 & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! % 51.12/7.77 [v9: $i] : ( ~ (not(v6) = v8) | ~ (implies(v8, v7) = v9) | ~ $i(v7) | % 51.12/7.77 ~ $i(v6) | ? [v10: $i] : (implies(v6, v9) = v10 & is_a_theorem(v10) = % 51.12/7.77 0 & $i(v10)))))) % 51.12/7.77 % 51.12/7.77 (hilbert_op_equiv) % 51.12/7.77 op_equiv % 51.12/7.77 % 51.12/7.77 (hilbert_op_implies_and) % 51.12/7.77 op_implies_and % 51.12/7.77 % 51.12/7.77 (hilbert_op_or) % 51.12/7.77 op_or % 51.12/7.77 % 51.12/7.77 (hilbert_or_1) % 51.12/7.77 ~ or_1 % 51.12/7.77 % 51.12/7.77 (implies_2) % 51.12/7.77 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 51.12/7.77 int] : ($i(v1) & $i(v0) & (( ~ (v5 = 0) & implies(v3, v2) = v4 & implies(v0, % 51.12/7.77 v2) = v3 & implies(v0, v1) = v2 & is_a_theorem(v4) = v5 & $i(v4) & % 51.12/7.77 $i(v3) & $i(v2) & ~ implies_2) | (implies_2 & ! [v6: $i] : ! [v7: $i] % 51.12/7.77 : ! [v8: $i] : ( ~ (implies(v6, v7) = v8) | ~ $i(v7) | ~ $i(v6) | ? % 51.12/7.77 [v9: $i] : ? [v10: $i] : (implies(v9, v8) = v10 & implies(v6, v8) = % 51.12/7.78 v9 & is_a_theorem(v10) = 0 & $i(v10) & $i(v9)))))) % 51.12/7.78 % 51.12/7.78 (luka_cn2) % 51.12/7.78 cn2 % 51.12/7.78 % 51.12/7.78 (luka_modus_ponens) % 51.12/7.78 modus_ponens % 51.12/7.78 % 51.12/7.78 (luka_op_equiv) % 51.12/7.78 op_equiv % 51.12/7.78 % 51.12/7.78 (luka_op_or) % 51.12/7.78 op_or % 51.12/7.78 % 51.12/7.78 (modus_ponens) % 51.12/7.78 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? % 51.12/7.78 [v5: int] : ($i(v1) & $i(v0) & ((v4 = 0 & v2 = 0 & ~ (v5 = 0) & implies(v0, % 51.12/7.78 v1) = v3 & is_a_theorem(v3) = 0 & is_a_theorem(v1) = v5 & % 51.12/7.78 is_a_theorem(v0) = 0 & $i(v3) & ~ modus_ponens) | (modus_ponens & ! % 51.12/7.78 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (implies(v6, v7) = v8) | ~ % 51.12/7.78 $i(v7) | ~ $i(v6) | ? [v9: int] : ? [v10: int] : ? [v11: int] : % 51.12/7.78 ((v11 = 0 & is_a_theorem(v7) = 0) | ( ~ (v10 = 0) & is_a_theorem(v8) = % 51.12/7.78 v10) | ( ~ (v9 = 0) & is_a_theorem(v6) = v9)))))) % 51.12/7.78 % 51.12/7.78 (op_equiv) % 51.12/7.79 ~ op_equiv | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (equiv(v0, v1) = % 51.12/7.79 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (and(v3, v4) = % 51.12/7.79 v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3 & $i(v4) & $i(v3) & % 51.12/7.79 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v1, % 51.12/7.79 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 51.12/7.79 (and(v4, v2) = v3 & equiv(v0, v1) = v3 & implies(v0, v1) = v4 & $i(v4) & % 51.12/7.79 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, % 51.12/7.79 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 51.12/7.79 (and(v2, v4) = v3 & equiv(v0, v1) = v3 & implies(v1, v0) = v4 & $i(v4) & % 51.12/7.79 $i(v3)))) % 51.12/7.79 % 51.12/7.79 (op_implies_and) % 51.12/7.79 ~ op_implies_and | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 51.12/7.79 ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 51.12/7.79 $i] : (not(v3) = v4 & implies(v0, v1) = v4 & $i(v4))) & ! [v0: $i] : ! % 51.12/7.79 [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 51.12/7.79 | ? [v3: $i] : ? [v4: $i] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = % 51.12/7.79 v3 & $i(v4) & $i(v3) & $i(v2)))) % 51.12/7.79 % 51.12/7.79 (op_or) % 51.12/7.79 ~ op_or | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 51.12/7.79 $i] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ~ % 51.12/7.79 $i(v1) | ~ $i(v0) | ? [v5: $i] : (or(v0, v1) = v5 & not(v4) = v5 & % 51.12/7.79 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = % 51.12/7.79 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 51.12/7.79 (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3 & $i(v5) & % 51.12/7.79 $i(v4) & $i(v3) & $i(v2)))) % 51.12/7.79 % 51.12/7.79 (or_1) % 51.12/7.80 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ($i(v1) % 51.12/7.80 & $i(v0) & (( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v0, v2) = v3 & % 51.12/7.80 is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & ~ or_1) | (or_1 & ! [v5: $i] % 51.12/7.80 : ! [v6: $i] : ! [v7: $i] : ( ~ (or(v5, v6) = v7) | ~ $i(v6) | ~ % 51.12/7.80 $i(v5) | ? [v8: $i] : (implies(v5, v7) = v8 & is_a_theorem(v8) = 0 & % 51.12/7.80 $i(v8)))))) % 51.12/7.80 % 51.12/7.80 (function-axioms) % 51.61/7.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3, % 51.61/7.80 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 51.61/7.80 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = % 51.61/7.80 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 51.61/7.80 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 51.61/7.80 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ % 51.61/7.80 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 51.61/7.80 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 51.61/7.80 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_a_theorem(v2) = v1) % 51.61/7.80 | ~ (is_a_theorem(v2) = v0)) % 51.61/7.80 % 51.61/7.80 Further assumptions not needed in the proof: % 51.61/7.80 -------------------------------------------- % 51.61/7.80 and_1, and_2, and_3, cn1, cn3, equivalence_1, equivalence_2, equivalence_3, % 51.61/7.80 implies_1, implies_3, kn1, kn2, kn3, luka_cn1, luka_cn3, luka_op_implies, % 51.61/7.80 modus_tollens, op_and, op_implies_or, or_2, or_3, r1, r2, r3, r4, r5, % 51.61/7.80 substitution_of_equivalents, use_substitution_of_equivalents % 51.61/7.80 % 51.61/7.80 Those formulas are unsatisfiable: % 51.61/7.80 --------------------------------- % 51.61/7.80 % 51.61/7.80 Begin of proof % 51.61/7.80 | % 51.61/7.80 | ALPHA: (function-axioms) implies: % 51.61/7.80 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 51.61/7.80 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) % 51.61/7.80 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1) % 51.61/7.80 | | ~ (not(v2) = v0)) % 51.61/7.81 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 51.61/7.81 | (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0)) % 51.61/7.81 | % 51.61/7.81 | DELTA: instantiating (or_1) with fresh symbols all_14_0, all_14_1, all_14_2, % 51.61/7.81 | all_14_3, all_14_4 gives: % 51.61/7.81 | (4) $i(all_14_3) & $i(all_14_4) & (( ~ (all_14_0 = 0) & or(all_14_4, % 51.61/7.81 | all_14_3) = all_14_2 & implies(all_14_4, all_14_2) = all_14_1 & % 51.61/7.81 | is_a_theorem(all_14_1) = all_14_0 & $i(all_14_1) & $i(all_14_2) & % 51.61/7.81 | ~ or_1) | (or_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 51.61/7.81 | (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 51.61/7.81 | (implies(v0, v2) = v3 & is_a_theorem(v3) = 0 & $i(v3))))) % 51.61/7.81 | % 51.61/7.81 | ALPHA: (4) implies: % 51.61/7.81 | (5) $i(all_14_4) % 51.61/7.81 | (6) $i(all_14_3) % 51.61/7.81 | (7) ( ~ (all_14_0 = 0) & or(all_14_4, all_14_3) = all_14_2 & % 51.61/7.81 | implies(all_14_4, all_14_2) = all_14_1 & is_a_theorem(all_14_1) = % 51.61/7.81 | all_14_0 & $i(all_14_1) & $i(all_14_2) & ~ or_1) | (or_1 & ! [v0: % 51.61/7.81 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2) | ~ $i(v1) % 51.61/7.81 | | ~ $i(v0) | ? [v3: $i] : (implies(v0, v2) = v3 & % 51.61/7.81 | is_a_theorem(v3) = 0 & $i(v3)))) % 51.61/7.81 | % 51.61/7.81 | DELTA: instantiating (cn2) with fresh symbols all_26_0, all_26_1, all_26_2, % 51.61/7.81 | all_26_3, all_26_4, all_26_5 gives: % 51.61/7.82 | (8) $i(all_26_4) & $i(all_26_5) & (( ~ (all_26_0 = 0) & not(all_26_5) = % 51.61/7.82 | all_26_3 & implies(all_26_3, all_26_4) = all_26_2 & % 51.61/7.82 | implies(all_26_5, all_26_2) = all_26_1 & is_a_theorem(all_26_1) = % 51.61/7.82 | all_26_0 & $i(all_26_1) & $i(all_26_2) & $i(all_26_3) & ~ cn2) | % 51.61/7.82 | (cn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 51.61/7.82 | (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ $i(v1) | ~ % 51.61/7.82 | $i(v0) | ? [v4: $i] : (implies(v0, v3) = v4 & is_a_theorem(v4) = % 51.61/7.82 | 0 & $i(v4))))) % 51.61/7.82 | % 51.61/7.82 | ALPHA: (8) implies: % 51.61/7.82 | (9) ( ~ (all_26_0 = 0) & not(all_26_5) = all_26_3 & implies(all_26_3, % 51.61/7.82 | all_26_4) = all_26_2 & implies(all_26_5, all_26_2) = all_26_1 & % 51.61/7.82 | is_a_theorem(all_26_1) = all_26_0 & $i(all_26_1) & $i(all_26_2) & % 51.61/7.82 | $i(all_26_3) & ~ cn2) | (cn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: % 51.61/7.82 | $i] : ! [v3: $i] : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) % 51.61/7.82 | | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (implies(v0, v3) = v4 & % 51.61/7.82 | is_a_theorem(v4) = 0 & $i(v4)))) % 51.61/7.82 | % 51.61/7.82 | DELTA: instantiating (implies_2) with fresh symbols all_28_0, all_28_1, % 51.61/7.82 | all_28_2, all_28_3, all_28_4, all_28_5 gives: % 51.61/7.82 | (10) $i(all_28_4) & $i(all_28_5) & (( ~ (all_28_0 = 0) & implies(all_28_2, % 51.61/7.82 | all_28_3) = all_28_1 & implies(all_28_5, all_28_3) = all_28_2 & % 51.61/7.82 | implies(all_28_5, all_28_4) = all_28_3 & is_a_theorem(all_28_1) = % 51.61/7.82 | all_28_0 & $i(all_28_1) & $i(all_28_2) & $i(all_28_3) & ~ % 51.61/7.82 | implies_2) | (implies_2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 51.61/7.82 | : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 51.61/7.82 | : ? [v4: $i] : (implies(v3, v2) = v4 & implies(v0, v2) = v3 & % 51.61/7.82 | is_a_theorem(v4) = 0 & $i(v4) & $i(v3))))) % 51.61/7.82 | % 51.61/7.82 | ALPHA: (10) implies: % 51.61/7.83 | (11) ( ~ (all_28_0 = 0) & implies(all_28_2, all_28_3) = all_28_1 & % 51.61/7.83 | implies(all_28_5, all_28_3) = all_28_2 & implies(all_28_5, all_28_4) % 51.61/7.83 | = all_28_3 & is_a_theorem(all_28_1) = all_28_0 & $i(all_28_1) & % 51.61/7.83 | $i(all_28_2) & $i(all_28_3) & ~ implies_2) | (implies_2 & ! [v0: % 51.61/7.83 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ % 51.61/7.83 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (implies(v3, v2) % 51.61/7.83 | = v4 & implies(v0, v2) = v3 & is_a_theorem(v4) = 0 & $i(v4) & % 51.61/7.83 | $i(v3)))) % 51.61/7.83 | % 51.61/7.83 | DELTA: instantiating (modus_ponens) with fresh symbols all_32_0, all_32_1, % 51.61/7.83 | all_32_2, all_32_3, all_32_4, all_32_5 gives: % 51.61/7.83 | (12) $i(all_32_4) & $i(all_32_5) & ((all_32_1 = 0 & all_32_3 = 0 & ~ % 51.61/7.83 | (all_32_0 = 0) & implies(all_32_5, all_32_4) = all_32_2 & % 51.61/7.83 | is_a_theorem(all_32_2) = 0 & is_a_theorem(all_32_4) = all_32_0 & % 51.61/7.83 | is_a_theorem(all_32_5) = 0 & $i(all_32_2) & ~ modus_ponens) | % 51.61/7.83 | (modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 51.61/7.83 | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 51.61/7.83 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & is_a_theorem(v1) = 0) | % 51.61/7.83 | ( ~ (v4 = 0) & is_a_theorem(v2) = v4) | ( ~ (v3 = 0) & % 51.61/7.83 | is_a_theorem(v0) = v3))))) % 51.61/7.83 | % 51.61/7.83 | ALPHA: (12) implies: % 51.61/7.83 | (13) (all_32_1 = 0 & all_32_3 = 0 & ~ (all_32_0 = 0) & implies(all_32_5, % 51.61/7.83 | all_32_4) = all_32_2 & is_a_theorem(all_32_2) = 0 & % 51.61/7.83 | is_a_theorem(all_32_4) = all_32_0 & is_a_theorem(all_32_5) = 0 & % 51.61/7.83 | $i(all_32_2) & ~ modus_ponens) | (modus_ponens & ! [v0: $i] : ! % 51.61/7.83 | [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ % 51.61/7.83 | $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & % 51.61/7.83 | is_a_theorem(v1) = 0) | ( ~ (v4 = 0) & is_a_theorem(v2) = v4) % 51.61/7.83 | | ( ~ (v3 = 0) & is_a_theorem(v0) = v3)))) % 51.61/7.83 | % 51.61/7.83 | BETA: splitting (7) gives: % 51.61/7.83 | % 51.61/7.83 | Case 1: % 51.61/7.83 | | % 51.61/7.83 | | (14) ~ (all_14_0 = 0) & or(all_14_4, all_14_3) = all_14_2 & % 51.61/7.83 | | implies(all_14_4, all_14_2) = all_14_1 & is_a_theorem(all_14_1) = % 51.61/7.83 | | all_14_0 & $i(all_14_1) & $i(all_14_2) & ~ or_1 % 51.61/7.83 | | % 51.61/7.83 | | ALPHA: (14) implies: % 51.61/7.83 | | (15) ~ (all_14_0 = 0) % 51.61/7.83 | | (16) $i(all_14_2) % 51.61/7.83 | | (17) is_a_theorem(all_14_1) = all_14_0 % 51.61/7.83 | | (18) implies(all_14_4, all_14_2) = all_14_1 % 51.61/7.83 | | (19) or(all_14_4, all_14_3) = all_14_2 % 51.61/7.83 | | % 51.61/7.83 | | BETA: splitting (op_implies_and) gives: % 51.61/7.83 | | % 51.61/7.83 | | Case 1: % 51.61/7.83 | | | % 51.61/7.83 | | | (20) ~ op_implies_and % 51.61/7.83 | | | % 51.61/7.84 | | | PRED_UNIFY: (20), (hilbert_op_implies_and) imply: % 51.61/7.84 | | | (21) $false % 51.61/7.84 | | | % 51.61/7.84 | | | CLOSE: (21) is inconsistent. % 51.61/7.84 | | | % 51.61/7.84 | | Case 2: % 51.61/7.84 | | | % 51.61/7.84 | | | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 51.61/7.84 | | | (and(v0, v2) = v3) | ~ (not(v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 51.61/7.84 | | | ? [v4: $i] : (not(v3) = v4 & implies(v0, v1) = v4 & $i(v4))) & % 51.61/7.84 | | | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = % 51.61/7.84 | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 51.61/7.84 | | | (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3 & $i(v4) & % 51.61/7.84 | | | $i(v3) & $i(v2))) % 51.61/7.84 | | | % 51.61/7.84 | | | ALPHA: (22) implies: % 51.61/7.84 | | | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = % 51.61/7.84 | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 51.61/7.84 | | | (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3 & $i(v4) & % 51.61/7.84 | | | $i(v3) & $i(v2))) % 51.61/7.84 | | | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 51.61/7.84 | | | (and(v0, v2) = v3) | ~ (not(v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 51.61/7.84 | | | ? [v4: $i] : (not(v3) = v4 & implies(v0, v1) = v4 & $i(v4))) % 51.61/7.84 | | | % 51.61/7.84 | | | BETA: splitting (op_or) gives: % 51.61/7.84 | | | % 51.61/7.84 | | | Case 1: % 51.61/7.84 | | | | % 51.61/7.84 | | | | (25) ~ op_or % 51.61/7.84 | | | | % 51.61/7.84 | | | | PRED_UNIFY: (25), (luka_op_or) imply: % 51.61/7.84 | | | | (26) $false % 51.61/7.84 | | | | % 51.61/7.84 | | | | CLOSE: (26) is inconsistent. % 51.61/7.84 | | | | % 51.61/7.84 | | | Case 2: % 51.61/7.84 | | | | % 51.61/7.85 | | | | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 51.61/7.85 | | | | $i] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) % 51.61/7.85 | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (or(v0, v1) = % 51.61/7.85 | | | | v5 & not(v4) = v5 & $i(v5))) & ! [v0: $i] : ! [v1: $i] : % 51.61/7.85 | | | | ! [v2: $i] : ( ~ (or(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 51.61/7.85 | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (and(v3, v4) = v5 & % 51.61/7.85 | | | | not(v5) = v2 & not(v1) = v4 & not(v0) = v3 & $i(v5) & $i(v4) % 51.61/7.85 | | | | & $i(v3) & $i(v2))) % 51.61/7.85 | | | | % 51.61/7.85 | | | | ALPHA: (27) implies: % 51.61/7.85 | | | | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2) % 51.61/7.85 | | | | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 51.61/7.85 | | | | $i] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & % 51.61/7.85 | | | | not(v0) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 51.61/7.85 | | | | % 51.61/7.85 | | | | BETA: splitting (13) gives: % 51.61/7.85 | | | | % 51.61/7.85 | | | | Case 1: % 51.61/7.85 | | | | | % 51.61/7.85 | | | | | (29) all_32_1 = 0 & all_32_3 = 0 & ~ (all_32_0 = 0) & % 51.61/7.85 | | | | | implies(all_32_5, all_32_4) = all_32_2 & % 51.61/7.85 | | | | | is_a_theorem(all_32_2) = 0 & is_a_theorem(all_32_4) = all_32_0 % 51.61/7.85 | | | | | & is_a_theorem(all_32_5) = 0 & $i(all_32_2) & ~ modus_ponens % 51.61/7.85 | | | | | % 51.61/7.85 | | | | | ALPHA: (29) implies: % 51.61/7.85 | | | | | (30) ~ modus_ponens % 51.61/7.85 | | | | | % 51.61/7.85 | | | | | PRED_UNIFY: (30), (luka_modus_ponens) imply: % 51.61/7.85 | | | | | (31) $false % 51.61/7.85 | | | | | % 51.61/7.85 | | | | | CLOSE: (31) is inconsistent. % 51.61/7.85 | | | | | % 51.61/7.85 | | | | Case 2: % 51.61/7.85 | | | | | % 51.61/7.85 | | | | | (32) modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 51.61/7.85 | | | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 51.61/7.85 | | | | | int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & % 51.61/7.85 | | | | | is_a_theorem(v1) = 0) | ( ~ (v4 = 0) & is_a_theorem(v2) % 51.61/7.85 | | | | | = v4) | ( ~ (v3 = 0) & is_a_theorem(v0) = v3))) % 51.61/7.85 | | | | | % 51.61/7.85 | | | | | ALPHA: (32) implies: % 51.61/7.85 | | | | | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) % 51.61/7.85 | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 51.61/7.85 | | | | | int] : ? [v5: int] : ((v5 = 0 & is_a_theorem(v1) = 0) | ( % 51.61/7.85 | | | | | ~ (v4 = 0) & is_a_theorem(v2) = v4) | ( ~ (v3 = 0) & % 51.61/7.85 | | | | | is_a_theorem(v0) = v3))) % 51.61/7.85 | | | | | % 51.61/7.85 | | | | | BETA: splitting (op_equiv) gives: % 51.61/7.85 | | | | | % 51.61/7.85 | | | | | Case 1: % 51.61/7.85 | | | | | | % 51.61/7.85 | | | | | | (34) ~ op_equiv % 51.61/7.85 | | | | | | % 51.61/7.85 | | | | | | PRED_UNIFY: (34), (luka_op_equiv) imply: % 51.61/7.85 | | | | | | (35) $false % 51.61/7.85 | | | | | | % 51.61/7.85 | | | | | | CLOSE: (35) is inconsistent. % 51.61/7.85 | | | | | | % 51.61/7.85 | | | | | Case 2: % 51.61/7.85 | | | | | | % 51.61/7.86 | | | | | | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (equiv(v0, v1) % 51.61/7.86 | | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 51.61/7.86 | | | | | | $i] : (and(v3, v4) = v2 & implies(v1, v0) = v4 & % 51.61/7.86 | | | | | | implies(v0, v1) = v3 & $i(v4) & $i(v3) & $i(v2))) & ! % 51.61/7.86 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v1, v0) % 51.61/7.86 | | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 51.61/7.86 | | | | | | $i] : (and(v4, v2) = v3 & equiv(v0, v1) = v3 & % 51.61/7.86 | | | | | | implies(v0, v1) = v4 & $i(v4) & $i(v3))) & ! [v0: $i] : % 51.61/7.86 | | | | | | ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ % 51.61/7.86 | | | | | | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (and(v2, % 51.61/7.86 | | | | | | v4) = v3 & equiv(v0, v1) = v3 & implies(v1, v0) = v4 & % 51.61/7.86 | | | | | | $i(v4) & $i(v3))) % 51.61/7.86 | | | | | | % 51.61/7.86 | | | | | | ALPHA: (36) implies: % 51.61/7.86 | | | | | | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, % 51.61/7.86 | | | | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 51.61/7.86 | | | | | | [v4: $i] : (and(v2, v4) = v3 & equiv(v0, v1) = v3 & % 51.61/7.86 | | | | | | implies(v1, v0) = v4 & $i(v4) & $i(v3))) % 51.61/7.86 | | | | | | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v1, % 51.61/7.86 | | | | | | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 51.61/7.86 | | | | | | [v4: $i] : (and(v4, v2) = v3 & equiv(v0, v1) = v3 & % 51.61/7.86 | | | | | | implies(v0, v1) = v4 & $i(v4) & $i(v3))) % 51.61/7.86 | | | | | | % 51.61/7.86 | | | | | | BETA: splitting (9) gives: % 51.61/7.86 | | | | | | % 51.61/7.86 | | | | | | Case 1: % 51.61/7.86 | | | | | | | % 51.61/7.86 | | | | | | | (39) ~ (all_26_0 = 0) & not(all_26_5) = all_26_3 & % 51.61/7.86 | | | | | | | implies(all_26_3, all_26_4) = all_26_2 & implies(all_26_5, % 51.61/7.86 | | | | | | | all_26_2) = all_26_1 & is_a_theorem(all_26_1) = all_26_0 % 51.61/7.86 | | | | | | | & $i(all_26_1) & $i(all_26_2) & $i(all_26_3) & ~ cn2 % 51.61/7.86 | | | | | | | % 51.61/7.86 | | | | | | | ALPHA: (39) implies: % 51.61/7.86 | | | | | | | (40) ~ cn2 % 51.61/7.86 | | | | | | | % 51.61/7.86 | | | | | | | PRED_UNIFY: (40), (luka_cn2) imply: % 51.61/7.86 | | | | | | | (41) $false % 51.61/7.86 | | | | | | | % 51.61/7.86 | | | | | | | CLOSE: (41) is inconsistent. % 51.61/7.86 | | | | | | | % 51.61/7.86 | | | | | | Case 2: % 51.61/7.86 | | | | | | | % 51.61/7.86 | | | | | | | (42) cn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 51.61/7.86 | | | | | | | $i] : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) | % 51.61/7.87 | | | | | | | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (implies(v0, v3) = % 51.61/7.87 | | | | | | | v4 & is_a_theorem(v4) = 0 & $i(v4))) % 51.61/7.87 | | | | | | | % 51.61/7.87 | | | | | | | ALPHA: (42) implies: % 51.61/7.87 | | | | | | | (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 51.61/7.87 | | | | | | | ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ $i(v1) % 51.61/7.87 | | | | | | | | ~ $i(v0) | ? [v4: $i] : (implies(v0, v3) = v4 & % 51.61/7.87 | | | | | | | is_a_theorem(v4) = 0 & $i(v4))) % 51.61/7.87 | | | | | | | % 51.61/7.87 | | | | | | | GROUND_INST: instantiating (38) with all_14_2, all_14_4, all_14_1, % 51.61/7.87 | | | | | | | simplifying with (5), (16), (18) gives: % 51.61/7.87 | | | | | | | (44) ? [v0: $i] : ? [v1: $i] : (and(v1, all_14_1) = v0 & % 51.61/7.87 | | | | | | | equiv(all_14_2, all_14_4) = v0 & implies(all_14_2, % 51.61/7.87 | | | | | | | all_14_4) = v1 & $i(v1) & $i(v0)) % 51.61/7.87 | | | | | | | % 51.61/7.87 | | | | | | | GROUND_INST: instantiating (37) with all_14_4, all_14_2, all_14_1, % 51.61/7.87 | | | | | | | simplifying with (5), (16), (18) gives: % 51.61/7.87 | | | | | | | (45) ? [v0: $i] : ? [v1: $i] : (and(all_14_1, v1) = v0 & % 51.61/7.87 | | | | | | | equiv(all_14_4, all_14_2) = v0 & implies(all_14_2, % 51.61/7.87 | | | | | | | all_14_4) = v1 & $i(v1) & $i(v0)) % 51.61/7.87 | | | | | | | % 51.61/7.87 | | | | | | | GROUND_INST: instantiating (23) with all_14_4, all_14_2, all_14_1, % 51.61/7.87 | | | | | | | simplifying with (5), (16), (18) gives: % 51.61/7.87 | | | | | | | (46) ? [v0: $i] : ? [v1: $i] : (and(all_14_4, v0) = v1 & % 51.61/7.87 | | | | | | | not(v1) = all_14_1 & not(all_14_2) = v0 & $i(v1) & % 51.61/7.87 | | | | | | | $i(v0) & $i(all_14_1)) % 51.61/7.87 | | | | | | | % 51.61/7.87 | | | | | | | GROUND_INST: instantiating (28) with all_14_4, all_14_3, all_14_2, % 51.61/7.87 | | | | | | | simplifying with (5), (6), (19) gives: % 51.61/7.87 | | | | | | | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (and(v0, v1) = % 51.61/7.87 | | | | | | | v2 & not(v2) = all_14_2 & not(all_14_3) = v1 & % 51.61/7.87 | | | | | | | not(all_14_4) = v0 & $i(v2) & $i(v1) & $i(v0) & % 51.61/7.87 | | | | | | | $i(all_14_2)) % 51.61/7.87 | | | | | | | % 51.61/7.87 | | | | | | | DELTA: instantiating (45) with fresh symbols all_98_0, all_98_1 % 51.61/7.87 | | | | | | | gives: % 51.61/7.87 | | | | | | | (48) and(all_14_1, all_98_0) = all_98_1 & equiv(all_14_4, % 51.61/7.87 | | | | | | | all_14_2) = all_98_1 & implies(all_14_2, all_14_4) = % 51.61/7.87 | | | | | | | all_98_0 & $i(all_98_0) & $i(all_98_1) % 51.61/7.87 | | | | | | | % 51.61/7.87 | | | | | | | ALPHA: (48) implies: % 51.61/7.87 | | | | | | | (49) implies(all_14_2, all_14_4) = all_98_0 % 51.61/7.87 | | | | | | | % 51.61/7.87 | | | | | | | DELTA: instantiating (44) with fresh symbols all_100_0, all_100_1 % 51.61/7.87 | | | | | | | gives: % 51.61/7.88 | | | | | | | (50) and(all_100_0, all_14_1) = all_100_1 & equiv(all_14_2, % 51.61/7.88 | | | | | | | all_14_4) = all_100_1 & implies(all_14_2, all_14_4) = % 51.61/7.88 | | | | | | | all_100_0 & $i(all_100_0) & $i(all_100_1) % 51.61/7.88 | | | | | | | % 51.61/7.88 | | | | | | | ALPHA: (50) implies: % 51.61/7.88 | | | | | | | (51) implies(all_14_2, all_14_4) = all_100_0 % 51.61/7.88 | | | | | | | % 51.61/7.88 | | | | | | | DELTA: instantiating (46) with fresh symbols all_103_0, all_103_1 % 51.61/7.88 | | | | | | | gives: % 51.61/7.88 | | | | | | | (52) and(all_14_4, all_103_1) = all_103_0 & not(all_103_0) = % 51.61/7.88 | | | | | | | all_14_1 & not(all_14_2) = all_103_1 & $i(all_103_0) & % 51.61/7.88 | | | | | | | $i(all_103_1) & $i(all_14_1) % 51.61/7.88 | | | | | | | % 51.61/7.88 | | | | | | | ALPHA: (52) implies: % 51.61/7.88 | | | | | | | (53) $i(all_14_1) % 51.61/7.88 | | | | | | | % 51.61/7.88 | | | | | | | DELTA: instantiating (47) with fresh symbols all_105_0, all_105_1, % 51.61/7.88 | | | | | | | all_105_2 gives: % 51.61/7.88 | | | | | | | (54) and(all_105_2, all_105_1) = all_105_0 & not(all_105_0) = % 51.61/7.88 | | | | | | | all_14_2 & not(all_14_3) = all_105_1 & not(all_14_4) = % 51.61/7.88 | | | | | | | all_105_2 & $i(all_105_0) & $i(all_105_1) & $i(all_105_2) % 51.61/7.88 | | | | | | | & $i(all_14_2) % 51.61/7.88 | | | | | | | % 51.61/7.88 | | | | | | | ALPHA: (54) implies: % 51.61/7.88 | | | | | | | (55) $i(all_105_2) % 51.61/7.88 | | | | | | | (56) not(all_14_4) = all_105_2 % 51.61/7.88 | | | | | | | (57) not(all_14_3) = all_105_1 % 51.61/7.88 | | | | | | | (58) not(all_105_0) = all_14_2 % 51.61/7.88 | | | | | | | (59) and(all_105_2, all_105_1) = all_105_0 % 51.61/7.88 | | | | | | | % 51.61/7.88 | | | | | | | GROUND_INST: instantiating (3) with all_98_0, all_100_0, all_14_4, % 51.61/7.88 | | | | | | | all_14_2, simplifying with (49), (51) gives: % 51.61/7.88 | | | | | | | (60) all_100_0 = all_98_0 % 51.61/7.88 | | | | | | | % 51.61/7.88 | | | | | | | GROUND_INST: instantiating (23) with all_14_2, all_14_4, all_98_0, % 51.61/7.88 | | | | | | | simplifying with (5), (16), (49) gives: % 51.61/7.88 | | | | | | | (61) ? [v0: $i] : ? [v1: $i] : (and(all_14_2, v0) = v1 & % 51.61/7.88 | | | | | | | not(v1) = all_98_0 & not(all_14_4) = v0 & $i(v1) & % 51.61/7.88 | | | | | | | $i(v0) & $i(all_98_0)) % 51.61/7.88 | | | | | | | % 51.61/7.88 | | | | | | | GROUND_INST: instantiating (24) with all_105_2, all_14_3, % 51.61/7.88 | | | | | | | all_105_1, all_105_0, simplifying with (6), (55), % 51.61/7.88 | | | | | | | (57), (59) gives: % 51.61/7.88 | | | | | | | (62) ? [v0: $i] : (not(all_105_0) = v0 & implies(all_105_2, % 51.61/7.88 | | | | | | | all_14_3) = v0 & $i(v0)) % 51.61/7.88 | | | | | | | % 51.61/7.88 | | | | | | | DELTA: instantiating (62) with fresh symbol all_128_0 gives: % 51.61/7.88 | | | | | | | (63) not(all_105_0) = all_128_0 & implies(all_105_2, all_14_3) % 51.61/7.88 | | | | | | | = all_128_0 & $i(all_128_0) % 51.61/7.88 | | | | | | | % 51.61/7.88 | | | | | | | ALPHA: (63) implies: % 51.61/7.88 | | | | | | | (64) $i(all_128_0) % 51.61/7.88 | | | | | | | (65) implies(all_105_2, all_14_3) = all_128_0 % 51.61/7.88 | | | | | | | (66) not(all_105_0) = all_128_0 % 51.61/7.88 | | | | | | | % 51.61/7.88 | | | | | | | DELTA: instantiating (61) with fresh symbols all_144_0, all_144_1 % 51.61/7.88 | | | | | | | gives: % 51.61/7.89 | | | | | | | (67) and(all_14_2, all_144_1) = all_144_0 & not(all_144_0) = % 51.61/7.89 | | | | | | | all_98_0 & not(all_14_4) = all_144_1 & $i(all_144_0) & % 51.61/7.89 | | | | | | | $i(all_144_1) & $i(all_98_0) % 51.61/7.89 | | | | | | | % 51.61/7.89 | | | | | | | ALPHA: (67) implies: % 51.61/7.89 | | | | | | | (68) not(all_14_4) = all_144_1 % 51.61/7.89 | | | | | | | % 51.61/7.89 | | | | | | | GROUND_INST: instantiating (2) with all_105_2, all_144_1, % 51.61/7.89 | | | | | | | all_14_4, simplifying with (56), (68) gives: % 51.61/7.89 | | | | | | | (69) all_144_1 = all_105_2 % 51.61/7.89 | | | | | | | % 51.61/7.89 | | | | | | | GROUND_INST: instantiating (2) with all_14_2, all_128_0, % 51.61/7.89 | | | | | | | all_105_0, simplifying with (58), (66) gives: % 51.61/7.89 | | | | | | | (70) all_128_0 = all_14_2 % 51.61/7.89 | | | | | | | % 51.61/7.89 | | | | | | | REDUCE: (65), (70) imply: % 51.61/7.89 | | | | | | | (71) implies(all_105_2, all_14_3) = all_14_2 % 51.61/7.89 | | | | | | | % 51.61/7.89 | | | | | | | BETA: splitting (11) gives: % 51.61/7.89 | | | | | | | % 51.61/7.89 | | | | | | | Case 1: % 51.61/7.89 | | | | | | | | % 51.61/7.89 | | | | | | | | % 51.61/7.89 | | | | | | | | GROUND_INST: instantiating (43) with all_14_4, all_14_3, % 51.61/7.89 | | | | | | | | all_105_2, all_14_2, simplifying with (5), (6), % 51.61/7.89 | | | | | | | | (56), (71) gives: % 51.61/7.89 | | | | | | | | (72) ? [v0: $i] : (implies(all_14_4, all_14_2) = v0 & % 51.61/7.89 | | | | | | | | is_a_theorem(v0) = 0 & $i(v0)) % 51.61/7.89 | | | | | | | | % 51.61/7.89 | | | | | | | | DELTA: instantiating (72) with fresh symbol all_239_0 gives: % 51.61/7.89 | | | | | | | | (73) implies(all_14_4, all_14_2) = all_239_0 & % 51.61/7.89 | | | | | | | | is_a_theorem(all_239_0) = 0 & $i(all_239_0) % 51.61/7.89 | | | | | | | | % 51.61/7.89 | | | | | | | | ALPHA: (73) implies: % 51.61/7.89 | | | | | | | | (74) implies(all_14_4, all_14_2) = all_239_0 % 51.61/7.89 | | | | | | | | (75) is_a_theorem(all_239_0) = 0 % 51.61/7.89 | | | | | | | | % 51.61/7.89 | | | | | | | | GROUND_INST: instantiating (3) with all_14_1, all_239_0, % 51.61/7.89 | | | | | | | | all_14_2, all_14_4, simplifying with (18), (74) % 51.61/7.89 | | | | | | | | gives: % 51.61/7.89 | | | | | | | | (76) all_239_0 = all_14_1 % 51.61/7.89 | | | | | | | | % 51.61/7.89 | | | | | | | | REDUCE: (75), (76) imply: % 51.61/7.89 | | | | | | | | (77) is_a_theorem(all_14_1) = 0 % 51.61/7.89 | | | | | | | | % 51.61/7.89 | | | | | | | | REF_CLOSE: (1), (15), (17), (77) are inconsistent by sub-proof % 51.61/7.89 | | | | | | | | #1. % 51.61/7.89 | | | | | | | | % 51.61/7.89 | | | | | | | Case 2: % 51.61/7.89 | | | | | | | | % 51.61/7.90 | | | | | | | | (78) implies_2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( % 51.61/7.90 | | | | | | | | ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 51.61/7.90 | | | | | | | | [v3: $i] : ? [v4: $i] : (implies(v3, v2) = v4 & % 51.61/7.90 | | | | | | | | implies(v0, v2) = v3 & is_a_theorem(v4) = 0 & $i(v4) % 51.61/7.90 | | | | | | | | & $i(v3))) % 51.61/7.90 | | | | | | | | % 51.61/7.90 | | | | | | | | ALPHA: (78) implies: % 52.10/7.90 | | | | | | | | (79) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 52.10/7.90 | | | | | | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.10/7.90 | | | | | | | | [v3: $i] : ? [v4: $i] : (implies(v3, v2) = v4 & % 52.10/7.90 | | | | | | | | implies(v0, v2) = v3 & is_a_theorem(v4) = 0 & $i(v4) % 52.10/7.90 | | | | | | | | & $i(v3))) % 52.10/7.90 | | | | | | | | % 52.10/7.90 | | | | | | | | GROUND_INST: instantiating (79) with all_14_4, all_14_2, % 52.10/7.90 | | | | | | | | all_14_1, simplifying with (5), (16), (18) gives: % 52.10/7.90 | | | | | | | | (80) ? [v0: $i] : ? [v1: $i] : (implies(v0, all_14_1) = v1 % 52.10/7.90 | | | | | | | | & implies(all_14_4, all_14_1) = v0 & is_a_theorem(v1) % 52.10/7.90 | | | | | | | | = 0 & $i(v1) & $i(v0)) % 52.10/7.90 | | | | | | | | % 52.10/7.90 | | | | | | | | DELTA: instantiating (80) with fresh symbols all_231_0, % 52.10/7.90 | | | | | | | | all_231_1 gives: % 52.10/7.90 | | | | | | | | (81) implies(all_231_1, all_14_1) = all_231_0 & % 52.10/7.90 | | | | | | | | implies(all_14_4, all_14_1) = all_231_1 & % 52.10/7.90 | | | | | | | | is_a_theorem(all_231_0) = 0 & $i(all_231_0) & % 52.10/7.90 | | | | | | | | $i(all_231_1) % 52.10/7.90 | | | | | | | | % 52.10/7.90 | | | | | | | | ALPHA: (81) implies: % 52.10/7.90 | | | | | | | | (82) $i(all_231_1) % 52.10/7.90 | | | | | | | | (83) is_a_theorem(all_231_0) = 0 % 52.10/7.90 | | | | | | | | (84) implies(all_231_1, all_14_1) = all_231_0 % 52.10/7.90 | | | | | | | | % 52.10/7.90 | | | | | | | | GROUND_INST: instantiating (43) with all_14_4, all_14_3, % 52.10/7.90 | | | | | | | | all_105_2, all_14_2, simplifying with (5), (6), % 52.10/7.90 | | | | | | | | (56), (71) gives: % 52.10/7.90 | | | | | | | | (85) ? [v0: $i] : (implies(all_14_4, all_14_2) = v0 & % 52.10/7.90 | | | | | | | | is_a_theorem(v0) = 0 & $i(v0)) % 52.10/7.90 | | | | | | | | % 52.10/7.90 | | | | | | | | GROUND_INST: instantiating (33) with all_231_1, all_14_1, % 52.10/7.90 | | | | | | | | all_231_0, simplifying with (53), (82), (84) gives: % 52.10/7.90 | | | | | | | | (86) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & % 52.10/7.90 | | | | | | | | is_a_theorem(all_14_1) = 0) | ( ~ (v1 = 0) & % 52.10/7.90 | | | | | | | | is_a_theorem(all_231_0) = v1) | ( ~ (v0 = 0) & % 52.10/7.90 | | | | | | | | is_a_theorem(all_231_1) = v0)) % 52.10/7.90 | | | | | | | | % 52.10/7.90 | | | | | | | | DELTA: instantiating (85) with fresh symbol all_256_0 gives: % 52.10/7.90 | | | | | | | | (87) implies(all_14_4, all_14_2) = all_256_0 & % 52.10/7.90 | | | | | | | | is_a_theorem(all_256_0) = 0 & $i(all_256_0) % 52.10/7.90 | | | | | | | | % 52.10/7.90 | | | | | | | | ALPHA: (87) implies: % 52.10/7.90 | | | | | | | | (88) is_a_theorem(all_256_0) = 0 % 52.10/7.90 | | | | | | | | (89) implies(all_14_4, all_14_2) = all_256_0 % 52.10/7.90 | | | | | | | | % 52.10/7.91 | | | | | | | | DELTA: instantiating (86) with fresh symbols all_488_0, % 52.10/7.91 | | | | | | | | all_488_1, all_488_2 gives: % 52.10/7.91 | | | | | | | | (90) (all_488_0 = 0 & is_a_theorem(all_14_1) = 0) | ( ~ % 52.10/7.91 | | | | | | | | (all_488_1 = 0) & is_a_theorem(all_231_0) = all_488_1) % 52.10/7.91 | | | | | | | | | ( ~ (all_488_2 = 0) & is_a_theorem(all_231_1) = % 52.10/7.91 | | | | | | | | all_488_2) % 52.10/7.91 | | | | | | | | % 52.10/7.91 | | | | | | | | BETA: splitting (90) gives: % 52.10/7.91 | | | | | | | | % 52.10/7.91 | | | | | | | | Case 1: % 52.10/7.91 | | | | | | | | | % 52.10/7.91 | | | | | | | | | (91) all_488_0 = 0 & is_a_theorem(all_14_1) = 0 % 52.10/7.91 | | | | | | | | | % 52.10/7.91 | | | | | | | | | ALPHA: (91) implies: % 52.10/7.91 | | | | | | | | | (92) is_a_theorem(all_14_1) = 0 % 52.10/7.91 | | | | | | | | | % 52.10/7.91 | | | | | | | | | REF_CLOSE: (1), (15), (17), (92) are inconsistent by sub-proof % 52.10/7.91 | | | | | | | | | #1. % 52.10/7.91 | | | | | | | | | % 52.10/7.91 | | | | | | | | Case 2: % 52.10/7.91 | | | | | | | | | % 52.10/7.91 | | | | | | | | | (93) ( ~ (all_488_1 = 0) & is_a_theorem(all_231_0) = % 52.10/7.91 | | | | | | | | | all_488_1) | ( ~ (all_488_2 = 0) & % 52.10/7.91 | | | | | | | | | is_a_theorem(all_231_1) = all_488_2) % 52.10/7.91 | | | | | | | | | % 52.10/7.91 | | | | | | | | | BETA: splitting (93) gives: % 52.10/7.91 | | | | | | | | | % 52.10/7.91 | | | | | | | | | Case 1: % 52.10/7.91 | | | | | | | | | | % 52.10/7.91 | | | | | | | | | | (94) ~ (all_488_1 = 0) & is_a_theorem(all_231_0) = % 52.10/7.91 | | | | | | | | | | all_488_1 % 52.10/7.91 | | | | | | | | | | % 52.10/7.91 | | | | | | | | | | ALPHA: (94) implies: % 52.10/7.91 | | | | | | | | | | (95) ~ (all_488_1 = 0) % 52.10/7.91 | | | | | | | | | | (96) is_a_theorem(all_231_0) = all_488_1 % 52.10/7.91 | | | | | | | | | | % 52.10/7.91 | | | | | | | | | | GROUND_INST: instantiating (1) with 0, all_488_1, all_231_0, % 52.10/7.91 | | | | | | | | | | simplifying with (83), (96) gives: % 52.10/7.91 | | | | | | | | | | (97) all_488_1 = 0 % 52.10/7.91 | | | | | | | | | | % 52.10/7.91 | | | | | | | | | | REDUCE: (95), (97) imply: % 52.10/7.91 | | | | | | | | | | (98) $false % 52.10/7.91 | | | | | | | | | | % 52.10/7.91 | | | | | | | | | | CLOSE: (98) is inconsistent. % 52.10/7.91 | | | | | | | | | | % 52.10/7.91 | | | | | | | | | Case 2: % 52.10/7.91 | | | | | | | | | | % 52.10/7.91 | | | | | | | | | | % 52.10/7.91 | | | | | | | | | | GROUND_INST: instantiating (3) with all_14_1, all_256_0, % 52.10/7.91 | | | | | | | | | | all_14_2, all_14_4, simplifying with (18), (89) % 52.10/7.91 | | | | | | | | | | gives: % 52.10/7.91 | | | | | | | | | | (99) all_256_0 = all_14_1 % 52.10/7.91 | | | | | | | | | | % 52.10/7.91 | | | | | | | | | | REDUCE: (88), (99) imply: % 52.10/7.91 | | | | | | | | | | (100) is_a_theorem(all_14_1) = 0 % 52.10/7.91 | | | | | | | | | | % 52.10/7.91 | | | | | | | | | | REF_CLOSE: (1), (15), (17), (100) are inconsistent by % 52.10/7.91 | | | | | | | | | | sub-proof #1. % 52.10/7.91 | | | | | | | | | | % 52.10/7.91 | | | | | | | | | End of split % 52.10/7.91 | | | | | | | | | % 52.10/7.91 | | | | | | | | End of split % 52.10/7.91 | | | | | | | | % 52.10/7.91 | | | | | | | End of split % 52.10/7.91 | | | | | | | % 52.10/7.91 | | | | | | End of split % 52.10/7.91 | | | | | | % 52.10/7.91 | | | | | End of split % 52.10/7.91 | | | | | % 52.10/7.91 | | | | End of split % 52.10/7.91 | | | | % 52.10/7.91 | | | End of split % 52.10/7.91 | | | % 52.10/7.91 | | End of split % 52.10/7.91 | | % 52.10/7.91 | Case 2: % 52.10/7.91 | | % 52.10/7.91 | | (101) or_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = % 52.10/7.91 | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (implies(v0, v2) = % 52.10/7.91 | | v3 & is_a_theorem(v3) = 0 & $i(v3))) % 52.10/7.91 | | % 52.10/7.91 | | ALPHA: (101) implies: % 52.10/7.91 | | (102) or_1 % 52.10/7.91 | | % 52.10/7.91 | | PRED_UNIFY: (102), (hilbert_or_1) imply: % 52.10/7.91 | | (103) $false % 52.10/7.91 | | % 52.10/7.91 | | CLOSE: (103) is inconsistent. % 52.10/7.91 | | % 52.10/7.91 | End of split % 52.10/7.91 | % 52.10/7.91 End of proof % 52.10/7.91 % 52.10/7.91 Sub-proof #1 shows that the following formulas are inconsistent: % 52.10/7.91 ---------------------------------------------------------------- % 52.10/7.91 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 52.10/7.91 (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) % 52.10/7.91 (2) is_a_theorem(all_14_1) = all_14_0 % 52.10/7.91 (3) is_a_theorem(all_14_1) = 0 % 52.10/7.91 (4) ~ (all_14_0 = 0) % 52.10/7.91 % 52.10/7.91 Begin of proof % 52.10/7.91 | % 52.10/7.92 | GROUND_INST: instantiating (1) with all_14_0, 0, all_14_1, simplifying with % 52.10/7.92 | (2), (3) gives: % 52.10/7.92 | (5) all_14_0 = 0 % 52.10/7.92 | % 52.10/7.92 | REDUCE: (4), (5) imply: % 52.10/7.92 | (6) $false % 52.10/7.92 | % 52.10/7.92 | CLOSE: (6) is inconsistent. % 52.10/7.92 | % 52.10/7.92 End of proof % 52.10/7.92 % SZS output end Proof for theBenchmark % 52.10/7.92 % 52.10/7.92 7370ms %------------------------------------------------------------------------------