%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL512+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 : n006.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 12:54:16 PM UTC 2026 % Result : Theorem 14.24s 2.67s % Output : Proof 21.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL512+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.35 % Computer : n006.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 17:14:01 UTC 2026 % 0.13/0.36 % CPUTime : % 0.13/0.37 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.70/0.70 ________ _____ % 0.70/0.70 ___ __ \_________(_)________________________________ % 0.70/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.70/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.70/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.70/0.70 % 0.70/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.70/0.70 (2023-06-19) % 0.70/0.70 % 0.70/0.70 (c) Philipp Rümmer, 2009-2023 % 0.70/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.70/0.70 Amanda Stjerna. % 0.70/0.71 Free software under BSD-3-Clause. % 0.70/0.71 % 0.70/0.71 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.70/0.71 % 0.70/0.71 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.73 Running up to 7 provers in parallel. % 0.70/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.09/1.32 Prover 4: Preprocessing ... % 4.09/1.32 Prover 1: Preprocessing ... % 4.09/1.39 Prover 3: Preprocessing ... % 4.09/1.39 Prover 5: Preprocessing ... % 4.09/1.39 Prover 6: Preprocessing ... % 4.09/1.39 Prover 0: Preprocessing ... % 4.09/1.39 Prover 2: Preprocessing ... % 11.07/2.26 Prover 5: Proving ... % 11.07/2.28 Prover 6: Constructing countermodel ... % 11.87/2.31 Prover 1: Constructing countermodel ... % 11.87/2.32 Prover 3: Constructing countermodel ... % 11.87/2.33 Prover 4: Constructing countermodel ... % 12.65/2.43 Prover 0: Proving ... % 12.65/2.46 Prover 2: Proving ... % 14.24/2.66 Prover 5: proved (1919ms) % 14.24/2.66 % 14.24/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.24/2.67 % 14.24/2.67 Prover 6: stopped % 14.24/2.67 Prover 0: stopped % 14.24/2.68 Prover 2: stopped % 14.24/2.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.24/2.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.24/2.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.24/2.69 Prover 3: stopped % 14.24/2.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.24/2.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.02/2.78 Prover 13: Preprocessing ... % 15.02/2.80 Prover 8: Preprocessing ... % 15.80/2.81 Prover 10: Preprocessing ... % 15.80/2.82 Prover 7: Preprocessing ... % 15.80/2.82 Prover 11: Preprocessing ... % 17.90/3.09 Prover 7: Constructing countermodel ... % 17.90/3.09 Prover 8: Warning: ignoring some quantifiers % 17.90/3.15 Prover 8: Constructing countermodel ... % 17.90/3.16 Prover 13: Constructing countermodel ... % 18.97/3.26 Prover 10: Constructing countermodel ... % 19.77/3.36 Prover 4: Found proof (size 65) % 19.77/3.36 Prover 4: proved (2620ms) % 19.77/3.37 Prover 8: stopped % 19.77/3.37 Prover 7: stopped % 19.77/3.37 Prover 10: stopped % 19.77/3.37 Prover 13: stopped % 19.77/3.37 Prover 1: stopped % 19.77/3.37 Prover 11: Constructing countermodel ... % 19.77/3.38 Prover 11: stopped % 19.77/3.38 % 19.77/3.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.77/3.38 % 20.49/3.40 % SZS output start Proof for theBenchmark % 20.49/3.41 Assumptions after simplification: % 20.49/3.41 --------------------------------- % 20.49/3.41 % 20.49/3.41 (equivalence_1) % 20.49/3.47 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 20.49/3.47 int] : ($i(v1) & $i(v0) & (( ~ (v5 = 0) & equiv(v0, v1) = v2 & implies(v2, % 20.49/3.47 v3) = v4 & implies(v0, v1) = v3 & is_a_theorem(v4) = v5 & $i(v4) & % 20.49/3.47 $i(v3) & $i(v2) & ~ equivalence_1) | (equivalence_1 & ! [v6: $i] : ! % 20.49/3.47 [v7: $i] : ! [v8: $i] : ( ~ (equiv(v6, v7) = v8) | ~ $i(v7) | ~ % 20.49/3.47 $i(v6) | ? [v9: $i] : ? [v10: $i] : (implies(v8, v9) = v10 & % 20.49/3.47 implies(v6, v7) = v9 & is_a_theorem(v10) = 0 & $i(v10) & $i(v9))) & % 20.49/3.47 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (implies(v6, v7) = v8) | ~ % 20.49/3.47 $i(v7) | ~ $i(v6) | ? [v9: $i] : ? [v10: $i] : (equiv(v6, v7) = v9 % 20.49/3.47 & implies(v9, v8) = v10 & is_a_theorem(v10) = 0 & $i(v10) & % 20.49/3.48 $i(v9)))))) % 20.49/3.48 % 20.49/3.48 (hilbert_equivalence_1) % 20.49/3.48 ~ equivalence_1 % 20.49/3.48 % 20.49/3.48 (hilbert_op_equiv) % 20.49/3.48 op_equiv % 20.49/3.48 % 20.49/3.48 (kn2) % 20.49/3.48 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ($i(v1) % 20.49/3.48 & $i(v0) & (( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, v0) = v3 & % 20.49/3.48 is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & ~ kn2) | (kn2 & ! [v5: $i] : % 20.49/3.48 ! [v6: $i] : ! [v7: $i] : ( ~ (and(v5, v6) = v7) | ~ $i(v6) | ~ % 20.49/3.48 $i(v5) | ? [v8: $i] : (implies(v7, v5) = v8 & is_a_theorem(v8) = 0 & % 20.49/3.48 $i(v8)))))) % 20.49/3.48 % 20.49/3.48 (modus_ponens) % 20.49/3.49 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? % 20.49/3.49 [v5: int] : ($i(v1) & $i(v0) & ((v4 = 0 & v2 = 0 & ~ (v5 = 0) & implies(v0, % 20.49/3.49 v1) = v3 & is_a_theorem(v3) = 0 & is_a_theorem(v1) = v5 & % 20.49/3.49 is_a_theorem(v0) = 0 & $i(v3) & ~ modus_ponens) | (modus_ponens & ! % 20.49/3.49 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (implies(v6, v7) = v8) | ~ % 20.49/3.49 $i(v7) | ~ $i(v6) | ? [v9: any] : ? [v10: any] : ? [v11: any] : % 20.49/3.49 (is_a_theorem(v8) = v10 & is_a_theorem(v7) = v11 & is_a_theorem(v6) = % 20.49/3.49 v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0)))))) % 20.49/3.49 % 20.49/3.49 (op_equiv) % 20.95/3.50 ~ op_equiv | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (equiv(v0, v1) = % 20.95/3.50 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (and(v3, v4) = % 20.95/3.50 v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3 & $i(v4) & $i(v3) & % 20.95/3.50 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v1, % 20.95/3.50 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 20.95/3.50 (and(v4, v2) = v3 & equiv(v0, v1) = v3 & implies(v0, v1) = v4 & $i(v4) & % 20.95/3.50 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, % 20.95/3.50 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 20.95/3.50 (and(v2, v4) = v3 & equiv(v0, v1) = v3 & implies(v1, v0) = v4 & $i(v4) & % 20.95/3.50 $i(v3)))) % 20.95/3.50 % 20.95/3.50 (rosser_kn2) % 20.95/3.50 kn2 % 20.95/3.50 % 20.95/3.50 (rosser_modus_ponens) % 20.95/3.50 modus_ponens % 20.95/3.50 % 20.95/3.50 (rosser_op_equiv) % 20.95/3.50 op_equiv % 20.95/3.50 % 20.95/3.50 (substitution_of_equivalents) % 20.95/3.50 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ($i(v1) & $i(v0) & % 20.95/3.50 ((v3 = 0 & ~ (v1 = v0) & equiv(v0, v1) = v2 & is_a_theorem(v2) = 0 & $i(v2) % 20.95/3.50 & ~ substitution_of_equivalents) | (substitution_of_equivalents & ! % 20.95/3.50 [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v5 = v4 | ~ (equiv(v4, v5) = % 20.95/3.50 v6) | ~ $i(v5) | ~ $i(v4) | ? [v7: int] : ( ~ (v7 = 0) & % 20.95/3.50 is_a_theorem(v6) = v7))))) % 20.95/3.50 % 20.95/3.50 (use_substitution_of_equivalents) % 20.95/3.50 substitution_of_equivalents % 20.95/3.50 % 20.95/3.50 (function-axioms) % 20.95/3.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3, % 20.95/3.51 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.95/3.51 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = % 20.95/3.51 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 20.95/3.51 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 20.95/3.51 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ % 20.95/3.51 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 20.95/3.51 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 20.95/3.51 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_a_theorem(v2) = v1) % 20.95/3.51 | ~ (is_a_theorem(v2) = v0)) % 20.95/3.51 % 20.95/3.51 Further assumptions not needed in the proof: % 20.95/3.51 -------------------------------------------- % 20.95/3.51 and_1, and_2, and_3, cn1, cn2, cn3, equivalence_2, equivalence_3, % 20.95/3.51 hilbert_op_implies_and, hilbert_op_or, implies_1, implies_2, implies_3, kn1, % 20.95/3.51 kn3, modus_tollens, op_and, op_implies_and, op_implies_or, op_or, or_1, or_2, % 20.95/3.51 or_3, r1, r2, r3, r4, r5, rosser_kn1, rosser_kn3, rosser_op_implies_and, % 20.95/3.51 rosser_op_or % 20.95/3.51 % 20.95/3.51 Those formulas are unsatisfiable: % 20.95/3.51 --------------------------------- % 20.95/3.51 % 20.95/3.51 Begin of proof % 20.95/3.51 | % 20.95/3.51 | ALPHA: (function-axioms) implies: % 20.95/3.52 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.95/3.52 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) % 20.95/3.52 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.95/3.52 | (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0)) % 20.95/3.52 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.95/3.52 | (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) % 20.95/3.52 | % 20.95/3.52 | DELTA: instantiating (substitution_of_equivalents) with fresh symbols all_8_0, % 20.95/3.52 | all_8_1, all_8_2, all_8_3 gives: % 20.95/3.52 | (4) $i(all_8_2) & $i(all_8_3) & ((all_8_0 = 0 & ~ (all_8_2 = all_8_3) & % 20.95/3.52 | equiv(all_8_3, all_8_2) = all_8_1 & is_a_theorem(all_8_1) = 0 & % 20.95/3.52 | $i(all_8_1) & ~ substitution_of_equivalents) | % 20.95/3.52 | (substitution_of_equivalents & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.95/3.52 | $i] : (v1 = v0 | ~ (equiv(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 20.95/3.52 | | ? [v3: int] : ( ~ (v3 = 0) & is_a_theorem(v2) = v3)))) % 20.95/3.52 | % 20.95/3.52 | ALPHA: (4) implies: % 20.95/3.52 | (5) (all_8_0 = 0 & ~ (all_8_2 = all_8_3) & equiv(all_8_3, all_8_2) = % 20.95/3.52 | all_8_1 & is_a_theorem(all_8_1) = 0 & $i(all_8_1) & ~ % 20.95/3.52 | substitution_of_equivalents) | (substitution_of_equivalents & ! [v0: % 20.95/3.52 | $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (equiv(v0, v1) = % 20.95/3.52 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 20.95/3.53 | is_a_theorem(v2) = v3))) % 20.95/3.53 | % 20.95/3.53 | DELTA: instantiating (kn2) with fresh symbols all_20_0, all_20_1, all_20_2, % 20.95/3.53 | all_20_3, all_20_4 gives: % 20.95/3.53 | (6) $i(all_20_3) & $i(all_20_4) & (( ~ (all_20_0 = 0) & and(all_20_4, % 20.95/3.53 | all_20_3) = all_20_2 & implies(all_20_2, all_20_4) = all_20_1 & % 20.95/3.53 | is_a_theorem(all_20_1) = all_20_0 & $i(all_20_1) & $i(all_20_2) & % 20.95/3.53 | ~ kn2) | (kn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 20.95/3.53 | (and(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 20.95/3.53 | (implies(v2, v0) = v3 & is_a_theorem(v3) = 0 & $i(v3))))) % 20.95/3.53 | % 20.95/3.53 | ALPHA: (6) implies: % 20.95/3.53 | (7) ( ~ (all_20_0 = 0) & and(all_20_4, all_20_3) = all_20_2 & % 20.95/3.53 | implies(all_20_2, all_20_4) = all_20_1 & is_a_theorem(all_20_1) = % 20.95/3.53 | all_20_0 & $i(all_20_1) & $i(all_20_2) & ~ kn2) | (kn2 & ! [v0: $i] % 20.95/3.53 | : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = v2) | ~ $i(v1) | ~ % 20.95/3.53 | $i(v0) | ? [v3: $i] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0 % 20.95/3.53 | & $i(v3)))) % 20.95/3.53 | % 20.95/3.53 | DELTA: instantiating (modus_ponens) with fresh symbols all_32_0, all_32_1, % 20.95/3.53 | all_32_2, all_32_3, all_32_4, all_32_5 gives: % 20.95/3.53 | (8) $i(all_32_4) & $i(all_32_5) & ((all_32_1 = 0 & all_32_3 = 0 & ~ % 20.95/3.53 | (all_32_0 = 0) & implies(all_32_5, all_32_4) = all_32_2 & % 20.95/3.53 | is_a_theorem(all_32_2) = 0 & is_a_theorem(all_32_4) = all_32_0 & % 20.95/3.53 | is_a_theorem(all_32_5) = 0 & $i(all_32_2) & ~ modus_ponens) | % 20.95/3.53 | (modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 20.95/3.53 | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 20.95/3.53 | ? [v4: any] : ? [v5: any] : (is_a_theorem(v2) = v4 & % 20.95/3.53 | is_a_theorem(v1) = v5 & is_a_theorem(v0) = v3 & ( ~ (v4 = 0) | % 20.95/3.53 | ~ (v3 = 0) | v5 = 0))))) % 20.95/3.53 | % 20.95/3.53 | ALPHA: (8) implies: % 20.95/3.54 | (9) (all_32_1 = 0 & all_32_3 = 0 & ~ (all_32_0 = 0) & implies(all_32_5, % 20.95/3.54 | all_32_4) = all_32_2 & is_a_theorem(all_32_2) = 0 & % 20.95/3.54 | is_a_theorem(all_32_4) = all_32_0 & is_a_theorem(all_32_5) = 0 & % 20.95/3.54 | $i(all_32_2) & ~ modus_ponens) | (modus_ponens & ! [v0: $i] : ! % 20.95/3.54 | [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ % 20.95/3.54 | $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 20.95/3.54 | (is_a_theorem(v2) = v4 & is_a_theorem(v1) = v5 & is_a_theorem(v0) = % 20.95/3.54 | v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))) % 20.95/3.54 | % 20.95/3.54 | DELTA: instantiating (equivalence_1) with fresh symbols all_42_0, all_42_1, % 20.95/3.54 | all_42_2, all_42_3, all_42_4, all_42_5 gives: % 20.95/3.54 | (10) $i(all_42_4) & $i(all_42_5) & (( ~ (all_42_0 = 0) & equiv(all_42_5, % 20.95/3.54 | all_42_4) = all_42_3 & implies(all_42_3, all_42_2) = all_42_1 & % 20.95/3.54 | implies(all_42_5, all_42_4) = all_42_2 & is_a_theorem(all_42_1) = % 20.95/3.54 | all_42_0 & $i(all_42_1) & $i(all_42_2) & $i(all_42_3) & ~ % 20.95/3.54 | equivalence_1) | (equivalence_1 & ! [v0: $i] : ! [v1: $i] : ! % 20.95/3.54 | [v2: $i] : ( ~ (equiv(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 20.95/3.54 | [v3: $i] : ? [v4: $i] : (implies(v2, v3) = v4 & implies(v0, v1) % 20.95/3.54 | = v3 & is_a_theorem(v4) = 0 & $i(v4) & $i(v3))) & ! [v0: $i] % 20.95/3.54 | : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ % 20.95/3.54 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (equiv(v0, v1) % 20.95/3.54 | = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0 & $i(v4) & % 20.95/3.54 | $i(v3))))) % 20.95/3.54 | % 20.95/3.54 | ALPHA: (10) implies: % 20.95/3.54 | (11) $i(all_42_5) % 20.95/3.54 | (12) $i(all_42_4) % 20.95/3.55 | (13) ( ~ (all_42_0 = 0) & equiv(all_42_5, all_42_4) = all_42_3 & % 20.95/3.55 | implies(all_42_3, all_42_2) = all_42_1 & implies(all_42_5, all_42_4) % 20.95/3.55 | = all_42_2 & is_a_theorem(all_42_1) = all_42_0 & $i(all_42_1) & % 20.95/3.55 | $i(all_42_2) & $i(all_42_3) & ~ equivalence_1) | (equivalence_1 & % 20.95/3.55 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (equiv(v0, v1) = v2) | % 20.95/3.55 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (implies(v2, % 20.95/3.55 | v3) = v4 & implies(v0, v1) = v3 & is_a_theorem(v4) = 0 & % 20.95/3.55 | $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( % 20.95/3.55 | ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 20.95/3.55 | ? [v4: $i] : (equiv(v0, v1) = v3 & implies(v3, v2) = v4 & % 20.95/3.55 | is_a_theorem(v4) = 0 & $i(v4) & $i(v3)))) % 20.95/3.55 | % 20.95/3.55 | BETA: splitting (13) gives: % 20.95/3.55 | % 20.95/3.55 | Case 1: % 20.95/3.55 | | % 20.95/3.55 | | (14) ~ (all_42_0 = 0) & equiv(all_42_5, all_42_4) = all_42_3 & % 20.95/3.55 | | implies(all_42_3, all_42_2) = all_42_1 & implies(all_42_5, all_42_4) % 20.95/3.55 | | = all_42_2 & is_a_theorem(all_42_1) = all_42_0 & $i(all_42_1) & % 20.95/3.55 | | $i(all_42_2) & $i(all_42_3) & ~ equivalence_1 % 20.95/3.55 | | % 20.95/3.55 | | ALPHA: (14) implies: % 20.95/3.55 | | (15) ~ (all_42_0 = 0) % 20.95/3.55 | | (16) $i(all_42_3) % 20.95/3.55 | | (17) $i(all_42_2) % 20.95/3.55 | | (18) is_a_theorem(all_42_1) = all_42_0 % 20.95/3.55 | | (19) implies(all_42_5, all_42_4) = all_42_2 % 20.95/3.55 | | (20) implies(all_42_3, all_42_2) = all_42_1 % 20.95/3.55 | | (21) equiv(all_42_5, all_42_4) = all_42_3 % 20.95/3.55 | | % 20.95/3.55 | | BETA: splitting (7) gives: % 20.95/3.55 | | % 20.95/3.55 | | Case 1: % 20.95/3.55 | | | % 20.95/3.55 | | | (22) ~ (all_20_0 = 0) & and(all_20_4, all_20_3) = all_20_2 & % 20.95/3.55 | | | implies(all_20_2, all_20_4) = all_20_1 & is_a_theorem(all_20_1) = % 20.95/3.55 | | | all_20_0 & $i(all_20_1) & $i(all_20_2) & ~ kn2 % 20.95/3.55 | | | % 20.95/3.55 | | | ALPHA: (22) implies: % 20.95/3.56 | | | (23) ~ kn2 % 20.95/3.56 | | | % 20.95/3.56 | | | PRED_UNIFY: (23), (rosser_kn2) imply: % 20.95/3.56 | | | (24) $false % 20.95/3.56 | | | % 20.95/3.56 | | | CLOSE: (24) is inconsistent. % 20.95/3.56 | | | % 20.95/3.56 | | Case 2: % 20.95/3.56 | | | % 20.95/3.56 | | | (25) kn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = % 20.95/3.56 | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (implies(v2, v0) = % 20.95/3.56 | | | v3 & is_a_theorem(v3) = 0 & $i(v3))) % 20.95/3.56 | | | % 20.95/3.56 | | | ALPHA: (25) implies: % 20.95/3.56 | | | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (and(v0, v1) = v2) | % 20.95/3.56 | | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (implies(v2, v0) = v3 & % 20.95/3.56 | | | is_a_theorem(v3) = 0 & $i(v3))) % 20.95/3.56 | | | % 20.95/3.56 | | | BETA: splitting (9) gives: % 20.95/3.56 | | | % 20.95/3.56 | | | Case 1: % 20.95/3.56 | | | | % 20.95/3.56 | | | | (27) all_32_1 = 0 & all_32_3 = 0 & ~ (all_32_0 = 0) & % 20.95/3.56 | | | | implies(all_32_5, all_32_4) = all_32_2 & is_a_theorem(all_32_2) % 20.95/3.56 | | | | = 0 & is_a_theorem(all_32_4) = all_32_0 & is_a_theorem(all_32_5) % 20.95/3.56 | | | | = 0 & $i(all_32_2) & ~ modus_ponens % 20.95/3.56 | | | | % 20.95/3.56 | | | | ALPHA: (27) implies: % 20.95/3.56 | | | | (28) ~ modus_ponens % 20.95/3.56 | | | | % 20.95/3.56 | | | | PRED_UNIFY: (28), (rosser_modus_ponens) imply: % 20.95/3.56 | | | | (29) $false % 20.95/3.56 | | | | % 20.95/3.56 | | | | CLOSE: (29) is inconsistent. % 20.95/3.56 | | | | % 20.95/3.56 | | | Case 2: % 20.95/3.56 | | | | % 20.95/3.57 | | | | (30) modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 20.95/3.57 | | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] % 20.95/3.57 | | | | : ? [v4: any] : ? [v5: any] : (is_a_theorem(v2) = v4 & % 20.95/3.57 | | | | is_a_theorem(v1) = v5 & is_a_theorem(v0) = v3 & ( ~ (v4 = 0) % 20.95/3.57 | | | | | ~ (v3 = 0) | v5 = 0))) % 20.95/3.57 | | | | % 20.95/3.57 | | | | ALPHA: (30) implies: % 20.95/3.57 | | | | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = % 20.95/3.57 | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 20.95/3.57 | | | | ? [v5: any] : (is_a_theorem(v2) = v4 & is_a_theorem(v1) = v5 & % 20.95/3.57 | | | | is_a_theorem(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = % 20.95/3.57 | | | | 0))) % 20.95/3.57 | | | | % 20.95/3.57 | | | | BETA: splitting (op_equiv) gives: % 20.95/3.57 | | | | % 20.95/3.57 | | | | Case 1: % 20.95/3.57 | | | | | % 20.95/3.57 | | | | | (32) ~ op_equiv % 20.95/3.57 | | | | | % 20.95/3.57 | | | | | PRED_UNIFY: (32), (rosser_op_equiv) imply: % 20.95/3.57 | | | | | (33) $false % 20.95/3.57 | | | | | % 20.95/3.57 | | | | | CLOSE: (33) is inconsistent. % 20.95/3.57 | | | | | % 20.95/3.57 | | | | Case 2: % 20.95/3.57 | | | | | % 20.95/3.57 | | | | | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (equiv(v0, v1) = % 20.95/3.57 | | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 20.95/3.57 | | | | | (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = % 20.95/3.57 | | | | | v3 & $i(v4) & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: % 20.95/3.57 | | | | | $i] : ! [v2: $i] : ( ~ (implies(v1, v0) = v2) | ~ $i(v1) | % 20.95/3.57 | | | | | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (and(v4, v2) = v3 & % 20.95/3.57 | | | | | equiv(v0, v1) = v3 & implies(v0, v1) = v4 & $i(v4) & % 20.95/3.57 | | | | | $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 20.95/3.57 | | | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 20.95/3.57 | | | | | : ? [v4: $i] : (and(v2, v4) = v3 & equiv(v0, v1) = v3 & % 20.95/3.57 | | | | | implies(v1, v0) = v4 & $i(v4) & $i(v3))) % 20.95/3.57 | | | | | % 20.95/3.57 | | | | | ALPHA: (34) implies: % 20.95/3.58 | | | | | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) % 20.95/3.58 | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] % 20.95/3.58 | | | | | : (and(v2, v4) = v3 & equiv(v0, v1) = v3 & implies(v1, v0) = % 20.95/3.58 | | | | | v4 & $i(v4) & $i(v3))) % 20.95/3.58 | | | | | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v1, v0) % 20.95/3.58 | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] % 20.95/3.58 | | | | | : (and(v4, v2) = v3 & equiv(v0, v1) = v3 & implies(v0, v1) = % 20.95/3.58 | | | | | v4 & $i(v4) & $i(v3))) % 20.95/3.58 | | | | | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (equiv(v0, v1) = % 20.95/3.58 | | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 20.95/3.58 | | | | | (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = % 20.95/3.58 | | | | | v3 & $i(v4) & $i(v3) & $i(v2))) % 20.95/3.58 | | | | | % 20.95/3.58 | | | | | BETA: splitting (5) gives: % 20.95/3.58 | | | | | % 20.95/3.58 | | | | | Case 1: % 20.95/3.58 | | | | | | % 20.95/3.58 | | | | | | (38) all_8_0 = 0 & ~ (all_8_2 = all_8_3) & equiv(all_8_3, % 20.95/3.58 | | | | | | all_8_2) = all_8_1 & is_a_theorem(all_8_1) = 0 & % 20.95/3.58 | | | | | | $i(all_8_1) & ~ substitution_of_equivalents % 20.95/3.58 | | | | | | % 20.95/3.58 | | | | | | ALPHA: (38) implies: % 20.95/3.58 | | | | | | (39) ~ substitution_of_equivalents % 20.95/3.58 | | | | | | % 20.95/3.58 | | | | | | PRED_UNIFY: (39), (use_substitution_of_equivalents) imply: % 20.95/3.58 | | | | | | (40) $false % 20.95/3.58 | | | | | | % 20.95/3.58 | | | | | | CLOSE: (40) is inconsistent. % 20.95/3.58 | | | | | | % 20.95/3.58 | | | | | Case 2: % 20.95/3.58 | | | | | | % 20.95/3.58 | | | | | | % 20.95/3.59 | | | | | | GROUND_INST: instantiating (36) with all_42_4, all_42_5, all_42_2, % 20.95/3.59 | | | | | | simplifying with (11), (12), (19) gives: % 20.95/3.59 | | | | | | (41) ? [v0: $i] : ? [v1: $i] : (and(v1, all_42_2) = v0 & % 20.95/3.59 | | | | | | equiv(all_42_4, all_42_5) = v0 & implies(all_42_4, % 20.95/3.59 | | | | | | all_42_5) = v1 & $i(v1) & $i(v0)) % 20.95/3.59 | | | | | | % 20.95/3.59 | | | | | | GROUND_INST: instantiating (35) with all_42_5, all_42_4, all_42_2, % 20.95/3.59 | | | | | | simplifying with (11), (12), (19) gives: % 20.95/3.59 | | | | | | (42) ? [v0: $i] : ? [v1: $i] : (and(all_42_2, v1) = v0 & % 20.95/3.59 | | | | | | equiv(all_42_5, all_42_4) = v0 & implies(all_42_4, % 20.95/3.59 | | | | | | all_42_5) = v1 & $i(v1) & $i(v0)) % 20.95/3.59 | | | | | | % 20.95/3.59 | | | | | | GROUND_INST: instantiating (31) with all_42_3, all_42_2, all_42_1, % 20.95/3.59 | | | | | | simplifying with (16), (17), (20) gives: % 20.95/3.59 | | | | | | (43) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 20.95/3.59 | | | | | | (is_a_theorem(all_42_1) = v1 & is_a_theorem(all_42_2) = v2 & % 20.95/3.59 | | | | | | is_a_theorem(all_42_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | % 20.95/3.59 | | | | | | v2 = 0)) % 20.95/3.59 | | | | | | % 20.95/3.59 | | | | | | GROUND_INST: instantiating (37) with all_42_5, all_42_4, all_42_3, % 20.95/3.59 | | | | | | simplifying with (11), (12), (21) gives: % 20.95/3.59 | | | | | | (44) ? [v0: $i] : ? [v1: $i] : (and(v0, v1) = all_42_3 & % 20.95/3.59 | | | | | | implies(all_42_4, all_42_5) = v1 & implies(all_42_5, % 20.95/3.59 | | | | | | all_42_4) = v0 & $i(v1) & $i(v0) & $i(all_42_3)) % 20.95/3.59 | | | | | | % 20.95/3.59 | | | | | | DELTA: instantiating (42) with fresh symbols all_100_0, all_100_1 % 20.95/3.59 | | | | | | gives: % 20.95/3.60 | | | | | | (45) and(all_42_2, all_100_0) = all_100_1 & equiv(all_42_5, % 20.95/3.60 | | | | | | all_42_4) = all_100_1 & implies(all_42_4, all_42_5) = % 20.95/3.60 | | | | | | all_100_0 & $i(all_100_0) & $i(all_100_1) % 20.95/3.60 | | | | | | % 20.95/3.60 | | | | | | ALPHA: (45) implies: % 21.45/3.60 | | | | | | (46) implies(all_42_4, all_42_5) = all_100_0 % 21.45/3.60 | | | | | | (47) equiv(all_42_5, all_42_4) = all_100_1 % 21.45/3.60 | | | | | | (48) and(all_42_2, all_100_0) = all_100_1 % 21.45/3.60 | | | | | | % 21.45/3.60 | | | | | | DELTA: instantiating (41) with fresh symbols all_102_0, all_102_1 % 21.45/3.60 | | | | | | gives: % 21.45/3.60 | | | | | | (49) and(all_102_0, all_42_2) = all_102_1 & equiv(all_42_4, % 21.45/3.60 | | | | | | all_42_5) = all_102_1 & implies(all_42_4, all_42_5) = % 21.45/3.60 | | | | | | all_102_0 & $i(all_102_0) & $i(all_102_1) % 21.45/3.60 | | | | | | % 21.45/3.60 | | | | | | ALPHA: (49) implies: % 21.45/3.60 | | | | | | (50) $i(all_102_0) % 21.45/3.60 | | | | | | (51) implies(all_42_4, all_42_5) = all_102_0 % 21.45/3.60 | | | | | | % 21.45/3.60 | | | | | | DELTA: instantiating (43) with fresh symbols all_108_0, all_108_1, % 21.45/3.60 | | | | | | all_108_2 gives: % 21.45/3.60 | | | | | | (52) is_a_theorem(all_42_1) = all_108_1 & is_a_theorem(all_42_2) % 21.45/3.60 | | | | | | = all_108_0 & is_a_theorem(all_42_3) = all_108_2 & ( ~ % 21.45/3.60 | | | | | | (all_108_1 = 0) | ~ (all_108_2 = 0) | all_108_0 = 0) % 21.45/3.60 | | | | | | % 21.45/3.60 | | | | | | ALPHA: (52) implies: % 21.45/3.60 | | | | | | (53) is_a_theorem(all_42_1) = all_108_1 % 21.45/3.60 | | | | | | % 21.45/3.60 | | | | | | DELTA: instantiating (44) with fresh symbols all_112_0, all_112_1 % 21.45/3.60 | | | | | | gives: % 21.45/3.60 | | | | | | (54) and(all_112_1, all_112_0) = all_42_3 & implies(all_42_4, % 21.45/3.60 | | | | | | all_42_5) = all_112_0 & implies(all_42_5, all_42_4) = % 21.45/3.60 | | | | | | all_112_1 & $i(all_112_0) & $i(all_112_1) & $i(all_42_3) % 21.45/3.60 | | | | | | % 21.45/3.60 | | | | | | ALPHA: (54) implies: % 21.45/3.60 | | | | | | (55) $i(all_112_1) % 21.45/3.60 | | | | | | (56) implies(all_42_5, all_42_4) = all_112_1 % 21.45/3.60 | | | | | | (57) implies(all_42_4, all_42_5) = all_112_0 % 21.45/3.60 | | | | | | % 21.45/3.61 | | | | | | GROUND_INST: instantiating (1) with all_42_0, all_108_1, all_42_1, % 21.45/3.61 | | | | | | simplifying with (18), (53) gives: % 21.45/3.61 | | | | | | (58) all_108_1 = all_42_0 % 21.45/3.61 | | | | | | % 21.45/3.61 | | | | | | GROUND_INST: instantiating (2) with all_42_2, all_112_1, all_42_4, % 21.45/3.61 | | | | | | all_42_5, simplifying with (19), (56) gives: % 21.45/3.61 | | | | | | (59) all_112_1 = all_42_2 % 21.45/3.61 | | | | | | % 21.45/3.61 | | | | | | GROUND_INST: instantiating (2) with all_102_0, all_112_0, all_42_5, % 21.45/3.61 | | | | | | all_42_4, simplifying with (51), (57) gives: % 21.45/3.61 | | | | | | (60) all_112_0 = all_102_0 % 21.45/3.61 | | | | | | % 21.45/3.61 | | | | | | GROUND_INST: instantiating (2) with all_100_0, all_112_0, all_42_5, % 21.45/3.61 | | | | | | all_42_4, simplifying with (46), (57) gives: % 21.45/3.61 | | | | | | (61) all_112_0 = all_100_0 % 21.45/3.61 | | | | | | % 21.45/3.61 | | | | | | GROUND_INST: instantiating (3) with all_42_3, all_100_1, all_42_4, % 21.45/3.61 | | | | | | all_42_5, simplifying with (21), (47) gives: % 21.45/3.61 | | | | | | (62) all_100_1 = all_42_3 % 21.45/3.61 | | | | | | % 21.45/3.61 | | | | | | COMBINE_EQS: (60), (61) imply: % 21.45/3.61 | | | | | | (63) all_102_0 = all_100_0 % 21.45/3.61 | | | | | | % 21.45/3.61 | | | | | | SIMP: (63) implies: % 21.45/3.61 | | | | | | (64) all_102_0 = all_100_0 % 21.45/3.61 | | | | | | % 21.45/3.61 | | | | | | REDUCE: (48), (62) imply: % 21.45/3.61 | | | | | | (65) and(all_42_2, all_100_0) = all_42_3 % 21.45/3.61 | | | | | | % 21.45/3.61 | | | | | | REDUCE: (50), (64) imply: % 21.45/3.61 | | | | | | (66) $i(all_100_0) % 21.45/3.61 | | | | | | % 21.45/3.61 | | | | | | GROUND_INST: instantiating (26) with all_42_2, all_100_0, all_42_3, % 21.45/3.61 | | | | | | simplifying with (17), (65), (66) gives: % 21.45/3.61 | | | | | | (67) ? [v0: $i] : (implies(all_42_3, all_42_2) = v0 & % 21.45/3.61 | | | | | | is_a_theorem(v0) = 0 & $i(v0)) % 21.45/3.61 | | | | | | % 21.45/3.61 | | | | | | DELTA: instantiating (67) with fresh symbol all_150_0 gives: % 21.45/3.61 | | | | | | (68) implies(all_42_3, all_42_2) = all_150_0 & % 21.45/3.61 | | | | | | is_a_theorem(all_150_0) = 0 & $i(all_150_0) % 21.45/3.61 | | | | | | % 21.45/3.62 | | | | | | ALPHA: (68) implies: % 21.45/3.62 | | | | | | (69) is_a_theorem(all_150_0) = 0 % 21.45/3.62 | | | | | | (70) implies(all_42_3, all_42_2) = all_150_0 % 21.45/3.62 | | | | | | % 21.45/3.62 | | | | | | GROUND_INST: instantiating (2) with all_42_1, all_150_0, all_42_2, % 21.45/3.62 | | | | | | all_42_3, simplifying with (20), (70) gives: % 21.45/3.62 | | | | | | (71) all_150_0 = all_42_1 % 21.45/3.62 | | | | | | % 21.45/3.62 | | | | | | REDUCE: (69), (71) imply: % 21.45/3.62 | | | | | | (72) is_a_theorem(all_42_1) = 0 % 21.45/3.62 | | | | | | % 21.45/3.62 | | | | | | GROUND_INST: instantiating (1) with all_42_0, 0, all_42_1, % 21.45/3.62 | | | | | | simplifying with (18), (72) gives: % 21.45/3.62 | | | | | | (73) all_42_0 = 0 % 21.45/3.62 | | | | | | % 21.45/3.62 | | | | | | REDUCE: (15), (73) imply: % 21.45/3.62 | | | | | | (74) $false % 21.45/3.62 | | | | | | % 21.45/3.62 | | | | | | CLOSE: (74) is inconsistent. % 21.45/3.62 | | | | | | % 21.45/3.62 | | | | | End of split % 21.45/3.62 | | | | | % 21.45/3.62 | | | | End of split % 21.45/3.62 | | | | % 21.45/3.62 | | | End of split % 21.45/3.62 | | | % 21.45/3.62 | | End of split % 21.45/3.62 | | % 21.45/3.62 | Case 2: % 21.45/3.62 | | % 21.45/3.62 | | (75) equivalence_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 21.45/3.62 | | (equiv(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 21.45/3.62 | | [v4: $i] : (implies(v2, v3) = v4 & implies(v0, v1) = v3 & % 21.45/3.62 | | is_a_theorem(v4) = 0 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: % 21.45/3.62 | | $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ % 21.45/3.62 | | $i(v0) | ? [v3: $i] : ? [v4: $i] : (equiv(v0, v1) = v3 & % 21.45/3.62 | | implies(v3, v2) = v4 & is_a_theorem(v4) = 0 & $i(v4) & $i(v3))) % 21.45/3.62 | | % 21.45/3.62 | | ALPHA: (75) implies: % 21.45/3.62 | | (76) equivalence_1 % 21.45/3.62 | | % 21.45/3.62 | | PRED_UNIFY: (76), (hilbert_equivalence_1) imply: % 21.45/3.63 | | (77) $false % 21.45/3.63 | | % 21.45/3.63 | | CLOSE: (77) is inconsistent. % 21.45/3.63 | | % 21.45/3.63 | End of split % 21.45/3.63 | % 21.45/3.63 End of proof % 21.45/3.63 % SZS output end Proof for theBenchmark % 21.45/3.63 % 21.45/3.63 2918ms %------------------------------------------------------------------------------