%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL484+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 12:54:14 PM UTC 2026 % Result : Theorem 15.86s 2.81s % Output : Proof 23.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL484+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.37 % Computer : n018.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sat Sep 5 09:45:18 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.39 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. % 0.50/0.57 ________ _____ % 0.50/0.57 ___ __ \_________(_)________________________________ % 0.50/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.50/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.50/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.50/0.57 % 0.50/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.50/0.57 (2023-06-19) % 0.50/0.57 % 0.50/0.57 (c) Philipp Rümmer, 2009-2023 % 0.50/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.50/0.57 Amanda Stjerna. % 0.50/0.57 Free software under BSD-3-Clause. % 0.50/0.57 % 0.50/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.50/0.57 % 0.50/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.50/0.58 Running up to 7 provers in parallel. % 0.50/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.50/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.50/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.50/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.50/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.50/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.50/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.10/1.33 Prover 1: Preprocessing ... % 4.10/1.33 Prover 4: Preprocessing ... % 4.10/1.35 Prover 5: Preprocessing ... % 4.10/1.35 Prover 0: Preprocessing ... % 4.10/1.35 Prover 6: Preprocessing ... % 4.10/1.35 Prover 3: Preprocessing ... % 4.10/1.35 Prover 2: Preprocessing ... % 11.11/2.27 Prover 5: Proving ... % 11.91/2.30 Prover 1: Constructing countermodel ... % 11.91/2.33 Prover 6: Constructing countermodel ... % 11.91/2.38 Prover 3: Constructing countermodel ... % 12.67/2.42 Prover 0: Proving ... % 12.67/2.47 Prover 4: Constructing countermodel ... % 13.45/2.60 Prover 2: Proving ... % 15.86/2.81 Prover 0: proved (2222ms) % 15.86/2.81 % 15.86/2.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.86/2.81 % 15.86/2.81 Prover 3: stopped % 15.86/2.82 Prover 5: stopped % 15.86/2.82 Prover 6: stopped % 15.86/2.83 Prover 2: stopped % 15.86/2.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.86/2.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.86/2.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.86/2.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.86/2.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.59/2.91 Prover 7: Preprocessing ... % 16.59/2.99 Prover 10: Preprocessing ... % 16.59/3.00 Prover 11: Preprocessing ... % 16.59/3.01 Prover 13: Preprocessing ... % 16.59/3.01 Prover 8: Preprocessing ... % 18.95/3.27 Prover 7: Constructing countermodel ... % 18.95/3.30 Prover 13: Constructing countermodel ... % 19.76/3.40 Prover 10: Constructing countermodel ... % 20.53/3.44 Prover 11: Constructing countermodel ... % 20.53/3.46 Prover 8: Warning: ignoring some quantifiers % 21.33/3.50 Prover 8: Constructing countermodel ... % 21.33/3.53 Prover 1: gave up % 21.33/3.56 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 22.11/3.64 Prover 4: Found proof (size 52) % 22.11/3.64 Prover 4: proved (3058ms) % 22.11/3.64 Prover 8: stopped % 22.11/3.64 Prover 10: stopped % 22.11/3.65 Prover 11: stopped % 22.11/3.65 Prover 7: stopped % 22.11/3.65 Prover 16: Preprocessing ... % 22.11/3.65 Prover 13: stopped % 22.11/3.70 Prover 16: stopped % 22.11/3.70 % 22.11/3.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.11/3.70 % 22.75/3.70 % SZS output start Proof for theBenchmark % 22.75/3.71 Assumptions after simplification: % 22.75/3.71 --------------------------------- % 22.75/3.71 % 22.75/3.71 (hilbert_implies_1) % 22.75/3.71 ~ implies_1 % 22.75/3.71 % 22.75/3.71 (implies_1) % 22.75/3.74 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ($i(v1) % 22.75/3.74 & $i(v0) & (( ~ (v4 = 0) & implies(v1, v0) = v2 & implies(v0, v2) = v3 & % 22.75/3.74 is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & ~ implies_1) | (implies_1 & % 22.75/3.74 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (implies(v6, v5) = v7) | ~ % 22.75/3.74 $i(v6) | ~ $i(v5) | ? [v8: $i] : (implies(v5, v7) = v8 & % 22.75/3.74 is_a_theorem(v8) = 0 & $i(v8)))))) % 22.75/3.74 % 22.75/3.74 (modus_ponens) % 22.75/3.74 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? % 22.75/3.74 [v5: int] : ($i(v1) & $i(v0) & ((v4 = 0 & v2 = 0 & ~ (v5 = 0) & implies(v0, % 22.75/3.74 v1) = v3 & is_a_theorem(v3) = 0 & is_a_theorem(v1) = v5 & % 22.75/3.74 is_a_theorem(v0) = 0 & $i(v3) & ~ modus_ponens) | (modus_ponens & ! % 22.75/3.74 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (implies(v6, v7) = v8) | ~ % 22.75/3.74 $i(v7) | ~ $i(v6) | ? [v9: any] : ? [v10: any] : ? [v11: any] : % 22.75/3.74 (is_a_theorem(v8) = v10 & is_a_theorem(v7) = v11 & is_a_theorem(v6) = % 22.75/3.74 v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0)))))) % 22.75/3.74 % 22.75/3.74 (op_implies_or) % 22.75/3.74 ~ op_implies_or | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 22.75/3.74 ~ (or(v2, v1) = v3) | ~ (not(v0) = v2) | ~ $i(v1) | ~ $i(v0) | % 22.75/3.74 (implies(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 22.75/3.74 : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (or(v3, % 22.75/3.74 v1) = v2 & not(v0) = v3 & $i(v3) & $i(v2)))) % 22.75/3.74 % 22.75/3.74 (principia_modus_ponens) % 22.75/3.74 modus_ponens % 22.75/3.74 % 22.75/3.74 (principia_op_implies_or) % 22.75/3.74 op_implies_or % 22.75/3.74 % 22.75/3.74 (principia_r2) % 22.75/3.75 r2 % 22.75/3.75 % 22.75/3.75 (principia_r4) % 22.75/3.75 r4 % 22.75/3.75 % 22.75/3.75 (r2) % 22.75/3.75 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ($i(v1) % 22.75/3.75 & $i(v0) & (( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v1, v2) = v3 & % 22.75/3.75 is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & ~ r2) | (r2 & ! [v5: $i] : % 22.75/3.75 ! [v6: $i] : ! [v7: $i] : ( ~ (or(v5, v6) = v7) | ~ $i(v6) | ~ $i(v5) % 22.75/3.75 | ? [v8: $i] : (implies(v6, v7) = v8 & is_a_theorem(v8) = 0 & % 22.75/3.75 $i(v8)))))) % 22.75/3.75 % 22.75/3.75 (r4) % 22.75/3.75 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 22.75/3.75 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ($i(v2) & $i(v1) & $i(v0) & % 22.75/3.75 (( ~ (v8 = 0) & or(v1, v5) = v6 & or(v1, v2) = v3 & or(v0, v3) = v4 & or(v0, % 22.75/3.75 v2) = v5 & implies(v4, v6) = v7 & is_a_theorem(v7) = v8 & $i(v7) & % 22.75/3.75 $i(v6) & $i(v5) & $i(v4) & $i(v3) & ~ r4) | (r4 & ! [v9: $i] : ! % 22.75/3.75 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ (or(v10, % 22.75/3.75 v12) = v13) | ~ (or(v9, v11) = v12) | ~ $i(v11) | ~ $i(v10) | % 22.75/3.75 ~ $i(v9) | ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : (or(v10, v11) % 22.75/3.75 = v14 & or(v9, v14) = v15 & implies(v15, v13) = v16 & % 22.75/3.76 is_a_theorem(v16) = 0 & $i(v16) & $i(v15) & $i(v14))) & ! [v9: $i] % 22.75/3.76 : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ % 22.75/3.76 (or(v10, v11) = v12) | ~ (or(v9, v12) = v13) | ~ $i(v11) | ~ % 22.75/3.76 $i(v10) | ~ $i(v9) | ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : % 22.75/3.76 (or(v10, v14) = v15 & or(v9, v11) = v14 & implies(v13, v15) = v16 & % 22.75/3.76 is_a_theorem(v16) = 0 & $i(v16) & $i(v15) & $i(v14)))))) % 22.75/3.76 % 22.75/3.76 (function-axioms) % 22.75/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3, % 22.75/3.76 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 22.75/3.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = % 22.75/3.76 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 22.75/3.76 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 22.75/3.76 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ % 22.75/3.76 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 22.75/3.76 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 22.75/3.76 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_a_theorem(v2) = v1) % 22.75/3.76 | ~ (is_a_theorem(v2) = v0)) % 22.75/3.76 % 22.75/3.76 Further assumptions not needed in the proof: % 22.75/3.76 -------------------------------------------- % 22.75/3.76 and_1, and_2, and_3, cn1, cn2, cn3, equivalence_1, equivalence_2, equivalence_3, % 22.75/3.76 hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or, implies_2, implies_3, % 22.75/3.76 kn1, kn2, kn3, modus_tollens, op_and, op_equiv, op_implies_and, op_or, or_1, % 22.75/3.76 or_2, or_3, principia_op_and, principia_op_equiv, principia_r1, principia_r3, % 22.75/3.76 principia_r5, r1, r3, r5, substitution_of_equivalents, % 22.75/3.76 use_substitution_of_equivalents % 22.75/3.76 % 22.75/3.76 Those formulas are unsatisfiable: % 22.75/3.76 --------------------------------- % 22.75/3.76 % 22.75/3.76 Begin of proof % 22.75/3.76 | % 22.75/3.76 | ALPHA: (function-axioms) implies: % 22.75/3.76 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.75/3.76 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) % 22.75/3.76 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.75/3.76 | (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0)) % 22.75/3.76 | % 22.75/3.76 | DELTA: instantiating (r2) with fresh symbols all_18_0, all_18_1, all_18_2, % 22.75/3.76 | all_18_3, all_18_4 gives: % 22.75/3.77 | (3) $i(all_18_3) & $i(all_18_4) & (( ~ (all_18_0 = 0) & or(all_18_4, % 22.75/3.77 | all_18_3) = all_18_2 & implies(all_18_3, all_18_2) = all_18_1 & % 22.75/3.77 | is_a_theorem(all_18_1) = all_18_0 & $i(all_18_1) & $i(all_18_2) & % 22.75/3.77 | ~ r2) | (r2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, % 22.75/3.77 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 22.75/3.77 | (implies(v1, v2) = v3 & is_a_theorem(v3) = 0 & $i(v3))))) % 22.75/3.77 | % 22.75/3.77 | ALPHA: (3) implies: % 22.75/3.77 | (4) ( ~ (all_18_0 = 0) & or(all_18_4, all_18_3) = all_18_2 & % 22.75/3.77 | implies(all_18_3, all_18_2) = all_18_1 & is_a_theorem(all_18_1) = % 22.75/3.77 | all_18_0 & $i(all_18_1) & $i(all_18_2) & ~ r2) | (r2 & ! [v0: $i] : % 22.75/3.77 | ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2) | ~ $i(v1) | ~ % 22.75/3.77 | $i(v0) | ? [v3: $i] : (implies(v1, v2) = v3 & is_a_theorem(v3) = 0 % 22.75/3.77 | & $i(v3)))) % 22.75/3.77 | % 22.75/3.77 | DELTA: instantiating (implies_1) with fresh symbols all_20_0, all_20_1, % 22.75/3.77 | all_20_2, all_20_3, all_20_4 gives: % 22.75/3.77 | (5) $i(all_20_3) & $i(all_20_4) & (( ~ (all_20_0 = 0) & implies(all_20_3, % 22.75/3.77 | all_20_4) = all_20_2 & implies(all_20_4, all_20_2) = all_20_1 & % 22.75/3.77 | is_a_theorem(all_20_1) = all_20_0 & $i(all_20_1) & $i(all_20_2) & % 22.75/3.77 | ~ implies_1) | (implies_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 22.75/3.77 | : ( ~ (implies(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 22.75/3.77 | : (implies(v0, v2) = v3 & is_a_theorem(v3) = 0 & $i(v3))))) % 22.75/3.77 | % 22.75/3.77 | ALPHA: (5) implies: % 22.75/3.77 | (6) $i(all_20_4) % 22.75/3.77 | (7) $i(all_20_3) % 22.75/3.77 | (8) ( ~ (all_20_0 = 0) & implies(all_20_3, all_20_4) = all_20_2 & % 22.75/3.77 | implies(all_20_4, all_20_2) = all_20_1 & is_a_theorem(all_20_1) = % 22.75/3.77 | all_20_0 & $i(all_20_1) & $i(all_20_2) & ~ implies_1) | (implies_1 & % 22.75/3.77 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v1, v0) = v2) % 22.75/3.77 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (implies(v0, v2) = v3 & % 22.75/3.77 | is_a_theorem(v3) = 0 & $i(v3)))) % 22.75/3.77 | % 22.75/3.77 | DELTA: instantiating (modus_ponens) with fresh symbols all_32_0, all_32_1, % 22.75/3.77 | all_32_2, all_32_3, all_32_4, all_32_5 gives: % 22.75/3.78 | (9) $i(all_32_4) & $i(all_32_5) & ((all_32_1 = 0 & all_32_3 = 0 & ~ % 22.75/3.78 | (all_32_0 = 0) & implies(all_32_5, all_32_4) = all_32_2 & % 22.75/3.78 | is_a_theorem(all_32_2) = 0 & is_a_theorem(all_32_4) = all_32_0 & % 22.75/3.78 | is_a_theorem(all_32_5) = 0 & $i(all_32_2) & ~ modus_ponens) | % 22.75/3.78 | (modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 22.75/3.78 | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 22.75/3.78 | ? [v4: any] : ? [v5: any] : (is_a_theorem(v2) = v4 & % 22.75/3.78 | is_a_theorem(v1) = v5 & is_a_theorem(v0) = v3 & ( ~ (v4 = 0) | % 22.75/3.78 | ~ (v3 = 0) | v5 = 0))))) % 22.75/3.78 | % 22.75/3.78 | ALPHA: (9) implies: % 22.75/3.78 | (10) (all_32_1 = 0 & all_32_3 = 0 & ~ (all_32_0 = 0) & implies(all_32_5, % 22.75/3.78 | all_32_4) = all_32_2 & is_a_theorem(all_32_2) = 0 & % 22.75/3.78 | is_a_theorem(all_32_4) = all_32_0 & is_a_theorem(all_32_5) = 0 & % 22.75/3.78 | $i(all_32_2) & ~ modus_ponens) | (modus_ponens & ! [v0: $i] : ! % 22.75/3.78 | [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ % 22.75/3.78 | $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 22.75/3.78 | (is_a_theorem(v2) = v4 & is_a_theorem(v1) = v5 & is_a_theorem(v0) % 22.75/3.78 | = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))) % 22.75/3.78 | % 22.75/3.78 | DELTA: instantiating (r4) with fresh symbols all_52_0, all_52_1, all_52_2, % 22.75/3.78 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8 gives: % 22.75/3.78 | (11) $i(all_52_6) & $i(all_52_7) & $i(all_52_8) & (( ~ (all_52_0 = 0) & % 22.75/3.78 | or(all_52_7, all_52_3) = all_52_2 & or(all_52_7, all_52_6) = % 22.75/3.79 | all_52_5 & or(all_52_8, all_52_5) = all_52_4 & or(all_52_8, % 22.75/3.79 | all_52_6) = all_52_3 & implies(all_52_4, all_52_2) = all_52_1 & % 22.75/3.79 | is_a_theorem(all_52_1) = all_52_0 & $i(all_52_1) & $i(all_52_2) & % 22.75/3.79 | $i(all_52_3) & $i(all_52_4) & $i(all_52_5) & ~ r4) | (r4 & ! % 22.75/3.79 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 22.75/3.79 | ( ~ (or(v1, v3) = v4) | ~ (or(v0, v2) = v3) | ~ $i(v2) | ~ % 22.75/3.79 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 22.75/3.79 | (or(v1, v2) = v5 & or(v0, v5) = v6 & implies(v6, v4) = v7 & % 22.75/3.79 | is_a_theorem(v7) = 0 & $i(v7) & $i(v6) & $i(v5))) & ! [v0: % 22.75/3.79 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 22.75/3.79 | ~ (or(v1, v2) = v3) | ~ (or(v0, v3) = v4) | ~ $i(v2) | ~ % 22.75/3.79 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 22.75/3.79 | (or(v1, v5) = v6 & or(v0, v2) = v5 & implies(v4, v6) = v7 & % 22.75/3.79 | is_a_theorem(v7) = 0 & $i(v7) & $i(v6) & $i(v5))))) % 22.75/3.79 | % 22.75/3.79 | ALPHA: (11) implies: % 22.75/3.79 | (12) ( ~ (all_52_0 = 0) & or(all_52_7, all_52_3) = all_52_2 & or(all_52_7, % 22.75/3.79 | all_52_6) = all_52_5 & or(all_52_8, all_52_5) = all_52_4 & % 22.75/3.79 | or(all_52_8, all_52_6) = all_52_3 & implies(all_52_4, all_52_2) = % 22.75/3.79 | all_52_1 & is_a_theorem(all_52_1) = all_52_0 & $i(all_52_1) & % 22.75/3.79 | $i(all_52_2) & $i(all_52_3) & $i(all_52_4) & $i(all_52_5) & ~ r4) | % 22.75/3.79 | (r4 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 22.75/3.79 | $i] : ( ~ (or(v1, v3) = v4) | ~ (or(v0, v2) = v3) | ~ $i(v2) | % 22.75/3.79 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 22.75/3.79 | (or(v1, v2) = v5 & or(v0, v5) = v6 & implies(v6, v4) = v7 & % 22.75/3.79 | is_a_theorem(v7) = 0 & $i(v7) & $i(v6) & $i(v5))) & ! [v0: $i] % 22.75/3.79 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 22.75/3.79 | (or(v1, v2) = v3) | ~ (or(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | % 22.75/3.79 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (or(v1, v5) % 22.75/3.79 | = v6 & or(v0, v2) = v5 & implies(v4, v6) = v7 & is_a_theorem(v7) % 22.75/3.79 | = 0 & $i(v7) & $i(v6) & $i(v5)))) % 22.75/3.79 | % 22.75/3.79 | BETA: splitting (8) gives: % 22.75/3.79 | % 22.75/3.79 | Case 1: % 22.75/3.79 | | % 22.75/3.79 | | (13) ~ (all_20_0 = 0) & implies(all_20_3, all_20_4) = all_20_2 & % 22.75/3.79 | | implies(all_20_4, all_20_2) = all_20_1 & is_a_theorem(all_20_1) = % 22.75/3.79 | | all_20_0 & $i(all_20_1) & $i(all_20_2) & ~ implies_1 % 22.75/3.79 | | % 22.75/3.79 | | ALPHA: (13) implies: % 22.75/3.79 | | (14) ~ (all_20_0 = 0) % 22.75/3.79 | | (15) $i(all_20_2) % 22.75/3.79 | | (16) is_a_theorem(all_20_1) = all_20_0 % 22.75/3.79 | | (17) implies(all_20_4, all_20_2) = all_20_1 % 22.75/3.79 | | (18) implies(all_20_3, all_20_4) = all_20_2 % 22.75/3.79 | | % 22.75/3.79 | | BETA: splitting (op_implies_or) gives: % 22.75/3.79 | | % 22.75/3.79 | | Case 1: % 22.75/3.79 | | | % 22.75/3.79 | | | (19) ~ op_implies_or % 22.75/3.79 | | | % 22.75/3.79 | | | PRED_UNIFY: (19), (principia_op_implies_or) imply: % 22.75/3.79 | | | (20) $false % 22.75/3.80 | | | % 22.75/3.80 | | | CLOSE: (20) is inconsistent. % 22.75/3.80 | | | % 22.75/3.80 | | Case 2: % 22.75/3.80 | | | % 23.23/3.80 | | | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 23.23/3.80 | | | (or(v2, v1) = v3) | ~ (not(v0) = v2) | ~ $i(v1) | ~ $i(v0) | % 23.23/3.80 | | | (implies(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : % 23.23/3.80 | | | ! [v2: $i] : ( ~ (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 23.23/3.80 | | | ? [v3: $i] : (or(v3, v1) = v2 & not(v0) = v3 & $i(v3) & $i(v2))) % 23.23/3.80 | | | % 23.23/3.80 | | | ALPHA: (21) implies: % 23.23/3.80 | | | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) = % 23.23/3.80 | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (or(v3, v1) = v2 & % 23.23/3.80 | | | not(v0) = v3 & $i(v3) & $i(v2))) % 23.23/3.80 | | | % 23.23/3.80 | | | BETA: splitting (4) gives: % 23.23/3.80 | | | % 23.23/3.80 | | | Case 1: % 23.23/3.80 | | | | % 23.23/3.80 | | | | (23) ~ (all_18_0 = 0) & or(all_18_4, all_18_3) = all_18_2 & % 23.23/3.80 | | | | implies(all_18_3, all_18_2) = all_18_1 & is_a_theorem(all_18_1) % 23.23/3.80 | | | | = all_18_0 & $i(all_18_1) & $i(all_18_2) & ~ r2 % 23.23/3.80 | | | | % 23.23/3.80 | | | | ALPHA: (23) implies: % 23.23/3.80 | | | | (24) ~ r2 % 23.23/3.80 | | | | % 23.23/3.80 | | | | PRED_UNIFY: (24), (principia_r2) imply: % 23.23/3.80 | | | | (25) $false % 23.23/3.80 | | | | % 23.23/3.80 | | | | CLOSE: (25) is inconsistent. % 23.23/3.80 | | | | % 23.23/3.80 | | | Case 2: % 23.23/3.80 | | | | % 23.23/3.80 | | | | (26) r2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = % 23.23/3.80 | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (implies(v1, v2) % 23.23/3.80 | | | | = v3 & is_a_theorem(v3) = 0 & $i(v3))) % 23.23/3.80 | | | | % 23.23/3.80 | | | | ALPHA: (26) implies: % 23.23/3.80 | | | | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (or(v0, v1) = v2) % 23.23/3.80 | | | | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (implies(v1, v2) = v3 % 23.23/3.80 | | | | & is_a_theorem(v3) = 0 & $i(v3))) % 23.23/3.80 | | | | % 23.23/3.80 | | | | BETA: splitting (10) gives: % 23.23/3.80 | | | | % 23.23/3.80 | | | | Case 1: % 23.23/3.80 | | | | | % 23.23/3.80 | | | | | (28) all_32_1 = 0 & all_32_3 = 0 & ~ (all_32_0 = 0) & % 23.23/3.80 | | | | | implies(all_32_5, all_32_4) = all_32_2 & % 23.23/3.80 | | | | | is_a_theorem(all_32_2) = 0 & is_a_theorem(all_32_4) = all_32_0 % 23.23/3.80 | | | | | & is_a_theorem(all_32_5) = 0 & $i(all_32_2) & ~ modus_ponens % 23.23/3.80 | | | | | % 23.23/3.80 | | | | | ALPHA: (28) implies: % 23.23/3.80 | | | | | (29) ~ modus_ponens % 23.23/3.80 | | | | | % 23.23/3.80 | | | | | PRED_UNIFY: (29), (principia_modus_ponens) imply: % 23.23/3.81 | | | | | (30) $false % 23.23/3.81 | | | | | % 23.23/3.81 | | | | | CLOSE: (30) is inconsistent. % 23.23/3.81 | | | | | % 23.23/3.81 | | | | Case 2: % 23.23/3.81 | | | | | % 23.23/3.81 | | | | | (31) modus_ponens & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 23.23/3.81 | | | | | (implies(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 23.23/3.81 | | | | | any] : ? [v4: any] : ? [v5: any] : (is_a_theorem(v2) = % 23.23/3.81 | | | | | v4 & is_a_theorem(v1) = v5 & is_a_theorem(v0) = v3 & ( ~ % 23.23/3.81 | | | | | (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 23.23/3.81 | | | | | % 23.23/3.81 | | | | | ALPHA: (31) implies: % 23.23/3.81 | | | | | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (implies(v0, v1) % 23.23/3.81 | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 23.23/3.81 | | | | | any] : ? [v5: any] : (is_a_theorem(v2) = v4 & % 23.23/3.81 | | | | | is_a_theorem(v1) = v5 & is_a_theorem(v0) = v3 & ( ~ (v4 = % 23.23/3.81 | | | | | 0) | ~ (v3 = 0) | v5 = 0))) % 23.23/3.81 | | | | | % 23.23/3.81 | | | | | BETA: splitting (12) gives: % 23.23/3.81 | | | | | % 23.23/3.81 | | | | | Case 1: % 23.23/3.81 | | | | | | % 23.23/3.81 | | | | | | (33) ~ (all_52_0 = 0) & or(all_52_7, all_52_3) = all_52_2 & % 23.23/3.81 | | | | | | or(all_52_7, all_52_6) = all_52_5 & or(all_52_8, all_52_5) = % 23.23/3.81 | | | | | | all_52_4 & or(all_52_8, all_52_6) = all_52_3 & % 23.23/3.81 | | | | | | implies(all_52_4, all_52_2) = all_52_1 & % 23.23/3.81 | | | | | | is_a_theorem(all_52_1) = all_52_0 & $i(all_52_1) & % 23.23/3.81 | | | | | | $i(all_52_2) & $i(all_52_3) & $i(all_52_4) & $i(all_52_5) & % 23.23/3.81 | | | | | | ~ r4 % 23.23/3.81 | | | | | | % 23.23/3.81 | | | | | | ALPHA: (33) implies: % 23.23/3.81 | | | | | | (34) ~ r4 % 23.23/3.81 | | | | | | % 23.23/3.81 | | | | | | PRED_UNIFY: (34), (principia_r4) imply: % 23.23/3.81 | | | | | | (35) $false % 23.23/3.81 | | | | | | % 23.23/3.81 | | | | | | CLOSE: (35) is inconsistent. % 23.23/3.81 | | | | | | % 23.23/3.81 | | | | | Case 2: % 23.23/3.81 | | | | | | % 23.23/3.81 | | | | | | % 23.23/3.81 | | | | | | GROUND_INST: instantiating (32) with all_20_4, all_20_2, all_20_1, % 23.23/3.81 | | | | | | simplifying with (6), (15), (17) gives: % 23.23/3.81 | | | | | | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.23/3.81 | | | | | | (is_a_theorem(all_20_1) = v1 & is_a_theorem(all_20_2) = v2 & % 23.23/3.81 | | | | | | is_a_theorem(all_20_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | % 23.23/3.81 | | | | | | v2 = 0)) % 23.23/3.81 | | | | | | % 23.23/3.81 | | | | | | GROUND_INST: instantiating (22) with all_20_3, all_20_4, all_20_2, % 23.23/3.81 | | | | | | simplifying with (6), (7), (18) gives: % 23.23/3.81 | | | | | | (37) ? [v0: $i] : (or(v0, all_20_4) = all_20_2 & not(all_20_3) = % 23.23/3.81 | | | | | | v0 & $i(v0) & $i(all_20_2)) % 23.23/3.81 | | | | | | % 23.23/3.81 | | | | | | DELTA: instantiating (37) with fresh symbol all_114_0 gives: % 23.23/3.81 | | | | | | (38) or(all_114_0, all_20_4) = all_20_2 & not(all_20_3) = % 23.23/3.81 | | | | | | all_114_0 & $i(all_114_0) & $i(all_20_2) % 23.23/3.81 | | | | | | % 23.23/3.81 | | | | | | ALPHA: (38) implies: % 23.23/3.81 | | | | | | (39) $i(all_114_0) % 23.23/3.81 | | | | | | (40) or(all_114_0, all_20_4) = all_20_2 % 23.23/3.81 | | | | | | % 23.23/3.81 | | | | | | DELTA: instantiating (36) with fresh symbols all_126_0, all_126_1, % 23.23/3.81 | | | | | | all_126_2 gives: % 23.23/3.82 | | | | | | (41) is_a_theorem(all_20_1) = all_126_1 & is_a_theorem(all_20_2) % 23.23/3.82 | | | | | | = all_126_0 & is_a_theorem(all_20_4) = all_126_2 & ( ~ % 23.23/3.82 | | | | | | (all_126_1 = 0) | ~ (all_126_2 = 0) | all_126_0 = 0) % 23.23/3.82 | | | | | | % 23.23/3.82 | | | | | | ALPHA: (41) implies: % 23.23/3.82 | | | | | | (42) is_a_theorem(all_20_1) = all_126_1 % 23.23/3.82 | | | | | | % 23.23/3.82 | | | | | | GROUND_INST: instantiating (1) with all_20_0, all_126_1, all_20_1, % 23.23/3.82 | | | | | | simplifying with (16), (42) gives: % 23.23/3.82 | | | | | | (43) all_126_1 = all_20_0 % 23.23/3.82 | | | | | | % 23.23/3.82 | | | | | | GROUND_INST: instantiating (27) with all_114_0, all_20_4, all_20_2, % 23.23/3.82 | | | | | | simplifying with (6), (39), (40) gives: % 23.23/3.82 | | | | | | (44) ? [v0: $i] : (implies(all_20_4, all_20_2) = v0 & % 23.23/3.82 | | | | | | is_a_theorem(v0) = 0 & $i(v0)) % 23.23/3.82 | | | | | | % 23.23/3.82 | | | | | | DELTA: instantiating (44) with fresh symbol all_182_0 gives: % 23.23/3.82 | | | | | | (45) implies(all_20_4, all_20_2) = all_182_0 & % 23.23/3.82 | | | | | | is_a_theorem(all_182_0) = 0 & $i(all_182_0) % 23.23/3.82 | | | | | | % 23.23/3.82 | | | | | | ALPHA: (45) implies: % 23.23/3.82 | | | | | | (46) is_a_theorem(all_182_0) = 0 % 23.23/3.82 | | | | | | (47) implies(all_20_4, all_20_2) = all_182_0 % 23.23/3.82 | | | | | | % 23.23/3.82 | | | | | | GROUND_INST: instantiating (2) with all_20_1, all_182_0, all_20_2, % 23.23/3.82 | | | | | | all_20_4, simplifying with (17), (47) gives: % 23.23/3.82 | | | | | | (48) all_182_0 = all_20_1 % 23.23/3.82 | | | | | | % 23.23/3.82 | | | | | | REDUCE: (46), (48) imply: % 23.23/3.82 | | | | | | (49) is_a_theorem(all_20_1) = 0 % 23.23/3.82 | | | | | | % 23.23/3.82 | | | | | | GROUND_INST: instantiating (1) with all_20_0, 0, all_20_1, % 23.23/3.82 | | | | | | simplifying with (16), (49) gives: % 23.23/3.82 | | | | | | (50) all_20_0 = 0 % 23.23/3.82 | | | | | | % 23.23/3.82 | | | | | | REDUCE: (14), (50) imply: % 23.23/3.82 | | | | | | (51) $false % 23.23/3.82 | | | | | | % 23.23/3.82 | | | | | | CLOSE: (51) is inconsistent. % 23.23/3.82 | | | | | | % 23.23/3.82 | | | | | End of split % 23.23/3.82 | | | | | % 23.23/3.82 | | | | End of split % 23.23/3.82 | | | | % 23.23/3.82 | | | End of split % 23.23/3.82 | | | % 23.23/3.82 | | End of split % 23.23/3.82 | | % 23.23/3.82 | Case 2: % 23.23/3.82 | | % 23.23/3.82 | | (52) implies_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 23.23/3.82 | | (implies(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 23.23/3.82 | | (implies(v0, v2) = v3 & is_a_theorem(v3) = 0 & $i(v3))) % 23.23/3.82 | | % 23.23/3.82 | | ALPHA: (52) implies: % 23.23/3.82 | | (53) implies_1 % 23.23/3.82 | | % 23.23/3.82 | | PRED_UNIFY: (53), (hilbert_implies_1) imply: % 23.23/3.82 | | (54) $false % 23.23/3.82 | | % 23.23/3.82 | | CLOSE: (54) is inconsistent. % 23.23/3.82 | | % 23.23/3.82 | End of split % 23.23/3.82 | % 23.23/3.82 End of proof % 23.23/3.82 % SZS output end Proof for theBenchmark % 23.23/3.82 % 23.23/3.82 3256ms %------------------------------------------------------------------------------