%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL455+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 : n031.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 12:54:11 PM UTC 2026 % Result : Theorem 18.12s 3.36s % Output : Proof 25.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.04 % Problem : LCL455+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.06 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.41 % Computer : n031.cluster.edu % 0.14/0.41 % Model : x86_64 x86_64 % 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.41 % Memory : 8046.5625MB % 0.14/0.41 % OS : Linux 6.8.0-71-generic % 0.14/0.41 % CPULimit : 300 % 0.14/0.41 % WCLimit : 300 % 0.14/0.41 % DateTime : Sat Sep 5 06:33:09 UTC 2026 % 0.14/0.41 % CPUTime : % 0.14/0.44 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. % 0.79/0.89 ________ _____ % 0.79/0.89 ___ __ \_________(_)________________________________ % 0.79/0.89 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.79/0.89 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.79/0.89 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.79/0.89 % 0.79/0.89 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.79/0.89 (2023-06-19) % 0.79/0.89 % 0.79/0.89 (c) Philipp Rümmer, 2009-2023 % 0.79/0.89 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.79/0.89 Amanda Stjerna. % 0.79/0.89 Free software under BSD-3-Clause. % 0.79/0.89 % 0.79/0.89 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.79/0.89 % 0.79/0.89 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 1.00/0.92 Running up to 7 provers in parallel. % 1.00/0.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 1.00/0.94 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 1.00/0.94 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 1.00/0.94 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 1.00/0.94 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 1.00/0.94 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 1.00/0.94 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.69/1.70 Prover 4: Preprocessing ... % 5.46/1.72 Prover 0: Preprocessing ... % 5.46/1.72 Prover 6: Preprocessing ... % 5.46/1.73 Prover 2: Preprocessing ... % 5.46/1.73 Prover 3: Preprocessing ... % 5.46/1.73 Prover 5: Preprocessing ... % 5.46/1.74 Prover 1: Preprocessing ... % 14.13/2.84 Prover 6: Constructing countermodel ... % 15.73/3.13 Prover 1: Constructing countermodel ... % 17.28/3.27 Prover 5: Proving ... % 18.12/3.33 Prover 3: Constructing countermodel ... % 18.12/3.35 Prover 6: proved (2413ms) % 18.12/3.35 % 18.12/3.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.12/3.36 % 18.12/3.37 Prover 3: stopped % 18.12/3.37 Prover 4: Constructing countermodel ... % 18.12/3.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 18.12/3.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.83/3.40 Prover 5: stopped % 18.83/3.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 18.83/3.49 Prover 0: Proving ... % 19.62/3.51 Prover 0: stopped % 19.62/3.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 19.62/3.54 Prover 7: Preprocessing ... % 19.62/3.55 Prover 8: Preprocessing ... % 19.62/3.57 Prover 2: Proving ... % 19.62/3.60 Prover 10: Preprocessing ... % 19.62/3.60 Prover 2: stopped % 20.43/3.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 22.04/3.80 Prover 11: Preprocessing ... % 22.04/3.85 Prover 13: Preprocessing ... % 22.04/3.86 Prover 1: Found proof (size 19) % 22.04/3.86 Prover 1: proved (2930ms) % 22.04/3.87 Prover 4: stopped % 22.04/3.87 Prover 7: stopped % 22.81/3.93 Prover 10: Constructing countermodel ... % 22.81/3.95 Prover 10: stopped % 23.55/4.03 Prover 11: stopped % 23.55/4.03 Prover 13: stopped % 24.12/4.12 Prover 8: Warning: ignoring some quantifiers % 24.12/4.14 Prover 8: Constructing countermodel ... % 24.12/4.16 Prover 8: stopped % 24.12/4.16 % 24.12/4.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 24.12/4.16 % 24.12/4.17 % SZS output start Proof for theBenchmark % 24.12/4.18 Assumptions after simplification: % 24.12/4.18 --------------------------------- % 24.12/4.18 % 24.12/4.18 (hilbert_or_2) % 24.12/4.19 or_2 % 24.12/4.19 % 24.12/4.19 (or_2) % 24.85/4.27 (or_2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (or(v0, % 24.85/4.27 v1) = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~ $i(v0) | % 24.85/4.27 is_a_theorem(v3) = 0)) | ( ~ or_2 & ? [v0: $i] : ? [v1: $i] : ? [v2: % 24.85/4.27 $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & % 24.85/4.27 implies(v1, v2) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & % 24.85/4.27 $i(v0))) % 24.85/4.27 % 24.85/4.27 (principia_r2) % 24.85/4.27 ~ r2 % 24.85/4.27 % 24.85/4.27 (r2) % 24.85/4.28 (r2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (or(v0, v1) % 24.85/4.28 = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~ $i(v0) | % 24.85/4.28 is_a_theorem(v3) = 0)) | ( ~ r2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 24.85/4.28 : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v1, % 24.85/4.28 v2) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))) % 24.85/4.28 % 24.85/4.28 (function-axioms) % 24.85/4.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3, % 24.85/4.30 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 24.85/4.30 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = % 24.85/4.30 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 24.85/4.30 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 24.85/4.30 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ % 24.85/4.30 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 24.85/4.30 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 24.85/4.30 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_a_theorem(v2) = v1) % 24.85/4.30 | ~ (is_a_theorem(v2) = v0)) % 24.85/4.30 % 24.85/4.30 Further assumptions not needed in the proof: % 24.85/4.30 -------------------------------------------- % 24.85/4.30 and_1, and_2, and_3, cn1, cn2, cn3, equivalence_1, equivalence_2, equivalence_3, % 24.85/4.30 hilbert_and_1, hilbert_and_2, hilbert_and_3, hilbert_equivalence_1, % 24.85/4.30 hilbert_equivalence_2, hilbert_equivalence_3, hilbert_implies_1, % 24.85/4.30 hilbert_implies_2, hilbert_implies_3, hilbert_modus_ponens, % 24.85/4.30 hilbert_modus_tollens, hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or, % 24.85/4.30 hilbert_or_1, hilbert_or_3, implies_1, implies_2, implies_3, kn1, kn2, kn3, % 24.85/4.30 modus_ponens, modus_tollens, op_and, op_equiv, op_implies_and, op_implies_or, % 24.85/4.30 op_or, or_1, or_3, principia_op_and, principia_op_equiv, % 24.85/4.30 principia_op_implies_or, r1, r3, r4, r5, substitution_of_equivalents, % 24.85/4.30 use_substitution_of_equivalents % 24.85/4.30 % 24.85/4.30 Those formulas are unsatisfiable: % 24.85/4.30 --------------------------------- % 24.85/4.30 % 24.85/4.30 Begin of proof % 24.85/4.31 | % 24.85/4.31 | ALPHA: (function-axioms) implies: % 24.85/4.31 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 24.85/4.31 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) % 24.85/4.31 | % 24.85/4.31 | BETA: splitting (or_2) gives: % 24.85/4.31 | % 24.85/4.31 | Case 1: % 24.85/4.31 | | % 24.85/4.32 | | (2) or_2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 24.85/4.32 | | (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~ % 24.85/4.32 | | $i(v0) | is_a_theorem(v3) = 0) % 24.85/4.32 | | % 24.85/4.32 | | ALPHA: (2) implies: % 24.85/4.32 | | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (or(v0, % 24.85/4.32 | | v1) = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~ $i(v0) | % 24.85/4.32 | | is_a_theorem(v3) = 0) % 24.85/4.32 | | % 24.85/4.32 | | BETA: splitting (r2) gives: % 24.85/4.32 | | % 24.85/4.32 | | Case 1: % 24.85/4.32 | | | % 24.85/4.33 | | | (4) r2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 24.85/4.33 | | | (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~ % 24.85/4.33 | | | $i(v0) | is_a_theorem(v3) = 0) % 24.85/4.33 | | | % 24.85/4.33 | | | ALPHA: (4) implies: % 24.85/4.33 | | | (5) r2 % 24.85/4.33 | | | % 24.85/4.33 | | | PRED_UNIFY: (5), (principia_r2) imply: % 24.85/4.33 | | | (6) $false % 24.85/4.33 | | | % 24.85/4.33 | | | CLOSE: (6) is inconsistent. % 24.85/4.33 | | | % 24.85/4.33 | | Case 2: % 24.85/4.33 | | | % 24.85/4.33 | | | (7) ~ r2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 24.85/4.33 | | | [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v1, v2) = v3 & % 24.85/4.33 | | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 24.85/4.33 | | | % 24.85/4.33 | | | ALPHA: (7) implies: % 24.85/4.34 | | | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 24.85/4.34 | | | int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v1, v2) = v3 & % 24.85/4.34 | | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 24.85/4.34 | | | % 24.85/4.34 | | | DELTA: instantiating (8) with fresh symbols all_88_0, all_88_1, all_88_2, % 24.85/4.34 | | | all_88_3, all_88_4 gives: % 24.85/4.34 | | | (9) ~ (all_88_0 = 0) & or(all_88_4, all_88_3) = all_88_2 & % 24.85/4.34 | | | implies(all_88_3, all_88_2) = all_88_1 & is_a_theorem(all_88_1) = % 24.85/4.34 | | | all_88_0 & $i(all_88_1) & $i(all_88_2) & $i(all_88_3) & % 24.85/4.34 | | | $i(all_88_4) % 24.85/4.34 | | | % 24.85/4.34 | | | ALPHA: (9) implies: % 24.85/4.35 | | | (10) ~ (all_88_0 = 0) % 24.85/4.35 | | | (11) $i(all_88_4) % 24.85/4.35 | | | (12) $i(all_88_3) % 24.85/4.35 | | | (13) is_a_theorem(all_88_1) = all_88_0 % 24.85/4.35 | | | (14) implies(all_88_3, all_88_2) = all_88_1 % 24.85/4.35 | | | (15) or(all_88_4, all_88_3) = all_88_2 % 24.85/4.35 | | | % 25.36/4.35 | | | GROUND_INST: instantiating (3) with all_88_4, all_88_3, all_88_2, % 25.36/4.35 | | | all_88_1, simplifying with (11), (12), (14), (15) gives: % 25.36/4.35 | | | (16) is_a_theorem(all_88_1) = 0 % 25.36/4.35 | | | % 25.36/4.35 | | | GROUND_INST: instantiating (1) with all_88_0, 0, all_88_1, simplifying % 25.36/4.35 | | | with (13), (16) gives: % 25.36/4.35 | | | (17) all_88_0 = 0 % 25.36/4.35 | | | % 25.36/4.35 | | | REDUCE: (10), (17) imply: % 25.36/4.35 | | | (18) $false % 25.36/4.35 | | | % 25.36/4.35 | | | CLOSE: (18) is inconsistent. % 25.36/4.35 | | | % 25.36/4.35 | | End of split % 25.36/4.35 | | % 25.36/4.35 | Case 2: % 25.36/4.35 | | % 25.36/4.36 | | (19) ~ or_2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 25.36/4.36 | | [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v1, v2) = v3 & % 25.36/4.36 | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 25.36/4.36 | | % 25.36/4.36 | | ALPHA: (19) implies: % 25.36/4.36 | | (20) ~ or_2 % 25.36/4.36 | | % 25.36/4.36 | | PRED_UNIFY: (20), (hilbert_or_2) imply: % 25.36/4.36 | | (21) $false % 25.36/4.36 | | % 25.36/4.36 | | CLOSE: (21) is inconsistent. % 25.36/4.36 | | % 25.36/4.36 | End of split % 25.36/4.36 | % 25.36/4.36 End of proof % 25.36/4.36 % SZS output end Proof for theBenchmark % 25.36/4.36 % 25.36/4.36 3466ms %------------------------------------------------------------------------------