%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL506+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 : n012.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 12:54:15 PM UTC 2026 % Result : Theorem 8.65s 1.75s % Output : Proof 10.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.01 % Problem : LCL506+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.02 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.05/0.29 % Computer : n012.cluster.edu % 0.05/0.29 % Model : x86_64 x86_64 % 0.05/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.05/0.29 % Memory : 8046.5625MB % 0.05/0.29 % OS : Linux 6.8.0-71-generic % 0.05/0.30 % CPULimit : 300 % 0.05/0.30 % WCLimit : 300 % 0.05/0.30 % DateTime : Fri Sep 4 22:27:12 UTC 2026 % 0.05/0.30 % CPUTime : % 0.05/0.31 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. % 0.27/0.48 ________ _____ % 0.27/0.48 ___ __ \_________(_)________________________________ % 0.27/0.48 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.27/0.48 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.27/0.48 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.27/0.48 % 0.27/0.48 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.27/0.48 (2023-06-19) % 0.27/0.49 % 0.27/0.49 (c) Philipp Rümmer, 2009-2023 % 0.27/0.49 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.27/0.49 Amanda Stjerna. % 0.27/0.49 Free software under BSD-3-Clause. % 0.27/0.49 % 0.27/0.49 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.27/0.49 % 0.27/0.49 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.27/0.50 Running up to 7 provers in parallel. % 0.27/0.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.27/0.50 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.27/0.50 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.27/0.50 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.27/0.50 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.27/0.50 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.27/0.50 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.39/0.96 Prover 1: Preprocessing ... % 2.39/0.96 Prover 4: Preprocessing ... % 2.39/1.02 Prover 2: Preprocessing ... % 2.39/1.02 Prover 5: Preprocessing ... % 2.39/1.02 Prover 3: Preprocessing ... % 2.39/1.02 Prover 0: Preprocessing ... % 2.39/1.02 Prover 6: Preprocessing ... % 7.85/1.60 Prover 5: Proving ... % 7.85/1.62 Prover 6: Constructing countermodel ... % 7.85/1.62 Prover 3: Constructing countermodel ... % 7.85/1.63 Prover 1: Constructing countermodel ... % 7.85/1.66 Prover 0: Proving ... % 7.85/1.67 Prover 4: Constructing countermodel ... % 8.65/1.74 Prover 6: proved (1237ms) % 8.65/1.74 % 8.65/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.65/1.75 % 8.65/1.75 Prover 3: proved (1241ms) % 8.65/1.75 % 8.65/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.65/1.75 % 8.65/1.75 Prover 0: stopped % 8.65/1.75 Prover 5: stopped % 8.65/1.75 Prover 2: Proving ... % 8.65/1.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.65/1.76 Prover 2: stopped % 8.65/1.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.65/1.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.65/1.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.65/1.76 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.44/1.82 Prover 8: Preprocessing ... % 9.44/1.83 Prover 7: Preprocessing ... % 9.44/1.84 Prover 11: Preprocessing ... % 9.44/1.85 Prover 13: Preprocessing ... % 9.44/1.85 Prover 1: Found proof (size 18) % 9.44/1.85 Prover 1: proved (1352ms) % 9.44/1.86 Prover 10: Preprocessing ... % 9.44/1.86 Prover 4: stopped % 10.24/1.91 Prover 11: stopped % 10.24/1.93 Prover 7: stopped % 10.24/1.95 Prover 10: stopped % 10.24/1.95 Prover 13: stopped % 10.24/2.01 Prover 8: Warning: ignoring some quantifiers % 10.90/2.02 Prover 8: Constructing countermodel ... % 10.90/2.03 Prover 8: stopped % 10.90/2.03 % 10.90/2.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.90/2.03 % 10.90/2.03 % SZS output start Proof for theBenchmark % 10.90/2.04 Assumptions after simplification: % 10.90/2.04 --------------------------------- % 10.90/2.04 % 10.90/2.04 (and_1) % 10.90/2.07 (and_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (and(v0, % 10.90/2.07 v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 10.90/2.07 is_a_theorem(v3) = 0)) | ( ~ and_1 & ? [v0: $i] : ? [v1: $i] : ? [v2: % 10.90/2.07 $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & % 10.90/2.07 implies(v2, v0) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & % 10.90/2.07 $i(v0))) % 10.90/2.07 % 10.90/2.07 (hilbert_and_1) % 10.90/2.07 ~ and_1 % 10.90/2.07 % 10.90/2.07 (kn2) % 10.90/2.07 (kn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (and(v0, % 10.90/2.07 v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 10.90/2.07 is_a_theorem(v3) = 0)) | ( ~ kn2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 10.90/2.07 : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, % 10.90/2.07 v0) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))) % 10.90/2.07 % 10.90/2.07 (rosser_kn2) % 10.90/2.07 kn2 % 10.90/2.07 % 10.90/2.07 (function-axioms) % 10.90/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3, % 10.90/2.08 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 10.90/2.08 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = % 10.90/2.08 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 10.90/2.08 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 10.90/2.08 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ % 10.90/2.08 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 10.90/2.08 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 10.90/2.08 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_a_theorem(v2) = v1) % 10.90/2.08 | ~ (is_a_theorem(v2) = v0)) % 10.90/2.08 % 10.90/2.08 Further assumptions not needed in the proof: % 10.90/2.08 -------------------------------------------- % 10.90/2.08 and_2, and_3, cn1, cn2, cn3, equivalence_1, equivalence_2, equivalence_3, % 10.90/2.08 hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or, implies_1, implies_2, % 10.90/2.08 implies_3, kn1, kn3, modus_ponens, modus_tollens, op_and, op_equiv, % 10.90/2.08 op_implies_and, op_implies_or, op_or, or_1, or_2, or_3, r1, r2, r3, r4, r5, % 10.90/2.08 rosser_kn1, rosser_kn3, rosser_modus_ponens, rosser_op_equiv, % 10.90/2.08 rosser_op_implies_and, rosser_op_or, substitution_of_equivalents, % 10.90/2.08 use_substitution_of_equivalents % 10.90/2.08 % 10.90/2.08 Those formulas are unsatisfiable: % 10.90/2.08 --------------------------------- % 10.90/2.08 % 10.90/2.08 Begin of proof % 10.90/2.08 | % 10.90/2.08 | ALPHA: (function-axioms) implies: % 10.90/2.08 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.90/2.08 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0)) % 10.90/2.08 | % 10.90/2.08 | BETA: splitting (kn2) gives: % 10.90/2.08 | % 10.90/2.08 | Case 1: % 10.90/2.08 | | % 10.90/2.08 | | (2) kn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.90/2.08 | | (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ % 10.90/2.08 | | $i(v0) | is_a_theorem(v3) = 0) % 10.90/2.08 | | % 10.90/2.08 | | ALPHA: (2) implies: % 10.90/2.08 | | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (and(v0, % 10.90/2.08 | | v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 10.90/2.08 | | is_a_theorem(v3) = 0) % 10.90/2.08 | | % 10.90/2.08 | | BETA: splitting (and_1) gives: % 10.90/2.08 | | % 10.90/2.08 | | Case 1: % 10.90/2.08 | | | % 10.90/2.08 | | | (4) and_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.90/2.08 | | | (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ % 10.90/2.08 | | | $i(v0) | is_a_theorem(v3) = 0) % 10.90/2.08 | | | % 10.90/2.08 | | | ALPHA: (4) implies: % 10.90/2.08 | | | (5) and_1 % 10.90/2.08 | | | % 10.90/2.09 | | | PRED_UNIFY: (5), (hilbert_and_1) imply: % 10.90/2.09 | | | (6) $false % 10.90/2.09 | | | % 10.90/2.09 | | | CLOSE: (6) is inconsistent. % 10.90/2.09 | | | % 10.90/2.09 | | Case 2: % 10.90/2.09 | | | % 10.90/2.09 | | | (7) ~ and_1 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 10.90/2.09 | | | ? [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, v0) = % 10.90/2.09 | | | v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.90/2.09 | | | % 10.90/2.09 | | | ALPHA: (7) implies: % 10.90/2.09 | | | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 10.90/2.09 | | | int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, v0) = v3 & % 10.90/2.09 | | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.90/2.09 | | | % 10.90/2.09 | | | DELTA: instantiating (8) with fresh symbols all_40_0, all_40_1, all_40_2, % 10.90/2.09 | | | all_40_3, all_40_4 gives: % 10.90/2.09 | | | (9) ~ (all_40_0 = 0) & and(all_40_4, all_40_3) = all_40_2 & % 10.90/2.09 | | | implies(all_40_2, all_40_4) = all_40_1 & is_a_theorem(all_40_1) = % 10.90/2.09 | | | all_40_0 & $i(all_40_1) & $i(all_40_2) & $i(all_40_3) & % 10.90/2.09 | | | $i(all_40_4) % 10.90/2.09 | | | % 10.90/2.09 | | | ALPHA: (9) implies: % 10.90/2.09 | | | (10) ~ (all_40_0 = 0) % 10.90/2.09 | | | (11) $i(all_40_4) % 10.90/2.09 | | | (12) $i(all_40_3) % 10.90/2.09 | | | (13) is_a_theorem(all_40_1) = all_40_0 % 10.90/2.09 | | | (14) implies(all_40_2, all_40_4) = all_40_1 % 10.90/2.09 | | | (15) and(all_40_4, all_40_3) = all_40_2 % 10.90/2.09 | | | % 10.90/2.09 | | | GROUND_INST: instantiating (3) with all_40_4, all_40_3, all_40_2, % 10.90/2.09 | | | all_40_1, simplifying with (11), (12), (14), (15) gives: % 10.90/2.09 | | | (16) is_a_theorem(all_40_1) = 0 % 10.90/2.09 | | | % 10.90/2.09 | | | GROUND_INST: instantiating (1) with all_40_0, 0, all_40_1, simplifying % 10.90/2.09 | | | with (13), (16) gives: % 10.90/2.09 | | | (17) all_40_0 = 0 % 10.90/2.09 | | | % 10.90/2.09 | | | REDUCE: (10), (17) imply: % 10.90/2.09 | | | (18) $false % 10.90/2.09 | | | % 10.90/2.09 | | | CLOSE: (18) is inconsistent. % 10.90/2.09 | | | % 10.90/2.09 | | End of split % 10.90/2.09 | | % 10.90/2.10 | Case 2: % 10.90/2.10 | | % 10.90/2.10 | | (19) ~ kn2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 10.90/2.10 | | [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, v0) = v3 & % 10.90/2.10 | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.90/2.10 | | % 10.90/2.10 | | ALPHA: (19) implies: % 10.90/2.10 | | (20) ~ kn2 % 10.90/2.10 | | % 10.90/2.10 | | PRED_UNIFY: (20), (rosser_kn2) imply: % 10.90/2.10 | | (21) $false % 10.90/2.10 | | % 10.90/2.10 | | CLOSE: (21) is inconsistent. % 10.90/2.10 | | % 10.90/2.10 | End of split % 10.90/2.10 | % 10.90/2.10 End of proof % 10.90/2.10 % SZS output end Proof for theBenchmark % 10.90/2.10 % 10.90/2.10 1611ms %------------------------------------------------------------------------------