%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0. % 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 12:54:25 PM UTC 2026 % Result : Theorem 7.29s 1.77s % Output : Proof 10.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.34 % Computer : n006.cluster.edu % 0.10/0.34 % Model : x86_64 x86_64 % 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.34 % Memory : 8046.5625MB % 0.10/0.34 % OS : Linux 6.8.0-71-generic % 0.10/0.35 % CPULimit : 300 % 0.10/0.35 % WCLimit : 300 % 0.10/0.35 % DateTime : Fri Sep 4 19:38:16 UTC 2026 % 0.10/0.35 % CPUTime : % 0.13/0.36 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.73/0.70 ________ _____ % 0.73/0.70 ___ __ \_________(_)________________________________ % 0.73/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.73/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.73/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.73/0.70 % 0.73/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.73/0.70 (2023-06-19) % 0.73/0.70 % 0.73/0.70 (c) Philipp Rümmer, 2009-2023 % 0.73/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.73/0.70 Amanda Stjerna. % 0.73/0.70 Free software under BSD-3-Clause. % 0.73/0.70 % 0.73/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.73/0.70 % 0.73/0.70 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.72 Running up to 7 provers in parallel. % 0.73/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.73/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.73/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.73/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.73/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.73/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.73/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.91/1.15 Prover 4: Preprocessing ... % 2.91/1.16 Prover 1: Preprocessing ... % 2.91/1.19 Prover 5: Preprocessing ... % 2.91/1.19 Prover 6: Preprocessing ... % 2.91/1.19 Prover 0: Preprocessing ... % 2.91/1.19 Prover 2: Preprocessing ... % 2.91/1.19 Prover 3: Preprocessing ... % 4.96/1.45 Prover 2: Constructing countermodel ... % 4.96/1.45 Prover 5: Constructing countermodel ... % 4.96/1.47 Prover 3: Constructing countermodel ... % 5.71/1.53 Prover 6: Proving ... % 5.71/1.58 Prover 1: Constructing countermodel ... % 5.71/1.59 Prover 4: Constructing countermodel ... % 6.52/1.61 Prover 0: Proving ... % 7.29/1.77 Prover 2: proved (1033ms) % 7.29/1.77 % 7.29/1.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.29/1.77 % 7.29/1.77 Prover 3: stopped % 7.29/1.77 Prover 5: stopped % 7.29/1.78 Prover 0: stopped % 7.29/1.78 Prover 6: stopped % 7.29/1.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.29/1.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.29/1.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.29/1.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.29/1.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.08/1.85 Prover 7: Preprocessing ... % 8.08/1.86 Prover 11: Preprocessing ... % 8.08/1.88 Prover 10: Preprocessing ... % 8.08/1.88 Prover 8: Preprocessing ... % 8.08/1.89 Prover 13: Preprocessing ... % 8.84/1.91 Prover 7: Constructing countermodel ... % 8.84/1.94 Prover 10: Constructing countermodel ... % 8.84/1.94 Prover 13: Constructing countermodel ... % 10.02/2.06 Prover 10: Found proof (size 13) % 10.02/2.06 Prover 10: proved (283ms) % 10.02/2.06 Prover 1: stopped % 10.02/2.06 Prover 4: stopped % 10.02/2.06 Prover 13: stopped % 10.02/2.06 Prover 7: stopped % 10.02/2.10 Prover 8: Warning: ignoring some quantifiers % 10.02/2.12 Prover 8: Constructing countermodel ... % 10.02/2.12 Prover 8: stopped % 10.02/2.13 Prover 11: Constructing countermodel ... % 10.02/2.13 Prover 11: stopped % 10.02/2.13 % 10.02/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.02/2.13 % 10.02/2.14 % SZS output start Proof for theBenchmark % 10.02/2.14 Assumptions after simplification: % 10.02/2.14 --------------------------------- % 10.02/2.14 % 10.02/2.14 (main) % 10.59/2.17 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & r1(v0, v1) & ~ p1(v1) & ! % 10.59/2.17 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 10.59/2.17 ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | ? [v5: $i] : % 10.59/2.17 ($i(v5) & r1(v2, v5) & ~ p1(v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 10.59/2.17 $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ r1(v3, v4) | ~ r1(v2, v3) | % 10.59/2.17 ~ r1(v0, v2) | ? [v5: $i] : ($i(v5) & ((p1(v5) & r1(v4, v5)) | (r1(v2, % 10.59/2.17 v5) & ! [v6: $i] : ( ~ $i(v6) | ~ p1(v6) | ~ r1(v5, v6)))))) & % 10.59/2.17 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ p1(v2) | ~ r1(v2, % 10.59/2.17 v3) | ~ r1(v0, v2) | ? [v4: $i] : ($i(v4) & p1(v4) & r1(v3, v4))) & ! % 10.59/2.17 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ r1(v2, v3) | ~ r1(v0, % 10.59/2.17 v2) | p1(v2) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p1(v4))) & ! % 10.59/2.17 [v2: $i] : ( ~ $i(v2) | ~ r1(v1, v2) | p1(v2)) & ! [v2: $i] : ( ~ $i(v2) | % 10.59/2.17 ~ r1(v0, v2) | ? [v3: $i] : ($i(v3) & r1(v2, v3)))) % 10.59/2.17 % 10.59/2.17 Those formulas are unsatisfiable: % 10.59/2.17 --------------------------------- % 10.59/2.17 % 10.59/2.17 Begin of proof % 10.59/2.18 | % 10.59/2.18 | DELTA: instantiating (main) with fresh symbols all_2_0, all_2_1 gives: % 10.59/2.19 | (1) $i(all_2_0) & $i(all_2_1) & r1(all_2_1, all_2_0) & ~ p1(all_2_0) & ! % 10.59/2.19 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 10.59/2.19 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_1, v0) | p1(v2) % 10.59/2.19 | | ? [v3: $i] : ($i(v3) & r1(v0, v3) & ~ p1(v3))) & ! [v0: $i] : ! % 10.59/2.19 | [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, % 10.59/2.19 | v2) | ~ r1(v0, v1) | ~ r1(all_2_1, v0) | ? [v3: $i] : ($i(v3) & % 10.59/2.19 | ((p1(v3) & r1(v2, v3)) | (r1(v0, v3) & ! [v4: $i] : ( ~ $i(v4) | % 10.59/2.19 | ~ p1(v4) | ~ r1(v3, v4)))))) & ! [v0: $i] : ! [v1: $i] : ( % 10.59/2.19 | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_2_1, v0) % 10.59/2.19 | | ? [v2: $i] : ($i(v2) & p1(v2) & r1(v1, v2))) & ! [v0: $i] : ! % 10.59/2.19 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_1, v0) % 10.59/2.19 | | p1(v0) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p1(v2))) & ! [v0: % 10.59/2.19 | $i] : ( ~ $i(v0) | ~ r1(all_2_0, v0) | p1(v0)) & ! [v0: $i] : ( ~ % 10.59/2.19 | $i(v0) | ~ r1(all_2_1, v0) | ? [v1: $i] : ($i(v1) & r1(v0, v1))) % 10.59/2.19 | % 10.59/2.19 | ALPHA: (1) implies: % 10.59/2.19 | (2) ~ p1(all_2_0) % 10.59/2.19 | (3) r1(all_2_1, all_2_0) % 10.59/2.19 | (4) $i(all_2_0) % 10.59/2.19 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_1, v0) | ? [v1: $i] : ($i(v1) & % 10.59/2.19 | r1(v0, v1))) % 10.59/2.20 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_0, v0) | p1(v0)) % 10.81/2.20 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ % 10.81/2.20 | r1(all_2_1, v0) | p1(v0) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ % 10.81/2.20 | p1(v2))) % 10.81/2.20 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 10.81/2.20 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_1, v0) | p1(v2) % 10.81/2.20 | | ? [v3: $i] : ($i(v3) & r1(v0, v3) & ~ p1(v3))) % 10.81/2.20 | % 10.81/2.20 | GROUND_INST: instantiating (5) with all_2_0, simplifying with (3), (4) gives: % 10.81/2.20 | (9) ? [v0: $i] : ($i(v0) & r1(all_2_0, v0)) % 10.81/2.20 | % 10.81/2.20 | DELTA: instantiating (9) with fresh symbol all_10_0 gives: % 10.81/2.20 | (10) $i(all_10_0) & r1(all_2_0, all_10_0) % 10.81/2.20 | % 10.81/2.20 | ALPHA: (10) implies: % 10.81/2.20 | (11) r1(all_2_0, all_10_0) % 10.81/2.20 | (12) $i(all_10_0) % 10.81/2.20 | % 10.81/2.20 | GROUND_INST: instantiating (7) with all_2_0, all_10_0, simplifying with (2), % 10.81/2.20 | (3), (4), (11), (12) gives: % 10.81/2.21 | (13) ? [v0: $i] : ($i(v0) & r1(all_10_0, v0) & ~ p1(v0)) % 10.81/2.21 | % 10.81/2.21 | DELTA: instantiating (13) with fresh symbol all_18_0 gives: % 10.81/2.21 | (14) $i(all_18_0) & r1(all_10_0, all_18_0) & ~ p1(all_18_0) % 10.81/2.21 | % 10.81/2.21 | ALPHA: (14) implies: % 10.81/2.21 | (15) ~ p1(all_18_0) % 10.81/2.21 | (16) r1(all_10_0, all_18_0) % 10.81/2.21 | (17) $i(all_18_0) % 10.81/2.21 | % 10.81/2.21 | GROUND_INST: instantiating (8) with all_2_0, all_10_0, all_18_0, simplifying % 10.81/2.21 | with (3), (4), (11), (12), (15), (16), (17) gives: % 10.81/2.21 | (18) ? [v0: $i] : ($i(v0) & r1(all_2_0, v0) & ~ p1(v0)) % 10.81/2.21 | % 10.81/2.21 | DELTA: instantiating (18) with fresh symbol all_25_0 gives: % 10.81/2.21 | (19) $i(all_25_0) & r1(all_2_0, all_25_0) & ~ p1(all_25_0) % 10.81/2.21 | % 10.81/2.21 | ALPHA: (19) implies: % 10.81/2.21 | (20) ~ p1(all_25_0) % 10.81/2.21 | (21) r1(all_2_0, all_25_0) % 10.81/2.21 | (22) $i(all_25_0) % 10.81/2.21 | % 10.81/2.21 | GROUND_INST: instantiating (6) with all_25_0, simplifying with (20), (21), % 10.81/2.21 | (22) gives: % 10.81/2.21 | (23) $false % 10.81/2.21 | % 10.81/2.21 | CLOSE: (23) is inconsistent. % 10.81/2.21 | % 10.81/2.21 End of proof % 10.81/2.21 % SZS output end Proof for theBenchmark % 10.81/2.21 % 10.81/2.21 1510ms %------------------------------------------------------------------------------