%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL682+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 : 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 12:54:42 PM UTC 2026 % Result : Theorem 4.18s 1.17s % Output : Proof 5.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.01 % Problem : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.02 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.03/0.30 % Computer : n012.cluster.edu % 0.03/0.30 % Model : x86_64 x86_64 % 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.03/0.30 % Memory : 8046.5625MB % 0.03/0.30 % OS : Linux 6.8.0-71-generic % 0.03/0.30 % CPULimit : 300 % 0.03/0.30 % WCLimit : 300 % 0.03/0.30 % DateTime : Fri Sep 4 16:06:28 UTC 2026 % 0.03/0.30 % CPUTime : % 0.03/0.31 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. % 0.26/0.48 ________ _____ % 0.26/0.48 ___ __ \_________(_)________________________________ % 0.26/0.48 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.26/0.48 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.26/0.48 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.26/0.48 % 0.26/0.48 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.26/0.48 (2023-06-19) % 0.26/0.48 % 0.26/0.48 (c) Philipp Rümmer, 2009-2023 % 0.26/0.48 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.26/0.48 Amanda Stjerna. % 0.26/0.48 Free software under BSD-3-Clause. % 0.26/0.48 % 0.26/0.48 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.26/0.48 % 0.26/0.48 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.26/0.49 Running up to 7 provers in parallel. % 0.26/0.49 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.26/0.49 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.26/0.49 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.26/0.49 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.26/0.49 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.26/0.49 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.26/0.50 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.96/0.80 Prover 1: Preprocessing ... % 1.68/0.80 Prover 4: Preprocessing ... % 1.68/0.85 Prover 0: Preprocessing ... % 1.68/0.85 Prover 5: Preprocessing ... % 1.68/0.85 Prover 2: Preprocessing ... % 1.68/0.85 Prover 3: Preprocessing ... % 1.68/0.85 Prover 6: Preprocessing ... % 2.40/0.96 Prover 2: Proving ... % 2.40/0.96 Prover 5: Proving ... % 3.38/1.03 Prover 6: Proving ... % 3.38/1.04 Prover 3: Constructing countermodel ... % 3.38/1.04 Prover 1: Constructing countermodel ... % 3.38/1.06 Prover 0: Proving ... % 3.38/1.06 Prover 4: Constructing countermodel ... % 4.18/1.16 Prover 3: proved (671ms) % 4.18/1.17 % 4.18/1.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.18/1.17 % 4.18/1.17 Prover 2: stopped % 4.18/1.17 Prover 0: stopped % 4.18/1.17 Prover 6: stopped % 4.18/1.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.18/1.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.18/1.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.18/1.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.18/1.17 Prover 5: stopped % 4.18/1.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.18/1.19 Prover 8: Preprocessing ... % 4.18/1.20 Prover 7: Preprocessing ... % 4.74/1.21 Prover 7: Warning: ignoring some quantifiers % 4.74/1.21 Prover 13: Preprocessing ... % 4.74/1.21 Prover 7: Constructing countermodel ... % 4.74/1.22 Prover 10: Preprocessing ... % 4.74/1.22 Prover 11: Preprocessing ... % 4.74/1.24 Prover 10: Warning: ignoring some quantifiers % 4.74/1.24 Prover 10: Constructing countermodel ... % 4.74/1.25 Prover 13: Warning: ignoring some quantifiers % 4.74/1.25 Prover 13: Constructing countermodel ... % 4.74/1.28 Prover 8: Warning: ignoring some quantifiers % 4.74/1.29 Prover 10: Found proof (size 4) % 4.74/1.29 Prover 10: proved (122ms) % 4.74/1.29 Prover 13: stopped % 4.74/1.29 Prover 7: stopped % 4.74/1.29 Prover 4: stopped % 4.74/1.29 Prover 8: Constructing countermodel ... % 4.74/1.30 Prover 1: stopped % 5.50/1.30 Prover 8: stopped % 5.50/1.31 Prover 11: Constructing countermodel ... % 5.50/1.31 Prover 11: stopped % 5.50/1.31 % 5.50/1.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.50/1.31 % 5.50/1.32 % SZS output start Proof for theBenchmark % 5.50/1.32 Assumptions after simplification: % 5.50/1.32 --------------------------------- % 5.50/1.32 % 5.50/1.32 (main) % 5.50/1.33 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 5.50/1.33 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v8) & $i(v7) & $i(v6) & % 5.50/1.33 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & r1(v7, v8) & r1(v5, % 5.50/1.33 v6) & r1(v3, v4) & r1(v1, v2) & r1(v0, v7) & r1(v0, v5) & r1(v0, v3) & % 5.50/1.33 r1(v0, v1) & ~ p11(v2) & ~ p13(v6) & ~ p15(v8) & ~ p12(v4) & ! [v9: $i] % 5.50/1.33 : ! [v10: $i] : ( ~ $i(v10) | ~ $i(v9) | ~ r1(v9, v10) | ~ r1(v0, v9) | % 5.50/1.33 p14(v10)) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~ $i(v9) | ~ % 5.50/1.33 r1(v9, v10) | ~ r1(v0, v9) | p12(v10)) & ! [v9: $i] : ! [v10: $i] : ( ~ % 5.50/1.33 $i(v10) | ~ $i(v9) | ~ r1(v9, v10) | ~ r1(v0, v9) | p16(v10))) % 5.50/1.33 % 5.50/1.33 Further assumptions not needed in the proof: % 5.50/1.33 -------------------------------------------- % 5.50/1.33 reflexivity, transitivity % 5.50/1.33 % 5.50/1.33 Those formulas are unsatisfiable: % 5.50/1.33 --------------------------------- % 5.50/1.33 % 5.50/1.33 Begin of proof % 5.50/1.33 | % 5.50/1.33 | DELTA: instantiating (main) with fresh symbols all_4_0, all_4_1, all_4_2, % 5.50/1.33 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8 gives: % 5.50/1.34 | (1) $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & $i(all_4_3) & $i(all_4_4) & % 5.50/1.34 | $i(all_4_5) & $i(all_4_6) & $i(all_4_7) & $i(all_4_8) & r1(all_4_1, % 5.50/1.34 | all_4_0) & r1(all_4_3, all_4_2) & r1(all_4_5, all_4_4) & r1(all_4_7, % 5.50/1.34 | all_4_6) & r1(all_4_8, all_4_1) & r1(all_4_8, all_4_3) & r1(all_4_8, % 5.50/1.34 | all_4_5) & r1(all_4_8, all_4_7) & ~ p11(all_4_6) & ~ p13(all_4_2) & % 5.50/1.34 | ~ p15(all_4_0) & ~ p12(all_4_4) & ! [v0: $i] : ! [v1: $i] : ( ~ % 5.50/1.34 | $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_4_8, v0) | p14(v1)) & % 5.50/1.34 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ % 5.50/1.34 | r1(all_4_8, v0) | p12(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | % 5.50/1.34 | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_4_8, v0) | p16(v1)) % 5.50/1.34 | % 5.50/1.34 | ALPHA: (1) implies: % 5.50/1.34 | (2) ~ p12(all_4_4) % 5.50/1.34 | (3) r1(all_4_8, all_4_5) % 5.50/1.34 | (4) r1(all_4_5, all_4_4) % 5.50/1.34 | (5) $i(all_4_5) % 5.50/1.34 | (6) $i(all_4_4) % 5.50/1.34 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ % 5.50/1.34 | r1(all_4_8, v0) | p12(v1)) % 5.50/1.34 | % 5.50/1.35 | GROUND_INST: instantiating (7) with all_4_5, all_4_4, simplifying with (2), % 5.50/1.35 | (3), (4), (5), (6) gives: % 5.50/1.35 | (8) $false % 5.50/1.35 | % 5.50/1.35 | CLOSE: (8) is inconsistent. % 5.50/1.35 | % 5.50/1.35 End of proof % 5.50/1.35 % SZS output end Proof for theBenchmark % 5.50/1.35 % 5.50/1.35 869ms %------------------------------------------------------------------------------