%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL961_11 : TPTP v9.3.1. Released v8.2.0. % 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 12:55:10 PM UTC 2026 % Result : Theorem 4.85s 1.32s % Output : Proof 6.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL961_11 : TPTP v9.3.1. Released v8.2.0. % 0.00/0.03 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.36 % Computer : n006.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.37 % CPULimit : 300 % 0.09/0.37 % WCLimit : 300 % 0.09/0.37 % DateTime : Sat Sep 5 17:03:16 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.39 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. % 0.47/0.58 ________ _____ % 0.47/0.58 ___ __ \_________(_)________________________________ % 0.47/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.47/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.47/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.47/0.58 % 0.47/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.47/0.58 (2023-06-19) % 0.47/0.58 % 0.47/0.58 (c) Philipp Rümmer, 2009-2023 % 0.47/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.47/0.58 Amanda Stjerna. % 0.47/0.58 Free software under BSD-3-Clause. % 0.47/0.58 % 0.47/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.47/0.58 % 0.47/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.47/0.59 Running up to 7 provers in parallel. % 0.47/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.47/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.47/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.47/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.47/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.47/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.47/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.85/0.97 Prover 4: Preprocessing ... % 1.85/0.97 Prover 1: Preprocessing ... % 2.78/1.04 Prover 2: Preprocessing ... % 2.78/1.04 Prover 5: Preprocessing ... % 2.78/1.04 Prover 3: Preprocessing ... % 2.78/1.04 Prover 6: Preprocessing ... % 2.78/1.05 Prover 0: Preprocessing ... % 3.55/1.13 Prover 1: Constructing countermodel ... % 3.55/1.15 Prover 2: Proving ... % 3.55/1.16 Prover 5: Proving ... % 3.55/1.18 Prover 4: Constructing countermodel ... % 3.55/1.19 Prover 6: Proving ... % 4.11/1.21 Prover 3: Constructing countermodel ... % 4.11/1.21 Prover 0: Proving ... % 4.85/1.31 Prover 3: proved (708ms) % 4.85/1.32 % 4.85/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.85/1.32 % 4.85/1.32 Prover 2: stopped % 4.85/1.32 Prover 6: stopped % 4.85/1.32 Prover 0: stopped % 4.85/1.32 Prover 5: stopped % 4.85/1.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.85/1.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.85/1.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.85/1.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.85/1.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.85/1.38 Prover 10: Preprocessing ... % 4.85/1.38 Prover 8: Preprocessing ... % 4.85/1.38 Prover 13: Preprocessing ... % 4.85/1.38 Prover 4: Found proof (size 13) % 4.85/1.38 Prover 4: proved (777ms) % 4.85/1.38 Prover 1: stopped % 4.85/1.38 Prover 7: Preprocessing ... % 4.85/1.38 Prover 11: Preprocessing ... % 5.59/1.40 Prover 13: Warning: ignoring some quantifiers % 5.59/1.40 Prover 10: Warning: ignoring some quantifiers % 5.59/1.40 Prover 13: Constructing countermodel ... % 5.59/1.40 Prover 13: stopped % 5.59/1.40 Prover 10: Constructing countermodel ... % 5.59/1.40 Prover 10: stopped % 5.59/1.41 Prover 7: Warning: ignoring some quantifiers % 5.59/1.41 Prover 7: Constructing countermodel ... % 5.59/1.42 Prover 7: stopped % 5.59/1.44 Prover 8: Warning: ignoring some quantifiers % 5.59/1.44 Prover 8: Constructing countermodel ... % 5.59/1.45 Prover 8: stopped % 5.59/1.46 Prover 11: Constructing countermodel ... % 5.59/1.46 Prover 11: stopped % 5.59/1.46 % 5.59/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.59/1.46 % 5.59/1.47 % SZS output start Proof for theBenchmark % 5.59/1.47 Assumptions after simplification: % 5.59/1.47 --------------------------------- % 5.59/1.47 % 5.59/1.47 (mrel_universal) % 6.08/1.53 ! [v0: $ki_world] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ % 6.08/1.53 ($ki_accessible(v0, v1) = v2) | ~ $ki_world(v1) | ~ $ki_world(v0)) % 6.08/1.53 % 6.08/1.53 (verify) % 6.08/1.55 $ki_world($ki_local_world) & ? [v0: $ki_world] : ? [v1: $ki_world] : ? [v2: % 6.08/1.55 int] : ? [v3: $ki_world] : ? [v4: $ki_world] : ? [v5: int] : ( ~ (v5 = 0) % 6.08/1.55 & ~ (v2 = 0) & q(v4) = v5 & p(v1) = v2 & $ki_accessible(v3, v4) = 0 & % 6.08/1.55 $ki_accessible(v0, v1) = 0 & $ki_accessible($ki_local_world, v3) = 0 & % 6.08/1.55 $ki_accessible($ki_local_world, v0) = 0 & $ki_world(v4) & $ki_world(v3) & % 6.08/1.55 $ki_world(v1) & $ki_world(v0) & ! [v6: $ki_world] : ! [v7: int] : (v7 = 0 % 6.08/1.55 | ~ (q(v6) = v7) | ~ $ki_world(v6) | ? [v8: int] : ( ~ (v8 = 0) & % 6.08/1.55 $ki_accessible(v0, v6) = v8)) & ! [v6: $ki_world] : ! [v7: int] : (v7 % 6.08/1.55 = 0 | ~ (p(v6) = v7) | ~ $ki_world(v6) | ? [v8: int] : ( ~ (v8 = 0) & % 6.08/1.55 $ki_accessible(v3, v6) = v8)) & ! [v6: $ki_world] : ( ~ % 6.08/1.55 ($ki_accessible(v3, v6) = 0) | ~ $ki_world(v6) | p(v6) = 0) & ! [v6: % 6.08/1.55 $ki_world] : ( ~ ($ki_accessible(v0, v6) = 0) | ~ $ki_world(v6) | q(v6) = % 6.08/1.55 0)) % 6.08/1.55 % 6.08/1.55 Those formulas are unsatisfiable: % 6.08/1.55 --------------------------------- % 6.08/1.55 % 6.08/1.55 Begin of proof % 6.08/1.55 | % 6.08/1.55 | ALPHA: (verify) implies: % 6.08/1.56 | (1) ? [v0: $ki_world] : ? [v1: $ki_world] : ? [v2: int] : ? [v3: % 6.08/1.56 | $ki_world] : ? [v4: $ki_world] : ? [v5: int] : ( ~ (v5 = 0) & ~ % 6.08/1.56 | (v2 = 0) & q(v4) = v5 & p(v1) = v2 & $ki_accessible(v3, v4) = 0 & % 6.08/1.56 | $ki_accessible(v0, v1) = 0 & $ki_accessible($ki_local_world, v3) = 0 % 6.08/1.56 | & $ki_accessible($ki_local_world, v0) = 0 & $ki_world(v4) & % 6.08/1.56 | $ki_world(v3) & $ki_world(v1) & $ki_world(v0) & ! [v6: $ki_world] : % 6.08/1.57 | ! [v7: int] : (v7 = 0 | ~ (q(v6) = v7) | ~ $ki_world(v6) | ? [v8: % 6.08/1.57 | int] : ( ~ (v8 = 0) & $ki_accessible(v0, v6) = v8)) & ! [v6: % 6.08/1.57 | $ki_world] : ! [v7: int] : (v7 = 0 | ~ (p(v6) = v7) | ~ % 6.08/1.57 | $ki_world(v6) | ? [v8: int] : ( ~ (v8 = 0) & $ki_accessible(v3, % 6.08/1.57 | v6) = v8)) & ! [v6: $ki_world] : ( ~ ($ki_accessible(v3, v6) = % 6.08/1.57 | 0) | ~ $ki_world(v6) | p(v6) = 0) & ! [v6: $ki_world] : ( ~ % 6.08/1.57 | ($ki_accessible(v0, v6) = 0) | ~ $ki_world(v6) | q(v6) = 0)) % 6.08/1.57 | % 6.08/1.57 | DELTA: instantiating (1) with fresh symbols all_7_0, all_7_1, all_7_2, % 6.08/1.57 | all_7_3, all_7_4, all_7_5 gives: % 6.08/1.58 | (2) ~ (all_7_0 = 0) & ~ (all_7_3 = 0) & q(all_7_1) = all_7_0 & p(all_7_4) % 6.08/1.58 | = all_7_3 & $ki_accessible(all_7_2, all_7_1) = 0 & % 6.08/1.58 | $ki_accessible(all_7_5, all_7_4) = 0 & $ki_accessible($ki_local_world, % 6.08/1.58 | all_7_2) = 0 & $ki_accessible($ki_local_world, all_7_5) = 0 & % 6.08/1.58 | $ki_world(all_7_1) & $ki_world(all_7_2) & $ki_world(all_7_4) & % 6.08/1.58 | $ki_world(all_7_5) & ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ % 6.08/1.58 | (q(v0) = v1) | ~ $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 6.08/1.58 | $ki_accessible(all_7_5, v0) = v2)) & ! [v0: $ki_world] : ! [v1: % 6.08/1.58 | int] : (v1 = 0 | ~ (p(v0) = v1) | ~ $ki_world(v0) | ? [v2: int] : % 6.08/1.58 | ( ~ (v2 = 0) & $ki_accessible(all_7_2, v0) = v2)) & ! [v0: % 6.08/1.58 | $ki_world] : ( ~ ($ki_accessible(all_7_2, v0) = 0) | ~ $ki_world(v0) % 6.08/1.58 | | p(v0) = 0) & ! [v0: $ki_world] : ( ~ ($ki_accessible(all_7_5, v0) % 6.08/1.58 | = 0) | ~ $ki_world(v0) | q(v0) = 0) % 6.08/1.58 | % 6.08/1.58 | ALPHA: (2) implies: % 6.08/1.58 | (3) ~ (all_7_0 = 0) % 6.08/1.58 | (4) $ki_world(all_7_5) % 6.08/1.58 | (5) $ki_world(all_7_1) % 6.08/1.58 | (6) q(all_7_1) = all_7_0 % 6.08/1.58 | (7) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (q(v0) = v1) | ~ % 6.08/1.58 | $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) & $ki_accessible(all_7_5, % 6.08/1.58 | v0) = v2)) % 6.08/1.59 | % 6.08/1.59 | GROUND_INST: instantiating (7) with all_7_1, all_7_0, simplifying with (5), % 6.08/1.59 | (6) gives: % 6.08/1.59 | (8) all_7_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & $ki_accessible(all_7_5, % 6.08/1.59 | all_7_1) = v0) % 6.08/1.59 | % 6.08/1.59 | BETA: splitting (8) gives: % 6.08/1.59 | % 6.08/1.59 | Case 1: % 6.08/1.59 | | % 6.08/1.59 | | (9) all_7_0 = 0 % 6.08/1.59 | | % 6.08/1.59 | | REDUCE: (3), (9) imply: % 6.08/1.59 | | (10) $false % 6.08/1.59 | | % 6.08/1.59 | | CLOSE: (10) is inconsistent. % 6.08/1.59 | | % 6.08/1.59 | Case 2: % 6.08/1.59 | | % 6.08/1.59 | | (11) ? [v0: int] : ( ~ (v0 = 0) & $ki_accessible(all_7_5, all_7_1) = v0) % 6.08/1.59 | | % 6.08/1.59 | | DELTA: instantiating (11) with fresh symbol all_20_0 gives: % 6.08/1.59 | | (12) ~ (all_20_0 = 0) & $ki_accessible(all_7_5, all_7_1) = all_20_0 % 6.08/1.59 | | % 6.08/1.59 | | ALPHA: (12) implies: % 6.08/1.59 | | (13) ~ (all_20_0 = 0) % 6.08/1.60 | | (14) $ki_accessible(all_7_5, all_7_1) = all_20_0 % 6.08/1.60 | | % 6.08/1.60 | | GROUND_INST: instantiating (mrel_universal) with all_7_5, all_7_1, all_20_0, % 6.08/1.60 | | simplifying with (4), (5), (14) gives: % 6.08/1.60 | | (15) all_20_0 = 0 % 6.08/1.60 | | % 6.08/1.60 | | REDUCE: (13), (15) imply: % 6.54/1.60 | | (16) $false % 6.54/1.60 | | % 6.54/1.60 | | CLOSE: (16) is inconsistent. % 6.54/1.60 | | % 6.54/1.60 | End of split % 6.54/1.60 | % 6.54/1.60 End of proof % 6.54/1.60 % SZS output end Proof for theBenchmark % 6.54/1.60 % 6.54/1.60 1013ms %------------------------------------------------------------------------------