%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL646+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 : n015.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 12:54:28 PM UTC 2026 % Result : Theorem 5.33s 1.51s % Output : Proof 6.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL646+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 % 0.10/0.36 % Computer : n015.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.37 % DateTime : Sat Sep 5 11:44:12 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.39 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. % 0.70/0.73 ________ _____ % 0.70/0.73 ___ __ \_________(_)________________________________ % 0.70/0.73 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.70/0.73 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.70/0.73 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.70/0.73 % 0.70/0.73 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.70/0.73 (2023-06-19) % 0.70/0.73 % 0.70/0.73 (c) Philipp Rümmer, 2009-2023 % 0.70/0.73 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.70/0.73 Amanda Stjerna. % 0.70/0.73 Free software under BSD-3-Clause. % 0.70/0.73 % 0.70/0.73 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.70/0.73 % 0.70/0.73 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.75 Running up to 7 provers in parallel. % 0.70/0.76 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.76 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.76 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.76 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.76 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.76 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.76 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.73/1.11 Prover 4: Preprocessing ... % 1.73/1.12 Prover 1: Preprocessing ... % 2.49/1.19 Prover 5: Preprocessing ... % 2.49/1.19 Prover 6: Preprocessing ... % 2.49/1.19 Prover 3: Preprocessing ... % 2.49/1.19 Prover 0: Preprocessing ... % 2.49/1.20 Prover 2: Preprocessing ... % 3.79/1.33 Prover 2: Constructing countermodel ... % 3.79/1.33 Prover 5: Constructing countermodel ... % 3.79/1.36 Prover 1: Constructing countermodel ... % 3.79/1.36 Prover 4: Constructing countermodel ... % 3.79/1.39 Prover 6: Proving ... % 4.55/1.41 Prover 0: Proving ... % 4.55/1.44 Prover 3: Constructing countermodel ... % 5.33/1.50 Prover 2: proved (741ms) % 5.33/1.50 % 5.33/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.33/1.51 % 5.33/1.51 Prover 5: proved (739ms) % 5.33/1.51 % 5.33/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.33/1.51 % 5.33/1.51 Prover 3: stopped % 5.33/1.51 Prover 6: stopped % 5.33/1.51 Prover 0: stopped % 5.33/1.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.33/1.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.33/1.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.33/1.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.33/1.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.33/1.56 Prover 10: Preprocessing ... % 5.33/1.56 Prover 13: Preprocessing ... % 5.33/1.57 Prover 7: Preprocessing ... % 5.33/1.57 Prover 11: Preprocessing ... % 5.33/1.57 Prover 8: Preprocessing ... % 5.33/1.57 Prover 10: Constructing countermodel ... % 5.33/1.59 Prover 13: Constructing countermodel ... % 5.33/1.59 Prover 1: Found proof (size 14) % 5.33/1.59 Prover 1: proved (835ms) % 5.33/1.59 Prover 4: Found proof (size 8) % 5.33/1.59 Prover 4: proved (835ms) % 5.33/1.59 Prover 10: stopped % 5.33/1.60 Prover 13: stopped % 6.11/1.60 Prover 11: stopped % 6.11/1.60 Prover 7: Constructing countermodel ... % 6.11/1.61 Prover 7: stopped % 6.11/1.66 Prover 8: Warning: ignoring some quantifiers % 6.11/1.67 Prover 8: Constructing countermodel ... % 6.11/1.67 Prover 8: stopped % 6.11/1.67 % 6.11/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.11/1.67 % 6.11/1.68 % SZS output start Proof for theBenchmark % 6.11/1.68 Assumptions after simplification: % 6.11/1.68 --------------------------------- % 6.11/1.68 % 6.11/1.68 (main) % 6.59/1.75 ? [v0: $i] : ($i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p4(v1) = % 6.59/1.75 v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) & ! % 6.59/1.75 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p2(v1) = v2) | ~ $i(v1) | ? [v3: % 6.59/1.75 int] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) & ! [v1: $i] : ! [v2: int] : % 6.59/1.75 (v2 = 0 | ~ (p6(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 6.59/1.75 r1(v0, v1) = v3)) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & p1(v1) = % 6.59/1.75 v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 6.59/1.75 & p3(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : ? [v2: int] : ( % 6.59/1.75 ~ (v2 = 0) & p5(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : ? % 6.59/1.76 [v2: int] : ( ~ (v2 = 0) & p2(v1) = v2 & r1(v0, v1) = 0 & $i(v1))) % 6.59/1.76 % 6.59/1.76 (function-axioms) % 6.59/1.77 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 6.59/1.77 [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0: % 6.59/1.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.59/1.77 ~ (p1(v2) = v1) | ~ (p1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 6.59/1.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (p3(v2) = v1) | ~ (p3(v2) % 6.59/1.77 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 6.59/1.77 $i] : (v1 = v0 | ~ (p5(v2) = v1) | ~ (p5(v2) = v0)) & ! [v0: % 6.59/1.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.59/1.77 ~ (p4(v2) = v1) | ~ (p4(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 6.59/1.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (p2(v2) = v1) | ~ (p2(v2) % 6.59/1.77 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 6.59/1.77 $i] : (v1 = v0 | ~ (p6(v2) = v1) | ~ (p6(v2) = v0)) % 6.59/1.77 % 6.59/1.77 Those formulas are unsatisfiable: % 6.59/1.77 --------------------------------- % 6.59/1.77 % 6.59/1.77 Begin of proof % 6.59/1.77 | % 6.59/1.77 | ALPHA: (function-axioms) implies: % 6.59/1.77 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.59/1.77 | ! [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) % 6.59/1.77 | % 6.59/1.77 | DELTA: instantiating (main) with fresh symbol all_3_0 gives: % 6.59/1.78 | (2) $i(all_3_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p4(v0) = v1) | % 6.59/1.78 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_3_0, v0) = v2)) & ! % 6.59/1.78 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p2(v0) = v1) | ~ $i(v0) | ? % 6.59/1.78 | [v2: int] : ( ~ (v2 = 0) & r1(all_3_0, v0) = v2)) & ! [v0: $i] : ! % 6.59/1.78 | [v1: int] : (v1 = 0 | ~ (p6(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 6.59/1.78 | (v2 = 0) & r1(all_3_0, v0) = v2)) & ? [v0: $i] : ? [v1: int] : ( % 6.59/1.78 | ~ (v1 = 0) & p1(v0) = v1 & r1(all_3_0, v0) = 0 & $i(v0)) & ? [v0: % 6.59/1.78 | $i] : ? [v1: int] : ( ~ (v1 = 0) & p3(v0) = v1 & r1(all_3_0, v0) = 0 % 6.59/1.78 | & $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p5(v0) = v1 & % 6.59/1.78 | r1(all_3_0, v0) = 0 & $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 % 6.59/1.78 | = 0) & p2(v0) = v1 & r1(all_3_0, v0) = 0 & $i(v0)) % 6.59/1.78 | % 6.59/1.78 | ALPHA: (2) implies: % 6.59/1.79 | (3) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p2(v0) = v1) | ~ $i(v0) | % 6.59/1.79 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_3_0, v0) = v2)) % 6.59/1.79 | (4) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p2(v0) = v1 & r1(all_3_0, % 6.59/1.79 | v0) = 0 & $i(v0)) % 6.59/1.79 | % 6.59/1.79 | DELTA: instantiating (4) with fresh symbols all_12_0, all_12_1 gives: % 6.59/1.79 | (5) ~ (all_12_0 = 0) & p2(all_12_1) = all_12_0 & r1(all_3_0, all_12_1) = 0 % 6.59/1.79 | & $i(all_12_1) % 6.59/1.79 | % 6.59/1.79 | ALPHA: (5) implies: % 6.59/1.79 | (6) ~ (all_12_0 = 0) % 6.59/1.79 | (7) $i(all_12_1) % 6.59/1.79 | (8) r1(all_3_0, all_12_1) = 0 % 6.59/1.79 | (9) p2(all_12_1) = all_12_0 % 6.59/1.79 | % 6.59/1.79 | GROUND_INST: instantiating (3) with all_12_1, all_12_0, simplifying with (7), % 6.59/1.79 | (9) gives: % 6.59/1.79 | (10) all_12_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_3_0, all_12_1) = % 6.59/1.79 | v0) % 6.59/1.79 | % 6.59/1.79 | BETA: splitting (10) gives: % 6.59/1.79 | % 6.59/1.80 | Case 1: % 6.59/1.80 | | % 6.59/1.80 | | (11) all_12_0 = 0 % 6.59/1.80 | | % 6.59/1.80 | | REDUCE: (6), (11) imply: % 6.59/1.80 | | (12) $false % 6.94/1.80 | | % 6.94/1.80 | | CLOSE: (12) is inconsistent. % 6.94/1.80 | | % 6.94/1.80 | Case 2: % 6.94/1.80 | | % 6.94/1.80 | | (13) ? [v0: int] : ( ~ (v0 = 0) & r1(all_3_0, all_12_1) = v0) % 6.94/1.80 | | % 6.94/1.80 | | DELTA: instantiating (13) with fresh symbol all_21_0 gives: % 6.94/1.80 | | (14) ~ (all_21_0 = 0) & r1(all_3_0, all_12_1) = all_21_0 % 6.94/1.80 | | % 6.94/1.80 | | ALPHA: (14) implies: % 6.94/1.80 | | (15) ~ (all_21_0 = 0) % 6.94/1.80 | | (16) r1(all_3_0, all_12_1) = all_21_0 % 6.94/1.80 | | % 6.94/1.80 | | GROUND_INST: instantiating (1) with 0, all_21_0, all_12_1, all_3_0, % 6.94/1.80 | | simplifying with (8), (16) gives: % 6.94/1.80 | | (17) all_21_0 = 0 % 6.94/1.80 | | % 6.94/1.80 | | REDUCE: (15), (17) imply: % 6.94/1.80 | | (18) $false % 6.94/1.80 | | % 6.94/1.80 | | CLOSE: (18) is inconsistent. % 6.94/1.80 | | % 6.94/1.80 | End of split % 6.94/1.80 | % 6.94/1.80 End of proof % 6.94/1.80 % SZS output end Proof for theBenchmark % 6.94/1.80 % 6.94/1.80 1073ms %------------------------------------------------------------------------------