%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL664+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 : n004.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 12:54:35 PM UTC 2026 % Result : Theorem 5.15s 1.66s % Output : Proof 7.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL664+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 : n004.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 % 0.10/0.36 % DateTime : Sun Sep 6 01:40:15 UTC 2026 % 0.10/0.37 % CPUTime : % 0.14/0.38 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. % 0.64/0.73 ________ _____ % 0.64/0.73 ___ __ \_________(_)________________________________ % 0.64/0.73 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.64/0.73 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.64/0.73 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.64/0.73 % 0.64/0.73 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.64/0.73 (2023-06-19) % 0.64/0.73 % 0.64/0.73 (c) Philipp Rümmer, 2009-2023 % 0.64/0.73 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.64/0.73 Amanda Stjerna. % 0.64/0.73 Free software under BSD-3-Clause. % 0.64/0.73 % 0.64/0.73 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.64/0.73 % 0.64/0.73 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.64/0.75 Running up to 7 provers in parallel. % 0.64/0.77 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.64/0.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.64/0.77 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.64/0.77 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.64/0.77 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.64/0.77 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.64/0.77 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.15/1.25 Prover 4: Preprocessing ... % 2.15/1.25 Prover 1: Preprocessing ... % 2.84/1.32 Prover 0: Preprocessing ... % 2.84/1.32 Prover 6: Preprocessing ... % 2.84/1.32 Prover 3: Preprocessing ... % 2.84/1.32 Prover 5: Preprocessing ... % 2.84/1.32 Prover 2: Preprocessing ... % 3.63/1.47 Prover 5: Proving ... % 3.63/1.47 Prover 2: Proving ... % 4.37/1.53 Prover 6: Proving ... % 4.37/1.53 Prover 1: Constructing countermodel ... % 4.37/1.54 Prover 3: Constructing countermodel ... % 4.37/1.54 Prover 0: Proving ... % 4.37/1.55 Prover 4: Constructing countermodel ... % 5.15/1.65 Prover 5: proved (883ms) % 5.15/1.66 % 5.15/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.15/1.66 % 5.15/1.66 Prover 2: proved (889ms) % 5.15/1.66 % 5.15/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.15/1.66 % 5.15/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.15/1.66 Prover 6: stopped % 5.15/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.15/1.67 Prover 3: proved (901ms) % 5.15/1.67 % 5.15/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.15/1.67 % 5.15/1.67 Prover 0: stopped % 5.15/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.15/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.15/1.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.93/1.71 Prover 7: Preprocessing ... % 5.93/1.71 Prover 10: Preprocessing ... % 5.93/1.71 Prover 8: Preprocessing ... % 5.93/1.72 Prover 13: Preprocessing ... % 5.93/1.72 Prover 11: Preprocessing ... % 5.93/1.73 Prover 10: Warning: ignoring some quantifiers % 5.93/1.74 Prover 10: Constructing countermodel ... % 5.93/1.74 Prover 13: Warning: ignoring some quantifiers % 5.93/1.74 Prover 7: Warning: ignoring some quantifiers % 5.93/1.74 Prover 13: Constructing countermodel ... % 5.93/1.74 Prover 7: Constructing countermodel ... % 5.93/1.76 Prover 1: Found proof (size 14) % 5.93/1.76 Prover 1: proved (996ms) % 5.93/1.76 Prover 13: stopped % 5.93/1.76 Prover 4: stopped % 5.93/1.77 Prover 7: stopped % 5.93/1.77 Prover 10: stopped % 5.93/1.78 Prover 8: Warning: ignoring some quantifiers % 5.93/1.78 Prover 8: Constructing countermodel ... % 5.93/1.79 Prover 8: stopped % 6.65/1.82 Prover 11: Constructing countermodel ... % 6.65/1.82 Prover 11: stopped % 6.65/1.82 % 6.65/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.65/1.82 % 6.65/1.83 % SZS output start Proof for theBenchmark % 6.65/1.83 Assumptions after simplification: % 6.65/1.83 --------------------------------- % 6.65/1.83 % 6.65/1.83 (main) % 7.13/1.90 ? [v0: $i] : ($i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p14(v1) = % 7.13/1.90 v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) & ! % 7.13/1.90 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p12(v1) = v2) | ~ $i(v1) | ? [v3: % 7.13/1.90 int] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) & ! [v1: $i] : ! [v2: int] : % 7.13/1.90 (v2 = 0 | ~ (p16(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 7.13/1.90 r1(v0, v1) = v3)) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & p11(v1) % 7.13/1.90 = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = % 7.13/1.90 0) & p13(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : ? [v2: % 7.13/1.90 int] : ( ~ (v2 = 0) & p15(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: % 7.13/1.90 $i] : ? [v2: int] : ( ~ (v2 = 0) & p12(v1) = v2 & r1(v0, v1) = 0 & % 7.13/1.90 $i(v1))) % 7.13/1.90 % 7.13/1.90 (function-axioms) % 7.13/1.91 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 7.13/1.92 [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0: % 7.13/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.13/1.92 ~ (p11(v2) = v1) | ~ (p11(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 7.13/1.92 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (p13(v2) = v1) | ~ % 7.13/1.92 (p13(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 7.13/1.92 ! [v2: $i] : (v1 = v0 | ~ (p15(v2) = v1) | ~ (p15(v2) = v0)) & ! [v0: % 7.13/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.13/1.92 ~ (p14(v2) = v1) | ~ (p14(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 7.13/1.92 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (p12(v2) = v1) | ~ % 7.13/1.92 (p12(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 7.13/1.92 ! [v2: $i] : (v1 = v0 | ~ (p16(v2) = v1) | ~ (p16(v2) = v0)) % 7.13/1.92 % 7.13/1.92 Further assumptions not needed in the proof: % 7.13/1.92 -------------------------------------------- % 7.13/1.92 reflexivity % 7.13/1.92 % 7.13/1.92 Those formulas are unsatisfiable: % 7.13/1.92 --------------------------------- % 7.13/1.92 % 7.13/1.92 Begin of proof % 7.13/1.92 | % 7.13/1.92 | ALPHA: (function-axioms) implies: % 7.13/1.92 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.13/1.92 | ! [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) % 7.13/1.92 | % 7.13/1.93 | DELTA: instantiating (main) with fresh symbol all_4_0 gives: % 7.13/1.94 | (2) $i(all_4_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p14(v0) = v1) % 7.13/1.94 | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_4_0, v0) = v2)) & % 7.13/1.94 | ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p12(v0) = v1) | ~ $i(v0) | % 7.13/1.94 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_4_0, v0) = v2)) & ! [v0: $i] : % 7.13/1.94 | ! [v1: int] : (v1 = 0 | ~ (p16(v0) = v1) | ~ $i(v0) | ? [v2: int] : % 7.13/1.94 | ( ~ (v2 = 0) & r1(all_4_0, v0) = v2)) & ? [v0: $i] : ? [v1: int] : % 7.13/1.94 | ( ~ (v1 = 0) & p11(v0) = v1 & r1(all_4_0, v0) = 0 & $i(v0)) & ? [v0: % 7.13/1.94 | $i] : ? [v1: int] : ( ~ (v1 = 0) & p13(v0) = v1 & r1(all_4_0, v0) = % 7.13/1.94 | 0 & $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p15(v0) = % 7.13/1.94 | v1 & r1(all_4_0, v0) = 0 & $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~ % 7.13/1.94 | (v1 = 0) & p12(v0) = v1 & r1(all_4_0, v0) = 0 & $i(v0)) % 7.13/1.94 | % 7.13/1.94 | ALPHA: (2) implies: % 7.13/1.94 | (3) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p12(v0) = v1) | ~ $i(v0) | % 7.13/1.94 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_4_0, v0) = v2)) % 7.13/1.94 | (4) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p12(v0) = v1 & r1(all_4_0, % 7.13/1.94 | v0) = 0 & $i(v0)) % 7.13/1.94 | % 7.13/1.94 | DELTA: instantiating (4) with fresh symbols all_13_0, all_13_1 gives: % 7.13/1.95 | (5) ~ (all_13_0 = 0) & p12(all_13_1) = all_13_0 & r1(all_4_0, all_13_1) = % 7.13/1.95 | 0 & $i(all_13_1) % 7.13/1.95 | % 7.13/1.95 | ALPHA: (5) implies: % 7.13/1.95 | (6) ~ (all_13_0 = 0) % 7.13/1.95 | (7) $i(all_13_1) % 7.13/1.95 | (8) r1(all_4_0, all_13_1) = 0 % 7.13/1.95 | (9) p12(all_13_1) = all_13_0 % 7.13/1.95 | % 7.13/1.95 | GROUND_INST: instantiating (3) with all_13_1, all_13_0, simplifying with (7), % 7.13/1.95 | (9) gives: % 7.13/1.95 | (10) all_13_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_4_0, all_13_1) = % 7.13/1.95 | v0) % 7.13/1.95 | % 7.13/1.95 | BETA: splitting (10) gives: % 7.13/1.95 | % 7.13/1.95 | Case 1: % 7.13/1.95 | | % 7.13/1.95 | | (11) all_13_0 = 0 % 7.13/1.95 | | % 7.13/1.95 | | REDUCE: (6), (11) imply: % 7.13/1.96 | | (12) $false % 7.13/1.96 | | % 7.13/1.96 | | CLOSE: (12) is inconsistent. % 7.13/1.96 | | % 7.13/1.96 | Case 2: % 7.13/1.96 | | % 7.13/1.96 | | (13) ? [v0: int] : ( ~ (v0 = 0) & r1(all_4_0, all_13_1) = v0) % 7.13/1.96 | | % 7.13/1.96 | | DELTA: instantiating (13) with fresh symbol all_22_0 gives: % 7.13/1.96 | | (14) ~ (all_22_0 = 0) & r1(all_4_0, all_13_1) = all_22_0 % 7.13/1.96 | | % 7.13/1.96 | | ALPHA: (14) implies: % 7.13/1.96 | | (15) ~ (all_22_0 = 0) % 7.13/1.96 | | (16) r1(all_4_0, all_13_1) = all_22_0 % 7.13/1.96 | | % 7.13/1.96 | | GROUND_INST: instantiating (1) with 0, all_22_0, all_13_1, all_4_0, % 7.13/1.96 | | simplifying with (8), (16) gives: % 7.13/1.96 | | (17) all_22_0 = 0 % 7.13/1.96 | | % 7.13/1.96 | | REDUCE: (15), (17) imply: % 7.13/1.96 | | (18) $false % 7.13/1.96 | | % 7.13/1.96 | | CLOSE: (18) is inconsistent. % 7.13/1.96 | | % 7.13/1.96 | End of split % 7.13/1.96 | % 7.13/1.96 End of proof % 7.13/1.96 % SZS output end Proof for theBenchmark % 7.13/1.96 % 7.13/1.96 1232ms %------------------------------------------------------------------------------