%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL658+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 12:54:33 PM UTC 2026 % Result : Theorem 27.50s 4.31s % Output : Proof 31.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL658+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 % 0.10/0.37 % Computer : n015.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sat Sep 5 09:08:57 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. % 0.66/0.73 ________ _____ % 0.66/0.73 ___ __ \_________(_)________________________________ % 0.66/0.73 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.66/0.73 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.66/0.73 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.66/0.73 % 0.66/0.73 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.66/0.73 (2023-06-19) % 0.66/0.73 % 0.66/0.73 (c) Philipp Rümmer, 2009-2023 % 0.66/0.73 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.66/0.73 Amanda Stjerna. % 0.66/0.73 Free software under BSD-3-Clause. % 0.66/0.73 % 0.66/0.73 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.66/0.73 % 0.66/0.74 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.76 Running up to 7 provers in parallel. % 0.66/0.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.77 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.77 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.77 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.77 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.77 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.77 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.91/1.32 Prover 1: Preprocessing ... % 3.91/1.33 Prover 4: Preprocessing ... % 3.91/1.35 Prover 0: Preprocessing ... % 3.91/1.35 Prover 6: Preprocessing ... % 3.91/1.36 Prover 2: Preprocessing ... % 3.91/1.36 Prover 5: Preprocessing ... % 3.91/1.37 Prover 3: Preprocessing ... % 7.89/1.81 Prover 5: Proving ... % 7.89/1.81 Prover 2: Proving ... % 9.79/2.09 Prover 6: Proving ... % 9.79/2.13 Prover 1: Constructing countermodel ... % 9.79/2.14 Prover 3: Constructing countermodel ... % 18.85/3.21 Prover 0: Proving ... % 21.20/3.55 Prover 4: Constructing countermodel ... % 27.50/4.31 Prover 5: proved (3541ms) % 27.50/4.31 % 27.50/4.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 27.50/4.31 % 27.50/4.31 Prover 6: stopped % 27.50/4.31 Prover 2: stopped % 27.50/4.32 Prover 3: stopped % 27.50/4.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 27.50/4.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 27.50/4.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 27.50/4.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 27.50/4.36 Prover 0: stopped % 27.50/4.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 28.28/4.43 Prover 10: Preprocessing ... % 28.28/4.46 Prover 10: Warning: ignoring some quantifiers % 28.28/4.46 Prover 10: Constructing countermodel ... % 28.28/4.46 Prover 13: Preprocessing ... % 28.28/4.49 Prover 8: Preprocessing ... % 28.28/4.49 Prover 11: Preprocessing ... % 28.28/4.49 Prover 7: Preprocessing ... % 29.09/4.51 Prover 13: Warning: ignoring some quantifiers % 29.09/4.52 Prover 13: Constructing countermodel ... % 29.09/4.59 Prover 7: Warning: ignoring some quantifiers % 29.86/4.61 Prover 7: Constructing countermodel ... % 29.86/4.63 Prover 8: Warning: ignoring some quantifiers % 29.86/4.64 Prover 8: Constructing countermodel ... % 29.86/4.67 Prover 10: Found proof (size 44) % 29.86/4.67 Prover 10: proved (353ms) % 29.86/4.67 Prover 7: stopped % 29.86/4.67 Prover 8: stopped % 29.86/4.67 Prover 4: stopped % 29.86/4.68 Prover 13: stopped % 29.86/4.68 Prover 1: stopped % 30.57/4.73 Prover 11: stopped % 30.57/4.73 % 30.57/4.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 30.57/4.73 % 30.57/4.73 % SZS output start Proof for theBenchmark % 30.57/4.74 Assumptions after simplification: % 30.57/4.74 --------------------------------- % 30.57/4.74 % 30.57/4.74 (main) % 30.57/4.77 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & % 30.57/4.78 $i(v1) & $i(v0) & r1(v1, v3) & r1(v1, v2) & r1(v0, v1) & ~ p1(v3) & ! [v4: % 30.57/4.78 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | % 30.57/4.78 ~ $i(v5) | ~ $i(v4) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ % 30.57/4.78 r1(v0, v4) | p1(v7) | ? [v8: $i] : ($i(v8) & r1(v5, v8) & ~ p1(v8))) & % 30.57/4.78 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) % 30.57/4.78 | ~ p1(v4) | ~ r1(v4, v6) | ~ r1(v4, v5) | ~ r1(v0, v4) | p1(v6) | ? % 30.57/4.78 [v7: $i] : ? [v8: $i] : ($i(v8) & $i(v7) & ((p1(v7) & r1(v7, v8) & r1(v5, % 30.57/4.78 v7) & ~ p1(v8)) | (p1(v7) & r1(v7, v8) & r1(v4, v7) & ~ p1(v8) & % 30.57/4.78 ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) % 30.57/4.78 | ~ $i(v9) | ~ p1(v10) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ % 30.57/4.78 r1(v7, v9) | p1(v11) | p1(v9)) & ! [v9: $i] : ! [v10: $i] : ! % 30.57/4.78 [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ p1(v10) | ~ % 30.57/4.78 r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v7, v9) | p1(v11) | ? [v12: % 30.57/4.78 $i] : ($i(v12) & r1(v9, v12) & ~ p1(v12))))))) & ! [v4: $i] : % 30.57/4.78 ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ r1(v5, % 30.57/4.78 v6) | ~ r1(v4, v5) | ~ r1(v0, v4) | p1(v6) | ? [v7: $i] : ? [v8: $i] % 30.57/4.78 : ($i(v8) & $i(v7) & ((p1(v7) & r1(v7, v8) & r1(v6, v7) & ~ p1(v8)) | % 30.57/4.78 (r1(v4, v7) & ~ p1(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | % 30.57/4.78 ~ $i(v9) | ~ p1(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) | % 30.57/4.78 p1(v10)))))) & ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) % 30.57/4.78 | ~ r1(v4, v5) | ~ r1(v0, v4) | p1(v4) | ? [v6: $i] : ($i(v6) & % 30.57/4.78 ((r1(v5, v6) & ~ p1(v6)) | (r1(v4, v6) & ~ p1(v6) & ! [v7: $i] : ! % 30.57/4.78 [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p1(v7) | ~ r1(v7, v8) | ~ % 30.57/4.78 r1(v6, v7) | p1(v8)))))) & ! [v4: $i] : ( ~ $i(v4) | ~ r1(v2, % 30.57/4.78 v4) | p1(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ r1(v1, v4) | p1(v4) | ? % 30.57/4.78 [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & p1(v5) & r1(v5, v6) & r1(v4, % 30.57/4.78 v5) & ~ p1(v6)))) % 30.57/4.78 % 30.57/4.78 Further assumptions not needed in the proof: % 30.57/4.78 -------------------------------------------- % 30.57/4.78 reflexivity % 30.57/4.78 % 30.57/4.78 Those formulas are unsatisfiable: % 30.57/4.78 --------------------------------- % 30.57/4.78 % 30.57/4.78 Begin of proof % 30.57/4.78 | % 30.57/4.78 | DELTA: instantiating (main) with fresh symbols all_3_0, all_3_1, all_3_2, % 30.57/4.78 | all_3_3 gives: % 31.05/4.80 | (1) $i(all_3_0) & $i(all_3_1) & $i(all_3_2) & $i(all_3_3) & r1(all_3_2, % 31.05/4.80 | all_3_0) & r1(all_3_2, all_3_1) & r1(all_3_3, all_3_2) & ~ % 31.05/4.80 | p1(all_3_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 31.05/4.80 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ % 31.05/4.80 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_3, v0) | p1(v3) | ? [v4: % 31.05/4.80 | $i] : ($i(v4) & r1(v1, v4) & ~ p1(v4))) & ! [v0: $i] : ! [v1: % 31.05/4.80 | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | % 31.05/4.80 | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_3_3, v0) | p1(v2) | ? [v3: % 31.05/4.80 | $i] : ? [v4: $i] : ($i(v4) & $i(v3) & ((p1(v3) & r1(v3, v4) & % 31.05/4.80 | r1(v1, v3) & ~ p1(v4)) | (p1(v3) & r1(v3, v4) & r1(v0, v3) & % 31.05/4.80 | ~ p1(v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) % 31.05/4.80 | | ~ $i(v6) | ~ $i(v5) | ~ p1(v6) | ~ r1(v6, v7) | ~ % 31.05/4.80 | r1(v5, v6) | ~ r1(v3, v5) | p1(v7) | p1(v5)) & ! [v5: $i] : % 31.05/4.80 | ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) % 31.05/4.80 | | ~ p1(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v3, v5) | % 31.05/4.80 | p1(v7) | ? [v8: $i] : ($i(v8) & r1(v5, v8) & ~ p1(v8))))))) % 31.05/4.80 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 31.05/4.80 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_3, v0) | p1(v2) % 31.05/4.80 | | ? [v3: $i] : ? [v4: $i] : ($i(v4) & $i(v3) & ((p1(v3) & r1(v3, % 31.05/4.80 | v4) & r1(v2, v3) & ~ p1(v4)) | (r1(v0, v3) & ~ p1(v3) & ! % 31.05/4.80 | [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ p1(v5) | % 31.05/4.80 | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v6)))))) & ! [v0: $i] : ! % 31.05/4.80 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_3_3, v0) % 31.05/4.80 | | p1(v0) | ? [v2: $i] : ($i(v2) & ((r1(v1, v2) & ~ p1(v2)) | % 31.05/4.80 | (r1(v0, v2) & ~ p1(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) % 31.05/4.80 | | ~ $i(v3) | ~ p1(v3) | ~ r1(v3, v4) | ~ r1(v2, v3) | % 31.05/4.80 | p1(v4)))))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_1, v0) | % 31.05/4.80 | p1(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2, v0) | p1(v0) | ? % 31.05/4.80 | [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) & % 31.05/4.80 | r1(v0, v1) & ~ p1(v2))) % 31.05/4.80 | % 31.05/4.81 | ALPHA: (1) implies: % 31.05/4.81 | (2) ~ p1(all_3_0) % 31.05/4.81 | (3) r1(all_3_3, all_3_2) % 31.05/4.81 | (4) r1(all_3_2, all_3_1) % 31.05/4.81 | (5) r1(all_3_2, all_3_0) % 31.05/4.81 | (6) $i(all_3_2) % 31.05/4.81 | (7) $i(all_3_1) % 31.05/4.81 | (8) $i(all_3_0) % 31.05/4.81 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2, v0) | p1(v0) | ? [v1: $i] : % 31.05/4.81 | ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) & r1(v0, v1) & ~ % 31.05/4.81 | p1(v2))) % 31.05/4.81 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_1, v0) | p1(v0)) % 31.05/4.81 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | % 31.05/4.81 | ~ r1(all_3_3, v0) | p1(v0) | ? [v2: $i] : ($i(v2) & ((r1(v1, v2) & % 31.05/4.81 | ~ p1(v2)) | (r1(v0, v2) & ~ p1(v2) & ! [v3: $i] : ! [v4: % 31.05/4.81 | $i] : ( ~ $i(v4) | ~ $i(v3) | ~ p1(v3) | ~ r1(v3, v4) | % 31.05/4.81 | ~ r1(v2, v3) | p1(v4)))))) % 31.05/4.82 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 31.05/4.82 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_3, v0) | p1(v2) % 31.05/4.82 | | ? [v3: $i] : ? [v4: $i] : ($i(v4) & $i(v3) & ((p1(v3) & r1(v3, % 31.05/4.82 | v4) & r1(v2, v3) & ~ p1(v4)) | (r1(v0, v3) & ~ p1(v3) & ! % 31.05/4.82 | [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ p1(v5) | % 31.05/4.82 | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v6)))))) % 31.05/4.82 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 31.05/4.82 | $i(v0) | ~ p1(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_3_3, % 31.05/4.82 | v0) | p1(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v4) & $i(v3) & % 31.05/4.82 | ((p1(v3) & r1(v3, v4) & r1(v1, v3) & ~ p1(v4)) | (p1(v3) & r1(v3, % 31.05/4.82 | v4) & r1(v0, v3) & ~ p1(v4) & ! [v5: $i] : ! [v6: $i] : % 31.05/4.82 | ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ p1(v6) | % 31.05/4.82 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v7) | % 31.05/4.82 | p1(v5)) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 31.05/4.82 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ p1(v6) | ~ r1(v6, v7) | % 31.05/4.82 | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v7) | ? [v8: $i] : % 31.05/4.82 | ($i(v8) & r1(v5, v8) & ~ p1(v8))))))) % 31.05/4.83 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | % 31.05/4.83 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | % 31.05/4.83 | ~ r1(v0, v1) | ~ r1(all_3_3, v0) | p1(v3) | ? [v4: $i] : ($i(v4) & % 31.05/4.83 | r1(v1, v4) & ~ p1(v4))) % 31.05/4.83 | % 31.05/4.83 | GROUND_INST: instantiating (11) with all_3_2, all_3_1, simplifying with (3), % 31.05/4.83 | (4), (6), (7) gives: % 31.05/4.83 | (15) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) | % 31.05/4.83 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 31.05/4.83 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) % 31.05/4.83 | | p1(v2))))) % 31.05/4.83 | % 31.05/4.83 | BETA: splitting (15) gives: % 31.05/4.83 | % 31.05/4.83 | Case 1: % 31.05/4.83 | | % 31.05/4.83 | | (16) p1(all_3_2) % 31.05/4.83 | | % 31.05/4.83 | | GROUND_INST: instantiating (13) with all_3_2, all_3_1, all_3_0, simplifying % 31.05/4.83 | | with (2), (3), (4), (5), (6), (7), (8), (16) gives: % 31.05/4.84 | | (17) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0, v1) % 31.05/4.84 | | & r1(all_3_1, v0) & ~ p1(v1)) | (p1(v0) & r1(v0, v1) & % 31.05/4.84 | | r1(all_3_2, v0) & ~ p1(v1) & ! [v2: $i] : ! [v3: $i] : ! % 31.05/4.84 | | [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~ % 31.05/4.84 | | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | % 31.05/4.84 | | p1(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 31.05/4.84 | | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~ r1(v3, v4) | % 31.05/4.84 | | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | ? [v5: $i] : % 31.05/4.84 | | ($i(v5) & r1(v2, v5) & ~ p1(v5)))))) % 31.05/4.84 | | % 31.05/4.84 | | DELTA: instantiating (17) with fresh symbols all_46_0, all_46_1 gives: % 31.05/4.84 | | (18) $i(all_46_0) & $i(all_46_1) & ((p1(all_46_1) & r1(all_46_1, % 31.05/4.84 | | all_46_0) & r1(all_3_1, all_46_1) & ~ p1(all_46_0)) | % 31.05/4.84 | | (p1(all_46_1) & r1(all_46_1, all_46_0) & r1(all_3_2, all_46_1) & % 31.05/4.84 | | ~ p1(all_46_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 31.05/4.84 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | % 31.05/4.84 | | ~ r1(v0, v1) | ~ r1(all_46_1, v0) | p1(v2) | p1(v0)) & ! % 31.05/4.84 | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | % 31.05/4.84 | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 31.05/4.84 | | r1(all_46_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, v3) % 31.05/4.84 | | & ~ p1(v3))))) % 31.05/4.84 | | % 31.05/4.84 | | ALPHA: (18) implies: % 31.05/4.85 | | (19) $i(all_46_1) % 31.05/4.85 | | (20) $i(all_46_0) % 31.05/4.85 | | (21) (p1(all_46_1) & r1(all_46_1, all_46_0) & r1(all_3_1, all_46_1) & ~ % 31.05/4.85 | | p1(all_46_0)) | (p1(all_46_1) & r1(all_46_1, all_46_0) & % 31.05/4.85 | | r1(all_3_2, all_46_1) & ~ p1(all_46_0) & ! [v0: $i] : ! [v1: % 31.05/4.85 | | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 31.05/4.85 | | p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_46_1, v0) | % 31.05/4.85 | | p1(v2) | p1(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 31.05/4.85 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ % 31.05/4.85 | | r1(v0, v1) | ~ r1(all_46_1, v0) | p1(v2) | ? [v3: $i] : % 31.05/4.85 | | ($i(v3) & r1(v0, v3) & ~ p1(v3)))) % 31.05/4.85 | | % 31.05/4.85 | | BETA: splitting (21) gives: % 31.05/4.85 | | % 31.05/4.85 | | Case 1: % 31.05/4.85 | | | % 31.05/4.85 | | | (22) p1(all_46_1) & r1(all_46_1, all_46_0) & r1(all_3_1, all_46_1) & ~ % 31.05/4.85 | | | p1(all_46_0) % 31.05/4.85 | | | % 31.05/4.85 | | | ALPHA: (22) implies: % 31.05/4.85 | | | (23) ~ p1(all_46_0) % 31.05/4.85 | | | (24) r1(all_3_1, all_46_1) % 31.05/4.85 | | | (25) r1(all_46_1, all_46_0) % 31.05/4.85 | | | % 31.05/4.85 | | | GROUND_INST: instantiating (14) with all_3_2, all_3_1, all_46_1, all_46_0, % 31.05/4.86 | | | simplifying with (3), (4), (6), (7), (19), (20), (23), (24), % 31.05/4.86 | | | (25) gives: % 31.05/4.86 | | | (26) ? [v0: $i] : ($i(v0) & r1(all_3_1, v0) & ~ p1(v0)) % 31.05/4.86 | | | % 31.05/4.86 | | | DELTA: instantiating (26) with fresh symbol all_76_0 gives: % 31.05/4.86 | | | (27) $i(all_76_0) & r1(all_3_1, all_76_0) & ~ p1(all_76_0) % 31.05/4.86 | | | % 31.05/4.86 | | | ALPHA: (27) implies: % 31.05/4.86 | | | (28) ~ p1(all_76_0) % 31.05/4.86 | | | (29) r1(all_3_1, all_76_0) % 31.05/4.86 | | | (30) $i(all_76_0) % 31.05/4.86 | | | % 31.05/4.86 | | | GROUND_INST: instantiating (10) with all_76_0, simplifying with (28), % 31.05/4.86 | | | (29), (30) gives: % 31.05/4.86 | | | (31) $false % 31.05/4.86 | | | % 31.05/4.86 | | | CLOSE: (31) is inconsistent. % 31.05/4.86 | | | % 31.05/4.86 | | Case 2: % 31.05/4.86 | | | % 31.05/4.86 | | | (32) p1(all_46_1) & r1(all_46_1, all_46_0) & r1(all_3_2, all_46_1) & ~ % 31.05/4.86 | | | p1(all_46_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 31.05/4.86 | | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ % 31.05/4.86 | | | r1(v0, v1) | ~ r1(all_46_1, v0) | p1(v2) | p1(v0)) & ! [v0: % 31.05/4.86 | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 31.05/4.87 | | | $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 31.05/4.87 | | | r1(all_46_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, v3) & % 31.05/4.87 | | | ~ p1(v3))) % 31.05/4.87 | | | % 31.05/4.87 | | | ALPHA: (32) implies: % 31.05/4.87 | | | (33) ~ p1(all_46_0) % 31.05/4.87 | | | (34) r1(all_3_2, all_46_1) % 31.05/4.87 | | | (35) r1(all_46_1, all_46_0) % 31.05/4.87 | | | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | % 31.05/4.87 | | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 31.05/4.87 | | | r1(all_46_1, v0) | p1(v2) | p1(v0)) % 31.05/4.87 | | | % 31.05/4.87 | | | GROUND_INST: instantiating (12) with all_3_2, all_46_1, all_46_0, % 31.05/4.87 | | | simplifying with (3), (6), (19), (20), (33), (34), (35) % 31.05/4.87 | | | gives: % 31.05/4.87 | | | (37) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0, % 31.05/4.87 | | | v1) & r1(all_46_0, v0) & ~ p1(v1)) | (r1(all_3_2, v0) & % 31.05/4.87 | | | ~ p1(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 31.05/4.87 | | | $i(v2) | ~ p1(v2) | ~ r1(v2, v3) | ~ r1(v0, v2) | % 31.05/4.87 | | | p1(v3))))) % 31.05/4.87 | | | % 31.05/4.87 | | | DELTA: instantiating (37) with fresh symbols all_77_0, all_77_1 gives: % 31.05/4.87 | | | (38) $i(all_77_0) & $i(all_77_1) & ((p1(all_77_1) & r1(all_77_1, % 31.05/4.88 | | | all_77_0) & r1(all_46_0, all_77_1) & ~ p1(all_77_0)) | % 31.05/4.88 | | | (r1(all_3_2, all_77_1) & ~ p1(all_77_1) & ! [v0: $i] : ! [v1: % 31.05/4.88 | | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | % 31.05/4.88 | | | ~ r1(all_77_1, v0) | p1(v1)))) % 31.05/4.88 | | | % 31.05/4.88 | | | ALPHA: (38) implies: % 31.05/4.88 | | | (39) $i(all_77_1) % 31.05/4.88 | | | (40) $i(all_77_0) % 31.05/4.88 | | | (41) (p1(all_77_1) & r1(all_77_1, all_77_0) & r1(all_46_0, all_77_1) & % 31.05/4.88 | | | ~ p1(all_77_0)) | (r1(all_3_2, all_77_1) & ~ p1(all_77_1) & ! % 31.05/4.88 | | | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ % 31.05/4.88 | | | r1(v0, v1) | ~ r1(all_77_1, v0) | p1(v1))) % 31.05/4.88 | | | % 31.05/4.88 | | | BETA: splitting (41) gives: % 31.05/4.88 | | | % 31.05/4.88 | | | Case 1: % 31.05/4.88 | | | | % 31.05/4.88 | | | | (42) p1(all_77_1) & r1(all_77_1, all_77_0) & r1(all_46_0, all_77_1) & % 31.05/4.88 | | | | ~ p1(all_77_0) % 31.05/4.88 | | | | % 31.05/4.88 | | | | ALPHA: (42) implies: % 31.05/4.88 | | | | (43) ~ p1(all_77_0) % 31.05/4.88 | | | | (44) r1(all_46_0, all_77_1) % 31.05/4.88 | | | | (45) r1(all_77_1, all_77_0) % 31.05/4.88 | | | | (46) p1(all_77_1) % 31.05/4.88 | | | | % 31.05/4.88 | | | | GROUND_INST: instantiating (36) with all_46_0, all_77_1, all_77_0, % 31.05/4.88 | | | | simplifying with (20), (33), (35), (39), (40), (43), (44), % 31.05/4.88 | | | | (45), (46) gives: % 31.05/4.88 | | | | (47) $false % 31.05/4.88 | | | | % 31.05/4.88 | | | | CLOSE: (47) is inconsistent. % 31.05/4.88 | | | | % 31.05/4.88 | | | Case 2: % 31.05/4.88 | | | | % 31.05/4.89 | | | | (48) r1(all_3_2, all_77_1) & ~ p1(all_77_1) & ! [v0: $i] : ! [v1: % 31.05/4.89 | | | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ % 31.05/4.89 | | | | r1(all_77_1, v0) | p1(v1)) % 31.05/4.89 | | | | % 31.05/4.89 | | | | ALPHA: (48) implies: % 31.05/4.89 | | | | (49) ~ p1(all_77_1) % 31.05/4.89 | | | | (50) r1(all_3_2, all_77_1) % 31.05/4.89 | | | | (51) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | % 31.05/4.89 | | | | ~ r1(v0, v1) | ~ r1(all_77_1, v0) | p1(v1)) % 31.05/4.89 | | | | % 31.05/4.89 | | | | GROUND_INST: instantiating (9) with all_77_1, simplifying with (39), % 31.05/4.89 | | | | (49), (50) gives: % 31.05/4.89 | | | | (52) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0, % 31.05/4.89 | | | | v1) & r1(all_77_1, v0) & ~ p1(v1)) % 31.05/4.89 | | | | % 31.05/4.89 | | | | DELTA: instantiating (52) with fresh symbols all_115_0, all_115_1 gives: % 31.05/4.89 | | | | (53) $i(all_115_0) & $i(all_115_1) & p1(all_115_1) & r1(all_115_1, % 31.05/4.89 | | | | all_115_0) & r1(all_77_1, all_115_1) & ~ p1(all_115_0) % 31.05/4.89 | | | | % 31.05/4.89 | | | | ALPHA: (53) implies: % 31.05/4.89 | | | | (54) ~ p1(all_115_0) % 31.05/4.89 | | | | (55) r1(all_77_1, all_115_1) % 31.05/4.89 | | | | (56) r1(all_115_1, all_115_0) % 31.05/4.89 | | | | (57) p1(all_115_1) % 31.05/4.89 | | | | (58) $i(all_115_1) % 31.05/4.89 | | | | (59) $i(all_115_0) % 31.05/4.89 | | | | % 31.05/4.90 | | | | GROUND_INST: instantiating (51) with all_115_1, all_115_0, simplifying % 31.05/4.90 | | | | with (54), (55), (56), (57), (58), (59) gives: % 31.05/4.90 | | | | (60) $false % 31.05/4.90 | | | | % 31.05/4.90 | | | | CLOSE: (60) is inconsistent. % 31.05/4.90 | | | | % 31.05/4.90 | | | End of split % 31.05/4.90 | | | % 31.54/4.90 | | End of split % 31.54/4.90 | | % 31.54/4.90 | Case 2: % 31.54/4.90 | | % 31.54/4.90 | | (61) ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) | % 31.54/4.90 | | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 31.54/4.90 | | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, % 31.54/4.90 | | v1) | p1(v2))))) % 31.54/4.90 | | % 31.54/4.90 | | DELTA: instantiating (61) with fresh symbol all_41_0 gives: % 31.54/4.90 | | (62) $i(all_41_0) & ((r1(all_3_1, all_41_0) & ~ p1(all_41_0)) | % 31.54/4.90 | | (r1(all_3_2, all_41_0) & ~ p1(all_41_0) & ! [v0: $i] : ! [v1: % 31.54/4.90 | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ % 31.54/4.90 | | r1(all_41_0, v0) | p1(v1)))) % 31.54/4.90 | | % 31.54/4.90 | | ALPHA: (62) implies: % 31.54/4.90 | | (63) $i(all_41_0) % 31.54/4.90 | | (64) (r1(all_3_1, all_41_0) & ~ p1(all_41_0)) | (r1(all_3_2, all_41_0) & % 31.54/4.90 | | ~ p1(all_41_0) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 31.54/4.90 | | $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_41_0, v0) | % 31.54/4.90 | | p1(v1))) % 31.54/4.90 | | % 31.54/4.90 | | BETA: splitting (64) gives: % 31.54/4.90 | | % 31.54/4.90 | | Case 1: % 31.54/4.90 | | | % 31.54/4.91 | | | (65) r1(all_3_1, all_41_0) & ~ p1(all_41_0) % 31.54/4.91 | | | % 31.54/4.91 | | | ALPHA: (65) implies: % 31.54/4.91 | | | (66) ~ p1(all_41_0) % 31.54/4.91 | | | (67) r1(all_3_1, all_41_0) % 31.54/4.91 | | | % 31.54/4.91 | | | GROUND_INST: instantiating (10) with all_41_0, simplifying with (63), % 31.54/4.91 | | | (66), (67) gives: % 31.54/4.91 | | | (68) $false % 31.54/4.91 | | | % 31.54/4.91 | | | CLOSE: (68) is inconsistent. % 31.54/4.91 | | | % 31.54/4.91 | | Case 2: % 31.54/4.91 | | | % 31.54/4.91 | | | (69) r1(all_3_2, all_41_0) & ~ p1(all_41_0) & ! [v0: $i] : ! [v1: % 31.54/4.91 | | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ % 31.54/4.91 | | | r1(all_41_0, v0) | p1(v1)) % 31.54/4.91 | | | % 31.54/4.91 | | | ALPHA: (69) implies: % 31.54/4.91 | | | (70) ~ p1(all_41_0) % 31.54/4.91 | | | (71) r1(all_3_2, all_41_0) % 31.54/4.91 | | | (72) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | % 31.54/4.91 | | | ~ r1(v0, v1) | ~ r1(all_41_0, v0) | p1(v1)) % 31.54/4.91 | | | % 31.54/4.91 | | | GROUND_INST: instantiating (9) with all_41_0, simplifying with (63), (70), % 31.54/4.91 | | | (71) gives: % 31.54/4.91 | | | (73) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0, v1) % 31.54/4.91 | | | & r1(all_41_0, v0) & ~ p1(v1)) % 31.54/4.91 | | | % 31.54/4.91 | | | DELTA: instantiating (73) with fresh symbols all_76_0, all_76_1 gives: % 31.54/4.91 | | | (74) $i(all_76_0) & $i(all_76_1) & p1(all_76_1) & r1(all_76_1, % 31.54/4.91 | | | all_76_0) & r1(all_41_0, all_76_1) & ~ p1(all_76_0) % 31.54/4.91 | | | % 31.54/4.91 | | | ALPHA: (74) implies: % 31.54/4.91 | | | (75) ~ p1(all_76_0) % 31.54/4.91 | | | (76) r1(all_41_0, all_76_1) % 31.54/4.91 | | | (77) r1(all_76_1, all_76_0) % 31.54/4.91 | | | (78) p1(all_76_1) % 31.54/4.91 | | | (79) $i(all_76_1) % 31.54/4.92 | | | (80) $i(all_76_0) % 31.54/4.92 | | | % 31.54/4.92 | | | GROUND_INST: instantiating (72) with all_76_1, all_76_0, simplifying with % 31.54/4.92 | | | (75), (76), (77), (78), (79), (80) gives: % 31.54/4.92 | | | (81) $false % 31.54/4.92 | | | % 31.54/4.92 | | | CLOSE: (81) is inconsistent. % 31.54/4.92 | | | % 31.54/4.92 | | End of split % 31.54/4.92 | | % 31.54/4.92 | End of split % 31.54/4.92 | % 31.54/4.92 End of proof % 31.54/4.92 % SZS output end Proof for theBenchmark % 31.54/4.92 % 31.54/4.92 4181ms %------------------------------------------------------------------------------