%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL638+1.005 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.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 12:54:25 PM UTC 2026 % Result : Theorem 62.94s 8.71s % Output : Proof 64.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL638+1.005 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.36 % Computer : n002.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 % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Fri Sep 4 13:47:35 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.38 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. % 0.48/0.58 ________ _____ % 0.48/0.58 ___ __ \_________(_)________________________________ % 0.48/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.48/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.48/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.48/0.58 % 0.48/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.48/0.58 (2023-06-19) % 0.48/0.58 % 0.48/0.58 (c) Philipp Rümmer, 2009-2023 % 0.48/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.48/0.58 Amanda Stjerna. % 0.48/0.58 Free software under BSD-3-Clause. % 0.48/0.58 % 0.48/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.48/0.58 % 0.48/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.48/0.59 Running up to 7 provers in parallel. % 0.48/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.48/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.48/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.48/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.48/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.48/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.48/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.38/1.59 Prover 1: Preprocessing ... % 6.38/1.60 Prover 5: Preprocessing ... % 6.38/1.60 Prover 3: Preprocessing ... % 7.16/1.60 Prover 2: Preprocessing ... % 7.16/1.62 Prover 6: Preprocessing ... % 7.16/1.64 Prover 4: Preprocessing ... % 7.16/1.66 Prover 0: Preprocessing ... % 12.70/2.36 Prover 2: Constructing countermodel ... % 14.25/2.52 Prover 5: Constructing countermodel ... % 17.40/3.02 Prover 6: Proving ... % 18.89/3.15 Prover 1: Constructing countermodel ... % 18.89/3.16 Prover 4: Constructing countermodel ... % 19.72/3.25 Prover 3: Constructing countermodel ... % 19.72/3.26 Prover 0: Proving ... % 62.20/8.67 Prover 1: Found proof (size 69) % 62.20/8.68 Prover 1: proved (8069ms) % 62.20/8.68 Prover 5: stopped % 62.20/8.68 Prover 2: stopped % 62.20/8.68 Prover 3: stopped % 62.20/8.68 Prover 6: stopped % 62.20/8.69 Prover 4: stopped % 62.94/8.71 Prover 0: stopped % 62.94/8.71 % 62.94/8.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 62.94/8.71 % 62.94/8.72 % SZS output start Proof for theBenchmark % 62.94/8.72 Assumptions after simplification: % 62.94/8.72 --------------------------------- % 62.94/8.72 % 62.94/8.73 (main) % 63.41/8.90 ? [v0: $i] : ($i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p1(v1) = % 63.41/8.90 v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3) | ! % 63.91/8.90 [v3: $i] : ( ~ (r1(v1, v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : % 63.91/8.90 ( ~ (v5 = 0) & r1(v3, v4) = 0 & p1(v4) = v5 & $i(v4)))) & ! [v1: $i] : % 63.91/8.90 ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) % 63.91/8.90 & r1(v1, v2) = 0 & p1(v2) = v3 & $i(v2)) | ! [v2: $i] : ( ~ (r1(v1, v2) % 63.91/8.90 = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (p1(v3) = % 63.91/8.90 v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & r1(v2, v3) = v5)))) % 63.91/8.90 & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1, v2) % 63.91/8.90 = 0 & $i(v2) & ! [v3: $i] : ( ~ (p1(v3) = 0) | ~ $i(v3) | ? [v4: int] % 63.91/8.90 : ( ~ (v4 = 0) & r1(v2, v3) = v4))) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 63.91/8.90 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ? % 63.91/8.90 [v4: $i] : (r1(v3, v4) = 0 & p1(v4) = 0 & $i(v4))))) & ! [v1: $i] : ( % 63.91/8.90 ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2))) % 63.91/8.90 & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: % 63.91/8.90 int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 63.91/8.90 0) & r1(v1, v2) = v4) | ! [v4: $i] : ( ~ (r1(v2, v4) = 0) | ~ % 63.91/8.90 $i(v4) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & r1(v4, v5) = 0 & % 63.91/8.90 p1(v5) = v6 & $i(v5))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ % 63.91/8.90 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? % 63.91/8.90 [v4: int] : ( ~ (v4 = 0) & r1(v2, v3) = 0 & p1(v3) = v4 & $i(v3)) | ! % 63.91/8.90 [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: int] % 63.91/8.90 : (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) % 63.91/8.90 & r1(v3, v4) = v6))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ % 63.91/8.90 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i] : % 63.91/8.90 (r1(v2, v3) = 0 & $i(v3) & ! [v4: $i] : ( ~ (p1(v4) = 0) | ~ $i(v4) | % 63.91/8.90 ? [v5: int] : ( ~ (v5 = 0) & r1(v3, v4) = v5))) | ! [v3: $i] : ( ~ % 63.91/8.90 (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ % 63.91/8.90 $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & p1(v5) = 0 & $i(v5)))))) & % 63.91/8.90 ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, % 63.91/8.90 v2) = 0) | ~ $i(v2) | ? [v3: $i] : (r1(v2, v3) = 0 & $i(v3)))) & % 63.91/8.90 ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, % 63.91/8.90 v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 63.91/8.90 (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & r1(v2, v3) = % 63.91/8.90 v5) | ! [v5: $i] : ( ~ (r1(v3, v5) = 0) | ~ $i(v5) | ? [v6: $i] : % 63.91/8.90 ? [v7: int] : ( ~ (v7 = 0) & r1(v5, v6) = 0 & p1(v6) = v7 & % 63.91/8.90 $i(v6)))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! % 63.91/8.90 [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, % 63.91/8.90 v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 63.91/8.90 r1(v3, v4) = 0 & p1(v4) = v5 & $i(v4)) | ! [v4: $i] : ( ~ (r1(v3, % 63.91/8.90 v4) = 0) | ~ $i(v4) | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ % 63.91/8.90 (p1(v5) = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & r1(v4, % 63.91/8.90 v5) = v7)))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ % 63.91/8.90 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( % 63.91/8.90 ~ (r1(v2, v3) = 0) | ~ $i(v3) | ? [v4: $i] : (r1(v3, v4) = 0 & % 63.91/8.90 $i(v4) & ! [v5: $i] : ( ~ (p1(v5) = 0) | ~ $i(v5) | ? [v6: int] : % 63.91/8.90 ( ~ (v6 = 0) & r1(v4, v5) = v6))) | ! [v4: $i] : ( ~ (r1(v3, v4) % 63.91/8.90 = 0) | ~ $i(v4) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) % 63.91/8.90 | ? [v6: $i] : (r1(v5, v6) = 0 & p1(v6) = 0 & $i(v6))))))) & ! % 63.91/8.90 [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) % 63.91/8.90 = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ? % 63.91/8.90 [v4: $i] : (r1(v3, v4) = 0 & $i(v4))))) & ! [v1: $i] : ( ~ (r1(v0, % 63.91/8.90 v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) % 63.91/8.90 | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: % 63.91/8.90 int] : (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ % 63.91/8.90 (v6 = 0) & r1(v3, v4) = v6) | ! [v6: $i] : ( ~ (r1(v4, v6) = 0) | % 63.91/8.90 ~ $i(v6) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & r1(v6, v7) % 63.91/8.90 = 0 & p1(v7) = v8 & $i(v7))))))) & ! [v1: $i] : ( ~ (r1(v0, v1) % 63.91/8.91 = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! % 63.91/8.91 [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, % 63.91/8.91 v4) = 0) | ~ $i(v4) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) % 63.91/8.91 & r1(v4, v5) = 0 & p1(v5) = v6 & $i(v5)) | ! [v5: $i] : ( ~ % 63.91/8.91 (r1(v4, v5) = 0) | ~ $i(v5) | ! [v6: $i] : ! [v7: int] : (v7 = % 63.91/8.91 0 | ~ (p1(v6) = v7) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & % 63.91/8.91 r1(v5, v6) = v8))))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | % 63.91/8.91 ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : % 63.91/8.91 ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) | % 63.91/8.91 ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & $i(v5) & ! [v6: $i] : ( % 63.91/8.91 ~ (p1(v6) = 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & % 63.91/8.91 r1(v5, v6) = v7))) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ % 63.91/8.91 $i(v5) | ! [v6: $i] : ( ~ (r1(v5, v6) = 0) | ~ $i(v6) | ? [v7: % 63.91/8.91 $i] : (r1(v6, v7) = 0 & p1(v7) = 0 & $i(v7)))))))) & ! [v1: % 63.91/8.91 $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 63.91/8.91 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! % 63.91/8.91 [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4, % 63.91/8.91 v5) = 0 & $i(v5)))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ % 63.91/8.91 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( % 63.91/8.91 ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) | % 63.91/8.91 ~ $i(v4) | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (p1(v5) = v6) | % 63.91/8.91 ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & r1(v4, v5) = v7) | ! % 63.91/8.91 [v7: $i] : ( ~ (r1(v5, v7) = 0) | ~ $i(v7) | ? [v8: $i] : ? % 63.91/8.91 [v9: int] : ( ~ (v9 = 0) & r1(v7, v8) = 0 & p1(v8) = v9 & % 63.91/8.91 $i(v8)))))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) % 63.91/8.91 | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ % 63.91/8.91 (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ % 63.91/8.91 $i(v4) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) | ? [v6: % 63.91/8.91 $i] : ? [v7: int] : ( ~ (v7 = 0) & r1(v5, v6) = 0 & p1(v6) = v7 % 63.91/8.91 & $i(v6)) | ! [v6: $i] : ( ~ (r1(v5, v6) = 0) | ~ $i(v6) | ! % 63.91/8.91 [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (p1(v7) = v8) | ~ $i(v7) % 63.91/8.91 | ? [v9: int] : ( ~ (v9 = 0) & r1(v6, v7) = v9)))))))) & ! % 63.91/8.91 [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) % 63.91/8.91 = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! % 63.91/8.91 [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ! [v5: $i] : ( ~ % 63.91/8.91 (r1(v4, v5) = 0) | ~ $i(v5) | ? [v6: $i] : (r1(v5, v6) = 0 & % 63.91/8.91 $i(v6) & ! [v7: $i] : ( ~ (p1(v7) = 0) | ~ $i(v7) | ? [v8: % 63.91/8.91 int] : ( ~ (v8 = 0) & r1(v6, v7) = v8))) | ! [v6: $i] : ( ~ % 63.91/8.91 (r1(v5, v6) = 0) | ~ $i(v6) | ! [v7: $i] : ( ~ (r1(v6, v7) = % 63.91/8.91 0) | ~ $i(v7) | ? [v8: $i] : (r1(v7, v8) = 0 & p1(v8) = 0 % 63.91/8.91 & $i(v8))))))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ % 63.91/8.91 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( % 63.91/8.91 ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) | % 63.91/8.91 ~ $i(v4) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) | ? [v6: % 63.91/8.91 $i] : (r1(v5, v6) = 0 & $i(v6))))))) & ! [v1: $i] : ( ~ (r1(v0, % 63.91/8.91 v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) % 63.91/8.91 | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ % 63.91/8.91 (r1(v3, v4) = 0) | ~ $i(v4) | ! [v5: $i] : ( ~ (p1(v5) = 0) | ~ % 63.91/8.91 $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & r1(v4, v5) = v6) | ! [v6: % 63.91/8.91 $i] : ( ~ (r1(v5, v6) = 0) | ~ $i(v6) | ? [v7: $i] : (r1(v6, % 63.91/8.91 v7) = 0 & p1(v7) = 0 & $i(v7)))))))) & ! [v1: $i] : ( ~ % 63.91/8.91 (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ % 63.91/8.91 $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : % 63.91/8.91 ( ~ (p1(v4) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & r1(v3, % 63.91/8.91 v4) = v5) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) | ? % 63.91/8.91 [v6: $i] : (r1(v5, v6) = 0 & p1(v6) = 0 & $i(v6))))))) & ! [v1: % 63.91/8.91 $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 63.91/8.91 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (p1(v3) = 0) | ~ $i(v3) | ? [v4: % 63.91/8.91 int] : ( ~ (v4 = 0) & r1(v2, v3) = v4) | ! [v4: $i] : ( ~ (r1(v3, % 63.91/8.91 v4) = 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & p1(v5) = % 63.91/8.91 0 & $i(v5)))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | % 63.91/8.91 ! [v2: $i] : ( ~ (p1(v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 63.91/8.91 r1(v1, v2) = v3) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ? % 63.91/8.91 [v4: $i] : (r1(v3, v4) = 0 & p1(v4) = 0 & $i(v4))))) & ! [v1: $i] : ( % 63.91/8.91 ~ (p1(v1) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) = % 63.91/8.91 v2) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i] : % 63.91/8.91 (r1(v2, v3) = 0 & p1(v3) = 0 & $i(v3)))) & ? [v1: $i] : (r1(v0, v1) = 0 % 63.91/8.92 & $i(v1) & ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ? [v3: $i] : (r1(v2, % 63.91/8.92 v3) = 0 & $i(v3) & ? [v4: $i] : (r1(v3, v4) = 0 & $i(v4) & ? [v5: % 63.91/8.92 $i] : ? [v6: int] : ( ~ (v6 = 0) & r1(v4, v5) = 0 & p1(v5) = v6 & % 63.91/8.92 $i(v5) & ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (p1(v7) = v8) | % 63.91/8.92 ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & r1(v5, v7) = % 63.91/8.92 v9)))))))) % 63.91/8.92 % 63.91/8.92 (function-axioms) % 63.91/8.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 63.91/8.92 [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0: % 63.91/8.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 63.91/8.92 ~ (p1(v2) = v1) | ~ (p1(v2) = v0)) % 63.91/8.92 % 63.91/8.92 Those formulas are unsatisfiable: % 63.91/8.92 --------------------------------- % 63.91/8.92 % 63.91/8.92 Begin of proof % 63.91/8.92 | % 63.91/8.92 | ALPHA: (function-axioms) implies: % 63.91/8.92 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 63.91/8.92 | ! [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) % 63.91/8.92 | % 63.91/8.93 | DELTA: instantiating (main) with fresh symbol all_3_0 gives: % 63.91/9.00 | (2) $i(all_3_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | % 63.91/9.00 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_3_0, v0) = v2) | ! % 63.91/9.00 | [v2: $i] : ( ~ (r1(v0, v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 63.91/9.00 | int] : ( ~ (v4 = 0) & r1(v2, v3) = 0 & p1(v3) = v4 & $i(v3)))) & % 63.91/9.00 | ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 63.91/9.00 | [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 & $i(v1)) | % 63.91/9.00 | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: % 63.91/9.00 | int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( % 63.91/9.00 | ~ (v4 = 0) & r1(v1, v2) = v4)))) & ! [v0: $i] : ( ~ % 63.91/9.00 | (r1(all_3_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0 & % 63.91/9.00 | $i(v1) & ! [v2: $i] : ( ~ (p1(v2) = 0) | ~ $i(v2) | ? [v3: int] % 63.91/9.00 | : ( ~ (v3 = 0) & r1(v1, v2) = v3))) | ! [v1: $i] : ( ~ (r1(v0, % 63.91/9.00 | v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ % 63.91/9.00 | $i(v2) | ? [v3: $i] : (r1(v2, v3) = 0 & p1(v3) = 0 & $i(v3))))) % 63.91/9.00 | & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 63.91/9.00 | (r1(v0, v1) = 0 & $i(v1))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) % 63.91/9.00 | | ~ $i(v0) | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p1(v1) = v2) % 63.91/9.00 | | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3) | ! % 63.91/9.00 | [v3: $i] : ( ~ (r1(v1, v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: % 63.91/9.00 | int] : ( ~ (v5 = 0) & r1(v3, v4) = 0 & p1(v4) = v5 & $i(v4))))) % 63.91/9.00 | & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( % 63.91/9.00 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : ( ~ % 63.91/9.00 | (v3 = 0) & r1(v1, v2) = 0 & p1(v2) = v3 & $i(v2)) | ! [v2: $i] : % 63.91/9.00 | ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: int] : (v4 % 63.91/9.00 | = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = % 63.91/9.00 | 0) & r1(v2, v3) = v5))))) & ! [v0: $i] : ( ~ (r1(all_3_0, % 63.91/9.00 | v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ % 63.91/9.00 | $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] : ( ~ % 63.91/9.00 | (p1(v3) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & r1(v2, % 63.91/9.00 | v3) = v4))) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ % 63.91/9.00 | $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ? [v4: % 63.91/9.00 | $i] : (r1(v3, v4) = 0 & p1(v4) = 0 & $i(v4)))))) & ! [v0: % 63.91/9.00 | $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 63.91/9.00 | (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 & % 63.91/9.00 | $i(v2)))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | % 63.91/9.00 | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! % 63.91/9.00 | [v3: int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : % 63.91/9.00 | ( ~ (v4 = 0) & r1(v1, v2) = v4) | ! [v4: $i] : ( ~ (r1(v2, v4) = % 63.91/9.00 | 0) | ~ $i(v4) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 63.91/9.00 | r1(v4, v5) = 0 & p1(v5) = v6 & $i(v5)))))) & ! [v0: $i] : ( % 63.91/9.00 | ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = % 63.91/9.00 | 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | % 63.91/9.00 | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & r1(v2, v3) = 0 & % 63.91/9.00 | p1(v3) = v4 & $i(v3)) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ % 63.91/9.00 | $i(v3) | ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (p1(v4) = % 63.91/9.00 | v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & r1(v3, v4) % 63.91/9.00 | = v6)))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ % 63.91/9.00 | $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] % 63.91/9.00 | : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i] : (r1(v2, v3) = 0 % 63.91/9.00 | & $i(v3) & ! [v4: $i] : ( ~ (p1(v4) = 0) | ~ $i(v4) | ? [v5: % 63.91/9.00 | int] : ( ~ (v5 = 0) & r1(v3, v4) = v5))) | ! [v3: $i] : ( % 63.91/9.00 | ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) % 63.91/9.00 | = 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & p1(v5) = % 63.91/9.00 | 0 & $i(v5))))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) % 63.91/9.00 | | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! % 63.91/9.00 | [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i] : (r1(v2, % 63.91/9.00 | v3) = 0 & $i(v3))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = % 63.91/9.00 | 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | % 63.91/9.00 | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! % 63.91/9.00 | [v4: int] : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] % 63.91/9.00 | : ( ~ (v5 = 0) & r1(v2, v3) = v5) | ! [v5: $i] : ( ~ (r1(v3, % 63.91/9.00 | v5) = 0) | ~ $i(v5) | ? [v6: $i] : ? [v7: int] : ( ~ % 63.91/9.00 | (v7 = 0) & r1(v5, v6) = 0 & p1(v6) = v7 & $i(v6))))))) & ! % 63.91/9.00 | [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 63.91/9.00 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | % 63.91/9.00 | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ? % 63.91/9.00 | [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & r1(v3, v4) = 0 & % 63.91/9.00 | p1(v4) = v5 & $i(v4)) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) | % 63.91/9.00 | ~ $i(v4) | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (p1(v5) % 63.91/9.00 | = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & r1(v4, % 63.91/9.00 | v5) = v7))))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = % 63.91/9.00 | 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | % 63.91/9.00 | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ % 63.91/9.00 | (r1(v2, v3) = 0) | ~ $i(v3) | ? [v4: $i] : (r1(v3, v4) = 0 & % 63.91/9.00 | $i(v4) & ! [v5: $i] : ( ~ (p1(v5) = 0) | ~ $i(v5) | ? [v6: % 63.91/9.00 | int] : ( ~ (v6 = 0) & r1(v4, v5) = v6))) | ! [v4: $i] : % 63.91/9.00 | ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ! [v5: $i] : ( ~ (r1(v4, % 63.91/9.00 | v5) = 0) | ~ $i(v5) | ? [v6: $i] : (r1(v5, v6) = 0 & % 63.91/9.00 | p1(v6) = 0 & $i(v6)))))))) & ! [v0: $i] : ( ~ % 63.91/9.00 | (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = % 63.91/9.00 | 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | % 63.91/9.00 | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ? [v4: $i] : % 63.91/9.00 | (r1(v3, v4) = 0 & $i(v4)))))) & ! [v0: $i] : ( ~ (r1(all_3_0, % 63.91/9.00 | v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ % 63.91/9.00 | $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: % 63.91/9.00 | $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: % 63.91/9.00 | int] : (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int] % 63.91/9.00 | : ( ~ (v6 = 0) & r1(v3, v4) = v6) | ! [v6: $i] : ( ~ (r1(v4, % 63.91/9.00 | v6) = 0) | ~ $i(v6) | ? [v7: $i] : ? [v8: int] : ( ~ % 63.91/9.00 | (v8 = 0) & r1(v6, v7) = 0 & p1(v7) = v8 & $i(v7)))))))) & % 63.91/9.00 | ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 63.91/9.00 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | % 63.91/9.00 | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! % 63.91/9.00 | [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ? [v5: $i] : ? % 63.91/9.00 | [v6: int] : ( ~ (v6 = 0) & r1(v4, v5) = 0 & p1(v5) = v6 & % 63.91/9.00 | $i(v5)) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) | % 63.91/9.00 | ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (p1(v6) = v7) | ~ % 63.91/9.00 | $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & r1(v5, v6) = % 63.91/9.00 | v8)))))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | % 63.91/9.00 | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: % 63.91/9.00 | $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ % 63.91/9.01 | (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) = % 63.91/9.01 | 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & $i(v5) & % 63.91/9.01 | ! [v6: $i] : ( ~ (p1(v6) = 0) | ~ $i(v6) | ? [v7: int] : % 63.91/9.01 | ( ~ (v7 = 0) & r1(v5, v6) = v7))) | ! [v5: $i] : ( ~ % 63.91/9.01 | (r1(v4, v5) = 0) | ~ $i(v5) | ! [v6: $i] : ( ~ (r1(v5, % 63.91/9.01 | v6) = 0) | ~ $i(v6) | ? [v7: $i] : (r1(v6, v7) = 0 % 63.91/9.01 | & p1(v7) = 0 & $i(v7))))))))) & ! [v0: $i] : ( ~ % 63.91/9.01 | (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = % 63.91/9.01 | 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | % 63.91/9.01 | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( % 63.91/9.01 | ~ (r1(v3, v4) = 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) = % 63.91/9.01 | 0 & $i(v5))))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) % 63.91/9.01 | | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! % 63.91/9.01 | [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ % 63.91/9.01 | (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (p1(v4) = 0) | % 63.91/9.01 | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & r1(v3, v4) = v5) | % 63.91/9.01 | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) | ? [v6: $i] : % 63.91/9.01 | (r1(v5, v6) = 0 & p1(v6) = 0 & $i(v6)))))))) & ! [v0: $i] % 63.91/9.01 | : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) % 63.91/9.01 | = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) % 63.91/9.01 | | ! [v3: $i] : ( ~ (p1(v3) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ % 63.91/9.01 | (v4 = 0) & r1(v2, v3) = v4) | ! [v4: $i] : ( ~ (r1(v3, v4) = % 63.91/9.01 | 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & p1(v5) = 0 % 63.91/9.01 | & $i(v5))))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | % 63.91/9.01 | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: % 63.91/9.01 | $i] : ( ~ (p1(v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) % 63.91/9.01 | & r1(v1, v2) = v3) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ % 63.91/9.01 | $i(v3) | ? [v4: $i] : (r1(v3, v4) = 0 & p1(v4) = 0 & % 63.91/9.01 | $i(v4)))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ % 63.91/9.01 | $i(v0) | ! [v1: $i] : ( ~ (p1(v1) = 0) | ~ $i(v1) | ? [v2: int] : % 63.91/9.01 | ( ~ (v2 = 0) & r1(v0, v1) = v2) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 63.91/9.01 | 0) | ~ $i(v2) | ? [v3: $i] : (r1(v2, v3) = 0 & p1(v3) = 0 & % 63.91/9.01 | $i(v3))))) & ! [v0: $i] : ( ~ (p1(v0) = 0) | ~ $i(v0) | ? % 63.91/9.01 | [v1: int] : ( ~ (v1 = 0) & r1(all_3_0, v0) = v1) | ! [v1: $i] : ( ~ % 63.91/9.01 | (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 & % 63.91/9.01 | p1(v2) = 0 & $i(v2)))) & ? [v0: $i] : (r1(all_3_0, v0) = 0 & % 63.91/9.01 | $i(v0) & ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1) & ? [v2: $i] : % 63.91/9.01 | (r1(v1, v2) = 0 & $i(v2) & ? [v3: $i] : (r1(v2, v3) = 0 & $i(v3) & % 63.91/9.01 | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & r1(v3, v4) = 0 & % 63.91/9.01 | p1(v4) = v5 & $i(v4) & ! [v6: $i] : ! [v7: int] : (v7 = 0 | % 63.91/9.01 | ~ (p1(v6) = v7) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) % 63.91/9.01 | & r1(v4, v6) = v8))))))) % 63.91/9.01 | % 63.91/9.01 | ALPHA: (2) implies: % 63.91/9.01 | (3) ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 63.91/9.01 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | % 63.91/9.01 | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! % 63.91/9.01 | [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ? [v5: $i] : % 63.91/9.01 | (r1(v4, v5) = 0 & $i(v5))))))) % 63.91/9.02 | (4) ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 63.91/9.02 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | % 63.91/9.02 | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! % 63.91/9.02 | [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ? [v5: $i] : ? % 63.91/9.02 | [v6: int] : ( ~ (v6 = 0) & r1(v4, v5) = 0 & p1(v5) = v6 & % 63.91/9.02 | $i(v5)) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) | % 63.91/9.02 | ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (p1(v6) = v7) | ~ % 63.91/9.02 | $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & r1(v5, v6) = % 63.91/9.02 | v8)))))))) % 63.91/9.02 | (5) ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 63.91/9.02 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | % 63.91/9.02 | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! % 63.91/9.02 | [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (p1(v4) = v5) | ~ % 63.91/9.02 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & r1(v3, v4) = v6) | ! % 63.91/9.02 | [v6: $i] : ( ~ (r1(v4, v6) = 0) | ~ $i(v6) | ? [v7: $i] : % 63.91/9.02 | ? [v8: int] : ( ~ (v8 = 0) & r1(v6, v7) = 0 & p1(v7) = v8 & % 63.91/9.02 | $i(v7)))))))) % 63.91/9.03 | (6) ? [v0: $i] : (r1(all_3_0, v0) = 0 & $i(v0) & ? [v1: $i] : (r1(v0, v1) % 63.91/9.03 | = 0 & $i(v1) & ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ? [v3: $i] % 63.91/9.03 | : (r1(v2, v3) = 0 & $i(v3) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 % 63.91/9.03 | = 0) & r1(v3, v4) = 0 & p1(v4) = v5 & $i(v4) & ! [v6: $i] % 63.91/9.03 | : ! [v7: int] : (v7 = 0 | ~ (p1(v6) = v7) | ~ $i(v6) | ? % 63.91/9.03 | [v8: int] : ( ~ (v8 = 0) & r1(v4, v6) = v8))))))) % 63.91/9.03 | % 63.91/9.03 | DELTA: instantiating (6) with fresh symbol all_6_0 gives: % 63.91/9.03 | (7) r1(all_3_0, all_6_0) = 0 & $i(all_6_0) & ? [v0: $i] : (r1(all_6_0, v0) % 63.91/9.03 | = 0 & $i(v0) & ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1) & ? [v2: $i] : % 63.91/9.03 | (r1(v1, v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~ (v4 = % 63.91/9.03 | 0) & r1(v2, v3) = 0 & p1(v3) = v4 & $i(v3) & ! [v5: $i] : ! % 63.91/9.03 | [v6: int] : (v6 = 0 | ~ (p1(v5) = v6) | ~ $i(v5) | ? [v7: % 63.91/9.03 | int] : ( ~ (v7 = 0) & r1(v3, v5) = v7)))))) % 63.91/9.03 | % 63.91/9.03 | ALPHA: (7) implies: % 63.91/9.03 | (8) $i(all_6_0) % 63.91/9.03 | (9) r1(all_3_0, all_6_0) = 0 % 64.57/9.03 | (10) ? [v0: $i] : (r1(all_6_0, v0) = 0 & $i(v0) & ? [v1: $i] : (r1(v0, % 64.57/9.03 | v1) = 0 & $i(v1) & ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ? % 64.57/9.04 | [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & r1(v2, v3) = 0 & p1(v3) % 64.57/9.04 | = v4 & $i(v3) & ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ % 64.57/9.04 | (p1(v5) = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & % 64.57/9.04 | r1(v3, v5) = v7)))))) % 64.57/9.04 | % 64.57/9.04 | DELTA: instantiating (10) with fresh symbol all_8_0 gives: % 64.57/9.04 | (11) r1(all_6_0, all_8_0) = 0 & $i(all_8_0) & ? [v0: $i] : (r1(all_8_0, % 64.57/9.04 | v0) = 0 & $i(v0) & ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1) & ? % 64.57/9.04 | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & r1(v1, v2) = 0 & p1(v2) = % 64.57/9.04 | v3 & $i(v2) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (p1(v4) % 64.57/9.04 | = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & r1(v2, v4) % 64.57/9.04 | = v6))))) % 64.57/9.04 | % 64.57/9.04 | ALPHA: (11) implies: % 64.57/9.04 | (12) $i(all_8_0) % 64.57/9.04 | (13) r1(all_6_0, all_8_0) = 0 % 64.57/9.04 | (14) ? [v0: $i] : (r1(all_8_0, v0) = 0 & $i(v0) & ? [v1: $i] : (r1(v0, % 64.57/9.04 | v1) = 0 & $i(v1) & ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 64.57/9.04 | r1(v1, v2) = 0 & p1(v2) = v3 & $i(v2) & ! [v4: $i] : ! [v5: % 64.57/9.04 | int] : (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int] : % 64.57/9.04 | ( ~ (v6 = 0) & r1(v2, v4) = v6))))) % 64.57/9.04 | % 64.57/9.04 | DELTA: instantiating (14) with fresh symbol all_10_0 gives: % 64.57/9.05 | (15) r1(all_8_0, all_10_0) = 0 & $i(all_10_0) & ? [v0: $i] : (r1(all_10_0, % 64.57/9.05 | v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 64.57/9.05 | r1(v0, v1) = 0 & p1(v1) = v2 & $i(v1) & ! [v3: $i] : ! [v4: int] % 64.57/9.05 | : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 % 64.57/9.05 | = 0) & r1(v1, v3) = v5)))) % 64.57/9.05 | % 64.57/9.05 | ALPHA: (15) implies: % 64.57/9.05 | (16) $i(all_10_0) % 64.57/9.05 | (17) r1(all_8_0, all_10_0) = 0 % 64.57/9.05 | (18) ? [v0: $i] : (r1(all_10_0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 64.57/9.05 | int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 & $i(v1) & ! % 64.57/9.05 | [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | % 64.57/9.05 | ? [v5: int] : ( ~ (v5 = 0) & r1(v1, v3) = v5)))) % 64.57/9.05 | % 64.57/9.05 | DELTA: instantiating (18) with fresh symbol all_12_0 gives: % 64.57/9.05 | (19) r1(all_10_0, all_12_0) = 0 & $i(all_12_0) & ? [v0: $i] : ? [v1: int] % 64.57/9.05 | : ( ~ (v1 = 0) & r1(all_12_0, v0) = 0 & p1(v0) = v1 & $i(v0) & ! [v2: % 64.57/9.05 | $i] : ! [v3: int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? % 64.57/9.05 | [v4: int] : ( ~ (v4 = 0) & r1(v0, v2) = v4))) % 64.57/9.05 | % 64.57/9.05 | ALPHA: (19) implies: % 64.57/9.05 | (20) $i(all_12_0) % 64.57/9.05 | (21) r1(all_10_0, all_12_0) = 0 % 64.57/9.06 | (22) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & r1(all_12_0, v0) = 0 & % 64.57/9.06 | p1(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 64.57/9.06 | (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & r1(v0, % 64.57/9.06 | v2) = v4))) % 64.57/9.06 | % 64.57/9.06 | DELTA: instantiating (22) with fresh symbols all_14_0, all_14_1 gives: % 64.57/9.06 | (23) ~ (all_14_0 = 0) & r1(all_12_0, all_14_1) = 0 & p1(all_14_1) = % 64.57/9.06 | all_14_0 & $i(all_14_1) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 64.57/9.06 | (p1(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 64.57/9.06 | r1(all_14_1, v0) = v2)) % 64.57/9.06 | % 64.57/9.06 | ALPHA: (23) implies: % 64.57/9.06 | (24) ~ (all_14_0 = 0) % 64.57/9.06 | (25) $i(all_14_1) % 64.57/9.06 | (26) p1(all_14_1) = all_14_0 % 64.57/9.06 | (27) r1(all_12_0, all_14_1) = 0 % 64.57/9.06 | (28) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) | % 64.57/9.06 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_14_1, v0) = v2)) % 64.57/9.06 | % 64.57/9.06 | GROUND_INST: instantiating (5) with all_6_0, simplifying with (8), (9) gives: % 64.57/9.06 | (29) ! [v0: $i] : ( ~ (r1(all_6_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( % 64.57/9.06 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 64.57/9.06 | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 64.57/9.06 | (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & % 64.57/9.06 | r1(v2, v3) = v5) | ! [v5: $i] : ( ~ (r1(v3, v5) = 0) | ~ % 64.57/9.06 | $i(v5) | ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & r1(v5, % 64.57/9.07 | v6) = 0 & p1(v6) = v7 & $i(v6))))))) % 64.57/9.07 | % 64.57/9.07 | GROUND_INST: instantiating (4) with all_6_0, simplifying with (8), (9) gives: % 64.57/9.07 | (30) ! [v0: $i] : ( ~ (r1(all_6_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( % 64.57/9.07 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 64.57/9.07 | 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ % 64.57/9.07 | $i(v3) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & r1(v3, % 64.57/9.07 | v4) = 0 & p1(v4) = v5 & $i(v4)) | ! [v4: $i] : ( ~ % 64.57/9.07 | (r1(v3, v4) = 0) | ~ $i(v4) | ! [v5: $i] : ! [v6: int] : % 64.57/9.07 | (v6 = 0 | ~ (p1(v5) = v6) | ~ $i(v5) | ? [v7: int] : ( ~ % 64.57/9.07 | (v7 = 0) & r1(v4, v5) = v7))))))) % 64.57/9.07 | % 64.57/9.07 | GROUND_INST: instantiating (3) with all_6_0, simplifying with (8), (9) gives: % 64.57/9.07 | (31) ! [v0: $i] : ( ~ (r1(all_6_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( % 64.57/9.07 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 64.57/9.07 | 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ % 64.57/9.07 | $i(v3) | ? [v4: $i] : (r1(v3, v4) = 0 & $i(v4)))))) % 64.57/9.07 | % 64.57/9.07 | GROUND_INST: instantiating (30) with all_8_0, simplifying with (12), (13) % 64.57/9.07 | gives: % 64.57/9.07 | (32) ! [v0: $i] : ( ~ (r1(all_8_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( % 64.57/9.07 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 64.57/9.07 | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 64.57/9.07 | r1(v2, v3) = 0 & p1(v3) = v4 & $i(v3)) | ! [v3: $i] : ( ~ % 64.57/9.07 | (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: int] : % 64.57/9.07 | (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ % 64.57/9.07 | (v6 = 0) & r1(v3, v4) = v6)))))) % 64.57/9.07 | % 64.57/9.07 | GROUND_INST: instantiating (29) with all_8_0, simplifying with (12), (13) % 64.57/9.07 | gives: % 64.57/9.08 | (33) ! [v0: $i] : ( ~ (r1(all_8_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( % 64.57/9.08 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int] : (v3 % 64.57/9.08 | = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) % 64.57/9.08 | & r1(v1, v2) = v4) | ! [v4: $i] : ( ~ (r1(v2, v4) = 0) | ~ % 64.57/9.08 | $i(v4) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & r1(v4, % 64.57/9.08 | v5) = 0 & p1(v5) = v6 & $i(v5)))))) % 64.57/9.08 | % 64.57/9.08 | GROUND_INST: instantiating (31) with all_8_0, simplifying with (12), (13) % 64.57/9.08 | gives: % 64.57/9.08 | (34) ! [v0: $i] : ( ~ (r1(all_8_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( % 64.57/9.08 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 64.57/9.08 | 0) | ~ $i(v2) | ? [v3: $i] : (r1(v2, v3) = 0 & $i(v3))))) % 64.57/9.08 | % 64.57/9.08 | GROUND_INST: instantiating (32) with all_10_0, simplifying with (16), (17) % 64.57/9.08 | gives: % 64.57/9.08 | (35) ! [v0: $i] : ( ~ (r1(all_10_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( % 64.57/9.08 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : ( ~ % 64.57/9.08 | (v3 = 0) & r1(v1, v2) = 0 & p1(v2) = v3 & $i(v2)) | ! [v2: $i] % 64.57/9.08 | : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: int] : % 64.57/9.08 | (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 % 64.57/9.08 | = 0) & r1(v2, v3) = v5))))) % 64.57/9.08 | % 64.57/9.08 | GROUND_INST: instantiating (33) with all_10_0, simplifying with (16), (17) % 64.57/9.08 | gives: % 64.57/9.08 | (36) ! [v0: $i] : ( ~ (r1(all_10_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : % 64.57/9.08 | ! [v2: int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ? [v3: int] % 64.57/9.08 | : ( ~ (v3 = 0) & r1(v0, v1) = v3) | ! [v3: $i] : ( ~ (r1(v1, v3) % 64.57/9.08 | = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 64.57/9.08 | r1(v3, v4) = 0 & p1(v4) = v5 & $i(v4))))) % 64.57/9.08 | % 64.57/9.08 | GROUND_INST: instantiating (34) with all_10_0, simplifying with (16), (17) % 64.57/9.08 | gives: % 64.57/9.08 | (37) ! [v0: $i] : ( ~ (r1(all_10_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( % 64.57/9.08 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 & % 64.57/9.08 | $i(v2)))) % 64.57/9.09 | % 64.57/9.09 | GROUND_INST: instantiating (35) with all_12_0, simplifying with (20), (21) % 64.57/9.09 | gives: % 64.57/9.09 | (38) ! [v0: $i] : ( ~ (r1(all_12_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 64.57/9.09 | ? [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 & $i(v1)) % 64.57/9.09 | | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! % 64.57/9.09 | [v3: int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] % 64.57/9.09 | : ( ~ (v4 = 0) & r1(v1, v2) = v4)))) % 64.57/9.09 | % 64.57/9.09 | GROUND_INST: instantiating (36) with all_12_0, simplifying with (20), (21) % 64.57/9.09 | gives: % 64.57/9.09 | (39) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) | % 64.57/9.09 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_12_0, v0) = v2) | ! [v2: $i] : % 64.57/9.09 | ( ~ (r1(v0, v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ % 64.57/9.09 | (v4 = 0) & r1(v2, v3) = 0 & p1(v3) = v4 & $i(v3)))) % 64.57/9.09 | % 64.57/9.09 | GROUND_INST: instantiating (37) with all_12_0, simplifying with (20), (21) % 64.57/9.09 | gives: % 64.57/9.09 | (40) ! [v0: $i] : ( ~ (r1(all_12_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 64.57/9.09 | (r1(v0, v1) = 0 & $i(v1))) % 64.57/9.09 | % 64.57/9.09 | GROUND_INST: instantiating (38) with all_14_1, simplifying with (25), (27) % 64.57/9.09 | gives: % 64.57/9.09 | (41) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & r1(all_14_1, v0) = 0 & % 64.57/9.09 | p1(v0) = v1 & $i(v0)) | ! [v0: $i] : ( ~ (r1(all_14_1, v0) = 0) | % 64.57/9.09 | ~ $i(v0) | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p1(v1) = v2) | % 64.57/9.09 | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3))) % 64.57/9.09 | % 64.57/9.09 | GROUND_INST: instantiating (39) with all_14_1, all_14_0, simplifying with % 64.57/9.09 | (25), (26) gives: % 64.57/9.09 | (42) all_14_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_12_0, all_14_1) = % 64.57/9.09 | v0) | ! [v0: $i] : ( ~ (r1(all_14_1, v0) = 0) | ~ $i(v0) | ? [v1: % 64.57/9.09 | $i] : ? [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 & % 64.57/9.09 | $i(v1))) % 64.57/9.09 | % 64.57/9.09 | GROUND_INST: instantiating (40) with all_14_1, simplifying with (25), (27) % 64.57/9.09 | gives: % 64.57/9.09 | (43) ? [v0: $i] : (r1(all_14_1, v0) = 0 & $i(v0)) % 64.57/9.09 | % 64.57/9.09 | DELTA: instantiating (43) with fresh symbol all_80_0 gives: % 64.57/9.09 | (44) r1(all_14_1, all_80_0) = 0 & $i(all_80_0) % 64.57/9.09 | % 64.57/9.09 | ALPHA: (44) implies: % 64.57/9.09 | (45) $i(all_80_0) % 64.57/9.10 | (46) r1(all_14_1, all_80_0) = 0 % 64.57/9.10 | % 64.57/9.10 | BETA: splitting (42) gives: % 64.57/9.10 | % 64.57/9.10 | Case 1: % 64.57/9.10 | | % 64.57/9.10 | | (47) all_14_0 = 0 % 64.57/9.10 | | % 64.57/9.10 | | REDUCE: (24), (47) imply: % 64.57/9.10 | | (48) $false % 64.57/9.10 | | % 64.57/9.10 | | CLOSE: (48) is inconsistent. % 64.57/9.10 | | % 64.57/9.10 | Case 2: % 64.57/9.10 | | % 64.57/9.10 | | (49) ? [v0: int] : ( ~ (v0 = 0) & r1(all_12_0, all_14_1) = v0) | ! [v0: % 64.57/9.10 | | $i] : ( ~ (r1(all_14_1, v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 64.57/9.10 | | [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 & $i(v1))) % 64.57/9.10 | | % 64.57/9.10 | | BETA: splitting (49) gives: % 64.57/9.10 | | % 64.57/9.10 | | Case 1: % 64.57/9.10 | | | % 64.57/9.10 | | | (50) ? [v0: int] : ( ~ (v0 = 0) & r1(all_12_0, all_14_1) = v0) % 64.57/9.10 | | | % 64.57/9.10 | | | DELTA: instantiating (50) with fresh symbol all_94_0 gives: % 64.57/9.10 | | | (51) ~ (all_94_0 = 0) & r1(all_12_0, all_14_1) = all_94_0 % 64.57/9.10 | | | % 64.57/9.10 | | | ALPHA: (51) implies: % 64.57/9.10 | | | (52) ~ (all_94_0 = 0) % 64.57/9.10 | | | (53) r1(all_12_0, all_14_1) = all_94_0 % 64.57/9.10 | | | % 64.57/9.10 | | | GROUND_INST: instantiating (1) with 0, all_94_0, all_14_1, all_12_0, % 64.57/9.10 | | | simplifying with (27), (53) gives: % 64.57/9.10 | | | (54) all_94_0 = 0 % 64.57/9.10 | | | % 64.57/9.10 | | | REDUCE: (52), (54) imply: % 64.57/9.10 | | | (55) $false % 64.57/9.10 | | | % 64.57/9.10 | | | CLOSE: (55) is inconsistent. % 64.57/9.10 | | | % 64.57/9.10 | | Case 2: % 64.57/9.10 | | | % 64.57/9.10 | | | (56) ! [v0: $i] : ( ~ (r1(all_14_1, v0) = 0) | ~ $i(v0) | ? [v1: $i] % 64.57/9.10 | | | : ? [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 & % 64.57/9.10 | | | $i(v1))) % 64.57/9.10 | | | % 64.57/9.10 | | | GROUND_INST: instantiating (56) with all_80_0, simplifying with (45), (46) % 64.57/9.10 | | | gives: % 64.57/9.10 | | | (57) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & r1(all_80_0, v0) = 0 & % 64.57/9.10 | | | p1(v0) = v1 & $i(v0)) % 64.57/9.10 | | | % 64.57/9.10 | | | DELTA: instantiating (57) with fresh symbols all_137_0, all_137_1 gives: % 64.57/9.11 | | | (58) ~ (all_137_0 = 0) & r1(all_80_0, all_137_1) = 0 & p1(all_137_1) = % 64.57/9.11 | | | all_137_0 & $i(all_137_1) % 64.57/9.11 | | | % 64.57/9.11 | | | ALPHA: (58) implies: % 64.57/9.11 | | | (59) ~ (all_137_0 = 0) % 64.57/9.11 | | | (60) $i(all_137_1) % 64.57/9.11 | | | (61) p1(all_137_1) = all_137_0 % 64.57/9.11 | | | (62) r1(all_80_0, all_137_1) = 0 % 64.57/9.11 | | | % 64.57/9.11 | | | BETA: splitting (41) gives: % 64.57/9.11 | | | % 64.57/9.11 | | | Case 1: % 64.57/9.11 | | | | % 64.57/9.11 | | | | (63) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & r1(all_14_1, v0) = 0 % 64.57/9.11 | | | | & p1(v0) = v1 & $i(v0)) % 64.57/9.11 | | | | % 64.57/9.11 | | | | DELTA: instantiating (63) with fresh symbols all_358_0, all_358_1 gives: % 64.57/9.11 | | | | (64) ~ (all_358_0 = 0) & r1(all_14_1, all_358_1) = 0 & p1(all_358_1) % 64.57/9.11 | | | | = all_358_0 & $i(all_358_1) % 64.57/9.11 | | | | % 64.57/9.11 | | | | ALPHA: (64) implies: % 64.57/9.11 | | | | (65) ~ (all_358_0 = 0) % 64.57/9.11 | | | | (66) $i(all_358_1) % 64.57/9.11 | | | | (67) p1(all_358_1) = all_358_0 % 64.57/9.11 | | | | (68) r1(all_14_1, all_358_1) = 0 % 64.57/9.11 | | | | % 64.57/9.11 | | | | GROUND_INST: instantiating (28) with all_358_1, all_358_0, simplifying % 64.57/9.11 | | | | with (66), (67) gives: % 64.57/9.11 | | | | (69) all_358_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_14_1, % 64.57/9.11 | | | | all_358_1) = v0) % 64.57/9.11 | | | | % 64.57/9.11 | | | | BETA: splitting (69) gives: % 64.57/9.11 | | | | % 64.57/9.11 | | | | Case 1: % 64.57/9.11 | | | | | % 64.57/9.11 | | | | | (70) all_358_0 = 0 % 64.57/9.11 | | | | | % 64.57/9.11 | | | | | REDUCE: (65), (70) imply: % 64.57/9.11 | | | | | (71) $false % 64.57/9.11 | | | | | % 64.57/9.11 | | | | | CLOSE: (71) is inconsistent. % 64.57/9.11 | | | | | % 64.57/9.11 | | | | Case 2: % 64.57/9.11 | | | | | % 64.57/9.11 | | | | | (72) ? [v0: int] : ( ~ (v0 = 0) & r1(all_14_1, all_358_1) = v0) % 64.57/9.11 | | | | | % 64.57/9.11 | | | | | DELTA: instantiating (72) with fresh symbol all_609_0 gives: % 64.57/9.11 | | | | | (73) ~ (all_609_0 = 0) & r1(all_14_1, all_358_1) = all_609_0 % 64.57/9.11 | | | | | % 64.57/9.11 | | | | | ALPHA: (73) implies: % 64.57/9.11 | | | | | (74) ~ (all_609_0 = 0) % 64.57/9.11 | | | | | (75) r1(all_14_1, all_358_1) = all_609_0 % 64.57/9.11 | | | | | % 64.57/9.11 | | | | | GROUND_INST: instantiating (1) with 0, all_609_0, all_358_1, all_14_1, % 64.57/9.11 | | | | | simplifying with (68), (75) gives: % 64.57/9.11 | | | | | (76) all_609_0 = 0 % 64.57/9.11 | | | | | % 64.57/9.11 | | | | | REDUCE: (74), (76) imply: % 64.57/9.11 | | | | | (77) $false % 64.57/9.11 | | | | | % 64.57/9.11 | | | | | CLOSE: (77) is inconsistent. % 64.57/9.11 | | | | | % 64.57/9.11 | | | | End of split % 64.57/9.11 | | | | % 64.57/9.11 | | | Case 2: % 64.57/9.11 | | | | % 64.57/9.11 | | | | (78) ! [v0: $i] : ( ~ (r1(all_14_1, v0) = 0) | ~ $i(v0) | ! [v1: % 64.57/9.11 | | | | $i] : ! [v2: int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) % 64.57/9.11 | | | | | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3))) % 64.57/9.11 | | | | % 64.57/9.11 | | | | GROUND_INST: instantiating (78) with all_80_0, simplifying with (45), % 64.57/9.11 | | | | (46) gives: % 64.57/9.12 | | | | (79) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ % 64.57/9.12 | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_80_0, v0) = v2)) % 64.57/9.12 | | | | % 64.57/9.12 | | | | GROUND_INST: instantiating (79) with all_137_1, all_137_0, simplifying % 64.57/9.12 | | | | with (60), (61) gives: % 64.57/9.12 | | | | (80) all_137_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_80_0, % 64.57/9.12 | | | | all_137_1) = v0) % 64.57/9.12 | | | | % 64.57/9.12 | | | | BETA: splitting (80) gives: % 64.57/9.12 | | | | % 64.57/9.12 | | | | Case 1: % 64.57/9.12 | | | | | % 64.57/9.12 | | | | | (81) all_137_0 = 0 % 64.57/9.12 | | | | | % 64.57/9.12 | | | | | REDUCE: (59), (81) imply: % 64.57/9.12 | | | | | (82) $false % 64.57/9.12 | | | | | % 64.57/9.12 | | | | | CLOSE: (82) is inconsistent. % 64.57/9.12 | | | | | % 64.57/9.12 | | | | Case 2: % 64.57/9.12 | | | | | % 64.57/9.12 | | | | | (83) ? [v0: int] : ( ~ (v0 = 0) & r1(all_80_0, all_137_1) = v0) % 64.57/9.12 | | | | | % 64.57/9.12 | | | | | DELTA: instantiating (83) with fresh symbol all_363_0 gives: % 64.57/9.12 | | | | | (84) ~ (all_363_0 = 0) & r1(all_80_0, all_137_1) = all_363_0 % 64.57/9.12 | | | | | % 64.57/9.12 | | | | | ALPHA: (84) implies: % 64.57/9.12 | | | | | (85) ~ (all_363_0 = 0) % 64.57/9.12 | | | | | (86) r1(all_80_0, all_137_1) = all_363_0 % 64.57/9.12 | | | | | % 64.57/9.12 | | | | | GROUND_INST: instantiating (1) with 0, all_363_0, all_137_1, all_80_0, % 64.57/9.12 | | | | | simplifying with (62), (86) gives: % 64.57/9.12 | | | | | (87) all_363_0 = 0 % 64.57/9.12 | | | | | % 64.57/9.12 | | | | | REDUCE: (85), (87) imply: % 64.57/9.12 | | | | | (88) $false % 64.57/9.12 | | | | | % 64.57/9.12 | | | | | CLOSE: (88) is inconsistent. % 64.57/9.12 | | | | | % 64.57/9.12 | | | | End of split % 64.57/9.12 | | | | % 64.57/9.12 | | | End of split % 64.57/9.12 | | | % 64.57/9.12 | | End of split % 64.57/9.12 | | % 64.57/9.12 | End of split % 64.57/9.12 | % 64.57/9.12 End of proof % 64.57/9.12 % SZS output end Proof for theBenchmark % 64.57/9.12 % 64.57/9.12 8536ms %------------------------------------------------------------------------------