%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL672+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 : n017.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 12:54:38 PM UTC 2026 % Result : Theorem 15.61s 3.00s % Output : Proof 21.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL672+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 : n017.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 : Sat Sep 5 14:29:52 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. % 0.71/0.71 ________ _____ % 0.71/0.71 ___ __ \_________(_)________________________________ % 0.71/0.71 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.71/0.71 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.71/0.71 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.71/0.71 % 0.71/0.71 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.71/0.71 (2023-06-19) % 0.71/0.71 % 0.71/0.71 (c) Philipp Rümmer, 2009-2023 % 0.71/0.71 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.71/0.71 Amanda Stjerna. % 0.71/0.71 Free software under BSD-3-Clause. % 0.71/0.71 % 0.71/0.71 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.71/0.71 % 0.71/0.71 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.74 Running up to 7 provers in parallel. % 0.71/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.78/1.40 Prover 4: Preprocessing ... % 3.78/1.42 Prover 1: Preprocessing ... % 3.78/1.44 Prover 6: Preprocessing ... % 3.78/1.44 Prover 2: Preprocessing ... % 3.78/1.44 Prover 0: Preprocessing ... % 3.78/1.45 Prover 3: Preprocessing ... % 3.78/1.46 Prover 5: Preprocessing ... % 6.16/1.74 Prover 5: Proving ... % 6.16/1.74 Prover 2: Proving ... % 7.73/1.93 Prover 6: Proving ... % 7.73/1.93 Prover 0: Proving ... % 7.73/1.94 Prover 3: Constructing countermodel ... % 7.73/2.00 Prover 1: Constructing countermodel ... % 7.73/2.03 Prover 4: Constructing countermodel ... % 15.61/3.00 Prover 3: proved (2250ms) % 15.61/3.00 % 15.61/3.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.61/3.00 % 15.61/3.01 Prover 2: stopped % 15.61/3.01 Prover 0: stopped % 15.61/3.01 Prover 5: stopped % 15.61/3.01 Prover 6: stopped % 15.61/3.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.61/3.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.61/3.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.61/3.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.61/3.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.65/3.08 Prover 8: Preprocessing ... % 16.65/3.14 Prover 7: Preprocessing ... % 17.48/3.15 Prover 10: Preprocessing ... % 17.48/3.15 Prover 8: Warning: ignoring some quantifiers % 17.48/3.16 Prover 8: Constructing countermodel ... % 17.48/3.19 Prover 13: Preprocessing ... % 17.48/3.19 Prover 10: Warning: ignoring some quantifiers % 17.48/3.19 Prover 10: Constructing countermodel ... % 17.48/3.19 Prover 7: Warning: ignoring some quantifiers % 17.90/3.20 Prover 7: Constructing countermodel ... % 17.90/3.20 Prover 11: Preprocessing ... % 17.90/3.25 Prover 13: Warning: ignoring some quantifiers % 17.90/3.26 Prover 13: Constructing countermodel ... % 19.50/3.40 Prover 1: Found proof (size 87) % 19.50/3.40 Prover 1: proved (2655ms) % 19.50/3.40 Prover 7: stopped % 19.50/3.40 Prover 8: stopped % 19.50/3.40 Prover 13: stopped % 19.50/3.40 Prover 10: stopped % 19.50/3.40 Prover 11: Constructing countermodel ... % 19.50/3.41 Prover 11: stopped % 19.50/3.41 Prover 4: stopped % 19.50/3.41 % 19.50/3.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.50/3.41 % 19.50/3.42 % SZS output start Proof for theBenchmark % 19.50/3.43 Assumptions after simplification: % 19.50/3.43 --------------------------------- % 19.50/3.43 % 19.50/3.43 (main) % 20.01/3.52 ? [v0: $i] : ($i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & p1(v1) = % 20.01/3.52 v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 20.01/3.52 & p2(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : (r1(v0, v1) = 0 & % 20.01/3.52 $i(v1) & ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, % 20.01/3.52 v2) = 0 & $i(v2)) & ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ! [v3: % 20.01/3.52 $i] : ! [v4: int] : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: % 20.01/3.52 int] : ( ~ (v5 = 0) & r1(v2, v3) = v5)))) & ( ! [v1: $i] : ! [v2: % 20.01/3.52 int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = % 20.01/3.52 0) & r1(v0, v1) = v3)) | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 20.01/3.52 (p2(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = % 20.01/3.52 v3)) | ( ! [v1: $i] : ( ~ (p1(v1) = 0) | ~ $i(v1) | ? [v2: int] : ( % 20.01/3.52 ~ (v2 = 0) & r1(v0, v1) = v2) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | % 20.01/3.52 ~ $i(v2) | ? [v3: $i] : (p1(v3) = 0 & r1(v2, v3) = 0 & $i(v3)))) & % 20.01/3.52 ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1, % 20.01/3.52 v2) = 0 & $i(v2))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ % 20.01/3.52 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i] % 20.01/3.52 : ? [v4: int] : ( ~ (v4 = 0) & p1(v3) = v4 & r1(v2, v3) = 0 & % 20.01/3.52 $i(v3))) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? % 20.01/3.52 [v3: $i] : (r1(v2, v3) = 0 & $i(v3) & ! [v4: $i] : ! [v5: int] : % 20.01/3.52 (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = % 20.01/3.52 0) & r1(v3, v4) = v6))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = % 20.01/3.52 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! % 20.01/3.52 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | % 20.01/3.52 ? [v5: int] : ( ~ (v5 = 0) & r1(v2, v3) = v5)) | ! [v3: $i] : ( ~ % 20.01/3.52 (r1(v2, v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ( ~ % 20.01/3.52 (v5 = 0) & p1(v4) = v5 & r1(v3, v4) = 0 & $i(v4)))))))) % 20.01/3.52 % 20.01/3.52 (reflexivity) % 20.01/3.52 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (r1(v0, v0) = v1) | ~ $i(v0)) % 20.01/3.52 % 20.01/3.52 (function-axioms) % 20.01/3.53 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 20.01/3.53 [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0: % 20.01/3.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 20.01/3.53 ~ (p1(v2) = v1) | ~ (p1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.01/3.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (p2(v2) = v1) | ~ (p2(v2) % 20.01/3.53 = v0)) % 20.01/3.53 % 20.01/3.53 Further assumptions not needed in the proof: % 20.01/3.53 -------------------------------------------- % 20.01/3.53 transitivity % 20.01/3.53 % 20.01/3.53 Those formulas are unsatisfiable: % 20.01/3.53 --------------------------------- % 20.01/3.53 % 20.01/3.53 Begin of proof % 20.01/3.53 | % 20.01/3.53 | ALPHA: (function-axioms) implies: % 20.01/3.54 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.01/3.54 | ! [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) % 20.01/3.54 | % 20.01/3.54 | DELTA: instantiating (main) with fresh symbol all_5_0 gives: % 20.01/3.56 | (2) $i(all_5_0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p1(v0) = v1 & % 20.01/3.56 | r1(all_5_0, v0) = 0 & $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 % 20.01/3.56 | = 0) & p2(v0) = v1 & r1(all_5_0, v0) = 0 & $i(v0)) & ? [v0: $i] : % 20.01/3.56 | (r1(all_5_0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = % 20.01/3.56 | 0) & p1(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : % 20.01/3.56 | (r1(v0, v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.01/3.56 | (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & r1(v1, % 20.01/3.56 | v2) = v4)))) & ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 20.01/3.56 | (p1(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 20.01/3.56 | r1(all_5_0, v0) = v2)) | ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 20.01/3.56 | ~ (p2(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 20.01/3.56 | r1(all_5_0, v0) = v2)) | ( ! [v0: $i] : ( ~ (p1(v0) = 0) | ~ % 20.01/3.56 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & r1(all_5_0, v0) = v1) | ! % 20.01/3.56 | [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : % 20.01/3.56 | (p1(v2) = 0 & r1(v1, v2) = 0 & $i(v2)))) & ! [v0: $i] : ( ~ % 20.01/3.56 | (r1(all_5_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0 % 20.01/3.56 | & $i(v1))) & ! [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ % 20.01/3.56 | $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: % 20.01/3.56 | $i] : ? [v3: int] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) % 20.01/3.56 | = 0 & $i(v2))) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ % 20.01/3.56 | $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] : % 20.01/3.56 | ! [v4: int] : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? % 20.01/3.56 | [v5: int] : ( ~ (v5 = 0) & r1(v2, v3) = v5))))) & ! [v0: % 20.01/3.56 | $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 20.01/3.56 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int] : (v3 % 20.01/3.56 | = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 20.01/3.56 | 0) & r1(v1, v2) = v4)) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 20.01/3.56 | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) % 20.01/3.56 | & p1(v3) = v4 & r1(v2, v3) = 0 & $i(v3))))))) % 20.01/3.56 | % 20.01/3.56 | ALPHA: (2) implies: % 20.01/3.58 | (3) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) | % 20.01/3.58 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_5_0, v0) = v2)) | ! [v0: $i] : % 20.01/3.58 | ! [v1: int] : (v1 = 0 | ~ (p2(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( % 20.01/3.58 | ~ (v2 = 0) & r1(all_5_0, v0) = v2)) | ( ! [v0: $i] : ( ~ (p1(v0) = % 20.01/3.58 | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & r1(all_5_0, v0) = % 20.01/3.58 | v1) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: % 20.01/3.58 | $i] : (p1(v2) = 0 & r1(v1, v2) = 0 & $i(v2)))) & ! [v0: $i] : % 20.01/3.58 | ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0 % 20.01/3.58 | & $i(v1))) & ! [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) % 20.01/3.58 | | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? % 20.01/3.58 | [v3: int] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0 & % 20.01/3.58 | $i(v2))) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? % 20.01/3.58 | [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] : ! [v4: int] % 20.01/3.58 | : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ % 20.01/3.58 | (v5 = 0) & r1(v2, v3) = v5))))) & ! [v0: $i] : ( ~ % 20.01/3.58 | (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = % 20.01/3.58 | 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.01/3.58 | (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & % 20.01/3.58 | r1(v1, v2) = v4)) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ % 20.01/3.58 | $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & p1(v3) = % 20.01/3.58 | v4 & r1(v2, v3) = 0 & $i(v3)))))) % 20.01/3.58 | (4) ? [v0: $i] : (r1(all_5_0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 20.01/3.58 | int] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ? % 20.01/3.58 | [v1: $i] : (r1(v0, v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: int] : % 20.01/3.58 | (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 20.01/3.58 | 0) & r1(v1, v2) = v4)))) % 20.01/3.58 | (5) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p2(v0) = v1 & r1(all_5_0, % 20.01/3.58 | v0) = 0 & $i(v0)) % 20.01/3.58 | (6) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_5_0, % 20.01/3.58 | v0) = 0 & $i(v0)) % 20.01/3.58 | % 20.01/3.58 | DELTA: instantiating (5) with fresh symbols all_7_0, all_7_1 gives: % 20.01/3.58 | (7) ~ (all_7_0 = 0) & p2(all_7_1) = all_7_0 & r1(all_5_0, all_7_1) = 0 & % 20.01/3.58 | $i(all_7_1) % 20.01/3.58 | % 20.01/3.58 | ALPHA: (7) implies: % 20.01/3.59 | (8) ~ (all_7_0 = 0) % 20.01/3.59 | (9) $i(all_7_1) % 20.01/3.59 | (10) r1(all_5_0, all_7_1) = 0 % 20.01/3.59 | (11) p2(all_7_1) = all_7_0 % 20.01/3.59 | % 20.01/3.59 | DELTA: instantiating (6) with fresh symbols all_9_0, all_9_1 gives: % 20.01/3.59 | (12) ~ (all_9_0 = 0) & p1(all_9_1) = all_9_0 & r1(all_5_0, all_9_1) = 0 & % 20.01/3.59 | $i(all_9_1) % 20.01/3.59 | % 20.01/3.59 | ALPHA: (12) implies: % 20.01/3.59 | (13) ~ (all_9_0 = 0) % 20.01/3.59 | (14) $i(all_9_1) % 20.01/3.59 | (15) r1(all_5_0, all_9_1) = 0 % 20.01/3.59 | (16) p1(all_9_1) = all_9_0 % 20.01/3.59 | % 20.01/3.59 | DELTA: instantiating (4) with fresh symbol all_11_0 gives: % 20.01/3.59 | (17) r1(all_5_0, all_11_0) = 0 & $i(all_11_0) & ? [v0: $i] : ? [v1: int] % 20.01/3.59 | : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_11_0, v0) = 0 & $i(v0)) & ? % 20.01/3.59 | [v0: $i] : (r1(all_11_0, v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: int] % 20.01/3.59 | : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = % 20.01/3.59 | 0) & r1(v0, v1) = v3))) % 20.01/3.59 | % 20.01/3.59 | ALPHA: (17) implies: % 20.01/3.59 | (18) $i(all_11_0) % 20.01/3.59 | (19) r1(all_5_0, all_11_0) = 0 % 20.01/3.60 | (20) ? [v0: $i] : (r1(all_11_0, v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: % 20.01/3.60 | int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ % 20.01/3.60 | (v3 = 0) & r1(v0, v1) = v3))) % 20.50/3.60 | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_11_0, % 20.50/3.60 | v0) = 0 & $i(v0)) % 20.50/3.60 | % 20.50/3.60 | DELTA: instantiating (21) with fresh symbols all_13_0, all_13_1 gives: % 20.50/3.60 | (22) ~ (all_13_0 = 0) & p1(all_13_1) = all_13_0 & r1(all_11_0, all_13_1) = % 20.50/3.60 | 0 & $i(all_13_1) % 20.50/3.60 | % 20.50/3.60 | ALPHA: (22) implies: % 20.50/3.60 | (23) ~ (all_13_0 = 0) % 20.50/3.60 | (24) $i(all_13_1) % 20.50/3.60 | (25) r1(all_11_0, all_13_1) = 0 % 20.50/3.60 | (26) p1(all_13_1) = all_13_0 % 20.50/3.60 | % 20.50/3.60 | DELTA: instantiating (20) with fresh symbol all_15_0 gives: % 20.50/3.60 | (27) r1(all_11_0, all_15_0) = 0 & $i(all_15_0) & ! [v0: $i] : ! [v1: int] % 20.50/3.60 | : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) % 20.50/3.60 | & r1(all_15_0, v0) = v2)) % 20.50/3.60 | % 20.50/3.60 | ALPHA: (27) implies: % 20.50/3.60 | (28) $i(all_15_0) % 20.50/3.60 | (29) r1(all_11_0, all_15_0) = 0 % 20.50/3.60 | (30) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) | % 20.50/3.60 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_15_0, v0) = v2)) % 20.50/3.60 | % 20.50/3.60 | BETA: splitting (3) gives: % 20.50/3.60 | % 20.50/3.61 | Case 1: % 20.50/3.61 | | % 20.50/3.61 | | (31) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) % 20.50/3.61 | | | ? [v2: int] : ( ~ (v2 = 0) & r1(all_5_0, v0) = v2)) % 20.50/3.61 | | % 20.50/3.61 | | GROUND_INST: instantiating (31) with all_9_1, all_9_0, simplifying with % 20.50/3.61 | | (14), (16) gives: % 20.50/3.61 | | (32) all_9_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_5_0, all_9_1) = % 20.50/3.61 | | v0) % 20.50/3.61 | | % 20.50/3.61 | | BETA: splitting (32) gives: % 20.50/3.61 | | % 20.50/3.61 | | Case 1: % 20.50/3.61 | | | % 20.50/3.61 | | | (33) all_9_0 = 0 % 20.50/3.61 | | | % 20.50/3.61 | | | REDUCE: (13), (33) imply: % 20.50/3.61 | | | (34) $false % 20.50/3.61 | | | % 20.50/3.61 | | | CLOSE: (34) is inconsistent. % 20.50/3.61 | | | % 20.50/3.61 | | Case 2: % 20.50/3.61 | | | % 20.50/3.61 | | | (35) ? [v0: int] : ( ~ (v0 = 0) & r1(all_5_0, all_9_1) = v0) % 20.50/3.61 | | | % 20.50/3.61 | | | DELTA: instantiating (35) with fresh symbol all_35_0 gives: % 20.50/3.61 | | | (36) ~ (all_35_0 = 0) & r1(all_5_0, all_9_1) = all_35_0 % 20.50/3.61 | | | % 20.50/3.61 | | | ALPHA: (36) implies: % 20.50/3.62 | | | (37) ~ (all_35_0 = 0) % 20.50/3.62 | | | (38) r1(all_5_0, all_9_1) = all_35_0 % 20.50/3.62 | | | % 20.50/3.62 | | | GROUND_INST: instantiating (1) with 0, all_35_0, all_9_1, all_5_0, % 20.50/3.62 | | | simplifying with (15), (38) gives: % 20.50/3.62 | | | (39) all_35_0 = 0 % 20.50/3.62 | | | % 20.50/3.62 | | | REDUCE: (37), (39) imply: % 20.50/3.62 | | | (40) $false % 20.50/3.62 | | | % 20.50/3.62 | | | CLOSE: (40) is inconsistent. % 20.50/3.62 | | | % 20.50/3.62 | | End of split % 20.50/3.62 | | % 20.50/3.62 | Case 2: % 20.50/3.62 | | % 20.50/3.63 | | (41) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p2(v0) = v1) | ~ $i(v0) % 20.50/3.63 | | | ? [v2: int] : ( ~ (v2 = 0) & r1(all_5_0, v0) = v2)) | ( ! [v0: % 20.50/3.63 | | $i] : ( ~ (p1(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 20.50/3.63 | | & r1(all_5_0, v0) = v1) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | % 20.50/3.63 | | ~ $i(v1) | ? [v2: $i] : (p1(v2) = 0 & r1(v1, v2) = 0 & % 20.50/3.63 | | $i(v2)))) & ! [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ % 20.50/3.63 | | $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1))) & ! [v0: $i] % 20.50/3.63 | | : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 20.50/3.63 | | (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : ( % 20.50/3.63 | | ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0 & $i(v2))) | ! % 20.50/3.63 | | [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : % 20.50/3.63 | | (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] : ! [v4: int] : (v4 = % 20.50/3.63 | | 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 % 20.50/3.63 | | = 0) & r1(v2, v3) = v5))))) & ! [v0: $i] : ( ~ % 20.50/3.63 | | (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, % 20.50/3.63 | | v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int] : (v3 = % 20.50/3.63 | | 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 20.50/3.63 | | 0) & r1(v1, v2) = v4)) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 20.50/3.63 | | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) % 20.50/3.63 | | & p1(v3) = v4 & r1(v2, v3) = 0 & $i(v3)))))) % 20.50/3.63 | | % 20.50/3.63 | | BETA: splitting (41) gives: % 20.50/3.63 | | % 20.50/3.63 | | Case 1: % 20.50/3.63 | | | % 20.50/3.63 | | | (42) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p2(v0) = v1) | ~ % 20.50/3.63 | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_5_0, v0) = v2)) % 20.50/3.63 | | | % 20.50/3.63 | | | GROUND_INST: instantiating (42) with all_7_1, all_7_0, simplifying with % 20.50/3.63 | | | (9), (11) gives: % 20.50/3.63 | | | (43) all_7_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_5_0, all_7_1) = % 20.50/3.63 | | | v0) % 20.50/3.63 | | | % 20.50/3.63 | | | BETA: splitting (43) gives: % 20.50/3.63 | | | % 20.50/3.63 | | | Case 1: % 20.50/3.63 | | | | % 20.50/3.63 | | | | (44) all_7_0 = 0 % 20.50/3.63 | | | | % 20.50/3.63 | | | | REDUCE: (8), (44) imply: % 20.50/3.63 | | | | (45) $false % 20.50/3.63 | | | | % 20.50/3.63 | | | | CLOSE: (45) is inconsistent. % 20.50/3.63 | | | | % 20.50/3.63 | | | Case 2: % 20.50/3.63 | | | | % 20.50/3.63 | | | | (46) ? [v0: int] : ( ~ (v0 = 0) & r1(all_5_0, all_7_1) = v0) % 20.50/3.64 | | | | % 20.50/3.64 | | | | DELTA: instantiating (46) with fresh symbol all_35_0 gives: % 20.50/3.64 | | | | (47) ~ (all_35_0 = 0) & r1(all_5_0, all_7_1) = all_35_0 % 20.50/3.64 | | | | % 20.50/3.64 | | | | ALPHA: (47) implies: % 20.50/3.64 | | | | (48) ~ (all_35_0 = 0) % 20.50/3.64 | | | | (49) r1(all_5_0, all_7_1) = all_35_0 % 20.50/3.64 | | | | % 20.50/3.64 | | | | GROUND_INST: instantiating (1) with 0, all_35_0, all_7_1, all_5_0, % 20.50/3.64 | | | | simplifying with (10), (49) gives: % 20.50/3.64 | | | | (50) all_35_0 = 0 % 20.50/3.64 | | | | % 20.50/3.64 | | | | REDUCE: (48), (50) imply: % 20.50/3.64 | | | | (51) $false % 20.50/3.64 | | | | % 20.50/3.64 | | | | CLOSE: (51) is inconsistent. % 20.50/3.64 | | | | % 20.50/3.64 | | | End of split % 20.50/3.64 | | | % 20.50/3.64 | | Case 2: % 20.50/3.64 | | | % 20.50/3.65 | | | (52) ! [v0: $i] : ( ~ (p1(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 20.50/3.65 | | | (v1 = 0) & r1(all_5_0, v0) = v1) | ! [v1: $i] : ( ~ (r1(v0, % 20.50/3.65 | | | v1) = 0) | ~ $i(v1) | ? [v2: $i] : (p1(v2) = 0 & r1(v1, % 20.50/3.65 | | | v2) = 0 & $i(v2)))) & ! [v0: $i] : ( ~ (r1(all_5_0, v0) = % 20.50/3.65 | | | 0) | ~ $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1))) & ! % 20.50/3.65 | | | [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( % 20.50/3.65 | | | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : % 20.50/3.65 | | | ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0 & $i(v2))) | ! % 20.50/3.65 | | | [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : % 20.50/3.65 | | | (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] : ! [v4: int] : (v4 = % 20.50/3.65 | | | 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 % 20.50/3.65 | | | = 0) & r1(v2, v3) = v5))))) & ! [v0: $i] : ( ~ % 20.50/3.65 | | | (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, % 20.50/3.65 | | | v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int] : (v3 = % 20.50/3.65 | | | 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 20.50/3.65 | | | 0) & r1(v1, v2) = v4)) | ! [v2: $i] : ( ~ (r1(v1, v2) = % 20.50/3.65 | | | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) % 20.50/3.65 | | | & p1(v3) = v4 & r1(v2, v3) = 0 & $i(v3))))) % 20.50/3.65 | | | % 20.50/3.65 | | | ALPHA: (52) implies: % 20.50/3.65 | | | (53) ! [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] % 20.50/3.65 | | | : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int] % 20.50/3.65 | | | : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ % 20.50/3.65 | | | (v4 = 0) & r1(v1, v2) = v4)) | ! [v2: $i] : ( ~ (r1(v1, % 20.50/3.66 | | | v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ % 20.50/3.66 | | | (v4 = 0) & p1(v3) = v4 & r1(v2, v3) = 0 & $i(v3))))) % 20.50/3.66 | | | (54) ! [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] % 20.50/3.66 | | | : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] % 20.50/3.66 | | | : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0 & $i(v2))) | ! % 20.50/3.66 | | | [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : % 20.50/3.66 | | | (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] : ! [v4: int] : (v4 = % 20.50/3.66 | | | 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 % 20.50/3.66 | | | = 0) & r1(v2, v3) = v5))))) % 20.50/3.66 | | | % 20.50/3.66 | | | GROUND_INST: instantiating (54) with all_11_0, simplifying with (18), (19) % 20.50/3.66 | | | gives: % 20.50/3.66 | | | (55) ! [v0: $i] : ( ~ (r1(all_11_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] % 20.50/3.66 | | | : ? [v2: int] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0 & % 20.50/3.66 | | | $i(v1))) | ! [v0: $i] : ( ~ (r1(all_11_0, v0) = 0) | ~ % 20.50/3.66 | | | $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1) & ! [v2: $i] : % 20.50/3.66 | | | ! [v3: int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: % 20.50/3.66 | | | int] : ( ~ (v4 = 0) & r1(v1, v2) = v4)))) % 20.50/3.66 | | | % 20.50/3.66 | | | GROUND_INST: instantiating (53) with all_11_0, simplifying with (18), (19) % 20.50/3.66 | | | gives: % 20.50/3.67 | | | (56) ! [v0: $i] : ( ~ (r1(all_11_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] % 20.50/3.67 | | | : ! [v2: int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ? % 20.50/3.67 | | | [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) | ! [v1: $i] : ( % 20.50/3.67 | | | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : % 20.50/3.67 | | | ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0 & $i(v2)))) % 20.50/3.67 | | | % 20.50/3.67 | | | GROUND_INST: instantiating (56) with all_13_1, simplifying with (24), (25) % 20.50/3.67 | | | gives: % 20.50/3.67 | | | (57) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ % 20.50/3.67 | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_13_1, v0) = v2)) | % 20.50/3.67 | | | ! [v0: $i] : ( ~ (r1(all_13_1, v0) = 0) | ~ $i(v0) | ? [v1: $i] % 20.50/3.67 | | | : ? [v2: int] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0 & % 20.50/3.67 | | | $i(v1))) % 20.50/3.67 | | | % 20.50/3.67 | | | BETA: splitting (55) gives: % 20.50/3.67 | | | % 20.50/3.67 | | | Case 1: % 20.50/3.67 | | | | % 20.50/3.67 | | | | (58) ! [v0: $i] : ( ~ (r1(all_11_0, v0) = 0) | ~ $i(v0) | ? [v1: % 20.50/3.67 | | | | $i] : ? [v2: int] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) % 20.50/3.67 | | | | = 0 & $i(v1))) % 20.50/3.67 | | | | % 20.50/3.67 | | | | GROUND_INST: instantiating (58) with all_15_0, simplifying with (28), % 20.50/3.67 | | | | (29) gives: % 20.50/3.67 | | | | (59) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p1(v0) = v1 & % 20.50/3.67 | | | | r1(all_15_0, v0) = 0 & $i(v0)) % 20.50/3.67 | | | | % 20.50/3.67 | | | | DELTA: instantiating (59) with fresh symbols all_54_0, all_54_1 gives: % 20.50/3.67 | | | | (60) ~ (all_54_0 = 0) & p1(all_54_1) = all_54_0 & r1(all_15_0, % 20.50/3.67 | | | | all_54_1) = 0 & $i(all_54_1) % 20.50/3.67 | | | | % 20.50/3.67 | | | | ALPHA: (60) implies: % 20.50/3.68 | | | | (61) ~ (all_54_0 = 0) % 20.50/3.68 | | | | (62) $i(all_54_1) % 20.50/3.68 | | | | (63) r1(all_15_0, all_54_1) = 0 % 20.50/3.68 | | | | (64) p1(all_54_1) = all_54_0 % 20.50/3.68 | | | | % 20.50/3.68 | | | | GROUND_INST: instantiating (30) with all_54_1, all_54_0, simplifying % 20.50/3.68 | | | | with (62), (64) gives: % 20.50/3.68 | | | | (65) all_54_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_15_0, % 20.50/3.68 | | | | all_54_1) = v0) % 20.50/3.68 | | | | % 20.50/3.68 | | | | BETA: splitting (65) gives: % 20.50/3.68 | | | | % 20.50/3.68 | | | | Case 1: % 20.50/3.68 | | | | | % 20.50/3.68 | | | | | (66) all_54_0 = 0 % 20.50/3.68 | | | | | % 20.50/3.68 | | | | | REDUCE: (61), (66) imply: % 20.50/3.68 | | | | | (67) $false % 20.50/3.68 | | | | | % 20.50/3.68 | | | | | CLOSE: (67) is inconsistent. % 20.50/3.68 | | | | | % 20.50/3.68 | | | | Case 2: % 20.50/3.68 | | | | | % 20.50/3.68 | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & r1(all_15_0, all_54_1) = v0) % 20.50/3.68 | | | | | % 20.50/3.68 | | | | | DELTA: instantiating (68) with fresh symbol all_72_0 gives: % 20.50/3.68 | | | | | (69) ~ (all_72_0 = 0) & r1(all_15_0, all_54_1) = all_72_0 % 20.50/3.68 | | | | | % 20.50/3.68 | | | | | ALPHA: (69) implies: % 20.50/3.68 | | | | | (70) ~ (all_72_0 = 0) % 20.50/3.68 | | | | | (71) r1(all_15_0, all_54_1) = all_72_0 % 20.50/3.68 | | | | | % 20.50/3.68 | | | | | GROUND_INST: instantiating (1) with 0, all_72_0, all_54_1, all_15_0, % 20.50/3.68 | | | | | simplifying with (63), (71) gives: % 20.50/3.68 | | | | | (72) all_72_0 = 0 % 20.50/3.68 | | | | | % 20.50/3.68 | | | | | REDUCE: (70), (72) imply: % 20.50/3.68 | | | | | (73) $false % 20.50/3.68 | | | | | % 20.50/3.68 | | | | | CLOSE: (73) is inconsistent. % 20.50/3.68 | | | | | % 20.50/3.68 | | | | End of split % 20.50/3.68 | | | | % 20.50/3.68 | | | Case 2: % 20.50/3.68 | | | | % 20.50/3.69 | | | | (74) ! [v0: $i] : ( ~ (r1(all_11_0, v0) = 0) | ~ $i(v0) | ? [v1: % 20.50/3.69 | | | | $i] : (r1(v0, v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: int] % 20.50/3.69 | | | | : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( % 20.50/3.69 | | | | ~ (v4 = 0) & r1(v1, v2) = v4)))) % 20.50/3.69 | | | | % 20.50/3.69 | | | | GROUND_INST: instantiating (74) with all_13_1, simplifying with (24), % 20.50/3.69 | | | | (25) gives: % 20.50/3.69 | | | | (75) ? [v0: $i] : (r1(all_13_1, v0) = 0 & $i(v0) & ! [v1: $i] : ! % 20.50/3.69 | | | | [v2: int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ? [v3: % 20.50/3.69 | | | | int] : ( ~ (v3 = 0) & r1(v0, v1) = v3))) % 20.50/3.69 | | | | % 20.50/3.69 | | | | DELTA: instantiating (75) with fresh symbol all_58_0 gives: % 20.50/3.69 | | | | (76) r1(all_13_1, all_58_0) = 0 & $i(all_58_0) & ! [v0: $i] : ! % 20.50/3.69 | | | | [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) | ? [v2: % 20.50/3.69 | | | | int] : ( ~ (v2 = 0) & r1(all_58_0, v0) = v2)) % 20.50/3.69 | | | | % 20.50/3.69 | | | | ALPHA: (76) implies: % 20.50/3.69 | | | | (77) $i(all_58_0) % 20.50/3.69 | | | | (78) r1(all_13_1, all_58_0) = 0 % 20.50/3.69 | | | | (79) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ % 20.50/3.69 | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_58_0, v0) = v2)) % 20.50/3.69 | | | | % 20.50/3.69 | | | | BETA: splitting (57) gives: % 20.50/3.69 | | | | % 20.50/3.69 | | | | Case 1: % 20.50/3.69 | | | | | % 20.50/3.69 | | | | | (80) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ % 20.50/3.69 | | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_13_1, v0) = % 20.50/3.69 | | | | | v2)) % 20.50/3.69 | | | | | % 20.50/3.69 | | | | | GROUND_INST: instantiating (80) with all_13_1, all_13_0, simplifying % 20.50/3.69 | | | | | with (24), (26) gives: % 20.50/3.70 | | | | | (81) all_13_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_13_1, % 20.50/3.70 | | | | | all_13_1) = v0) % 20.50/3.70 | | | | | % 20.50/3.70 | | | | | BETA: splitting (81) gives: % 20.50/3.70 | | | | | % 20.50/3.70 | | | | | Case 1: % 20.50/3.70 | | | | | | % 20.50/3.70 | | | | | | (82) all_13_0 = 0 % 20.50/3.70 | | | | | | % 20.50/3.70 | | | | | | REDUCE: (23), (82) imply: % 20.50/3.70 | | | | | | (83) $false % 20.50/3.70 | | | | | | % 20.50/3.70 | | | | | | CLOSE: (83) is inconsistent. % 20.50/3.70 | | | | | | % 20.50/3.70 | | | | | Case 2: % 20.50/3.70 | | | | | | % 21.00/3.70 | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & r1(all_13_1, all_13_1) = v0) % 21.00/3.70 | | | | | | % 21.00/3.70 | | | | | | DELTA: instantiating (84) with fresh symbol all_155_0 gives: % 21.00/3.70 | | | | | | (85) ~ (all_155_0 = 0) & r1(all_13_1, all_13_1) = all_155_0 % 21.00/3.70 | | | | | | % 21.00/3.70 | | | | | | ALPHA: (85) implies: % 21.00/3.70 | | | | | | (86) ~ (all_155_0 = 0) % 21.00/3.70 | | | | | | (87) r1(all_13_1, all_13_1) = all_155_0 % 21.00/3.70 | | | | | | % 21.00/3.70 | | | | | | GROUND_INST: instantiating (reflexivity) with all_13_1, all_155_0, % 21.00/3.70 | | | | | | simplifying with (24), (87) gives: % 21.00/3.70 | | | | | | (88) all_155_0 = 0 % 21.00/3.70 | | | | | | % 21.00/3.70 | | | | | | REDUCE: (86), (88) imply: % 21.00/3.70 | | | | | | (89) $false % 21.00/3.70 | | | | | | % 21.00/3.70 | | | | | | CLOSE: (89) is inconsistent. % 21.00/3.70 | | | | | | % 21.00/3.70 | | | | | End of split % 21.00/3.70 | | | | | % 21.00/3.70 | | | | Case 2: % 21.00/3.70 | | | | | % 21.00/3.70 | | | | | (90) ! [v0: $i] : ( ~ (r1(all_13_1, v0) = 0) | ~ $i(v0) | ? [v1: % 21.00/3.70 | | | | | $i] : ? [v2: int] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, % 21.00/3.70 | | | | | v1) = 0 & $i(v1))) % 21.00/3.70 | | | | | % 21.00/3.70 | | | | | GROUND_INST: instantiating (90) with all_58_0, simplifying with (77), % 21.00/3.70 | | | | | (78) gives: % 21.00/3.70 | | | | | (91) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p1(v0) = v1 & % 21.00/3.70 | | | | | r1(all_58_0, v0) = 0 & $i(v0)) % 21.00/3.70 | | | | | % 21.00/3.70 | | | | | DELTA: instantiating (91) with fresh symbols all_145_0, all_145_1 % 21.00/3.70 | | | | | gives: % 21.00/3.70 | | | | | (92) ~ (all_145_0 = 0) & p1(all_145_1) = all_145_0 & r1(all_58_0, % 21.00/3.70 | | | | | all_145_1) = 0 & $i(all_145_1) % 21.00/3.70 | | | | | % 21.00/3.70 | | | | | ALPHA: (92) implies: % 21.00/3.71 | | | | | (93) ~ (all_145_0 = 0) % 21.00/3.71 | | | | | (94) $i(all_145_1) % 21.00/3.71 | | | | | (95) r1(all_58_0, all_145_1) = 0 % 21.00/3.71 | | | | | (96) p1(all_145_1) = all_145_0 % 21.00/3.71 | | | | | % 21.00/3.71 | | | | | GROUND_INST: instantiating (79) with all_145_1, all_145_0, simplifying % 21.00/3.71 | | | | | with (94), (96) gives: % 21.00/3.71 | | | | | (97) all_145_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_58_0, % 21.00/3.71 | | | | | all_145_1) = v0) % 21.00/3.71 | | | | | % 21.00/3.71 | | | | | BETA: splitting (97) gives: % 21.00/3.71 | | | | | % 21.00/3.71 | | | | | Case 1: % 21.00/3.71 | | | | | | % 21.00/3.71 | | | | | | (98) all_145_0 = 0 % 21.00/3.71 | | | | | | % 21.00/3.71 | | | | | | REDUCE: (93), (98) imply: % 21.00/3.71 | | | | | | (99) $false % 21.00/3.71 | | | | | | % 21.00/3.71 | | | | | | CLOSE: (99) is inconsistent. % 21.00/3.71 | | | | | | % 21.00/3.71 | | | | | Case 2: % 21.00/3.71 | | | | | | % 21.00/3.71 | | | | | | (100) ? [v0: int] : ( ~ (v0 = 0) & r1(all_58_0, all_145_1) = v0) % 21.00/3.71 | | | | | | % 21.00/3.71 | | | | | | DELTA: instantiating (100) with fresh symbol all_164_0 gives: % 21.00/3.71 | | | | | | (101) ~ (all_164_0 = 0) & r1(all_58_0, all_145_1) = all_164_0 % 21.00/3.71 | | | | | | % 21.00/3.71 | | | | | | ALPHA: (101) implies: % 21.00/3.71 | | | | | | (102) ~ (all_164_0 = 0) % 21.00/3.71 | | | | | | (103) r1(all_58_0, all_145_1) = all_164_0 % 21.00/3.71 | | | | | | % 21.00/3.71 | | | | | | GROUND_INST: instantiating (1) with 0, all_164_0, all_145_1, % 21.00/3.71 | | | | | | all_58_0, simplifying with (95), (103) gives: % 21.00/3.71 | | | | | | (104) all_164_0 = 0 % 21.00/3.71 | | | | | | % 21.00/3.71 | | | | | | REDUCE: (102), (104) imply: % 21.00/3.71 | | | | | | (105) $false % 21.00/3.71 | | | | | | % 21.00/3.71 | | | | | | CLOSE: (105) is inconsistent. % 21.00/3.71 | | | | | | % 21.00/3.71 | | | | | End of split % 21.00/3.71 | | | | | % 21.00/3.71 | | | | End of split % 21.00/3.71 | | | | % 21.00/3.71 | | | End of split % 21.00/3.71 | | | % 21.00/3.71 | | End of split % 21.00/3.71 | | % 21.00/3.71 | End of split % 21.00/3.71 | % 21.00/3.71 End of proof % 21.00/3.71 % SZS output end Proof for theBenchmark % 21.00/3.71 % 21.00/3.71 2998ms %------------------------------------------------------------------------------