%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC332+1 : TPTP v8.1.2. Released v2.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n010.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 20:50:52 EDT 2023 % Result : Theorem 54.17s 7.89s % Output : Proof 225.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC332+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n010.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Mon Aug 28 17:10:19 EDT 2023 % 0.14/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.43/1.55 Prover 1: Preprocessing ... % 5.43/1.56 Prover 4: Preprocessing ... % 6.31/1.59 Prover 3: Preprocessing ... % 6.31/1.59 Prover 6: Preprocessing ... % 6.31/1.59 Prover 0: Preprocessing ... % 6.31/1.59 Prover 2: Preprocessing ... % 6.31/1.60 Prover 5: Preprocessing ... % 15.83/2.87 Prover 2: Proving ... % 16.38/3.00 Prover 5: Constructing countermodel ... % 16.89/3.03 Prover 1: Constructing countermodel ... % 16.89/3.03 Prover 6: Proving ... % 17.35/3.12 Prover 3: Constructing countermodel ... % 20.96/3.60 Prover 4: Constructing countermodel ... % 22.96/3.82 Prover 0: Proving ... % 54.17/7.89 Prover 3: proved (7256ms) % 54.17/7.89 % 54.17/7.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 54.17/7.89 % 54.17/7.89 Prover 2: stopped % 54.17/7.89 Prover 0: stopped % 54.17/7.89 Prover 5: stopped % 54.17/7.89 Prover 6: stopped % 54.17/7.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 54.17/7.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 54.17/7.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 54.17/7.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 54.17/7.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 55.44/8.09 Prover 13: Preprocessing ... % 55.44/8.13 Prover 7: Preprocessing ... % 55.44/8.13 Prover 8: Preprocessing ... % 55.44/8.14 Prover 10: Preprocessing ... % 55.44/8.14 Prover 11: Preprocessing ... % 57.15/8.27 Prover 7: Constructing countermodel ... % 57.15/8.31 Prover 10: Constructing countermodel ... % 57.15/8.31 Prover 13: Constructing countermodel ... % 59.48/8.60 Prover 8: Warning: ignoring some quantifiers % 59.48/8.63 Prover 8: Constructing countermodel ... % 64.65/9.27 Prover 11: Constructing countermodel ... % 88.53/12.38 Prover 13: stopped % 88.53/12.38 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 89.57/12.56 Prover 16: Preprocessing ... % 91.37/12.77 Prover 16: Constructing countermodel ... % 115.83/15.98 Prover 1: stopped % 115.83/15.98 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 117.28/16.14 Prover 19: Preprocessing ... % 120.06/16.47 Prover 19: Warning: ignoring some quantifiers % 120.06/16.49 Prover 19: Constructing countermodel ... % 128.43/17.65 Prover 16: stopped % 142.21/19.56 Prover 19: stopped % 187.85/27.97 Prover 4: stopped % 191.42/28.98 Prover 7: stopped % 224.15/38.70 Prover 8: Found proof (size 382) % 224.15/38.70 Prover 8: proved (30654ms) % 224.15/38.70 Prover 11: stopped % 224.15/38.72 Prover 10: stopped % 224.15/38.72 % 224.15/38.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 224.15/38.72 % 224.44/38.74 % SZS output start Proof for theBenchmark % 224.44/38.75 Assumptions after simplification: % 224.44/38.75 --------------------------------- % 224.44/38.75 % 224.44/38.75 (ax13) % 224.51/38.78 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ? % 224.51/38.78 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 224.51/38.78 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) | % 224.51/38.78 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 224.51/38.78 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~ % 224.51/38.78 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 224.51/38.78 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) | % 224.51/38.78 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) | % 224.51/38.78 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 = % 224.51/38.78 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) = % 224.51/38.78 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] : % 224.51/38.78 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 & % 224.51/38.78 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ? % 224.51/38.78 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 & % 224.51/38.78 app(v7, v9) = v0 & $i(v9) & $i(v8))))))))) % 224.51/38.78 % 224.51/38.79 (ax15) % 224.51/38.79 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 224.51/38.79 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 224.51/38.79 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 224.51/38.79 % 224.51/38.79 (ax17) % 224.51/38.79 ssList(nil) = 0 & $i(nil) % 224.51/38.79 % 224.51/38.79 (ax2) % 224.51/38.79 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) & % 224.51/38.79 ssItem(v1) = 0 & $i(v1))) % 224.51/38.79 % 224.51/38.79 (ax20) % 224.51/38.79 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 224.51/38.79 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 224.51/38.79 ssItem(v2) = 0 & $i(v2)))) % 224.51/38.79 % 224.51/38.79 (ax23) % 224.51/38.79 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 224.51/38.79 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 224.51/38.79 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 224.51/38.79 % 224.51/38.79 (ax25) % 224.51/38.79 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 224.51/38.79 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 224.51/38.79 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 224.51/38.79 % 224.51/38.79 (ax4) % 224.51/38.80 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | % 224.51/38.80 ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: $i] % 224.51/38.80 : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 | ! [v2: % 224.51/38.80 $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = % 224.51/38.80 0) & ssItem(v2) = v3))))) % 224.51/38.80 % 224.51/38.80 (ax54) % 224.51/38.80 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : (v1 = v0 | ~ % 224.51/38.80 (segmentP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : % 224.51/38.80 (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 224.51/38.80 % 224.51/38.80 (ax57) % 224.51/38.80 $i(nil) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | % 224.51/38.80 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 224.51/38.80 % 224.51/38.80 (ax59) % 224.51/38.80 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.51/38.80 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 224.51/38.80 (v2 = 0) | v3 = 0))) % 224.51/38.80 % 224.51/38.80 (ax61) % 224.51/38.80 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.51/38.80 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 224.51/38.80 (v2 = 0) | v3 = 0))) % 224.51/38.80 % 224.51/38.80 (ax63) % 224.51/38.80 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.51/38.80 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 224.51/38.80 (v2 = 0) | v3 = 0))) % 224.51/38.80 % 224.51/38.80 (ax65) % 224.51/38.80 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.51/38.80 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 224.51/38.80 (v2 = 0) | v3 = 0))) % 224.51/38.80 % 224.51/38.80 (ax68) % 224.51/38.80 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.51/38.80 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 224.51/38.80 ~ (v2 = 0) | v3 = 0))) % 224.51/38.80 % 224.51/38.80 (ax7) % 224.51/38.81 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 224.51/38.81 ( ~ (segmentP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 224.51/38.81 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : ? [v4: $i] : % 224.51/38.81 (ssList(v3) = 0 & app(v3, v1) = v4 & $i(v4) & $i(v3) & ? [v5: $i] : % 224.51/38.81 (ssList(v5) = 0 & app(v4, v5) = v0 & $i(v5)))) & (v2 = 0 | ! [v3: % 224.51/38.81 $i] : ! [v4: $i] : ( ~ (app(v3, v1) = v4) | ~ $i(v3) | ? [v5: % 224.51/38.81 int] : ( ~ (v5 = 0) & ssList(v3) = v5) | ! [v5: $i] : ( ~ % 224.51/38.81 (app(v4, v5) = v0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & % 224.51/38.81 ssList(v5) = v6))))))) % 224.51/38.81 % 224.51/38.81 (ax71) % 224.51/38.81 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.51/38.81 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 224.51/38.81 ~ (v2 = 0) | v3 = 0))) % 224.51/38.81 % 224.51/38.81 (ax72) % 224.51/38.81 duplicatefreeP(nil) = 0 & $i(nil) % 224.51/38.81 % 224.51/38.81 (ax73) % 224.51/38.81 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.51/38.81 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 224.51/38.81 (v2 = 0) | v3 = 0))) % 224.51/38.81 % 224.51/38.81 (ax74) % 224.51/38.81 equalelemsP(nil) = 0 & $i(nil) % 224.51/38.81 % 224.51/38.81 (co1) % 224.51/38.81 $i(nil) & ? [v0: $i] : ? [v1: any] : (equalelemsP(v0) = v1 & ssList(v0) = 0 % 224.51/38.81 & $i(v0) & ? [v2: $i] : ? [v3: any] : (segmentP(v2, v0) = v3 & ssList(v2) % 224.51/38.81 = 0 & $i(v2) & ? [v4: $i] : ? [v5: any] : (singletonP(v4) = v5 & % 224.51/38.81 ssList(v4) = 0 & $i(v4) & ? [v6: any] : (v4 = v0 & v3 = 0 & ~ (v1 = 0) % 224.51/38.81 & neq(v2, nil) = v6 & ( ~ (v6 = 0) | v5 = 0))))) % 224.51/38.81 % 224.51/38.81 (function-axioms) % 224.75/38.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 224.75/38.82 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 224.75/38.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 224.75/38.82 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 224.75/38.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 224.75/38.82 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 224.75/38.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 224.75/38.82 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 224.75/38.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 224.75/38.82 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 224.75/38.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 224.75/38.82 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 224.75/38.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 224.75/38.82 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 224.75/38.82 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 224.75/38.82 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 224.75/38.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 224.75/38.82 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 224.75/38.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 224.75/38.82 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 224.75/38.82 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 224.75/38.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 224.75/38.82 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 224.75/38.82 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 224.75/38.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 224.75/38.82 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.75/38.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 224.75/38.82 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.75/38.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 224.75/38.82 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.75/38.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 224.75/38.82 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.75/38.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 224.75/38.82 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.75/38.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 224.75/38.82 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.75/38.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 224.75/38.82 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.75/38.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 224.75/38.82 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.75/38.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 224.75/38.82 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 224.75/38.82 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ? % 224.75/38.82 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (gt(v1, v0) = v2) & ? % 224.75/38.82 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (geq(v1, v0) = v2) & ? % 224.75/38.82 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (lt(v1, v0) = v2) & ? % 224.75/38.82 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (leq(v1, v0) = v2) & ? % 224.75/38.82 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (segmentP(v1, v0) = v2) % 224.75/38.82 & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (rearsegP(v1, v0) = % 224.75/38.82 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 224.75/38.82 (frontsegP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 224.75/38.82 MultipleValueBool] : (memberP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 224.75/38.82 [v2: MultipleValueBool] : (neq(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 224.75/38.82 [v2: $i] : (cons(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 224.75/38.82 $i] : (app(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] % 224.75/38.82 : (equalelemsP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.75/38.82 (duplicatefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.75/38.82 (strictorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.75/38.82 (totalorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.75/38.82 (strictorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.75/38.82 (totalorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.75/38.82 (cyclefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.75/38.82 (singletonP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssList(v0) % 224.75/38.82 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssItem(v0) = v1) & ? % 224.75/38.82 [v0: $i] : ? [v1: $i] : (tl(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 224.75/38.82 (hd(v0) = v1 & $i(v1)) % 224.75/38.82 % 224.75/38.82 Further assumptions not needed in the proof: % 224.75/38.82 -------------------------------------------- % 224.75/38.83 ax1, ax10, ax11, ax12, ax14, ax16, ax18, ax19, ax21, ax22, ax24, ax26, ax27, % 224.75/38.83 ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, % 224.75/38.83 ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, % 224.75/38.83 ax52, ax53, ax55, ax56, ax58, ax6, ax60, ax62, ax64, ax66, ax67, ax69, ax70, % 224.75/38.83 ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85, ax86, % 224.75/38.83 ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 224.75/38.83 % 224.75/38.83 Those formulas are unsatisfiable: % 224.75/38.83 --------------------------------- % 224.75/38.83 % 224.75/38.83 Begin of proof % 224.75/38.83 | % 224.75/38.83 | ALPHA: (ax4) implies: % 224.75/38.83 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | ? % 224.75/38.83 | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: % 224.75/38.83 | $i] : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 % 224.75/38.83 | | ! [v2: $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: % 224.75/38.83 | int] : ( ~ (v3 = 0) & ssItem(v2) = v3))))) % 224.75/38.83 | % 224.75/38.83 | ALPHA: (ax17) implies: % 224.75/38.83 | (2) ssList(nil) = 0 % 224.75/38.83 | % 224.75/38.83 | ALPHA: (ax20) implies: % 224.75/38.83 | (3) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 224.75/38.83 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 224.75/38.83 | ssItem(v2) = 0 & $i(v2)))) % 224.75/38.83 | % 224.75/38.83 | ALPHA: (ax57) implies: % 224.75/38.83 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ~ % 224.75/38.83 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 224.75/38.83 | % 224.75/38.83 | ALPHA: (ax59) implies: % 224.75/38.83 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.75/38.83 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 224.75/38.83 | ~ (v2 = 0) | v3 = 0))) % 224.75/38.83 | % 224.75/38.83 | ALPHA: (ax61) implies: % 224.75/38.83 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.75/38.83 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 224.75/38.83 | ( ~ (v2 = 0) | v3 = 0))) % 224.75/38.83 | % 224.75/38.83 | ALPHA: (ax63) implies: % 224.75/38.83 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.75/38.83 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 224.75/38.83 | ( ~ (v2 = 0) | v3 = 0))) % 224.75/38.83 | % 224.75/38.83 | ALPHA: (ax65) implies: % 224.75/38.84 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.75/38.84 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 224.75/38.84 | & ( ~ (v2 = 0) | v3 = 0))) % 224.75/38.84 | % 224.75/38.84 | ALPHA: (ax68) implies: % 224.75/38.84 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.75/38.84 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 224.75/38.84 | & ( ~ (v2 = 0) | v3 = 0))) % 224.75/38.84 | % 224.75/38.84 | ALPHA: (ax71) implies: % 224.75/38.84 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.75/38.84 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = % 224.75/38.84 | v2 & ( ~ (v2 = 0) | v3 = 0))) % 224.75/38.84 | % 224.75/38.84 | ALPHA: (ax72) implies: % 224.75/38.84 | (11) duplicatefreeP(nil) = 0 % 224.75/38.84 | % 224.75/38.84 | ALPHA: (ax73) implies: % 224.75/38.84 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.75/38.84 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 224.75/38.84 | ( ~ (v2 = 0) | v3 = 0))) % 224.75/38.84 | % 224.75/38.84 | ALPHA: (ax74) implies: % 224.75/38.84 | (13) equalelemsP(nil) = 0 % 224.75/38.84 | % 224.75/38.84 | ALPHA: (co1) implies: % 224.75/38.84 | (14) $i(nil) % 224.75/38.84 | (15) ? [v0: $i] : ? [v1: any] : (equalelemsP(v0) = v1 & ssList(v0) = 0 & % 224.75/38.84 | $i(v0) & ? [v2: $i] : ? [v3: any] : (segmentP(v2, v0) = v3 & % 224.75/38.84 | ssList(v2) = 0 & $i(v2) & ? [v4: $i] : ? [v5: any] : % 224.75/38.84 | (singletonP(v4) = v5 & ssList(v4) = 0 & $i(v4) & ? [v6: any] : % 224.75/38.84 | (v4 = v0 & v3 = 0 & ~ (v1 = 0) & neq(v2, nil) = v6 & ( ~ (v6 = % 224.75/38.84 | 0) | v5 = 0))))) % 224.75/38.84 | % 224.75/38.84 | ALPHA: (function-axioms) implies: % 224.75/38.84 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 224.75/38.84 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 224.75/38.84 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 224.75/38.84 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 224.75/38.84 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 224.75/38.84 | : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0)) % 224.75/38.84 | % 224.75/38.84 | DELTA: instantiating (ax2) with fresh symbol all_137_0 gives: % 224.75/38.84 | (19) ssItem(all_137_0) = 0 & $i(all_137_0) & ? [v0: any] : ( ~ (v0 = % 224.75/38.84 | all_137_0) & ssItem(v0) = 0 & $i(v0)) % 224.75/38.84 | % 224.75/38.84 | ALPHA: (19) implies: % 224.75/38.84 | (20) ? [v0: any] : ( ~ (v0 = all_137_0) & ssItem(v0) = 0 & $i(v0)) % 224.75/38.84 | % 224.75/38.84 | DELTA: instantiating (15) with fresh symbols all_139_0, all_139_1 gives: % 224.75/38.85 | (21) equalelemsP(all_139_1) = all_139_0 & ssList(all_139_1) = 0 & % 224.75/38.85 | $i(all_139_1) & ? [v0: $i] : ? [v1: any] : (segmentP(v0, all_139_1) % 224.75/38.85 | = v1 & ssList(v0) = 0 & $i(v0) & ? [v2: $i] : ? [v3: any] : % 224.75/38.85 | (singletonP(v2) = v3 & ssList(v2) = 0 & $i(v2) & ? [v4: any] : (v2 % 224.75/38.85 | = all_139_1 & v1 = 0 & ~ (all_139_0 = 0) & neq(v0, nil) = v4 & % 224.75/38.85 | ( ~ (v4 = 0) | v3 = 0)))) % 224.75/38.85 | % 224.75/38.85 | ALPHA: (21) implies: % 224.75/38.85 | (22) equalelemsP(all_139_1) = all_139_0 % 224.75/38.85 | (23) ? [v0: $i] : ? [v1: any] : (segmentP(v0, all_139_1) = v1 & % 224.75/38.85 | ssList(v0) = 0 & $i(v0) & ? [v2: $i] : ? [v3: any] : % 224.75/38.85 | (singletonP(v2) = v3 & ssList(v2) = 0 & $i(v2) & ? [v4: any] : (v2 % 224.75/38.85 | = all_139_1 & v1 = 0 & ~ (all_139_0 = 0) & neq(v0, nil) = v4 & % 224.75/38.85 | ( ~ (v4 = 0) | v3 = 0)))) % 224.75/38.85 | % 224.75/38.85 | DELTA: instantiating (20) with fresh symbol all_141_0 gives: % 224.75/38.85 | (24) ~ (all_141_0 = all_137_0) & ssItem(all_141_0) = 0 & $i(all_141_0) % 224.75/38.85 | % 224.75/38.85 | ALPHA: (24) implies: % 224.75/38.85 | (25) $i(all_141_0) % 224.75/38.85 | (26) ssItem(all_141_0) = 0 % 224.75/38.85 | % 224.75/38.85 | DELTA: instantiating (23) with fresh symbols all_143_0, all_143_1 gives: % 224.75/38.85 | (27) segmentP(all_143_1, all_139_1) = all_143_0 & ssList(all_143_1) = 0 & % 224.75/38.85 | $i(all_143_1) & ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & % 224.75/38.85 | ssList(v0) = 0 & $i(v0) & ? [v2: any] : (v0 = all_139_1 & all_143_0 % 224.75/38.85 | = 0 & ~ (all_139_0 = 0) & neq(all_143_1, nil) = v2 & ( ~ (v2 = 0) % 224.75/38.85 | | v1 = 0))) % 224.75/38.85 | % 224.75/38.85 | ALPHA: (27) implies: % 224.75/38.85 | (28) $i(all_143_1) % 224.75/38.85 | (29) ssList(all_143_1) = 0 % 224.75/38.85 | (30) segmentP(all_143_1, all_139_1) = all_143_0 % 224.93/38.85 | (31) ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 & % 224.93/38.85 | $i(v0) & ? [v2: any] : (v0 = all_139_1 & all_143_0 = 0 & ~ % 224.93/38.85 | (all_139_0 = 0) & neq(all_143_1, nil) = v2 & ( ~ (v2 = 0) | v1 = % 224.93/38.85 | 0))) % 224.93/38.85 | % 224.93/38.85 | DELTA: instantiating (31) with fresh symbols all_145_0, all_145_1 gives: % 224.93/38.85 | (32) singletonP(all_145_1) = all_145_0 & ssList(all_145_1) = 0 & % 224.93/38.85 | $i(all_145_1) & ? [v0: any] : (all_145_1 = all_139_1 & all_143_0 = 0 % 224.93/38.85 | & ~ (all_139_0 = 0) & neq(all_143_1, nil) = v0 & ( ~ (v0 = 0) | % 224.93/38.85 | all_145_0 = 0)) % 224.93/38.85 | % 224.93/38.85 | ALPHA: (32) implies: % 224.93/38.85 | (33) $i(all_145_1) % 224.93/38.85 | (34) ssList(all_145_1) = 0 % 224.93/38.85 | (35) singletonP(all_145_1) = all_145_0 % 224.93/38.85 | (36) ? [v0: any] : (all_145_1 = all_139_1 & all_143_0 = 0 & ~ (all_139_0 % 224.93/38.85 | = 0) & neq(all_143_1, nil) = v0 & ( ~ (v0 = 0) | all_145_0 = 0)) % 224.93/38.85 | % 224.93/38.85 | DELTA: instantiating (36) with fresh symbol all_147_0 gives: % 224.93/38.85 | (37) all_145_1 = all_139_1 & all_143_0 = 0 & ~ (all_139_0 = 0) & % 224.93/38.85 | neq(all_143_1, nil) = all_147_0 & ( ~ (all_147_0 = 0) | all_145_0 = 0) % 224.93/38.85 | % 224.93/38.85 | ALPHA: (37) implies: % 224.93/38.85 | (38) all_143_0 = 0 % 224.93/38.85 | (39) all_145_1 = all_139_1 % 224.93/38.85 | (40) ~ (all_139_0 = 0) % 224.93/38.86 | (41) neq(all_143_1, nil) = all_147_0 % 224.93/38.86 | (42) ~ (all_147_0 = 0) | all_145_0 = 0 % 224.93/38.86 | % 224.93/38.86 | REDUCE: (30), (38) imply: % 224.93/38.86 | (43) segmentP(all_143_1, all_139_1) = 0 % 224.93/38.86 | % 224.93/38.86 | REDUCE: (35), (39) imply: % 224.93/38.86 | (44) singletonP(all_139_1) = all_145_0 % 224.93/38.86 | % 224.93/38.86 | REDUCE: (34), (39) imply: % 224.93/38.86 | (45) ssList(all_139_1) = 0 % 224.93/38.86 | % 224.93/38.86 | REDUCE: (33), (39) imply: % 224.93/38.86 | (46) $i(all_139_1) % 224.93/38.86 | % 224.93/38.86 | GROUND_INST: instantiating (ax25) with nil, simplifying with (2), (14) gives: % 224.93/38.86 | (47) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.93/38.86 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 224.93/38.86 | ( ~ (v2 = 0) | v3 = nil))) % 224.93/38.86 | % 224.93/38.86 | GROUND_INST: instantiating (ax23) with nil, simplifying with (2), (14) gives: % 224.93/38.86 | (48) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.93/38.86 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 224.93/38.86 | ( ~ (v2 = 0) | v3 = v0))) % 224.93/38.86 | % 224.93/38.86 | GROUND_INST: instantiating (3) with all_139_1, simplifying with (45), (46) % 224.93/38.86 | gives: % 224.93/38.86 | (49) all_139_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 224.93/38.86 | : (cons(v1, v0) = all_139_1 & ssItem(v1) = 0 & $i(v1))) % 224.93/38.86 | % 224.93/38.86 | GROUND_INST: instantiating (3) with all_143_1, simplifying with (28), (29) % 224.93/38.86 | gives: % 224.93/38.86 | (50) all_143_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 224.93/38.86 | : (cons(v1, v0) = all_143_1 & ssItem(v1) = 0 & $i(v1))) % 224.93/38.86 | % 224.93/38.86 | GROUND_INST: instantiating (ax7) with all_143_1, simplifying with (28), (29) % 224.93/38.86 | gives: % 224.93/38.86 | (51) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(all_143_1, v0) = v1) | ~ % 224.93/38.86 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = % 224.93/38.86 | 0) | ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & app(v2, v0) % 224.93/38.86 | = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 & % 224.93/38.86 | app(v3, v4) = all_143_1 & $i(v4)))) & (v1 = 0 | ! [v2: $i] % 224.93/38.86 | : ! [v3: $i] : ( ~ (app(v2, v0) = v3) | ~ $i(v2) | ? [v4: % 224.93/38.86 | int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] : ( ~ % 224.93/38.86 | (app(v3, v4) = all_143_1) | ~ $i(v4) | ? [v5: int] : ( ~ % 224.93/38.86 | (v5 = 0) & ssList(v4) = v5)))))) % 224.93/38.86 | % 224.93/38.86 | GROUND_INST: instantiating (ax15) with all_143_1, simplifying with (28), (29) % 224.93/38.86 | gives: % 224.93/38.87 | (52) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_143_1, v0) = v1) | ~ $i(v0) % 224.93/38.87 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 224.93/38.87 | ~ (v0 = all_143_1)) & (v1 = 0 | v0 = all_143_1))) % 224.93/38.87 | % 224.93/38.87 | GROUND_INST: instantiating (ax54) with all_143_1, simplifying with (28), (29) % 224.93/38.87 | gives: % 224.93/38.87 | (53) ! [v0: any] : (v0 = all_143_1 | ~ (segmentP(all_143_1, v0) = 0) | ~ % 224.93/38.87 | $i(v0) | ? [v1: any] : ? [v2: any] : (segmentP(v0, all_143_1) = v2 % 224.93/38.87 | & ssList(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 224.93/38.87 | % 224.93/38.87 | GROUND_INST: instantiating (1) with all_139_1, all_145_0, simplifying with % 224.93/38.87 | (44), (46) gives: % 224.93/38.87 | (54) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) | (( ~ % 224.93/38.87 | (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_139_1 & % 224.93/38.87 | ssItem(v0) = 0 & $i(v0))) & (all_145_0 = 0 | ! [v0: $i] : ( ~ % 224.93/38.87 | (cons(v0, nil) = all_139_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 224.93/38.87 | = 0) & ssItem(v0) = v1)))) % 224.93/38.87 | % 224.93/38.87 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (11), (14) % 224.93/38.87 | gives: % 224.93/38.87 | (55) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 224.93/38.87 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) | % 224.93/38.87 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | ! % 224.93/38.87 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) | % 224.93/38.87 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = % 224.93/38.87 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 224.93/38.87 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil) % 224.93/38.87 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 224.93/38.87 | v8)))))) % 224.93/38.87 | % 224.93/38.87 | GROUND_INST: instantiating (53) with all_139_1, simplifying with (43), (46) % 224.93/38.87 | gives: % 224.93/38.87 | (56) all_143_1 = all_139_1 | ? [v0: any] : ? [v1: any] : % 224.93/38.87 | (segmentP(all_139_1, all_143_1) = v1 & ssList(all_139_1) = v0 & ( ~ % 224.93/38.87 | (v1 = 0) | ~ (v0 = 0))) % 224.93/38.87 | % 224.93/38.87 | GROUND_INST: instantiating (52) with nil, all_147_0, simplifying with (14), % 224.93/38.87 | (41) gives: % 224.93/38.87 | (57) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_147_0 = 0) % 224.93/38.87 | | ~ (all_143_1 = nil)) & (all_147_0 = 0 | all_143_1 = nil)) % 224.93/38.87 | % 224.93/38.87 | GROUND_INST: instantiating (51) with all_139_1, 0, simplifying with (43), (46) % 224.93/38.87 | gives: % 224.93/38.88 | (58) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_139_1) = v1 % 224.93/38.88 | & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & app(v1, v2) = % 224.93/38.88 | all_143_1 & $i(v2))) | ? [v0: int] : ( ~ (v0 = 0) & % 224.93/38.88 | ssList(all_139_1) = v0) % 224.93/38.88 | % 224.93/38.88 | BETA: splitting (55) gives: % 224.93/38.88 | % 224.93/38.88 | Case 1: % 224.93/38.88 | | % 224.93/38.88 | | (59) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 224.93/38.88 | | % 224.93/38.88 | | DELTA: instantiating (59) with fresh symbol all_378_0 gives: % 224.93/38.88 | | (60) ~ (all_378_0 = 0) & ssList(nil) = all_378_0 % 224.93/38.88 | | % 224.93/38.88 | | REF_CLOSE: (2), (17), (60) are inconsistent by sub-proof #3. % 224.93/38.88 | | % 224.93/38.88 | Case 2: % 224.93/38.88 | | % 224.93/38.88 | | (61) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 224.93/38.88 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = % 224.93/38.88 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 224.93/38.88 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) | % 224.93/38.88 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i] % 224.93/38.88 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ % 224.93/38.88 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = % 224.93/38.88 | | 0) & ssList(v6) = v8)))))) % 224.93/38.88 | | % 224.93/38.88 | | BETA: splitting (58) gives: % 224.93/38.88 | | % 224.93/38.88 | | Case 1: % 224.93/38.88 | | | % 224.93/38.88 | | | (62) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_139_1) = % 224.93/38.88 | | | v1 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & app(v1, % 224.93/38.88 | | | v2) = all_143_1 & $i(v2))) % 224.93/38.88 | | | % 224.93/38.88 | | | DELTA: instantiating (62) with fresh symbols all_341_0, all_341_1 gives: % 224.93/38.88 | | | (63) ssList(all_341_1) = 0 & app(all_341_1, all_139_1) = all_341_0 & % 224.93/38.88 | | | $i(all_341_0) & $i(all_341_1) & ? [v0: $i] : (ssList(v0) = 0 & % 224.93/38.88 | | | app(all_341_0, v0) = all_143_1 & $i(v0)) % 224.93/38.88 | | | % 224.93/38.88 | | | ALPHA: (63) implies: % 224.93/38.88 | | | (64) $i(all_341_1) % 224.93/38.88 | | | (65) app(all_341_1, all_139_1) = all_341_0 % 224.93/38.88 | | | (66) ssList(all_341_1) = 0 % 224.93/38.88 | | | % 224.93/38.88 | | | BETA: splitting (42) gives: % 224.93/38.88 | | | % 224.93/38.88 | | | Case 1: % 224.93/38.88 | | | | % 224.93/38.88 | | | | (67) ~ (all_147_0 = 0) % 224.93/38.88 | | | | % 224.93/38.88 | | | | BETA: splitting (57) gives: % 224.93/38.88 | | | | % 224.93/38.88 | | | | Case 1: % 224.93/38.88 | | | | | % 224.93/38.88 | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 224.93/38.88 | | | | | % 224.93/38.88 | | | | | DELTA: instantiating (68) with fresh symbol all_378_0 gives: % 224.93/38.88 | | | | | (69) ~ (all_378_0 = 0) & ssList(nil) = all_378_0 % 224.93/38.88 | | | | | % 224.93/38.88 | | | | | REF_CLOSE: (2), (17), (69) are inconsistent by sub-proof #3. % 224.93/38.88 | | | | | % 224.93/38.88 | | | | Case 2: % 224.93/38.88 | | | | | % 224.93/38.88 | | | | | (70) ( ~ (all_147_0 = 0) | ~ (all_143_1 = nil)) & (all_147_0 = 0 | % 224.93/38.88 | | | | | all_143_1 = nil) % 224.93/38.88 | | | | | % 224.93/38.88 | | | | | ALPHA: (70) implies: % 224.93/38.88 | | | | | (71) all_147_0 = 0 | all_143_1 = nil % 224.93/38.88 | | | | | % 224.93/38.88 | | | | | BETA: splitting (71) gives: % 224.93/38.88 | | | | | % 224.93/38.88 | | | | | Case 1: % 224.93/38.88 | | | | | | % 224.93/38.88 | | | | | | (72) all_143_1 = nil % 224.93/38.88 | | | | | | % 224.93/38.88 | | | | | | REF_CLOSE: (4), (13), (17), (18), (22), (40), (45), (46), (49), % 224.93/38.88 | | | | | | (56), (72) are inconsistent by sub-proof #1. % 224.93/38.88 | | | | | | % 224.93/38.88 | | | | | Case 2: % 224.93/38.88 | | | | | | % 224.93/38.89 | | | | | | (73) all_147_0 = 0 % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | | REDUCE: (67), (73) imply: % 224.93/38.89 | | | | | | (74) $false % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | | CLOSE: (74) is inconsistent. % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | End of split % 224.93/38.89 | | | | | % 224.93/38.89 | | | | End of split % 224.93/38.89 | | | | % 224.93/38.89 | | | Case 2: % 224.93/38.89 | | | | % 224.93/38.89 | | | | (75) all_145_0 = 0 % 224.93/38.89 | | | | % 224.93/38.89 | | | | BETA: splitting (54) gives: % 224.93/38.89 | | | | % 224.93/38.89 | | | | Case 1: % 224.93/38.89 | | | | | % 224.93/38.89 | | | | | (76) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 224.93/38.89 | | | | | % 224.93/38.89 | | | | | REF_CLOSE: (17), (45), (76) are inconsistent by sub-proof #2. % 224.93/38.89 | | | | | % 224.93/38.89 | | | | Case 2: % 224.93/38.89 | | | | | % 224.93/38.89 | | | | | (77) ( ~ (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_139_1 % 224.93/38.89 | | | | | & ssItem(v0) = 0 & $i(v0))) & (all_145_0 = 0 | ! [v0: $i] % 224.93/38.89 | | | | | : ( ~ (cons(v0, nil) = all_139_1) | ~ $i(v0) | ? [v1: int] % 224.93/38.89 | | | | | : ( ~ (v1 = 0) & ssItem(v0) = v1))) % 224.93/38.89 | | | | | % 224.93/38.89 | | | | | ALPHA: (77) implies: % 224.93/38.89 | | | | | (78) ~ (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_139_1 % 224.93/38.89 | | | | | & ssItem(v0) = 0 & $i(v0)) % 224.93/38.89 | | | | | % 224.93/38.89 | | | | | BETA: splitting (78) gives: % 224.93/38.89 | | | | | % 224.93/38.89 | | | | | Case 1: % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | | (79) ~ (all_145_0 = 0) % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | | REDUCE: (75), (79) imply: % 224.93/38.89 | | | | | | (80) $false % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | | CLOSE: (80) is inconsistent. % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | Case 2: % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | | (81) ? [v0: $i] : (cons(v0, nil) = all_139_1 & ssItem(v0) = 0 & % 224.93/38.89 | | | | | | $i(v0)) % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | | DELTA: instantiating (81) with fresh symbol all_385_0 gives: % 224.93/38.89 | | | | | | (82) cons(all_385_0, nil) = all_139_1 & ssItem(all_385_0) = 0 & % 224.93/38.89 | | | | | | $i(all_385_0) % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | | ALPHA: (82) implies: % 224.93/38.89 | | | | | | (83) $i(all_385_0) % 224.93/38.89 | | | | | | (84) ssItem(all_385_0) = 0 % 224.93/38.89 | | | | | | (85) cons(all_385_0, nil) = all_139_1 % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | | BETA: splitting (50) gives: % 224.93/38.89 | | | | | | % 224.93/38.89 | | | | | | Case 1: % 224.93/38.89 | | | | | | | % 224.93/38.89 | | | | | | | (86) all_143_1 = nil % 224.93/38.89 | | | | | | | % 224.93/38.89 | | | | | | | REF_CLOSE: (4), (13), (17), (18), (22), (40), (45), (46), (49), % 224.93/38.89 | | | | | | | (56), (86) are inconsistent by sub-proof #1. % 224.93/38.89 | | | | | | | % 224.93/38.89 | | | | | | Case 2: % 224.93/38.89 | | | | | | | % 224.93/38.89 | | | | | | | (87) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 224.93/38.89 | | | | | | | (cons(v1, v0) = all_143_1 & ssItem(v1) = 0 & $i(v1))) % 224.93/38.89 | | | | | | | % 224.93/38.89 | | | | | | | DELTA: instantiating (87) with fresh symbol all_391_0 gives: % 224.93/38.89 | | | | | | | (88) ssList(all_391_0) = 0 & $i(all_391_0) & ? [v0: $i] : % 224.93/38.89 | | | | | | | (cons(v0, all_391_0) = all_143_1 & ssItem(v0) = 0 & % 224.93/38.89 | | | | | | | $i(v0)) % 224.93/38.89 | | | | | | | % 224.93/38.89 | | | | | | | ALPHA: (88) implies: % 224.93/38.89 | | | | | | | (89) $i(all_391_0) % 224.93/38.89 | | | | | | | (90) ssList(all_391_0) = 0 % 224.93/38.89 | | | | | | | (91) ? [v0: $i] : (cons(v0, all_391_0) = all_143_1 & % 224.93/38.89 | | | | | | | ssItem(v0) = 0 & $i(v0)) % 224.93/38.89 | | | | | | | % 224.93/38.89 | | | | | | | DELTA: instantiating (91) with fresh symbol all_393_0 gives: % 224.93/38.89 | | | | | | | (92) cons(all_393_0, all_391_0) = all_143_1 & ssItem(all_393_0) % 224.93/38.89 | | | | | | | = 0 & $i(all_393_0) % 224.93/38.89 | | | | | | | % 224.93/38.89 | | | | | | | ALPHA: (92) implies: % 224.93/38.89 | | | | | | | (93) $i(all_393_0) % 224.93/38.89 | | | | | | | (94) ssItem(all_393_0) = 0 % 224.93/38.89 | | | | | | | (95) cons(all_393_0, all_391_0) = all_143_1 % 224.93/38.89 | | | | | | | % 224.93/38.89 | | | | | | | BETA: splitting (49) gives: % 224.93/38.89 | | | | | | | % 224.93/38.89 | | | | | | | Case 1: % 224.93/38.89 | | | | | | | | % 224.93/38.89 | | | | | | | | (96) all_139_1 = nil % 224.93/38.89 | | | | | | | | % 224.93/38.89 | | | | | | | | REDUCE: (22), (96) imply: % 224.93/38.89 | | | | | | | | (97) equalelemsP(nil) = all_139_0 % 224.93/38.89 | | | | | | | | % 224.93/38.89 | | | | | | | | GROUND_INST: instantiating (18) with 0, all_139_0, nil, % 224.93/38.89 | | | | | | | | simplifying with (13), (97) gives: % 224.93/38.89 | | | | | | | | (98) all_139_0 = 0 % 224.93/38.89 | | | | | | | | % 224.93/38.89 | | | | | | | | REDUCE: (40), (98) imply: % 224.93/38.89 | | | | | | | | (99) $false % 224.93/38.89 | | | | | | | | % 224.93/38.89 | | | | | | | | CLOSE: (99) is inconsistent. % 224.93/38.89 | | | | | | | | % 224.93/38.89 | | | | | | | Case 2: % 224.93/38.89 | | | | | | | | % 224.93/38.89 | | | | | | | | (100) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 224.93/38.89 | | | | | | | | (cons(v1, v0) = all_139_1 & ssItem(v1) = 0 & $i(v1))) % 224.93/38.90 | | | | | | | | % 224.93/38.90 | | | | | | | | DELTA: instantiating (100) with fresh symbol all_401_0 gives: % 224.93/38.90 | | | | | | | | (101) ssList(all_401_0) = 0 & $i(all_401_0) & ? [v0: $i] : % 224.93/38.90 | | | | | | | | (cons(v0, all_401_0) = all_139_1 & ssItem(v0) = 0 & % 224.93/38.90 | | | | | | | | $i(v0)) % 224.93/38.90 | | | | | | | | % 224.93/38.90 | | | | | | | | ALPHA: (101) implies: % 224.93/38.90 | | | | | | | | (102) $i(all_401_0) % 224.93/38.90 | | | | | | | | (103) ssList(all_401_0) = 0 % 224.93/38.90 | | | | | | | | (104) ? [v0: $i] : (cons(v0, all_401_0) = all_139_1 & % 224.93/38.90 | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 224.93/38.90 | | | | | | | | % 224.93/38.90 | | | | | | | | DELTA: instantiating (104) with fresh symbol all_403_0 gives: % 224.93/38.90 | | | | | | | | (105) cons(all_403_0, all_401_0) = all_139_1 & % 224.93/38.90 | | | | | | | | ssItem(all_403_0) = 0 & $i(all_403_0) % 224.93/38.90 | | | | | | | | % 224.93/38.90 | | | | | | | | ALPHA: (105) implies: % 224.93/38.90 | | | | | | | | (106) $i(all_403_0) % 224.93/38.90 | | | | | | | | (107) ssItem(all_403_0) = 0 % 224.93/38.90 | | | | | | | | (108) cons(all_403_0, all_401_0) = all_139_1 % 224.93/38.90 | | | | | | | | % 224.93/38.90 | | | | | | | | BETA: splitting (56) gives: % 224.93/38.90 | | | | | | | | % 224.93/38.90 | | | | | | | | Case 1: % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | (109) all_143_1 = all_139_1 % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | REDUCE: (95), (109) imply: % 224.93/38.90 | | | | | | | | | (110) cons(all_393_0, all_391_0) = all_139_1 % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | GROUND_INST: instantiating (61) with all_393_0, simplifying % 224.93/38.90 | | | | | | | | | with (93), (94) gives: % 224.93/38.90 | | | | | | | | | (111) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! % 224.93/38.90 | | | | | | | | | [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ! % 224.93/38.90 | | | | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 224.93/38.90 | | | | | | | | | (cons(all_393_0, v2) = v3) | ~ (app(v1, v3) = % 224.93/38.90 | | | | | | | | | v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) % 224.93/38.90 | | | | | | | | | & ssList(v2) = v5) | ! [v5: $i] : ! [v6: % 224.93/38.90 | | | | | | | | | $i] : ( ~ (v0 = all_393_0) | ~ % 224.93/38.90 | | | | | | | | | (cons(all_393_0, v5) = v6) | ~ (app(v4, v6) % 224.93/38.90 | | | | | | | | | = nil) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 % 224.93/38.90 | | | | | | | | | = 0) & ssList(v5) = v7))))) % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | GROUND_INST: instantiating (47) with all_385_0, all_139_1, % 224.93/38.90 | | | | | | | | | simplifying with (83), (85) gives: % 224.93/38.90 | | | | | | | | | (112) ? [v0: any] : ? [v1: $i] : (tl(all_139_1) = v1 & % 224.93/38.90 | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 % 224.93/38.90 | | | | | | | | | = nil)) % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | GROUND_INST: instantiating (48) with all_385_0, all_139_1, % 224.93/38.90 | | | | | | | | | simplifying with (83), (85) gives: % 224.93/38.90 | | | | | | | | | (113) ? [v0: any] : ? [v1: $i] : (hd(all_139_1) = v1 & % 224.93/38.90 | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 % 224.93/38.90 | | | | | | | | | = all_385_0)) % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | GROUND_INST: instantiating (12) with all_385_0, all_139_1, % 224.93/38.90 | | | | | | | | | simplifying with (83), (85) gives: % 224.93/38.90 | | | | | | | | | (114) ? [v0: any] : ? [v1: any] : (equalelemsP(all_139_1) % 224.93/38.90 | | | | | | | | | = v1 & ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = % 224.93/38.90 | | | | | | | | | 0)) % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | GROUND_INST: instantiating (9) with all_385_0, all_139_1, % 224.93/38.90 | | | | | | | | | simplifying with (83), (85) gives: % 224.93/38.90 | | | | | | | | | (115) ? [v0: any] : ? [v1: any] : % 224.93/38.90 | | | | | | | | | (strictorderedP(all_139_1) = v1 & ssItem(all_385_0) = % 224.93/38.90 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | GROUND_INST: instantiating (8) with all_385_0, all_139_1, % 224.93/38.90 | | | | | | | | | simplifying with (83), (85) gives: % 224.93/38.90 | | | | | | | | | (116) ? [v0: any] : ? [v1: any] : % 224.93/38.90 | | | | | | | | | (totalorderedP(all_139_1) = v1 & ssItem(all_385_0) = % 224.93/38.90 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | GROUND_INST: instantiating (7) with all_385_0, all_139_1, % 224.93/38.90 | | | | | | | | | simplifying with (83), (85) gives: % 224.93/38.90 | | | | | | | | | (117) ? [v0: any] : ? [v1: any] : % 224.93/38.90 | | | | | | | | | (strictorderP(all_139_1) = v1 & ssItem(all_385_0) = % 224.93/38.90 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | GROUND_INST: instantiating (6) with all_385_0, all_139_1, % 224.93/38.90 | | | | | | | | | simplifying with (83), (85) gives: % 224.93/38.90 | | | | | | | | | (118) ? [v0: any] : ? [v1: any] : (totalorderP(all_139_1) % 224.93/38.90 | | | | | | | | | = v1 & ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = % 224.93/38.90 | | | | | | | | | 0)) % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | GROUND_INST: instantiating (5) with all_385_0, all_139_1, % 224.93/38.90 | | | | | | | | | simplifying with (83), (85) gives: % 224.93/38.90 | | | | | | | | | (119) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_139_1) % 224.93/38.90 | | | | | | | | | = v1 & ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = % 224.93/38.90 | | | | | | | | | 0)) % 224.93/38.90 | | | | | | | | | % 224.93/38.90 | | | | | | | | | GROUND_INST: instantiating (111) with all_385_0, simplifying % 224.93/38.90 | | | | | | | | | with (83), (84) gives: % 224.93/38.91 | | | | | | | | | (120) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! % 224.93/38.91 | | | | | | | | | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 224.93/38.91 | | | | | | | | | (cons(all_393_0, v1) = v2) | ~ (app(v0, v2) = % 224.93/38.91 | | | | | | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 224.93/38.91 | | | | | | | | | ssList(v1) = v4) | ! [v4: $i] : ! [v5: $i] : % 224.93/38.91 | | | | | | | | | ( ~ (all_393_0 = all_385_0) | ~ (cons(all_385_0, % 224.93/38.91 | | | | | | | | | v4) = v5) | ~ (app(v3, v5) = nil) | ~ % 224.93/38.91 | | | | | | | | | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & % 224.93/38.91 | | | | | | | | | ssList(v4) = v6)))) % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | GROUND_INST: instantiating (120) with all_341_1, simplifying % 224.93/38.91 | | | | | | | | | with (64), (66) gives: % 224.93/38.91 | | | | | | | | | (121) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 224.93/38.91 | | | | | | | | | (cons(all_393_0, v0) = v1) | ~ (app(all_341_1, v1) % 224.93/38.91 | | | | | | | | | = v2) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 224.93/38.91 | | | | | | | | | ssList(v0) = v3) | ! [v3: $i] : ! [v4: $i] : ( % 224.93/38.91 | | | | | | | | | ~ (all_393_0 = all_385_0) | ~ (cons(all_385_0, % 224.93/38.91 | | | | | | | | | v3) = v4) | ~ (app(v2, v4) = nil) | ~ % 224.93/38.91 | | | | | | | | | $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v3) % 224.93/38.91 | | | | | | | | | = v5))) % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | GROUND_INST: instantiating (121) with all_391_0, all_139_1, % 224.93/38.91 | | | | | | | | | all_341_0, simplifying with (65), (89), (110) % 224.93/38.91 | | | | | | | | | gives: % 224.93/38.91 | | | | | | | | | (122) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_391_0) = v0) % 224.93/38.91 | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : ( ~ (all_393_0 = % 224.93/38.91 | | | | | | | | | all_385_0) | ~ (cons(all_385_0, v0) = v1) | ~ % 224.93/38.91 | | | | | | | | | (app(all_341_0, v1) = nil) | ~ $i(v0) | ? [v2: % 224.93/38.91 | | | | | | | | | int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | DELTA: instantiating (114) with fresh symbols all_1673_0, % 224.93/38.91 | | | | | | | | | all_1673_1 gives: % 224.93/38.91 | | | | | | | | | (123) equalelemsP(all_139_1) = all_1673_0 & % 224.93/38.91 | | | | | | | | | ssItem(all_385_0) = all_1673_1 & ( ~ (all_1673_1 = 0) % 224.93/38.91 | | | | | | | | | | all_1673_0 = 0) % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | ALPHA: (123) implies: % 224.93/38.91 | | | | | | | | | (124) ssItem(all_385_0) = all_1673_1 % 224.93/38.91 | | | | | | | | | (125) equalelemsP(all_139_1) = all_1673_0 % 224.93/38.91 | | | | | | | | | (126) ~ (all_1673_1 = 0) | all_1673_0 = 0 % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | DELTA: instantiating (119) with fresh symbols all_1675_0, % 224.93/38.91 | | | | | | | | | all_1675_1 gives: % 224.93/38.91 | | | | | | | | | (127) cyclefreeP(all_139_1) = all_1675_0 & % 224.93/38.91 | | | | | | | | | ssItem(all_385_0) = all_1675_1 & ( ~ (all_1675_1 = 0) % 224.93/38.91 | | | | | | | | | | all_1675_0 = 0) % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | ALPHA: (127) implies: % 224.93/38.91 | | | | | | | | | (128) ssItem(all_385_0) = all_1675_1 % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | DELTA: instantiating (118) with fresh symbols all_1677_0, % 224.93/38.91 | | | | | | | | | all_1677_1 gives: % 224.93/38.91 | | | | | | | | | (129) totalorderP(all_139_1) = all_1677_0 & % 224.93/38.91 | | | | | | | | | ssItem(all_385_0) = all_1677_1 & ( ~ (all_1677_1 = 0) % 224.93/38.91 | | | | | | | | | | all_1677_0 = 0) % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | ALPHA: (129) implies: % 224.93/38.91 | | | | | | | | | (130) ssItem(all_385_0) = all_1677_1 % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | DELTA: instantiating (117) with fresh symbols all_1679_0, % 224.93/38.91 | | | | | | | | | all_1679_1 gives: % 224.93/38.91 | | | | | | | | | (131) strictorderP(all_139_1) = all_1679_0 & % 224.93/38.91 | | | | | | | | | ssItem(all_385_0) = all_1679_1 & ( ~ (all_1679_1 = 0) % 224.93/38.91 | | | | | | | | | | all_1679_0 = 0) % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | ALPHA: (131) implies: % 224.93/38.91 | | | | | | | | | (132) ssItem(all_385_0) = all_1679_1 % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | DELTA: instantiating (116) with fresh symbols all_1681_0, % 224.93/38.91 | | | | | | | | | all_1681_1 gives: % 224.93/38.91 | | | | | | | | | (133) totalorderedP(all_139_1) = all_1681_0 & % 224.93/38.91 | | | | | | | | | ssItem(all_385_0) = all_1681_1 & ( ~ (all_1681_1 = 0) % 224.93/38.91 | | | | | | | | | | all_1681_0 = 0) % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | ALPHA: (133) implies: % 224.93/38.91 | | | | | | | | | (134) ssItem(all_385_0) = all_1681_1 % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | DELTA: instantiating (115) with fresh symbols all_1683_0, % 224.93/38.91 | | | | | | | | | all_1683_1 gives: % 224.93/38.91 | | | | | | | | | (135) strictorderedP(all_139_1) = all_1683_0 & % 224.93/38.91 | | | | | | | | | ssItem(all_385_0) = all_1683_1 & ( ~ (all_1683_1 = 0) % 224.93/38.91 | | | | | | | | | | all_1683_0 = 0) % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | ALPHA: (135) implies: % 224.93/38.91 | | | | | | | | | (136) ssItem(all_385_0) = all_1683_1 % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | DELTA: instantiating (113) with fresh symbols all_1685_0, % 224.93/38.91 | | | | | | | | | all_1685_1 gives: % 224.93/38.91 | | | | | | | | | (137) hd(all_139_1) = all_1685_0 & ssItem(all_385_0) = % 224.93/38.91 | | | | | | | | | all_1685_1 & $i(all_1685_0) & ( ~ (all_1685_1 = 0) | % 224.93/38.91 | | | | | | | | | all_1685_0 = all_385_0) % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | ALPHA: (137) implies: % 224.93/38.91 | | | | | | | | | (138) ssItem(all_385_0) = all_1685_1 % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | DELTA: instantiating (112) with fresh symbols all_1687_0, % 224.93/38.91 | | | | | | | | | all_1687_1 gives: % 224.93/38.91 | | | | | | | | | (139) tl(all_139_1) = all_1687_0 & ssItem(all_385_0) = % 224.93/38.91 | | | | | | | | | all_1687_1 & $i(all_1687_0) & ( ~ (all_1687_1 = 0) | % 224.93/38.91 | | | | | | | | | all_1687_0 = nil) % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | ALPHA: (139) implies: % 224.93/38.91 | | | | | | | | | (140) ssItem(all_385_0) = all_1687_1 % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | BETA: splitting (122) gives: % 224.93/38.91 | | | | | | | | | % 224.93/38.91 | | | | | | | | | Case 1: % 224.93/38.91 | | | | | | | | | | % 224.93/38.91 | | | | | | | | | | (141) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_391_0) = % 224.93/38.91 | | | | | | | | | | v0) % 224.93/38.91 | | | | | | | | | | % 224.93/38.91 | | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_1794_0 % 224.93/38.91 | | | | | | | | | | gives: % 224.93/38.91 | | | | | | | | | | (142) ~ (all_1794_0 = 0) & ssList(all_391_0) = % 224.93/38.91 | | | | | | | | | | all_1794_0 % 224.93/38.91 | | | | | | | | | | % 224.93/38.91 | | | | | | | | | | ALPHA: (142) implies: % 224.93/38.91 | | | | | | | | | | (143) ~ (all_1794_0 = 0) % 224.93/38.91 | | | | | | | | | | (144) ssList(all_391_0) = all_1794_0 % 224.93/38.91 | | | | | | | | | | % 224.93/38.91 | | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_1796_0 % 224.93/38.91 | | | | | | | | | | gives: % 224.93/38.91 | | | | | | | | | | (145) ~ (all_1796_0 = 0) & ssList(all_391_0) = % 224.93/38.91 | | | | | | | | | | all_1796_0 % 224.93/38.91 | | | | | | | | | | % 224.93/38.91 | | | | | | | | | | ALPHA: (145) implies: % 224.93/38.91 | | | | | | | | | | (146) ssList(all_391_0) = all_1796_0 % 224.93/38.91 | | | | | | | | | | % 224.93/38.91 | | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_1798_0 % 224.93/38.91 | | | | | | | | | | gives: % 224.93/38.91 | | | | | | | | | | (147) ~ (all_1798_0 = 0) & ssList(all_391_0) = % 224.93/38.91 | | | | | | | | | | all_1798_0 % 224.93/38.91 | | | | | | | | | | % 224.93/38.91 | | | | | | | | | | ALPHA: (147) implies: % 224.93/38.91 | | | | | | | | | | (148) ssList(all_391_0) = all_1798_0 % 224.93/38.91 | | | | | | | | | | % 224.93/38.91 | | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_1800_0 % 224.93/38.91 | | | | | | | | | | gives: % 224.93/38.92 | | | | | | | | | | (149) ~ (all_1800_0 = 0) & ssList(all_391_0) = % 224.93/38.92 | | | | | | | | | | all_1800_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | ALPHA: (149) implies: % 224.93/38.92 | | | | | | | | | | (150) ssList(all_391_0) = all_1800_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_1802_0 % 224.93/38.92 | | | | | | | | | | gives: % 224.93/38.92 | | | | | | | | | | (151) ~ (all_1802_0 = 0) & ssList(all_391_0) = % 224.93/38.92 | | | | | | | | | | all_1802_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | ALPHA: (151) implies: % 224.93/38.92 | | | | | | | | | | (152) ssList(all_391_0) = all_1802_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_1818_0 % 224.93/38.92 | | | | | | | | | | gives: % 224.93/38.92 | | | | | | | | | | (153) ~ (all_1818_0 = 0) & ssList(all_391_0) = % 224.93/38.92 | | | | | | | | | | all_1818_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | ALPHA: (153) implies: % 224.93/38.92 | | | | | | | | | | (154) ssList(all_391_0) = all_1818_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_1820_0 % 224.93/38.92 | | | | | | | | | | gives: % 224.93/38.92 | | | | | | | | | | (155) ~ (all_1820_0 = 0) & ssList(all_391_0) = % 224.93/38.92 | | | | | | | | | | all_1820_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | ALPHA: (155) implies: % 224.93/38.92 | | | | | | | | | | (156) ssList(all_391_0) = all_1820_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_1822_0 % 224.93/38.92 | | | | | | | | | | gives: % 224.93/38.92 | | | | | | | | | | (157) ~ (all_1822_0 = 0) & ssList(all_391_0) = % 224.93/38.92 | | | | | | | | | | all_1822_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | ALPHA: (157) implies: % 224.93/38.92 | | | | | | | | | | (158) ssList(all_391_0) = all_1822_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_1824_0 % 224.93/38.92 | | | | | | | | | | gives: % 224.93/38.92 | | | | | | | | | | (159) ~ (all_1824_0 = 0) & ssList(all_391_0) = % 224.93/38.92 | | | | | | | | | | all_1824_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | ALPHA: (159) implies: % 224.93/38.92 | | | | | | | | | | (160) ssList(all_391_0) = all_1824_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_1826_0 % 224.93/38.92 | | | | | | | | | | gives: % 224.93/38.92 | | | | | | | | | | (161) ~ (all_1826_0 = 0) & ssList(all_391_0) = % 224.93/38.92 | | | | | | | | | | all_1826_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | ALPHA: (161) implies: % 224.93/38.92 | | | | | | | | | | (162) ssList(all_391_0) = all_1826_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_1802_0, all_391_0, % 224.93/38.92 | | | | | | | | | | simplifying with (90), (152) gives: % 224.93/38.92 | | | | | | | | | | (163) all_1802_0 = 0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1802_0, all_1818_0, % 224.93/38.92 | | | | | | | | | | all_391_0, simplifying with (152), (154) gives: % 224.93/38.92 | | | | | | | | | | (164) all_1818_0 = all_1802_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1794_0, all_1820_0, % 224.93/38.92 | | | | | | | | | | all_391_0, simplifying with (144), (156) gives: % 224.93/38.92 | | | | | | | | | | (165) all_1820_0 = all_1794_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1818_0, all_1822_0, % 224.93/38.92 | | | | | | | | | | all_391_0, simplifying with (154), (158) gives: % 224.93/38.92 | | | | | | | | | | (166) all_1822_0 = all_1818_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1796_0, all_1822_0, % 224.93/38.92 | | | | | | | | | | all_391_0, simplifying with (146), (158) gives: % 224.93/38.92 | | | | | | | | | | (167) all_1822_0 = all_1796_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1820_0, all_1824_0, % 224.93/38.92 | | | | | | | | | | all_391_0, simplifying with (156), (160) gives: % 224.93/38.92 | | | | | | | | | | (168) all_1824_0 = all_1820_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1802_0, all_1824_0, % 224.93/38.92 | | | | | | | | | | all_391_0, simplifying with (152), (160) gives: % 224.93/38.92 | | | | | | | | | | (169) all_1824_0 = all_1802_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1798_0, all_1824_0, % 224.93/38.92 | | | | | | | | | | all_391_0, simplifying with (148), (160) gives: % 224.93/38.92 | | | | | | | | | | (170) all_1824_0 = all_1798_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1824_0, all_1826_0, % 224.93/38.92 | | | | | | | | | | all_391_0, simplifying with (160), (162) gives: % 224.93/38.92 | | | | | | | | | | (171) all_1826_0 = all_1824_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1800_0, all_1826_0, % 224.93/38.92 | | | | | | | | | | all_391_0, simplifying with (150), (162) gives: % 224.93/38.92 | | | | | | | | | | (172) all_1826_0 = all_1800_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (171), (172) imply: % 224.93/38.92 | | | | | | | | | | (173) all_1824_0 = all_1800_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | SIMP: (173) implies: % 224.93/38.92 | | | | | | | | | | (174) all_1824_0 = all_1800_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (169), (174) imply: % 224.93/38.92 | | | | | | | | | | (175) all_1802_0 = all_1800_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | SIMP: (175) implies: % 224.93/38.92 | | | | | | | | | | (176) all_1802_0 = all_1800_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (170), (174) imply: % 224.93/38.92 | | | | | | | | | | (177) all_1800_0 = all_1798_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (168), (174) imply: % 224.93/38.92 | | | | | | | | | | (178) all_1820_0 = all_1800_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | SIMP: (178) implies: % 224.93/38.92 | | | | | | | | | | (179) all_1820_0 = all_1800_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (166), (167) imply: % 224.93/38.92 | | | | | | | | | | (180) all_1818_0 = all_1796_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | SIMP: (180) implies: % 224.93/38.92 | | | | | | | | | | (181) all_1818_0 = all_1796_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (165), (179) imply: % 224.93/38.92 | | | | | | | | | | (182) all_1800_0 = all_1794_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | SIMP: (182) implies: % 224.93/38.92 | | | | | | | | | | (183) all_1800_0 = all_1794_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (164), (181) imply: % 224.93/38.92 | | | | | | | | | | (184) all_1802_0 = all_1796_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | SIMP: (184) implies: % 224.93/38.92 | | | | | | | | | | (185) all_1802_0 = all_1796_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (163), (185) imply: % 224.93/38.92 | | | | | | | | | | (186) all_1796_0 = 0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (176), (185) imply: % 224.93/38.92 | | | | | | | | | | (187) all_1800_0 = all_1796_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | SIMP: (187) implies: % 224.93/38.92 | | | | | | | | | | (188) all_1800_0 = all_1796_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (177), (183) imply: % 224.93/38.92 | | | | | | | | | | (189) all_1798_0 = all_1794_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (177), (188) imply: % 224.93/38.92 | | | | | | | | | | (190) all_1798_0 = all_1796_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (189), (190) imply: % 224.93/38.92 | | | | | | | | | | (191) all_1796_0 = all_1794_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | SIMP: (191) implies: % 224.93/38.92 | | | | | | | | | | (192) all_1796_0 = all_1794_0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | COMBINE_EQS: (186), (192) imply: % 224.93/38.92 | | | | | | | | | | (193) all_1794_0 = 0 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | REDUCE: (143), (193) imply: % 224.93/38.92 | | | | | | | | | | (194) $false % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | CLOSE: (194) is inconsistent. % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | Case 2: % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1673_1, all_1677_1, % 224.93/38.92 | | | | | | | | | | all_385_0, simplifying with (124), (130) gives: % 224.93/38.92 | | | | | | | | | | (195) all_1677_1 = all_1673_1 % 224.93/38.92 | | | | | | | | | | % 224.93/38.92 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1675_1, all_1683_1, % 224.93/38.92 | | | | | | | | | | all_385_0, simplifying with (128), (136) gives: % 224.93/38.93 | | | | | | | | | | (196) all_1683_1 = all_1675_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_1685_1, all_385_0, % 224.93/38.93 | | | | | | | | | | simplifying with (84), (138) gives: % 224.93/38.93 | | | | | | | | | | (197) all_1685_1 = 0 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1681_1, all_1685_1, % 224.93/38.93 | | | | | | | | | | all_385_0, simplifying with (134), (138) gives: % 224.93/38.93 | | | | | | | | | | (198) all_1685_1 = all_1681_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1685_1, all_1687_1, % 224.93/38.93 | | | | | | | | | | all_385_0, simplifying with (138), (140) gives: % 224.93/38.93 | | | | | | | | | | (199) all_1687_1 = all_1685_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1683_1, all_1687_1, % 224.93/38.93 | | | | | | | | | | all_385_0, simplifying with (136), (140) gives: % 224.93/38.93 | | | | | | | | | | (200) all_1687_1 = all_1683_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1679_1, all_1687_1, % 224.93/38.93 | | | | | | | | | | all_385_0, simplifying with (132), (140) gives: % 224.93/38.93 | | | | | | | | | | (201) all_1687_1 = all_1679_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1677_1, all_1687_1, % 224.93/38.93 | | | | | | | | | | all_385_0, simplifying with (130), (140) gives: % 224.93/38.93 | | | | | | | | | | (202) all_1687_1 = all_1677_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | GROUND_INST: instantiating (18) with all_139_0, all_1673_0, % 224.93/38.93 | | | | | | | | | | all_139_1, simplifying with (22), (125) gives: % 224.93/38.93 | | | | | | | | | | (203) all_1673_0 = all_139_0 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | COMBINE_EQS: (199), (201) imply: % 224.93/38.93 | | | | | | | | | | (204) all_1685_1 = all_1679_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | SIMP: (204) implies: % 224.93/38.93 | | | | | | | | | | (205) all_1685_1 = all_1679_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | COMBINE_EQS: (200), (201) imply: % 224.93/38.93 | | | | | | | | | | (206) all_1683_1 = all_1679_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | SIMP: (206) implies: % 224.93/38.93 | | | | | | | | | | (207) all_1683_1 = all_1679_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | COMBINE_EQS: (201), (202) imply: % 224.93/38.93 | | | | | | | | | | (208) all_1679_1 = all_1677_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | COMBINE_EQS: (198), (205) imply: % 224.93/38.93 | | | | | | | | | | (209) all_1681_1 = all_1679_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | COMBINE_EQS: (197), (198) imply: % 224.93/38.93 | | | | | | | | | | (210) all_1681_1 = 0 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | COMBINE_EQS: (196), (207) imply: % 224.93/38.93 | | | | | | | | | | (211) all_1679_1 = all_1675_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | SIMP: (211) implies: % 224.93/38.93 | | | | | | | | | | (212) all_1679_1 = all_1675_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | COMBINE_EQS: (209), (210) imply: % 224.93/38.93 | | | | | | | | | | (213) all_1679_1 = 0 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | SIMP: (213) implies: % 224.93/38.93 | | | | | | | | | | (214) all_1679_1 = 0 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | COMBINE_EQS: (208), (212) imply: % 224.93/38.93 | | | | | | | | | | (215) all_1677_1 = all_1675_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | SIMP: (215) implies: % 224.93/38.93 | | | | | | | | | | (216) all_1677_1 = all_1675_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | COMBINE_EQS: (212), (214) imply: % 224.93/38.93 | | | | | | | | | | (217) all_1675_1 = 0 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | COMBINE_EQS: (195), (216) imply: % 224.93/38.93 | | | | | | | | | | (218) all_1675_1 = all_1673_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | SIMP: (218) implies: % 224.93/38.93 | | | | | | | | | | (219) all_1675_1 = all_1673_1 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | COMBINE_EQS: (217), (219) imply: % 224.93/38.93 | | | | | | | | | | (220) all_1673_1 = 0 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | SIMP: (220) implies: % 224.93/38.93 | | | | | | | | | | (221) all_1673_1 = 0 % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | BETA: splitting (126) gives: % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | Case 1: % 224.93/38.93 | | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | | (222) ~ (all_1673_1 = 0) % 224.93/38.93 | | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | | REDUCE: (221), (222) imply: % 224.93/38.93 | | | | | | | | | | | (223) $false % 224.93/38.93 | | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | | CLOSE: (223) is inconsistent. % 224.93/38.93 | | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | Case 2: % 224.93/38.93 | | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | | (224) all_1673_0 = 0 % 224.93/38.93 | | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | | COMBINE_EQS: (203), (224) imply: % 224.93/38.93 | | | | | | | | | | | (225) all_139_0 = 0 % 224.93/38.93 | | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | | SIMP: (225) implies: % 224.93/38.93 | | | | | | | | | | | (226) all_139_0 = 0 % 224.93/38.93 | | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | | REDUCE: (40), (226) imply: % 224.93/38.93 | | | | | | | | | | | (227) $false % 224.93/38.93 | | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | | CLOSE: (227) is inconsistent. % 224.93/38.93 | | | | | | | | | | | % 224.93/38.93 | | | | | | | | | | End of split % 224.93/38.93 | | | | | | | | | | % 224.93/38.93 | | | | | | | | | End of split % 224.93/38.93 | | | | | | | | | % 224.93/38.93 | | | | | | | | Case 2: % 224.93/38.93 | | | | | | | | | % 224.93/38.93 | | | | | | | | | % 224.93/38.93 | | | | | | | | | GROUND_INST: instantiating (61) with all_403_0, simplifying % 224.93/38.93 | | | | | | | | | with (106), (107) gives: % 224.93/38.93 | | | | | | | | | (228) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! % 224.93/38.93 | | | | | | | | | [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ! % 224.93/38.93 | | | | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 224.93/38.93 | | | | | | | | | (cons(all_403_0, v2) = v3) | ~ (app(v1, v3) = % 224.93/38.93 | | | | | | | | | v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) % 224.93/38.93 | | | | | | | | | & ssList(v2) = v5) | ! [v5: $i] : ! [v6: % 224.93/38.93 | | | | | | | | | $i] : ( ~ (v0 = all_403_0) | ~ % 224.93/38.93 | | | | | | | | | (cons(all_403_0, v5) = v6) | ~ (app(v4, v6) % 224.93/38.93 | | | | | | | | | = nil) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 % 224.93/38.93 | | | | | | | | | = 0) & ssList(v5) = v7))))) % 224.93/38.93 | | | | | | | | | % 224.93/38.93 | | | | | | | | | GROUND_INST: instantiating (47) with all_385_0, all_139_1, % 224.93/38.93 | | | | | | | | | simplifying with (83), (85) gives: % 224.93/38.93 | | | | | | | | | (229) ? [v0: any] : ? [v1: $i] : (tl(all_139_1) = v1 & % 224.93/38.93 | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 % 224.93/38.93 | | | | | | | | | = nil)) % 224.93/38.93 | | | | | | | | | % 224.93/38.93 | | | | | | | | | GROUND_INST: instantiating (48) with all_385_0, all_139_1, % 224.93/38.93 | | | | | | | | | simplifying with (83), (85) gives: % 224.93/38.93 | | | | | | | | | (230) ? [v0: any] : ? [v1: $i] : (hd(all_139_1) = v1 & % 224.93/38.93 | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 % 224.93/38.93 | | | | | | | | | = all_385_0)) % 224.93/38.93 | | | | | | | | | % 225.34/38.93 | | | | | | | | | GROUND_INST: instantiating (12) with all_385_0, all_139_1, % 225.34/38.93 | | | | | | | | | simplifying with (83), (85) gives: % 225.34/38.93 | | | | | | | | | (231) ? [v0: any] : ? [v1: any] : (equalelemsP(all_139_1) % 225.34/38.93 | | | | | | | | | = v1 & ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = % 225.34/38.93 | | | | | | | | | 0)) % 225.34/38.93 | | | | | | | | | % 225.34/38.93 | | | | | | | | | GROUND_INST: instantiating (10) with all_385_0, all_139_1, % 225.34/38.93 | | | | | | | | | simplifying with (83), (85) gives: % 225.34/38.93 | | | | | | | | | (232) ? [v0: any] : ? [v1: any] : % 225.34/38.93 | | | | | | | | | (duplicatefreeP(all_139_1) = v1 & ssItem(all_385_0) = % 225.34/38.93 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 225.34/38.93 | | | | | | | | | % 225.34/38.93 | | | | | | | | | GROUND_INST: instantiating (9) with all_385_0, all_139_1, % 225.34/38.93 | | | | | | | | | simplifying with (83), (85) gives: % 225.34/38.94 | | | | | | | | | (233) ? [v0: any] : ? [v1: any] : % 225.34/38.94 | | | | | | | | | (strictorderedP(all_139_1) = v1 & ssItem(all_385_0) = % 225.34/38.94 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | GROUND_INST: instantiating (8) with all_385_0, all_139_1, % 225.34/38.94 | | | | | | | | | simplifying with (83), (85) gives: % 225.34/38.94 | | | | | | | | | (234) ? [v0: any] : ? [v1: any] : % 225.34/38.94 | | | | | | | | | (totalorderedP(all_139_1) = v1 & ssItem(all_385_0) = % 225.34/38.94 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | GROUND_INST: instantiating (7) with all_385_0, all_139_1, % 225.34/38.94 | | | | | | | | | simplifying with (83), (85) gives: % 225.34/38.94 | | | | | | | | | (235) ? [v0: any] : ? [v1: any] : % 225.34/38.94 | | | | | | | | | (strictorderP(all_139_1) = v1 & ssItem(all_385_0) = % 225.34/38.94 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | GROUND_INST: instantiating (6) with all_385_0, all_139_1, % 225.34/38.94 | | | | | | | | | simplifying with (83), (85) gives: % 225.34/38.94 | | | | | | | | | (236) ? [v0: any] : ? [v1: any] : (totalorderP(all_139_1) % 225.34/38.94 | | | | | | | | | = v1 & ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = % 225.34/38.94 | | | | | | | | | 0)) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | GROUND_INST: instantiating (5) with all_385_0, all_139_1, % 225.34/38.94 | | | | | | | | | simplifying with (83), (85) gives: % 225.34/38.94 | | | | | | | | | (237) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_139_1) % 225.34/38.94 | | | | | | | | | = v1 & ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = % 225.34/38.94 | | | | | | | | | 0)) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | GROUND_INST: instantiating (228) with all_141_0, simplifying % 225.34/38.94 | | | | | | | | | with (25), (26) gives: % 225.34/38.94 | | | | | | | | | (238) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! % 225.34/38.94 | | | | | | | | | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 225.34/38.94 | | | | | | | | | (cons(all_403_0, v1) = v2) | ~ (app(v0, v2) = % 225.34/38.94 | | | | | | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 225.34/38.94 | | | | | | | | | ssList(v1) = v4) | ! [v4: $i] : ! [v5: $i] : % 225.34/38.94 | | | | | | | | | ( ~ (all_403_0 = all_141_0) | ~ (cons(all_141_0, % 225.34/38.94 | | | | | | | | | v4) = v5) | ~ (app(v3, v5) = nil) | ~ % 225.34/38.94 | | | | | | | | | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & % 225.34/38.94 | | | | | | | | | ssList(v4) = v6)))) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | GROUND_INST: instantiating (238) with all_341_1, simplifying % 225.34/38.94 | | | | | | | | | with (64), (66) gives: % 225.34/38.94 | | | | | | | | | (239) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 225.34/38.94 | | | | | | | | | (cons(all_403_0, v0) = v1) | ~ (app(all_341_1, v1) % 225.34/38.94 | | | | | | | | | = v2) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 225.34/38.94 | | | | | | | | | ssList(v0) = v3) | ! [v3: $i] : ! [v4: $i] : ( % 225.34/38.94 | | | | | | | | | ~ (all_403_0 = all_141_0) | ~ (cons(all_141_0, % 225.34/38.94 | | | | | | | | | v3) = v4) | ~ (app(v2, v4) = nil) | ~ % 225.34/38.94 | | | | | | | | | $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v3) % 225.34/38.94 | | | | | | | | | = v5))) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | GROUND_INST: instantiating (239) with all_401_0, all_139_1, % 225.34/38.94 | | | | | | | | | all_341_0, simplifying with (65), (102), (108) % 225.34/38.94 | | | | | | | | | gives: % 225.34/38.94 | | | | | | | | | (240) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_401_0) = v0) % 225.34/38.94 | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : ( ~ (all_403_0 = % 225.34/38.94 | | | | | | | | | all_141_0) | ~ (cons(all_141_0, v0) = v1) | ~ % 225.34/38.94 | | | | | | | | | (app(all_341_0, v1) = nil) | ~ $i(v0) | ? [v2: % 225.34/38.94 | | | | | | | | | int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | DELTA: instantiating (232) with fresh symbols all_1770_0, % 225.34/38.94 | | | | | | | | | all_1770_1 gives: % 225.34/38.94 | | | | | | | | | (241) duplicatefreeP(all_139_1) = all_1770_0 & % 225.34/38.94 | | | | | | | | | ssItem(all_385_0) = all_1770_1 & ( ~ (all_1770_1 = 0) % 225.34/38.94 | | | | | | | | | | all_1770_0 = 0) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | ALPHA: (241) implies: % 225.34/38.94 | | | | | | | | | (242) ssItem(all_385_0) = all_1770_1 % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | DELTA: instantiating (237) with fresh symbols all_1772_0, % 225.34/38.94 | | | | | | | | | all_1772_1 gives: % 225.34/38.94 | | | | | | | | | (243) cyclefreeP(all_139_1) = all_1772_0 & % 225.34/38.94 | | | | | | | | | ssItem(all_385_0) = all_1772_1 & ( ~ (all_1772_1 = 0) % 225.34/38.94 | | | | | | | | | | all_1772_0 = 0) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | ALPHA: (243) implies: % 225.34/38.94 | | | | | | | | | (244) ssItem(all_385_0) = all_1772_1 % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | DELTA: instantiating (236) with fresh symbols all_1774_0, % 225.34/38.94 | | | | | | | | | all_1774_1 gives: % 225.34/38.94 | | | | | | | | | (245) totalorderP(all_139_1) = all_1774_0 & % 225.34/38.94 | | | | | | | | | ssItem(all_385_0) = all_1774_1 & ( ~ (all_1774_1 = 0) % 225.34/38.94 | | | | | | | | | | all_1774_0 = 0) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | ALPHA: (245) implies: % 225.34/38.94 | | | | | | | | | (246) ssItem(all_385_0) = all_1774_1 % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | DELTA: instantiating (235) with fresh symbols all_1776_0, % 225.34/38.94 | | | | | | | | | all_1776_1 gives: % 225.34/38.94 | | | | | | | | | (247) strictorderP(all_139_1) = all_1776_0 & % 225.34/38.94 | | | | | | | | | ssItem(all_385_0) = all_1776_1 & ( ~ (all_1776_1 = 0) % 225.34/38.94 | | | | | | | | | | all_1776_0 = 0) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | ALPHA: (247) implies: % 225.34/38.94 | | | | | | | | | (248) ssItem(all_385_0) = all_1776_1 % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | DELTA: instantiating (234) with fresh symbols all_1778_0, % 225.34/38.94 | | | | | | | | | all_1778_1 gives: % 225.34/38.94 | | | | | | | | | (249) totalorderedP(all_139_1) = all_1778_0 & % 225.34/38.94 | | | | | | | | | ssItem(all_385_0) = all_1778_1 & ( ~ (all_1778_1 = 0) % 225.34/38.94 | | | | | | | | | | all_1778_0 = 0) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | ALPHA: (249) implies: % 225.34/38.94 | | | | | | | | | (250) ssItem(all_385_0) = all_1778_1 % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | DELTA: instantiating (231) with fresh symbols all_1780_0, % 225.34/38.94 | | | | | | | | | all_1780_1 gives: % 225.34/38.94 | | | | | | | | | (251) equalelemsP(all_139_1) = all_1780_0 & % 225.34/38.94 | | | | | | | | | ssItem(all_385_0) = all_1780_1 & ( ~ (all_1780_1 = 0) % 225.34/38.94 | | | | | | | | | | all_1780_0 = 0) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | ALPHA: (251) implies: % 225.34/38.94 | | | | | | | | | (252) ssItem(all_385_0) = all_1780_1 % 225.34/38.94 | | | | | | | | | (253) equalelemsP(all_139_1) = all_1780_0 % 225.34/38.94 | | | | | | | | | (254) ~ (all_1780_1 = 0) | all_1780_0 = 0 % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | DELTA: instantiating (233) with fresh symbols all_1782_0, % 225.34/38.94 | | | | | | | | | all_1782_1 gives: % 225.34/38.94 | | | | | | | | | (255) strictorderedP(all_139_1) = all_1782_0 & % 225.34/38.94 | | | | | | | | | ssItem(all_385_0) = all_1782_1 & ( ~ (all_1782_1 = 0) % 225.34/38.94 | | | | | | | | | | all_1782_0 = 0) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | ALPHA: (255) implies: % 225.34/38.94 | | | | | | | | | (256) ssItem(all_385_0) = all_1782_1 % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | DELTA: instantiating (230) with fresh symbols all_1784_0, % 225.34/38.94 | | | | | | | | | all_1784_1 gives: % 225.34/38.94 | | | | | | | | | (257) hd(all_139_1) = all_1784_0 & ssItem(all_385_0) = % 225.34/38.94 | | | | | | | | | all_1784_1 & $i(all_1784_0) & ( ~ (all_1784_1 = 0) | % 225.34/38.94 | | | | | | | | | all_1784_0 = all_385_0) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | ALPHA: (257) implies: % 225.34/38.94 | | | | | | | | | (258) ssItem(all_385_0) = all_1784_1 % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | DELTA: instantiating (229) with fresh symbols all_1786_0, % 225.34/38.94 | | | | | | | | | all_1786_1 gives: % 225.34/38.94 | | | | | | | | | (259) tl(all_139_1) = all_1786_0 & ssItem(all_385_0) = % 225.34/38.94 | | | | | | | | | all_1786_1 & $i(all_1786_0) & ( ~ (all_1786_1 = 0) | % 225.34/38.94 | | | | | | | | | all_1786_0 = nil) % 225.34/38.94 | | | | | | | | | % 225.34/38.94 | | | | | | | | | ALPHA: (259) implies: % 225.34/38.95 | | | | | | | | | (260) ssItem(all_385_0) = all_1786_1 % 225.34/38.95 | | | | | | | | | % 225.34/38.95 | | | | | | | | | BETA: splitting (240) gives: % 225.34/38.95 | | | | | | | | | % 225.34/38.95 | | | | | | | | | Case 1: % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | (261) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_401_0) = % 225.34/38.95 | | | | | | | | | | v0) % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | DELTA: instantiating (261) with fresh symbol all_1805_0 % 225.34/38.95 | | | | | | | | | | gives: % 225.34/38.95 | | | | | | | | | | (262) ~ (all_1805_0 = 0) & ssList(all_401_0) = % 225.34/38.95 | | | | | | | | | | all_1805_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | ALPHA: (262) implies: % 225.34/38.95 | | | | | | | | | | (263) ~ (all_1805_0 = 0) % 225.34/38.95 | | | | | | | | | | (264) ssList(all_401_0) = all_1805_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | DELTA: instantiating (261) with fresh symbol all_1807_0 % 225.34/38.95 | | | | | | | | | | gives: % 225.34/38.95 | | | | | | | | | | (265) ~ (all_1807_0 = 0) & ssList(all_401_0) = % 225.34/38.95 | | | | | | | | | | all_1807_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | ALPHA: (265) implies: % 225.34/38.95 | | | | | | | | | | (266) ssList(all_401_0) = all_1807_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | DELTA: instantiating (261) with fresh symbol all_1809_0 % 225.34/38.95 | | | | | | | | | | gives: % 225.34/38.95 | | | | | | | | | | (267) ~ (all_1809_0 = 0) & ssList(all_401_0) = % 225.34/38.95 | | | | | | | | | | all_1809_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | ALPHA: (267) implies: % 225.34/38.95 | | | | | | | | | | (268) ssList(all_401_0) = all_1809_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | DELTA: instantiating (261) with fresh symbol all_1811_0 % 225.34/38.95 | | | | | | | | | | gives: % 225.34/38.95 | | | | | | | | | | (269) ~ (all_1811_0 = 0) & ssList(all_401_0) = % 225.34/38.95 | | | | | | | | | | all_1811_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | ALPHA: (269) implies: % 225.34/38.95 | | | | | | | | | | (270) ssList(all_401_0) = all_1811_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | DELTA: instantiating (261) with fresh symbol all_1813_0 % 225.34/38.95 | | | | | | | | | | gives: % 225.34/38.95 | | | | | | | | | | (271) ~ (all_1813_0 = 0) & ssList(all_401_0) = % 225.34/38.95 | | | | | | | | | | all_1813_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | ALPHA: (271) implies: % 225.34/38.95 | | | | | | | | | | (272) ssList(all_401_0) = all_1813_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | DELTA: instantiating (261) with fresh symbol all_1815_0 % 225.34/38.95 | | | | | | | | | | gives: % 225.34/38.95 | | | | | | | | | | (273) ~ (all_1815_0 = 0) & ssList(all_401_0) = % 225.34/38.95 | | | | | | | | | | all_1815_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | ALPHA: (273) implies: % 225.34/38.95 | | | | | | | | | | (274) ssList(all_401_0) = all_1815_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_1809_0, all_401_0, % 225.34/38.95 | | | | | | | | | | simplifying with (103), (268) gives: % 225.34/38.95 | | | | | | | | | | (275) all_1809_0 = 0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1805_0, all_1809_0, % 225.34/38.95 | | | | | | | | | | all_401_0, simplifying with (264), (268) gives: % 225.34/38.95 | | | | | | | | | | (276) all_1809_0 = all_1805_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1811_0, all_1813_0, % 225.34/38.95 | | | | | | | | | | all_401_0, simplifying with (270), (272) gives: % 225.34/38.95 | | | | | | | | | | (277) all_1813_0 = all_1811_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1809_0, all_1813_0, % 225.34/38.95 | | | | | | | | | | all_401_0, simplifying with (268), (272) gives: % 225.34/38.95 | | | | | | | | | | (278) all_1813_0 = all_1809_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1813_0, all_1815_0, % 225.34/38.95 | | | | | | | | | | all_401_0, simplifying with (272), (274) gives: % 225.34/38.95 | | | | | | | | | | (279) all_1815_0 = all_1813_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (17) with all_1807_0, all_1815_0, % 225.34/38.95 | | | | | | | | | | all_401_0, simplifying with (266), (274) gives: % 225.34/38.95 | | | | | | | | | | (280) all_1815_0 = all_1807_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (279), (280) imply: % 225.34/38.95 | | | | | | | | | | (281) all_1813_0 = all_1807_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | SIMP: (281) implies: % 225.34/38.95 | | | | | | | | | | (282) all_1813_0 = all_1807_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (277), (282) imply: % 225.34/38.95 | | | | | | | | | | (283) all_1811_0 = all_1807_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (277), (278) imply: % 225.34/38.95 | | | | | | | | | | (284) all_1811_0 = all_1809_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (283), (284) imply: % 225.34/38.95 | | | | | | | | | | (285) all_1809_0 = all_1807_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | SIMP: (285) implies: % 225.34/38.95 | | | | | | | | | | (286) all_1809_0 = all_1807_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (275), (286) imply: % 225.34/38.95 | | | | | | | | | | (287) all_1807_0 = 0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (276), (286) imply: % 225.34/38.95 | | | | | | | | | | (288) all_1807_0 = all_1805_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (287), (288) imply: % 225.34/38.95 | | | | | | | | | | (289) all_1805_0 = 0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | REDUCE: (263), (289) imply: % 225.34/38.95 | | | | | | | | | | (290) $false % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | CLOSE: (290) is inconsistent. % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | Case 2: % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1774_1, all_1778_1, % 225.34/38.95 | | | | | | | | | | all_385_0, simplifying with (246), (250) gives: % 225.34/38.95 | | | | | | | | | | (291) all_1778_1 = all_1774_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_1782_1, all_385_0, % 225.34/38.95 | | | | | | | | | | simplifying with (84), (256) gives: % 225.34/38.95 | | | | | | | | | | (292) all_1782_1 = 0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1774_1, all_1782_1, % 225.34/38.95 | | | | | | | | | | all_385_0, simplifying with (246), (256) gives: % 225.34/38.95 | | | | | | | | | | (293) all_1782_1 = all_1774_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1772_1, all_1782_1, % 225.34/38.95 | | | | | | | | | | all_385_0, simplifying with (244), (256) gives: % 225.34/38.95 | | | | | | | | | | (294) all_1782_1 = all_1772_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1780_1, all_1784_1, % 225.34/38.95 | | | | | | | | | | all_385_0, simplifying with (252), (258) gives: % 225.34/38.95 | | | | | | | | | | (295) all_1784_1 = all_1780_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1778_1, all_1784_1, % 225.34/38.95 | | | | | | | | | | all_385_0, simplifying with (250), (258) gives: % 225.34/38.95 | | | | | | | | | | (296) all_1784_1 = all_1778_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1770_1, all_1784_1, % 225.34/38.95 | | | | | | | | | | all_385_0, simplifying with (242), (258) gives: % 225.34/38.95 | | | | | | | | | | (297) all_1784_1 = all_1770_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1778_1, all_1786_1, % 225.34/38.95 | | | | | | | | | | all_385_0, simplifying with (250), (260) gives: % 225.34/38.95 | | | | | | | | | | (298) all_1786_1 = all_1778_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (16) with all_1776_1, all_1786_1, % 225.34/38.95 | | | | | | | | | | all_385_0, simplifying with (248), (260) gives: % 225.34/38.95 | | | | | | | | | | (299) all_1786_1 = all_1776_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | GROUND_INST: instantiating (18) with all_139_0, all_1780_0, % 225.34/38.95 | | | | | | | | | | all_139_1, simplifying with (22), (253) gives: % 225.34/38.95 | | | | | | | | | | (300) all_1780_0 = all_139_0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (298), (299) imply: % 225.34/38.95 | | | | | | | | | | (301) all_1778_1 = all_1776_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | SIMP: (301) implies: % 225.34/38.95 | | | | | | | | | | (302) all_1778_1 = all_1776_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (295), (296) imply: % 225.34/38.95 | | | | | | | | | | (303) all_1780_1 = all_1778_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (295), (297) imply: % 225.34/38.95 | | | | | | | | | | (304) all_1780_1 = all_1770_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (293), (294) imply: % 225.34/38.95 | | | | | | | | | | (305) all_1774_1 = all_1772_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | SIMP: (305) implies: % 225.34/38.95 | | | | | | | | | | (306) all_1774_1 = all_1772_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (292), (294) imply: % 225.34/38.95 | | | | | | | | | | (307) all_1772_1 = 0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (303), (304) imply: % 225.34/38.95 | | | | | | | | | | (308) all_1778_1 = all_1770_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | SIMP: (308) implies: % 225.34/38.95 | | | | | | | | | | (309) all_1778_1 = all_1770_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (302), (309) imply: % 225.34/38.95 | | | | | | | | | | (310) all_1776_1 = all_1770_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (291), (302) imply: % 225.34/38.95 | | | | | | | | | | (311) all_1776_1 = all_1774_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (310), (311) imply: % 225.34/38.95 | | | | | | | | | | (312) all_1774_1 = all_1770_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | SIMP: (312) implies: % 225.34/38.95 | | | | | | | | | | (313) all_1774_1 = all_1770_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (306), (313) imply: % 225.34/38.95 | | | | | | | | | | (314) all_1772_1 = all_1770_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | SIMP: (314) implies: % 225.34/38.95 | | | | | | | | | | (315) all_1772_1 = all_1770_1 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (307), (315) imply: % 225.34/38.95 | | | | | | | | | | (316) all_1770_1 = 0 % 225.34/38.95 | | | | | | | | | | % 225.34/38.95 | | | | | | | | | | COMBINE_EQS: (304), (316) imply: % 225.34/38.96 | | | | | | | | | | (317) all_1780_1 = 0 % 225.34/38.96 | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | BETA: splitting (254) gives: % 225.34/38.96 | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | Case 1: % 225.34/38.96 | | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | | (318) ~ (all_1780_1 = 0) % 225.34/38.96 | | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | | REDUCE: (317), (318) imply: % 225.34/38.96 | | | | | | | | | | | (319) $false % 225.34/38.96 | | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | | CLOSE: (319) is inconsistent. % 225.34/38.96 | | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | Case 2: % 225.34/38.96 | | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | | (320) all_1780_0 = 0 % 225.34/38.96 | | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | | COMBINE_EQS: (300), (320) imply: % 225.34/38.96 | | | | | | | | | | | (321) all_139_0 = 0 % 225.34/38.96 | | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | | SIMP: (321) implies: % 225.34/38.96 | | | | | | | | | | | (322) all_139_0 = 0 % 225.34/38.96 | | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | | REDUCE: (40), (322) imply: % 225.34/38.96 | | | | | | | | | | | (323) $false % 225.34/38.96 | | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | | CLOSE: (323) is inconsistent. % 225.34/38.96 | | | | | | | | | | | % 225.34/38.96 | | | | | | | | | | End of split % 225.34/38.96 | | | | | | | | | | % 225.34/38.96 | | | | | | | | | End of split % 225.34/38.96 | | | | | | | | | % 225.34/38.96 | | | | | | | | End of split % 225.34/38.96 | | | | | | | | % 225.34/38.96 | | | | | | | End of split % 225.34/38.96 | | | | | | | % 225.34/38.96 | | | | | | End of split % 225.34/38.96 | | | | | | % 225.34/38.96 | | | | | End of split % 225.34/38.96 | | | | | % 225.34/38.96 | | | | End of split % 225.34/38.96 | | | | % 225.34/38.96 | | | End of split % 225.34/38.96 | | | % 225.34/38.96 | | Case 2: % 225.34/38.96 | | | % 225.34/38.96 | | | (324) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 225.34/38.96 | | | % 225.34/38.96 | | | DELTA: instantiating (324) with fresh symbol all_341_0 gives: % 225.34/38.96 | | | (325) ~ (all_341_0 = 0) & ssList(all_139_1) = all_341_0 % 225.34/38.96 | | | % 225.34/38.96 | | | ALPHA: (325) implies: % 225.34/38.96 | | | (326) ~ (all_341_0 = 0) % 225.34/38.96 | | | (327) ssList(all_139_1) = all_341_0 % 225.34/38.96 | | | % 225.34/38.96 | | | GROUND_INST: instantiating (17) with 0, all_341_0, all_139_1, simplifying % 225.34/38.96 | | | with (45), (327) gives: % 225.34/38.96 | | | (328) all_341_0 = 0 % 225.34/38.96 | | | % 225.34/38.96 | | | REDUCE: (326), (328) imply: % 225.34/38.96 | | | (329) $false % 225.34/38.96 | | | % 225.34/38.96 | | | CLOSE: (329) is inconsistent. % 225.34/38.96 | | | % 225.34/38.96 | | End of split % 225.34/38.96 | | % 225.34/38.96 | End of split % 225.34/38.96 | % 225.34/38.96 End of proof % 225.34/38.96 % 225.34/38.96 Sub-proof #1 shows that the following formulas are inconsistent: % 225.34/38.96 ---------------------------------------------------------------- % 225.34/38.96 (1) all_139_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 225.34/38.96 (cons(v1, v0) = all_139_1 & ssItem(v1) = 0 & $i(v1))) % 225.34/38.96 (2) all_143_1 = nil % 225.34/38.96 (3) ~ (all_139_0 = 0) % 225.34/38.96 (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ~ % 225.34/38.96 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 225.34/38.96 (5) equalelemsP(nil) = 0 % 225.34/38.96 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 225.34/38.96 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 225.34/38.96 (7) $i(all_139_1) % 225.34/38.96 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 225.34/38.96 (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0)) % 225.34/38.96 (9) equalelemsP(all_139_1) = all_139_0 % 225.34/38.96 (10) all_143_1 = all_139_1 | ? [v0: any] : ? [v1: any] : % 225.34/38.96 (segmentP(all_139_1, all_143_1) = v1 & ssList(all_139_1) = v0 & ( ~ (v1 % 225.34/38.96 = 0) | ~ (v0 = 0))) % 225.34/38.96 (11) ssList(all_139_1) = 0 % 225.34/38.96 % 225.34/38.96 Begin of proof % 225.34/38.96 | % 225.34/38.96 | BETA: splitting (1) gives: % 225.34/38.96 | % 225.34/38.96 | Case 1: % 225.34/38.96 | | % 225.34/38.96 | | (12) all_139_1 = nil % 225.34/38.96 | | % 225.34/38.96 | | REDUCE: (9), (12) imply: % 225.34/38.96 | | (13) equalelemsP(nil) = all_139_0 % 225.34/38.96 | | % 225.34/38.96 | | GROUND_INST: instantiating (8) with 0, all_139_0, nil, simplifying with (5), % 225.34/38.96 | | (13) gives: % 225.34/38.96 | | (14) all_139_0 = 0 % 225.34/38.96 | | % 225.34/38.96 | | REDUCE: (3), (14) imply: % 225.34/38.96 | | (15) $false % 225.34/38.96 | | % 225.34/38.96 | | CLOSE: (15) is inconsistent. % 225.34/38.96 | | % 225.34/38.96 | Case 2: % 225.34/38.96 | | % 225.34/38.96 | | (16) ~ (all_139_1 = nil) % 225.34/38.96 | | % 225.34/38.96 | | BETA: splitting (10) gives: % 225.34/38.96 | | % 225.34/38.96 | | Case 1: % 225.34/38.96 | | | % 225.34/38.96 | | | (17) all_143_1 = all_139_1 % 225.34/38.96 | | | % 225.34/38.96 | | | COMBINE_EQS: (2), (17) imply: % 225.34/38.96 | | | (18) all_139_1 = nil % 225.34/38.96 | | | % 225.34/38.96 | | | SIMP: (18) implies: % 225.34/38.96 | | | (19) all_139_1 = nil % 225.34/38.96 | | | % 225.34/38.96 | | | REDUCE: (16), (19) imply: % 225.34/38.96 | | | (20) $false % 225.34/38.96 | | | % 225.34/38.96 | | | CLOSE: (20) is inconsistent. % 225.34/38.96 | | | % 225.34/38.96 | | Case 2: % 225.34/38.96 | | | % 225.34/38.96 | | | (21) ? [v0: any] : ? [v1: any] : (segmentP(all_139_1, all_143_1) = v1 % 225.34/38.96 | | | & ssList(all_139_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 225.34/38.96 | | | % 225.34/38.96 | | | DELTA: instantiating (21) with fresh symbols all_395_0, all_395_1 gives: % 225.34/38.96 | | | (22) segmentP(all_139_1, all_143_1) = all_395_0 & ssList(all_139_1) = % 225.34/38.96 | | | all_395_1 & ( ~ (all_395_0 = 0) | ~ (all_395_1 = 0)) % 225.34/38.96 | | | % 225.34/38.96 | | | ALPHA: (22) implies: % 225.34/38.96 | | | (23) ssList(all_139_1) = all_395_1 % 225.34/38.96 | | | (24) segmentP(all_139_1, all_143_1) = all_395_0 % 225.34/38.96 | | | (25) ~ (all_395_0 = 0) | ~ (all_395_1 = 0) % 225.34/38.96 | | | % 225.34/38.96 | | | REDUCE: (2), (24) imply: % 225.34/38.96 | | | (26) segmentP(all_139_1, nil) = all_395_0 % 225.34/38.96 | | | % 225.34/38.96 | | | GROUND_INST: instantiating (6) with 0, all_395_1, all_139_1, simplifying % 225.34/38.96 | | | with (11), (23) gives: % 225.34/38.96 | | | (27) all_395_1 = 0 % 225.34/38.96 | | | % 225.34/38.96 | | | BETA: splitting (25) gives: % 225.34/38.96 | | | % 225.34/38.96 | | | Case 1: % 225.34/38.96 | | | | % 225.34/38.96 | | | | (28) ~ (all_395_0 = 0) % 225.34/38.96 | | | | % 225.34/38.96 | | | | GROUND_INST: instantiating (4) with all_139_1, all_395_0, simplifying % 225.34/38.96 | | | | with (7), (26) gives: % 225.34/38.96 | | | | (29) all_395_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) % 225.34/38.96 | | | | = v0) % 225.34/38.96 | | | | % 225.34/38.96 | | | | BETA: splitting (29) gives: % 225.34/38.96 | | | | % 225.34/38.96 | | | | Case 1: % 225.34/38.96 | | | | | % 225.34/38.96 | | | | | (30) all_395_0 = 0 % 225.34/38.96 | | | | | % 225.34/38.96 | | | | | REDUCE: (28), (30) imply: % 225.34/38.96 | | | | | (31) $false % 225.34/38.96 | | | | | % 225.34/38.96 | | | | | CLOSE: (31) is inconsistent. % 225.34/38.96 | | | | | % 225.34/38.96 | | | | Case 2: % 225.34/38.96 | | | | | % 225.34/38.96 | | | | | (32) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 225.34/38.96 | | | | | % 225.34/38.96 | | | | | REF_CLOSE: (6), (11), (32) are inconsistent by sub-proof #2. % 225.34/38.96 | | | | | % 225.34/38.96 | | | | End of split % 225.34/38.96 | | | | % 225.34/38.96 | | | Case 2: % 225.34/38.96 | | | | % 225.34/38.96 | | | | (33) ~ (all_395_1 = 0) % 225.34/38.96 | | | | % 225.34/38.96 | | | | REDUCE: (27), (33) imply: % 225.34/38.96 | | | | (34) $false % 225.34/38.96 | | | | % 225.34/38.96 | | | | CLOSE: (34) is inconsistent. % 225.34/38.96 | | | | % 225.34/38.96 | | | End of split % 225.34/38.96 | | | % 225.34/38.96 | | End of split % 225.34/38.96 | | % 225.34/38.96 | End of split % 225.34/38.96 | % 225.34/38.96 End of proof % 225.34/38.96 % 225.34/38.96 Sub-proof #2 shows that the following formulas are inconsistent: % 225.34/38.96 ---------------------------------------------------------------- % 225.34/38.96 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 225.34/38.96 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 225.34/38.96 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 225.34/38.97 (3) ssList(all_139_1) = 0 % 225.34/38.97 % 225.34/38.97 Begin of proof % 225.34/38.97 | % 225.34/38.97 | DELTA: instantiating (1) with fresh symbol all_446_0 gives: % 225.34/38.97 | (4) ~ (all_446_0 = 0) & ssList(all_139_1) = all_446_0 % 225.34/38.97 | % 225.34/38.97 | ALPHA: (4) implies: % 225.34/38.97 | (5) ~ (all_446_0 = 0) % 225.34/38.97 | (6) ssList(all_139_1) = all_446_0 % 225.34/38.97 | % 225.34/38.97 | GROUND_INST: instantiating (2) with 0, all_446_0, all_139_1, simplifying with % 225.34/38.97 | (3), (6) gives: % 225.34/38.97 | (7) all_446_0 = 0 % 225.34/38.97 | % 225.34/38.97 | REDUCE: (5), (7) imply: % 225.34/38.97 | (8) $false % 225.34/38.97 | % 225.34/38.97 | CLOSE: (8) is inconsistent. % 225.34/38.97 | % 225.34/38.97 End of proof % 225.34/38.97 % 225.34/38.97 Sub-proof #3 shows that the following formulas are inconsistent: % 225.34/38.97 ---------------------------------------------------------------- % 225.34/38.97 (1) ~ (all_378_0 = 0) & ssList(nil) = all_378_0 % 225.34/38.97 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 225.34/38.97 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 225.34/38.97 (3) ssList(nil) = 0 % 225.34/38.97 % 225.34/38.97 Begin of proof % 225.34/38.97 | % 225.34/38.97 | ALPHA: (1) implies: % 225.34/38.97 | (4) ~ (all_378_0 = 0) % 225.34/38.97 | (5) ssList(nil) = all_378_0 % 225.34/38.97 | % 225.34/38.97 | GROUND_INST: instantiating (2) with 0, all_378_0, nil, simplifying with (3), % 225.34/38.97 | (5) gives: % 225.34/38.97 | (6) all_378_0 = 0 % 225.34/38.97 | % 225.34/38.97 | REDUCE: (4), (6) imply: % 225.34/38.97 | (7) $false % 225.34/38.97 | % 225.34/38.97 | CLOSE: (7) is inconsistent. % 225.34/38.97 | % 225.34/38.97 End of proof % 225.34/38.97 % SZS output end Proof for theBenchmark % 225.34/38.97 % 225.34/38.97 38357ms %------------------------------------------------------------------------------