%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC379+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 : n029.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 20:51:08 EDT 2023 % Result : Theorem 30.46s 4.75s % Output : Proof 163.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC379+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 18:43:11 EDT 2023 % 0.12/0.33 % CPUTime : % 0.61/0.59 ________ _____ % 0.61/0.59 ___ __ \_________(_)________________________________ % 0.61/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.59 % 0.61/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.59 (2023-06-19) % 0.61/0.59 % 0.61/0.59 (c) Philipp Rümmer, 2009-2023 % 0.61/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.59 Amanda Stjerna. % 0.61/0.59 Free software under BSD-3-Clause. % 0.61/0.59 % 0.61/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.59 % 0.61/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.61/0.60 Running up to 7 provers in parallel. % 0.61/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.61/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 7.11/1.64 Prover 1: Preprocessing ... % 7.11/1.64 Prover 3: Preprocessing ... % 7.11/1.64 Prover 6: Preprocessing ... % 7.11/1.64 Prover 4: Preprocessing ... % 7.11/1.65 Prover 2: Preprocessing ... % 7.11/1.65 Prover 5: Preprocessing ... % 7.11/1.65 Prover 0: Preprocessing ... % 16.15/2.90 Prover 2: Proving ... % 16.78/2.97 Prover 5: Constructing countermodel ... % 17.26/3.03 Prover 1: Constructing countermodel ... % 17.26/3.05 Prover 3: Constructing countermodel ... % 17.26/3.05 Prover 6: Proving ... % 24.74/4.01 Prover 4: Constructing countermodel ... % 26.10/4.23 Prover 0: Proving ... % 30.46/4.75 Prover 0: proved (4132ms) % 30.46/4.75 % 30.46/4.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 30.46/4.75 % 30.46/4.75 Prover 5: stopped % 30.46/4.75 Prover 3: stopped % 30.46/4.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 30.46/4.76 Prover 2: stopped % 30.46/4.77 Prover 6: stopped % 30.46/4.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 30.46/4.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 30.46/4.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 30.46/4.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 32.12/5.00 Prover 7: Preprocessing ... % 32.12/5.03 Prover 10: Preprocessing ... % 32.89/5.05 Prover 11: Preprocessing ... % 32.89/5.06 Prover 13: Preprocessing ... % 32.89/5.07 Prover 8: Preprocessing ... % 34.11/5.21 Prover 10: Constructing countermodel ... % 34.36/5.31 Prover 7: Constructing countermodel ... % 35.64/5.45 Prover 13: Constructing countermodel ... % 36.43/5.50 Prover 8: Warning: ignoring some quantifiers % 36.43/5.52 Prover 8: Constructing countermodel ... % 41.80/6.23 Prover 11: Constructing countermodel ... % 70.49/9.93 Prover 13: stopped % 70.49/9.94 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 71.70/10.07 Prover 16: Preprocessing ... % 72.88/10.20 Prover 16: Constructing countermodel ... % 115.68/15.68 Prover 16: stopped % 115.68/15.68 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 116.83/15.85 Prover 19: Preprocessing ... % 117.79/15.96 Prover 1: stopped % 119.53/16.20 Prover 19: Warning: ignoring some quantifiers % 119.53/16.22 Prover 19: Constructing countermodel ... % 142.18/19.42 Prover 19: stopped % 162.67/23.18 Prover 8: Found proof (size 447) % 162.67/23.18 Prover 8: proved (18347ms) % 162.67/23.19 Prover 7: stopped % 162.67/23.19 Prover 10: stopped % 162.67/23.19 Prover 4: stopped % 162.67/23.19 Prover 11: stopped % 162.67/23.19 % 162.67/23.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 162.67/23.19 % 162.78/23.21 % SZS output start Proof for theBenchmark % 162.78/23.21 Assumptions after simplification: % 162.78/23.21 --------------------------------- % 162.78/23.21 % 162.78/23.21 (ax13) % 162.85/23.24 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ? % 162.85/23.24 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 162.85/23.24 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) | % 162.85/23.25 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 162.85/23.25 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~ % 162.85/23.25 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 162.85/23.25 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) | % 162.85/23.25 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) | % 162.85/23.25 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 = % 162.85/23.25 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) = % 162.85/23.25 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] : % 162.85/23.25 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 & % 162.85/23.25 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ? % 162.85/23.25 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 & % 162.85/23.25 app(v7, v9) = v0 & $i(v9) & $i(v8))))))))) % 162.85/23.25 % 162.85/23.25 (ax16) % 162.85/23.25 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 162.85/23.25 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 162.85/23.25 (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 162.85/23.25 % 162.85/23.25 (ax17) % 162.85/23.25 ssList(nil) = 0 & $i(nil) % 162.85/23.25 % 162.85/23.25 (ax2) % 162.85/23.25 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) & % 162.85/23.25 ssItem(v1) = 0 & $i(v1))) % 162.85/23.25 % 162.85/23.25 (ax20) % 162.85/23.25 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 162.85/23.25 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 162.85/23.25 ssItem(v2) = 0 & $i(v2)))) % 162.85/23.25 % 162.85/23.25 (ax23) % 162.85/23.25 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 162.85/23.25 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 162.85/23.25 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 162.85/23.25 % 162.85/23.25 (ax25) % 162.85/23.26 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 162.85/23.26 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 162.85/23.26 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 162.85/23.26 % 162.85/23.26 (ax3) % 162.85/23.26 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 162.85/23.26 ( ~ (memberP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 162.85/23.26 ssItem(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : (ssList(v3) = 0 & % 162.85/23.26 $i(v3) & ? [v4: $i] : ? [v5: $i] : (ssList(v4) = 0 & cons(v1, v4) % 162.85/23.26 = v5 & app(v3, v5) = v0 & $i(v5) & $i(v4)))) & (v2 = 0 | ! [v3: % 162.85/23.26 $i] : ( ~ (ssList(v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: $i] : % 162.85/23.26 ( ~ (cons(v1, v4) = v5) | ~ (app(v3, v5) = v0) | ~ $i(v4) | ? % 162.85/23.26 [v6: int] : ( ~ (v6 = 0) & ssList(v4) = v6))))))) % 162.85/23.26 % 162.85/23.26 (ax38) % 162.85/23.26 $i(nil) & ! [v0: $i] : ( ~ (memberP(nil, v0) = 0) | ~ $i(v0) | ? [v1: int] % 162.85/23.26 : ( ~ (v1 = 0) & ssItem(v0) = v1)) % 162.85/23.26 % 162.85/23.26 (ax44) % 162.85/23.27 ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) % 162.85/23.27 = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, v2) = v3) | % 162.85/23.27 ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] % 162.85/23.27 : ! [v5: $i] : ! [v6: any] : ( ~ (frontsegP(v3, v5) = v6) | ~ % 162.85/23.27 (cons(v1, v4) = v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] : % 162.85/23.27 (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = % 162.85/23.27 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = % 162.85/23.27 v0))))))))) % 162.85/23.27 % 162.85/23.27 (ax60) % 162.85/23.27 cyclefreeP(nil) = 0 & $i(nil) % 162.85/23.27 % 162.85/23.27 (ax62) % 162.85/23.27 totalorderP(nil) = 0 & $i(nil) % 162.85/23.27 % 162.85/23.27 (ax72) % 162.85/23.27 duplicatefreeP(nil) = 0 & $i(nil) % 162.85/23.27 % 162.85/23.27 (ax8) % 162.85/23.27 ! [v0: $i] : ! [v1: any] : ( ~ (cyclefreeP(v0) = v1) | ~ $i(v0) | ? [v2: % 162.85/23.27 int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : ( ~ % 162.85/23.27 (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: any] : ( ~ % 162.85/23.27 (leq(v2, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : % 162.85/23.27 (leq(v3, v2) = v6 & ssItem(v3) = v5 & ( ~ (v5 = 0) | ! [v7: $i] : ( % 162.85/23.27 ~ (ssList(v7) = 0) | ~ $i(v7) | ! [v8: $i] : ! [v9: $i] : % 162.85/23.27 ! [v10: $i] : ( ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v10) % 162.85/23.27 | ~ $i(v8) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v8) = % 162.85/23.27 v11) | ! [v11: $i] : ! [v12: $i] : ( ~ (v6 = 0) | ~ (v4 % 162.85/23.27 = 0) | ~ (cons(v3, v11) = v12) | ~ (app(v10, v12) = % 162.85/23.27 v0) | ~ $i(v11) | ? [v13: int] : ( ~ (v13 = 0) & % 162.85/23.27 ssList(v11) = v13))))))))) & (v1 = 0 | ? [v2: $i] : % 162.85/23.27 (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 162.85/23.27 (leq(v3, v2) = v5 & leq(v2, v3) = v4 & ssItem(v3) = 0 & $i(v3) & ? % 162.85/23.27 [v6: $i] : (ssList(v6) = 0 & $i(v6) & ? [v7: $i] : ? [v8: $i] : ? % 162.85/23.27 [v9: $i] : (ssList(v7) = 0 & cons(v2, v7) = v8 & app(v6, v8) = v9 % 162.85/23.27 & $i(v9) & $i(v8) & $i(v7) & ? [v10: $i] : ? [v11: $i] : (v5 = % 162.85/23.28 0 & v4 = 0 & ssList(v10) = 0 & cons(v3, v10) = v11 & app(v9, % 162.85/23.28 v11) = v0 & $i(v11) & $i(v10))))))))) % 162.85/23.28 % 162.85/23.28 (ax86) % 162.85/23.28 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (tl(v0) = v1) | ~ $i(v0) | ? [v2: % 162.85/23.28 int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : ! [v3: $i] : (v0 = % 162.85/23.28 nil | ~ (app(v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? % 162.85/23.28 [v6: $i] : (tl(v5) = v6 & ssList(v2) = v4 & app(v0, v2) = v5 & $i(v6) & % 162.85/23.28 $i(v5) & ( ~ (v4 = 0) | v6 = v3)))) % 162.85/23.28 % 162.85/23.28 (ax9) % 162.85/23.28 ! [v0: $i] : ! [v1: any] : ( ~ (totalorderP(v0) = v1) | ~ $i(v0) | ? [v2: % 162.85/23.28 int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : ( ~ % 162.85/23.28 (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: any] : ( ~ % 162.85/23.28 (leq(v2, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : % 162.85/23.28 (leq(v3, v2) = v6 & ssItem(v3) = v5 & ( ~ (v5 = 0) | ! [v7: $i] : ( % 162.85/23.28 ~ (ssList(v7) = 0) | ~ $i(v7) | ! [v8: $i] : ! [v9: $i] : % 162.85/23.28 ! [v10: $i] : ( ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v10) % 162.85/23.28 | ~ $i(v8) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v8) = % 162.85/23.28 v11) | ! [v11: $i] : ! [v12: $i] : (v6 = 0 | v4 = 0 | ~ % 162.85/23.28 (cons(v3, v11) = v12) | ~ (app(v10, v12) = v0) | ~ % 162.85/23.28 $i(v11) | ? [v13: int] : ( ~ (v13 = 0) & ssList(v11) = % 162.85/23.28 v13))))))))) & (v1 = 0 | ? [v2: $i] : (ssItem(v2) = 0 & % 162.85/23.28 $i(v2) & ? [v3: $i] : ? [v4: any] : ? [v5: any] : (leq(v3, v2) = v5 % 162.85/23.28 & leq(v2, v3) = v4 & ssItem(v3) = 0 & $i(v3) & ? [v6: $i] : % 162.85/23.28 (ssList(v6) = 0 & $i(v6) & ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 162.85/23.28 (ssList(v7) = 0 & cons(v2, v7) = v8 & app(v6, v8) = v9 & $i(v9) & % 162.85/23.28 $i(v8) & $i(v7) & ? [v10: $i] : ? [v11: $i] : ( ~ (v5 = 0) & % 162.85/23.28 ~ (v4 = 0) & ssList(v10) = 0 & cons(v3, v10) = v11 & app(v9, % 162.85/23.28 v11) = v0 & $i(v11) & $i(v10))))))))) % 162.85/23.28 % 162.85/23.28 (co1) % 162.85/23.29 ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 & % 162.85/23.29 $i(v1) & ! [v2: $i] : ! [v3: any] : ( ~ (memberP(v0, v2) = v3) | ~ % 162.85/23.29 $i(v2) | ? [v4: any] : ? [v5: any] : (memberP(v1, v2) = v5 & % 162.85/23.29 ssItem(v2) = v4 & ( ~ (v4 = 0) | (( ~ (v5 = 0) | v3 = 0 | ? [v6: $i] % 162.85/23.29 : ( ~ (v6 = v2) & leq(v6, v2) = 0 & memberP(v1, v6) = 0 & % 162.85/23.29 ssItem(v6) = 0 & $i(v6))) & ( ~ (v3 = 0) | (v5 = 0 & ! [v6: % 162.85/23.29 $i] : (v6 = v2 | ~ (memberP(v1, v6) = 0) | ~ $i(v6) | ? % 162.85/23.29 [v7: any] : ? [v8: any] : (leq(v6, v2) = v8 & ssItem(v6) = % 162.85/23.29 v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))))))))) & ? [v2: $i] : % 162.85/23.29 ? [v3: any] : ? [v4: any] : (memberP(v1, v2) = v4 & memberP(v0, v2) = v3 % 162.85/23.29 & ssItem(v2) = 0 & $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0) | ? [v5: $i] : ( % 162.85/23.29 ~ (v5 = v2) & leq(v5, v2) = 0 & memberP(v1, v5) = 0 & ssItem(v5) = 0 % 162.85/23.29 & $i(v5))) & (v3 = 0 | (v4 = 0 & ! [v5: $i] : (v5 = v2 | ~ % 162.85/23.29 (memberP(v1, v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] : % 162.85/23.29 (leq(v5, v2) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = % 162.85/23.29 0))))))))) % 162.85/23.29 % 162.85/23.29 (function-axioms) % 162.85/23.30 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 162.85/23.30 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 162.85/23.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 162.85/23.30 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 162.85/23.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 162.85/23.30 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 162.85/23.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 162.85/23.30 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 162.85/23.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 162.85/23.30 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 162.85/23.30 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 162.85/23.30 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 162.85/23.30 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 162.85/23.30 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 162.85/23.30 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 162.85/23.30 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 162.85/23.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 162.85/23.30 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 162.85/23.30 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 162.85/23.30 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 162.85/23.30 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 162.85/23.30 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 162.85/23.30 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 162.85/23.30 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 162.85/23.30 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 162.85/23.30 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 162.85/23.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 162.85/23.30 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 162.85/23.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 162.85/23.30 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 162.85/23.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 162.85/23.30 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 162.85/23.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 162.85/23.30 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 162.85/23.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 162.85/23.30 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 162.85/23.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 162.85/23.30 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 162.85/23.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 162.85/23.30 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 162.85/23.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 162.85/23.30 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 162.85/23.30 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ? % 162.85/23.30 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (gt(v1, v0) = v2) & ? % 162.85/23.30 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (geq(v1, v0) = v2) & ? % 162.85/23.30 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (lt(v1, v0) = v2) & ? % 162.85/23.30 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (leq(v1, v0) = v2) & ? % 162.85/23.30 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (segmentP(v1, v0) = v2) % 162.85/23.30 & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (rearsegP(v1, v0) = % 162.85/23.30 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 162.85/23.30 (frontsegP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 162.85/23.30 MultipleValueBool] : (memberP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 162.85/23.30 [v2: MultipleValueBool] : (neq(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 162.85/23.30 [v2: $i] : (cons(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 162.85/23.30 $i] : (app(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] % 162.85/23.30 : (equalelemsP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 162.85/23.30 (duplicatefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 162.85/23.30 (strictorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 162.85/23.30 (totalorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 162.85/23.30 (strictorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 162.85/23.30 (totalorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 162.85/23.30 (cyclefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 162.85/23.30 (singletonP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssList(v0) % 162.85/23.30 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssItem(v0) = v1) & ? % 162.85/23.30 [v0: $i] : ? [v1: $i] : (tl(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 162.85/23.30 (hd(v0) = v1 & $i(v1)) % 162.85/23.30 % 162.85/23.30 Further assumptions not needed in the proof: % 162.85/23.30 -------------------------------------------- % 162.85/23.30 ax1, ax10, ax11, ax12, ax14, ax15, ax18, ax19, ax21, ax22, ax24, ax26, ax27, % 162.85/23.30 ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax39, ax4, ax40, % 162.85/23.30 ax41, ax42, ax43, ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, % 162.85/23.30 ax54, ax55, ax56, ax57, ax58, ax59, ax6, ax61, ax63, ax64, ax65, ax66, ax67, % 162.85/23.30 ax68, ax69, ax7, ax70, ax71, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax80, % 162.85/23.30 ax81, ax82, ax83, ax84, ax85, ax87, ax88, ax89, ax90, ax91, ax92, ax93, ax94, % 162.85/23.30 ax95 % 162.85/23.30 % 162.85/23.30 Those formulas are unsatisfiable: % 162.85/23.30 --------------------------------- % 162.85/23.30 % 162.85/23.30 Begin of proof % 162.85/23.30 | % 162.85/23.31 | ALPHA: (ax17) implies: % 162.85/23.31 | (1) ssList(nil) = 0 % 162.85/23.31 | % 162.85/23.31 | ALPHA: (ax20) implies: % 162.85/23.31 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 162.85/23.31 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 162.85/23.31 | ssItem(v2) = 0 & $i(v2)))) % 162.85/23.31 | % 162.85/23.31 | ALPHA: (ax38) implies: % 162.85/23.31 | (3) ! [v0: $i] : ( ~ (memberP(nil, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( % 162.85/23.31 | ~ (v1 = 0) & ssItem(v0) = v1)) % 162.85/23.31 | % 162.85/23.31 | ALPHA: (ax60) implies: % 162.85/23.31 | (4) cyclefreeP(nil) = 0 % 162.85/23.31 | % 162.85/23.31 | ALPHA: (ax62) implies: % 162.85/23.31 | (5) totalorderP(nil) = 0 % 162.85/23.31 | % 162.85/23.31 | ALPHA: (ax72) implies: % 162.85/23.31 | (6) duplicatefreeP(nil) = 0 % 162.85/23.31 | % 162.85/23.31 | ALPHA: (ax86) implies: % 162.85/23.31 | (7) $i(nil) % 162.85/23.31 | % 162.85/23.31 | ALPHA: (function-axioms) implies: % 162.85/23.31 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 162.85/23.31 | (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 162.85/23.31 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 162.85/23.31 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 162.85/23.31 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 162.85/23.31 | : ! [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, % 162.85/23.31 | v2) = v0)) % 163.32/23.31 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 163.32/23.31 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 163.32/23.31 | v0)) % 163.32/23.31 | % 163.32/23.31 | DELTA: instantiating (ax2) with fresh symbol all_137_0 gives: % 163.32/23.31 | (12) ssItem(all_137_0) = 0 & $i(all_137_0) & ? [v0: any] : ( ~ (v0 = % 163.32/23.31 | all_137_0) & ssItem(v0) = 0 & $i(v0)) % 163.32/23.31 | % 163.32/23.31 | ALPHA: (12) implies: % 163.32/23.31 | (13) $i(all_137_0) % 163.32/23.31 | (14) ssItem(all_137_0) = 0 % 163.32/23.31 | % 163.32/23.31 | DELTA: instantiating (co1) with fresh symbol all_139_0 gives: % 163.32/23.32 | (15) ssList(all_139_0) = 0 & $i(all_139_0) & ? [v0: $i] : (ssList(v0) = 0 % 163.32/23.32 | & $i(v0) & ! [v1: $i] : ! [v2: any] : ( ~ (memberP(all_139_0, v1) % 163.32/23.32 | = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (memberP(v0, % 163.32/23.32 | v1) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 % 163.32/23.32 | = 0 | ? [v5: $i] : ( ~ (v5 = v1) & leq(v5, v1) = 0 & % 163.32/23.32 | memberP(v0, v5) = 0 & ssItem(v5) = 0 & $i(v5))) & ( ~ % 163.32/23.32 | (v2 = 0) | (v4 = 0 & ! [v5: $i] : (v5 = v1 | ~ % 163.32/23.32 | (memberP(v0, v5) = 0) | ~ $i(v5) | ? [v6: any] : ? % 163.32/23.32 | [v7: any] : (leq(v5, v1) = v7 & ssItem(v5) = v6 & ( ~ % 163.32/23.32 | (v7 = 0) | ~ (v6 = 0)))))))))) & ? [v1: $i] : ? % 163.32/23.32 | [v2: any] : ? [v3: any] : (memberP(v0, v1) = v3 & % 163.32/23.32 | memberP(all_139_0, v1) = v2 & ssItem(v1) = 0 & $i(v1) & ( ~ (v3 = % 163.32/23.32 | 0) | ~ (v2 = 0) | ? [v4: $i] : ( ~ (v4 = v1) & leq(v4, v1) = % 163.32/23.32 | 0 & memberP(v0, v4) = 0 & ssItem(v4) = 0 & $i(v4))) & (v2 = 0 % 163.32/23.32 | | (v3 = 0 & ! [v4: $i] : (v4 = v1 | ~ (memberP(v0, v4) = 0) | % 163.32/23.32 | ~ $i(v4) | ? [v5: any] : ? [v6: any] : (leq(v4, v1) = v6 & % 163.32/23.32 | ssItem(v4) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))))))) % 163.32/23.32 | % 163.32/23.32 | ALPHA: (15) implies: % 163.32/23.32 | (16) $i(all_139_0) % 163.32/23.32 | (17) ssList(all_139_0) = 0 % 163.32/23.32 | (18) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: any] : % 163.32/23.32 | ( ~ (memberP(all_139_0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 163.32/23.32 | [v4: any] : (memberP(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) % 163.32/23.32 | | (( ~ (v4 = 0) | v2 = 0 | ? [v5: $i] : ( ~ (v5 = v1) & % 163.32/23.32 | leq(v5, v1) = 0 & memberP(v0, v5) = 0 & ssItem(v5) = 0 & % 163.32/23.32 | $i(v5))) & ( ~ (v2 = 0) | (v4 = 0 & ! [v5: $i] : (v5 = % 163.32/23.32 | v1 | ~ (memberP(v0, v5) = 0) | ~ $i(v5) | ? [v6: % 163.32/23.32 | any] : ? [v7: any] : (leq(v5, v1) = v7 & ssItem(v5) % 163.32/23.32 | = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))))))))) & ? [v1: % 163.32/23.32 | $i] : ? [v2: any] : ? [v3: any] : (memberP(v0, v1) = v3 & % 163.32/23.32 | memberP(all_139_0, v1) = v2 & ssItem(v1) = 0 & $i(v1) & ( ~ (v3 = % 163.32/23.32 | 0) | ~ (v2 = 0) | ? [v4: $i] : ( ~ (v4 = v1) & leq(v4, v1) = % 163.32/23.32 | 0 & memberP(v0, v4) = 0 & ssItem(v4) = 0 & $i(v4))) & (v2 = 0 % 163.32/23.32 | | (v3 = 0 & ! [v4: $i] : (v4 = v1 | ~ (memberP(v0, v4) = 0) | % 163.32/23.32 | ~ $i(v4) | ? [v5: any] : ? [v6: any] : (leq(v4, v1) = v6 & % 163.32/23.32 | ssItem(v4) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))))))) % 163.32/23.32 | % 163.32/23.32 | DELTA: instantiating (18) with fresh symbol all_143_0 gives: % 163.32/23.33 | (19) ssList(all_143_0) = 0 & $i(all_143_0) & ! [v0: $i] : ! [v1: any] : ( % 163.32/23.33 | ~ (memberP(all_139_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 163.32/23.33 | any] : (memberP(all_143_0, v0) = v3 & ssItem(v0) = v2 & ( ~ (v2 = % 163.32/23.33 | 0) | (( ~ (v3 = 0) | v1 = 0 | ? [v4: $i] : ( ~ (v4 = v0) & % 163.32/23.33 | leq(v4, v0) = 0 & memberP(all_143_0, v4) = 0 & ssItem(v4) % 163.32/23.33 | = 0 & $i(v4))) & ( ~ (v1 = 0) | (v3 = 0 & ! [v4: $i] : % 163.32/23.33 | (v4 = v0 | ~ (memberP(all_143_0, v4) = 0) | ~ $i(v4) | % 163.32/23.33 | ? [v5: any] : ? [v6: any] : (leq(v4, v0) = v6 & % 163.32/23.33 | ssItem(v4) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))))))))) % 163.32/23.33 | & ? [v0: $i] : ? [v1: any] : ? [v2: any] : (memberP(all_143_0, v0) % 163.32/23.33 | = v2 & memberP(all_139_0, v0) = v1 & ssItem(v0) = 0 & $i(v0) & ( ~ % 163.32/23.33 | (v2 = 0) | ~ (v1 = 0) | ? [v3: $i] : ( ~ (v3 = v0) & leq(v3, v0) % 163.32/23.33 | = 0 & memberP(all_143_0, v3) = 0 & ssItem(v3) = 0 & $i(v3))) & % 163.32/23.33 | (v1 = 0 | (v2 = 0 & ! [v3: $i] : (v3 = v0 | ~ (memberP(all_143_0, % 163.32/23.33 | v3) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : % 163.32/23.33 | (leq(v3, v0) = v5 & ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = % 163.32/23.33 | 0))))))) % 163.32/23.33 | % 163.32/23.33 | ALPHA: (19) implies: % 163.32/23.33 | (20) $i(all_143_0) % 163.32/23.33 | (21) ssList(all_143_0) = 0 % 163.32/23.33 | (22) ! [v0: $i] : ! [v1: any] : ( ~ (memberP(all_139_0, v0) = v1) | ~ % 163.32/23.33 | $i(v0) | ? [v2: any] : ? [v3: any] : (memberP(all_143_0, v0) = v3 % 163.32/23.33 | & ssItem(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = 0) | v1 = 0 | ? % 163.32/23.33 | [v4: $i] : ( ~ (v4 = v0) & leq(v4, v0) = 0 & % 163.32/23.33 | memberP(all_143_0, v4) = 0 & ssItem(v4) = 0 & $i(v4))) & ( % 163.32/23.33 | ~ (v1 = 0) | (v3 = 0 & ! [v4: $i] : (v4 = v0 | ~ % 163.32/23.33 | (memberP(all_143_0, v4) = 0) | ~ $i(v4) | ? [v5: any] % 163.32/23.33 | : ? [v6: any] : (leq(v4, v0) = v6 & ssItem(v4) = v5 & ( % 163.32/23.33 | ~ (v6 = 0) | ~ (v5 = 0)))))))))) % 163.32/23.33 | (23) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (memberP(all_143_0, v0) = % 163.32/23.33 | v2 & memberP(all_139_0, v0) = v1 & ssItem(v0) = 0 & $i(v0) & ( ~ (v2 % 163.32/23.33 | = 0) | ~ (v1 = 0) | ? [v3: $i] : ( ~ (v3 = v0) & leq(v3, v0) = % 163.32/23.33 | 0 & memberP(all_143_0, v3) = 0 & ssItem(v3) = 0 & $i(v3))) & (v1 % 163.32/23.33 | = 0 | (v2 = 0 & ! [v3: $i] : (v3 = v0 | ~ (memberP(all_143_0, % 163.32/23.33 | v3) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : % 163.32/23.33 | (leq(v3, v0) = v5 & ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = % 163.32/23.33 | 0))))))) % 163.32/23.33 | % 163.32/23.33 | DELTA: instantiating (23) with fresh symbols all_146_0, all_146_1, all_146_2 % 163.32/23.33 | gives: % 163.32/23.34 | (24) memberP(all_143_0, all_146_2) = all_146_0 & memberP(all_139_0, % 163.32/23.34 | all_146_2) = all_146_1 & ssItem(all_146_2) = 0 & $i(all_146_2) & ( ~ % 163.32/23.34 | (all_146_0 = 0) | ~ (all_146_1 = 0) | ? [v0: any] : ( ~ (v0 = % 163.32/23.34 | all_146_2) & leq(v0, all_146_2) = 0 & memberP(all_143_0, v0) = 0 % 163.32/23.34 | & ssItem(v0) = 0 & $i(v0))) & (all_146_1 = 0 | (all_146_0 = 0 & ! % 163.32/23.34 | [v0: any] : (v0 = all_146_2 | ~ (memberP(all_143_0, v0) = 0) | ~ % 163.32/23.34 | $i(v0) | ? [v1: any] : ? [v2: any] : (leq(v0, all_146_2) = v2 % 163.32/23.34 | & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))))) % 163.32/23.34 | % 163.32/23.34 | ALPHA: (24) implies: % 163.32/23.34 | (25) $i(all_146_2) % 163.32/23.34 | (26) ssItem(all_146_2) = 0 % 163.32/23.34 | (27) memberP(all_139_0, all_146_2) = all_146_1 % 163.32/23.34 | (28) memberP(all_143_0, all_146_2) = all_146_0 % 163.32/23.34 | (29) all_146_1 = 0 | (all_146_0 = 0 & ! [v0: any] : (v0 = all_146_2 | ~ % 163.32/23.34 | (memberP(all_143_0, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 163.32/23.34 | any] : (leq(v0, all_146_2) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) % 163.32/23.34 | | ~ (v1 = 0))))) % 163.32/23.34 | (30) ~ (all_146_0 = 0) | ~ (all_146_1 = 0) | ? [v0: any] : ( ~ (v0 = % 163.32/23.34 | all_146_2) & leq(v0, all_146_2) = 0 & memberP(all_143_0, v0) = 0 & % 163.32/23.34 | ssItem(v0) = 0 & $i(v0)) % 163.32/23.34 | % 163.32/23.34 | GROUND_INST: instantiating (ax44) with all_146_2, simplifying with (25), (26) % 163.32/23.34 | gives: % 163.32/23.34 | (31) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 163.32/23.34 | $i] : ( ~ (cons(all_146_2, v1) = v2) | ~ $i(v1) | ? [v3: int] : % 163.32/23.34 | ( ~ (v3 = 0) & ssList(v1) = v3) | ! [v3: $i] : ! [v4: $i] : ! % 163.32/23.34 | [v5: any] : ( ~ (frontsegP(v2, v4) = v5) | ~ (cons(v0, v3) = v4) % 163.32/23.34 | | ~ $i(v3) | ? [v6: any] : ? [v7: any] : (frontsegP(v1, v3) = % 163.32/23.34 | v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | ~ (v0 = % 163.32/23.34 | all_146_2) | v5 = 0) & ( ~ (v5 = 0) | (v7 = 0 & v0 = % 163.32/23.34 | all_146_2)))))))) % 163.32/23.34 | % 163.32/23.34 | GROUND_INST: instantiating (2) with all_139_0, simplifying with (16), (17) % 163.32/23.34 | gives: % 163.32/23.34 | (32) all_139_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 163.32/23.34 | : (cons(v1, v0) = all_139_0 & ssItem(v1) = 0 & $i(v1))) % 163.32/23.34 | % 163.32/23.34 | GROUND_INST: instantiating (ax3) with all_139_0, simplifying with (16), (17) % 163.32/23.34 | gives: % 163.32/23.35 | (33) ! [v0: $i] : ! [v1: any] : ( ~ (memberP(all_139_0, v0) = v1) | ~ % 163.32/23.35 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v0) = v2) | (( ~ (v1 = % 163.32/23.35 | 0) | ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ? % 163.32/23.35 | [v4: $i] : (ssList(v3) = 0 & cons(v0, v3) = v4 & app(v2, v4) = % 163.32/23.35 | all_139_0 & $i(v4) & $i(v3)))) & (v1 = 0 | ! [v2: $i] : ( ~ % 163.32/23.35 | (ssList(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ( ~ % 163.32/23.35 | (cons(v0, v3) = v4) | ~ (app(v2, v4) = all_139_0) | ~ % 163.32/23.35 | $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v3) = v5)))))) % 163.32/23.35 | % 163.32/23.35 | GROUND_INST: instantiating (2) with all_143_0, simplifying with (20), (21) % 163.32/23.35 | gives: % 163.32/23.35 | (34) all_143_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 163.32/23.35 | : (cons(v1, v0) = all_143_0 & ssItem(v1) = 0 & $i(v1))) % 163.32/23.35 | % 163.32/23.35 | GROUND_INST: instantiating (ax3) with all_143_0, simplifying with (20), (21) % 163.32/23.35 | gives: % 163.32/23.35 | (35) ! [v0: $i] : ! [v1: any] : ( ~ (memberP(all_143_0, v0) = v1) | ~ % 163.32/23.35 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v0) = v2) | (( ~ (v1 = % 163.32/23.35 | 0) | ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ? % 163.32/23.35 | [v4: $i] : (ssList(v3) = 0 & cons(v0, v3) = v4 & app(v2, v4) = % 163.32/23.35 | all_143_0 & $i(v4) & $i(v3)))) & (v1 = 0 | ! [v2: $i] : ( ~ % 163.32/23.35 | (ssList(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ( ~ % 163.32/23.35 | (cons(v0, v3) = v4) | ~ (app(v2, v4) = all_143_0) | ~ % 163.32/23.35 | $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v3) = v5)))))) % 163.32/23.35 | % 163.32/23.35 | GROUND_INST: instantiating (22) with all_146_2, all_146_1, simplifying with % 163.32/23.35 | (25), (27) gives: % 163.32/23.35 | (36) ? [v0: any] : ? [v1: any] : (memberP(all_143_0, all_146_2) = v1 & % 163.32/23.35 | ssItem(all_146_2) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = 0) | all_146_1 = % 163.32/23.35 | 0 | ? [v2: any] : ( ~ (v2 = all_146_2) & leq(v2, all_146_2) = % 163.32/23.35 | 0 & memberP(all_143_0, v2) = 0 & ssItem(v2) = 0 & $i(v2))) & % 163.32/23.35 | ( ~ (all_146_1 = 0) | (v1 = 0 & ! [v2: any] : (v2 = all_146_2 | % 163.32/23.35 | ~ (memberP(all_143_0, v2) = 0) | ~ $i(v2) | ? [v3: any] % 163.32/23.35 | : ? [v4: any] : (leq(v2, all_146_2) = v4 & ssItem(v2) = % 163.32/23.35 | v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))))))) % 163.32/23.35 | % 163.32/23.35 | GROUND_INST: instantiating (ax8) with nil, 0, simplifying with (4), (7) gives: % 163.32/23.36 | (37) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 163.32/23.36 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : ( ~ % 163.32/23.36 | (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 163.32/23.36 | (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | ! [v5: $i] : % 163.32/23.36 | ( ~ (ssList(v5) = 0) | ~ $i(v5) | ! [v6: $i] : ! [v7: $i] : % 163.32/23.36 | ! [v8: $i] : ( ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = % 163.32/23.36 | v8) | ~ $i(v6) | ? [v9: int] : ( ~ (v9 = 0) & % 163.32/23.36 | ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] : ( ~ (v4 % 163.32/23.36 | = 0) | ~ (v2 = 0) | ~ (cons(v1, v9) = v10) | ~ % 163.32/23.36 | (app(v8, v10) = nil) | ~ $i(v9) | ? [v11: int] : ( ~ % 163.32/23.36 | (v11 = 0) & ssList(v9) = v11)))))))) % 163.32/23.36 | % 163.32/23.36 | GROUND_INST: instantiating (ax9) with nil, 0, simplifying with (5), (7) gives: % 163.32/23.36 | (38) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 163.32/23.36 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : ( ~ % 163.32/23.36 | (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 163.32/23.36 | (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | ! [v5: $i] : % 163.32/23.36 | ( ~ (ssList(v5) = 0) | ~ $i(v5) | ! [v6: $i] : ! [v7: $i] : % 163.32/23.36 | ! [v8: $i] : ( ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = % 163.32/23.36 | v8) | ~ $i(v6) | ? [v9: int] : ( ~ (v9 = 0) & % 163.32/23.36 | ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] : (v4 = 0 % 163.32/23.36 | | v2 = 0 | ~ (cons(v1, v9) = v10) | ~ (app(v8, v10) = % 163.32/23.36 | nil) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & % 163.32/23.36 | ssList(v9) = v11)))))))) % 163.32/23.36 | % 163.32/23.36 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (6), (7) % 163.32/23.36 | gives: % 163.32/23.36 | (39) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 163.32/23.36 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) | % 163.32/23.36 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | ! % 163.32/23.36 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) | % 163.32/23.36 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = % 163.32/23.36 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 163.32/23.36 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil) % 163.32/23.36 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 163.32/23.36 | v8)))))) % 163.32/23.36 | % 163.32/23.36 | GROUND_INST: instantiating (35) with all_146_2, all_146_0, simplifying with % 163.32/23.36 | (25), (28) gives: % 163.32/23.36 | (40) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_146_2) = v0) | (( ~ % 163.32/23.36 | (all_146_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: % 163.32/23.36 | $i] : ? [v2: $i] : (ssList(v1) = 0 & cons(all_146_2, v1) = v2 % 163.32/23.36 | & app(v0, v2) = all_143_0 & $i(v2) & $i(v1)))) & (all_146_0 = % 163.32/23.36 | 0 | ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : % 163.32/23.36 | ! [v2: $i] : ( ~ (cons(all_146_2, v1) = v2) | ~ (app(v0, v2) = % 163.32/23.36 | all_143_0) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 163.32/23.36 | ssList(v1) = v3))))) % 163.32/23.36 | % 163.32/23.36 | GROUND_INST: instantiating (31) with all_137_0, simplifying with (13), (14) % 163.32/23.36 | gives: % 163.32/23.37 | (41) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_146_2, v0) = v1) | ~ $i(v0) % 163.32/23.37 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : ! % 163.32/23.37 | [v3: $i] : ! [v4: any] : ( ~ (frontsegP(v1, v3) = v4) | ~ % 163.32/23.37 | (cons(all_137_0, v2) = v3) | ~ $i(v2) | ? [v5: any] : ? [v6: % 163.32/23.37 | any] : (frontsegP(v0, v2) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0) % 163.32/23.37 | | (( ~ (v6 = 0) | ~ (all_146_2 = all_137_0) | v4 = 0) & ( ~ % 163.32/23.37 | (v4 = 0) | (v6 = 0 & all_146_2 = all_137_0))))))) % 163.32/23.37 | % 163.32/23.37 | GROUND_INST: instantiating (33) with all_146_2, all_146_1, simplifying with % 163.32/23.37 | (25), (27) gives: % 163.32/23.37 | (42) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_146_2) = v0) | (( ~ % 163.32/23.37 | (all_146_1 = 0) | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: % 163.32/23.37 | $i] : ? [v2: $i] : (ssList(v1) = 0 & cons(all_146_2, v1) = v2 % 163.32/23.37 | & app(v0, v2) = all_139_0 & $i(v2) & $i(v1)))) & (all_146_1 = % 163.32/23.37 | 0 | ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : % 163.32/23.37 | ! [v2: $i] : ( ~ (cons(all_146_2, v1) = v2) | ~ (app(v0, v2) = % 163.32/23.37 | all_139_0) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 163.32/23.37 | ssList(v1) = v3))))) % 163.32/23.37 | % 163.32/23.37 | DELTA: instantiating (36) with fresh symbols all_317_0, all_317_1 gives: % 163.32/23.37 | (43) memberP(all_143_0, all_146_2) = all_317_0 & ssItem(all_146_2) = % 163.32/23.37 | all_317_1 & ( ~ (all_317_1 = 0) | (( ~ (all_317_0 = 0) | all_146_1 = 0 % 163.32/23.37 | | ? [v0: any] : ( ~ (v0 = all_146_2) & leq(v0, all_146_2) = 0 & % 163.32/23.37 | memberP(all_143_0, v0) = 0 & ssItem(v0) = 0 & $i(v0))) & ( ~ % 163.32/23.37 | (all_146_1 = 0) | (all_317_0 = 0 & ! [v0: any] : (v0 = % 163.32/23.37 | all_146_2 | ~ (memberP(all_143_0, v0) = 0) | ~ $i(v0) | ? % 163.32/23.37 | [v1: any] : ? [v2: any] : (leq(v0, all_146_2) = v2 & % 163.32/23.37 | ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))))))) % 163.32/23.37 | % 163.32/23.37 | ALPHA: (43) implies: % 163.32/23.37 | (44) ssItem(all_146_2) = all_317_1 % 163.32/23.37 | (45) memberP(all_143_0, all_146_2) = all_317_0 % 163.32/23.37 | (46) ~ (all_317_1 = 0) | (( ~ (all_317_0 = 0) | all_146_1 = 0 | ? [v0: % 163.32/23.37 | any] : ( ~ (v0 = all_146_2) & leq(v0, all_146_2) = 0 & % 163.32/23.37 | memberP(all_143_0, v0) = 0 & ssItem(v0) = 0 & $i(v0))) & ( ~ % 163.32/23.37 | (all_146_1 = 0) | (all_317_0 = 0 & ! [v0: any] : (v0 = all_146_2 % 163.32/23.37 | | ~ (memberP(all_143_0, v0) = 0) | ~ $i(v0) | ? [v1: any] : % 163.32/23.37 | ? [v2: any] : (leq(v0, all_146_2) = v2 & ssItem(v0) = v1 & ( % 163.32/23.37 | ~ (v2 = 0) | ~ (v1 = 0))))))) % 163.32/23.37 | % 163.32/23.37 | BETA: splitting (37) gives: % 163.32/23.37 | % 163.32/23.37 | Case 1: % 163.32/23.37 | | % 163.32/23.37 | | (47) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 163.32/23.37 | | % 163.32/23.37 | | REF_CLOSE: (1), (9), (47) are inconsistent by sub-proof #2. % 163.32/23.37 | | % 163.32/23.37 | Case 2: % 163.32/23.37 | | % 163.32/23.37 | | (48) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 163.32/23.37 | | [v2: any] : ( ~ (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 163.32/23.37 | | [v4: any] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | % 163.32/23.37 | | ! [v5: $i] : ( ~ (ssList(v5) = 0) | ~ $i(v5) | ! [v6: $i] % 163.32/23.37 | | : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v0, v6) = v7) | ~ % 163.32/23.37 | | (app(v5, v7) = v8) | ~ $i(v6) | ? [v9: int] : ( ~ (v9 % 163.32/23.37 | | = 0) & ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] % 163.32/23.37 | | : ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (cons(v1, v9) = v10) | % 163.32/23.37 | | ~ (app(v8, v10) = nil) | ~ $i(v9) | ? [v11: int] : % 163.32/23.37 | | ( ~ (v11 = 0) & ssList(v9) = v11)))))))) % 163.32/23.37 | | % 163.32/23.38 | | BETA: splitting (39) gives: % 163.32/23.38 | | % 163.32/23.38 | | Case 1: % 163.32/23.38 | | | % 163.32/23.38 | | | (49) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 163.32/23.38 | | | % 163.32/23.38 | | | REF_CLOSE: (1), (9), (49) are inconsistent by sub-proof #2. % 163.32/23.38 | | | % 163.32/23.38 | | Case 2: % 163.32/23.38 | | | % 163.32/23.38 | | | (50) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 163.32/23.38 | | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = % 163.32/23.38 | | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 163.32/23.38 | | | ( ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) % 163.32/23.38 | | | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: % 163.32/23.38 | | | $i] : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = % 163.32/23.38 | | | v7) | ~ (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: % 163.32/23.38 | | | int] : ( ~ (v8 = 0) & ssList(v6) = v8)))))) % 163.32/23.38 | | | % 163.32/23.38 | | | GROUND_INST: instantiating (50) with all_146_2, simplifying with (25), % 163.32/23.38 | | | (26) gives: % 163.32/23.38 | | | (51) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 163.32/23.38 | | | (ssList(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ! % 163.32/23.38 | | | [v4: $i] : ( ~ (cons(all_146_2, v2) = v3) | ~ (app(v1, v3) = % 163.32/23.38 | | | v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v2) % 163.32/23.38 | | | = v5) | ! [v5: $i] : ! [v6: $i] : ( ~ (v0 = all_146_2) | % 163.32/23.38 | | | ~ (cons(all_146_2, v5) = v6) | ~ (app(v4, v6) = nil) | % 163.32/23.38 | | | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & ssList(v5) = % 163.32/23.38 | | | v7))))) % 163.32/23.38 | | | % 163.32/23.38 | | | GROUND_INST: instantiating (51) with all_137_0, simplifying with (13), % 163.32/23.38 | | | (14) gives: % 163.32/23.38 | | | (52) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 163.32/23.38 | | | [v2: $i] : ! [v3: $i] : ( ~ (cons(all_146_2, v1) = v2) | ~ % 163.32/23.38 | | | (app(v0, v2) = v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 163.32/23.38 | | | ssList(v1) = v4) | ! [v4: $i] : ! [v5: $i] : ( ~ % 163.32/23.38 | | | (all_146_2 = all_137_0) | ~ (cons(all_137_0, v4) = v5) | ~ % 163.32/23.38 | | | (app(v3, v5) = nil) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = % 163.32/23.38 | | | 0) & ssList(v4) = v6)))) % 163.32/23.38 | | | % 163.32/23.38 | | | BETA: splitting (38) gives: % 163.32/23.38 | | | % 163.32/23.38 | | | Case 1: % 163.32/23.38 | | | | % 163.32/23.38 | | | | (53) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 163.32/23.38 | | | | % 163.32/23.38 | | | | REF_CLOSE: (1), (9), (53) are inconsistent by sub-proof #2. % 163.32/23.38 | | | | % 163.32/23.38 | | | Case 2: % 163.32/23.38 | | | | % 163.32/23.38 | | | | (54) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : % 163.32/23.38 | | | | ! [v2: any] : ( ~ (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: % 163.32/23.38 | | | | any] : ? [v4: any] : (leq(v1, v0) = v4 & ssItem(v1) = v3 % 163.32/23.38 | | | | & ( ~ (v3 = 0) | ! [v5: $i] : ( ~ (ssList(v5) = 0) | ~ % 163.32/23.38 | | | | $i(v5) | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 163.32/23.38 | | | | (cons(v0, v6) = v7) | ~ (app(v5, v7) = v8) | ~ % 163.32/23.38 | | | | $i(v6) | ? [v9: int] : ( ~ (v9 = 0) & ssList(v6) = % 163.32/23.38 | | | | v9) | ! [v9: $i] : ! [v10: $i] : (v4 = 0 | v2 = % 163.32/23.38 | | | | 0 | ~ (cons(v1, v9) = v10) | ~ (app(v8, v10) = % 163.32/23.38 | | | | nil) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) % 163.32/23.38 | | | | & ssList(v9) = v11)))))))) % 163.32/23.38 | | | | % 163.32/23.38 | | | | GROUND_INST: instantiating (8) with 0, all_317_1, all_146_2, simplifying % 163.32/23.38 | | | | with (26), (44) gives: % 163.32/23.38 | | | | (55) all_317_1 = 0 % 163.32/23.38 | | | | % 163.32/23.38 | | | | GROUND_INST: instantiating (10) with all_146_0, all_317_0, all_146_2, % 163.32/23.38 | | | | all_143_0, simplifying with (28), (45) gives: % 163.32/23.38 | | | | (56) all_317_0 = all_146_0 % 163.32/23.38 | | | | % 163.32/23.38 | | | | BETA: splitting (29) gives: % 163.32/23.38 | | | | % 163.32/23.38 | | | | Case 1: % 163.32/23.38 | | | | | % 163.32/23.38 | | | | | (57) all_146_1 = 0 % 163.32/23.38 | | | | | % 163.32/23.38 | | | | | REDUCE: (27), (57) imply: % 163.32/23.38 | | | | | (58) memberP(all_139_0, all_146_2) = 0 % 163.32/23.38 | | | | | % 163.32/23.38 | | | | | BETA: splitting (46) gives: % 163.32/23.38 | | | | | % 163.32/23.38 | | | | | Case 1: % 163.32/23.38 | | | | | | % 163.32/23.38 | | | | | | (59) ~ (all_317_1 = 0) % 163.32/23.38 | | | | | | % 163.32/23.38 | | | | | | REDUCE: (55), (59) imply: % 163.32/23.38 | | | | | | (60) $false % 163.32/23.38 | | | | | | % 163.32/23.38 | | | | | | CLOSE: (60) is inconsistent. % 163.32/23.38 | | | | | | % 163.32/23.38 | | | | | Case 2: % 163.32/23.38 | | | | | | % 163.32/23.39 | | | | | | (61) ( ~ (all_317_0 = 0) | all_146_1 = 0 | ? [v0: any] : ( ~ (v0 % 163.32/23.39 | | | | | | = all_146_2) & leq(v0, all_146_2) = 0 & % 163.32/23.39 | | | | | | memberP(all_143_0, v0) = 0 & ssItem(v0) = 0 & $i(v0))) & % 163.32/23.39 | | | | | | ( ~ (all_146_1 = 0) | (all_317_0 = 0 & ! [v0: any] : (v0 = % 163.32/23.39 | | | | | | all_146_2 | ~ (memberP(all_143_0, v0) = 0) | ~ % 163.32/23.39 | | | | | | $i(v0) | ? [v1: any] : ? [v2: any] : (leq(v0, % 163.32/23.39 | | | | | | all_146_2) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | % 163.32/23.39 | | | | | | ~ (v1 = 0)))))) % 163.32/23.39 | | | | | | % 163.32/23.39 | | | | | | ALPHA: (61) implies: % 163.32/23.39 | | | | | | (62) ~ (all_146_1 = 0) | (all_317_0 = 0 & ! [v0: any] : (v0 = % 163.32/23.39 | | | | | | all_146_2 | ~ (memberP(all_143_0, v0) = 0) | ~ $i(v0) % 163.32/23.39 | | | | | | | ? [v1: any] : ? [v2: any] : (leq(v0, all_146_2) = v2 % 163.32/23.39 | | | | | | & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))) % 163.32/23.39 | | | | | | % 163.32/23.39 | | | | | | BETA: splitting (62) gives: % 163.32/23.39 | | | | | | % 163.32/23.39 | | | | | | Case 1: % 163.32/23.39 | | | | | | | % 163.32/23.39 | | | | | | | (63) ~ (all_146_1 = 0) % 163.32/23.39 | | | | | | | % 163.32/23.39 | | | | | | | REDUCE: (57), (63) imply: % 163.32/23.39 | | | | | | | (64) $false % 163.32/23.39 | | | | | | | % 163.32/23.39 | | | | | | | CLOSE: (64) is inconsistent. % 163.32/23.39 | | | | | | | % 163.32/23.39 | | | | | | Case 2: % 163.32/23.39 | | | | | | | % 163.32/23.39 | | | | | | | (65) all_317_0 = 0 & ! [v0: any] : (v0 = all_146_2 | ~ % 163.32/23.39 | | | | | | | (memberP(all_143_0, v0) = 0) | ~ $i(v0) | ? [v1: any] % 163.32/23.39 | | | | | | | : ? [v2: any] : (leq(v0, all_146_2) = v2 & ssItem(v0) = % 163.32/23.39 | | | | | | | v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 163.32/23.39 | | | | | | | % 163.32/23.39 | | | | | | | ALPHA: (65) implies: % 163.32/23.39 | | | | | | | (66) all_317_0 = 0 % 163.32/23.39 | | | | | | | (67) ! [v0: any] : (v0 = all_146_2 | ~ (memberP(all_143_0, % 163.32/23.39 | | | | | | | v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : % 163.32/23.39 | | | | | | | (leq(v0, all_146_2) = v2 & ssItem(v0) = v1 & ( ~ (v2 = % 163.32/23.39 | | | | | | | 0) | ~ (v1 = 0)))) % 163.32/23.39 | | | | | | | % 163.32/23.39 | | | | | | | COMBINE_EQS: (56), (66) imply: % 163.32/23.39 | | | | | | | (68) all_146_0 = 0 % 163.32/23.39 | | | | | | | % 163.32/23.39 | | | | | | | BETA: splitting (42) gives: % 163.32/23.39 | | | | | | | % 163.32/23.39 | | | | | | | Case 1: % 163.32/23.39 | | | | | | | | % 163.32/23.39 | | | | | | | | (69) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_146_2) = v0) % 163.32/23.39 | | | | | | | | % 163.32/23.39 | | | | | | | | DELTA: instantiating (69) with fresh symbol all_438_0 gives: % 163.32/23.39 | | | | | | | | (70) ~ (all_438_0 = 0) & ssItem(all_146_2) = all_438_0 % 163.32/23.39 | | | | | | | | % 163.32/23.39 | | | | | | | | REF_CLOSE: (8), (26), (30), (68), (69), (70) are inconsistent by % 163.32/23.39 | | | | | | | | sub-proof #1. % 163.32/23.39 | | | | | | | | % 163.32/23.39 | | | | | | | Case 2: % 163.32/23.39 | | | | | | | | % 163.70/23.39 | | | | | | | | (71) ( ~ (all_146_1 = 0) | ? [v0: $i] : (ssList(v0) = 0 & % 163.70/23.39 | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : (ssList(v1) = 0 % 163.70/23.39 | | | | | | | | & cons(all_146_2, v1) = v2 & app(v0, v2) = % 163.70/23.39 | | | | | | | | all_139_0 & $i(v2) & $i(v1)))) & (all_146_1 = 0 | % 163.70/23.39 | | | | | | | | ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! % 163.70/23.39 | | | | | | | | [v1: $i] : ! [v2: $i] : ( ~ (cons(all_146_2, v1) = % 163.70/23.39 | | | | | | | | v2) | ~ (app(v0, v2) = all_139_0) | ~ $i(v1) | % 163.70/23.39 | | | | | | | | ? [v3: int] : ( ~ (v3 = 0) & ssList(v1) = v3)))) % 163.70/23.39 | | | | | | | | % 163.70/23.39 | | | | | | | | ALPHA: (71) implies: % 163.70/23.39 | | | | | | | | (72) ~ (all_146_1 = 0) | ? [v0: $i] : (ssList(v0) = 0 & % 163.70/23.39 | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : (ssList(v1) = 0 & % 163.70/23.39 | | | | | | | | cons(all_146_2, v1) = v2 & app(v0, v2) = all_139_0 & % 163.70/23.39 | | | | | | | | $i(v2) & $i(v1))) % 163.70/23.39 | | | | | | | | % 163.70/23.39 | | | | | | | | BETA: splitting (30) gives: % 163.70/23.39 | | | | | | | | % 163.70/23.39 | | | | | | | | Case 1: % 163.70/23.39 | | | | | | | | | % 163.70/23.39 | | | | | | | | | (73) ~ (all_146_0 = 0) % 163.70/23.39 | | | | | | | | | % 163.70/23.39 | | | | | | | | | REDUCE: (68), (73) imply: % 163.70/23.39 | | | | | | | | | (74) $false % 163.70/23.39 | | | | | | | | | % 163.70/23.39 | | | | | | | | | CLOSE: (74) is inconsistent. % 163.70/23.39 | | | | | | | | | % 163.70/23.39 | | | | | | | | Case 2: % 163.70/23.39 | | | | | | | | | % 163.70/23.39 | | | | | | | | | (75) ~ (all_146_1 = 0) | ? [v0: any] : ( ~ (v0 = % 163.70/23.39 | | | | | | | | | all_146_2) & leq(v0, all_146_2) = 0 & % 163.70/23.39 | | | | | | | | | memberP(all_143_0, v0) = 0 & ssItem(v0) = 0 & % 163.70/23.39 | | | | | | | | | $i(v0)) % 163.70/23.39 | | | | | | | | | % 163.70/23.39 | | | | | | | | | BETA: splitting (40) gives: % 163.70/23.39 | | | | | | | | | % 163.70/23.39 | | | | | | | | | Case 1: % 163.70/23.39 | | | | | | | | | | % 163.70/23.39 | | | | | | | | | | (76) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_146_2) = % 163.70/23.39 | | | | | | | | | | v0) % 163.70/23.39 | | | | | | | | | | % 163.70/23.39 | | | | | | | | | | DELTA: instantiating (76) with fresh symbol all_443_0 gives: % 163.70/23.39 | | | | | | | | | | (77) ~ (all_443_0 = 0) & ssItem(all_146_2) = all_443_0 % 163.70/23.39 | | | | | | | | | | % 163.70/23.39 | | | | | | | | | | ALPHA: (77) implies: % 163.70/23.39 | | | | | | | | | | (78) ~ (all_443_0 = 0) % 163.70/23.39 | | | | | | | | | | (79) ssItem(all_146_2) = all_443_0 % 163.70/23.39 | | | | | | | | | | % 163.70/23.39 | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_443_0, all_146_2, % 163.70/23.39 | | | | | | | | | | simplifying with (26), (79) gives: % 163.70/23.39 | | | | | | | | | | (80) all_443_0 = 0 % 163.70/23.39 | | | | | | | | | | % 163.70/23.39 | | | | | | | | | | REDUCE: (78), (80) imply: % 163.70/23.39 | | | | | | | | | | (81) $false % 163.70/23.39 | | | | | | | | | | % 163.70/23.39 | | | | | | | | | | CLOSE: (81) is inconsistent. % 163.70/23.39 | | | | | | | | | | % 163.70/23.39 | | | | | | | | | Case 2: % 163.70/23.39 | | | | | | | | | | % 163.70/23.39 | | | | | | | | | | (82) ( ~ (all_146_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 % 163.70/23.39 | | | | | | | | | | & $i(v0) & ? [v1: $i] : ? [v2: $i] : % 163.70/23.39 | | | | | | | | | | (ssList(v1) = 0 & cons(all_146_2, v1) = v2 & % 163.70/23.39 | | | | | | | | | | app(v0, v2) = all_143_0 & $i(v2) & $i(v1)))) & % 163.70/23.39 | | | | | | | | | | (all_146_0 = 0 | ! [v0: $i] : ( ~ (ssList(v0) = 0) % 163.70/23.39 | | | | | | | | | | | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( ~ % 163.70/23.39 | | | | | | | | | | (cons(all_146_2, v1) = v2) | ~ (app(v0, v2) = % 163.70/23.39 | | | | | | | | | | all_143_0) | ~ $i(v1) | ? [v3: int] : ( ~ % 163.70/23.39 | | | | | | | | | | (v3 = 0) & ssList(v1) = v3)))) % 163.70/23.39 | | | | | | | | | | % 163.70/23.39 | | | | | | | | | | ALPHA: (82) implies: % 163.70/23.40 | | | | | | | | | | (83) ~ (all_146_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & % 163.70/23.40 | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : (ssList(v1) = % 163.70/23.40 | | | | | | | | | | 0 & cons(all_146_2, v1) = v2 & app(v0, v2) = % 163.70/23.40 | | | | | | | | | | all_143_0 & $i(v2) & $i(v1))) % 163.70/23.40 | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | BETA: splitting (72) gives: % 163.70/23.40 | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | Case 1: % 163.70/23.40 | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | (84) ~ (all_146_1 = 0) % 163.70/23.40 | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | REDUCE: (57), (84) imply: % 163.70/23.40 | | | | | | | | | | | (85) $false % 163.70/23.40 | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | CLOSE: (85) is inconsistent. % 163.70/23.40 | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | Case 2: % 163.70/23.40 | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | (86) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: % 163.70/23.40 | | | | | | | | | | | $i] : ? [v2: $i] : (ssList(v1) = 0 & % 163.70/23.40 | | | | | | | | | | | cons(all_146_2, v1) = v2 & app(v0, v2) = % 163.70/23.40 | | | | | | | | | | | all_139_0 & $i(v2) & $i(v1))) % 163.70/23.40 | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | DELTA: instantiating (86) with fresh symbol all_445_0 % 163.70/23.40 | | | | | | | | | | | gives: % 163.70/23.40 | | | | | | | | | | | (87) ssList(all_445_0) = 0 & $i(all_445_0) & ? [v0: % 163.70/23.40 | | | | | | | | | | | $i] : ? [v1: $i] : (ssList(v0) = 0 & % 163.70/23.40 | | | | | | | | | | | cons(all_146_2, v0) = v1 & app(all_445_0, v1) = % 163.70/23.40 | | | | | | | | | | | all_139_0 & $i(v1) & $i(v0)) % 163.70/23.40 | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | ALPHA: (87) implies: % 163.70/23.40 | | | | | | | | | | | (88) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & % 163.70/23.40 | | | | | | | | | | | cons(all_146_2, v0) = v1 & app(all_445_0, v1) = % 163.70/23.40 | | | | | | | | | | | all_139_0 & $i(v1) & $i(v0)) % 163.70/23.40 | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | DELTA: instantiating (88) with fresh symbols all_447_0, % 163.70/23.40 | | | | | | | | | | | all_447_1 gives: % 163.70/23.40 | | | | | | | | | | | (89) ssList(all_447_1) = 0 & cons(all_146_2, all_447_1) % 163.70/23.40 | | | | | | | | | | | = all_447_0 & app(all_445_0, all_447_0) = % 163.70/23.40 | | | | | | | | | | | all_139_0 & $i(all_447_0) & $i(all_447_1) % 163.70/23.40 | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | ALPHA: (89) implies: % 163.70/23.40 | | | | | | | | | | | (90) $i(all_447_1) % 163.70/23.40 | | | | | | | | | | | (91) cons(all_146_2, all_447_1) = all_447_0 % 163.70/23.40 | | | | | | | | | | | (92) ssList(all_447_1) = 0 % 163.70/23.40 | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | BETA: splitting (75) gives: % 163.70/23.40 | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | Case 1: % 163.70/23.40 | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | (93) ~ (all_146_1 = 0) % 163.70/23.40 | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | REDUCE: (57), (93) imply: % 163.70/23.40 | | | | | | | | | | | | (94) $false % 163.70/23.40 | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | CLOSE: (94) is inconsistent. % 163.70/23.40 | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | Case 2: % 163.70/23.40 | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | (95) ? [v0: any] : ( ~ (v0 = all_146_2) & leq(v0, % 163.70/23.40 | | | | | | | | | | | | all_146_2) = 0 & memberP(all_143_0, v0) = 0 & % 163.70/23.40 | | | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 163.70/23.40 | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | DELTA: instantiating (95) with fresh symbol all_453_0 % 163.70/23.40 | | | | | | | | | | | | gives: % 163.70/23.40 | | | | | | | | | | | | (96) ~ (all_453_0 = all_146_2) & leq(all_453_0, % 163.70/23.40 | | | | | | | | | | | | all_146_2) = 0 & memberP(all_143_0, all_453_0) = % 163.70/23.40 | | | | | | | | | | | | 0 & ssItem(all_453_0) = 0 & $i(all_453_0) % 163.70/23.40 | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | ALPHA: (96) implies: % 163.70/23.40 | | | | | | | | | | | | (97) ~ (all_453_0 = all_146_2) % 163.70/23.40 | | | | | | | | | | | | (98) $i(all_453_0) % 163.70/23.40 | | | | | | | | | | | | (99) ssItem(all_453_0) = 0 % 163.70/23.40 | | | | | | | | | | | | (100) memberP(all_143_0, all_453_0) = 0 % 163.70/23.40 | | | | | | | | | | | | (101) leq(all_453_0, all_146_2) = 0 % 163.70/23.40 | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | BETA: splitting (83) gives: % 163.70/23.40 | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | Case 1: % 163.70/23.40 | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | (102) ~ (all_146_0 = 0) % 163.70/23.40 | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | REDUCE: (68), (102) imply: % 163.70/23.40 | | | | | | | | | | | | | (103) $false % 163.70/23.40 | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | CLOSE: (103) is inconsistent. % 163.70/23.40 | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | Case 2: % 163.70/23.40 | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | (104) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: % 163.70/23.40 | | | | | | | | | | | | | $i] : ? [v2: $i] : (ssList(v1) = 0 & % 163.70/23.40 | | | | | | | | | | | | | cons(all_146_2, v1) = v2 & app(v0, v2) = % 163.70/23.40 | | | | | | | | | | | | | all_143_0 & $i(v2) & $i(v1))) % 163.70/23.40 | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | DELTA: instantiating (104) with fresh symbol all_458_0 % 163.70/23.40 | | | | | | | | | | | | | gives: % 163.70/23.40 | | | | | | | | | | | | | (105) ssList(all_458_0) = 0 & $i(all_458_0) & ? [v0: % 163.70/23.40 | | | | | | | | | | | | | $i] : ? [v1: $i] : (ssList(v0) = 0 & % 163.70/23.40 | | | | | | | | | | | | | cons(all_146_2, v0) = v1 & app(all_458_0, v1) = % 163.70/23.40 | | | | | | | | | | | | | all_143_0 & $i(v1) & $i(v0)) % 163.70/23.40 | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | ALPHA: (105) implies: % 163.70/23.40 | | | | | | | | | | | | | (106) $i(all_458_0) % 163.70/23.40 | | | | | | | | | | | | | (107) ssList(all_458_0) = 0 % 163.70/23.40 | | | | | | | | | | | | | (108) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & % 163.70/23.40 | | | | | | | | | | | | | cons(all_146_2, v0) = v1 & app(all_458_0, v1) = % 163.70/23.40 | | | | | | | | | | | | | all_143_0 & $i(v1) & $i(v0)) % 163.70/23.40 | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | DELTA: instantiating (108) with fresh symbols all_460_0, % 163.70/23.40 | | | | | | | | | | | | | all_460_1 gives: % 163.70/23.40 | | | | | | | | | | | | | (109) ssList(all_460_1) = 0 & cons(all_146_2, all_460_1) % 163.70/23.40 | | | | | | | | | | | | | = all_460_0 & app(all_458_0, all_460_0) = % 163.70/23.40 | | | | | | | | | | | | | all_143_0 & $i(all_460_0) & $i(all_460_1) % 163.70/23.40 | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | ALPHA: (109) implies: % 163.70/23.40 | | | | | | | | | | | | | (110) $i(all_460_1) % 163.70/23.40 | | | | | | | | | | | | | (111) app(all_458_0, all_460_0) = all_143_0 % 163.70/23.40 | | | | | | | | | | | | | (112) cons(all_146_2, all_460_1) = all_460_0 % 163.70/23.40 | | | | | | | | | | | | | (113) ssList(all_460_1) = 0 % 163.70/23.40 | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | BETA: splitting (32) gives: % 163.70/23.40 | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | Case 1: % 163.70/23.40 | | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | | (114) all_139_0 = nil % 163.70/23.40 | | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | | REDUCE: (58), (114) imply: % 163.70/23.40 | | | | | | | | | | | | | | (115) memberP(nil, all_146_2) = 0 % 163.70/23.40 | | | | | | | | | | | | | | % 163.70/23.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (48) with all_453_0, simplifying % 163.70/23.40 | | | | | | | | | | | | | | with (98), (99) gives: % 163.70/23.40 | | | | | | | | | | | | | | (116) ! [v0: $i] : ! [v1: any] : ( ~ (leq(all_453_0, % 163.70/23.40 | | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 163.70/23.41 | | | | | | | | | | | | | | [v3: any] : (leq(v0, all_453_0) = v3 & % 163.70/23.41 | | | | | | | | | | | | | | ssItem(v0) = v2 & ( ~ (v2 = 0) | ! [v4: $i] : % 163.70/23.41 | | | | | | | | | | | | | | ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 163.70/23.41 | | | | | | | | | | | | | | $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 163.70/23.41 | | | | | | | | | | | | | | (cons(all_453_0, v5) = v6) | ~ (app(v4, % 163.70/23.41 | | | | | | | | | | | | | | v6) = v7) | ~ $i(v5) | ? [v8: int] % 163.70/23.41 | | | | | | | | | | | | | | : ( ~ (v8 = 0) & ssList(v5) = v8) | ! % 163.70/23.41 | | | | | | | | | | | | | | [v8: $i] : ! [v9: $i] : ( ~ (v3 = 0) | % 163.70/23.41 | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (cons(v0, v8) = v9) | % 163.70/23.41 | | | | | | | | | | | | | | ~ (app(v7, v9) = nil) | ~ $i(v8) | ? % 163.70/23.41 | | | | | | | | | | | | | | [v10: int] : ( ~ (v10 = 0) & % 163.70/23.41 | | | | | | | | | | | | | | ssList(v8) = v10))))))) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (54) with all_453_0, simplifying % 163.70/23.41 | | | | | | | | | | | | | | with (98), (99) gives: % 163.70/23.41 | | | | | | | | | | | | | | (117) ! [v0: $i] : ! [v1: any] : ( ~ (leq(all_453_0, % 163.70/23.41 | | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 163.70/23.41 | | | | | | | | | | | | | | [v3: any] : (leq(v0, all_453_0) = v3 & % 163.70/23.41 | | | | | | | | | | | | | | ssItem(v0) = v2 & ( ~ (v2 = 0) | ! [v4: $i] : % 163.70/23.41 | | | | | | | | | | | | | | ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 163.70/23.41 | | | | | | | | | | | | | | $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 163.70/23.41 | | | | | | | | | | | | | | (cons(all_453_0, v5) = v6) | ~ (app(v4, % 163.70/23.41 | | | | | | | | | | | | | | v6) = v7) | ~ $i(v5) | ? [v8: int] % 163.70/23.41 | | | | | | | | | | | | | | : ( ~ (v8 = 0) & ssList(v5) = v8) | ! % 163.70/23.41 | | | | | | | | | | | | | | [v8: $i] : ! [v9: $i] : (v3 = 0 | v1 = % 163.70/23.41 | | | | | | | | | | | | | | 0 | ~ (cons(v0, v8) = v9) | ~ % 163.70/23.41 | | | | | | | | | | | | | | (app(v7, v9) = nil) | ~ $i(v8) | ? % 163.70/23.41 | | | | | | | | | | | | | | [v10: int] : ( ~ (v10 = 0) & % 163.70/23.41 | | | | | | | | | | | | | | ssList(v8) = v10))))))) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (ax25) with all_447_1, simplifying % 163.70/23.41 | | | | | | | | | | | | | | with (90), (92) gives: % 163.70/23.41 | | | | | | | | | | | | | | (118) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, % 163.70/23.41 | | | | | | | | | | | | | | all_447_1) = v1) | ~ $i(v0) | ? [v2: any] % 163.70/23.41 | | | | | | | | | | | | | | : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & % 163.70/23.41 | | | | | | | | | | | | | | $i(v3) & ( ~ (v2 = 0) | v3 = all_447_1))) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (ax23) with all_447_1, simplifying % 163.70/23.41 | | | | | | | | | | | | | | with (90), (92) gives: % 163.70/23.41 | | | | | | | | | | | | | | (119) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, % 163.70/23.41 | | | | | | | | | | | | | | all_447_1) = v1) | ~ $i(v0) | ? [v2: any] % 163.70/23.41 | | | | | | | | | | | | | | : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & % 163.70/23.41 | | | | | | | | | | | | | | $i(v3) & ( ~ (v2 = 0) | v3 = v0))) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (ax16) with all_447_1, simplifying % 163.70/23.41 | | | | | | | | | | | | | | with (90), (92) gives: % 163.70/23.41 | | | | | | | | | | | | | | (120) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, % 163.70/23.41 | | | | | | | | | | | | | | all_447_1) = v1) | ~ $i(v0) | ? [v2: any] % 163.70/23.41 | | | | | | | | | | | | | | : ? [v3: any] : (ssList(v1) = v3 & ssItem(v0) = % 163.70/23.41 | | | | | | | | | | | | | | v2 & ( ~ (v2 = 0) | v3 = 0))) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (ax25) with all_460_1, simplifying % 163.70/23.41 | | | | | | | | | | | | | | with (110), (113) gives: % 163.70/23.41 | | | | | | | | | | | | | | (121) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, % 163.70/23.41 | | | | | | | | | | | | | | all_460_1) = v1) | ~ $i(v0) | ? [v2: any] % 163.70/23.41 | | | | | | | | | | | | | | : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & % 163.70/23.41 | | | | | | | | | | | | | | $i(v3) & ( ~ (v2 = 0) | v3 = all_460_1))) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (ax23) with all_460_1, simplifying % 163.70/23.41 | | | | | | | | | | | | | | with (110), (113) gives: % 163.70/23.41 | | | | | | | | | | | | | | (122) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, % 163.70/23.41 | | | | | | | | | | | | | | all_460_1) = v1) | ~ $i(v0) | ? [v2: any] % 163.70/23.41 | | | | | | | | | | | | | | : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & % 163.70/23.41 | | | | | | | | | | | | | | $i(v3) & ( ~ (v2 = 0) | v3 = v0))) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (ax16) with all_460_1, simplifying % 163.70/23.41 | | | | | | | | | | | | | | with (110), (113) gives: % 163.70/23.41 | | | | | | | | | | | | | | (123) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, % 163.70/23.41 | | | | | | | | | | | | | | all_460_1) = v1) | ~ $i(v0) | ? [v2: any] % 163.70/23.41 | | | | | | | | | | | | | | : ? [v3: any] : (ssList(v1) = v3 & ssItem(v0) = % 163.70/23.41 | | | | | | | | | | | | | | v2 & ( ~ (v2 = 0) | v3 = 0))) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_146_2, simplifying with % 163.70/23.41 | | | | | | | | | | | | | | (25), (115) gives: % 163.70/23.41 | | | | | | | | | | | | | | (124) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_146_2) = % 163.70/23.41 | | | | | | | | | | | | | | v0) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (122) with all_146_2, all_460_0, % 163.70/23.41 | | | | | | | | | | | | | | simplifying with (25), (112) gives: % 163.70/23.41 | | | | | | | | | | | | | | (125) ? [v0: any] : ? [v1: $i] : (hd(all_460_0) = v1 & % 163.70/23.41 | | | | | | | | | | | | | | ssItem(all_146_2) = v0 & $i(v1) & ( ~ (v0 = 0) | % 163.70/23.41 | | | | | | | | | | | | | | v1 = all_146_2)) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (121) with all_146_2, all_460_0, % 163.70/23.41 | | | | | | | | | | | | | | simplifying with (25), (112) gives: % 163.70/23.41 | | | | | | | | | | | | | | (126) ? [v0: any] : ? [v1: $i] : (tl(all_460_0) = v1 & % 163.70/23.41 | | | | | | | | | | | | | | ssItem(all_146_2) = v0 & $i(v1) & ( ~ (v0 = 0) | % 163.70/23.41 | | | | | | | | | | | | | | v1 = all_460_1)) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (117) with all_146_2, 0, simplifying % 163.70/23.41 | | | | | | | | | | | | | | with (25), (101) gives: % 163.70/23.41 | | | | | | | | | | | | | | (127) ? [v0: MultipleValueBool] : ? [v1: % 163.70/23.41 | | | | | | | | | | | | | | MultipleValueBool] : (leq(all_146_2, all_453_0) % 163.70/23.41 | | | | | | | | | | | | | | = v1 & ssItem(all_146_2) = v0) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (116) with all_146_2, 0, simplifying % 163.70/23.41 | | | | | | | | | | | | | | with (25), (101) gives: % 163.70/23.41 | | | | | | | | | | | | | | (128) ? [v0: any] : ? [v1: any] : (leq(all_146_2, % 163.70/23.41 | | | | | | | | | | | | | | all_453_0) = v1 & ssItem(all_146_2) = v0 & ( ~ % 163.70/23.41 | | | | | | | | | | | | | | (v0 = 0) | ! [v2: $i] : ( ~ (ssList(v2) = 0) % 163.70/23.41 | | | | | | | | | | | | | | | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! % 163.70/23.41 | | | | | | | | | | | | | | [v5: $i] : ( ~ (cons(all_453_0, v3) = v4) | % 163.70/23.41 | | | | | | | | | | | | | | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: % 163.70/23.41 | | | | | | | | | | | | | | int] : ( ~ (v6 = 0) & ssList(v3) = v6) | % 163.70/23.41 | | | | | | | | | | | | | | ! [v6: $i] : ! [v7: $i] : ( ~ (v1 = 0) | % 163.70/23.41 | | | | | | | | | | | | | | ~ (cons(all_146_2, v6) = v7) | ~ % 163.70/23.41 | | | | | | | | | | | | | | (app(v5, v7) = nil) | ~ $i(v6) | ? % 163.70/23.41 | | | | | | | | | | | | | | [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 163.70/23.41 | | | | | | | | | | | | | | v8)))))) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (123) with all_146_2, all_460_0, % 163.70/23.41 | | | | | | | | | | | | | | simplifying with (25), (112) gives: % 163.70/23.41 | | | | | | | | | | | | | | (129) ? [v0: any] : ? [v1: any] : (ssList(all_460_0) = % 163.70/23.41 | | | | | | | | | | | | | | v1 & ssItem(all_146_2) = v0 & ( ~ (v0 = 0) | v1 % 163.70/23.41 | | | | | | | | | | | | | | = 0)) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (120) with all_146_2, all_447_0, % 163.70/23.41 | | | | | | | | | | | | | | simplifying with (25), (91) gives: % 163.70/23.41 | | | | | | | | | | | | | | (130) ? [v0: any] : ? [v1: any] : (ssList(all_447_0) = % 163.70/23.41 | | | | | | | | | | | | | | v1 & ssItem(all_146_2) = v0 & ( ~ (v0 = 0) | v1 % 163.70/23.41 | | | | | | | | | | | | | | = 0)) % 163.70/23.41 | | | | | | | | | | | | | | % 163.70/23.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (119) with all_146_2, all_447_0, % 163.70/23.41 | | | | | | | | | | | | | | simplifying with (25), (91) gives: % 163.70/23.42 | | | | | | | | | | | | | | (131) ? [v0: any] : ? [v1: $i] : (hd(all_447_0) = v1 & % 163.70/23.42 | | | | | | | | | | | | | | ssItem(all_146_2) = v0 & $i(v1) & ( ~ (v0 = 0) | % 163.70/23.42 | | | | | | | | | | | | | | v1 = all_146_2)) % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (118) with all_146_2, all_447_0, % 163.70/23.42 | | | | | | | | | | | | | | simplifying with (25), (91) gives: % 163.70/23.42 | | | | | | | | | | | | | | (132) ? [v0: any] : ? [v1: $i] : (tl(all_447_0) = v1 & % 163.70/23.42 | | | | | | | | | | | | | | ssItem(all_146_2) = v0 & $i(v1) & ( ~ (v0 = 0) | % 163.70/23.42 | | | | | | | | | | | | | | v1 = all_447_1)) % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | DELTA: instantiating (124) with fresh symbol all_1053_0 % 163.70/23.42 | | | | | | | | | | | | | | gives: % 163.70/23.42 | | | | | | | | | | | | | | (133) ~ (all_1053_0 = 0) & ssItem(all_146_2) = % 163.70/23.42 | | | | | | | | | | | | | | all_1053_0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | ALPHA: (133) implies: % 163.70/23.42 | | | | | | | | | | | | | | (134) ~ (all_1053_0 = 0) % 163.70/23.42 | | | | | | | | | | | | | | (135) ssItem(all_146_2) = all_1053_0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | DELTA: instantiating (125) with fresh symbols all_1059_0, % 163.70/23.42 | | | | | | | | | | | | | | all_1059_1 gives: % 163.70/23.42 | | | | | | | | | | | | | | (136) hd(all_460_0) = all_1059_0 & ssItem(all_146_2) = % 163.70/23.42 | | | | | | | | | | | | | | all_1059_1 & $i(all_1059_0) & ( ~ (all_1059_1 = 0) % 163.70/23.42 | | | | | | | | | | | | | | | all_1059_0 = all_146_2) % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | ALPHA: (136) implies: % 163.70/23.42 | | | | | | | | | | | | | | (137) ssItem(all_146_2) = all_1059_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | DELTA: instantiating (126) with fresh symbols all_1061_0, % 163.70/23.42 | | | | | | | | | | | | | | all_1061_1 gives: % 163.70/23.42 | | | | | | | | | | | | | | (138) tl(all_460_0) = all_1061_0 & ssItem(all_146_2) = % 163.70/23.42 | | | | | | | | | | | | | | all_1061_1 & $i(all_1061_0) & ( ~ (all_1061_1 = 0) % 163.70/23.42 | | | | | | | | | | | | | | | all_1061_0 = all_460_1) % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | ALPHA: (138) implies: % 163.70/23.42 | | | | | | | | | | | | | | (139) ssItem(all_146_2) = all_1061_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | DELTA: instantiating (127) with fresh symbols all_1065_0, % 163.70/23.42 | | | | | | | | | | | | | | all_1065_1 gives: % 163.70/23.42 | | | | | | | | | | | | | | (140) leq(all_146_2, all_453_0) = all_1065_0 & % 163.70/23.42 | | | | | | | | | | | | | | ssItem(all_146_2) = all_1065_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | ALPHA: (140) implies: % 163.70/23.42 | | | | | | | | | | | | | | (141) ssItem(all_146_2) = all_1065_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | DELTA: instantiating (128) with fresh symbols all_1067_0, % 163.70/23.42 | | | | | | | | | | | | | | all_1067_1 gives: % 163.70/23.42 | | | | | | | | | | | | | | (142) leq(all_146_2, all_453_0) = all_1067_0 & % 163.70/23.42 | | | | | | | | | | | | | | ssItem(all_146_2) = all_1067_1 & ( ~ (all_1067_1 = % 163.70/23.42 | | | | | | | | | | | | | | 0) | ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ % 163.70/23.42 | | | | | | | | | | | | | | $i(v0) | ! [v1: $i] : ! [v2: $i] : ! [v3: % 163.70/23.42 | | | | | | | | | | | | | | $i] : ( ~ (cons(all_453_0, v1) = v2) | ~ % 163.70/23.42 | | | | | | | | | | | | | | (app(v0, v2) = v3) | ~ $i(v1) | ? [v4: % 163.70/23.42 | | | | | | | | | | | | | | int] : ( ~ (v4 = 0) & ssList(v1) = v4) | % 163.70/23.42 | | | | | | | | | | | | | | ! [v4: $i] : ! [v5: $i] : ( ~ (all_1067_0 = % 163.70/23.42 | | | | | | | | | | | | | | 0) | ~ (cons(all_146_2, v4) = v5) | ~ % 163.70/23.42 | | | | | | | | | | | | | | (app(v3, v5) = nil) | ~ $i(v4) | ? [v6: % 163.70/23.42 | | | | | | | | | | | | | | int] : ( ~ (v6 = 0) & ssList(v4) = % 163.70/23.42 | | | | | | | | | | | | | | v6))))) % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | ALPHA: (142) implies: % 163.70/23.42 | | | | | | | | | | | | | | (143) ssItem(all_146_2) = all_1067_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | DELTA: instantiating (129) with fresh symbols all_1069_0, % 163.70/23.42 | | | | | | | | | | | | | | all_1069_1 gives: % 163.70/23.42 | | | | | | | | | | | | | | (144) ssList(all_460_0) = all_1069_0 & ssItem(all_146_2) % 163.70/23.42 | | | | | | | | | | | | | | = all_1069_1 & ( ~ (all_1069_1 = 0) | all_1069_0 = % 163.70/23.42 | | | | | | | | | | | | | | 0) % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | ALPHA: (144) implies: % 163.70/23.42 | | | | | | | | | | | | | | (145) ssItem(all_146_2) = all_1069_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | DELTA: instantiating (130) with fresh symbols all_1071_0, % 163.70/23.42 | | | | | | | | | | | | | | all_1071_1 gives: % 163.70/23.42 | | | | | | | | | | | | | | (146) ssList(all_447_0) = all_1071_0 & ssItem(all_146_2) % 163.70/23.42 | | | | | | | | | | | | | | = all_1071_1 & ( ~ (all_1071_1 = 0) | all_1071_0 = % 163.70/23.42 | | | | | | | | | | | | | | 0) % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | ALPHA: (146) implies: % 163.70/23.42 | | | | | | | | | | | | | | (147) ssItem(all_146_2) = all_1071_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | DELTA: instantiating (131) with fresh symbols all_1075_0, % 163.70/23.42 | | | | | | | | | | | | | | all_1075_1 gives: % 163.70/23.42 | | | | | | | | | | | | | | (148) hd(all_447_0) = all_1075_0 & ssItem(all_146_2) = % 163.70/23.42 | | | | | | | | | | | | | | all_1075_1 & $i(all_1075_0) & ( ~ (all_1075_1 = 0) % 163.70/23.42 | | | | | | | | | | | | | | | all_1075_0 = all_146_2) % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | ALPHA: (148) implies: % 163.70/23.42 | | | | | | | | | | | | | | (149) ssItem(all_146_2) = all_1075_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | DELTA: instantiating (132) with fresh symbols all_1077_0, % 163.70/23.42 | | | | | | | | | | | | | | all_1077_1 gives: % 163.70/23.42 | | | | | | | | | | | | | | (150) tl(all_447_0) = all_1077_0 & ssItem(all_146_2) = % 163.70/23.42 | | | | | | | | | | | | | | all_1077_1 & $i(all_1077_0) & ( ~ (all_1077_1 = 0) % 163.70/23.42 | | | | | | | | | | | | | | | all_1077_0 = all_447_1) % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | ALPHA: (150) implies: % 163.70/23.42 | | | | | | | | | | | | | | (151) ssItem(all_146_2) = all_1077_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_1053_0, all_1065_1, % 163.70/23.42 | | | | | | | | | | | | | | all_146_2, simplifying with (135), (141) gives: % 163.70/23.42 | | | | | | | | | | | | | | (152) all_1065_1 = all_1053_0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_1075_1, all_146_2, % 163.70/23.42 | | | | | | | | | | | | | | simplifying with (26), (149) gives: % 163.70/23.42 | | | | | | | | | | | | | | (153) all_1075_1 = 0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_1069_1, all_1075_1, % 163.70/23.42 | | | | | | | | | | | | | | all_146_2, simplifying with (145), (149) gives: % 163.70/23.42 | | | | | | | | | | | | | | (154) all_1075_1 = all_1069_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_1067_1, all_1075_1, % 163.70/23.42 | | | | | | | | | | | | | | all_146_2, simplifying with (143), (149) gives: % 163.70/23.42 | | | | | | | | | | | | | | (155) all_1075_1 = all_1067_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_1071_1, all_1077_1, % 163.70/23.42 | | | | | | | | | | | | | | all_146_2, simplifying with (147), (151) gives: % 163.70/23.42 | | | | | | | | | | | | | | (156) all_1077_1 = all_1071_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_1067_1, all_1077_1, % 163.70/23.42 | | | | | | | | | | | | | | all_146_2, simplifying with (143), (151) gives: % 163.70/23.42 | | | | | | | | | | | | | | (157) all_1077_1 = all_1067_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_1065_1, all_1077_1, % 163.70/23.42 | | | | | | | | | | | | | | all_146_2, simplifying with (141), (151) gives: % 163.70/23.42 | | | | | | | | | | | | | | (158) all_1077_1 = all_1065_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_1061_1, all_1077_1, % 163.70/23.42 | | | | | | | | | | | | | | all_146_2, simplifying with (139), (151) gives: % 163.70/23.42 | | | | | | | | | | | | | | (159) all_1077_1 = all_1061_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_1059_1, all_1077_1, % 163.70/23.42 | | | | | | | | | | | | | | all_146_2, simplifying with (137), (151) gives: % 163.70/23.42 | | | | | | | | | | | | | | (160) all_1077_1 = all_1059_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (156), (160) imply: % 163.70/23.42 | | | | | | | | | | | | | | (161) all_1071_1 = all_1059_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (156), (159) imply: % 163.70/23.42 | | | | | | | | | | | | | | (162) all_1071_1 = all_1061_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (156), (158) imply: % 163.70/23.42 | | | | | | | | | | | | | | (163) all_1071_1 = all_1065_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (156), (157) imply: % 163.70/23.42 | | | | | | | | | | | | | | (164) all_1071_1 = all_1067_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (154), (155) imply: % 163.70/23.42 | | | | | | | | | | | | | | (165) all_1069_1 = all_1067_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (153), (154) imply: % 163.70/23.42 | | | | | | | | | | | | | | (166) all_1069_1 = 0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (162), (164) imply: % 163.70/23.42 | | | | | | | | | | | | | | (167) all_1067_1 = all_1061_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | SIMP: (167) implies: % 163.70/23.42 | | | | | | | | | | | | | | (168) all_1067_1 = all_1061_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (161), (162) imply: % 163.70/23.42 | | | | | | | | | | | | | | (169) all_1061_1 = all_1059_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (162), (163) imply: % 163.70/23.42 | | | | | | | | | | | | | | (170) all_1065_1 = all_1061_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | SIMP: (170) implies: % 163.70/23.42 | | | | | | | | | | | | | | (171) all_1065_1 = all_1061_1 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (165), (166) imply: % 163.70/23.42 | | | | | | | | | | | | | | (172) all_1067_1 = 0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | SIMP: (172) implies: % 163.70/23.42 | | | | | | | | | | | | | | (173) all_1067_1 = 0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (168), (173) imply: % 163.70/23.42 | | | | | | | | | | | | | | (174) all_1061_1 = 0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | SIMP: (174) implies: % 163.70/23.42 | | | | | | | | | | | | | | (175) all_1061_1 = 0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (152), (171) imply: % 163.70/23.42 | | | | | | | | | | | | | | (176) all_1061_1 = all_1053_0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | SIMP: (176) implies: % 163.70/23.42 | | | | | | | | | | | | | | (177) all_1061_1 = all_1053_0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (169), (177) imply: % 163.70/23.42 | | | | | | | | | | | | | | (178) all_1059_1 = all_1053_0 % 163.70/23.42 | | | | | | | | | | | | | | % 163.70/23.42 | | | | | | | | | | | | | | COMBINE_EQS: (169), (175) imply: % 163.70/23.43 | | | | | | | | | | | | | | (179) all_1059_1 = 0 % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | COMBINE_EQS: (178), (179) imply: % 163.70/23.43 | | | | | | | | | | | | | | (180) all_1053_0 = 0 % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | SIMP: (180) implies: % 163.70/23.43 | | | | | | | | | | | | | | (181) all_1053_0 = 0 % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | REDUCE: (134), (181) imply: % 163.70/23.43 | | | | | | | | | | | | | | (182) $false % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | CLOSE: (182) is inconsistent. % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | Case 2: % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | (183) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: % 163.70/23.43 | | | | | | | | | | | | | | $i] : (cons(v1, v0) = all_139_0 & ssItem(v1) = % 163.70/23.43 | | | | | | | | | | | | | | 0 & $i(v1))) % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | DELTA: instantiating (183) with fresh symbol all_484_0 % 163.70/23.43 | | | | | | | | | | | | | | gives: % 163.70/23.43 | | | | | | | | | | | | | | (184) ssList(all_484_0) = 0 & $i(all_484_0) & ? [v0: % 163.70/23.43 | | | | | | | | | | | | | | $i] : (cons(v0, all_484_0) = all_139_0 & % 163.70/23.43 | | | | | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | ALPHA: (184) implies: % 163.70/23.43 | | | | | | | | | | | | | | (185) ? [v0: $i] : (cons(v0, all_484_0) = all_139_0 & % 163.70/23.43 | | | | | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | DELTA: instantiating (185) with fresh symbol all_486_0 % 163.70/23.43 | | | | | | | | | | | | | | gives: % 163.70/23.43 | | | | | | | | | | | | | | (186) cons(all_486_0, all_484_0) = all_139_0 & % 163.70/23.43 | | | | | | | | | | | | | | ssItem(all_486_0) = 0 & $i(all_486_0) % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | ALPHA: (186) implies: % 163.70/23.43 | | | | | | | | | | | | | | (187) $i(all_486_0) % 163.70/23.43 | | | | | | | | | | | | | | (188) ssItem(all_486_0) = 0 % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | GROUND_INST: instantiating (51) with all_486_0, simplifying % 163.70/23.43 | | | | | | | | | | | | | | with (187), (188) gives: % 163.70/23.43 | | | | | | | | | | | | | | (189) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | % 163.70/23.43 | | | | | | | | | | | | | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 163.70/23.43 | | | | | | | | | | | | | | (cons(all_146_2, v1) = v2) | ~ (app(v0, v2) = % 163.70/23.43 | | | | | | | | | | | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = % 163.70/23.43 | | | | | | | | | | | | | | 0) & ssList(v1) = v4) | ! [v4: $i] : ! % 163.70/23.43 | | | | | | | | | | | | | | [v5: $i] : ( ~ (all_486_0 = all_146_2) | ~ % 163.70/23.43 | | | | | | | | | | | | | | (cons(all_146_2, v4) = v5) | ~ (app(v3, v5) % 163.70/23.43 | | | | | | | | | | | | | | = nil) | ~ $i(v4) | ? [v6: int] : ( ~ % 163.70/23.43 | | | | | | | | | | | | | | (v6 = 0) & ssList(v4) = v6)))) % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with all_458_0, simplifying % 163.70/23.43 | | | | | | | | | | | | | | with (106), (107) gives: % 163.70/23.43 | | | | | | | | | | | | | | (190) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 163.70/23.43 | | | | | | | | | | | | | | (cons(all_146_2, v0) = v1) | ~ (app(all_458_0, % 163.70/23.43 | | | | | | | | | | | | | | v1) = v2) | ~ $i(v0) | ? [v3: int] : ( ~ % 163.70/23.43 | | | | | | | | | | | | | | (v3 = 0) & ssList(v0) = v3) | ! [v3: $i] : ! % 163.70/23.43 | | | | | | | | | | | | | | [v4: $i] : ( ~ (all_146_2 = all_137_0) | ~ % 163.70/23.43 | | | | | | | | | | | | | | (cons(all_137_0, v3) = v4) | ~ (app(v2, v4) = % 163.70/23.43 | | | | | | | | | | | | | | nil) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = % 163.70/23.43 | | | | | | | | | | | | | | 0) & ssList(v3) = v5))) % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | GROUND_INST: instantiating (67) with all_453_0, simplifying % 163.70/23.43 | | | | | | | | | | | | | | with (98), (100) gives: % 163.70/23.43 | | | | | | | | | | | | | | (191) all_453_0 = all_146_2 | ? [v0: any] : ? [v1: % 163.70/23.43 | | | | | | | | | | | | | | any] : (leq(all_453_0, all_146_2) = v1 & % 163.70/23.43 | | | | | | | | | | | | | | ssItem(all_453_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 163.70/23.43 | | | | | | | | | | | | | | 0))) % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | GROUND_INST: instantiating (189) with all_458_0, simplifying % 163.70/23.43 | | | | | | | | | | | | | | with (106), (107) gives: % 163.70/23.43 | | | | | | | | | | | | | | (192) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 163.70/23.43 | | | | | | | | | | | | | | (cons(all_146_2, v0) = v1) | ~ (app(all_458_0, % 163.70/23.43 | | | | | | | | | | | | | | v1) = v2) | ~ $i(v0) | ? [v3: int] : ( ~ % 163.70/23.43 | | | | | | | | | | | | | | (v3 = 0) & ssList(v0) = v3) | ! [v3: $i] : ! % 163.70/23.43 | | | | | | | | | | | | | | [v4: $i] : ( ~ (all_486_0 = all_146_2) | ~ % 163.70/23.43 | | | | | | | | | | | | | | (cons(all_146_2, v3) = v4) | ~ (app(v2, v4) = % 163.70/23.43 | | | | | | | | | | | | | | nil) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = % 163.70/23.43 | | | | | | | | | | | | | | 0) & ssList(v3) = v5))) % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | GROUND_INST: instantiating (190) with all_460_1, all_460_0, % 163.70/23.43 | | | | | | | | | | | | | | all_143_0, simplifying with (110), (111), (112) % 163.70/23.43 | | | | | | | | | | | | | | gives: % 163.70/23.43 | | | | | | | | | | | | | | (193) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_460_1) = % 163.70/23.43 | | | | | | | | | | | | | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ (all_146_2 % 163.70/23.43 | | | | | | | | | | | | | | = all_137_0) | ~ (cons(all_137_0, v0) = v1) | % 163.70/23.43 | | | | | | | | | | | | | | ~ (app(all_143_0, v1) = nil) | ~ $i(v0) | ? % 163.70/23.43 | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | GROUND_INST: instantiating (192) with all_460_1, all_460_0, % 163.70/23.43 | | | | | | | | | | | | | | all_143_0, simplifying with (110), (111), (112) % 163.70/23.43 | | | | | | | | | | | | | | gives: % 163.70/23.43 | | | | | | | | | | | | | | (194) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_460_1) = % 163.70/23.43 | | | | | | | | | | | | | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ (all_486_0 % 163.70/23.43 | | | | | | | | | | | | | | = all_146_2) | ~ (cons(all_146_2, v0) = v1) | % 163.70/23.43 | | | | | | | | | | | | | | ~ (app(all_143_0, v1) = nil) | ~ $i(v0) | ? % 163.70/23.43 | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | BETA: splitting (191) gives: % 163.70/23.43 | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | Case 1: % 163.70/23.43 | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | (195) all_453_0 = all_146_2 % 163.70/23.43 | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | REDUCE: (97), (195) imply: % 163.70/23.43 | | | | | | | | | | | | | | | (196) $false % 163.70/23.43 | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 163.70/23.43 | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | Case 2: % 163.70/23.43 | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | (197) ? [v0: any] : ? [v1: any] : (leq(all_453_0, % 163.70/23.43 | | | | | | | | | | | | | | | all_146_2) = v1 & ssItem(all_453_0) = v0 & ( ~ % 163.70/23.43 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 163.70/23.43 | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 163.70/23.43 | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | Case 1: % 163.70/23.43 | | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | | (198) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_460_1) = % 163.70/23.43 | | | | | | | | | | | | | | | | v0) % 163.70/23.43 | | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | | DELTA: instantiating (198) with fresh symbol all_1489_0 % 163.70/23.43 | | | | | | | | | | | | | | | | gives: % 163.70/23.43 | | | | | | | | | | | | | | | | (199) ~ (all_1489_0 = 0) & ssList(all_460_1) = % 163.70/23.43 | | | | | | | | | | | | | | | | all_1489_0 % 163.70/23.43 | | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | | ALPHA: (199) implies: % 163.70/23.43 | | | | | | | | | | | | | | | | (200) ~ (all_1489_0 = 0) % 163.70/23.43 | | | | | | | | | | | | | | | | (201) ssList(all_460_1) = all_1489_0 % 163.70/23.43 | | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_1489_0, all_460_1, % 163.70/23.43 | | | | | | | | | | | | | | | | simplifying with (113), (201) gives: % 163.70/23.43 | | | | | | | | | | | | | | | | (202) all_1489_0 = 0 % 163.70/23.43 | | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | | REDUCE: (200), (202) imply: % 163.70/23.43 | | | | | | | | | | | | | | | | (203) $false % 163.70/23.43 | | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 163.70/23.43 | | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | Case 2: % 163.70/23.43 | | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | | DELTA: instantiating (197) with fresh symbols all_1488_0, % 163.70/23.43 | | | | | | | | | | | | | | | | all_1488_1 gives: % 163.70/23.43 | | | | | | | | | | | | | | | | (204) leq(all_453_0, all_146_2) = all_1488_0 & % 163.70/23.43 | | | | | | | | | | | | | | | | ssItem(all_453_0) = all_1488_1 & ( ~ (all_1488_0 = % 163.70/23.43 | | | | | | | | | | | | | | | | 0) | ~ (all_1488_1 = 0)) % 163.70/23.43 | | | | | | | | | | | | | | | | % 163.70/23.43 | | | | | | | | | | | | | | | | ALPHA: (204) implies: % 163.70/23.43 | | | | | | | | | | | | | | | | (205) ssItem(all_453_0) = all_1488_1 % 163.70/23.44 | | | | | | | | | | | | | | | | (206) leq(all_453_0, all_146_2) = all_1488_0 % 163.70/23.44 | | | | | | | | | | | | | | | | (207) ~ (all_1488_0 = 0) | ~ (all_1488_1 = 0) % 163.70/23.44 | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 163.70/23.44 | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | Case 1: % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | (208) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_460_1) = % 163.70/23.44 | | | | | | | | | | | | | | | | | v0) % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | DELTA: instantiating (208) with fresh symbol all_1527_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (209) ~ (all_1527_0 = 0) & ssList(all_460_1) = % 163.70/23.44 | | | | | | | | | | | | | | | | | all_1527_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | ALPHA: (209) implies: % 163.70/23.44 | | | | | | | | | | | | | | | | | (210) ~ (all_1527_0 = 0) % 163.70/23.44 | | | | | | | | | | | | | | | | | (211) ssList(all_460_1) = all_1527_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | DELTA: instantiating (208) with fresh symbol all_1529_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (212) ~ (all_1529_0 = 0) & ssList(all_460_1) = % 163.70/23.44 | | | | | | | | | | | | | | | | | all_1529_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | ALPHA: (212) implies: % 163.70/23.44 | | | | | | | | | | | | | | | | | (213) ssList(all_460_1) = all_1529_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | DELTA: instantiating (208) with fresh symbol all_1531_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (214) ~ (all_1531_0 = 0) & ssList(all_460_1) = % 163.70/23.44 | | | | | | | | | | | | | | | | | all_1531_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | ALPHA: (214) implies: % 163.70/23.44 | | | | | | | | | | | | | | | | | (215) ssList(all_460_1) = all_1531_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | DELTA: instantiating (208) with fresh symbol all_1533_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (216) ~ (all_1533_0 = 0) & ssList(all_460_1) = % 163.70/23.44 | | | | | | | | | | | | | | | | | all_1533_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | ALPHA: (216) implies: % 163.70/23.44 | | | | | | | | | | | | | | | | | (217) ssList(all_460_1) = all_1533_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | DELTA: instantiating (208) with fresh symbol all_1535_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (218) ~ (all_1535_0 = 0) & ssList(all_460_1) = % 163.70/23.44 | | | | | | | | | | | | | | | | | all_1535_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | ALPHA: (218) implies: % 163.70/23.44 | | | | | | | | | | | | | | | | | (219) ssList(all_460_1) = all_1535_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_1533_0, all_460_1, % 163.70/23.44 | | | | | | | | | | | | | | | | | simplifying with (113), (217) gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (220) all_1533_0 = 0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_1531_0, all_1533_0, % 163.70/23.44 | | | | | | | | | | | | | | | | | all_460_1, simplifying with (215), (217) gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (221) all_1533_0 = all_1531_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_1529_0, all_1533_0, % 163.70/23.44 | | | | | | | | | | | | | | | | | all_460_1, simplifying with (213), (217) gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (222) all_1533_0 = all_1529_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_1533_0, all_1535_0, % 163.70/23.44 | | | | | | | | | | | | | | | | | all_460_1, simplifying with (217), (219) gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (223) all_1535_0 = all_1533_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_1527_0, all_1535_0, % 163.70/23.44 | | | | | | | | | | | | | | | | | all_460_1, simplifying with (211), (219) gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (224) all_1535_0 = all_1527_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (224) imply: % 163.70/23.44 | | | | | | | | | | | | | | | | | (225) all_1533_0 = all_1527_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | SIMP: (225) implies: % 163.70/23.44 | | | | | | | | | | | | | | | | | (226) all_1533_0 = all_1527_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (226) imply: % 163.70/23.44 | | | | | | | | | | | | | | | | | (227) all_1531_0 = all_1527_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (220), (221) imply: % 163.70/23.44 | | | | | | | | | | | | | | | | | (228) all_1531_0 = 0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (222) imply: % 163.70/23.44 | | | | | | | | | | | | | | | | | (229) all_1531_0 = all_1529_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (228), (229) imply: % 163.70/23.44 | | | | | | | | | | | | | | | | | (230) all_1529_0 = 0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (229) imply: % 163.70/23.44 | | | | | | | | | | | | | | | | | (231) all_1529_0 = all_1527_0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (230), (231) imply: % 163.70/23.44 | | | | | | | | | | | | | | | | | (232) all_1527_0 = 0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | REDUCE: (210), (232) imply: % 163.70/23.44 | | | | | | | | | | | | | | | | | (233) $false % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent. % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | Case 2: % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_1488_1, all_453_0, % 163.70/23.44 | | | | | | | | | | | | | | | | | simplifying with (99), (205) gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (234) all_1488_1 = 0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_1488_0, all_146_2, % 163.70/23.44 | | | | | | | | | | | | | | | | | all_453_0, simplifying with (101), (206) gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | (235) all_1488_0 = 0 % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | BETA: splitting (207) gives: % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | Case 1: % 163.70/23.44 | | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | | (236) ~ (all_1488_0 = 0) % 163.70/23.44 | | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | | REDUCE: (235), (236) imply: % 163.70/23.44 | | | | | | | | | | | | | | | | | | (237) $false % 163.70/23.44 | | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | | CLOSE: (237) is inconsistent. % 163.70/23.44 | | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | Case 2: % 163.70/23.44 | | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | | (238) ~ (all_1488_1 = 0) % 163.70/23.44 | | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | | REDUCE: (234), (238) imply: % 163.70/23.44 | | | | | | | | | | | | | | | | | | (239) $false % 163.70/23.44 | | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent. % 163.70/23.44 | | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | | End of split % 163.70/23.44 | | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | | End of split % 163.70/23.44 | | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | | End of split % 163.70/23.44 | | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | | End of split % 163.70/23.44 | | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | | End of split % 163.70/23.44 | | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | | End of split % 163.70/23.44 | | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | | End of split % 163.70/23.44 | | | | | | | | | | | % 163.70/23.44 | | | | | | | | | | End of split % 163.70/23.44 | | | | | | | | | | % 163.70/23.44 | | | | | | | | | End of split % 163.70/23.44 | | | | | | | | | % 163.70/23.44 | | | | | | | | End of split % 163.70/23.44 | | | | | | | | % 163.70/23.44 | | | | | | | End of split % 163.70/23.44 | | | | | | | % 163.70/23.44 | | | | | | End of split % 163.70/23.44 | | | | | | % 163.70/23.44 | | | | | End of split % 163.70/23.44 | | | | | % 163.70/23.44 | | | | Case 2: % 163.70/23.44 | | | | | % 163.70/23.44 | | | | | (240) ~ (all_146_1 = 0) % 163.70/23.44 | | | | | (241) all_146_0 = 0 & ! [v0: any] : (v0 = all_146_2 | ~ % 163.70/23.44 | | | | | (memberP(all_143_0, v0) = 0) | ~ $i(v0) | ? [v1: any] : % 163.70/23.44 | | | | | ? [v2: any] : (leq(v0, all_146_2) = v2 & ssItem(v0) = v1 & % 163.70/23.44 | | | | | ( ~ (v2 = 0) | ~ (v1 = 0)))) % 163.70/23.44 | | | | | % 163.70/23.44 | | | | | ALPHA: (241) implies: % 163.70/23.44 | | | | | (242) all_146_0 = 0 % 163.70/23.44 | | | | | (243) ! [v0: any] : (v0 = all_146_2 | ~ (memberP(all_143_0, v0) = % 163.70/23.44 | | | | | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (leq(v0, % 163.70/23.44 | | | | | all_146_2) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ % 163.70/23.44 | | | | | (v1 = 0)))) % 163.70/23.44 | | | | | % 163.70/23.44 | | | | | COMBINE_EQS: (56), (242) imply: % 163.70/23.44 | | | | | (244) all_317_0 = 0 % 163.70/23.44 | | | | | % 163.70/23.44 | | | | | REDUCE: (28), (242) imply: % 163.70/23.44 | | | | | (245) memberP(all_143_0, all_146_2) = 0 % 163.70/23.44 | | | | | % 163.70/23.44 | | | | | BETA: splitting (40) gives: % 163.70/23.44 | | | | | % 163.70/23.44 | | | | | Case 1: % 163.70/23.44 | | | | | | % 163.70/23.44 | | | | | | (246) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_146_2) = v0) % 163.70/23.44 | | | | | | % 163.70/23.44 | | | | | | DELTA: instantiating (246) with fresh symbol all_438_0 gives: % 163.70/23.44 | | | | | | (247) ~ (all_438_0 = 0) & ssItem(all_146_2) = all_438_0 % 163.70/23.44 | | | | | | % 163.70/23.44 | | | | | | REF_CLOSE: (8), (26), (30), (242), (246), (247) are inconsistent by % 163.70/23.44 | | | | | | sub-proof #1. % 163.70/23.44 | | | | | | % 163.70/23.44 | | | | | Case 2: % 163.70/23.44 | | | | | | % 163.70/23.44 | | | | | | (248) ( ~ (all_146_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & % 163.70/23.44 | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : (ssList(v1) = 0 & % 163.70/23.44 | | | | | | cons(all_146_2, v1) = v2 & app(v0, v2) = all_143_0 & % 163.70/23.44 | | | | | | $i(v2) & $i(v1)))) & (all_146_0 = 0 | ! [v0: $i] : ( % 163.70/23.44 | | | | | | ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 163.70/23.44 | | | | | | $i] : ( ~ (cons(all_146_2, v1) = v2) | ~ (app(v0, % 163.70/23.44 | | | | | | v2) = all_143_0) | ~ $i(v1) | ? [v3: int] : ( ~ % 163.70/23.44 | | | | | | (v3 = 0) & ssList(v1) = v3)))) % 163.70/23.44 | | | | | | % 163.70/23.44 | | | | | | ALPHA: (248) implies: % 163.70/23.45 | | | | | | (249) ~ (all_146_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) % 163.70/23.45 | | | | | | & ? [v1: $i] : ? [v2: $i] : (ssList(v1) = 0 & % 163.70/23.45 | | | | | | cons(all_146_2, v1) = v2 & app(v0, v2) = all_143_0 & % 163.70/23.45 | | | | | | $i(v2) & $i(v1))) % 163.70/23.45 | | | | | | % 163.70/23.45 | | | | | | BETA: splitting (46) gives: % 163.70/23.45 | | | | | | % 163.70/23.45 | | | | | | Case 1: % 163.70/23.45 | | | | | | | % 163.70/23.45 | | | | | | | (250) ~ (all_317_1 = 0) % 163.70/23.45 | | | | | | | % 163.70/23.45 | | | | | | | REDUCE: (55), (250) imply: % 163.70/23.45 | | | | | | | (251) $false % 163.70/23.45 | | | | | | | % 163.70/23.45 | | | | | | | CLOSE: (251) is inconsistent. % 163.70/23.45 | | | | | | | % 163.70/23.45 | | | | | | Case 2: % 163.70/23.45 | | | | | | | % 163.70/23.45 | | | | | | | (252) ( ~ (all_317_0 = 0) | all_146_1 = 0 | ? [v0: any] : ( ~ % 163.70/23.45 | | | | | | | (v0 = all_146_2) & leq(v0, all_146_2) = 0 & % 163.70/23.45 | | | | | | | memberP(all_143_0, v0) = 0 & ssItem(v0) = 0 & % 163.70/23.45 | | | | | | | $i(v0))) & ( ~ (all_146_1 = 0) | (all_317_0 = 0 & ! % 163.70/23.45 | | | | | | | [v0: any] : (v0 = all_146_2 | ~ (memberP(all_143_0, % 163.70/23.45 | | | | | | | v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 163.70/23.45 | | | | | | | any] : (leq(v0, all_146_2) = v2 & ssItem(v0) = v1 % 163.70/23.45 | | | | | | | & ( ~ (v2 = 0) | ~ (v1 = 0)))))) % 163.70/23.45 | | | | | | | % 163.70/23.45 | | | | | | | ALPHA: (252) implies: % 163.70/23.45 | | | | | | | (253) ~ (all_317_0 = 0) | all_146_1 = 0 | ? [v0: any] : ( ~ % 163.70/23.45 | | | | | | | (v0 = all_146_2) & leq(v0, all_146_2) = 0 & % 163.70/23.45 | | | | | | | memberP(all_143_0, v0) = 0 & ssItem(v0) = 0 & $i(v0)) % 163.70/23.45 | | | | | | | % 163.70/23.45 | | | | | | | BETA: splitting (249) gives: % 163.70/23.45 | | | | | | | % 163.70/23.45 | | | | | | | Case 1: % 163.70/23.45 | | | | | | | | % 163.70/23.45 | | | | | | | | (254) ~ (all_146_0 = 0) % 163.70/23.45 | | | | | | | | % 163.70/23.45 | | | | | | | | REDUCE: (242), (254) imply: % 163.70/23.45 | | | | | | | | (255) $false % 163.70/23.45 | | | | | | | | % 163.70/23.45 | | | | | | | | CLOSE: (255) is inconsistent. % 163.70/23.45 | | | | | | | | % 163.70/23.45 | | | | | | | Case 2: % 163.70/23.45 | | | | | | | | % 163.70/23.45 | | | | | | | | (256) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 163.70/23.45 | | | | | | | | ? [v2: $i] : (ssList(v1) = 0 & cons(all_146_2, v1) = % 163.70/23.45 | | | | | | | | v2 & app(v0, v2) = all_143_0 & $i(v2) & $i(v1))) % 163.70/23.45 | | | | | | | | % 163.70/23.45 | | | | | | | | DELTA: instantiating (256) with fresh symbol all_445_0 gives: % 163.70/23.45 | | | | | | | | (257) ssList(all_445_0) = 0 & $i(all_445_0) & ? [v0: $i] : % 163.70/23.45 | | | | | | | | ? [v1: $i] : (ssList(v0) = 0 & cons(all_146_2, v0) = v1 % 163.70/23.45 | | | | | | | | & app(all_445_0, v1) = all_143_0 & $i(v1) & $i(v0)) % 163.70/23.45 | | | | | | | | % 163.70/23.45 | | | | | | | | ALPHA: (257) implies: % 163.70/23.45 | | | | | | | | (258) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & % 163.70/23.45 | | | | | | | | cons(all_146_2, v0) = v1 & app(all_445_0, v1) = % 163.70/23.45 | | | | | | | | all_143_0 & $i(v1) & $i(v0)) % 163.70/23.45 | | | | | | | | % 163.70/23.45 | | | | | | | | DELTA: instantiating (258) with fresh symbols all_447_0, % 163.70/23.45 | | | | | | | | all_447_1 gives: % 163.70/23.45 | | | | | | | | (259) ssList(all_447_1) = 0 & cons(all_146_2, all_447_1) = % 163.70/23.45 | | | | | | | | all_447_0 & app(all_445_0, all_447_0) = all_143_0 & % 163.70/23.45 | | | | | | | | $i(all_447_0) & $i(all_447_1) % 163.70/23.45 | | | | | | | | % 163.70/23.45 | | | | | | | | ALPHA: (259) implies: % 163.70/23.45 | | | | | | | | (260) $i(all_447_1) % 163.70/23.45 | | | | | | | | (261) cons(all_146_2, all_447_1) = all_447_0 % 163.70/23.45 | | | | | | | | (262) ssList(all_447_1) = 0 % 163.70/23.45 | | | | | | | | % 163.70/23.45 | | | | | | | | BETA: splitting (253) gives: % 163.70/23.45 | | | | | | | | % 163.70/23.45 | | | | | | | | Case 1: % 163.70/23.45 | | | | | | | | | % 163.70/23.45 | | | | | | | | | (263) ~ (all_317_0 = 0) % 163.70/23.45 | | | | | | | | | % 163.70/23.45 | | | | | | | | | REDUCE: (244), (263) imply: % 163.70/23.45 | | | | | | | | | (264) $false % 163.70/23.45 | | | | | | | | | % 163.70/23.45 | | | | | | | | | CLOSE: (264) is inconsistent. % 163.70/23.45 | | | | | | | | | % 163.70/23.45 | | | | | | | | Case 2: % 163.70/23.45 | | | | | | | | | % 163.70/23.45 | | | | | | | | | (265) all_146_1 = 0 | ? [v0: any] : ( ~ (v0 = all_146_2) & % 163.70/23.45 | | | | | | | | | leq(v0, all_146_2) = 0 & memberP(all_143_0, v0) = 0 % 163.70/23.45 | | | | | | | | | & ssItem(v0) = 0 & $i(v0)) % 163.70/23.45 | | | | | | | | | % 163.70/23.45 | | | | | | | | | BETA: splitting (265) gives: % 163.70/23.45 | | | | | | | | | % 163.70/23.45 | | | | | | | | | Case 1: % 163.70/23.45 | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | (266) all_146_1 = 0 % 163.70/23.45 | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | REDUCE: (240), (266) imply: % 163.70/23.45 | | | | | | | | | | (267) $false % 163.70/23.45 | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | CLOSE: (267) is inconsistent. % 163.70/23.45 | | | | | | | | | | % 163.70/23.45 | | | | | | | | | Case 2: % 163.70/23.45 | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | (268) ? [v0: any] : ( ~ (v0 = all_146_2) & leq(v0, % 163.70/23.45 | | | | | | | | | | all_146_2) = 0 & memberP(all_143_0, v0) = 0 & % 163.70/23.45 | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 163.70/23.45 | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | DELTA: instantiating (268) with fresh symbol all_456_0 % 163.70/23.45 | | | | | | | | | | gives: % 163.70/23.45 | | | | | | | | | | (269) ~ (all_456_0 = all_146_2) & leq(all_456_0, % 163.70/23.45 | | | | | | | | | | all_146_2) = 0 & memberP(all_143_0, all_456_0) = % 163.70/23.45 | | | | | | | | | | 0 & ssItem(all_456_0) = 0 & $i(all_456_0) % 163.70/23.45 | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | ALPHA: (269) implies: % 163.70/23.45 | | | | | | | | | | (270) ~ (all_456_0 = all_146_2) % 163.70/23.45 | | | | | | | | | | (271) $i(all_456_0) % 163.70/23.45 | | | | | | | | | | (272) ssItem(all_456_0) = 0 % 163.70/23.45 | | | | | | | | | | (273) memberP(all_143_0, all_456_0) = 0 % 163.70/23.45 | | | | | | | | | | (274) leq(all_456_0, all_146_2) = 0 % 163.70/23.45 | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | BETA: splitting (34) gives: % 163.70/23.45 | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | Case 1: % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | (275) all_143_0 = nil % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | REDUCE: (245), (275) imply: % 163.70/23.45 | | | | | | | | | | | (276) memberP(nil, all_146_2) = 0 % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_146_2, simplifying with % 163.70/23.45 | | | | | | | | | | | (25), (276) gives: % 163.70/23.45 | | | | | | | | | | | (277) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_146_2) = % 163.70/23.45 | | | | | | | | | | | v0) % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | DELTA: instantiating (277) with fresh symbol all_438_0 % 163.70/23.45 | | | | | | | | | | | gives: % 163.70/23.45 | | | | | | | | | | | (278) ~ (all_438_0 = 0) & ssItem(all_146_2) = all_438_0 % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | REF_CLOSE: (8), (26), (30), (242), (277), (278) are % 163.70/23.45 | | | | | | | | | | | inconsistent by sub-proof #1. % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | Case 2: % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | (279) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: % 163.70/23.45 | | | | | | | | | | | $i] : (cons(v1, v0) = all_143_0 & ssItem(v1) = % 163.70/23.45 | | | | | | | | | | | 0 & $i(v1))) % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | DELTA: instantiating (279) with fresh symbol all_470_0 % 163.70/23.45 | | | | | | | | | | | gives: % 163.70/23.45 | | | | | | | | | | | (280) ssList(all_470_0) = 0 & $i(all_470_0) & ? [v0: % 163.70/23.45 | | | | | | | | | | | $i] : (cons(v0, all_470_0) = all_143_0 & % 163.70/23.45 | | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | ALPHA: (280) implies: % 163.70/23.45 | | | | | | | | | | | (281) ? [v0: $i] : (cons(v0, all_470_0) = all_143_0 & % 163.70/23.45 | | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | DELTA: instantiating (281) with fresh symbol all_472_0 % 163.70/23.45 | | | | | | | | | | | gives: % 163.70/23.45 | | | | | | | | | | | (282) cons(all_472_0, all_470_0) = all_143_0 & % 163.70/23.45 | | | | | | | | | | | ssItem(all_472_0) = 0 & $i(all_472_0) % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | ALPHA: (282) implies: % 163.70/23.45 | | | | | | | | | | | (283) $i(all_472_0) % 163.70/23.45 | | | | | | | | | | | (284) ssItem(all_472_0) = 0 % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | GROUND_INST: instantiating (31) with all_472_0, simplifying % 163.70/23.45 | | | | | | | | | | | with (283), (284) gives: % 163.70/23.45 | | | | | | | | | | | (285) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_146_2, % 163.70/23.45 | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 163.70/23.45 | | | | | | | | | | | (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : ! % 163.70/23.45 | | | | | | | | | | | [v3: $i] : ! [v4: any] : ( ~ (frontsegP(v1, v3) % 163.70/23.45 | | | | | | | | | | | = v4) | ~ (cons(all_472_0, v2) = v3) | ~ % 163.70/23.45 | | | | | | | | | | | $i(v2) | ? [v5: any] : ? [v6: any] : % 163.70/23.45 | | | | | | | | | | | (frontsegP(v0, v2) = v6 & ssList(v2) = v5 & ( % 163.70/23.45 | | | | | | | | | | | ~ (v5 = 0) | (( ~ (v6 = 0) | ~ (all_472_0 % 163.70/23.45 | | | | | | | | | | | = all_146_2) | v4 = 0) & ( ~ (v4 = % 163.70/23.45 | | | | | | | | | | | 0) | (v6 = 0 & all_472_0 = % 163.70/23.45 | | | | | | | | | | | all_146_2))))))) % 163.70/23.45 | | | | | | | | | | | % 163.70/23.45 | | | | | | | | | | | GROUND_INST: instantiating (41) with all_447_1, all_447_0, % 163.70/23.45 | | | | | | | | | | | simplifying with (260), (261) gives: % 163.70/23.46 | | | | | | | | | | | (286) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_447_1) = % 163.70/23.46 | | | | | | | | | | | v0) | ! [v0: $i] : ! [v1: $i] : ! [v2: any] : % 163.70/23.46 | | | | | | | | | | | ( ~ (frontsegP(all_447_0, v1) = v2) | ~ % 163.70/23.46 | | | | | | | | | | | (cons(all_137_0, v0) = v1) | ~ $i(v0) | ? [v3: % 163.70/23.46 | | | | | | | | | | | any] : ? [v4: any] : (frontsegP(all_447_1, % 163.70/23.46 | | | | | | | | | | | v0) = v4 & ssList(v0) = v3 & ( ~ (v3 = 0) | % 163.70/23.46 | | | | | | | | | | | (( ~ (v4 = 0) | ~ (all_146_2 = all_137_0) | % 163.70/23.46 | | | | | | | | | | | v2 = 0) & ( ~ (v2 = 0) | (v4 = 0 & % 163.70/23.46 | | | | | | | | | | | all_146_2 = all_137_0)))))) % 163.70/23.46 | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | GROUND_INST: instantiating (243) with all_456_0, simplifying % 163.70/23.46 | | | | | | | | | | | with (271), (273) gives: % 163.70/23.46 | | | | | | | | | | | (287) all_456_0 = all_146_2 | ? [v0: any] : ? [v1: % 163.70/23.46 | | | | | | | | | | | any] : (leq(all_456_0, all_146_2) = v1 & % 163.70/23.46 | | | | | | | | | | | ssItem(all_456_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 163.70/23.46 | | | | | | | | | | | 0))) % 163.70/23.46 | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | GROUND_INST: instantiating (285) with all_447_1, all_447_0, % 163.70/23.46 | | | | | | | | | | | simplifying with (260), (261) gives: % 163.70/23.46 | | | | | | | | | | | (288) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_447_1) = % 163.70/23.46 | | | | | | | | | | | v0) | ! [v0: $i] : ! [v1: $i] : ! [v2: any] : % 163.70/23.46 | | | | | | | | | | | ( ~ (frontsegP(all_447_0, v1) = v2) | ~ % 163.70/23.46 | | | | | | | | | | | (cons(all_472_0, v0) = v1) | ~ $i(v0) | ? [v3: % 163.70/23.46 | | | | | | | | | | | any] : ? [v4: any] : (frontsegP(all_447_1, % 163.70/23.46 | | | | | | | | | | | v0) = v4 & ssList(v0) = v3 & ( ~ (v3 = 0) | % 163.70/23.46 | | | | | | | | | | | (( ~ (v4 = 0) | ~ (all_472_0 = all_146_2) | % 163.70/23.46 | | | | | | | | | | | v2 = 0) & ( ~ (v2 = 0) | (v4 = 0 & % 163.70/23.46 | | | | | | | | | | | all_472_0 = all_146_2)))))) % 163.70/23.46 | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | BETA: splitting (287) gives: % 163.70/23.46 | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | Case 1: % 163.70/23.46 | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | (289) all_456_0 = all_146_2 % 163.70/23.46 | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | REDUCE: (270), (289) imply: % 163.70/23.46 | | | | | | | | | | | | (290) $false % 163.70/23.46 | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | CLOSE: (290) is inconsistent. % 163.70/23.46 | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | Case 2: % 163.70/23.46 | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | (291) ? [v0: any] : ? [v1: any] : (leq(all_456_0, % 163.70/23.46 | | | | | | | | | | | | all_146_2) = v1 & ssItem(all_456_0) = v0 & ( ~ % 163.70/23.46 | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 163.70/23.46 | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | BETA: splitting (286) gives: % 163.70/23.46 | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | Case 1: % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | (292) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_447_1) = % 163.70/23.46 | | | | | | | | | | | | | v0) % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | DELTA: instantiating (292) with fresh symbol all_1260_0 % 163.70/23.46 | | | | | | | | | | | | | gives: % 163.70/23.46 | | | | | | | | | | | | | (293) ~ (all_1260_0 = 0) & ssList(all_447_1) = % 163.70/23.46 | | | | | | | | | | | | | all_1260_0 % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | ALPHA: (293) implies: % 163.70/23.46 | | | | | | | | | | | | | (294) ~ (all_1260_0 = 0) % 163.70/23.46 | | | | | | | | | | | | | (295) ssList(all_447_1) = all_1260_0 % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | DELTA: instantiating (292) with fresh symbol all_1262_0 % 163.70/23.46 | | | | | | | | | | | | | gives: % 163.70/23.46 | | | | | | | | | | | | | (296) ~ (all_1262_0 = 0) & ssList(all_447_1) = % 163.70/23.46 | | | | | | | | | | | | | all_1262_0 % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | ALPHA: (296) implies: % 163.70/23.46 | | | | | | | | | | | | | (297) ssList(all_447_1) = all_1262_0 % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_1262_0, all_447_1, % 163.70/23.46 | | | | | | | | | | | | | simplifying with (262), (297) gives: % 163.70/23.46 | | | | | | | | | | | | | (298) all_1262_0 = 0 % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_1260_0, all_1262_0, % 163.70/23.46 | | | | | | | | | | | | | all_447_1, simplifying with (295), (297) gives: % 163.70/23.46 | | | | | | | | | | | | | (299) all_1262_0 = all_1260_0 % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | COMBINE_EQS: (298), (299) imply: % 163.70/23.46 | | | | | | | | | | | | | (300) all_1260_0 = 0 % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | REDUCE: (294), (300) imply: % 163.70/23.46 | | | | | | | | | | | | | (301) $false % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | CLOSE: (301) is inconsistent. % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | Case 2: % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | DELTA: instantiating (291) with fresh symbols all_1260_0, % 163.70/23.46 | | | | | | | | | | | | | all_1260_1 gives: % 163.70/23.46 | | | | | | | | | | | | | (302) leq(all_456_0, all_146_2) = all_1260_0 & % 163.70/23.46 | | | | | | | | | | | | | ssItem(all_456_0) = all_1260_1 & ( ~ (all_1260_0 = % 163.70/23.46 | | | | | | | | | | | | | 0) | ~ (all_1260_1 = 0)) % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | ALPHA: (302) implies: % 163.70/23.46 | | | | | | | | | | | | | (303) ssItem(all_456_0) = all_1260_1 % 163.70/23.46 | | | | | | | | | | | | | (304) leq(all_456_0, all_146_2) = all_1260_0 % 163.70/23.46 | | | | | | | | | | | | | (305) ~ (all_1260_0 = 0) | ~ (all_1260_1 = 0) % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | BETA: splitting (288) gives: % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | Case 1: % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | (306) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_447_1) = % 163.70/23.46 | | | | | | | | | | | | | | v0) % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | DELTA: instantiating (306) with fresh symbol all_1284_0 % 163.70/23.46 | | | | | | | | | | | | | | gives: % 163.70/23.46 | | | | | | | | | | | | | | (307) ~ (all_1284_0 = 0) & ssList(all_447_1) = % 163.70/23.46 | | | | | | | | | | | | | | all_1284_0 % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | ALPHA: (307) implies: % 163.70/23.46 | | | | | | | | | | | | | | (308) ~ (all_1284_0 = 0) % 163.70/23.46 | | | | | | | | | | | | | | (309) ssList(all_447_1) = all_1284_0 % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | DELTA: instantiating (306) with fresh symbol all_1286_0 % 163.70/23.46 | | | | | | | | | | | | | | gives: % 163.70/23.46 | | | | | | | | | | | | | | (310) ~ (all_1286_0 = 0) & ssList(all_447_1) = % 163.70/23.46 | | | | | | | | | | | | | | all_1286_0 % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | ALPHA: (310) implies: % 163.70/23.46 | | | | | | | | | | | | | | (311) ssList(all_447_1) = all_1286_0 % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_1286_0, all_447_1, % 163.70/23.46 | | | | | | | | | | | | | | simplifying with (262), (311) gives: % 163.70/23.46 | | | | | | | | | | | | | | (312) all_1286_0 = 0 % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_1284_0, all_1286_0, % 163.70/23.46 | | | | | | | | | | | | | | all_447_1, simplifying with (309), (311) gives: % 163.70/23.46 | | | | | | | | | | | | | | (313) all_1286_0 = all_1284_0 % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | COMBINE_EQS: (312), (313) imply: % 163.70/23.46 | | | | | | | | | | | | | | (314) all_1284_0 = 0 % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | REDUCE: (308), (314) imply: % 163.70/23.46 | | | | | | | | | | | | | | (315) $false % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | CLOSE: (315) is inconsistent. % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | Case 2: % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_1260_1, all_456_0, % 163.70/23.46 | | | | | | | | | | | | | | simplifying with (272), (303) gives: % 163.70/23.46 | | | | | | | | | | | | | | (316) all_1260_1 = 0 % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_1260_0, all_146_2, % 163.70/23.46 | | | | | | | | | | | | | | all_456_0, simplifying with (274), (304) gives: % 163.70/23.46 | | | | | | | | | | | | | | (317) all_1260_0 = 0 % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | BETA: splitting (305) gives: % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | Case 1: % 163.70/23.46 | | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | | (318) ~ (all_1260_0 = 0) % 163.70/23.46 | | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | | REDUCE: (317), (318) imply: % 163.70/23.46 | | | | | | | | | | | | | | | (319) $false % 163.70/23.46 | | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | | CLOSE: (319) is inconsistent. % 163.70/23.46 | | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | Case 2: % 163.70/23.46 | | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | | (320) ~ (all_1260_1 = 0) % 163.70/23.46 | | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | | REDUCE: (316), (320) imply: % 163.70/23.46 | | | | | | | | | | | | | | | (321) $false % 163.70/23.46 | | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent. % 163.70/23.46 | | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | | End of split % 163.70/23.46 | | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | | End of split % 163.70/23.46 | | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | | End of split % 163.70/23.46 | | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | | End of split % 163.70/23.46 | | | | | | | | | | | % 163.70/23.46 | | | | | | | | | | End of split % 163.70/23.46 | | | | | | | | | | % 163.70/23.46 | | | | | | | | | End of split % 163.70/23.46 | | | | | | | | | % 163.70/23.46 | | | | | | | | End of split % 163.70/23.46 | | | | | | | | % 163.70/23.46 | | | | | | | End of split % 163.70/23.46 | | | | | | | % 163.70/23.46 | | | | | | End of split % 163.70/23.46 | | | | | | % 163.70/23.46 | | | | | End of split % 163.70/23.46 | | | | | % 163.70/23.46 | | | | End of split % 163.70/23.46 | | | | % 163.70/23.46 | | | End of split % 163.70/23.46 | | | % 163.70/23.46 | | End of split % 163.70/23.46 | | % 163.70/23.46 | End of split % 163.70/23.46 | % 163.70/23.46 End of proof % 163.70/23.46 % 163.70/23.46 Sub-proof #1 shows that the following formulas are inconsistent: % 163.70/23.46 ---------------------------------------------------------------- % 163.70/23.46 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 163.70/23.46 (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 163.70/23.46 (2) ~ (all_146_0 = 0) | ~ (all_146_1 = 0) | ? [v0: any] : ( ~ (v0 = % 163.70/23.46 all_146_2) & leq(v0, all_146_2) = 0 & memberP(all_143_0, v0) = 0 & % 163.70/23.46 ssItem(v0) = 0 & $i(v0)) % 163.70/23.46 (3) ssItem(all_146_2) = 0 % 163.70/23.46 (4) all_146_0 = 0 % 163.70/23.46 (5) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_146_2) = v0) % 163.70/23.46 (6) ~ (all_438_0 = 0) & ssItem(all_146_2) = all_438_0 % 163.70/23.46 % 163.70/23.46 Begin of proof % 163.70/23.46 | % 163.70/23.46 | ALPHA: (6) implies: % 163.70/23.46 | (7) ~ (all_438_0 = 0) % 163.70/23.46 | (8) ssItem(all_146_2) = all_438_0 % 163.70/23.46 | % 163.70/23.46 | BETA: splitting (2) gives: % 163.70/23.46 | % 163.70/23.46 | Case 1: % 163.70/23.46 | | % 163.70/23.46 | | (9) ~ (all_146_0 = 0) % 163.70/23.46 | | % 163.70/23.46 | | REDUCE: (4), (9) imply: % 163.70/23.46 | | (10) $false % 163.70/23.46 | | % 163.70/23.46 | | CLOSE: (10) is inconsistent. % 163.70/23.46 | | % 163.70/23.46 | Case 2: % 163.70/23.46 | | % 163.70/23.46 | | % 163.70/23.46 | | DELTA: instantiating (5) with fresh symbol all_446_0 gives: % 163.70/23.46 | | (11) ~ (all_446_0 = 0) & ssItem(all_146_2) = all_446_0 % 163.70/23.46 | | % 163.70/23.46 | | ALPHA: (11) implies: % 163.70/23.46 | | (12) ssItem(all_146_2) = all_446_0 % 163.70/23.46 | | % 163.70/23.46 | | GROUND_INST: instantiating (1) with 0, all_446_0, all_146_2, simplifying % 163.70/23.46 | | with (3), (12) gives: % 163.70/23.47 | | (13) all_446_0 = 0 % 163.70/23.47 | | % 163.70/23.47 | | GROUND_INST: instantiating (1) with all_438_0, all_446_0, all_146_2, % 163.70/23.47 | | simplifying with (8), (12) gives: % 163.70/23.47 | | (14) all_446_0 = all_438_0 % 163.70/23.47 | | % 163.70/23.47 | | COMBINE_EQS: (13), (14) imply: % 163.70/23.47 | | (15) all_438_0 = 0 % 163.70/23.47 | | % 163.70/23.47 | | REDUCE: (7), (15) imply: % 163.70/23.47 | | (16) $false % 163.70/23.47 | | % 163.70/23.47 | | CLOSE: (16) is inconsistent. % 163.70/23.47 | | % 163.70/23.47 | End of split % 163.70/23.47 | % 163.70/23.47 End of proof % 163.70/23.47 % 163.70/23.47 Sub-proof #2 shows that the following formulas are inconsistent: % 163.70/23.47 ---------------------------------------------------------------- % 163.70/23.47 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 163.70/23.47 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 163.70/23.47 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 163.70/23.47 (3) ssList(nil) = 0 % 163.70/23.47 % 163.70/23.47 Begin of proof % 163.70/23.47 | % 163.70/23.47 | DELTA: instantiating (1) with fresh symbol all_364_0 gives: % 163.70/23.47 | (4) ~ (all_364_0 = 0) & ssList(nil) = all_364_0 % 163.70/23.47 | % 163.70/23.47 | ALPHA: (4) implies: % 163.70/23.47 | (5) ~ (all_364_0 = 0) % 163.70/23.47 | (6) ssList(nil) = all_364_0 % 163.70/23.47 | % 163.70/23.47 | DELTA: instantiating (1) with fresh symbol all_366_0 gives: % 163.70/23.47 | (7) ~ (all_366_0 = 0) & ssList(nil) = all_366_0 % 163.70/23.47 | % 163.70/23.47 | ALPHA: (7) implies: % 163.70/23.47 | (8) ssList(nil) = all_366_0 % 163.70/23.47 | % 163.70/23.47 | DELTA: instantiating (1) with fresh symbol all_368_0 gives: % 163.70/23.47 | (9) ~ (all_368_0 = 0) & ssList(nil) = all_368_0 % 163.70/23.47 | % 163.70/23.47 | ALPHA: (9) implies: % 163.70/23.47 | (10) ssList(nil) = all_368_0 % 163.70/23.47 | % 163.70/23.47 | DELTA: instantiating (1) with fresh symbol all_370_0 gives: % 163.70/23.47 | (11) ~ (all_370_0 = 0) & ssList(nil) = all_370_0 % 163.70/23.47 | % 163.70/23.47 | ALPHA: (11) implies: % 163.70/23.47 | (12) ssList(nil) = all_370_0 % 163.70/23.47 | % 163.70/23.47 | DELTA: instantiating (1) with fresh symbol all_372_0 gives: % 163.70/23.47 | (13) ~ (all_372_0 = 0) & ssList(nil) = all_372_0 % 163.70/23.47 | % 163.70/23.47 | ALPHA: (13) implies: % 163.70/23.47 | (14) ssList(nil) = all_372_0 % 163.70/23.47 | % 163.70/23.47 | DELTA: instantiating (1) with fresh symbol all_374_0 gives: % 163.70/23.47 | (15) ~ (all_374_0 = 0) & ssList(nil) = all_374_0 % 163.70/23.47 | % 163.70/23.47 | ALPHA: (15) implies: % 163.70/23.47 | (16) ssList(nil) = all_374_0 % 163.70/23.47 | % 163.70/23.47 | DELTA: instantiating (1) with fresh symbol all_376_0 gives: % 163.70/23.47 | (17) ~ (all_376_0 = 0) & ssList(nil) = all_376_0 % 163.70/23.47 | % 163.70/23.47 | ALPHA: (17) implies: % 163.70/23.47 | (18) ssList(nil) = all_376_0 % 163.70/23.47 | % 163.70/23.47 | GROUND_INST: instantiating (2) with all_364_0, all_372_0, nil, simplifying % 163.70/23.47 | with (6), (14) gives: % 163.70/23.47 | (19) all_372_0 = all_364_0 % 163.70/23.47 | % 163.70/23.47 | GROUND_INST: instantiating (2) with 0, all_374_0, nil, simplifying with (3), % 163.70/23.47 | (16) gives: % 163.70/23.47 | (20) all_374_0 = 0 % 163.70/23.47 | % 163.70/23.47 | GROUND_INST: instantiating (2) with all_372_0, all_374_0, nil, simplifying % 163.70/23.47 | with (14), (16) gives: % 163.70/23.47 | (21) all_374_0 = all_372_0 % 163.70/23.47 | % 163.70/23.47 | GROUND_INST: instantiating (2) with all_370_0, all_374_0, nil, simplifying % 163.70/23.47 | with (12), (16) gives: % 163.70/23.47 | (22) all_374_0 = all_370_0 % 163.70/23.47 | % 163.70/23.47 | GROUND_INST: instantiating (2) with all_368_0, all_374_0, nil, simplifying % 163.70/23.47 | with (10), (16) gives: % 163.70/23.47 | (23) all_374_0 = all_368_0 % 163.70/23.47 | % 163.70/23.47 | GROUND_INST: instantiating (2) with all_370_0, all_376_0, nil, simplifying % 163.70/23.47 | with (12), (18) gives: % 163.70/23.47 | (24) all_376_0 = all_370_0 % 163.70/23.47 | % 163.70/23.47 | GROUND_INST: instantiating (2) with all_366_0, all_376_0, nil, simplifying % 163.70/23.47 | with (8), (18) gives: % 163.70/23.47 | (25) all_376_0 = all_366_0 % 163.70/23.47 | % 163.70/23.47 | COMBINE_EQS: (24), (25) imply: % 163.70/23.47 | (26) all_370_0 = all_366_0 % 163.70/23.47 | % 163.70/23.47 | SIMP: (26) implies: % 163.70/23.47 | (27) all_370_0 = all_366_0 % 163.70/23.47 | % 163.70/23.47 | COMBINE_EQS: (22), (23) imply: % 163.70/23.47 | (28) all_370_0 = all_368_0 % 163.70/23.47 | % 163.70/23.47 | SIMP: (28) implies: % 163.70/23.47 | (29) all_370_0 = all_368_0 % 163.70/23.47 | % 163.70/23.47 | COMBINE_EQS: (21), (23) imply: % 163.70/23.47 | (30) all_372_0 = all_368_0 % 163.70/23.47 | % 163.70/23.47 | SIMP: (30) implies: % 163.70/23.47 | (31) all_372_0 = all_368_0 % 163.70/23.47 | % 163.70/23.47 | COMBINE_EQS: (20), (23) imply: % 163.70/23.47 | (32) all_368_0 = 0 % 163.70/23.47 | % 163.70/23.47 | COMBINE_EQS: (19), (31) imply: % 163.70/23.47 | (33) all_368_0 = all_364_0 % 163.70/23.47 | % 163.70/23.47 | SIMP: (33) implies: % 163.70/23.47 | (34) all_368_0 = all_364_0 % 163.70/23.47 | % 163.70/23.47 | COMBINE_EQS: (27), (29) imply: % 163.70/23.47 | (35) all_368_0 = all_366_0 % 163.70/23.47 | % 163.70/23.47 | SIMP: (35) implies: % 163.70/23.47 | (36) all_368_0 = all_366_0 % 163.70/23.47 | % 163.70/23.47 | COMBINE_EQS: (34), (36) imply: % 163.70/23.47 | (37) all_366_0 = all_364_0 % 163.70/23.47 | % 163.70/23.47 | COMBINE_EQS: (32), (36) imply: % 163.70/23.47 | (38) all_366_0 = 0 % 163.70/23.47 | % 163.70/23.47 | COMBINE_EQS: (37), (38) imply: % 163.70/23.47 | (39) all_364_0 = 0 % 163.70/23.47 | % 163.70/23.47 | REDUCE: (5), (39) imply: % 163.70/23.47 | (40) $false % 163.70/23.47 | % 163.70/23.47 | CLOSE: (40) is inconsistent. % 163.70/23.47 | % 163.70/23.47 End of proof % 163.70/23.47 % SZS output end Proof for theBenchmark % 163.70/23.47 % 163.70/23.47 22877ms %------------------------------------------------------------------------------