%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC277+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 : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 20:50:36 EDT 2023 % Result : Theorem 71.96s 10.17s % Output : Proof 225.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC277+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.33 % Computer : n018.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Mon Aug 28 17:57:02 EDT 2023 % 0.14/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.69/1.64 Prover 1: Preprocessing ... % 6.69/1.65 Prover 0: Preprocessing ... % 6.69/1.67 Prover 3: Preprocessing ... % 6.69/1.67 Prover 2: Preprocessing ... % 6.69/1.67 Prover 5: Preprocessing ... % 7.11/1.70 Prover 4: Preprocessing ... % 7.11/1.70 Prover 6: Preprocessing ... % 16.33/2.95 Prover 2: Proving ... % 16.65/2.98 Prover 5: Constructing countermodel ... % 16.65/2.99 Prover 1: Constructing countermodel ... % 17.25/3.07 Prover 6: Proving ... % 17.62/3.10 Prover 3: Constructing countermodel ... % 22.50/3.74 Prover 0: Proving ... % 22.50/3.74 Prover 4: Constructing countermodel ... % 71.96/10.17 Prover 3: proved (9545ms) % 71.96/10.17 % 71.96/10.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 71.96/10.17 % 71.96/10.17 Prover 2: stopped % 71.96/10.17 Prover 6: stopped % 71.96/10.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 71.96/10.17 Prover 5: stopped % 71.96/10.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 71.96/10.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 71.96/10.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 71.96/10.18 Prover 0: stopped % 71.96/10.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 73.29/10.38 Prover 11: Preprocessing ... % 73.29/10.39 Prover 13: Preprocessing ... % 73.72/10.39 Prover 10: Preprocessing ... % 73.72/10.39 Prover 8: Preprocessing ... % 73.72/10.44 Prover 7: Preprocessing ... % 74.58/10.59 Prover 10: Constructing countermodel ... % 75.11/10.66 Prover 7: Constructing countermodel ... % 75.11/10.69 Prover 13: Constructing countermodel ... % 76.43/10.78 Prover 8: Warning: ignoring some quantifiers % 76.43/10.79 Prover 8: Constructing countermodel ... % 81.16/11.37 Prover 11: Constructing countermodel ... % 104.07/14.42 Prover 13: stopped % 104.70/14.45 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 105.51/14.60 Prover 16: Preprocessing ... % 106.36/14.70 Prover 16: Constructing countermodel ... % 116.11/15.98 Prover 1: stopped % 116.64/16.00 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 117.21/16.10 Prover 19: Preprocessing ... % 119.76/16.46 Prover 19: Warning: ignoring some quantifiers % 120.24/16.50 Prover 19: Constructing countermodel ... % 142.98/19.55 Prover 16: stopped % 144.40/19.76 Prover 19: stopped % 188.66/27.97 Prover 4: stopped % 198.57/30.14 Prover 7: stopped % 224.06/37.79 Prover 8: Found proof (size 419) % 224.06/37.79 Prover 8: proved (27518ms) % 224.06/37.80 Prover 11: stopped % 224.06/37.81 Prover 10: stopped % 224.06/37.81 % 224.06/37.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 224.06/37.81 % 224.36/37.85 % SZS output start Proof for theBenchmark % 224.36/37.86 Assumptions after simplification: % 224.36/37.86 --------------------------------- % 224.36/37.86 % 224.36/37.86 (ax11) % 224.56/37.92 ! [v0: $i] : ! [v1: any] : ( ~ (totalorderedP(v0) = v1) | ~ $i(v0) | ? % 224.56/37.92 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 224.56/37.92 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: any] : ( ~ % 224.56/37.92 (leq(v2, v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & % 224.56/37.92 ssItem(v3) = v5) | ! [v5: $i] : ( ~ (ssList(v5) = 0) | ~ $i(v5) % 224.56/37.92 | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2, v6) = % 224.56/37.92 v7) | ~ (app(v5, v7) = v8) | ~ $i(v6) | ? [v9: int] : ( ~ % 224.56/37.92 (v9 = 0) & ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] : (v4 % 224.56/37.92 = 0 | ~ (cons(v3, v9) = v10) | ~ (app(v8, v10) = v0) | ~ % 224.56/37.92 $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v9) = % 224.56/37.92 v11))))))) & (v1 = 0 | ? [v2: $i] : (ssItem(v2) = 0 & % 224.56/37.92 $i(v2) & ? [v3: $i] : ? [v4: any] : (leq(v2, v3) = v4 & ssItem(v3) = % 224.56/37.92 0 & $i(v3) & ? [v5: $i] : (ssList(v5) = 0 & $i(v5) & ? [v6: $i] : % 224.56/37.92 ? [v7: $i] : ? [v8: $i] : (ssList(v6) = 0 & cons(v2, v6) = v7 & % 224.56/37.92 app(v5, v7) = v8 & $i(v8) & $i(v7) & $i(v6) & ? [v9: $i] : ? % 224.56/37.92 [v10: $i] : ( ~ (v4 = 0) & ssList(v9) = 0 & cons(v3, v9) = v10 & % 224.56/37.92 app(v8, v10) = v0 & $i(v10) & $i(v9))))))))) % 224.56/37.92 % 224.56/37.92 (ax13) % 224.56/37.93 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ? % 224.56/37.93 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 224.56/37.93 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) | % 224.56/37.93 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 224.56/37.93 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~ % 224.56/37.93 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 224.56/37.93 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) | % 224.56/37.93 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) | % 224.56/37.93 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 = % 224.56/37.93 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) = % 224.56/37.93 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] : % 224.56/37.93 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 & % 224.56/37.93 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ? % 224.56/37.93 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 & % 224.56/37.93 app(v7, v9) = v0 & $i(v9) & $i(v8))))))))) % 224.56/37.93 % 224.56/37.93 (ax15) % 224.56/37.94 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 224.56/37.94 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 224.56/37.94 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 224.56/37.94 % 224.56/37.94 (ax17) % 224.56/37.94 ssList(nil) = 0 & $i(nil) % 224.56/37.94 % 224.56/37.94 (ax20) % 224.56/37.94 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 224.56/37.94 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 224.56/37.94 ssItem(v2) = 0 & $i(v2)))) % 224.56/37.94 % 224.56/37.94 (ax23) % 224.56/37.94 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 224.56/37.94 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 224.56/37.94 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 224.56/37.94 % 224.56/37.94 (ax25) % 224.56/37.94 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 224.56/37.94 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 224.56/37.94 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 224.56/37.94 % 224.56/37.94 (ax39) % 224.56/37.94 $i(nil) & ? [v0: int] : ( ~ (v0 = 0) & singletonP(nil) = v0) % 224.56/37.94 % 224.56/37.94 (ax4) % 224.56/37.94 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | % 224.56/37.94 ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: $i] % 224.56/37.94 : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 | ! [v2: % 224.56/37.94 $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = % 224.56/37.94 0) & ssItem(v2) = v3))))) % 224.56/37.94 % 224.56/37.94 (ax54) % 224.56/37.94 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : (v1 = v0 | ~ % 224.56/37.94 (segmentP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : % 224.56/37.94 (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 224.56/37.94 % 224.56/37.94 (ax58) % 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ % 224.83/37.95 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 % 224.83/37.95 = nil) & ( ~ (v0 = nil) | v1 = 0))) % 224.83/37.95 % 224.83/37.95 (ax59) % 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.83/37.95 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 224.83/37.95 (v2 = 0) | v3 = 0))) % 224.83/37.95 % 224.83/37.95 (ax61) % 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.83/37.95 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 224.83/37.95 (v2 = 0) | v3 = 0))) % 224.83/37.95 % 224.83/37.95 (ax63) % 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.83/37.95 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 224.83/37.95 (v2 = 0) | v3 = 0))) % 224.83/37.95 % 224.83/37.95 (ax65) % 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.83/37.95 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 224.83/37.95 (v2 = 0) | v3 = 0))) % 224.83/37.95 % 224.83/37.95 (ax66) % 224.83/37.95 totalorderedP(nil) = 0 & $i(nil) % 224.83/37.95 % 224.83/37.95 (ax68) % 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.83/37.95 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 224.83/37.95 ~ (v2 = 0) | v3 = 0))) % 224.83/37.95 % 224.83/37.95 (ax7) % 224.83/37.95 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 224.83/37.95 ( ~ (segmentP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 224.83/37.95 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : ? [v4: $i] : % 224.83/37.95 (ssList(v3) = 0 & app(v3, v1) = v4 & $i(v4) & $i(v3) & ? [v5: $i] : % 224.83/37.95 (ssList(v5) = 0 & app(v4, v5) = v0 & $i(v5)))) & (v2 = 0 | ! [v3: % 224.83/37.95 $i] : ! [v4: $i] : ( ~ (app(v3, v1) = v4) | ~ $i(v3) | ? [v5: % 224.83/37.95 int] : ( ~ (v5 = 0) & ssList(v3) = v5) | ! [v5: $i] : ( ~ % 224.83/37.95 (app(v4, v5) = v0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & % 224.83/37.95 ssList(v5) = v6))))))) % 224.83/37.95 % 224.83/37.95 (ax71) % 224.83/37.96 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.83/37.96 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 224.83/37.96 ~ (v2 = 0) | v3 = 0))) % 224.83/37.96 % 224.83/37.96 (ax72) % 224.88/37.96 duplicatefreeP(nil) = 0 & $i(nil) % 224.88/37.96 % 224.88/37.96 (ax73) % 224.88/37.96 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 224.88/37.96 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 224.88/37.96 (v2 = 0) | v3 = 0))) % 224.88/37.96 % 224.88/37.96 (co1) % 224.88/37.96 $i(nil) & ? [v0: $i] : ? [v1: any] : (totalorderedP(v0) = v1 & ssList(v0) = % 224.88/37.96 0 & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4: % 224.88/37.96 any] : (singletonP(v3) = v4 & ssList(v3) = 0 & $i(v3) & ? [v5: any] : % 224.88/37.96 (v3 = v0 & ~ (v1 = 0) & segmentP(v2, v0) = 0 & neq(v2, nil) = v5 & ( ~ % 224.88/37.96 (v5 = 0) | v4 = 0))))) % 224.88/37.96 % 224.88/37.96 (function-axioms) % 224.88/37.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 224.88/37.97 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 224.88/37.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 224.88/37.97 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 224.88/37.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 224.88/37.97 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 224.88/37.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 224.88/37.97 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 224.88/37.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 224.88/37.97 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 224.88/37.97 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 224.88/37.97 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 224.88/37.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 224.88/37.97 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 224.88/37.97 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 224.88/37.97 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 224.88/37.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 224.88/37.97 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 224.88/37.97 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 224.88/37.97 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 224.88/37.97 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 224.88/37.97 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 224.88/37.97 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 224.88/37.97 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 224.88/37.97 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 224.88/37.97 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 224.88/37.97 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 224.88/37.97 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 224.88/37.97 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 224.88/37.97 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 224.88/37.97 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 224.88/37.97 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 224.88/37.97 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 224.88/37.97 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 224.88/37.97 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ? % 224.88/37.97 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (gt(v1, v0) = v2) & ? % 224.88/37.97 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (geq(v1, v0) = v2) & ? % 224.88/37.97 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (lt(v1, v0) = v2) & ? % 224.88/37.97 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (leq(v1, v0) = v2) & ? % 224.88/37.97 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (segmentP(v1, v0) = v2) % 224.88/37.97 & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (rearsegP(v1, v0) = % 224.88/37.97 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 224.88/37.97 (frontsegP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 224.88/37.97 MultipleValueBool] : (memberP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 224.88/37.97 [v2: MultipleValueBool] : (neq(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 224.88/37.97 [v2: $i] : (cons(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 224.88/37.97 $i] : (app(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] % 224.88/37.97 : (equalelemsP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.88/37.97 (duplicatefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.88/37.97 (strictorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.88/37.97 (totalorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.88/37.97 (strictorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.88/37.97 (totalorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.88/37.97 (cyclefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 224.88/37.97 (singletonP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssList(v0) % 224.88/37.97 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssItem(v0) = v1) & ? % 224.88/37.97 [v0: $i] : ? [v1: $i] : (tl(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 224.88/37.97 (hd(v0) = v1 & $i(v1)) % 224.88/37.97 % 224.88/37.97 Further assumptions not needed in the proof: % 224.88/37.97 -------------------------------------------- % 224.88/37.97 ax1, ax10, ax12, ax14, ax16, ax18, ax19, ax2, ax21, ax22, ax24, ax26, ax27, % 224.88/37.97 ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax40, % 224.88/37.97 ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, % 224.88/37.97 ax53, ax55, ax56, ax57, ax6, ax60, ax62, ax64, ax67, ax69, ax70, ax74, ax75, % 224.88/37.97 ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85, ax86, ax87, % 224.88/37.97 ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 224.88/37.97 % 224.88/37.97 Those formulas are unsatisfiable: % 224.88/37.97 --------------------------------- % 224.88/37.97 % 224.88/37.97 Begin of proof % 224.88/37.98 | % 224.88/37.98 | ALPHA: (ax4) implies: % 224.88/37.98 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | ? % 224.88/37.98 | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: % 224.88/37.98 | $i] : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 % 224.88/37.98 | | ! [v2: $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: % 224.88/37.98 | int] : ( ~ (v3 = 0) & ssItem(v2) = v3))))) % 224.88/37.98 | % 224.88/37.98 | ALPHA: (ax17) implies: % 224.88/37.98 | (2) ssList(nil) = 0 % 224.88/37.98 | % 224.88/37.98 | ALPHA: (ax20) implies: % 224.88/37.98 | (3) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 224.88/37.98 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 224.88/37.98 | ssItem(v2) = 0 & $i(v2)))) % 224.88/37.98 | % 224.88/37.98 | ALPHA: (ax39) implies: % 224.88/37.98 | (4) ? [v0: int] : ( ~ (v0 = 0) & singletonP(nil) = v0) % 224.88/37.98 | % 224.88/37.98 | ALPHA: (ax58) implies: % 224.88/37.98 | (5) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ $i(v0) | % 224.88/37.98 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 = % 224.88/37.98 | nil) & ( ~ (v0 = nil) | v1 = 0))) % 224.88/37.98 | % 224.88/37.98 | ALPHA: (ax59) implies: % 224.88/37.98 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.88/37.98 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 224.88/37.98 | ~ (v2 = 0) | v3 = 0))) % 224.88/37.98 | % 224.88/37.98 | ALPHA: (ax61) implies: % 224.88/37.98 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.88/37.98 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 224.88/37.98 | ( ~ (v2 = 0) | v3 = 0))) % 224.88/37.98 | % 224.88/37.98 | ALPHA: (ax63) implies: % 224.88/37.98 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.88/37.98 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 224.88/37.98 | ( ~ (v2 = 0) | v3 = 0))) % 224.88/37.98 | % 224.88/37.98 | ALPHA: (ax65) implies: % 224.88/37.99 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.88/37.99 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 224.88/37.99 | & ( ~ (v2 = 0) | v3 = 0))) % 224.88/37.99 | % 224.88/37.99 | ALPHA: (ax66) implies: % 224.88/37.99 | (10) totalorderedP(nil) = 0 % 224.88/37.99 | % 224.88/37.99 | ALPHA: (ax68) implies: % 224.88/37.99 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.88/37.99 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = % 224.88/37.99 | v2 & ( ~ (v2 = 0) | v3 = 0))) % 224.88/37.99 | % 224.88/37.99 | ALPHA: (ax71) implies: % 224.88/37.99 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.88/37.99 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = % 224.88/37.99 | v2 & ( ~ (v2 = 0) | v3 = 0))) % 224.88/37.99 | % 224.88/37.99 | ALPHA: (ax72) implies: % 224.88/37.99 | (13) duplicatefreeP(nil) = 0 % 224.88/37.99 | % 224.88/37.99 | ALPHA: (ax73) implies: % 224.88/37.99 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.88/37.99 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 224.88/37.99 | ( ~ (v2 = 0) | v3 = 0))) % 224.88/37.99 | % 224.88/37.99 | ALPHA: (co1) implies: % 224.88/37.99 | (15) $i(nil) % 224.88/37.99 | (16) ? [v0: $i] : ? [v1: any] : (totalorderedP(v0) = v1 & ssList(v0) = 0 % 224.88/37.99 | & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ? % 224.88/37.99 | [v4: any] : (singletonP(v3) = v4 & ssList(v3) = 0 & $i(v3) & ? % 224.88/37.99 | [v5: any] : (v3 = v0 & ~ (v1 = 0) & segmentP(v2, v0) = 0 & % 224.88/37.99 | neq(v2, nil) = v5 & ( ~ (v5 = 0) | v4 = 0))))) % 224.88/37.99 | % 224.88/37.99 | ALPHA: (function-axioms) implies: % 224.88/37.99 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 224.88/37.99 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 224.88/37.99 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 224.88/37.99 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 224.88/37.99 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 224.88/37.99 | : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0)) % 224.88/37.99 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 224.88/37.99 | : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = % 224.88/37.99 | v0)) % 224.88/37.99 | % 224.88/38.00 | DELTA: instantiating (4) with fresh symbol all_127_0 gives: % 224.88/38.00 | (21) ~ (all_127_0 = 0) & singletonP(nil) = all_127_0 % 224.88/38.00 | % 224.88/38.00 | ALPHA: (21) implies: % 224.88/38.00 | (22) ~ (all_127_0 = 0) % 224.88/38.00 | (23) singletonP(nil) = all_127_0 % 224.88/38.00 | % 224.88/38.00 | DELTA: instantiating (16) with fresh symbols all_139_0, all_139_1 gives: % 224.88/38.00 | (24) totalorderedP(all_139_1) = all_139_0 & ssList(all_139_1) = 0 & % 224.88/38.00 | $i(all_139_1) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 224.88/38.00 | ? [v2: any] : (singletonP(v1) = v2 & ssList(v1) = 0 & $i(v1) & ? % 224.88/38.00 | [v3: any] : (v1 = all_139_1 & ~ (all_139_0 = 0) & segmentP(v0, % 224.88/38.00 | all_139_1) = 0 & neq(v0, nil) = v3 & ( ~ (v3 = 0) | v2 = 0)))) % 224.88/38.00 | % 224.88/38.00 | ALPHA: (24) implies: % 224.88/38.00 | (25) totalorderedP(all_139_1) = all_139_0 % 224.88/38.00 | (26) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 224.88/38.00 | (singletonP(v1) = v2 & ssList(v1) = 0 & $i(v1) & ? [v3: any] : (v1 % 224.88/38.00 | = all_139_1 & ~ (all_139_0 = 0) & segmentP(v0, all_139_1) = 0 & % 224.88/38.00 | neq(v0, nil) = v3 & ( ~ (v3 = 0) | v2 = 0)))) % 224.88/38.00 | % 224.88/38.00 | DELTA: instantiating (26) with fresh symbol all_143_0 gives: % 224.88/38.00 | (27) ssList(all_143_0) = 0 & $i(all_143_0) & ? [v0: $i] : ? [v1: any] : % 224.88/38.00 | (singletonP(v0) = v1 & ssList(v0) = 0 & $i(v0) & ? [v2: any] : (v0 = % 224.88/38.00 | all_139_1 & ~ (all_139_0 = 0) & segmentP(all_143_0, all_139_1) = % 224.88/38.00 | 0 & neq(all_143_0, nil) = v2 & ( ~ (v2 = 0) | v1 = 0))) % 224.88/38.00 | % 224.88/38.00 | ALPHA: (27) implies: % 224.88/38.00 | (28) $i(all_143_0) % 224.88/38.00 | (29) ssList(all_143_0) = 0 % 224.88/38.00 | (30) ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 & % 224.88/38.00 | $i(v0) & ? [v2: any] : (v0 = all_139_1 & ~ (all_139_0 = 0) & % 224.88/38.00 | segmentP(all_143_0, all_139_1) = 0 & neq(all_143_0, nil) = v2 & ( % 224.88/38.00 | ~ (v2 = 0) | v1 = 0))) % 224.88/38.00 | % 224.88/38.00 | DELTA: instantiating (30) with fresh symbols all_145_0, all_145_1 gives: % 224.88/38.01 | (31) singletonP(all_145_1) = all_145_0 & ssList(all_145_1) = 0 & % 224.88/38.01 | $i(all_145_1) & ? [v0: any] : (all_145_1 = all_139_1 & ~ (all_139_0 % 224.88/38.01 | = 0) & segmentP(all_143_0, all_139_1) = 0 & neq(all_143_0, nil) = % 224.88/38.01 | v0 & ( ~ (v0 = 0) | all_145_0 = 0)) % 224.88/38.01 | % 224.88/38.01 | ALPHA: (31) implies: % 224.88/38.01 | (32) $i(all_145_1) % 224.88/38.01 | (33) ssList(all_145_1) = 0 % 224.88/38.01 | (34) singletonP(all_145_1) = all_145_0 % 224.88/38.01 | (35) ? [v0: any] : (all_145_1 = all_139_1 & ~ (all_139_0 = 0) & % 224.88/38.01 | segmentP(all_143_0, all_139_1) = 0 & neq(all_143_0, nil) = v0 & ( ~ % 224.88/38.01 | (v0 = 0) | all_145_0 = 0)) % 224.88/38.01 | % 224.88/38.01 | DELTA: instantiating (35) with fresh symbol all_147_0 gives: % 224.88/38.01 | (36) all_145_1 = all_139_1 & ~ (all_139_0 = 0) & segmentP(all_143_0, % 224.88/38.01 | all_139_1) = 0 & neq(all_143_0, nil) = all_147_0 & ( ~ (all_147_0 = % 224.88/38.01 | 0) | all_145_0 = 0) % 224.88/38.01 | % 224.88/38.01 | ALPHA: (36) implies: % 224.88/38.01 | (37) all_145_1 = all_139_1 % 224.88/38.01 | (38) ~ (all_139_0 = 0) % 224.88/38.01 | (39) neq(all_143_0, nil) = all_147_0 % 224.88/38.01 | (40) segmentP(all_143_0, all_139_1) = 0 % 224.88/38.01 | (41) ~ (all_147_0 = 0) | all_145_0 = 0 % 224.88/38.01 | % 224.88/38.01 | REDUCE: (34), (37) imply: % 224.88/38.01 | (42) singletonP(all_139_1) = all_145_0 % 224.88/38.01 | % 224.88/38.01 | REDUCE: (33), (37) imply: % 224.88/38.01 | (43) ssList(all_139_1) = 0 % 224.88/38.01 | % 224.88/38.01 | REDUCE: (32), (37) imply: % 224.88/38.01 | (44) $i(all_139_1) % 224.88/38.01 | % 224.88/38.01 | GROUND_INST: instantiating (ax25) with nil, simplifying with (2), (15) gives: % 224.88/38.01 | (45) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.88/38.01 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 224.88/38.01 | ( ~ (v2 = 0) | v3 = nil))) % 224.88/38.01 | % 224.88/38.01 | GROUND_INST: instantiating (ax23) with nil, simplifying with (2), (15) gives: % 224.88/38.01 | (46) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 224.88/38.01 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 224.88/38.01 | ( ~ (v2 = 0) | v3 = v0))) % 224.88/38.01 | % 224.88/38.01 | GROUND_INST: instantiating (3) with all_139_1, simplifying with (43), (44) % 224.88/38.01 | gives: % 224.88/38.01 | (47) all_139_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 224.88/38.01 | : (cons(v1, v0) = all_139_1 & ssItem(v1) = 0 & $i(v1))) % 224.88/38.01 | % 224.88/38.01 | GROUND_INST: instantiating (3) with all_143_0, simplifying with (28), (29) % 224.88/38.01 | gives: % 224.88/38.01 | (48) all_143_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 224.88/38.01 | : (cons(v1, v0) = all_143_0 & ssItem(v1) = 0 & $i(v1))) % 224.88/38.01 | % 224.88/38.01 | GROUND_INST: instantiating (ax7) with all_143_0, simplifying with (28), (29) % 224.88/38.01 | gives: % 224.88/38.02 | (49) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(all_143_0, v0) = v1) | ~ % 224.88/38.02 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = % 224.88/38.02 | 0) | ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & app(v2, v0) % 224.88/38.02 | = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 & % 224.88/38.02 | app(v3, v4) = all_143_0 & $i(v4)))) & (v1 = 0 | ! [v2: $i] % 224.88/38.02 | : ! [v3: $i] : ( ~ (app(v2, v0) = v3) | ~ $i(v2) | ? [v4: % 224.88/38.02 | int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] : ( ~ % 224.88/38.02 | (app(v3, v4) = all_143_0) | ~ $i(v4) | ? [v5: int] : ( ~ % 224.88/38.02 | (v5 = 0) & ssList(v4) = v5)))))) % 224.88/38.02 | % 224.88/38.02 | GROUND_INST: instantiating (ax15) with all_143_0, simplifying with (28), (29) % 224.88/38.02 | gives: % 224.88/38.02 | (50) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_143_0, v0) = v1) | ~ $i(v0) % 224.88/38.02 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 224.88/38.02 | ~ (v0 = all_143_0)) & (v1 = 0 | v0 = all_143_0))) % 224.88/38.02 | % 224.88/38.02 | GROUND_INST: instantiating (ax54) with all_143_0, simplifying with (28), (29) % 224.88/38.02 | gives: % 224.88/38.02 | (51) ! [v0: any] : (v0 = all_143_0 | ~ (segmentP(all_143_0, v0) = 0) | ~ % 224.88/38.02 | $i(v0) | ? [v1: any] : ? [v2: any] : (segmentP(v0, all_143_0) = v2 % 224.88/38.02 | & ssList(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 224.88/38.02 | % 224.88/38.02 | GROUND_INST: instantiating (1) with all_139_1, all_145_0, simplifying with % 224.88/38.02 | (42), (44) gives: % 224.88/38.02 | (52) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) | (( ~ % 224.88/38.02 | (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_139_1 & % 224.88/38.02 | ssItem(v0) = 0 & $i(v0))) & (all_145_0 = 0 | ! [v0: $i] : ( ~ % 224.88/38.02 | (cons(v0, nil) = all_139_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 224.88/38.02 | = 0) & ssItem(v0) = v1)))) % 224.88/38.02 | % 224.88/38.02 | GROUND_INST: instantiating (ax11) with all_139_1, all_139_0, simplifying with % 224.88/38.02 | (25), (44) gives: % 224.88/38.02 | (53) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) | (( ~ % 224.88/38.02 | (all_139_0 = 0) | ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | % 224.88/38.02 | ! [v1: $i] : ! [v2: any] : ( ~ (leq(v0, v1) = v2) | ~ $i(v1) % 224.88/38.02 | | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: $i] % 224.88/38.02 | : ( ~ (ssList(v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: $i] % 224.88/38.02 | : ! [v6: $i] : ( ~ (cons(v0, v4) = v5) | ~ (app(v3, v5) = % 224.88/38.02 | v6) | ~ $i(v4) | ? [v7: int] : ( ~ (v7 = 0) & % 224.88/38.02 | ssList(v4) = v7) | ! [v7: $i] : ! [v8: $i] : (v2 = 0 | % 224.88/38.02 | ~ (cons(v1, v7) = v8) | ~ (app(v6, v8) = all_139_1) | % 224.88/38.02 | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & ssList(v7) = % 224.88/38.02 | v9))))))) & (all_139_0 = 0 | ? [v0: $i] : (ssItem(v0) % 224.88/38.02 | = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : (leq(v0, v1) = v2 & % 224.88/38.02 | ssItem(v1) = 0 & $i(v1) & ? [v3: $i] : (ssList(v3) = 0 & % 224.88/38.02 | $i(v3) & ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 224.88/38.02 | (ssList(v4) = 0 & cons(v0, v4) = v5 & app(v3, v5) = v6 & % 224.88/38.02 | $i(v6) & $i(v5) & $i(v4) & ? [v7: $i] : ? [v8: $i] : ( ~ % 224.88/38.02 | (v2 = 0) & ssList(v7) = 0 & cons(v1, v7) = v8 & app(v6, % 224.88/38.02 | v8) = all_139_1 & $i(v8) & $i(v7)))))))) % 224.88/38.02 | % 224.88/38.03 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (13), (15) % 224.88/38.03 | gives: % 224.88/38.03 | (54) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 224.88/38.03 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) | % 224.88/38.03 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | ! % 224.88/38.03 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) | % 224.88/38.03 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = % 224.88/38.03 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 224.88/38.03 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil) % 224.88/38.03 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 224.88/38.03 | v8)))))) % 224.88/38.03 | % 224.88/38.03 | GROUND_INST: instantiating (51) with all_139_1, simplifying with (40), (44) % 224.88/38.03 | gives: % 224.88/38.03 | (55) all_143_0 = all_139_1 | ? [v0: any] : ? [v1: any] : % 224.88/38.03 | (segmentP(all_139_1, all_143_0) = v1 & ssList(all_139_1) = v0 & ( ~ % 224.88/38.03 | (v1 = 0) | ~ (v0 = 0))) % 224.88/38.03 | % 224.88/38.03 | GROUND_INST: instantiating (50) with nil, all_147_0, simplifying with (15), % 224.88/38.03 | (39) gives: % 224.88/38.03 | (56) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_147_0 = 0) % 224.88/38.03 | | ~ (all_143_0 = nil)) & (all_147_0 = 0 | all_143_0 = nil)) % 224.88/38.03 | % 224.88/38.03 | GROUND_INST: instantiating (49) with all_139_1, 0, simplifying with (40), (44) % 224.88/38.03 | gives: % 224.88/38.03 | (57) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_139_1) = v1 % 224.88/38.03 | & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & app(v1, v2) = % 224.88/38.03 | all_143_0 & $i(v2))) | ? [v0: int] : ( ~ (v0 = 0) & % 224.88/38.03 | ssList(all_139_1) = v0) % 224.88/38.03 | % 224.88/38.03 | BETA: splitting (54) gives: % 224.88/38.03 | % 224.88/38.03 | Case 1: % 224.88/38.03 | | % 224.88/38.03 | | (58) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 224.88/38.03 | | % 224.88/38.03 | | REF_CLOSE: (2), (18), (58) are inconsistent by sub-proof #1. % 224.88/38.03 | | % 224.88/38.03 | Case 2: % 224.88/38.03 | | % 224.88/38.03 | | (59) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 224.88/38.03 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = % 224.88/38.03 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 224.88/38.03 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) | % 224.88/38.03 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i] % 224.88/38.03 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ % 224.88/38.03 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = % 224.88/38.03 | | 0) & ssList(v6) = v8)))))) % 224.88/38.03 | | % 224.88/38.03 | | BETA: splitting (53) gives: % 224.88/38.03 | | % 224.88/38.03 | | Case 1: % 224.88/38.03 | | | % 224.88/38.03 | | | (60) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 224.88/38.03 | | | % 224.88/38.03 | | | DELTA: instantiating (60) with fresh symbol all_340_0 gives: % 224.88/38.03 | | | (61) ~ (all_340_0 = 0) & ssList(all_139_1) = all_340_0 % 224.88/38.03 | | | % 224.88/38.03 | | | ALPHA: (61) implies: % 224.88/38.03 | | | (62) ~ (all_340_0 = 0) % 224.88/38.03 | | | (63) ssList(all_139_1) = all_340_0 % 224.88/38.03 | | | % 224.88/38.03 | | | DELTA: instantiating (60) with fresh symbol all_344_0 gives: % 224.88/38.04 | | | (64) ~ (all_344_0 = 0) & ssList(all_139_1) = all_344_0 % 224.88/38.04 | | | % 224.88/38.04 | | | ALPHA: (64) implies: % 224.88/38.04 | | | (65) ssList(all_139_1) = all_344_0 % 224.88/38.04 | | | % 224.88/38.04 | | | GROUND_INST: instantiating (18) with 0, all_344_0, all_139_1, simplifying % 224.88/38.04 | | | with (43), (65) gives: % 224.88/38.04 | | | (66) all_344_0 = 0 % 224.88/38.04 | | | % 224.88/38.04 | | | GROUND_INST: instantiating (18) with all_340_0, all_344_0, all_139_1, % 224.88/38.04 | | | simplifying with (63), (65) gives: % 224.88/38.04 | | | (67) all_344_0 = all_340_0 % 224.88/38.04 | | | % 224.88/38.04 | | | COMBINE_EQS: (66), (67) imply: % 224.88/38.04 | | | (68) all_340_0 = 0 % 224.88/38.04 | | | % 224.88/38.04 | | | REDUCE: (62), (68) imply: % 224.88/38.04 | | | (69) $false % 224.88/38.04 | | | % 224.88/38.04 | | | CLOSE: (69) is inconsistent. % 224.88/38.04 | | | % 224.88/38.04 | | Case 2: % 224.88/38.04 | | | % 224.88/38.04 | | | (70) ( ~ (all_139_0 = 0) | ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ % 224.88/38.04 | | | $i(v0) | ! [v1: $i] : ! [v2: any] : ( ~ (leq(v0, v1) = v2) | % 224.88/38.04 | | | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | % 224.88/38.04 | | | ! [v3: $i] : ( ~ (ssList(v3) = 0) | ~ $i(v3) | ! [v4: $i] % 224.88/38.04 | | | : ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v0, v4) = v5) | ~ % 224.88/38.04 | | | (app(v3, v5) = v6) | ~ $i(v4) | ? [v7: int] : ( ~ (v7 % 224.88/38.04 | | | = 0) & ssList(v4) = v7) | ! [v7: $i] : ! [v8: $i] % 224.88/38.04 | | | : (v2 = 0 | ~ (cons(v1, v7) = v8) | ~ (app(v6, v8) = % 224.88/38.04 | | | all_139_1) | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) % 224.88/38.04 | | | & ssList(v7) = v9))))))) & (all_139_0 = 0 | ? [v0: % 224.88/38.04 | | | $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 224.88/38.04 | | | (leq(v0, v1) = v2 & ssItem(v1) = 0 & $i(v1) & ? [v3: $i] : % 224.88/38.04 | | | (ssList(v3) = 0 & $i(v3) & ? [v4: $i] : ? [v5: $i] : ? % 224.88/38.04 | | | [v6: $i] : (ssList(v4) = 0 & cons(v0, v4) = v5 & app(v3, % 224.88/38.04 | | | v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ? [v7: $i] : ? % 224.88/38.04 | | | [v8: $i] : ( ~ (v2 = 0) & ssList(v7) = 0 & cons(v1, v7) % 224.88/38.04 | | | = v8 & app(v6, v8) = all_139_1 & $i(v8) & $i(v7))))))) % 224.88/38.04 | | | % 224.88/38.04 | | | ALPHA: (70) implies: % 224.88/38.04 | | | (71) all_139_0 = 0 | ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: % 224.88/38.04 | | | $i] : ? [v2: any] : (leq(v0, v1) = v2 & ssItem(v1) = 0 & % 224.88/38.04 | | | $i(v1) & ? [v3: $i] : (ssList(v3) = 0 & $i(v3) & ? [v4: $i] % 224.88/38.04 | | | : ? [v5: $i] : ? [v6: $i] : (ssList(v4) = 0 & cons(v0, v4) % 224.88/38.04 | | | = v5 & app(v3, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ? % 224.88/38.04 | | | [v7: $i] : ? [v8: $i] : ( ~ (v2 = 0) & ssList(v7) = 0 & % 224.88/38.04 | | | cons(v1, v7) = v8 & app(v6, v8) = all_139_1 & $i(v8) & % 224.88/38.04 | | | $i(v7)))))) % 224.88/38.04 | | | % 224.88/38.04 | | | BETA: splitting (57) gives: % 224.88/38.04 | | | % 224.88/38.04 | | | Case 1: % 224.88/38.04 | | | | % 224.88/38.04 | | | | (72) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_139_1) % 224.88/38.04 | | | | = v1 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & % 224.88/38.04 | | | | app(v1, v2) = all_143_0 & $i(v2))) % 224.88/38.04 | | | | % 224.88/38.04 | | | | DELTA: instantiating (72) with fresh symbols all_341_0, all_341_1 gives: % 224.88/38.04 | | | | (73) ssList(all_341_1) = 0 & app(all_341_1, all_139_1) = all_341_0 & % 224.88/38.04 | | | | $i(all_341_0) & $i(all_341_1) & ? [v0: $i] : (ssList(v0) = 0 & % 224.88/38.04 | | | | app(all_341_0, v0) = all_143_0 & $i(v0)) % 224.88/38.04 | | | | % 224.88/38.04 | | | | ALPHA: (73) implies: % 224.88/38.04 | | | | (74) $i(all_341_1) % 224.88/38.04 | | | | (75) app(all_341_1, all_139_1) = all_341_0 % 224.88/38.04 | | | | (76) ssList(all_341_1) = 0 % 224.88/38.04 | | | | % 224.88/38.04 | | | | BETA: splitting (71) gives: % 224.88/38.04 | | | | % 224.88/38.04 | | | | Case 1: % 224.88/38.04 | | | | | % 224.88/38.04 | | | | | (77) all_139_0 = 0 % 224.88/38.04 | | | | | % 224.88/38.04 | | | | | REDUCE: (38), (77) imply: % 224.88/38.04 | | | | | (78) $false % 224.88/38.04 | | | | | % 224.88/38.04 | | | | | CLOSE: (78) is inconsistent. % 224.88/38.04 | | | | | % 224.88/38.04 | | | | Case 2: % 224.88/38.04 | | | | | % 224.88/38.05 | | | | | (79) ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 224.88/38.05 | | | | | any] : (leq(v0, v1) = v2 & ssItem(v1) = 0 & $i(v1) & ? % 224.88/38.05 | | | | | [v3: $i] : (ssList(v3) = 0 & $i(v3) & ? [v4: $i] : ? % 224.88/38.05 | | | | | [v5: $i] : ? [v6: $i] : (ssList(v4) = 0 & cons(v0, v4) % 224.88/38.05 | | | | | = v5 & app(v3, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & % 224.88/38.05 | | | | | ? [v7: $i] : ? [v8: $i] : ( ~ (v2 = 0) & ssList(v7) = % 224.88/38.05 | | | | | 0 & cons(v1, v7) = v8 & app(v6, v8) = all_139_1 & % 224.88/38.05 | | | | | $i(v8) & $i(v7)))))) % 224.88/38.05 | | | | | % 224.88/38.05 | | | | | DELTA: instantiating (79) with fresh symbol all_353_0 gives: % 224.88/38.05 | | | | | (80) ssItem(all_353_0) = 0 & $i(all_353_0) & ? [v0: $i] : ? [v1: % 224.88/38.05 | | | | | any] : (leq(all_353_0, v0) = v1 & ssItem(v0) = 0 & $i(v0) & % 224.88/38.05 | | | | | ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ? % 224.88/38.05 | | | | | [v4: $i] : ? [v5: $i] : (ssList(v3) = 0 & cons(all_353_0, % 224.88/38.05 | | | | | v3) = v4 & app(v2, v4) = v5 & $i(v5) & $i(v4) & $i(v3) % 224.88/38.05 | | | | | & ? [v6: $i] : ? [v7: $i] : ( ~ (v1 = 0) & ssList(v6) % 224.88/38.05 | | | | | = 0 & cons(v0, v6) = v7 & app(v5, v7) = all_139_1 & % 224.88/38.05 | | | | | $i(v7) & $i(v6))))) % 224.88/38.05 | | | | | % 224.88/38.05 | | | | | ALPHA: (80) implies: % 224.88/38.05 | | | | | (81) $i(all_353_0) % 224.88/38.05 | | | | | (82) ssItem(all_353_0) = 0 % 224.88/38.05 | | | | | % 224.88/38.05 | | | | | BETA: splitting (41) gives: % 224.88/38.05 | | | | | % 224.88/38.05 | | | | | Case 1: % 224.88/38.05 | | | | | | % 224.88/38.05 | | | | | | (83) ~ (all_147_0 = 0) % 224.88/38.05 | | | | | | % 224.88/38.05 | | | | | | BETA: splitting (56) gives: % 224.88/38.05 | | | | | | % 224.88/38.05 | | | | | | Case 1: % 224.88/38.05 | | | | | | | % 224.88/38.05 | | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 224.88/38.05 | | | | | | | % 224.88/38.05 | | | | | | | REF_CLOSE: (2), (18), (84) are inconsistent by sub-proof #1. % 224.88/38.05 | | | | | | | % 224.88/38.05 | | | | | | Case 2: % 224.88/38.05 | | | | | | | % 224.88/38.05 | | | | | | | (85) ( ~ (all_147_0 = 0) | ~ (all_143_0 = nil)) & (all_147_0 = % 224.88/38.05 | | | | | | | 0 | all_143_0 = nil) % 224.88/38.05 | | | | | | | % 224.88/38.05 | | | | | | | ALPHA: (85) implies: % 224.88/38.05 | | | | | | | (86) all_147_0 = 0 | all_143_0 = nil % 224.88/38.05 | | | | | | | % 224.88/38.05 | | | | | | | BETA: splitting (86) gives: % 224.88/38.05 | | | | | | | % 224.88/38.05 | | | | | | | Case 1: % 224.88/38.05 | | | | | | | | % 224.88/38.05 | | | | | | | | (87) all_143_0 = nil % 224.88/38.05 | | | | | | | | % 224.88/38.05 | | | | | | | | REDUCE: (40), (87) imply: % 224.88/38.05 | | | | | | | | (88) segmentP(nil, all_139_1) = 0 % 224.88/38.05 | | | | | | | | % 224.88/38.05 | | | | | | | | BETA: splitting (47) gives: % 224.88/38.05 | | | | | | | | % 224.88/38.05 | | | | | | | | Case 1: % 224.88/38.05 | | | | | | | | | % 224.88/38.05 | | | | | | | | | (89) all_139_1 = nil % 224.88/38.05 | | | | | | | | | % 224.88/38.05 | | | | | | | | | REDUCE: (25), (89) imply: % 224.88/38.05 | | | | | | | | | (90) totalorderedP(nil) = all_139_0 % 224.88/38.05 | | | | | | | | | % 224.88/38.05 | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_139_0, nil, % 224.88/38.05 | | | | | | | | | simplifying with (10), (90) gives: % 224.88/38.05 | | | | | | | | | (91) all_139_0 = 0 % 224.88/38.05 | | | | | | | | | % 224.88/38.05 | | | | | | | | | REDUCE: (38), (91) imply: % 224.88/38.05 | | | | | | | | | (92) $false % 224.88/38.05 | | | | | | | | | % 224.88/38.05 | | | | | | | | | CLOSE: (92) is inconsistent. % 224.88/38.05 | | | | | | | | | % 224.88/38.05 | | | | | | | | Case 2: % 224.88/38.05 | | | | | | | | | % 224.88/38.05 | | | | | | | | | (93) ~ (all_139_1 = nil) % 224.88/38.05 | | | | | | | | | % 224.88/38.05 | | | | | | | | | GROUND_INST: instantiating (5) with all_139_1, 0, simplifying % 224.88/38.05 | | | | | | | | | with (44), (88) gives: % 224.88/38.05 | | | | | | | | | (94) all_139_1 = nil | ? [v0: int] : ( ~ (v0 = 0) & % 224.88/38.05 | | | | | | | | | ssList(all_139_1) = v0) % 224.88/38.05 | | | | | | | | | % 224.88/38.05 | | | | | | | | | BETA: splitting (94) gives: % 224.88/38.05 | | | | | | | | | % 224.88/38.05 | | | | | | | | | Case 1: % 224.88/38.05 | | | | | | | | | | % 224.88/38.05 | | | | | | | | | | (95) all_139_1 = nil % 224.88/38.05 | | | | | | | | | | % 224.88/38.05 | | | | | | | | | | REDUCE: (93), (95) imply: % 224.88/38.05 | | | | | | | | | | (96) $false % 224.88/38.05 | | | | | | | | | | % 224.88/38.05 | | | | | | | | | | CLOSE: (96) is inconsistent. % 224.88/38.05 | | | | | | | | | | % 224.88/38.05 | | | | | | | | | Case 2: % 224.88/38.05 | | | | | | | | | | % 224.88/38.05 | | | | | | | | | | (97) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = % 224.88/38.05 | | | | | | | | | | v0) % 224.88/38.05 | | | | | | | | | | % 224.88/38.05 | | | | | | | | | | DELTA: instantiating (97) with fresh symbol all_416_0 gives: % 224.88/38.05 | | | | | | | | | | (98) ~ (all_416_0 = 0) & ssList(all_139_1) = all_416_0 % 224.88/38.05 | | | | | | | | | | % 224.88/38.05 | | | | | | | | | | ALPHA: (98) implies: % 224.88/38.05 | | | | | | | | | | (99) ~ (all_416_0 = 0) % 224.88/38.05 | | | | | | | | | | (100) ssList(all_139_1) = all_416_0 % 224.88/38.05 | | | | | | | | | | % 224.88/38.05 | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_416_0, all_139_1, % 224.88/38.05 | | | | | | | | | | simplifying with (43), (100) gives: % 224.88/38.05 | | | | | | | | | | (101) all_416_0 = 0 % 224.88/38.05 | | | | | | | | | | % 224.88/38.05 | | | | | | | | | | REDUCE: (99), (101) imply: % 224.88/38.05 | | | | | | | | | | (102) $false % 224.88/38.05 | | | | | | | | | | % 224.88/38.05 | | | | | | | | | | CLOSE: (102) is inconsistent. % 224.88/38.05 | | | | | | | | | | % 224.88/38.05 | | | | | | | | | End of split % 224.88/38.05 | | | | | | | | | % 224.88/38.05 | | | | | | | | End of split % 224.88/38.05 | | | | | | | | % 224.88/38.05 | | | | | | | Case 2: % 224.88/38.05 | | | | | | | | % 224.88/38.05 | | | | | | | | (103) all_147_0 = 0 % 224.88/38.05 | | | | | | | | % 224.88/38.05 | | | | | | | | REDUCE: (83), (103) imply: % 224.88/38.05 | | | | | | | | (104) $false % 224.88/38.05 | | | | | | | | % 224.88/38.05 | | | | | | | | CLOSE: (104) is inconsistent. % 224.88/38.05 | | | | | | | | % 224.88/38.05 | | | | | | | End of split % 224.88/38.05 | | | | | | | % 224.88/38.05 | | | | | | End of split % 224.88/38.05 | | | | | | % 224.88/38.05 | | | | | Case 2: % 224.88/38.05 | | | | | | % 224.88/38.05 | | | | | | (105) all_145_0 = 0 % 224.88/38.05 | | | | | | (106) all_147_0 = 0 % 224.88/38.05 | | | | | | % 224.88/38.05 | | | | | | REDUCE: (42), (105) imply: % 224.88/38.05 | | | | | | (107) singletonP(all_139_1) = 0 % 224.88/38.05 | | | | | | % 224.88/38.05 | | | | | | BETA: splitting (56) gives: % 224.88/38.05 | | | | | | % 224.88/38.05 | | | | | | Case 1: % 224.88/38.05 | | | | | | | % 224.88/38.05 | | | | | | | (108) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 224.88/38.05 | | | | | | | % 224.88/38.05 | | | | | | | DELTA: instantiating (108) with fresh symbol all_378_0 gives: % 224.88/38.05 | | | | | | | (109) ~ (all_378_0 = 0) & ssList(nil) = all_378_0 % 224.88/38.05 | | | | | | | % 224.88/38.05 | | | | | | | ALPHA: (109) implies: % 224.88/38.05 | | | | | | | (110) ~ (all_378_0 = 0) % 224.88/38.05 | | | | | | | (111) ssList(nil) = all_378_0 % 224.88/38.06 | | | | | | | % 224.88/38.06 | | | | | | | GROUND_INST: instantiating (18) with 0, all_378_0, nil, % 224.88/38.06 | | | | | | | simplifying with (2), (111) gives: % 224.88/38.06 | | | | | | | (112) all_378_0 = 0 % 224.88/38.06 | | | | | | | % 224.88/38.06 | | | | | | | REDUCE: (110), (112) imply: % 224.88/38.06 | | | | | | | (113) $false % 224.88/38.06 | | | | | | | % 224.88/38.06 | | | | | | | CLOSE: (113) is inconsistent. % 224.88/38.06 | | | | | | | % 224.88/38.06 | | | | | | Case 2: % 224.88/38.06 | | | | | | | % 224.88/38.06 | | | | | | | (114) ( ~ (all_147_0 = 0) | ~ (all_143_0 = nil)) & (all_147_0 % 224.88/38.06 | | | | | | | = 0 | all_143_0 = nil) % 224.88/38.06 | | | | | | | % 224.88/38.06 | | | | | | | ALPHA: (114) implies: % 224.88/38.06 | | | | | | | (115) ~ (all_147_0 = 0) | ~ (all_143_0 = nil) % 224.88/38.06 | | | | | | | % 224.88/38.06 | | | | | | | BETA: splitting (52) gives: % 224.88/38.06 | | | | | | | % 224.88/38.06 | | | | | | | Case 1: % 224.88/38.06 | | | | | | | | % 224.88/38.06 | | | | | | | | (116) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 224.88/38.06 | | | | | | | | % 224.88/38.06 | | | | | | | | DELTA: instantiating (116) with fresh symbol all_379_0 gives: % 224.88/38.06 | | | | | | | | (117) ~ (all_379_0 = 0) & ssList(all_139_1) = all_379_0 % 224.88/38.06 | | | | | | | | % 224.88/38.06 | | | | | | | | ALPHA: (117) implies: % 224.88/38.06 | | | | | | | | (118) ~ (all_379_0 = 0) % 224.88/38.06 | | | | | | | | (119) ssList(all_139_1) = all_379_0 % 224.88/38.06 | | | | | | | | % 224.88/38.06 | | | | | | | | GROUND_INST: instantiating (18) with 0, all_379_0, all_139_1, % 224.88/38.06 | | | | | | | | simplifying with (43), (119) gives: % 224.88/38.06 | | | | | | | | (120) all_379_0 = 0 % 224.88/38.06 | | | | | | | | % 224.88/38.06 | | | | | | | | REDUCE: (118), (120) imply: % 224.88/38.06 | | | | | | | | (121) $false % 224.88/38.06 | | | | | | | | % 224.88/38.06 | | | | | | | | CLOSE: (121) is inconsistent. % 224.88/38.06 | | | | | | | | % 224.88/38.06 | | | | | | | Case 2: % 224.88/38.06 | | | | | | | | % 224.88/38.06 | | | | | | | | (122) ( ~ (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) = % 224.88/38.06 | | | | | | | | all_139_1 & ssItem(v0) = 0 & $i(v0))) & (all_145_0 % 224.88/38.06 | | | | | | | | = 0 | ! [v0: $i] : ( ~ (cons(v0, nil) = all_139_1) | % 224.88/38.06 | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 224.88/38.06 | | | | | | | | ssItem(v0) = v1))) % 224.88/38.06 | | | | | | | | % 224.88/38.06 | | | | | | | | ALPHA: (122) implies: % 224.88/38.06 | | | | | | | | (123) ~ (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) = % 224.88/38.06 | | | | | | | | all_139_1 & ssItem(v0) = 0 & $i(v0)) % 224.88/38.06 | | | | | | | | % 224.88/38.06 | | | | | | | | BETA: splitting (115) gives: % 224.88/38.06 | | | | | | | | % 224.88/38.06 | | | | | | | | Case 1: % 224.88/38.06 | | | | | | | | | % 224.88/38.06 | | | | | | | | | (124) ~ (all_143_0 = nil) % 224.88/38.06 | | | | | | | | | % 224.88/38.06 | | | | | | | | | BETA: splitting (123) gives: % 224.88/38.06 | | | | | | | | | % 224.88/38.06 | | | | | | | | | Case 1: % 224.88/38.06 | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | (125) ~ (all_145_0 = 0) % 224.88/38.06 | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | REDUCE: (105), (125) imply: % 224.88/38.06 | | | | | | | | | | (126) $false % 224.88/38.06 | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | CLOSE: (126) is inconsistent. % 224.88/38.06 | | | | | | | | | | % 224.88/38.06 | | | | | | | | | Case 2: % 224.88/38.06 | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | (127) ? [v0: $i] : (cons(v0, nil) = all_139_1 & % 224.88/38.06 | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 224.88/38.06 | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | DELTA: instantiating (127) with fresh symbol all_385_0 % 224.88/38.06 | | | | | | | | | | gives: % 224.88/38.06 | | | | | | | | | | (128) cons(all_385_0, nil) = all_139_1 & % 224.88/38.06 | | | | | | | | | | ssItem(all_385_0) = 0 & $i(all_385_0) % 224.88/38.06 | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | ALPHA: (128) implies: % 224.88/38.06 | | | | | | | | | | (129) $i(all_385_0) % 224.88/38.06 | | | | | | | | | | (130) ssItem(all_385_0) = 0 % 224.88/38.06 | | | | | | | | | | (131) cons(all_385_0, nil) = all_139_1 % 224.88/38.06 | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | BETA: splitting (48) gives: % 224.88/38.06 | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | Case 1: % 224.88/38.06 | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | (132) all_143_0 = nil % 224.88/38.06 | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | REDUCE: (124), (132) imply: % 224.88/38.06 | | | | | | | | | | | (133) $false % 224.88/38.06 | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | CLOSE: (133) is inconsistent. % 224.88/38.06 | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | Case 2: % 224.88/38.06 | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | (134) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: % 224.88/38.06 | | | | | | | | | | | $i] : (cons(v1, v0) = all_143_0 & ssItem(v1) = % 224.88/38.06 | | | | | | | | | | | 0 & $i(v1))) % 224.88/38.06 | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | DELTA: instantiating (134) with fresh symbol all_391_0 % 224.88/38.06 | | | | | | | | | | | gives: % 224.88/38.06 | | | | | | | | | | | (135) ssList(all_391_0) = 0 & $i(all_391_0) & ? [v0: % 224.88/38.06 | | | | | | | | | | | $i] : (cons(v0, all_391_0) = all_143_0 & % 224.88/38.06 | | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 224.88/38.06 | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | ALPHA: (135) implies: % 224.88/38.06 | | | | | | | | | | | (136) $i(all_391_0) % 224.88/38.06 | | | | | | | | | | | (137) ssList(all_391_0) = 0 % 224.88/38.06 | | | | | | | | | | | (138) ? [v0: $i] : (cons(v0, all_391_0) = all_143_0 & % 224.88/38.06 | | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 224.88/38.06 | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | DELTA: instantiating (138) with fresh symbol all_393_0 % 224.88/38.06 | | | | | | | | | | | gives: % 224.88/38.06 | | | | | | | | | | | (139) cons(all_393_0, all_391_0) = all_143_0 & % 224.88/38.06 | | | | | | | | | | | ssItem(all_393_0) = 0 & $i(all_393_0) % 224.88/38.06 | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | ALPHA: (139) implies: % 224.88/38.06 | | | | | | | | | | | (140) $i(all_393_0) % 224.88/38.06 | | | | | | | | | | | (141) ssItem(all_393_0) = 0 % 224.88/38.06 | | | | | | | | | | | (142) cons(all_393_0, all_391_0) = all_143_0 % 224.88/38.06 | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | BETA: splitting (47) gives: % 224.88/38.06 | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | Case 1: % 224.88/38.06 | | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | | (143) all_139_1 = nil % 224.88/38.06 | | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | | REDUCE: (107), (143) imply: % 224.88/38.06 | | | | | | | | | | | | (144) singletonP(nil) = 0 % 224.88/38.06 | | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_127_0, 0, nil, % 224.88/38.06 | | | | | | | | | | | | simplifying with (23), (144) gives: % 224.88/38.06 | | | | | | | | | | | | (145) all_127_0 = 0 % 224.88/38.06 | | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | | REDUCE: (22), (145) imply: % 224.88/38.06 | | | | | | | | | | | | (146) $false % 224.88/38.06 | | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | | CLOSE: (146) is inconsistent. % 224.88/38.06 | | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | Case 2: % 224.88/38.06 | | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | | (147) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: % 224.88/38.06 | | | | | | | | | | | | $i] : (cons(v1, v0) = all_139_1 & ssItem(v1) = % 224.88/38.06 | | | | | | | | | | | | 0 & $i(v1))) % 224.88/38.06 | | | | | | | | | | | | % 224.88/38.06 | | | | | | | | | | | | DELTA: instantiating (147) with fresh symbol all_401_0 % 224.88/38.06 | | | | | | | | | | | | gives: % 224.88/38.07 | | | | | | | | | | | | (148) ssList(all_401_0) = 0 & $i(all_401_0) & ? [v0: % 224.88/38.07 | | | | | | | | | | | | $i] : (cons(v0, all_401_0) = all_139_1 & % 224.88/38.07 | | | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 224.88/38.07 | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | ALPHA: (148) implies: % 224.88/38.07 | | | | | | | | | | | | (149) $i(all_401_0) % 224.88/38.07 | | | | | | | | | | | | (150) ssList(all_401_0) = 0 % 224.88/38.07 | | | | | | | | | | | | (151) ? [v0: $i] : (cons(v0, all_401_0) = all_139_1 & % 224.88/38.07 | | | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 224.88/38.07 | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | DELTA: instantiating (151) with fresh symbol all_403_0 % 224.88/38.07 | | | | | | | | | | | | gives: % 224.88/38.07 | | | | | | | | | | | | (152) cons(all_403_0, all_401_0) = all_139_1 & % 224.88/38.07 | | | | | | | | | | | | ssItem(all_403_0) = 0 & $i(all_403_0) % 224.88/38.07 | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | ALPHA: (152) implies: % 224.88/38.07 | | | | | | | | | | | | (153) $i(all_403_0) % 224.88/38.07 | | | | | | | | | | | | (154) ssItem(all_403_0) = 0 % 224.88/38.07 | | | | | | | | | | | | (155) cons(all_403_0, all_401_0) = all_139_1 % 224.88/38.07 | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | BETA: splitting (55) gives: % 224.88/38.07 | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | Case 1: % 224.88/38.07 | | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | | (156) all_143_0 = all_139_1 % 224.88/38.07 | | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | | REDUCE: (142), (156) imply: % 224.88/38.07 | | | | | | | | | | | | | (157) cons(all_393_0, all_391_0) = all_139_1 % 224.88/38.07 | | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (59) with all_393_0, simplifying % 224.88/38.07 | | | | | | | | | | | | | with (140), (141) gives: % 224.88/38.07 | | | | | | | | | | | | | (158) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | % 224.88/38.07 | | | | | | | | | | | | | ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | % 224.88/38.07 | | | | | | | | | | | | | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 224.88/38.07 | | | | | | | | | | | | | (cons(all_393_0, v2) = v3) | ~ (app(v1, v3) % 224.88/38.07 | | | | | | | | | | | | | = v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 % 224.88/38.07 | | | | | | | | | | | | | = 0) & ssList(v2) = v5) | ! [v5: $i] : % 224.88/38.07 | | | | | | | | | | | | | ! [v6: $i] : ( ~ (v0 = all_393_0) | ~ % 224.88/38.07 | | | | | | | | | | | | | (cons(all_393_0, v5) = v6) | ~ (app(v4, % 224.88/38.07 | | | | | | | | | | | | | v6) = nil) | ~ $i(v5) | ? [v7: int] % 224.88/38.07 | | | | | | | | | | | | | : ( ~ (v7 = 0) & ssList(v5) = v7))))) % 224.88/38.07 | | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (45) with all_385_0, all_139_1, % 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.07 | | | | | | | | | | | | | (159) ? [v0: any] : ? [v1: $i] : (tl(all_139_1) = v1 & % 224.88/38.07 | | | | | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) | % 224.88/38.07 | | | | | | | | | | | | | v1 = nil)) % 224.88/38.07 | | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (46) with all_385_0, all_139_1, % 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.07 | | | | | | | | | | | | | (160) ? [v0: any] : ? [v1: $i] : (hd(all_139_1) = v1 & % 224.88/38.07 | | | | | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) | % 224.88/38.07 | | | | | | | | | | | | | v1 = all_385_0)) % 224.88/38.07 | | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_385_0, all_139_1, % 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.07 | | | | | | | | | | | | | (161) ? [v0: any] : ? [v1: any] : % 224.88/38.07 | | | | | | | | | | | | | (strictorderedP(all_139_1) = v1 & % 224.88/38.07 | | | | | | | | | | | | | ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.88/38.07 | | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_385_0, all_139_1, % 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.07 | | | | | | | | | | | | | (162) ? [v0: any] : ? [v1: any] : % 224.88/38.07 | | | | | | | | | | | | | (totalorderedP(all_139_1) = v1 & ssItem(all_385_0) % 224.88/38.07 | | | | | | | | | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.88/38.07 | | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_385_0, all_139_1, % 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.07 | | | | | | | | | | | | | (163) ? [v0: any] : ? [v1: any] : % 224.88/38.07 | | | | | | | | | | | | | (strictorderP(all_139_1) = v1 & ssItem(all_385_0) % 224.88/38.07 | | | | | | | | | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.88/38.07 | | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_385_0, all_139_1, % 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.07 | | | | | | | | | | | | | (164) ? [v0: any] : ? [v1: any] : % 224.88/38.07 | | | | | | | | | | | | | (totalorderP(all_139_1) = v1 & ssItem(all_385_0) = % 224.88/38.07 | | | | | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.88/38.07 | | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (158) with all_353_0, simplifying % 224.88/38.07 | | | | | | | | | | | | | with (81), (82) gives: % 224.88/38.07 | | | | | | | | | | | | | (165) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | % 224.88/38.07 | | | | | | | | | | | | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 224.88/38.07 | | | | | | | | | | | | | (cons(all_393_0, v1) = v2) | ~ (app(v0, v2) = % 224.88/38.07 | | | | | | | | | | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = % 224.88/38.07 | | | | | | | | | | | | | 0) & ssList(v1) = v4) | ! [v4: $i] : ! % 224.88/38.07 | | | | | | | | | | | | | [v5: $i] : ( ~ (all_393_0 = all_353_0) | ~ % 224.88/38.07 | | | | | | | | | | | | | (cons(all_353_0, v4) = v5) | ~ (app(v3, v5) % 224.88/38.07 | | | | | | | | | | | | | = nil) | ~ $i(v4) | ? [v6: int] : ( ~ % 224.88/38.07 | | | | | | | | | | | | | (v6 = 0) & ssList(v4) = v6)))) % 224.88/38.07 | | | | | | | | | | | | | % 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (165) with all_341_1, simplifying % 224.88/38.07 | | | | | | | | | | | | | with (74), (76) gives: % 224.88/38.07 | | | | | | | | | | | | | (166) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 224.88/38.07 | | | | | | | | | | | | | (cons(all_393_0, v0) = v1) | ~ (app(all_341_1, % 224.88/38.07 | | | | | | | | | | | | | v1) = v2) | ~ $i(v0) | ? [v3: int] : ( ~ % 224.88/38.07 | | | | | | | | | | | | | (v3 = 0) & ssList(v0) = v3) | ! [v3: $i] : ! % 224.88/38.08 | | | | | | | | | | | | | [v4: $i] : ( ~ (all_393_0 = all_353_0) | ~ % 224.88/38.08 | | | | | | | | | | | | | (cons(all_353_0, v3) = v4) | ~ (app(v2, v4) = % 224.88/38.08 | | | | | | | | | | | | | nil) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = % 224.88/38.08 | | | | | | | | | | | | | 0) & ssList(v3) = v5))) % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | GROUND_INST: instantiating (166) with all_391_0, all_139_1, % 224.88/38.08 | | | | | | | | | | | | | all_341_0, simplifying with (75), (136), (157) % 224.88/38.08 | | | | | | | | | | | | | gives: % 224.88/38.08 | | | | | | | | | | | | | (167) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_391_0) = % 224.88/38.08 | | | | | | | | | | | | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ (all_393_0 % 224.88/38.08 | | | | | | | | | | | | | = all_353_0) | ~ (cons(all_353_0, v0) = v1) | % 224.88/38.08 | | | | | | | | | | | | | ~ (app(all_341_0, v1) = nil) | ~ $i(v0) | ? % 224.88/38.08 | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (164) with fresh symbols all_1799_0, % 224.88/38.08 | | | | | | | | | | | | | all_1799_1 gives: % 224.88/38.08 | | | | | | | | | | | | | (168) totalorderP(all_139_1) = all_1799_0 & % 224.88/38.08 | | | | | | | | | | | | | ssItem(all_385_0) = all_1799_1 & ( ~ (all_1799_1 = % 224.88/38.08 | | | | | | | | | | | | | 0) | all_1799_0 = 0) % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | ALPHA: (168) implies: % 224.88/38.08 | | | | | | | | | | | | | (169) ssItem(all_385_0) = all_1799_1 % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (163) with fresh symbols all_1801_0, % 224.88/38.08 | | | | | | | | | | | | | all_1801_1 gives: % 224.88/38.08 | | | | | | | | | | | | | (170) strictorderP(all_139_1) = all_1801_0 & % 224.88/38.08 | | | | | | | | | | | | | ssItem(all_385_0) = all_1801_1 & ( ~ (all_1801_1 = % 224.88/38.08 | | | | | | | | | | | | | 0) | all_1801_0 = 0) % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | ALPHA: (170) implies: % 224.88/38.08 | | | | | | | | | | | | | (171) ssItem(all_385_0) = all_1801_1 % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (162) with fresh symbols all_1803_0, % 224.88/38.08 | | | | | | | | | | | | | all_1803_1 gives: % 224.88/38.08 | | | | | | | | | | | | | (172) totalorderedP(all_139_1) = all_1803_0 & % 224.88/38.08 | | | | | | | | | | | | | ssItem(all_385_0) = all_1803_1 & ( ~ (all_1803_1 = % 224.88/38.08 | | | | | | | | | | | | | 0) | all_1803_0 = 0) % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | ALPHA: (172) implies: % 224.88/38.08 | | | | | | | | | | | | | (173) ssItem(all_385_0) = all_1803_1 % 224.88/38.08 | | | | | | | | | | | | | (174) totalorderedP(all_139_1) = all_1803_0 % 224.88/38.08 | | | | | | | | | | | | | (175) ~ (all_1803_1 = 0) | all_1803_0 = 0 % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (161) with fresh symbols all_1805_0, % 224.88/38.08 | | | | | | | | | | | | | all_1805_1 gives: % 224.88/38.08 | | | | | | | | | | | | | (176) strictorderedP(all_139_1) = all_1805_0 & % 224.88/38.08 | | | | | | | | | | | | | ssItem(all_385_0) = all_1805_1 & ( ~ (all_1805_1 = % 224.88/38.08 | | | | | | | | | | | | | 0) | all_1805_0 = 0) % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | ALPHA: (176) implies: % 224.88/38.08 | | | | | | | | | | | | | (177) ssItem(all_385_0) = all_1805_1 % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (160) with fresh symbols all_1807_0, % 224.88/38.08 | | | | | | | | | | | | | all_1807_1 gives: % 224.88/38.08 | | | | | | | | | | | | | (178) hd(all_139_1) = all_1807_0 & ssItem(all_385_0) = % 224.88/38.08 | | | | | | | | | | | | | all_1807_1 & $i(all_1807_0) & ( ~ (all_1807_1 = 0) % 224.88/38.08 | | | | | | | | | | | | | | all_1807_0 = all_385_0) % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | ALPHA: (178) implies: % 224.88/38.08 | | | | | | | | | | | | | (179) ssItem(all_385_0) = all_1807_1 % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (159) with fresh symbols all_1809_0, % 224.88/38.08 | | | | | | | | | | | | | all_1809_1 gives: % 224.88/38.08 | | | | | | | | | | | | | (180) tl(all_139_1) = all_1809_0 & ssItem(all_385_0) = % 224.88/38.08 | | | | | | | | | | | | | all_1809_1 & $i(all_1809_0) & ( ~ (all_1809_1 = 0) % 224.88/38.08 | | | | | | | | | | | | | | all_1809_0 = nil) % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | ALPHA: (180) implies: % 224.88/38.08 | | | | | | | | | | | | | (181) ssItem(all_385_0) = all_1809_1 % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | BETA: splitting (167) gives: % 224.88/38.08 | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | Case 1: % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | (182) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_391_0) = % 224.88/38.08 | | | | | | | | | | | | | | v0) % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1963_0 % 224.88/38.08 | | | | | | | | | | | | | | gives: % 224.88/38.08 | | | | | | | | | | | | | | (183) ~ (all_1963_0 = 0) & ssList(all_391_0) = % 224.88/38.08 | | | | | | | | | | | | | | all_1963_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (183) implies: % 224.88/38.08 | | | | | | | | | | | | | | (184) ~ (all_1963_0 = 0) % 224.88/38.08 | | | | | | | | | | | | | | (185) ssList(all_391_0) = all_1963_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1965_0 % 224.88/38.08 | | | | | | | | | | | | | | gives: % 224.88/38.08 | | | | | | | | | | | | | | (186) ~ (all_1965_0 = 0) & ssList(all_391_0) = % 224.88/38.08 | | | | | | | | | | | | | | all_1965_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (186) implies: % 224.88/38.08 | | | | | | | | | | | | | | (187) ssList(all_391_0) = all_1965_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1967_0 % 224.88/38.08 | | | | | | | | | | | | | | gives: % 224.88/38.08 | | | | | | | | | | | | | | (188) ~ (all_1967_0 = 0) & ssList(all_391_0) = % 224.88/38.08 | | | | | | | | | | | | | | all_1967_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (188) implies: % 224.88/38.08 | | | | | | | | | | | | | | (189) ssList(all_391_0) = all_1967_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1969_0 % 224.88/38.08 | | | | | | | | | | | | | | gives: % 224.88/38.08 | | | | | | | | | | | | | | (190) ~ (all_1969_0 = 0) & ssList(all_391_0) = % 224.88/38.08 | | | | | | | | | | | | | | all_1969_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (190) implies: % 224.88/38.08 | | | | | | | | | | | | | | (191) ssList(all_391_0) = all_1969_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1971_0 % 224.88/38.08 | | | | | | | | | | | | | | gives: % 224.88/38.08 | | | | | | | | | | | | | | (192) ~ (all_1971_0 = 0) & ssList(all_391_0) = % 224.88/38.08 | | | | | | | | | | | | | | all_1971_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (192) implies: % 224.88/38.08 | | | | | | | | | | | | | | (193) ssList(all_391_0) = all_1971_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1973_0 % 224.88/38.08 | | | | | | | | | | | | | | gives: % 224.88/38.08 | | | | | | | | | | | | | | (194) ~ (all_1973_0 = 0) & ssList(all_391_0) = % 224.88/38.08 | | | | | | | | | | | | | | all_1973_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (194) implies: % 224.88/38.08 | | | | | | | | | | | | | | (195) ssList(all_391_0) = all_1973_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1975_0 % 224.88/38.08 | | | | | | | | | | | | | | gives: % 224.88/38.08 | | | | | | | | | | | | | | (196) ~ (all_1975_0 = 0) & ssList(all_391_0) = % 224.88/38.08 | | | | | | | | | | | | | | all_1975_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (196) implies: % 224.88/38.08 | | | | | | | | | | | | | | (197) ssList(all_391_0) = all_1975_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1977_0 % 224.88/38.08 | | | | | | | | | | | | | | gives: % 224.88/38.08 | | | | | | | | | | | | | | (198) ~ (all_1977_0 = 0) & ssList(all_391_0) = % 224.88/38.08 | | | | | | | | | | | | | | all_1977_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (198) implies: % 224.88/38.08 | | | | | | | | | | | | | | (199) ssList(all_391_0) = all_1977_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_1969_0, all_391_0, % 224.88/38.08 | | | | | | | | | | | | | | simplifying with (137), (191) gives: % 224.88/38.08 | | | | | | | | | | | | | | (200) all_1969_0 = 0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1969_0, all_1971_0, % 224.88/38.08 | | | | | | | | | | | | | | all_391_0, simplifying with (191), (193) gives: % 224.88/38.08 | | | | | | | | | | | | | | (201) all_1971_0 = all_1969_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1963_0, all_1971_0, % 224.88/38.08 | | | | | | | | | | | | | | all_391_0, simplifying with (185), (193) gives: % 224.88/38.08 | | | | | | | | | | | | | | (202) all_1971_0 = all_1963_0 % 224.88/38.08 | | | | | | | | | | | | | | % 224.88/38.08 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1969_0, all_1973_0, % 224.88/38.08 | | | | | | | | | | | | | | all_391_0, simplifying with (191), (195) gives: % 224.88/38.09 | | | | | | | | | | | | | | (203) all_1973_0 = all_1969_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1965_0, all_1973_0, % 224.88/38.09 | | | | | | | | | | | | | | all_391_0, simplifying with (187), (195) gives: % 224.88/38.09 | | | | | | | | | | | | | | (204) all_1973_0 = all_1965_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1969_0, all_1975_0, % 224.88/38.09 | | | | | | | | | | | | | | all_391_0, simplifying with (191), (197) gives: % 224.88/38.09 | | | | | | | | | | | | | | (205) all_1975_0 = all_1969_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1975_0, all_1977_0, % 224.88/38.09 | | | | | | | | | | | | | | all_391_0, simplifying with (197), (199) gives: % 224.88/38.09 | | | | | | | | | | | | | | (206) all_1977_0 = all_1975_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1967_0, all_1977_0, % 224.88/38.09 | | | | | | | | | | | | | | all_391_0, simplifying with (189), (199) gives: % 224.88/38.09 | | | | | | | | | | | | | | (207) all_1977_0 = all_1967_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (206), (207) imply: % 224.88/38.09 | | | | | | | | | | | | | | (208) all_1975_0 = all_1967_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | SIMP: (208) implies: % 224.88/38.09 | | | | | | | | | | | | | | (209) all_1975_0 = all_1967_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (205), (209) imply: % 224.88/38.09 | | | | | | | | | | | | | | (210) all_1969_0 = all_1967_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | SIMP: (210) implies: % 224.88/38.09 | | | | | | | | | | | | | | (211) all_1969_0 = all_1967_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (203), (204) imply: % 224.88/38.09 | | | | | | | | | | | | | | (212) all_1969_0 = all_1965_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | SIMP: (212) implies: % 224.88/38.09 | | | | | | | | | | | | | | (213) all_1969_0 = all_1965_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (201), (202) imply: % 224.88/38.09 | | | | | | | | | | | | | | (214) all_1969_0 = all_1963_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | SIMP: (214) implies: % 224.88/38.09 | | | | | | | | | | | | | | (215) all_1969_0 = all_1963_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (211), (215) imply: % 224.88/38.09 | | | | | | | | | | | | | | (216) all_1967_0 = all_1963_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (200), (211) imply: % 224.88/38.09 | | | | | | | | | | | | | | (217) all_1967_0 = 0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (211), (213) imply: % 224.88/38.09 | | | | | | | | | | | | | | (218) all_1967_0 = all_1965_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (217), (218) imply: % 224.88/38.09 | | | | | | | | | | | | | | (219) all_1965_0 = 0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (216), (218) imply: % 224.88/38.09 | | | | | | | | | | | | | | (220) all_1965_0 = all_1963_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (219), (220) imply: % 224.88/38.09 | | | | | | | | | | | | | | (221) all_1963_0 = 0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | REDUCE: (184), (221) imply: % 224.88/38.09 | | | | | | | | | | | | | | (222) $false % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | Case 2: % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_1801_1, all_385_0, % 224.88/38.09 | | | | | | | | | | | | | | simplifying with (130), (171) gives: % 224.88/38.09 | | | | | | | | | | | | | | (223) all_1801_1 = 0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1801_1, all_1803_1, % 224.88/38.09 | | | | | | | | | | | | | | all_385_0, simplifying with (171), (173) gives: % 224.88/38.09 | | | | | | | | | | | | | | (224) all_1803_1 = all_1801_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1799_1, all_1807_1, % 224.88/38.09 | | | | | | | | | | | | | | all_385_0, simplifying with (169), (179) gives: % 224.88/38.09 | | | | | | | | | | | | | | (225) all_1807_1 = all_1799_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1807_1, all_1809_1, % 224.88/38.09 | | | | | | | | | | | | | | all_385_0, simplifying with (179), (181) gives: % 224.88/38.09 | | | | | | | | | | | | | | (226) all_1809_1 = all_1807_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1805_1, all_1809_1, % 224.88/38.09 | | | | | | | | | | | | | | all_385_0, simplifying with (177), (181) gives: % 224.88/38.09 | | | | | | | | | | | | | | (227) all_1809_1 = all_1805_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1803_1, all_1809_1, % 224.88/38.09 | | | | | | | | | | | | | | all_385_0, simplifying with (173), (181) gives: % 224.88/38.09 | | | | | | | | | | | | | | (228) all_1809_1 = all_1803_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_139_0, all_1803_0, % 224.88/38.09 | | | | | | | | | | | | | | all_139_1, simplifying with (25), (174) gives: % 224.88/38.09 | | | | | | | | | | | | | | (229) all_1803_0 = all_139_0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (227), (228) imply: % 224.88/38.09 | | | | | | | | | | | | | | (230) all_1805_1 = all_1803_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (226), (227) imply: % 224.88/38.09 | | | | | | | | | | | | | | (231) all_1807_1 = all_1805_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | SIMP: (231) implies: % 224.88/38.09 | | | | | | | | | | | | | | (232) all_1807_1 = all_1805_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (225), (232) imply: % 224.88/38.09 | | | | | | | | | | | | | | (233) all_1805_1 = all_1799_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | SIMP: (233) implies: % 224.88/38.09 | | | | | | | | | | | | | | (234) all_1805_1 = all_1799_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (230), (234) imply: % 224.88/38.09 | | | | | | | | | | | | | | (235) all_1803_1 = all_1799_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | SIMP: (235) implies: % 224.88/38.09 | | | | | | | | | | | | | | (236) all_1803_1 = all_1799_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (224), (236) imply: % 224.88/38.09 | | | | | | | | | | | | | | (237) all_1801_1 = all_1799_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | SIMP: (237) implies: % 224.88/38.09 | | | | | | | | | | | | | | (238) all_1801_1 = all_1799_1 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (223), (238) imply: % 224.88/38.09 | | | | | | | | | | | | | | (239) all_1799_1 = 0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (236), (239) imply: % 224.88/38.09 | | | | | | | | | | | | | | (240) all_1803_1 = 0 % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | BETA: splitting (175) gives: % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | Case 1: % 224.88/38.09 | | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | | (241) ~ (all_1803_1 = 0) % 224.88/38.09 | | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | | REDUCE: (240), (241) imply: % 224.88/38.09 | | | | | | | | | | | | | | | (242) $false % 224.88/38.09 | | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent. % 224.88/38.09 | | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | Case 2: % 224.88/38.09 | | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | | (243) all_1803_0 = 0 % 224.88/38.09 | | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | | COMBINE_EQS: (229), (243) imply: % 224.88/38.09 | | | | | | | | | | | | | | | (244) all_139_0 = 0 % 224.88/38.09 | | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | | SIMP: (244) implies: % 224.88/38.09 | | | | | | | | | | | | | | | (245) all_139_0 = 0 % 224.88/38.09 | | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | | REDUCE: (38), (245) imply: % 224.88/38.09 | | | | | | | | | | | | | | | (246) $false % 224.88/38.09 | | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent. % 224.88/38.09 | | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | | End of split % 224.88/38.09 | | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | End of split % 224.88/38.09 | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | Case 2: % 224.88/38.09 | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | (247) ? [v0: any] : ? [v1: any] : (segmentP(all_139_1, % 224.88/38.09 | | | | | | | | | | | | | all_143_0) = v1 & ssList(all_139_1) = v0 & ( ~ % 224.88/38.09 | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 224.88/38.09 | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | DELTA: instantiating (247) with fresh symbols all_417_0, % 224.88/38.09 | | | | | | | | | | | | | all_417_1 gives: % 224.88/38.09 | | | | | | | | | | | | | (248) segmentP(all_139_1, all_143_0) = all_417_0 & % 224.88/38.09 | | | | | | | | | | | | | ssList(all_139_1) = all_417_1 & ( ~ (all_417_0 = % 224.88/38.09 | | | | | | | | | | | | | 0) | ~ (all_417_1 = 0)) % 224.88/38.09 | | | | | | | | | | | | | % 224.88/38.09 | | | | | | | | | | | | | ALPHA: (248) implies: % 224.88/38.09 | | | | | | | | | | | | | (249) ssList(all_139_1) = all_417_1 % 224.88/38.10 | | | | | | | | | | | | | (250) ~ (all_417_0 = 0) | ~ (all_417_1 = 0) % 224.88/38.10 | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_417_1, all_139_1, % 224.88/38.10 | | | | | | | | | | | | | simplifying with (43), (249) gives: % 224.88/38.10 | | | | | | | | | | | | | (251) all_417_1 = 0 % 224.88/38.10 | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | BETA: splitting (250) gives: % 224.88/38.10 | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | Case 1: % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (59) with all_403_0, simplifying % 224.88/38.10 | | | | | | | | | | | | | | with (153), (154) gives: % 224.88/38.10 | | | | | | | | | | | | | | (252) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | % 224.88/38.10 | | | | | | | | | | | | | | ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | % 224.88/38.10 | | | | | | | | | | | | | | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 224.88/38.10 | | | | | | | | | | | | | | (cons(all_403_0, v2) = v3) | ~ (app(v1, v3) % 224.88/38.10 | | | | | | | | | | | | | | = v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 % 224.88/38.10 | | | | | | | | | | | | | | = 0) & ssList(v2) = v5) | ! [v5: $i] : % 224.88/38.10 | | | | | | | | | | | | | | ! [v6: $i] : ( ~ (v0 = all_403_0) | ~ % 224.88/38.10 | | | | | | | | | | | | | | (cons(all_403_0, v5) = v6) | ~ (app(v4, % 224.88/38.10 | | | | | | | | | | | | | | v6) = nil) | ~ $i(v5) | ? [v7: int] % 224.88/38.10 | | | | | | | | | | | | | | : ( ~ (v7 = 0) & ssList(v5) = v7))))) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (45) with all_385_0, all_139_1, % 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.10 | | | | | | | | | | | | | | (253) ? [v0: any] : ? [v1: $i] : (tl(all_139_1) = v1 & % 224.88/38.10 | | | | | | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) | % 224.88/38.10 | | | | | | | | | | | | | | v1 = nil)) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (46) with all_385_0, all_139_1, % 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.10 | | | | | | | | | | | | | | (254) ? [v0: any] : ? [v1: $i] : (hd(all_139_1) = v1 & % 224.88/38.10 | | | | | | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) | % 224.88/38.10 | | | | | | | | | | | | | | v1 = all_385_0)) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_385_0, all_139_1, % 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.10 | | | | | | | | | | | | | | (255) ? [v0: any] : ? [v1: any] : % 224.88/38.10 | | | | | | | | | | | | | | (equalelemsP(all_139_1) = v1 & ssItem(all_385_0) = % 224.88/38.10 | | | | | | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_385_0, all_139_1, % 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.10 | | | | | | | | | | | | | | (256) ? [v0: any] : ? [v1: any] : % 224.88/38.10 | | | | | | | | | | | | | | (duplicatefreeP(all_139_1) = v1 & % 224.88/38.10 | | | | | | | | | | | | | | ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_385_0, all_139_1, % 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.10 | | | | | | | | | | | | | | (257) ? [v0: any] : ? [v1: any] : % 224.88/38.10 | | | | | | | | | | | | | | (strictorderedP(all_139_1) = v1 & % 224.88/38.10 | | | | | | | | | | | | | | ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_385_0, all_139_1, % 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.10 | | | | | | | | | | | | | | (258) ? [v0: any] : ? [v1: any] : % 224.88/38.10 | | | | | | | | | | | | | | (totalorderedP(all_139_1) = v1 & ssItem(all_385_0) % 224.88/38.10 | | | | | | | | | | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_385_0, all_139_1, % 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.10 | | | | | | | | | | | | | | (259) ? [v0: any] : ? [v1: any] : % 224.88/38.10 | | | | | | | | | | | | | | (strictorderP(all_139_1) = v1 & ssItem(all_385_0) % 224.88/38.10 | | | | | | | | | | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_385_0, all_139_1, % 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.10 | | | | | | | | | | | | | | (260) ? [v0: any] : ? [v1: any] : % 224.88/38.10 | | | | | | | | | | | | | | (totalorderP(all_139_1) = v1 & ssItem(all_385_0) = % 224.88/38.10 | | | | | | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_385_0, all_139_1, % 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives: % 224.88/38.10 | | | | | | | | | | | | | | (261) ? [v0: any] : ? [v1: any] : % 224.88/38.10 | | | | | | | | | | | | | | (cyclefreeP(all_139_1) = v1 & ssItem(all_385_0) = % 224.88/38.10 | | | | | | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (252) with all_385_0, simplifying % 224.88/38.10 | | | | | | | | | | | | | | with (129), (130) gives: % 224.88/38.10 | | | | | | | | | | | | | | (262) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | % 224.88/38.10 | | | | | | | | | | | | | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 224.88/38.10 | | | | | | | | | | | | | | (cons(all_403_0, v1) = v2) | ~ (app(v0, v2) = % 224.88/38.10 | | | | | | | | | | | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = % 224.88/38.10 | | | | | | | | | | | | | | 0) & ssList(v1) = v4) | ! [v4: $i] : ! % 224.88/38.10 | | | | | | | | | | | | | | [v5: $i] : ( ~ (all_403_0 = all_385_0) | ~ % 224.88/38.10 | | | | | | | | | | | | | | (cons(all_385_0, v4) = v5) | ~ (app(v3, v5) % 224.88/38.10 | | | | | | | | | | | | | | = nil) | ~ $i(v4) | ? [v6: int] : ( ~ % 224.88/38.10 | | | | | | | | | | | | | | (v6 = 0) & ssList(v4) = v6)))) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (262) with all_341_1, simplifying % 224.88/38.10 | | | | | | | | | | | | | | with (74), (76) gives: % 224.88/38.10 | | | | | | | | | | | | | | (263) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 224.88/38.10 | | | | | | | | | | | | | | (cons(all_403_0, v0) = v1) | ~ (app(all_341_1, % 224.88/38.10 | | | | | | | | | | | | | | v1) = v2) | ~ $i(v0) | ? [v3: int] : ( ~ % 224.88/38.10 | | | | | | | | | | | | | | (v3 = 0) & ssList(v0) = v3) | ! [v3: $i] : ! % 224.88/38.10 | | | | | | | | | | | | | | [v4: $i] : ( ~ (all_403_0 = all_385_0) | ~ % 224.88/38.10 | | | | | | | | | | | | | | (cons(all_385_0, v3) = v4) | ~ (app(v2, v4) = % 224.88/38.10 | | | | | | | | | | | | | | nil) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = % 224.88/38.10 | | | | | | | | | | | | | | 0) & ssList(v3) = v5))) % 224.88/38.10 | | | | | | | | | | | | | | % 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (263) with all_401_0, all_139_1, % 224.88/38.10 | | | | | | | | | | | | | | all_341_0, simplifying with (75), (149), (155) % 224.88/38.10 | | | | | | | | | | | | | | gives: % 224.88/38.11 | | | | | | | | | | | | | | (264) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_401_0) = % 224.88/38.11 | | | | | | | | | | | | | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ (all_403_0 % 224.88/38.11 | | | | | | | | | | | | | | = all_385_0) | ~ (cons(all_385_0, v0) = v1) | % 224.88/38.11 | | | | | | | | | | | | | | ~ (app(all_341_0, v1) = nil) | ~ $i(v0) | ? % 224.88/38.11 | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (256) with fresh symbols all_1895_0, % 224.88/38.11 | | | | | | | | | | | | | | all_1895_1 gives: % 224.88/38.11 | | | | | | | | | | | | | | (265) duplicatefreeP(all_139_1) = all_1895_0 & % 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1895_1 & ( ~ (all_1895_1 = % 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1895_0 = 0) % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (265) implies: % 224.88/38.11 | | | | | | | | | | | | | | (266) ssItem(all_385_0) = all_1895_1 % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (255) with fresh symbols all_1897_0, % 224.88/38.11 | | | | | | | | | | | | | | all_1897_1 gives: % 224.88/38.11 | | | | | | | | | | | | | | (267) equalelemsP(all_139_1) = all_1897_0 & % 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1897_1 & ( ~ (all_1897_1 = % 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1897_0 = 0) % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (267) implies: % 224.88/38.11 | | | | | | | | | | | | | | (268) ssItem(all_385_0) = all_1897_1 % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (261) with fresh symbols all_1899_0, % 224.88/38.11 | | | | | | | | | | | | | | all_1899_1 gives: % 224.88/38.11 | | | | | | | | | | | | | | (269) cyclefreeP(all_139_1) = all_1899_0 & % 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1899_1 & ( ~ (all_1899_1 = % 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1899_0 = 0) % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (269) implies: % 224.88/38.11 | | | | | | | | | | | | | | (270) ssItem(all_385_0) = all_1899_1 % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (260) with fresh symbols all_1901_0, % 224.88/38.11 | | | | | | | | | | | | | | all_1901_1 gives: % 224.88/38.11 | | | | | | | | | | | | | | (271) totalorderP(all_139_1) = all_1901_0 & % 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1901_1 & ( ~ (all_1901_1 = % 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1901_0 = 0) % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (271) implies: % 224.88/38.11 | | | | | | | | | | | | | | (272) ssItem(all_385_0) = all_1901_1 % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (259) with fresh symbols all_1903_0, % 224.88/38.11 | | | | | | | | | | | | | | all_1903_1 gives: % 224.88/38.11 | | | | | | | | | | | | | | (273) strictorderP(all_139_1) = all_1903_0 & % 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1903_1 & ( ~ (all_1903_1 = % 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1903_0 = 0) % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (273) implies: % 224.88/38.11 | | | | | | | | | | | | | | (274) ssItem(all_385_0) = all_1903_1 % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (258) with fresh symbols all_1905_0, % 224.88/38.11 | | | | | | | | | | | | | | all_1905_1 gives: % 224.88/38.11 | | | | | | | | | | | | | | (275) totalorderedP(all_139_1) = all_1905_0 & % 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1905_1 & ( ~ (all_1905_1 = % 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1905_0 = 0) % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (275) implies: % 224.88/38.11 | | | | | | | | | | | | | | (276) ssItem(all_385_0) = all_1905_1 % 224.88/38.11 | | | | | | | | | | | | | | (277) totalorderedP(all_139_1) = all_1905_0 % 224.88/38.11 | | | | | | | | | | | | | | (278) ~ (all_1905_1 = 0) | all_1905_0 = 0 % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (257) with fresh symbols all_1907_0, % 224.88/38.11 | | | | | | | | | | | | | | all_1907_1 gives: % 224.88/38.11 | | | | | | | | | | | | | | (279) strictorderedP(all_139_1) = all_1907_0 & % 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1907_1 & ( ~ (all_1907_1 = % 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1907_0 = 0) % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (279) implies: % 224.88/38.11 | | | | | | | | | | | | | | (280) ssItem(all_385_0) = all_1907_1 % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (254) with fresh symbols all_1909_0, % 224.88/38.11 | | | | | | | | | | | | | | all_1909_1 gives: % 224.88/38.11 | | | | | | | | | | | | | | (281) hd(all_139_1) = all_1909_0 & ssItem(all_385_0) = % 224.88/38.11 | | | | | | | | | | | | | | all_1909_1 & $i(all_1909_0) & ( ~ (all_1909_1 = 0) % 224.88/38.11 | | | | | | | | | | | | | | | all_1909_0 = all_385_0) % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (281) implies: % 224.88/38.11 | | | | | | | | | | | | | | (282) ssItem(all_385_0) = all_1909_1 % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (253) with fresh symbols all_1911_0, % 224.88/38.11 | | | | | | | | | | | | | | all_1911_1 gives: % 224.88/38.11 | | | | | | | | | | | | | | (283) tl(all_139_1) = all_1911_0 & ssItem(all_385_0) = % 224.88/38.11 | | | | | | | | | | | | | | all_1911_1 & $i(all_1911_0) & ( ~ (all_1911_1 = 0) % 224.88/38.11 | | | | | | | | | | | | | | | all_1911_0 = nil) % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (283) implies: % 224.88/38.11 | | | | | | | | | | | | | | (284) ssItem(all_385_0) = all_1911_1 % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | BETA: splitting (264) gives: % 224.88/38.11 | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | Case 1: % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | (285) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_401_0) = % 224.88/38.11 | | | | | | | | | | | | | | | v0) % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1956_0 % 224.88/38.11 | | | | | | | | | | | | | | | gives: % 224.88/38.11 | | | | | | | | | | | | | | | (286) ~ (all_1956_0 = 0) & ssList(all_401_0) = % 224.88/38.11 | | | | | | | | | | | | | | | all_1956_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (286) implies: % 224.88/38.11 | | | | | | | | | | | | | | | (287) ~ (all_1956_0 = 0) % 224.88/38.11 | | | | | | | | | | | | | | | (288) ssList(all_401_0) = all_1956_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1958_0 % 224.88/38.11 | | | | | | | | | | | | | | | gives: % 224.88/38.11 | | | | | | | | | | | | | | | (289) ~ (all_1958_0 = 0) & ssList(all_401_0) = % 224.88/38.11 | | | | | | | | | | | | | | | all_1958_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (289) implies: % 224.88/38.11 | | | | | | | | | | | | | | | (290) ssList(all_401_0) = all_1958_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1960_0 % 224.88/38.11 | | | | | | | | | | | | | | | gives: % 224.88/38.11 | | | | | | | | | | | | | | | (291) ~ (all_1960_0 = 0) & ssList(all_401_0) = % 224.88/38.11 | | | | | | | | | | | | | | | all_1960_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (291) implies: % 224.88/38.11 | | | | | | | | | | | | | | | (292) ssList(all_401_0) = all_1960_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1972_0 % 224.88/38.11 | | | | | | | | | | | | | | | gives: % 224.88/38.11 | | | | | | | | | | | | | | | (293) ~ (all_1972_0 = 0) & ssList(all_401_0) = % 224.88/38.11 | | | | | | | | | | | | | | | all_1972_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (293) implies: % 224.88/38.11 | | | | | | | | | | | | | | | (294) ssList(all_401_0) = all_1972_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1974_0 % 224.88/38.11 | | | | | | | | | | | | | | | gives: % 224.88/38.11 | | | | | | | | | | | | | | | (295) ~ (all_1974_0 = 0) & ssList(all_401_0) = % 224.88/38.11 | | | | | | | | | | | | | | | all_1974_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (295) implies: % 224.88/38.11 | | | | | | | | | | | | | | | (296) ssList(all_401_0) = all_1974_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1976_0 % 224.88/38.11 | | | | | | | | | | | | | | | gives: % 224.88/38.11 | | | | | | | | | | | | | | | (297) ~ (all_1976_0 = 0) & ssList(all_401_0) = % 224.88/38.11 | | | | | | | | | | | | | | | all_1976_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (297) implies: % 224.88/38.11 | | | | | | | | | | | | | | | (298) ssList(all_401_0) = all_1976_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1978_0 % 224.88/38.11 | | | | | | | | | | | | | | | gives: % 224.88/38.11 | | | | | | | | | | | | | | | (299) ~ (all_1978_0 = 0) & ssList(all_401_0) = % 224.88/38.11 | | | | | | | | | | | | | | | all_1978_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (299) implies: % 224.88/38.11 | | | | | | | | | | | | | | | (300) ssList(all_401_0) = all_1978_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_1972_0, all_401_0, % 224.88/38.11 | | | | | | | | | | | | | | | simplifying with (150), (294) gives: % 224.88/38.11 | | | | | | | | | | | | | | | (301) all_1972_0 = 0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1958_0, all_1972_0, % 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (290), (294) gives: % 224.88/38.11 | | | | | | | | | | | | | | | (302) all_1972_0 = all_1958_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1974_0, all_1976_0, % 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (296), (298) gives: % 224.88/38.11 | | | | | | | | | | | | | | | (303) all_1976_0 = all_1974_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1956_0, all_1976_0, % 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (288), (298) gives: % 224.88/38.11 | | | | | | | | | | | | | | | (304) all_1976_0 = all_1956_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1976_0, all_1978_0, % 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (298), (300) gives: % 224.88/38.11 | | | | | | | | | | | | | | | (305) all_1978_0 = all_1976_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1972_0, all_1978_0, % 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (294), (300) gives: % 224.88/38.11 | | | | | | | | | | | | | | | (306) all_1978_0 = all_1972_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1960_0, all_1978_0, % 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (292), (300) gives: % 224.88/38.11 | | | | | | | | | | | | | | | (307) all_1978_0 = all_1960_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | COMBINE_EQS: (306), (307) imply: % 224.88/38.11 | | | | | | | | | | | | | | | (308) all_1972_0 = all_1960_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | SIMP: (308) implies: % 224.88/38.11 | | | | | | | | | | | | | | | (309) all_1972_0 = all_1960_0 % 224.88/38.11 | | | | | | | | | | | | | | | % 224.88/38.11 | | | | | | | | | | | | | | | COMBINE_EQS: (305), (307) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (310) all_1976_0 = all_1960_0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (310) implies: % 224.88/38.12 | | | | | | | | | | | | | | | (311) all_1976_0 = all_1960_0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (303), (311) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (312) all_1974_0 = all_1960_0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (303), (304) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (313) all_1974_0 = all_1956_0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (312), (313) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (314) all_1960_0 = all_1956_0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (314) implies: % 224.88/38.12 | | | | | | | | | | | | | | | (315) all_1960_0 = all_1956_0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (302), (309) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (316) all_1960_0 = all_1958_0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (316) implies: % 224.88/38.12 | | | | | | | | | | | | | | | (317) all_1960_0 = all_1958_0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (301), (302) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (318) all_1958_0 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (315), (317) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (319) all_1958_0 = all_1956_0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (319) implies: % 224.88/38.12 | | | | | | | | | | | | | | | (320) all_1958_0 = all_1956_0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (318), (320) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (321) all_1956_0 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | REDUCE: (287), (321) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (322) $false % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | CLOSE: (322) is inconsistent. % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | Case 2: % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1899_1, all_1901_1, % 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (270), (272) gives: % 224.88/38.12 | | | | | | | | | | | | | | | (323) all_1901_1 = all_1899_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1903_1, all_1905_1, % 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (274), (276) gives: % 224.88/38.12 | | | | | | | | | | | | | | | (324) all_1905_1 = all_1903_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1899_1, all_1905_1, % 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (270), (276) gives: % 224.88/38.12 | | | | | | | | | | | | | | | (325) all_1905_1 = all_1899_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1899_1, all_1907_1, % 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (270), (280) gives: % 224.88/38.12 | | | | | | | | | | | | | | | (326) all_1907_1 = all_1899_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1897_1, all_1907_1, % 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (268), (280) gives: % 224.88/38.12 | | | | | | | | | | | | | | | (327) all_1907_1 = all_1897_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_1909_1, all_385_0, % 224.88/38.12 | | | | | | | | | | | | | | | simplifying with (130), (282) gives: % 224.88/38.12 | | | | | | | | | | | | | | | (328) all_1909_1 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1901_1, all_1909_1, % 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (272), (282) gives: % 224.88/38.12 | | | | | | | | | | | | | | | (329) all_1909_1 = all_1901_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1905_1, all_1911_1, % 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (276), (284) gives: % 224.88/38.12 | | | | | | | | | | | | | | | (330) all_1911_1 = all_1905_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1895_1, all_1911_1, % 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (266), (284) gives: % 224.88/38.12 | | | | | | | | | | | | | | | (331) all_1911_1 = all_1895_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_139_0, all_1905_0, % 224.88/38.12 | | | | | | | | | | | | | | | all_139_1, simplifying with (25), (277) gives: % 224.88/38.12 | | | | | | | | | | | | | | | (332) all_1905_0 = all_139_0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (330), (331) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (333) all_1905_1 = all_1895_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (333) implies: % 224.88/38.12 | | | | | | | | | | | | | | | (334) all_1905_1 = all_1895_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (328), (329) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (335) all_1901_1 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (335) implies: % 224.88/38.12 | | | | | | | | | | | | | | | (336) all_1901_1 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (326), (327) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (337) all_1899_1 = all_1897_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (337) implies: % 224.88/38.12 | | | | | | | | | | | | | | | (338) all_1899_1 = all_1897_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (324), (325) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (339) all_1903_1 = all_1899_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (324), (334) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (340) all_1903_1 = all_1895_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (339), (340) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (341) all_1899_1 = all_1895_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (341) implies: % 224.88/38.12 | | | | | | | | | | | | | | | (342) all_1899_1 = all_1895_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (323), (336) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (343) all_1899_1 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (343) implies: % 224.88/38.12 | | | | | | | | | | | | | | | (344) all_1899_1 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (338), (344) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (345) all_1897_1 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (338), (342) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (346) all_1897_1 = all_1895_1 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (345), (346) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (347) all_1895_1 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (347) implies: % 224.88/38.12 | | | | | | | | | | | | | | | (348) all_1895_1 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (340), (348) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (349) all_1903_1 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (324), (349) imply: % 224.88/38.12 | | | | | | | | | | | | | | | (350) all_1905_1 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | BETA: splitting (278) gives: % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | Case 1: % 224.88/38.12 | | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | | (351) ~ (all_1905_1 = 0) % 224.88/38.12 | | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | | REDUCE: (350), (351) imply: % 224.88/38.12 | | | | | | | | | | | | | | | | (352) $false % 224.88/38.12 | | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | | CLOSE: (352) is inconsistent. % 224.88/38.12 | | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | Case 2: % 224.88/38.12 | | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | | (353) all_1905_0 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (353) imply: % 224.88/38.12 | | | | | | | | | | | | | | | | (354) all_139_0 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | | SIMP: (354) implies: % 224.88/38.12 | | | | | | | | | | | | | | | | (355) all_139_0 = 0 % 224.88/38.12 | | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | | REDUCE: (38), (355) imply: % 224.88/38.12 | | | | | | | | | | | | | | | | (356) $false % 224.88/38.12 | | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | | CLOSE: (356) is inconsistent. % 224.88/38.12 | | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | | End of split % 224.88/38.12 | | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | End of split % 224.88/38.12 | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | Case 2: % 224.88/38.12 | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | (357) ~ (all_417_1 = 0) % 224.88/38.12 | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | REDUCE: (251), (357) imply: % 224.88/38.12 | | | | | | | | | | | | | | (358) $false % 224.88/38.12 | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | | CLOSE: (358) is inconsistent. % 224.88/38.12 | | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | | End of split % 224.88/38.12 | | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | | End of split % 224.88/38.12 | | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | | End of split % 224.88/38.12 | | | | | | | | | | | % 224.88/38.12 | | | | | | | | | | End of split % 224.88/38.12 | | | | | | | | | | % 224.88/38.12 | | | | | | | | | End of split % 224.88/38.12 | | | | | | | | | % 224.88/38.12 | | | | | | | | Case 2: % 224.88/38.12 | | | | | | | | | % 224.88/38.12 | | | | | | | | | (359) ~ (all_147_0 = 0) % 224.88/38.12 | | | | | | | | | % 224.88/38.12 | | | | | | | | | REDUCE: (106), (359) imply: % 224.88/38.12 | | | | | | | | | (360) $false % 224.88/38.12 | | | | | | | | | % 224.88/38.12 | | | | | | | | | CLOSE: (360) is inconsistent. % 224.88/38.12 | | | | | | | | | % 224.88/38.12 | | | | | | | | End of split % 224.88/38.12 | | | | | | | | % 224.88/38.12 | | | | | | | End of split % 224.88/38.12 | | | | | | | % 224.88/38.12 | | | | | | End of split % 224.88/38.12 | | | | | | % 224.88/38.12 | | | | | End of split % 224.88/38.12 | | | | | % 224.88/38.12 | | | | End of split % 224.88/38.12 | | | | % 224.88/38.12 | | | Case 2: % 224.88/38.12 | | | | % 224.88/38.12 | | | | (361) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 224.88/38.12 | | | | % 224.88/38.12 | | | | DELTA: instantiating (361) with fresh symbol all_341_0 gives: % 224.88/38.12 | | | | (362) ~ (all_341_0 = 0) & ssList(all_139_1) = all_341_0 % 224.88/38.12 | | | | % 224.88/38.12 | | | | ALPHA: (362) implies: % 224.88/38.12 | | | | (363) ~ (all_341_0 = 0) % 224.88/38.12 | | | | (364) ssList(all_139_1) = all_341_0 % 224.88/38.12 | | | | % 224.88/38.12 | | | | GROUND_INST: instantiating (18) with 0, all_341_0, all_139_1, % 224.88/38.12 | | | | simplifying with (43), (364) gives: % 224.88/38.12 | | | | (365) all_341_0 = 0 % 224.88/38.12 | | | | % 224.88/38.12 | | | | REDUCE: (363), (365) imply: % 224.88/38.12 | | | | (366) $false % 224.88/38.12 | | | | % 224.88/38.12 | | | | CLOSE: (366) is inconsistent. % 224.88/38.12 | | | | % 224.88/38.12 | | | End of split % 224.88/38.12 | | | % 224.88/38.12 | | End of split % 224.88/38.12 | | % 224.88/38.12 | End of split % 224.88/38.12 | % 224.88/38.12 End of proof % 224.88/38.12 % 224.88/38.12 Sub-proof #1 shows that the following formulas are inconsistent: % 224.88/38.12 ---------------------------------------------------------------- % 224.88/38.13 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 224.88/38.13 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 224.88/38.13 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 224.88/38.13 (3) ssList(nil) = 0 % 224.88/38.13 % 224.88/38.13 Begin of proof % 224.88/38.13 | % 224.88/38.13 | DELTA: instantiating (1) with fresh symbol all_1950_0 gives: % 224.88/38.13 | (4) ~ (all_1950_0 = 0) & ssList(nil) = all_1950_0 % 224.88/38.13 | % 224.88/38.13 | ALPHA: (4) implies: % 224.88/38.13 | (5) ~ (all_1950_0 = 0) % 224.88/38.13 | (6) ssList(nil) = all_1950_0 % 224.88/38.13 | % 224.88/38.13 | DELTA: instantiating (1) with fresh symbol all_1952_0 gives: % 224.88/38.13 | (7) ~ (all_1952_0 = 0) & ssList(nil) = all_1952_0 % 224.88/38.13 | % 224.88/38.13 | ALPHA: (7) implies: % 224.88/38.13 | (8) ssList(nil) = all_1952_0 % 224.88/38.13 | % 224.88/38.13 | DELTA: instantiating (1) with fresh symbol all_1970_0 gives: % 225.46/38.13 | (9) ~ (all_1970_0 = 0) & ssList(nil) = all_1970_0 % 225.46/38.13 | % 225.46/38.13 | ALPHA: (9) implies: % 225.46/38.13 | (10) ssList(nil) = all_1970_0 % 225.46/38.13 | % 225.46/38.13 | DELTA: instantiating (1) with fresh symbol all_1972_0 gives: % 225.46/38.13 | (11) ~ (all_1972_0 = 0) & ssList(nil) = all_1972_0 % 225.46/38.13 | % 225.46/38.13 | ALPHA: (11) implies: % 225.46/38.13 | (12) ssList(nil) = all_1972_0 % 225.46/38.13 | % 225.46/38.13 | DELTA: instantiating (1) with fresh symbol all_1974_0 gives: % 225.46/38.13 | (13) ~ (all_1974_0 = 0) & ssList(nil) = all_1974_0 % 225.46/38.13 | % 225.46/38.13 | ALPHA: (13) implies: % 225.46/38.13 | (14) ssList(nil) = all_1974_0 % 225.46/38.13 | % 225.46/38.13 | DELTA: instantiating (1) with fresh symbol all_1976_0 gives: % 225.46/38.13 | (15) ~ (all_1976_0 = 0) & ssList(nil) = all_1976_0 % 225.46/38.13 | % 225.46/38.13 | ALPHA: (15) implies: % 225.46/38.13 | (16) ssList(nil) = all_1976_0 % 225.46/38.13 | % 225.46/38.13 | DELTA: instantiating (1) with fresh symbol all_1978_0 gives: % 225.46/38.13 | (17) ~ (all_1978_0 = 0) & ssList(nil) = all_1978_0 % 225.46/38.13 | % 225.46/38.13 | ALPHA: (17) implies: % 225.46/38.13 | (18) ssList(nil) = all_1978_0 % 225.46/38.13 | % 225.46/38.13 | GROUND_INST: instantiating (2) with all_1950_0, all_1952_0, nil, simplifying % 225.46/38.13 | with (6), (8) gives: % 225.46/38.13 | (19) all_1952_0 = all_1950_0 % 225.46/38.13 | % 225.46/38.13 | GROUND_INST: instantiating (2) with all_1952_0, all_1970_0, nil, simplifying % 225.46/38.13 | with (8), (10) gives: % 225.46/38.13 | (20) all_1970_0 = all_1952_0 % 225.46/38.13 | % 225.46/38.13 | GROUND_INST: instantiating (2) with all_1974_0, all_1976_0, nil, simplifying % 225.46/38.13 | with (14), (16) gives: % 225.46/38.13 | (21) all_1976_0 = all_1974_0 % 225.46/38.13 | % 225.46/38.13 | GROUND_INST: instantiating (2) with all_1972_0, all_1976_0, nil, simplifying % 225.46/38.13 | with (12), (16) gives: % 225.46/38.13 | (22) all_1976_0 = all_1972_0 % 225.46/38.13 | % 225.46/38.13 | GROUND_INST: instantiating (2) with all_1970_0, all_1976_0, nil, simplifying % 225.46/38.13 | with (10), (16) gives: % 225.46/38.13 | (23) all_1976_0 = all_1970_0 % 225.46/38.13 | % 225.46/38.13 | GROUND_INST: instantiating (2) with 0, all_1978_0, nil, simplifying with (3), % 225.46/38.13 | (18) gives: % 225.46/38.13 | (24) all_1978_0 = 0 % 225.46/38.13 | % 225.46/38.13 | GROUND_INST: instantiating (2) with all_1974_0, all_1978_0, nil, simplifying % 225.46/38.13 | with (14), (18) gives: % 225.46/38.13 | (25) all_1978_0 = all_1974_0 % 225.46/38.13 | % 225.46/38.13 | COMBINE_EQS: (24), (25) imply: % 225.46/38.13 | (26) all_1974_0 = 0 % 225.46/38.13 | % 225.46/38.13 | SIMP: (26) implies: % 225.46/38.13 | (27) all_1974_0 = 0 % 225.46/38.13 | % 225.46/38.13 | COMBINE_EQS: (21), (22) imply: % 225.46/38.13 | (28) all_1974_0 = all_1972_0 % 225.46/38.13 | % 225.46/38.13 | SIMP: (28) implies: % 225.46/38.13 | (29) all_1974_0 = all_1972_0 % 225.46/38.13 | % 225.46/38.13 | COMBINE_EQS: (22), (23) imply: % 225.46/38.13 | (30) all_1972_0 = all_1970_0 % 225.46/38.13 | % 225.46/38.13 | COMBINE_EQS: (27), (29) imply: % 225.46/38.13 | (31) all_1972_0 = 0 % 225.46/38.13 | % 225.46/38.13 | SIMP: (31) implies: % 225.46/38.13 | (32) all_1972_0 = 0 % 225.46/38.13 | % 225.46/38.13 | COMBINE_EQS: (30), (32) imply: % 225.46/38.13 | (33) all_1970_0 = 0 % 225.46/38.13 | % 225.46/38.13 | SIMP: (33) implies: % 225.46/38.13 | (34) all_1970_0 = 0 % 225.46/38.13 | % 225.46/38.13 | COMBINE_EQS: (20), (34) imply: % 225.46/38.13 | (35) all_1952_0 = 0 % 225.46/38.13 | % 225.46/38.13 | SIMP: (35) implies: % 225.46/38.13 | (36) all_1952_0 = 0 % 225.46/38.13 | % 225.46/38.13 | COMBINE_EQS: (19), (36) imply: % 225.46/38.13 | (37) all_1950_0 = 0 % 225.46/38.13 | % 225.46/38.13 | SIMP: (37) implies: % 225.46/38.13 | (38) all_1950_0 = 0 % 225.46/38.13 | % 225.46/38.13 | REDUCE: (5), (38) imply: % 225.46/38.13 | (39) $false % 225.46/38.13 | % 225.46/38.13 | CLOSE: (39) is inconsistent. % 225.46/38.13 | % 225.46/38.13 End of proof % 225.46/38.13 % SZS output end Proof for theBenchmark % 225.46/38.13 % 225.46/38.13 37535ms 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