TSTP Solution File: SWC098+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC098+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 : n015.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 20:49:38 EDT 2023
% Result : Theorem 24.45s 4.03s
% Output : Proof 139.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC098+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 17:14:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.78/1.47 Prover 1: Preprocessing ...
% 4.78/1.48 Prover 4: Preprocessing ...
% 4.78/1.50 Prover 2: Preprocessing ...
% 4.78/1.50 Prover 5: Preprocessing ...
% 4.78/1.50 Prover 6: Preprocessing ...
% 4.78/1.50 Prover 3: Preprocessing ...
% 4.78/1.50 Prover 0: Preprocessing ...
% 13.62/2.57 Prover 2: Proving ...
% 14.02/2.74 Prover 1: Constructing countermodel ...
% 14.02/2.76 Prover 6: Proving ...
% 14.02/2.77 Prover 5: Constructing countermodel ...
% 15.64/2.87 Prover 3: Constructing countermodel ...
% 22.09/3.75 Prover 4: Constructing countermodel ...
% 22.64/3.79 Prover 0: Proving ...
% 24.45/4.03 Prover 0: proved (3397ms)
% 24.45/4.03
% 24.45/4.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.45/4.03
% 24.45/4.03 Prover 3: stopped
% 24.45/4.03 Prover 5: stopped
% 24.45/4.05 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 24.45/4.05 Prover 6: stopped
% 24.45/4.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 24.45/4.05 Prover 2: stopped
% 24.45/4.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 24.45/4.05 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.94/4.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 26.17/4.28 Prover 10: Preprocessing ...
% 26.17/4.30 Prover 7: Preprocessing ...
% 26.17/4.31 Prover 8: Preprocessing ...
% 26.95/4.35 Prover 13: Preprocessing ...
% 26.95/4.38 Prover 11: Preprocessing ...
% 28.53/4.56 Prover 7: Constructing countermodel ...
% 28.53/4.59 Prover 10: Constructing countermodel ...
% 29.77/4.79 Prover 13: Constructing countermodel ...
% 29.77/4.81 Prover 8: Warning: ignoring some quantifiers
% 29.77/4.84 Prover 8: Constructing countermodel ...
% 39.23/5.93 Prover 11: Constructing countermodel ...
% 66.42/9.48 Prover 13: stopped
% 66.42/9.48 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 66.71/9.58 Prover 16: Preprocessing ...
% 68.57/9.82 Prover 16: Constructing countermodel ...
% 110.34/15.32 Prover 16: stopped
% 110.34/15.35 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 110.63/15.49 Prover 19: Preprocessing ...
% 114.71/15.97 Prover 1: stopped
% 115.99/16.25 Prover 19: Warning: ignoring some quantifiers
% 117.40/16.29 Prover 19: Constructing countermodel ...
% 135.79/19.09 Prover 19: stopped
% 137.76/19.34 Prover 8: Found proof (size 475)
% 137.76/19.34 Prover 8: proved (15260ms)
% 137.76/19.35 Prover 10: stopped
% 137.76/19.35 Prover 7: stopped
% 137.76/19.35 Prover 4: stopped
% 137.76/19.35 Prover 11: stopped
% 137.76/19.35
% 137.76/19.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 137.76/19.35
% 138.36/19.41 % SZS output start Proof for theBenchmark
% 138.36/19.42 Assumptions after simplification:
% 138.36/19.42 ---------------------------------
% 138.36/19.42
% 138.36/19.42 (ax17)
% 138.36/19.46 ssList(nil) = 0 & $i(nil)
% 138.36/19.46
% 138.36/19.46 (ax18)
% 138.36/19.46 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (cons(v1,
% 138.36/19.46 v0) = v0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v1) =
% 138.36/19.46 v2)))
% 138.36/19.46
% 138.36/19.46 (ax19)
% 138.36/19.47 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssList(v1)
% 138.36/19.47 = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v2, v0) = v3) |
% 138.36/19.47 ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i]
% 138.36/19.47 : ( ~ (cons(v4, v1) = v3) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) &
% 138.36/19.47 ssItem(v4) = v5) | (v4 = v2 & v1 = v0)))))
% 138.36/19.47
% 138.36/19.47 (ax2)
% 138.36/19.47 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) &
% 138.36/19.47 ssItem(v1) = 0 & $i(v1)))
% 138.36/19.47
% 138.36/19.47 (ax20)
% 138.36/19.47 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1:
% 138.36/19.47 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 138.36/19.47 ssItem(v2) = 0 & $i(v2))))
% 138.36/19.47
% 138.36/19.47 (ax22)
% 138.36/19.47 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (hd(v0) = v1) | ~ $i(v0)
% 138.36/19.47 | ? [v2: any] : ? [v3: any] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2
% 138.36/19.47 = 0) | v3 = 0)))
% 138.36/19.47
% 138.36/19.47 (ax23)
% 138.36/19.48 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 138.36/19.48 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) =
% 138.36/19.48 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1))))
% 138.36/19.48
% 138.36/19.48 (ax25)
% 138.36/19.48 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 138.36/19.48 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) =
% 138.36/19.48 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0))))
% 138.36/19.48
% 138.36/19.48 (ax3)
% 138.36/19.49 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 138.36/19.49 ( ~ (memberP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 138.36/19.49 ssItem(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : (ssList(v3) = 0 &
% 138.36/19.49 $i(v3) & ? [v4: $i] : ? [v5: $i] : (ssList(v4) = 0 & cons(v1, v4)
% 138.36/19.49 = v5 & app(v3, v5) = v0 & $i(v5) & $i(v4)))) & (v2 = 0 | ! [v3:
% 138.36/19.49 $i] : ( ~ (ssList(v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: $i] :
% 138.36/19.49 ( ~ (cons(v1, v4) = v5) | ~ (app(v3, v5) = v0) | ~ $i(v4) | ?
% 138.36/19.49 [v6: int] : ( ~ (v6 = 0) & ssList(v4) = v6)))))))
% 138.36/19.49
% 138.36/19.49 (ax38)
% 138.36/19.49 $i(nil) & ! [v0: $i] : ( ~ (memberP(nil, v0) = 0) | ~ $i(v0) | ? [v1: int]
% 138.36/19.49 : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 138.36/19.49
% 138.36/19.49 (ax44)
% 138.36/19.50 ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1)
% 138.36/19.50 = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, v2) = v3) |
% 138.36/19.50 ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i]
% 138.36/19.50 : ! [v5: $i] : ! [v6: any] : ( ~ (frontsegP(v3, v5) = v6) | ~
% 138.36/19.50 (cons(v1, v4) = v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] :
% 138.36/19.50 (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 =
% 138.36/19.50 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 =
% 138.36/19.50 v0)))))))))
% 138.36/19.50
% 138.36/19.50 (ax59)
% 138.81/19.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 138.81/19.50 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 138.81/19.50 (v2 = 0) | v3 = 0)))
% 138.81/19.50
% 138.81/19.50 (ax60)
% 138.81/19.50 cyclefreeP(nil) = 0 & $i(nil)
% 138.81/19.50
% 138.81/19.50 (ax61)
% 138.81/19.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 138.81/19.50 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 138.81/19.50 (v2 = 0) | v3 = 0)))
% 138.81/19.50
% 138.81/19.50 (ax62)
% 138.81/19.50 totalorderP(nil) = 0 & $i(nil)
% 138.81/19.50
% 138.81/19.50 (ax63)
% 138.81/19.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 138.81/19.50 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 138.81/19.50 (v2 = 0) | v3 = 0)))
% 138.81/19.50
% 138.81/19.50 (ax65)
% 138.81/19.51 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 138.81/19.51 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 138.81/19.51 (v2 = 0) | v3 = 0)))
% 138.81/19.51
% 138.81/19.51 (ax68)
% 138.81/19.51 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 138.81/19.51 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & (
% 138.81/19.51 ~ (v2 = 0) | v3 = 0)))
% 138.81/19.51
% 138.81/19.51 (ax71)
% 138.81/19.51 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 138.81/19.51 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 138.81/19.51 ~ (v2 = 0) | v3 = 0)))
% 138.81/19.51
% 138.81/19.51 (ax73)
% 138.81/19.51 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 138.81/19.51 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 138.81/19.51 (v2 = 0) | v3 = 0)))
% 138.81/19.51
% 138.81/19.51 (ax75)
% 138.81/19.51 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (hd(v0) = v1) | ~ $i(v0)
% 138.81/19.51 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (ssItem(v1) = 0 &
% 138.81/19.51 $i(v1)))
% 138.81/19.51
% 138.81/19.51 (ax8)
% 138.81/19.52 ! [v0: $i] : ! [v1: any] : ( ~ (cyclefreeP(v0) = v1) | ~ $i(v0) | ? [v2:
% 138.81/19.52 int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : ( ~
% 138.81/19.52 (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: any] : ( ~
% 138.81/19.52 (leq(v2, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] :
% 138.81/19.52 (leq(v3, v2) = v6 & ssItem(v3) = v5 & ( ~ (v5 = 0) | ! [v7: $i] : (
% 138.81/19.52 ~ (ssList(v7) = 0) | ~ $i(v7) | ! [v8: $i] : ! [v9: $i] :
% 138.81/19.52 ! [v10: $i] : ( ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v10)
% 138.81/19.52 | ~ $i(v8) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v8) =
% 138.81/19.52 v11) | ! [v11: $i] : ! [v12: $i] : ( ~ (v6 = 0) | ~ (v4
% 138.81/19.52 = 0) | ~ (cons(v3, v11) = v12) | ~ (app(v10, v12) =
% 138.81/19.52 v0) | ~ $i(v11) | ? [v13: int] : ( ~ (v13 = 0) &
% 138.81/19.52 ssList(v11) = v13))))))))) & (v1 = 0 | ? [v2: $i] :
% 138.81/19.52 (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4: any] : ? [v5: any] :
% 138.81/19.52 (leq(v3, v2) = v5 & leq(v2, v3) = v4 & ssItem(v3) = 0 & $i(v3) & ?
% 138.81/19.52 [v6: $i] : (ssList(v6) = 0 & $i(v6) & ? [v7: $i] : ? [v8: $i] : ?
% 138.81/19.52 [v9: $i] : (ssList(v7) = 0 & cons(v2, v7) = v8 & app(v6, v8) = v9
% 138.81/19.52 & $i(v9) & $i(v8) & $i(v7) & ? [v10: $i] : ? [v11: $i] : (v5 =
% 138.81/19.52 0 & v4 = 0 & ssList(v10) = 0 & cons(v3, v10) = v11 & app(v9,
% 138.81/19.52 v11) = v0 & $i(v11) & $i(v10)))))))))
% 138.81/19.52
% 138.81/19.52 (ax9)
% 138.81/19.53 ! [v0: $i] : ! [v1: any] : ( ~ (totalorderP(v0) = v1) | ~ $i(v0) | ? [v2:
% 138.81/19.53 int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : ( ~
% 138.81/19.53 (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: any] : ( ~
% 138.81/19.53 (leq(v2, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] :
% 138.81/19.53 (leq(v3, v2) = v6 & ssItem(v3) = v5 & ( ~ (v5 = 0) | ! [v7: $i] : (
% 138.81/19.53 ~ (ssList(v7) = 0) | ~ $i(v7) | ! [v8: $i] : ! [v9: $i] :
% 138.81/19.53 ! [v10: $i] : ( ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v10)
% 138.81/19.53 | ~ $i(v8) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v8) =
% 138.81/19.53 v11) | ! [v11: $i] : ! [v12: $i] : (v6 = 0 | v4 = 0 | ~
% 138.81/19.53 (cons(v3, v11) = v12) | ~ (app(v10, v12) = v0) | ~
% 138.81/19.53 $i(v11) | ? [v13: int] : ( ~ (v13 = 0) & ssList(v11) =
% 138.81/19.53 v13))))))))) & (v1 = 0 | ? [v2: $i] : (ssItem(v2) = 0 &
% 138.81/19.53 $i(v2) & ? [v3: $i] : ? [v4: any] : ? [v5: any] : (leq(v3, v2) = v5
% 138.81/19.53 & leq(v2, v3) = v4 & ssItem(v3) = 0 & $i(v3) & ? [v6: $i] :
% 138.81/19.53 (ssList(v6) = 0 & $i(v6) & ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 138.81/19.53 (ssList(v7) = 0 & cons(v2, v7) = v8 & app(v6, v8) = v9 & $i(v9) &
% 138.81/19.53 $i(v8) & $i(v7) & ? [v10: $i] : ? [v11: $i] : ( ~ (v5 = 0) &
% 138.81/19.53 ~ (v4 = 0) & ssList(v10) = 0 & cons(v3, v10) = v11 & app(v9,
% 138.81/19.53 v11) = v0 & $i(v11) & $i(v10)))))))))
% 138.81/19.53
% 138.81/19.53 (co1)
% 138.81/19.53 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) =
% 138.81/19.53 0 & $i(v1) & ! [v2: $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3:
% 138.81/19.53 any] : ? [v4: any] : (memberP(v1, v2) = v4 & ssItem(v2) = v3 & ( ~
% 138.81/19.53 (v4 = 0) | ~ (v3 = 0))) | ? [v3: $i] : ( ~ (v3 = v2) & leq(v2, v3)
% 138.81/19.53 = 0 & memberP(v1, v3) = 0 & ssItem(v3) = 0 & $i(v3))) & ( ~ (v1 = nil)
% 138.81/19.54 | ~ (v0 = nil)) & ( ? [v2: $i] : (memberP(v1, v2) = 0 & cons(v2, nil) =
% 138.81/19.54 v0 & ssItem(v2) = 0 & $i(v2) & ! [v3: $i] : (v3 = v2 | ~
% 138.81/19.54 (memberP(v1, v3) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] :
% 138.81/19.54 (leq(v2, v3) = v5 & ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 138.81/19.54 | (v1 = nil & v0 = nil))))
% 138.81/19.54
% 138.81/19.54 (function-axioms)
% 138.81/19.55 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 138.81/19.55 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 138.81/19.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 138.81/19.56 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 138.81/19.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 138.81/19.56 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 138.81/19.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 138.81/19.56 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 138.81/19.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 138.81/19.56 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 138.81/19.56 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 138.81/19.56 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 138.81/19.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 138.81/19.56 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 138.81/19.56 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 138.81/19.56 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 138.81/19.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 138.81/19.56 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 138.81/19.56 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 138.81/19.56 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 138.81/19.56 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 138.81/19.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 138.81/19.56 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 138.81/19.56 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 138.81/19.56 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 138.81/19.56 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 138.81/19.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 138.81/19.56 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 138.81/19.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 138.81/19.56 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 138.81/19.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 138.81/19.56 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 138.81/19.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 138.81/19.56 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 138.81/19.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 138.81/19.56 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 138.81/19.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 138.81/19.56 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 138.81/19.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 138.81/19.56 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 138.81/19.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 138.81/19.56 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 138.81/19.56 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ?
% 138.81/19.56 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (gt(v1, v0) = v2) & ?
% 138.81/19.56 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (geq(v1, v0) = v2) & ?
% 138.81/19.56 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (lt(v1, v0) = v2) & ?
% 138.81/19.56 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (leq(v1, v0) = v2) & ?
% 138.81/19.56 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (segmentP(v1, v0) = v2)
% 138.81/19.56 & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (rearsegP(v1, v0) =
% 138.81/19.56 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] :
% 138.81/19.56 (frontsegP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 138.81/19.56 MultipleValueBool] : (memberP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ?
% 138.81/19.56 [v2: MultipleValueBool] : (neq(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ?
% 138.81/19.56 [v2: $i] : (cons(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 138.81/19.56 $i] : (app(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool]
% 138.81/19.56 : (equalelemsP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 138.81/19.56 (duplicatefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 138.81/19.56 (strictorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 138.81/19.56 (totalorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 138.81/19.56 (strictorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 138.81/19.56 (totalorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 138.81/19.56 (cyclefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 138.81/19.56 (singletonP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssList(v0)
% 138.81/19.56 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssItem(v0) = v1) & ?
% 138.81/19.56 [v0: $i] : ? [v1: $i] : (tl(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 138.81/19.56 (hd(v0) = v1 & $i(v1))
% 138.81/19.56
% 138.81/19.56 Further assumptions not needed in the proof:
% 138.81/19.56 --------------------------------------------
% 138.81/19.56 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax21, ax24, ax26, ax27, ax28,
% 138.81/19.56 ax29, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax39, ax4, ax40, ax41,
% 138.81/19.56 ax42, ax43, ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54,
% 138.81/19.56 ax55, ax56, ax57, ax58, ax6, ax64, ax66, ax67, ax69, ax7, ax70, ax72, ax74,
% 138.81/19.56 ax76, ax77, ax78, ax79, ax80, ax81, ax82, ax83, ax84, ax85, ax86, ax87, ax88,
% 138.81/19.56 ax89, ax90, ax91, ax92, ax93, ax94, ax95
% 138.81/19.56
% 138.81/19.56 Those formulas are unsatisfiable:
% 138.81/19.56 ---------------------------------
% 138.81/19.56
% 138.81/19.56 Begin of proof
% 138.81/19.56 |
% 138.81/19.56 | ALPHA: (ax17) implies:
% 138.81/19.56 | (1) ssList(nil) = 0
% 138.81/19.56 |
% 138.81/19.56 | ALPHA: (ax20) implies:
% 138.81/19.57 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 138.81/19.57 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 138.81/19.57 | ssItem(v2) = 0 & $i(v2))))
% 138.81/19.57 |
% 138.81/19.57 | ALPHA: (ax22) implies:
% 138.81/19.57 | (3) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (hd(v0) = v1) | ~ $i(v0) |
% 138.81/19.57 | ? [v2: any] : ? [v3: any] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~
% 138.81/19.57 | (v2 = 0) | v3 = 0)))
% 138.81/19.57 |
% 138.81/19.57 | ALPHA: (ax38) implies:
% 138.81/19.57 | (4) ! [v0: $i] : ( ~ (memberP(nil, v0) = 0) | ~ $i(v0) | ? [v1: int] : (
% 138.81/19.57 | ~ (v1 = 0) & ssItem(v0) = v1))
% 138.81/19.57 |
% 138.81/19.57 | ALPHA: (ax59) implies:
% 138.81/19.57 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 138.81/19.57 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 138.81/19.57 | ~ (v2 = 0) | v3 = 0)))
% 138.81/19.57 |
% 138.81/19.57 | ALPHA: (ax60) implies:
% 138.81/19.57 | (6) cyclefreeP(nil) = 0
% 138.81/19.57 |
% 138.81/19.57 | ALPHA: (ax61) implies:
% 138.81/19.57 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 138.81/19.57 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 &
% 138.81/19.57 | ( ~ (v2 = 0) | v3 = 0)))
% 138.81/19.57 |
% 138.81/19.57 | ALPHA: (ax62) implies:
% 138.81/19.57 | (8) totalorderP(nil) = 0
% 138.81/19.57 |
% 138.81/19.57 | ALPHA: (ax63) implies:
% 138.81/19.57 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 138.81/19.57 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 &
% 138.81/19.57 | ( ~ (v2 = 0) | v3 = 0)))
% 138.81/19.57 |
% 138.81/19.57 | ALPHA: (ax65) implies:
% 138.81/19.58 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 138.81/19.58 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2
% 138.81/19.58 | & ( ~ (v2 = 0) | v3 = 0)))
% 138.81/19.58 |
% 138.81/19.58 | ALPHA: (ax68) implies:
% 138.81/19.58 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 138.81/19.58 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) =
% 138.81/19.58 | v2 & ( ~ (v2 = 0) | v3 = 0)))
% 138.81/19.58 |
% 138.81/19.58 | ALPHA: (ax71) implies:
% 138.81/19.58 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 138.81/19.58 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) =
% 138.81/19.58 | v2 & ( ~ (v2 = 0) | v3 = 0)))
% 138.81/19.58 |
% 138.81/19.58 | ALPHA: (ax73) implies:
% 138.81/19.58 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 138.81/19.58 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 &
% 138.81/19.58 | ( ~ (v2 = 0) | v3 = 0)))
% 138.81/19.58 |
% 138.81/19.58 | ALPHA: (ax75) implies:
% 138.81/19.58 | (14) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (hd(v0) = v1) | ~ $i(v0) |
% 138.81/19.58 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (ssItem(v1) = 0 &
% 138.81/19.58 | $i(v1)))
% 138.81/19.58 |
% 138.81/19.58 | ALPHA: (co1) implies:
% 138.81/19.58 | (15) $i(nil)
% 138.81/19.59 | (16) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0
% 138.81/19.59 | & $i(v1) & ! [v2: $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ?
% 138.81/19.59 | [v3: any] : ? [v4: any] : (memberP(v1, v2) = v4 & ssItem(v2) =
% 138.81/19.59 | v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | ? [v3: $i] : ( ~ (v3 =
% 138.81/19.59 | v2) & leq(v2, v3) = 0 & memberP(v1, v3) = 0 & ssItem(v3) = 0
% 138.81/19.59 | & $i(v3))) & ( ~ (v1 = nil) | ~ (v0 = nil)) & ( ? [v2: $i] :
% 138.81/19.59 | (memberP(v1, v2) = 0 & cons(v2, nil) = v0 & ssItem(v2) = 0 &
% 138.81/19.59 | $i(v2) & ! [v3: $i] : (v3 = v2 | ~ (memberP(v1, v3) = 0) |
% 138.81/19.59 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (leq(v2, v3) = v5 &
% 138.81/19.59 | ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) | (v1 =
% 138.81/19.59 | nil & v0 = nil))))
% 138.81/19.59 |
% 138.81/19.59 | ALPHA: (function-axioms) implies:
% 138.81/19.59 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 138.81/19.59 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 138.81/19.59 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 138.81/19.59 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 139.28/19.59 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (hd(v2) = v1)
% 139.28/19.59 | | ~ (hd(v2) = v0))
% 139.28/19.59 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 139.28/19.59 | : ! [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3,
% 139.28/19.59 | v2) = v0))
% 139.28/19.59 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 139.28/19.59 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 139.28/19.59 | v0))
% 139.28/19.59 | (22) ? [v0: $i] : ? [v1: $i] : (hd(v0) = v1 & $i(v1))
% 139.28/19.59 |
% 139.28/19.59 | DELTA: instantiating (22) with fresh symbols all_129_0, all_129_1 gives:
% 139.28/19.60 | (23) hd(all_129_1) = all_129_0 & $i(all_129_0)
% 139.28/19.60 |
% 139.28/19.60 | ALPHA: (23) implies:
% 139.28/19.60 | (24) hd(all_129_1) = all_129_0
% 139.28/19.60 |
% 139.28/19.60 | DELTA: instantiating (ax2) with fresh symbol all_137_0 gives:
% 139.28/19.60 | (25) ssItem(all_137_0) = 0 & $i(all_137_0) & ? [v0: any] : ( ~ (v0 =
% 139.28/19.60 | all_137_0) & ssItem(v0) = 0 & $i(v0))
% 139.28/19.60 |
% 139.28/19.60 | ALPHA: (25) implies:
% 139.28/19.60 | (26) ? [v0: any] : ( ~ (v0 = all_137_0) & ssItem(v0) = 0 & $i(v0))
% 139.28/19.60 |
% 139.28/19.60 | DELTA: instantiating (16) with fresh symbol all_139_0 gives:
% 139.28/19.60 | (27) ssList(all_139_0) = 0 & $i(all_139_0) & ? [v0: $i] : (ssList(v0) = 0
% 139.28/19.60 | & $i(v0) & ! [v1: $i] : ( ~ (cons(v1, nil) = all_139_0) | ~ $i(v1)
% 139.28/19.60 | | ? [v2: any] : ? [v3: any] : (memberP(v0, v1) = v3 & ssItem(v1)
% 139.28/19.60 | = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))) | ? [v2: $i] : ( ~ (v2 =
% 139.28/19.60 | v1) & leq(v1, v2) = 0 & memberP(v0, v2) = 0 & ssItem(v2) = 0 &
% 139.28/19.60 | $i(v2))) & ( ~ (v0 = nil) | ~ (all_139_0 = nil)) & ( ? [v1: $i]
% 139.28/19.60 | : (memberP(v0, v1) = 0 & cons(v1, nil) = all_139_0 & ssItem(v1) =
% 139.28/19.60 | 0 & $i(v1) & ! [v2: $i] : (v2 = v1 | ~ (memberP(v0, v2) = 0) |
% 139.28/19.60 | ~ $i(v2) | ? [v3: any] : ? [v4: any] : (leq(v1, v2) = v4 &
% 139.28/19.60 | ssItem(v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) | (v0 = nil
% 139.28/19.60 | & all_139_0 = nil)))
% 139.28/19.60 |
% 139.28/19.60 | ALPHA: (27) implies:
% 139.28/19.60 | (28) $i(all_139_0)
% 139.28/19.60 | (29) ssList(all_139_0) = 0
% 139.28/19.61 | (30) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ! [v1: $i] : ( ~ (cons(v1,
% 139.28/19.61 | nil) = all_139_0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] :
% 139.28/19.61 | (memberP(v0, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 =
% 139.28/19.61 | 0))) | ? [v2: $i] : ( ~ (v2 = v1) & leq(v1, v2) = 0 &
% 139.28/19.61 | memberP(v0, v2) = 0 & ssItem(v2) = 0 & $i(v2))) & ( ~ (v0 = nil)
% 139.28/19.61 | | ~ (all_139_0 = nil)) & ( ? [v1: $i] : (memberP(v0, v1) = 0 &
% 139.28/19.61 | cons(v1, nil) = all_139_0 & ssItem(v1) = 0 & $i(v1) & ! [v2:
% 139.28/19.61 | $i] : (v2 = v1 | ~ (memberP(v0, v2) = 0) | ~ $i(v2) | ?
% 139.28/19.61 | [v3: any] : ? [v4: any] : (leq(v1, v2) = v4 & ssItem(v2) = v3
% 139.28/19.61 | & ( ~ (v4 = 0) | ~ (v3 = 0))))) | (v0 = nil & all_139_0 =
% 139.28/19.61 | nil)))
% 139.28/19.61 |
% 139.28/19.61 | DELTA: instantiating (26) with fresh symbol all_141_0 gives:
% 139.28/19.61 | (31) ~ (all_141_0 = all_137_0) & ssItem(all_141_0) = 0 & $i(all_141_0)
% 139.28/19.61 |
% 139.28/19.61 | ALPHA: (31) implies:
% 139.28/19.61 | (32) $i(all_141_0)
% 139.28/19.61 | (33) ssItem(all_141_0) = 0
% 139.28/19.61 |
% 139.28/19.61 | DELTA: instantiating (30) with fresh symbol all_143_0 gives:
% 139.28/19.61 | (34) ssList(all_143_0) = 0 & $i(all_143_0) & ! [v0: $i] : ( ~ (cons(v0,
% 139.28/19.61 | nil) = all_139_0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 139.28/19.61 | (memberP(all_143_0, v0) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~
% 139.28/19.61 | (v1 = 0))) | ? [v1: $i] : ( ~ (v1 = v0) & leq(v0, v1) = 0 &
% 139.28/19.61 | memberP(all_143_0, v1) = 0 & ssItem(v1) = 0 & $i(v1))) & ( ~
% 139.28/19.61 | (all_143_0 = nil) | ~ (all_139_0 = nil)) & ( ? [v0: $i] :
% 139.28/19.61 | (memberP(all_143_0, v0) = 0 & cons(v0, nil) = all_139_0 & ssItem(v0)
% 139.28/19.61 | = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~ (memberP(all_143_0, v1)
% 139.28/19.61 | = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (leq(v0, v1)
% 139.28/19.61 | = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) |
% 139.28/19.61 | (all_143_0 = nil & all_139_0 = nil))
% 139.28/19.61 |
% 139.28/19.61 | ALPHA: (34) implies:
% 139.28/19.62 | (35) $i(all_143_0)
% 139.28/19.62 | (36) ssList(all_143_0) = 0
% 139.28/19.62 | (37) ? [v0: $i] : (memberP(all_143_0, v0) = 0 & cons(v0, nil) = all_139_0
% 139.28/19.62 | & ssItem(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~
% 139.28/19.62 | (memberP(all_143_0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3:
% 139.28/19.62 | any] : (leq(v0, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~
% 139.28/19.62 | (v2 = 0))))) | (all_143_0 = nil & all_139_0 = nil)
% 139.28/19.62 | (38) ~ (all_143_0 = nil) | ~ (all_139_0 = nil)
% 139.28/19.62 | (39) ! [v0: $i] : ( ~ (cons(v0, nil) = all_139_0) | ~ $i(v0) | ? [v1:
% 139.28/19.62 | any] : ? [v2: any] : (memberP(all_143_0, v0) = v2 & ssItem(v0) =
% 139.28/19.62 | v1 & ( ~ (v2 = 0) | ~ (v1 = 0))) | ? [v1: $i] : ( ~ (v1 = v0) &
% 139.28/19.62 | leq(v0, v1) = 0 & memberP(all_143_0, v1) = 0 & ssItem(v1) = 0 &
% 139.28/19.62 | $i(v1)))
% 139.28/19.62 |
% 139.28/19.62 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (15) gives:
% 139.28/19.63 | (40) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 139.28/19.63 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 139.28/19.63 | ( ~ (v2 = 0) | v3 = nil)))
% 139.28/19.63 |
% 139.28/19.63 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (15) gives:
% 139.28/19.63 | (41) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 139.28/19.63 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 139.28/19.63 | ( ~ (v2 = 0) | v3 = v0)))
% 139.28/19.63 |
% 139.28/19.63 | GROUND_INST: instantiating (ax18) with nil, simplifying with (1), (15) gives:
% 139.28/19.63 | (42) ! [v0: $i] : ( ~ (cons(v0, nil) = nil) | ~ $i(v0) | ? [v1: int] : (
% 139.28/19.63 | ~ (v1 = 0) & ssItem(v0) = v1))
% 139.28/19.63 |
% 139.28/19.63 | GROUND_INST: instantiating (2) with all_139_0, simplifying with (28), (29)
% 139.28/19.63 | gives:
% 139.28/19.63 | (43) all_139_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i]
% 139.28/19.63 | : (cons(v1, v0) = all_139_0 & ssItem(v1) = 0 & $i(v1)))
% 139.28/19.63 |
% 139.28/19.63 | GROUND_INST: instantiating (ax3) with all_143_0, simplifying with (35), (36)
% 139.28/19.63 | gives:
% 139.28/19.63 | (44) ! [v0: $i] : ! [v1: any] : ( ~ (memberP(all_143_0, v0) = v1) | ~
% 139.28/19.63 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v0) = v2) | (( ~ (v1 =
% 139.28/19.63 | 0) | ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ?
% 139.28/19.63 | [v4: $i] : (ssList(v3) = 0 & cons(v0, v3) = v4 & app(v2, v4) =
% 139.28/19.63 | all_143_0 & $i(v4) & $i(v3)))) & (v1 = 0 | ! [v2: $i] : ( ~
% 139.28/19.63 | (ssList(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ( ~
% 139.28/19.63 | (cons(v0, v3) = v4) | ~ (app(v2, v4) = all_143_0) | ~
% 139.28/19.63 | $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v3) = v5))))))
% 139.28/19.63 |
% 139.28/19.63 | GROUND_INST: instantiating (ax8) with nil, 0, simplifying with (6), (15)
% 139.28/19.63 | gives:
% 139.28/19.64 | (45) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~
% 139.28/19.64 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : ( ~
% 139.28/19.64 | (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] :
% 139.28/19.64 | (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | ! [v5: $i] :
% 139.28/19.64 | ( ~ (ssList(v5) = 0) | ~ $i(v5) | ! [v6: $i] : ! [v7: $i] :
% 139.28/19.64 | ! [v8: $i] : ( ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) =
% 139.28/19.64 | v8) | ~ $i(v6) | ? [v9: int] : ( ~ (v9 = 0) &
% 139.28/19.64 | ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] : ( ~ (v4
% 139.28/19.64 | = 0) | ~ (v2 = 0) | ~ (cons(v1, v9) = v10) | ~
% 139.28/19.64 | (app(v8, v10) = nil) | ~ $i(v9) | ? [v11: int] : ( ~
% 139.28/19.64 | (v11 = 0) & ssList(v9) = v11))))))))
% 139.28/19.64 |
% 139.28/19.64 | GROUND_INST: instantiating (ax9) with nil, 0, simplifying with (8), (15)
% 139.28/19.64 | gives:
% 139.28/19.64 | (46) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~
% 139.28/19.64 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : ( ~
% 139.28/19.64 | (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] :
% 139.28/19.64 | (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | ! [v5: $i] :
% 139.28/19.64 | ( ~ (ssList(v5) = 0) | ~ $i(v5) | ! [v6: $i] : ! [v7: $i] :
% 139.28/19.64 | ! [v8: $i] : ( ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) =
% 139.28/19.64 | v8) | ~ $i(v6) | ? [v9: int] : ( ~ (v9 = 0) &
% 139.28/19.64 | ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] : (v4 = 0
% 139.28/19.64 | | v2 = 0 | ~ (cons(v1, v9) = v10) | ~ (app(v8, v10) =
% 139.28/19.64 | nil) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) &
% 139.28/19.64 | ssList(v9) = v11))))))))
% 139.28/19.64 |
% 139.28/19.64 | GROUND_INST: instantiating (3) with all_129_1, all_129_0, simplifying with
% 139.28/19.64 | (24) gives:
% 139.28/19.65 | (47) all_129_1 = nil | ~ $i(all_129_1) | ? [v0: any] : ? [v1: any] :
% 139.28/19.65 | (ssList(all_129_1) = v0 & ssItem(all_129_0) = v1 & ( ~ (v0 = 0) | v1 =
% 139.28/19.65 | 0))
% 139.28/19.65 |
% 139.28/19.65 | GROUND_INST: instantiating (14) with all_129_1, all_129_0, simplifying with
% 139.28/19.65 | (24) gives:
% 139.28/19.65 | (48) all_129_1 = nil | ~ $i(all_129_1) | ? [v0: int] : ( ~ (v0 = 0) &
% 139.28/19.65 | ssList(all_129_1) = v0) | (ssItem(all_129_0) = 0 & $i(all_129_0))
% 139.28/19.65 |
% 139.28/19.65 | BETA: splitting (46) gives:
% 139.28/19.65 |
% 139.28/19.65 | Case 1:
% 139.28/19.65 | |
% 139.28/19.65 | | (49) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 139.28/19.65 | |
% 139.28/19.65 | | REF_CLOSE: (1), (18), (49) are inconsistent by sub-proof #1.
% 139.28/19.65 | |
% 139.28/19.65 | Case 2:
% 139.28/19.65 | |
% 139.28/19.65 | | (50) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : !
% 139.28/19.65 | | [v2: any] : ( ~ (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ?
% 139.28/19.65 | | [v4: any] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) |
% 139.28/19.65 | | ! [v5: $i] : ( ~ (ssList(v5) = 0) | ~ $i(v5) | ! [v6: $i]
% 139.28/19.65 | | : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v0, v6) = v7) | ~
% 139.28/19.65 | | (app(v5, v7) = v8) | ~ $i(v6) | ? [v9: int] : ( ~ (v9
% 139.28/19.65 | | = 0) & ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i]
% 139.28/19.65 | | : (v4 = 0 | v2 = 0 | ~ (cons(v1, v9) = v10) | ~
% 139.28/19.65 | | (app(v8, v10) = nil) | ~ $i(v9) | ? [v11: int] : ( ~
% 139.28/19.65 | | (v11 = 0) & ssList(v9) = v11))))))))
% 139.28/19.65 | |
% 139.28/19.65 | | BETA: splitting (45) gives:
% 139.28/19.65 | |
% 139.28/19.65 | | Case 1:
% 139.28/19.65 | | |
% 139.28/19.65 | | | (51) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 139.28/19.65 | | |
% 139.28/19.65 | | | REF_CLOSE: (1), (18), (51) are inconsistent by sub-proof #1.
% 139.28/19.65 | | |
% 139.28/19.65 | | Case 2:
% 139.28/19.65 | | |
% 139.28/19.66 | | | (52) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : !
% 139.28/19.66 | | | [v2: any] : ( ~ (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] :
% 139.28/19.66 | | | ? [v4: any] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 =
% 139.28/19.66 | | | 0) | ! [v5: $i] : ( ~ (ssList(v5) = 0) | ~ $i(v5) | !
% 139.28/19.66 | | | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v0, v6)
% 139.28/19.66 | | | = v7) | ~ (app(v5, v7) = v8) | ~ $i(v6) | ? [v9:
% 139.28/19.66 | | | int] : ( ~ (v9 = 0) & ssList(v6) = v9) | ! [v9: $i]
% 139.28/19.66 | | | : ! [v10: $i] : ( ~ (v4 = 0) | ~ (v2 = 0) | ~
% 139.28/19.66 | | | (cons(v1, v9) = v10) | ~ (app(v8, v10) = nil) | ~
% 139.28/19.66 | | | $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v9)
% 139.28/19.66 | | | = v11))))))))
% 139.28/19.66 | | |
% 139.28/19.66 | | | BETA: splitting (38) gives:
% 139.28/19.66 | | |
% 139.28/19.66 | | | Case 1:
% 139.28/19.66 | | | |
% 139.28/19.66 | | | | (53) ~ (all_143_0 = nil)
% 139.28/19.66 | | | |
% 139.28/19.66 | | | | BETA: splitting (37) gives:
% 139.28/19.66 | | | |
% 139.28/19.66 | | | | Case 1:
% 139.28/19.66 | | | | |
% 139.28/19.66 | | | | | (54) ? [v0: $i] : (memberP(all_143_0, v0) = 0 & cons(v0, nil) =
% 139.28/19.66 | | | | | all_139_0 & ssItem(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0
% 139.28/19.66 | | | | | | ~ (memberP(all_143_0, v1) = 0) | ~ $i(v1) | ? [v2:
% 139.28/19.66 | | | | | any] : ? [v3: any] : (leq(v0, v1) = v3 & ssItem(v1) =
% 139.28/19.66 | | | | | v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 139.28/19.66 | | | | |
% 139.28/19.66 | | | | | DELTA: instantiating (54) with fresh symbol all_345_0 gives:
% 139.28/19.66 | | | | | (55) memberP(all_143_0, all_345_0) = 0 & cons(all_345_0, nil) =
% 139.28/19.66 | | | | | all_139_0 & ssItem(all_345_0) = 0 & $i(all_345_0) & ! [v0:
% 139.28/19.66 | | | | | any] : (v0 = all_345_0 | ~ (memberP(all_143_0, v0) = 0) |
% 139.28/19.66 | | | | | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (leq(all_345_0, v0)
% 139.28/19.66 | | | | | = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 139.28/19.66 | | | | |
% 139.28/19.66 | | | | | ALPHA: (55) implies:
% 139.28/19.66 | | | | | (56) $i(all_345_0)
% 139.28/19.66 | | | | | (57) ssItem(all_345_0) = 0
% 139.28/19.66 | | | | | (58) cons(all_345_0, nil) = all_139_0
% 139.28/19.66 | | | | | (59) memberP(all_143_0, all_345_0) = 0
% 139.28/19.66 | | | | | (60) ! [v0: any] : (v0 = all_345_0 | ~ (memberP(all_143_0, v0) =
% 139.28/19.66 | | | | | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 139.28/19.66 | | | | | (leq(all_345_0, v0) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) |
% 139.28/19.66 | | | | | ~ (v1 = 0))))
% 139.28/19.66 | | | | |
% 139.28/19.66 | | | | | BETA: splitting (43) gives:
% 139.28/19.66 | | | | |
% 139.28/19.66 | | | | | Case 1:
% 139.28/19.66 | | | | | |
% 139.28/19.66 | | | | | | (61) all_139_0 = nil
% 139.28/19.66 | | | | | |
% 139.28/19.66 | | | | | | REDUCE: (58), (61) imply:
% 139.28/19.66 | | | | | | (62) cons(all_345_0, nil) = nil
% 139.28/19.66 | | | | | |
% 139.28/19.66 | | | | | | BETA: splitting (47) gives:
% 139.28/19.66 | | | | | |
% 139.28/19.67 | | | | | | Case 1:
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | GROUND_INST: instantiating (42) with all_345_0, simplifying with
% 139.28/19.67 | | | | | | | (56), (62) gives:
% 139.28/19.67 | | | | | | | (63) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_345_0) = v0)
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | GROUND_INST: instantiating (40) with all_345_0, nil, simplifying
% 139.28/19.67 | | | | | | | with (56), (62) gives:
% 139.28/19.67 | | | | | | | (64) ? [v0: any] : ? [v1: $i] : (tl(nil) = v1 &
% 139.28/19.67 | | | | | | | ssItem(all_345_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 139.28/19.67 | | | | | | | nil))
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | GROUND_INST: instantiating (41) with all_345_0, nil, simplifying
% 139.28/19.67 | | | | | | | with (56), (62) gives:
% 139.28/19.67 | | | | | | | (65) ? [v0: any] : ? [v1: $i] : (hd(nil) = v1 &
% 139.28/19.67 | | | | | | | ssItem(all_345_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 139.28/19.67 | | | | | | | all_345_0))
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | DELTA: instantiating (63) with fresh symbol all_579_0 gives:
% 139.28/19.67 | | | | | | | (66) ~ (all_579_0 = 0) & ssItem(all_345_0) = all_579_0
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | ALPHA: (66) implies:
% 139.28/19.67 | | | | | | | (67) ~ (all_579_0 = 0)
% 139.28/19.67 | | | | | | | (68) ssItem(all_345_0) = all_579_0
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | DELTA: instantiating (64) with fresh symbols all_581_0, all_581_1
% 139.28/19.67 | | | | | | | gives:
% 139.28/19.67 | | | | | | | (69) tl(nil) = all_581_0 & ssItem(all_345_0) = all_581_1 &
% 139.28/19.67 | | | | | | | $i(all_581_0) & ( ~ (all_581_1 = 0) | all_581_0 = nil)
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | ALPHA: (69) implies:
% 139.28/19.67 | | | | | | | (70) ssItem(all_345_0) = all_581_1
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | DELTA: instantiating (65) with fresh symbols all_583_0, all_583_1
% 139.28/19.67 | | | | | | | gives:
% 139.28/19.67 | | | | | | | (71) hd(nil) = all_583_0 & ssItem(all_345_0) = all_583_1 &
% 139.28/19.67 | | | | | | | $i(all_583_0) & ( ~ (all_583_1 = 0) | all_583_0 =
% 139.28/19.67 | | | | | | | all_345_0)
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | ALPHA: (71) implies:
% 139.28/19.67 | | | | | | | (72) ssItem(all_345_0) = all_583_1
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | GROUND_INST: instantiating (17) with all_579_0, all_581_1,
% 139.28/19.67 | | | | | | | all_345_0, simplifying with (68), (70) gives:
% 139.28/19.67 | | | | | | | (73) all_581_1 = all_579_0
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | GROUND_INST: instantiating (17) with 0, all_583_1, all_345_0,
% 139.28/19.67 | | | | | | | simplifying with (57), (72) gives:
% 139.28/19.67 | | | | | | | (74) all_583_1 = 0
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | GROUND_INST: instantiating (17) with all_581_1, all_583_1,
% 139.28/19.67 | | | | | | | all_345_0, simplifying with (70), (72) gives:
% 139.28/19.67 | | | | | | | (75) all_583_1 = all_581_1
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | COMBINE_EQS: (74), (75) imply:
% 139.28/19.67 | | | | | | | (76) all_581_1 = 0
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | SIMP: (76) implies:
% 139.28/19.67 | | | | | | | (77) all_581_1 = 0
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | COMBINE_EQS: (73), (77) imply:
% 139.28/19.67 | | | | | | | (78) all_579_0 = 0
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | SIMP: (78) implies:
% 139.28/19.67 | | | | | | | (79) all_579_0 = 0
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | REDUCE: (67), (79) imply:
% 139.28/19.67 | | | | | | | (80) $false
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | CLOSE: (80) is inconsistent.
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | Case 2:
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | (81) $i(all_129_1)
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | BETA: splitting (48) gives:
% 139.28/19.67 | | | | | | |
% 139.28/19.67 | | | | | | | Case 1:
% 139.28/19.67 | | | | | | | |
% 139.28/19.67 | | | | | | | | (82) ~ $i(all_129_1)
% 139.28/19.67 | | | | | | | |
% 139.28/19.67 | | | | | | | | PRED_UNIFY: (81), (82) imply:
% 139.28/19.67 | | | | | | | | (83) $false
% 139.28/19.67 | | | | | | | |
% 139.28/19.67 | | | | | | | | CLOSE: (83) is inconsistent.
% 139.28/19.67 | | | | | | | |
% 139.28/19.67 | | | | | | | Case 2:
% 139.28/19.67 | | | | | | | |
% 139.28/19.67 | | | | | | | |
% 139.28/19.68 | | | | | | | | GROUND_INST: instantiating (42) with all_345_0, simplifying with
% 139.28/19.68 | | | | | | | | (56), (62) gives:
% 139.28/19.68 | | | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_345_0) = v0)
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | GROUND_INST: instantiating (40) with all_345_0, nil, simplifying
% 139.28/19.68 | | | | | | | | with (56), (62) gives:
% 139.28/19.68 | | | | | | | | (85) ? [v0: any] : ? [v1: $i] : (tl(nil) = v1 &
% 139.28/19.68 | | | | | | | | ssItem(all_345_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 139.28/19.68 | | | | | | | | nil))
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | GROUND_INST: instantiating (41) with all_345_0, nil, simplifying
% 139.28/19.68 | | | | | | | | with (56), (62) gives:
% 139.28/19.68 | | | | | | | | (86) ? [v0: any] : ? [v1: $i] : (hd(nil) = v1 &
% 139.28/19.68 | | | | | | | | ssItem(all_345_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 139.28/19.68 | | | | | | | | all_345_0))
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | DELTA: instantiating (84) with fresh symbol all_591_0 gives:
% 139.28/19.68 | | | | | | | | (87) ~ (all_591_0 = 0) & ssItem(all_345_0) = all_591_0
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | ALPHA: (87) implies:
% 139.28/19.68 | | | | | | | | (88) ~ (all_591_0 = 0)
% 139.28/19.68 | | | | | | | | (89) ssItem(all_345_0) = all_591_0
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | DELTA: instantiating (85) with fresh symbols all_593_0,
% 139.28/19.68 | | | | | | | | all_593_1 gives:
% 139.28/19.68 | | | | | | | | (90) tl(nil) = all_593_0 & ssItem(all_345_0) = all_593_1 &
% 139.28/19.68 | | | | | | | | $i(all_593_0) & ( ~ (all_593_1 = 0) | all_593_0 = nil)
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | ALPHA: (90) implies:
% 139.28/19.68 | | | | | | | | (91) ssItem(all_345_0) = all_593_1
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | DELTA: instantiating (86) with fresh symbols all_595_0,
% 139.28/19.68 | | | | | | | | all_595_1 gives:
% 139.28/19.68 | | | | | | | | (92) hd(nil) = all_595_0 & ssItem(all_345_0) = all_595_1 &
% 139.28/19.68 | | | | | | | | $i(all_595_0) & ( ~ (all_595_1 = 0) | all_595_0 =
% 139.28/19.68 | | | | | | | | all_345_0)
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | ALPHA: (92) implies:
% 139.28/19.68 | | | | | | | | (93) ssItem(all_345_0) = all_595_1
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | GROUND_INST: instantiating (17) with all_591_0, all_593_1,
% 139.28/19.68 | | | | | | | | all_345_0, simplifying with (89), (91) gives:
% 139.28/19.68 | | | | | | | | (94) all_593_1 = all_591_0
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | GROUND_INST: instantiating (17) with 0, all_595_1, all_345_0,
% 139.28/19.68 | | | | | | | | simplifying with (57), (93) gives:
% 139.28/19.68 | | | | | | | | (95) all_595_1 = 0
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | GROUND_INST: instantiating (17) with all_593_1, all_595_1,
% 139.28/19.68 | | | | | | | | all_345_0, simplifying with (91), (93) gives:
% 139.28/19.68 | | | | | | | | (96) all_595_1 = all_593_1
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | COMBINE_EQS: (95), (96) imply:
% 139.28/19.68 | | | | | | | | (97) all_593_1 = 0
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | SIMP: (97) implies:
% 139.28/19.68 | | | | | | | | (98) all_593_1 = 0
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | COMBINE_EQS: (94), (98) imply:
% 139.28/19.68 | | | | | | | | (99) all_591_0 = 0
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | SIMP: (99) implies:
% 139.28/19.68 | | | | | | | | (100) all_591_0 = 0
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | REDUCE: (88), (100) imply:
% 139.28/19.68 | | | | | | | | (101) $false
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | | CLOSE: (101) is inconsistent.
% 139.28/19.68 | | | | | | | |
% 139.28/19.68 | | | | | | | End of split
% 139.28/19.68 | | | | | | |
% 139.28/19.68 | | | | | | End of split
% 139.28/19.68 | | | | | |
% 139.28/19.68 | | | | | Case 2:
% 139.28/19.68 | | | | | |
% 139.28/19.68 | | | | | | (102) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] :
% 139.28/19.68 | | | | | | (cons(v1, v0) = all_139_0 & ssItem(v1) = 0 & $i(v1)))
% 139.28/19.68 | | | | | |
% 139.28/19.68 | | | | | | DELTA: instantiating (102) with fresh symbol all_367_0 gives:
% 139.28/19.68 | | | | | | (103) ssList(all_367_0) = 0 & $i(all_367_0) & ? [v0: $i] :
% 139.28/19.68 | | | | | | (cons(v0, all_367_0) = all_139_0 & ssItem(v0) = 0 & $i(v0))
% 139.28/19.68 | | | | | |
% 139.28/19.68 | | | | | | ALPHA: (103) implies:
% 139.28/19.68 | | | | | | (104) $i(all_367_0)
% 139.28/19.68 | | | | | | (105) ssList(all_367_0) = 0
% 139.28/19.69 | | | | | | (106) ? [v0: $i] : (cons(v0, all_367_0) = all_139_0 & ssItem(v0)
% 139.28/19.69 | | | | | | = 0 & $i(v0))
% 139.28/19.69 | | | | | |
% 139.28/19.69 | | | | | | DELTA: instantiating (106) with fresh symbol all_369_0 gives:
% 139.28/19.69 | | | | | | (107) cons(all_369_0, all_367_0) = all_139_0 & ssItem(all_369_0)
% 139.28/19.69 | | | | | | = 0 & $i(all_369_0)
% 139.28/19.69 | | | | | |
% 139.28/19.69 | | | | | | ALPHA: (107) implies:
% 139.28/19.69 | | | | | | (108) $i(all_369_0)
% 139.28/19.69 | | | | | | (109) ssItem(all_369_0) = 0
% 139.28/19.69 | | | | | | (110) cons(all_369_0, all_367_0) = all_139_0
% 139.28/19.69 | | | | | |
% 139.28/19.69 | | | | | | GROUND_INST: instantiating (52) with all_345_0, simplifying with
% 139.28/19.69 | | | | | | (56), (57) gives:
% 139.28/19.69 | | | | | | (111) ! [v0: $i] : ! [v1: any] : ( ~ (leq(all_345_0, v0) = v1)
% 139.28/19.69 | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0,
% 139.28/19.69 | | | | | | all_345_0) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | !
% 139.28/19.69 | | | | | | [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5:
% 139.28/19.69 | | | | | | $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 139.28/19.69 | | | | | | (cons(all_345_0, v5) = v6) | ~ (app(v4, v6) =
% 139.28/19.69 | | | | | | v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) &
% 139.28/19.69 | | | | | | ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] :
% 139.28/19.69 | | | | | | ( ~ (v3 = 0) | ~ (v1 = 0) | ~ (cons(v0, v8) =
% 139.28/19.69 | | | | | | v9) | ~ (app(v7, v9) = nil) | ~ $i(v8) | ?
% 139.28/19.69 | | | | | | [v10: int] : ( ~ (v10 = 0) & ssList(v8) =
% 139.28/19.69 | | | | | | v10)))))))
% 139.28/19.69 | | | | | |
% 139.28/19.69 | | | | | | GROUND_INST: instantiating (50) with all_345_0, simplifying with
% 139.28/19.69 | | | | | | (56), (57) gives:
% 139.28/19.69 | | | | | | (112) ! [v0: $i] : ! [v1: any] : ( ~ (leq(all_345_0, v0) = v1)
% 139.28/19.69 | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0,
% 139.28/19.69 | | | | | | all_345_0) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | !
% 139.28/19.69 | | | | | | [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5:
% 139.76/19.69 | | | | | | $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 139.76/19.69 | | | | | | (cons(all_345_0, v5) = v6) | ~ (app(v4, v6) =
% 139.76/19.69 | | | | | | v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) &
% 139.76/19.69 | | | | | | ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] :
% 139.76/19.69 | | | | | | (v3 = 0 | v1 = 0 | ~ (cons(v0, v8) = v9) | ~
% 139.76/19.69 | | | | | | (app(v7, v9) = nil) | ~ $i(v8) | ? [v10: int]
% 139.76/19.69 | | | | | | : ( ~ (v10 = 0) & ssList(v8) = v10)))))))
% 139.76/19.69 | | | | | |
% 139.76/19.69 | | | | | | GROUND_INST: instantiating (ax44) with all_345_0, simplifying with
% 139.76/19.69 | | | | | | (56), (57) gives:
% 139.76/19.69 | | | | | | (113) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1:
% 139.76/19.69 | | | | | | $i] : ! [v2: $i] : ( ~ (cons(all_345_0, v1) = v2) | ~
% 139.76/19.69 | | | | | | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssList(v1) = v3)
% 139.76/19.69 | | | | | | | ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~
% 139.76/19.69 | | | | | | (frontsegP(v2, v4) = v5) | ~ (cons(v0, v3) = v4) |
% 139.76/19.69 | | | | | | ~ $i(v3) | ? [v6: any] : ? [v7: any] :
% 139.76/19.69 | | | | | | (frontsegP(v1, v3) = v7 & ssList(v3) = v6 & ( ~ (v6 =
% 139.76/19.69 | | | | | | 0) | (( ~ (v7 = 0) | ~ (v0 = all_345_0) | v5 =
% 139.76/19.69 | | | | | | 0) & ( ~ (v5 = 0) | (v7 = 0 & v0 =
% 139.76/19.69 | | | | | | all_345_0))))))))
% 139.76/19.69 | | | | | |
% 139.76/19.69 | | | | | | GROUND_INST: instantiating (ax44) with all_369_0, simplifying with
% 139.76/19.69 | | | | | | (108), (109) gives:
% 139.76/19.70 | | | | | | (114) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1:
% 139.76/19.70 | | | | | | $i] : ! [v2: $i] : ( ~ (cons(all_369_0, v1) = v2) | ~
% 139.76/19.70 | | | | | | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssList(v1) = v3)
% 139.76/19.70 | | | | | | | ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~
% 139.76/19.70 | | | | | | (frontsegP(v2, v4) = v5) | ~ (cons(v0, v3) = v4) |
% 139.76/19.70 | | | | | | ~ $i(v3) | ? [v6: any] : ? [v7: any] :
% 139.76/19.70 | | | | | | (frontsegP(v1, v3) = v7 & ssList(v3) = v6 & ( ~ (v6 =
% 139.76/19.70 | | | | | | 0) | (( ~ (v7 = 0) | ~ (v0 = all_369_0) | v5 =
% 139.76/19.70 | | | | | | 0) & ( ~ (v5 = 0) | (v7 = 0 & v0 =
% 139.76/19.70 | | | | | | all_369_0))))))))
% 139.76/19.70 | | | | | |
% 139.76/19.70 | | | | | | GROUND_INST: instantiating (39) with all_345_0, simplifying with
% 139.76/19.70 | | | | | | (56), (58) gives:
% 139.76/19.70 | | | | | | (115) ? [v0: any] : ? [v1: any] : (memberP(all_143_0,
% 139.76/19.70 | | | | | | all_345_0) = v1 & ssItem(all_345_0) = v0 & ( ~ (v1 = 0)
% 139.76/19.70 | | | | | | | ~ (v0 = 0))) | ? [v0: any] : ( ~ (v0 = all_345_0) &
% 139.76/19.70 | | | | | | leq(all_345_0, v0) = 0 & memberP(all_143_0, v0) = 0 &
% 139.76/19.70 | | | | | | ssItem(v0) = 0 & $i(v0))
% 139.76/19.70 | | | | | |
% 139.76/19.70 | | | | | | GROUND_INST: instantiating (40) with all_345_0, all_139_0,
% 139.76/19.70 | | | | | | simplifying with (56), (58) gives:
% 139.76/19.70 | | | | | | (116) ? [v0: any] : ? [v1: $i] : (tl(all_139_0) = v1 &
% 139.76/19.70 | | | | | | ssItem(all_345_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 139.76/19.70 | | | | | | nil))
% 139.76/19.70 | | | | | |
% 139.76/19.70 | | | | | | GROUND_INST: instantiating (41) with all_345_0, all_139_0,
% 139.76/19.70 | | | | | | simplifying with (56), (58) gives:
% 139.76/19.70 | | | | | | (117) ? [v0: any] : ? [v1: $i] : (hd(all_139_0) = v1 &
% 139.76/19.70 | | | | | | ssItem(all_345_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 139.76/19.70 | | | | | | all_345_0))
% 139.76/19.70 | | | | | |
% 139.76/19.70 | | | | | | GROUND_INST: instantiating (13) with all_345_0, all_139_0,
% 139.76/19.70 | | | | | | simplifying with (56), (58) gives:
% 139.76/19.70 | | | | | | (118) ? [v0: any] : ? [v1: any] : (equalelemsP(all_139_0) = v1
% 139.76/19.70 | | | | | | & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.70 | | | | | |
% 139.76/19.70 | | | | | | GROUND_INST: instantiating (12) with all_345_0, all_139_0,
% 139.76/19.70 | | | | | | simplifying with (56), (58) gives:
% 139.76/19.70 | | | | | | (119) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_139_0) =
% 139.76/19.70 | | | | | | v1 & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.70 | | | | | |
% 139.76/19.70 | | | | | | GROUND_INST: instantiating (11) with all_345_0, all_139_0,
% 139.76/19.70 | | | | | | simplifying with (56), (58) gives:
% 139.76/19.70 | | | | | | (120) ? [v0: any] : ? [v1: any] : (strictorderedP(all_139_0) =
% 139.76/19.70 | | | | | | v1 & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.70 | | | | | |
% 139.76/19.70 | | | | | | GROUND_INST: instantiating (10) with all_345_0, all_139_0,
% 139.76/19.70 | | | | | | simplifying with (56), (58) gives:
% 139.76/19.70 | | | | | | (121) ? [v0: any] : ? [v1: any] : (totalorderedP(all_139_0) =
% 139.76/19.70 | | | | | | v1 & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.70 | | | | | |
% 139.76/19.70 | | | | | | GROUND_INST: instantiating (9) with all_345_0, all_139_0,
% 139.76/19.70 | | | | | | simplifying with (56), (58) gives:
% 139.76/19.70 | | | | | | (122) ? [v0: any] : ? [v1: any] : (strictorderP(all_139_0) = v1
% 139.76/19.70 | | | | | | & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.70 | | | | | |
% 139.76/19.70 | | | | | | GROUND_INST: instantiating (7) with all_345_0, all_139_0,
% 139.76/19.71 | | | | | | simplifying with (56), (58) gives:
% 139.76/19.71 | | | | | | (123) ? [v0: any] : ? [v1: any] : (totalorderP(all_139_0) = v1
% 139.76/19.71 | | | | | | & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.71 | | | | | |
% 139.76/19.71 | | | | | | GROUND_INST: instantiating (5) with all_345_0, all_139_0,
% 139.76/19.71 | | | | | | simplifying with (56), (58) gives:
% 139.76/19.71 | | | | | | (124) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_139_0) = v1 &
% 139.76/19.71 | | | | | | ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.71 | | | | | |
% 139.76/19.71 | | | | | | GROUND_INST: instantiating (ax25) with all_367_0, simplifying with
% 139.76/19.71 | | | | | | (104), (105) gives:
% 139.76/19.71 | | | | | | (125) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, all_367_0) = v1)
% 139.76/19.71 | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (tl(v1) = v3 &
% 139.76/19.71 | | | | | | ssItem(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 139.76/19.71 | | | | | | all_367_0)))
% 139.76/19.71 | | | | | |
% 139.76/19.71 | | | | | | GROUND_INST: instantiating (ax23) with all_367_0, simplifying with
% 139.76/19.71 | | | | | | (104), (105) gives:
% 139.76/19.71 | | | | | | (126) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, all_367_0) = v1)
% 139.76/19.71 | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (hd(v1) = v3 &
% 139.76/19.71 | | | | | | ssItem(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v0)))
% 139.76/19.71 | | | | | |
% 139.76/19.71 | | | | | | GROUND_INST: instantiating (ax19) with all_367_0, simplifying with
% 139.76/19.71 | | | | | | (104), (105) gives:
% 139.76/19.71 | | | | | | (127) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1:
% 139.76/19.71 | | | | | | $i] : ! [v2: $i] : ( ~ (cons(v1, all_367_0) = v2) | ~
% 139.76/19.71 | | | | | | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3)
% 139.76/19.71 | | | | | | | ! [v3: $i] : ( ~ (cons(v3, v0) = v2) | ~ $i(v3) |
% 139.76/19.71 | | | | | | ? [v4: int] : ( ~ (v4 = 0) & ssItem(v3) = v4) | (v3 =
% 139.76/19.71 | | | | | | v1 & v0 = all_367_0))))
% 139.76/19.71 | | | | | |
% 139.76/19.71 | | | | | | GROUND_INST: instantiating (44) with all_345_0, 0, simplifying with
% 139.76/19.71 | | | | | | (56), (59) gives:
% 139.76/19.71 | | | | | | (128) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_345_0) = v0) | ?
% 139.76/19.71 | | | | | | [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2:
% 139.76/19.71 | | | | | | $i] : (ssList(v1) = 0 & cons(all_345_0, v1) = v2 &
% 139.76/19.71 | | | | | | app(v0, v2) = all_143_0 & $i(v2) & $i(v1)))
% 139.76/19.71 | | | | | |
% 139.76/19.71 | | | | | | GROUND_INST: instantiating (127) with all_139_0, simplifying with
% 139.76/19.71 | | | | | | (28), (29) gives:
% 139.76/19.71 | | | | | | (129) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, all_367_0) = v1)
% 139.76/19.71 | | | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v0) =
% 139.76/19.71 | | | | | | v2) | ! [v2: $i] : ( ~ (cons(v2, all_139_0) = v1) | ~
% 139.76/19.71 | | | | | | $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v2) = v3)
% 139.76/19.71 | | | | | | | (v2 = v0 & all_367_0 = all_139_0)))
% 139.76/19.71 | | | | | |
% 139.76/19.71 | | | | | | GROUND_INST: instantiating (113) with all_141_0, simplifying with
% 139.76/19.71 | | | | | | (32), (33) gives:
% 139.76/19.72 | | | | | | (130) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_345_0, v0) = v1)
% 139.76/19.72 | | | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) =
% 139.76/19.72 | | | | | | v2) | ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 139.76/19.72 | | | | | | (frontsegP(v1, v3) = v4) | ~ (cons(all_141_0, v2) =
% 139.76/19.72 | | | | | | v3) | ~ $i(v2) | ? [v5: any] : ? [v6: any] :
% 139.76/19.72 | | | | | | (frontsegP(v0, v2) = v6 & ssList(v2) = v5 & ( ~ (v5 =
% 139.76/19.72 | | | | | | 0) | (( ~ (v6 = 0) | ~ (all_345_0 = all_141_0) |
% 139.76/19.72 | | | | | | v4 = 0) & ( ~ (v4 = 0) | (v6 = 0 & all_345_0 =
% 139.76/19.72 | | | | | | all_141_0)))))))
% 139.76/19.72 | | | | | |
% 139.76/19.72 | | | | | | GROUND_INST: instantiating (126) with all_369_0, all_139_0,
% 139.76/19.72 | | | | | | simplifying with (108), (110) gives:
% 139.76/19.72 | | | | | | (131) ? [v0: any] : ? [v1: $i] : (hd(all_139_0) = v1 &
% 139.76/19.72 | | | | | | ssItem(all_369_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 139.76/19.72 | | | | | | all_369_0))
% 139.76/19.72 | | | | | |
% 139.76/19.72 | | | | | | GROUND_INST: instantiating (114) with all_141_0, simplifying with
% 139.76/19.72 | | | | | | (32), (33) gives:
% 139.76/19.72 | | | | | | (132) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_369_0, v0) = v1)
% 139.76/19.72 | | | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) =
% 139.76/19.72 | | | | | | v2) | ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 139.76/19.72 | | | | | | (frontsegP(v1, v3) = v4) | ~ (cons(all_141_0, v2) =
% 139.76/19.72 | | | | | | v3) | ~ $i(v2) | ? [v5: any] : ? [v6: any] :
% 139.76/19.72 | | | | | | (frontsegP(v0, v2) = v6 & ssList(v2) = v5 & ( ~ (v5 =
% 139.76/19.72 | | | | | | 0) | (( ~ (v6 = 0) | ~ (all_369_0 = all_141_0) |
% 139.76/19.72 | | | | | | v4 = 0) & ( ~ (v4 = 0) | (v6 = 0 & all_369_0 =
% 139.76/19.72 | | | | | | all_141_0)))))))
% 139.76/19.72 | | | | | |
% 139.76/19.72 | | | | | | GROUND_INST: instantiating (125) with all_369_0, all_139_0,
% 139.76/19.72 | | | | | | simplifying with (108), (110) gives:
% 139.76/19.72 | | | | | | (133) ? [v0: any] : ? [v1: $i] : (tl(all_139_0) = v1 &
% 139.76/19.72 | | | | | | ssItem(all_369_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 139.76/19.72 | | | | | | all_367_0))
% 139.76/19.72 | | | | | |
% 139.76/19.72 | | | | | | GROUND_INST: instantiating (129) with all_369_0, all_139_0,
% 139.76/19.72 | | | | | | simplifying with (108), (110) gives:
% 139.76/19.72 | | | | | | (134) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_369_0) = v0) | !
% 139.76/19.72 | | | | | | [v0: $i] : ( ~ (cons(v0, all_139_0) = all_139_0) | ~
% 139.76/19.72 | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & ssItem(v0) = v1) |
% 139.76/19.72 | | | | | | (v0 = all_369_0 & all_367_0 = all_139_0))
% 139.76/19.72 | | | | | |
% 139.76/19.72 | | | | | | GROUND_INST: instantiating (132) with all_367_0, all_139_0,
% 139.76/19.72 | | | | | | simplifying with (104), (110) gives:
% 139.76/19.72 | | | | | | (135) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_367_0) = v0) | !
% 139.76/19.72 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 139.76/19.72 | | | | | | (frontsegP(all_139_0, v1) = v2) | ~ (cons(all_141_0, v0)
% 139.76/19.72 | | | | | | = v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 139.76/19.72 | | | | | | (frontsegP(all_367_0, v0) = v4 & ssList(v0) = v3 & ( ~
% 139.76/19.72 | | | | | | (v3 = 0) | (( ~ (v4 = 0) | ~ (all_369_0 = all_141_0)
% 139.76/19.72 | | | | | | | v2 = 0) & ( ~ (v2 = 0) | (v4 = 0 & all_369_0 =
% 139.76/19.72 | | | | | | all_141_0))))))
% 139.76/19.72 | | | | | |
% 139.76/19.72 | | | | | | DELTA: instantiating (124) with fresh symbols all_814_0, all_814_1
% 139.76/19.72 | | | | | | gives:
% 139.76/19.72 | | | | | | (136) cyclefreeP(all_139_0) = all_814_0 & ssItem(all_345_0) =
% 139.76/19.72 | | | | | | all_814_1 & ( ~ (all_814_1 = 0) | all_814_0 = 0)
% 139.76/19.72 | | | | | |
% 139.76/19.72 | | | | | | ALPHA: (136) implies:
% 139.76/19.72 | | | | | | (137) ssItem(all_345_0) = all_814_1
% 139.76/19.72 | | | | | | (138) ~ (all_814_1 = 0) | all_814_0 = 0
% 139.76/19.72 | | | | | |
% 139.76/19.72 | | | | | | DELTA: instantiating (123) with fresh symbols all_816_0, all_816_1
% 139.76/19.72 | | | | | | gives:
% 139.76/19.72 | | | | | | (139) totalorderP(all_139_0) = all_816_0 & ssItem(all_345_0) =
% 139.76/19.72 | | | | | | all_816_1 & ( ~ (all_816_1 = 0) | all_816_0 = 0)
% 139.76/19.72 | | | | | |
% 139.76/19.72 | | | | | | ALPHA: (139) implies:
% 139.76/19.72 | | | | | | (140) ssItem(all_345_0) = all_816_1
% 139.76/19.72 | | | | | |
% 139.76/19.72 | | | | | | DELTA: instantiating (120) with fresh symbols all_818_0, all_818_1
% 139.76/19.72 | | | | | | gives:
% 139.76/19.72 | | | | | | (141) strictorderedP(all_139_0) = all_818_0 & ssItem(all_345_0) =
% 139.76/19.72 | | | | | | all_818_1 & ( ~ (all_818_1 = 0) | all_818_0 = 0)
% 139.76/19.72 | | | | | |
% 139.76/19.72 | | | | | | ALPHA: (141) implies:
% 139.76/19.73 | | | | | | (142) ssItem(all_345_0) = all_818_1
% 139.76/19.73 | | | | | | (143) ~ (all_818_1 = 0) | all_818_0 = 0
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | DELTA: instantiating (119) with fresh symbols all_820_0, all_820_1
% 139.76/19.73 | | | | | | gives:
% 139.76/19.73 | | | | | | (144) duplicatefreeP(all_139_0) = all_820_0 & ssItem(all_345_0) =
% 139.76/19.73 | | | | | | all_820_1 & ( ~ (all_820_1 = 0) | all_820_0 = 0)
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | ALPHA: (144) implies:
% 139.76/19.73 | | | | | | (145) ssItem(all_345_0) = all_820_1
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | DELTA: instantiating (118) with fresh symbols all_822_0, all_822_1
% 139.76/19.73 | | | | | | gives:
% 139.76/19.73 | | | | | | (146) equalelemsP(all_139_0) = all_822_0 & ssItem(all_345_0) =
% 139.76/19.73 | | | | | | all_822_1 & ( ~ (all_822_1 = 0) | all_822_0 = 0)
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | ALPHA: (146) implies:
% 139.76/19.73 | | | | | | (147) ssItem(all_345_0) = all_822_1
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | DELTA: instantiating (122) with fresh symbols all_824_0, all_824_1
% 139.76/19.73 | | | | | | gives:
% 139.76/19.73 | | | | | | (148) strictorderP(all_139_0) = all_824_0 & ssItem(all_345_0) =
% 139.76/19.73 | | | | | | all_824_1 & ( ~ (all_824_1 = 0) | all_824_0 = 0)
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | ALPHA: (148) implies:
% 139.76/19.73 | | | | | | (149) ssItem(all_345_0) = all_824_1
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | DELTA: instantiating (121) with fresh symbols all_826_0, all_826_1
% 139.76/19.73 | | | | | | gives:
% 139.76/19.73 | | | | | | (150) totalorderedP(all_139_0) = all_826_0 & ssItem(all_345_0) =
% 139.76/19.73 | | | | | | all_826_1 & ( ~ (all_826_1 = 0) | all_826_0 = 0)
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | ALPHA: (150) implies:
% 139.76/19.73 | | | | | | (151) ssItem(all_345_0) = all_826_1
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | DELTA: instantiating (117) with fresh symbols all_828_0, all_828_1
% 139.76/19.73 | | | | | | gives:
% 139.76/19.73 | | | | | | (152) hd(all_139_0) = all_828_0 & ssItem(all_345_0) = all_828_1 &
% 139.76/19.73 | | | | | | $i(all_828_0) & ( ~ (all_828_1 = 0) | all_828_0 =
% 139.76/19.73 | | | | | | all_345_0)
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | ALPHA: (152) implies:
% 139.76/19.73 | | | | | | (153) ssItem(all_345_0) = all_828_1
% 139.76/19.73 | | | | | | (154) hd(all_139_0) = all_828_0
% 139.76/19.73 | | | | | | (155) ~ (all_828_1 = 0) | all_828_0 = all_345_0
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | DELTA: instantiating (116) with fresh symbols all_830_0, all_830_1
% 139.76/19.73 | | | | | | gives:
% 139.76/19.73 | | | | | | (156) tl(all_139_0) = all_830_0 & ssItem(all_345_0) = all_830_1 &
% 139.76/19.73 | | | | | | $i(all_830_0) & ( ~ (all_830_1 = 0) | all_830_0 = nil)
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | ALPHA: (156) implies:
% 139.76/19.73 | | | | | | (157) ssItem(all_345_0) = all_830_1
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | DELTA: instantiating (131) with fresh symbols all_836_0, all_836_1
% 139.76/19.73 | | | | | | gives:
% 139.76/19.73 | | | | | | (158) hd(all_139_0) = all_836_0 & ssItem(all_369_0) = all_836_1 &
% 139.76/19.73 | | | | | | $i(all_836_0) & ( ~ (all_836_1 = 0) | all_836_0 =
% 139.76/19.73 | | | | | | all_369_0)
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | ALPHA: (158) implies:
% 139.76/19.73 | | | | | | (159) ssItem(all_369_0) = all_836_1
% 139.76/19.73 | | | | | | (160) hd(all_139_0) = all_836_0
% 139.76/19.73 | | | | | | (161) ~ (all_836_1 = 0) | all_836_0 = all_369_0
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | DELTA: instantiating (133) with fresh symbols all_838_0, all_838_1
% 139.76/19.73 | | | | | | gives:
% 139.76/19.73 | | | | | | (162) tl(all_139_0) = all_838_0 & ssItem(all_369_0) = all_838_1 &
% 139.76/19.73 | | | | | | $i(all_838_0) & ( ~ (all_838_1 = 0) | all_838_0 =
% 139.76/19.73 | | | | | | all_367_0)
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | ALPHA: (162) implies:
% 139.76/19.73 | | | | | | (163) ssItem(all_369_0) = all_838_1
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | BETA: splitting (135) gives:
% 139.76/19.73 | | | | | |
% 139.76/19.73 | | | | | | Case 1:
% 139.76/19.73 | | | | | | |
% 139.76/19.73 | | | | | | | (164) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_367_0) = v0)
% 139.76/19.73 | | | | | | |
% 139.76/19.73 | | | | | | | DELTA: instantiating (164) with fresh symbol all_864_0 gives:
% 139.76/19.73 | | | | | | | (165) ~ (all_864_0 = 0) & ssList(all_367_0) = all_864_0
% 139.76/19.73 | | | | | | |
% 139.76/19.73 | | | | | | | ALPHA: (165) implies:
% 139.76/19.73 | | | | | | | (166) ~ (all_864_0 = 0)
% 139.76/19.73 | | | | | | | (167) ssList(all_367_0) = all_864_0
% 139.76/19.73 | | | | | | |
% 139.76/19.73 | | | | | | | DELTA: instantiating (164) with fresh symbol all_866_0 gives:
% 139.76/19.73 | | | | | | | (168) ~ (all_866_0 = 0) & ssList(all_367_0) = all_866_0
% 139.76/19.73 | | | | | | |
% 139.76/19.73 | | | | | | | ALPHA: (168) implies:
% 139.76/19.73 | | | | | | | (169) ssList(all_367_0) = all_866_0
% 139.76/19.73 | | | | | | |
% 139.76/19.73 | | | | | | | GROUND_INST: instantiating (18) with 0, all_866_0, all_367_0,
% 139.76/19.73 | | | | | | | simplifying with (105), (169) gives:
% 139.76/19.73 | | | | | | | (170) all_866_0 = 0
% 139.76/19.73 | | | | | | |
% 139.76/19.73 | | | | | | | GROUND_INST: instantiating (18) with all_864_0, all_866_0,
% 139.76/19.73 | | | | | | | all_367_0, simplifying with (167), (169) gives:
% 139.76/19.73 | | | | | | | (171) all_866_0 = all_864_0
% 139.76/19.73 | | | | | | |
% 139.76/19.73 | | | | | | | COMBINE_EQS: (170), (171) imply:
% 139.76/19.73 | | | | | | | (172) all_864_0 = 0
% 139.76/19.73 | | | | | | |
% 139.76/19.73 | | | | | | | REDUCE: (166), (172) imply:
% 139.76/19.73 | | | | | | | (173) $false
% 139.76/19.73 | | | | | | |
% 139.76/19.73 | | | | | | | CLOSE: (173) is inconsistent.
% 139.76/19.73 | | | | | | |
% 139.76/19.74 | | | | | | Case 2:
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (17) with 0, all_820_1, all_345_0,
% 139.76/19.74 | | | | | | | simplifying with (57), (145) gives:
% 139.76/19.74 | | | | | | | (174) all_820_1 = 0
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (17) with all_818_1, all_820_1,
% 139.76/19.74 | | | | | | | all_345_0, simplifying with (142), (145) gives:
% 139.76/19.74 | | | | | | | (175) all_820_1 = all_818_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (17) with all_818_1, all_824_1,
% 139.76/19.74 | | | | | | | all_345_0, simplifying with (142), (149) gives:
% 139.76/19.74 | | | | | | | (176) all_824_1 = all_818_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (17) with all_814_1, all_824_1,
% 139.76/19.74 | | | | | | | all_345_0, simplifying with (137), (149) gives:
% 139.76/19.74 | | | | | | | (177) all_824_1 = all_814_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (17) with all_818_1, all_828_1,
% 139.76/19.74 | | | | | | | all_345_0, simplifying with (142), (153) gives:
% 139.76/19.74 | | | | | | | (178) all_828_1 = all_818_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (17) with all_816_1, all_828_1,
% 139.76/19.74 | | | | | | | all_345_0, simplifying with (140), (153) gives:
% 139.76/19.74 | | | | | | | (179) all_828_1 = all_816_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (17) with all_826_1, all_830_1,
% 139.76/19.74 | | | | | | | all_345_0, simplifying with (151), (157) gives:
% 139.76/19.74 | | | | | | | (180) all_830_1 = all_826_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (17) with all_824_1, all_830_1,
% 139.76/19.74 | | | | | | | all_345_0, simplifying with (149), (157) gives:
% 139.76/19.74 | | | | | | | (181) all_830_1 = all_824_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (17) with all_822_1, all_830_1,
% 139.76/19.74 | | | | | | | all_345_0, simplifying with (147), (157) gives:
% 139.76/19.74 | | | | | | | (182) all_830_1 = all_822_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (17) with 0, all_838_1, all_369_0,
% 139.76/19.74 | | | | | | | simplifying with (109), (163) gives:
% 139.76/19.74 | | | | | | | (183) all_838_1 = 0
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (17) with all_836_1, all_838_1,
% 139.76/19.74 | | | | | | | all_369_0, simplifying with (159), (163) gives:
% 139.76/19.74 | | | | | | | (184) all_838_1 = all_836_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | GROUND_INST: instantiating (19) with all_828_0, all_836_0,
% 139.76/19.74 | | | | | | | all_139_0, simplifying with (154), (160) gives:
% 139.76/19.74 | | | | | | | (185) all_836_0 = all_828_0
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (183), (184) imply:
% 139.76/19.74 | | | | | | | (186) all_836_1 = 0
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | SIMP: (186) implies:
% 139.76/19.74 | | | | | | | (187) all_836_1 = 0
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (180), (181) imply:
% 139.76/19.74 | | | | | | | (188) all_826_1 = all_824_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (180), (182) imply:
% 139.76/19.74 | | | | | | | (189) all_826_1 = all_822_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (178), (179) imply:
% 139.76/19.74 | | | | | | | (190) all_818_1 = all_816_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | SIMP: (190) implies:
% 139.76/19.74 | | | | | | | (191) all_818_1 = all_816_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (188), (189) imply:
% 139.76/19.74 | | | | | | | (192) all_824_1 = all_822_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | SIMP: (192) implies:
% 139.76/19.74 | | | | | | | (193) all_824_1 = all_822_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (176), (193) imply:
% 139.76/19.74 | | | | | | | (194) all_822_1 = all_818_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (177), (193) imply:
% 139.76/19.74 | | | | | | | (195) all_822_1 = all_814_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (194), (195) imply:
% 139.76/19.74 | | | | | | | (196) all_818_1 = all_814_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | SIMP: (196) implies:
% 139.76/19.74 | | | | | | | (197) all_818_1 = all_814_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (174), (175) imply:
% 139.76/19.74 | | | | | | | (198) all_818_1 = 0
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | SIMP: (198) implies:
% 139.76/19.74 | | | | | | | (199) all_818_1 = 0
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (191), (197) imply:
% 139.76/19.74 | | | | | | | (200) all_816_1 = all_814_1
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (191), (199) imply:
% 139.76/19.74 | | | | | | | (201) all_816_1 = 0
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (200), (201) imply:
% 139.76/19.74 | | | | | | | (202) all_814_1 = 0
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | COMBINE_EQS: (179), (201) imply:
% 139.76/19.74 | | | | | | | (203) all_828_1 = 0
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | BETA: splitting (115) gives:
% 139.76/19.74 | | | | | | |
% 139.76/19.74 | | | | | | | Case 1:
% 139.76/19.74 | | | | | | | |
% 139.76/19.74 | | | | | | | | (204) ? [v0: any] : ? [v1: any] : (memberP(all_143_0,
% 139.76/19.74 | | | | | | | | all_345_0) = v1 & ssItem(all_345_0) = v0 & ( ~ (v1
% 139.76/19.74 | | | | | | | | = 0) | ~ (v0 = 0)))
% 139.76/19.74 | | | | | | | |
% 139.76/19.74 | | | | | | | | DELTA: instantiating (204) with fresh symbols all_881_0,
% 139.76/19.74 | | | | | | | | all_881_1 gives:
% 139.76/19.74 | | | | | | | | (205) memberP(all_143_0, all_345_0) = all_881_0 &
% 139.76/19.74 | | | | | | | | ssItem(all_345_0) = all_881_1 & ( ~ (all_881_0 = 0) |
% 139.76/19.74 | | | | | | | | ~ (all_881_1 = 0))
% 139.76/19.74 | | | | | | | |
% 139.76/19.74 | | | | | | | | ALPHA: (205) implies:
% 139.76/19.74 | | | | | | | | (206) ssItem(all_345_0) = all_881_1
% 139.76/19.75 | | | | | | | | (207) memberP(all_143_0, all_345_0) = all_881_0
% 139.76/19.75 | | | | | | | | (208) ~ (all_881_0 = 0) | ~ (all_881_1 = 0)
% 139.76/19.75 | | | | | | | |
% 139.76/19.75 | | | | | | | | GROUND_INST: instantiating (17) with 0, all_881_1, all_345_0,
% 139.76/19.75 | | | | | | | | simplifying with (57), (206) gives:
% 139.76/19.75 | | | | | | | | (209) all_881_1 = 0
% 139.76/19.75 | | | | | | | |
% 139.76/19.75 | | | | | | | | GROUND_INST: instantiating (20) with 0, all_881_0, all_345_0,
% 139.76/19.75 | | | | | | | | all_143_0, simplifying with (59), (207) gives:
% 139.76/19.75 | | | | | | | | (210) all_881_0 = 0
% 139.76/19.75 | | | | | | | |
% 139.76/19.75 | | | | | | | | BETA: splitting (208) gives:
% 139.76/19.75 | | | | | | | |
% 139.76/19.75 | | | | | | | | Case 1:
% 139.76/19.75 | | | | | | | | |
% 139.76/19.75 | | | | | | | | | (211) ~ (all_881_0 = 0)
% 139.76/19.75 | | | | | | | | |
% 139.76/19.75 | | | | | | | | | REDUCE: (210), (211) imply:
% 139.76/19.75 | | | | | | | | | (212) $false
% 139.76/19.75 | | | | | | | | |
% 139.76/19.75 | | | | | | | | | CLOSE: (212) is inconsistent.
% 139.76/19.75 | | | | | | | | |
% 139.76/19.75 | | | | | | | | Case 2:
% 139.76/19.75 | | | | | | | | |
% 139.76/19.75 | | | | | | | | | (213) ~ (all_881_1 = 0)
% 139.76/19.75 | | | | | | | | |
% 139.76/19.75 | | | | | | | | | REDUCE: (209), (213) imply:
% 139.76/19.75 | | | | | | | | | (214) $false
% 139.76/19.75 | | | | | | | | |
% 139.76/19.75 | | | | | | | | | CLOSE: (214) is inconsistent.
% 139.76/19.75 | | | | | | | | |
% 139.76/19.75 | | | | | | | | End of split
% 139.76/19.75 | | | | | | | |
% 139.76/19.75 | | | | | | | Case 2:
% 139.76/19.75 | | | | | | | |
% 139.76/19.75 | | | | | | | | (215) ? [v0: any] : ( ~ (v0 = all_345_0) & leq(all_345_0,
% 139.76/19.75 | | | | | | | | v0) = 0 & memberP(all_143_0, v0) = 0 & ssItem(v0) =
% 139.76/19.75 | | | | | | | | 0 & $i(v0))
% 139.76/19.75 | | | | | | | |
% 139.76/19.75 | | | | | | | | DELTA: instantiating (215) with fresh symbol all_881_0 gives:
% 139.76/19.75 | | | | | | | | (216) ~ (all_881_0 = all_345_0) & leq(all_345_0, all_881_0)
% 139.76/19.75 | | | | | | | | = 0 & memberP(all_143_0, all_881_0) = 0 &
% 139.76/19.75 | | | | | | | | ssItem(all_881_0) = 0 & $i(all_881_0)
% 139.76/19.75 | | | | | | | |
% 139.76/19.75 | | | | | | | | ALPHA: (216) implies:
% 139.76/19.75 | | | | | | | | (217) ~ (all_881_0 = all_345_0)
% 139.76/19.75 | | | | | | | | (218) $i(all_881_0)
% 139.76/19.75 | | | | | | | | (219) ssItem(all_881_0) = 0
% 139.76/19.75 | | | | | | | | (220) memberP(all_143_0, all_881_0) = 0
% 139.76/19.75 | | | | | | | | (221) leq(all_345_0, all_881_0) = 0
% 139.76/19.75 | | | | | | | |
% 139.76/19.75 | | | | | | | | BETA: splitting (128) gives:
% 139.76/19.75 | | | | | | | |
% 139.76/19.75 | | | | | | | | Case 1:
% 139.76/19.75 | | | | | | | | |
% 139.76/19.75 | | | | | | | | | (222) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_345_0) = v0)
% 139.76/19.75 | | | | | | | | |
% 139.76/19.75 | | | | | | | | | BETA: splitting (134) gives:
% 139.76/19.75 | | | | | | | | |
% 139.76/19.75 | | | | | | | | | Case 1:
% 139.76/19.75 | | | | | | | | | |
% 139.76/19.75 | | | | | | | | | | (223) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_369_0) =
% 139.76/19.75 | | | | | | | | | | v0)
% 139.76/19.75 | | | | | | | | | |
% 139.76/19.75 | | | | | | | | | | DELTA: instantiating (222) with fresh symbol all_878_0
% 139.76/19.75 | | | | | | | | | | gives:
% 139.76/19.75 | | | | | | | | | | (224) ~ (all_878_0 = 0) & ssItem(all_345_0) = all_878_0
% 139.76/19.75 | | | | | | | | | |
% 139.76/19.75 | | | | | | | | | | ALPHA: (224) implies:
% 139.76/19.75 | | | | | | | | | | (225) ~ (all_878_0 = 0)
% 139.76/19.75 | | | | | | | | | | (226) ssItem(all_345_0) = all_878_0
% 139.76/19.75 | | | | | | | | | |
% 139.76/19.75 | | | | | | | | | | DELTA: instantiating (223) with fresh symbol all_880_0
% 139.76/19.75 | | | | | | | | | | gives:
% 139.76/19.75 | | | | | | | | | | (227) ~ (all_880_0 = 0) & ssItem(all_369_0) = all_880_0
% 139.76/19.75 | | | | | | | | | |
% 139.76/19.75 | | | | | | | | | | ALPHA: (227) implies:
% 139.76/19.75 | | | | | | | | | | (228) ssItem(all_369_0) = all_880_0
% 139.76/19.75 | | | | | | | | | |
% 139.76/19.75 | | | | | | | | | | DELTA: instantiating (222) with fresh symbol all_888_0
% 139.76/19.75 | | | | | | | | | | gives:
% 139.76/19.75 | | | | | | | | | | (229) ~ (all_888_0 = 0) & ssItem(all_345_0) = all_888_0
% 139.76/19.75 | | | | | | | | | |
% 139.76/19.75 | | | | | | | | | | ALPHA: (229) implies:
% 139.76/19.75 | | | | | | | | | | (230) ssItem(all_345_0) = all_888_0
% 139.76/19.75 | | | | | | | | | |
% 139.76/19.75 | | | | | | | | | | DELTA: instantiating (222) with fresh symbol all_910_0
% 139.76/19.75 | | | | | | | | | | gives:
% 139.76/19.75 | | | | | | | | | | (231) ~ (all_910_0 = 0) & ssItem(all_345_0) = all_910_0
% 139.76/19.75 | | | | | | | | | |
% 139.76/19.75 | | | | | | | | | | ALPHA: (231) implies:
% 139.76/19.75 | | | | | | | | | | (232) ssItem(all_345_0) = all_910_0
% 139.76/19.76 | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | BETA: splitting (161) gives:
% 139.76/19.76 | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | Case 1:
% 139.76/19.76 | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | (233) ~ (all_836_1 = 0)
% 139.76/19.76 | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | REDUCE: (187), (233) imply:
% 139.76/19.76 | | | | | | | | | | | (234) $false
% 139.76/19.76 | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | CLOSE: (234) is inconsistent.
% 139.76/19.76 | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | Case 2:
% 139.76/19.76 | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | (235) all_836_0 = all_369_0
% 139.76/19.76 | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | COMBINE_EQS: (185), (235) imply:
% 139.76/19.76 | | | | | | | | | | | (236) all_828_0 = all_369_0
% 139.76/19.76 | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | DELTA: instantiating (222) with fresh symbol all_921_0
% 139.76/19.76 | | | | | | | | | | | gives:
% 139.76/19.76 | | | | | | | | | | | (237) ~ (all_921_0 = 0) & ssItem(all_345_0) = all_921_0
% 139.76/19.76 | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | ALPHA: (237) implies:
% 139.76/19.76 | | | | | | | | | | | (238) ssItem(all_345_0) = all_921_0
% 139.76/19.76 | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | BETA: splitting (143) gives:
% 139.76/19.76 | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | Case 1:
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | (239) ~ (all_818_1 = 0)
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | REDUCE: (199), (239) imply:
% 139.76/19.76 | | | | | | | | | | | | (240) $false
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | Case 2:
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | DELTA: instantiating (222) with fresh symbol all_933_0
% 139.76/19.76 | | | | | | | | | | | | gives:
% 139.76/19.76 | | | | | | | | | | | | (241) ~ (all_933_0 = 0) & ssItem(all_345_0) = all_933_0
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | ALPHA: (241) implies:
% 139.76/19.76 | | | | | | | | | | | | (242) ssItem(all_345_0) = all_933_0
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | DELTA: instantiating (223) with fresh symbol all_944_0
% 139.76/19.76 | | | | | | | | | | | | gives:
% 139.76/19.76 | | | | | | | | | | | | (243) ~ (all_944_0 = 0) & ssItem(all_369_0) = all_944_0
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | ALPHA: (243) implies:
% 139.76/19.76 | | | | | | | | | | | | (244) ssItem(all_369_0) = all_944_0
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | DELTA: instantiating (223) with fresh symbol all_946_0
% 139.76/19.76 | | | | | | | | | | | | gives:
% 139.76/19.76 | | | | | | | | | | | | (245) ~ (all_946_0 = 0) & ssItem(all_369_0) = all_946_0
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | ALPHA: (245) implies:
% 139.76/19.76 | | | | | | | | | | | | (246) ssItem(all_369_0) = all_946_0
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | BETA: splitting (155) gives:
% 139.76/19.76 | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | Case 1:
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | (247) ~ (all_828_1 = 0)
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | REDUCE: (203), (247) imply:
% 139.76/19.76 | | | | | | | | | | | | | (248) $false
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | CLOSE: (248) is inconsistent.
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | Case 2:
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | (249) all_828_0 = all_345_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | COMBINE_EQS: (236), (249) imply:
% 139.76/19.76 | | | | | | | | | | | | | (250) all_369_0 = all_345_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | REDUCE: (246), (250) imply:
% 139.76/19.76 | | | | | | | | | | | | | (251) ssItem(all_345_0) = all_946_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | REDUCE: (244), (250) imply:
% 139.76/19.76 | | | | | | | | | | | | | (252) ssItem(all_345_0) = all_944_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | REDUCE: (228), (250) imply:
% 139.76/19.76 | | | | | | | | | | | | | (253) ssItem(all_345_0) = all_880_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_888_0, all_345_0,
% 139.76/19.76 | | | | | | | | | | | | | simplifying with (57), (230) gives:
% 139.76/19.76 | | | | | | | | | | | | | (254) all_888_0 = 0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_888_0, all_910_0,
% 139.76/19.76 | | | | | | | | | | | | | all_345_0, simplifying with (230), (232) gives:
% 139.76/19.76 | | | | | | | | | | | | | (255) all_910_0 = all_888_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_910_0, all_921_0,
% 139.76/19.76 | | | | | | | | | | | | | all_345_0, simplifying with (232), (238) gives:
% 139.76/19.76 | | | | | | | | | | | | | (256) all_921_0 = all_910_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_921_0, all_933_0,
% 139.76/19.76 | | | | | | | | | | | | | all_345_0, simplifying with (238), (242) gives:
% 139.76/19.76 | | | | | | | | | | | | | (257) all_933_0 = all_921_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_888_0, all_944_0,
% 139.76/19.76 | | | | | | | | | | | | | all_345_0, simplifying with (230), (252) gives:
% 139.76/19.76 | | | | | | | | | | | | | (258) all_944_0 = all_888_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_880_0, all_944_0,
% 139.76/19.76 | | | | | | | | | | | | | all_345_0, simplifying with (252), (253) gives:
% 139.76/19.76 | | | | | | | | | | | | | (259) all_944_0 = all_880_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_933_0, all_946_0,
% 139.76/19.76 | | | | | | | | | | | | | all_345_0, simplifying with (242), (251) gives:
% 139.76/19.76 | | | | | | | | | | | | | (260) all_946_0 = all_933_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_878_0, all_946_0,
% 139.76/19.76 | | | | | | | | | | | | | all_345_0, simplifying with (226), (251) gives:
% 139.76/19.76 | | | | | | | | | | | | | (261) all_946_0 = all_878_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | COMBINE_EQS: (260), (261) imply:
% 139.76/19.76 | | | | | | | | | | | | | (262) all_933_0 = all_878_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | SIMP: (262) implies:
% 139.76/19.76 | | | | | | | | | | | | | (263) all_933_0 = all_878_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | COMBINE_EQS: (258), (259) imply:
% 139.76/19.76 | | | | | | | | | | | | | (264) all_888_0 = all_880_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | SIMP: (264) implies:
% 139.76/19.76 | | | | | | | | | | | | | (265) all_888_0 = all_880_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | COMBINE_EQS: (257), (263) imply:
% 139.76/19.76 | | | | | | | | | | | | | (266) all_921_0 = all_878_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | SIMP: (266) implies:
% 139.76/19.76 | | | | | | | | | | | | | (267) all_921_0 = all_878_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | COMBINE_EQS: (256), (267) imply:
% 139.76/19.76 | | | | | | | | | | | | | (268) all_910_0 = all_878_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | SIMP: (268) implies:
% 139.76/19.76 | | | | | | | | | | | | | (269) all_910_0 = all_878_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | COMBINE_EQS: (255), (269) imply:
% 139.76/19.76 | | | | | | | | | | | | | (270) all_888_0 = all_878_0
% 139.76/19.76 | | | | | | | | | | | | |
% 139.76/19.76 | | | | | | | | | | | | | SIMP: (270) implies:
% 139.76/19.77 | | | | | | | | | | | | | (271) all_888_0 = all_878_0
% 139.76/19.77 | | | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | | | COMBINE_EQS: (254), (265) imply:
% 139.76/19.77 | | | | | | | | | | | | | (272) all_880_0 = 0
% 139.76/19.77 | | | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | | | COMBINE_EQS: (265), (271) imply:
% 139.76/19.77 | | | | | | | | | | | | | (273) all_880_0 = all_878_0
% 139.76/19.77 | | | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | | | COMBINE_EQS: (272), (273) imply:
% 139.76/19.77 | | | | | | | | | | | | | (274) all_878_0 = 0
% 139.76/19.77 | | | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | | | REDUCE: (225), (274) imply:
% 139.76/19.77 | | | | | | | | | | | | | (275) $false
% 139.76/19.77 | | | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | | | CLOSE: (275) is inconsistent.
% 139.76/19.77 | | | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | | End of split
% 139.76/19.77 | | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | End of split
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | End of split
% 139.76/19.77 | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | Case 2:
% 139.76/19.77 | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | DELTA: instantiating (222) with fresh symbol all_879_0
% 139.76/19.77 | | | | | | | | | | gives:
% 139.76/19.77 | | | | | | | | | | (276) ~ (all_879_0 = 0) & ssItem(all_345_0) = all_879_0
% 139.76/19.77 | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | ALPHA: (276) implies:
% 139.76/19.77 | | | | | | | | | | (277) ~ (all_879_0 = 0)
% 139.76/19.77 | | | | | | | | | | (278) ssItem(all_345_0) = all_879_0
% 139.76/19.77 | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | DELTA: instantiating (222) with fresh symbol all_887_0
% 139.76/19.77 | | | | | | | | | | gives:
% 139.76/19.77 | | | | | | | | | | (279) ~ (all_887_0 = 0) & ssItem(all_345_0) = all_887_0
% 139.76/19.77 | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | ALPHA: (279) implies:
% 139.76/19.77 | | | | | | | | | | (280) ssItem(all_345_0) = all_887_0
% 139.76/19.77 | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | BETA: splitting (138) gives:
% 139.76/19.77 | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | Case 1:
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | (281) ~ (all_814_1 = 0)
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | REDUCE: (202), (281) imply:
% 139.76/19.77 | | | | | | | | | | | (282) $false
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | CLOSE: (282) is inconsistent.
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | Case 2:
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | DELTA: instantiating (222) with fresh symbol all_909_0
% 139.76/19.77 | | | | | | | | | | | gives:
% 139.76/19.77 | | | | | | | | | | | (283) ~ (all_909_0 = 0) & ssItem(all_345_0) = all_909_0
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | ALPHA: (283) implies:
% 139.76/19.77 | | | | | | | | | | | (284) ssItem(all_345_0) = all_909_0
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_879_0, all_887_0,
% 139.76/19.77 | | | | | | | | | | | all_345_0, simplifying with (278), (280) gives:
% 139.76/19.77 | | | | | | | | | | | (285) all_887_0 = all_879_0
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_909_0, all_345_0,
% 139.76/19.77 | | | | | | | | | | | simplifying with (57), (284) gives:
% 139.76/19.77 | | | | | | | | | | | (286) all_909_0 = 0
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_887_0, all_909_0,
% 139.76/19.77 | | | | | | | | | | | all_345_0, simplifying with (280), (284) gives:
% 139.76/19.77 | | | | | | | | | | | (287) all_909_0 = all_887_0
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | COMBINE_EQS: (286), (287) imply:
% 139.76/19.77 | | | | | | | | | | | (288) all_887_0 = 0
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | SIMP: (288) implies:
% 139.76/19.77 | | | | | | | | | | | (289) all_887_0 = 0
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | COMBINE_EQS: (285), (289) imply:
% 139.76/19.77 | | | | | | | | | | | (290) all_879_0 = 0
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | SIMP: (290) implies:
% 139.76/19.77 | | | | | | | | | | | (291) all_879_0 = 0
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | REDUCE: (277), (291) imply:
% 139.76/19.77 | | | | | | | | | | | (292) $false
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | | CLOSE: (292) is inconsistent.
% 139.76/19.77 | | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | | End of split
% 139.76/19.77 | | | | | | | | | |
% 139.76/19.77 | | | | | | | | | End of split
% 139.76/19.77 | | | | | | | | |
% 139.76/19.77 | | | | | | | | Case 2:
% 139.76/19.77 | | | | | | | | |
% 139.76/19.77 | | | | | | | | | (293) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i]
% 139.76/19.77 | | | | | | | | | : ? [v2: $i] : (ssList(v1) = 0 & cons(all_345_0,
% 139.76/19.77 | | | | | | | | | v1) = v2 & app(v0, v2) = all_143_0 & $i(v2) &
% 139.76/19.77 | | | | | | | | | $i(v1)))
% 139.76/19.77 | | | | | | | | |
% 139.76/19.77 | | | | | | | | | DELTA: instantiating (293) with fresh symbol all_885_0 gives:
% 139.76/19.77 | | | | | | | | | (294) ssList(all_885_0) = 0 & $i(all_885_0) & ? [v0: $i] :
% 139.76/19.77 | | | | | | | | | ? [v1: $i] : (ssList(v0) = 0 & cons(all_345_0, v0) =
% 139.76/19.77 | | | | | | | | | v1 & app(all_885_0, v1) = all_143_0 & $i(v1) &
% 139.76/19.77 | | | | | | | | | $i(v0))
% 139.76/19.77 | | | | | | | | |
% 139.76/19.77 | | | | | | | | | ALPHA: (294) implies:
% 139.76/19.77 | | | | | | | | | (295) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 &
% 139.76/19.77 | | | | | | | | | cons(all_345_0, v0) = v1 & app(all_885_0, v1) =
% 139.76/19.77 | | | | | | | | | all_143_0 & $i(v1) & $i(v0))
% 139.76/19.77 | | | | | | | | |
% 139.76/19.77 | | | | | | | | | DELTA: instantiating (295) with fresh symbols all_887_0,
% 139.76/19.77 | | | | | | | | | all_887_1 gives:
% 139.76/19.77 | | | | | | | | | (296) ssList(all_887_1) = 0 & cons(all_345_0, all_887_1) =
% 139.76/19.77 | | | | | | | | | all_887_0 & app(all_885_0, all_887_0) = all_143_0 &
% 139.76/19.77 | | | | | | | | | $i(all_887_0) & $i(all_887_1)
% 139.76/19.77 | | | | | | | | |
% 139.76/19.77 | | | | | | | | | ALPHA: (296) implies:
% 139.76/19.78 | | | | | | | | | (297) $i(all_887_1)
% 139.76/19.78 | | | | | | | | | (298) cons(all_345_0, all_887_1) = all_887_0
% 139.76/19.78 | | | | | | | | | (299) ssList(all_887_1) = 0
% 139.76/19.78 | | | | | | | | |
% 139.76/19.78 | | | | | | | | | GROUND_INST: instantiating (130) with all_887_1, all_887_0,
% 139.76/19.78 | | | | | | | | | simplifying with (297), (298) gives:
% 139.76/19.78 | | | | | | | | | (300) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_887_1) = v0)
% 139.76/19.78 | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 139.76/19.78 | | | | | | | | | (frontsegP(all_887_0, v1) = v2) | ~
% 139.76/19.78 | | | | | | | | | (cons(all_141_0, v0) = v1) | ~ $i(v0) | ? [v3:
% 139.76/19.78 | | | | | | | | | any] : ? [v4: any] : (frontsegP(all_887_1, v0) =
% 139.76/19.78 | | | | | | | | | v4 & ssList(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 =
% 139.76/19.78 | | | | | | | | | 0) | ~ (all_345_0 = all_141_0) | v2 = 0)
% 139.76/19.78 | | | | | | | | | & ( ~ (v2 = 0) | (v4 = 0 & all_345_0 =
% 139.76/19.78 | | | | | | | | | all_141_0))))))
% 139.76/19.78 | | | | | | | | |
% 139.76/19.78 | | | | | | | | | GROUND_INST: instantiating (60) with all_881_0, simplifying
% 139.76/19.78 | | | | | | | | | with (218), (220) gives:
% 139.76/19.78 | | | | | | | | | (301) all_881_0 = all_345_0 | ? [v0: any] : ? [v1: any] :
% 139.76/19.78 | | | | | | | | | (leq(all_345_0, all_881_0) = v1 & ssItem(all_881_0) =
% 139.76/19.78 | | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 139.76/19.78 | | | | | | | | |
% 139.76/19.78 | | | | | | | | | GROUND_INST: instantiating (111) with all_881_0, 0, simplifying
% 139.76/19.78 | | | | | | | | | with (218), (221) gives:
% 139.76/19.78 | | | | | | | | | (302) ? [v0: any] : ? [v1: any] : (leq(all_881_0,
% 139.76/19.78 | | | | | | | | | all_345_0) = v1 & ssItem(all_881_0) = v0 & ( ~
% 139.76/19.78 | | | | | | | | | (v0 = 0) | ! [v2: $i] : ( ~ (ssList(v2) = 0) |
% 139.76/19.78 | | | | | | | | | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5:
% 139.76/19.78 | | | | | | | | | $i] : ( ~ (cons(all_345_0, v3) = v4) | ~
% 139.76/19.78 | | | | | | | | | (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int]
% 139.76/19.78 | | | | | | | | | : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6:
% 139.76/19.78 | | | | | | | | | $i] : ! [v7: $i] : ( ~ (v1 = 0) | ~
% 139.76/19.78 | | | | | | | | | (cons(all_881_0, v6) = v7) | ~ (app(v5,
% 139.76/19.78 | | | | | | | | | v7) = nil) | ~ $i(v6) | ? [v8: int] :
% 139.76/19.78 | | | | | | | | | ( ~ (v8 = 0) & ssList(v6) = v8))))))
% 139.76/19.78 | | | | | | | | |
% 139.76/19.78 | | | | | | | | | GROUND_INST: instantiating (112) with all_881_0, 0, simplifying
% 139.76/19.78 | | | | | | | | | with (218), (221) gives:
% 139.76/19.78 | | | | | | | | | (303) ? [v0: MultipleValueBool] : ? [v1:
% 139.76/19.78 | | | | | | | | | MultipleValueBool] : (leq(all_881_0, all_345_0) =
% 139.76/19.78 | | | | | | | | | v1 & ssItem(all_881_0) = v0)
% 139.76/19.78 | | | | | | | | |
% 139.76/19.78 | | | | | | | | | DELTA: instantiating (303) with fresh symbols all_1276_0,
% 139.76/19.78 | | | | | | | | | all_1276_1 gives:
% 139.76/19.78 | | | | | | | | | (304) leq(all_881_0, all_345_0) = all_1276_0 &
% 139.76/19.78 | | | | | | | | | ssItem(all_881_0) = all_1276_1
% 139.76/19.78 | | | | | | | | |
% 139.76/19.78 | | | | | | | | | ALPHA: (304) implies:
% 139.76/19.78 | | | | | | | | | (305) ssItem(all_881_0) = all_1276_1
% 139.76/19.78 | | | | | | | | |
% 139.76/19.78 | | | | | | | | | DELTA: instantiating (302) with fresh symbols all_1298_0,
% 139.76/19.78 | | | | | | | | | all_1298_1 gives:
% 139.76/19.78 | | | | | | | | | (306) leq(all_881_0, all_345_0) = all_1298_0 &
% 139.76/19.78 | | | | | | | | | ssItem(all_881_0) = all_1298_1 & ( ~ (all_1298_1 = 0)
% 139.76/19.78 | | | | | | | | | | ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) |
% 139.76/19.78 | | | | | | | | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 139.76/19.78 | | | | | | | | | (cons(all_345_0, v1) = v2) | ~ (app(v0, v2) =
% 139.76/19.78 | | | | | | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0)
% 139.76/19.78 | | | | | | | | | & ssList(v1) = v4) | ! [v4: $i] : ! [v5:
% 139.76/19.78 | | | | | | | | | $i] : ( ~ (all_1298_0 = 0) | ~
% 139.76/19.78 | | | | | | | | | (cons(all_881_0, v4) = v5) | ~ (app(v3, v5)
% 139.76/19.78 | | | | | | | | | = nil) | ~ $i(v4) | ? [v6: int] : ( ~ (v6
% 139.76/19.78 | | | | | | | | | = 0) & ssList(v4) = v6)))))
% 139.76/19.78 | | | | | | | | |
% 139.76/19.78 | | | | | | | | | ALPHA: (306) implies:
% 139.76/19.78 | | | | | | | | | (307) ssItem(all_881_0) = all_1298_1
% 139.76/19.78 | | | | | | | | |
% 139.76/19.78 | | | | | | | | | BETA: splitting (301) gives:
% 139.76/19.78 | | | | | | | | |
% 139.76/19.78 | | | | | | | | | Case 1:
% 139.76/19.78 | | | | | | | | | |
% 139.76/19.78 | | | | | | | | | | (308) all_881_0 = all_345_0
% 139.76/19.78 | | | | | | | | | |
% 139.76/19.78 | | | | | | | | | | REDUCE: (217), (308) imply:
% 139.76/19.78 | | | | | | | | | | (309) $false
% 139.76/19.78 | | | | | | | | | |
% 139.76/19.78 | | | | | | | | | | CLOSE: (309) is inconsistent.
% 139.76/19.78 | | | | | | | | | |
% 139.76/19.78 | | | | | | | | | Case 2:
% 139.76/19.78 | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | (310) ? [v0: any] : ? [v1: any] : (leq(all_345_0,
% 139.76/19.79 | | | | | | | | | | all_881_0) = v1 & ssItem(all_881_0) = v0 & ( ~
% 139.76/19.79 | | | | | | | | | | (v1 = 0) | ~ (v0 = 0)))
% 139.76/19.79 | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | DELTA: instantiating (310) with fresh symbols all_1327_0,
% 139.76/19.79 | | | | | | | | | | all_1327_1 gives:
% 139.76/19.79 | | | | | | | | | | (311) leq(all_345_0, all_881_0) = all_1327_0 &
% 139.76/19.79 | | | | | | | | | | ssItem(all_881_0) = all_1327_1 & ( ~ (all_1327_0 =
% 139.76/19.79 | | | | | | | | | | 0) | ~ (all_1327_1 = 0))
% 139.76/19.79 | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | ALPHA: (311) implies:
% 139.76/19.79 | | | | | | | | | | (312) ssItem(all_881_0) = all_1327_1
% 139.76/19.79 | | | | | | | | | | (313) leq(all_345_0, all_881_0) = all_1327_0
% 139.76/19.79 | | | | | | | | | | (314) ~ (all_1327_0 = 0) | ~ (all_1327_1 = 0)
% 139.76/19.79 | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | BETA: splitting (300) gives:
% 139.76/19.79 | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | Case 1:
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | (315) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_887_1) =
% 139.76/19.79 | | | | | | | | | | | v0)
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | DELTA: instantiating (315) with fresh symbol all_1327_0
% 139.76/19.79 | | | | | | | | | | | gives:
% 139.76/19.79 | | | | | | | | | | | (316) ~ (all_1327_0 = 0) & ssList(all_887_1) =
% 139.76/19.79 | | | | | | | | | | | all_1327_0
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | ALPHA: (316) implies:
% 139.76/19.79 | | | | | | | | | | | (317) ~ (all_1327_0 = 0)
% 139.76/19.79 | | | | | | | | | | | (318) ssList(all_887_1) = all_1327_0
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | DELTA: instantiating (315) with fresh symbol all_1329_0
% 139.76/19.79 | | | | | | | | | | | gives:
% 139.76/19.79 | | | | | | | | | | | (319) ~ (all_1329_0 = 0) & ssList(all_887_1) =
% 139.76/19.79 | | | | | | | | | | | all_1329_0
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | ALPHA: (319) implies:
% 139.76/19.79 | | | | | | | | | | | (320) ssList(all_887_1) = all_1329_0
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_1329_0, all_887_1,
% 139.76/19.79 | | | | | | | | | | | simplifying with (299), (320) gives:
% 139.76/19.79 | | | | | | | | | | | (321) all_1329_0 = 0
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1327_0, all_1329_0,
% 139.76/19.79 | | | | | | | | | | | all_887_1, simplifying with (318), (320) gives:
% 139.76/19.79 | | | | | | | | | | | (322) all_1329_0 = all_1327_0
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | COMBINE_EQS: (321), (322) imply:
% 139.76/19.79 | | | | | | | | | | | (323) all_1327_0 = 0
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | REDUCE: (317), (323) imply:
% 139.76/19.79 | | | | | | | | | | | (324) $false
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | CLOSE: (324) is inconsistent.
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | Case 2:
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_1298_1, all_881_0,
% 139.76/19.79 | | | | | | | | | | | simplifying with (219), (307) gives:
% 139.76/19.79 | | | | | | | | | | | (325) all_1298_1 = 0
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1298_1, all_1327_1,
% 139.76/19.79 | | | | | | | | | | | all_881_0, simplifying with (307), (312) gives:
% 139.76/19.79 | | | | | | | | | | | (326) all_1327_1 = all_1298_1
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1276_1, all_1327_1,
% 139.76/19.79 | | | | | | | | | | | all_881_0, simplifying with (305), (312) gives:
% 139.76/19.79 | | | | | | | | | | | (327) all_1327_1 = all_1276_1
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_1327_0, all_881_0,
% 139.76/19.79 | | | | | | | | | | | all_345_0, simplifying with (221), (313) gives:
% 139.76/19.79 | | | | | | | | | | | (328) all_1327_0 = 0
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | COMBINE_EQS: (326), (327) imply:
% 139.76/19.79 | | | | | | | | | | | (329) all_1298_1 = all_1276_1
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | SIMP: (329) implies:
% 139.76/19.79 | | | | | | | | | | | (330) all_1298_1 = all_1276_1
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | COMBINE_EQS: (325), (330) imply:
% 139.76/19.79 | | | | | | | | | | | (331) all_1276_1 = 0
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | COMBINE_EQS: (327), (331) imply:
% 139.76/19.79 | | | | | | | | | | | (332) all_1327_1 = 0
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | BETA: splitting (314) gives:
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | Case 1:
% 139.76/19.79 | | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | | (333) ~ (all_1327_0 = 0)
% 139.76/19.79 | | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | | REDUCE: (328), (333) imply:
% 139.76/19.79 | | | | | | | | | | | | (334) $false
% 139.76/19.79 | | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | | CLOSE: (334) is inconsistent.
% 139.76/19.79 | | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | Case 2:
% 139.76/19.79 | | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | | (335) ~ (all_1327_1 = 0)
% 139.76/19.79 | | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | | REDUCE: (332), (335) imply:
% 139.76/19.79 | | | | | | | | | | | | (336) $false
% 139.76/19.79 | | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | | CLOSE: (336) is inconsistent.
% 139.76/19.79 | | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | | End of split
% 139.76/19.79 | | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | | End of split
% 139.76/19.79 | | | | | | | | | |
% 139.76/19.79 | | | | | | | | | End of split
% 139.76/19.79 | | | | | | | | |
% 139.76/19.79 | | | | | | | | End of split
% 139.76/19.79 | | | | | | | |
% 139.76/19.79 | | | | | | | End of split
% 139.76/19.79 | | | | | | |
% 139.76/19.79 | | | | | | End of split
% 139.76/19.79 | | | | | |
% 139.76/19.79 | | | | | End of split
% 139.76/19.79 | | | | |
% 139.76/19.79 | | | | Case 2:
% 139.76/19.79 | | | | |
% 139.76/19.79 | | | | | (337) all_143_0 = nil & all_139_0 = nil
% 139.76/19.79 | | | | |
% 139.76/19.79 | | | | | ALPHA: (337) implies:
% 139.76/19.79 | | | | | (338) all_143_0 = nil
% 139.76/19.79 | | | | |
% 139.76/19.79 | | | | | REDUCE: (53), (338) imply:
% 139.76/19.79 | | | | | (339) $false
% 139.76/19.79 | | | | |
% 139.76/19.79 | | | | | CLOSE: (339) is inconsistent.
% 139.76/19.79 | | | | |
% 139.76/19.80 | | | | End of split
% 139.76/19.80 | | | |
% 139.76/19.80 | | | Case 2:
% 139.76/19.80 | | | |
% 139.76/19.80 | | | | (340) all_143_0 = nil
% 139.76/19.80 | | | | (341) ~ (all_139_0 = nil)
% 139.76/19.80 | | | |
% 139.76/19.80 | | | | BETA: splitting (37) gives:
% 139.76/19.80 | | | |
% 139.76/19.80 | | | | Case 1:
% 139.76/19.80 | | | | |
% 139.76/19.80 | | | | | (342) ? [v0: $i] : (memberP(all_143_0, v0) = 0 & cons(v0, nil) =
% 139.76/19.80 | | | | | all_139_0 & ssItem(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 =
% 139.76/19.80 | | | | | v0 | ~ (memberP(all_143_0, v1) = 0) | ~ $i(v1) | ?
% 139.76/19.80 | | | | | [v2: any] : ? [v3: any] : (leq(v0, v1) = v3 & ssItem(v1)
% 139.76/19.80 | | | | | = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 139.76/19.80 | | | | |
% 139.76/19.80 | | | | | DELTA: instantiating (342) with fresh symbol all_345_0 gives:
% 139.76/19.80 | | | | | (343) memberP(all_143_0, all_345_0) = 0 & cons(all_345_0, nil) =
% 139.76/19.80 | | | | | all_139_0 & ssItem(all_345_0) = 0 & $i(all_345_0) & ! [v0:
% 139.76/19.80 | | | | | any] : (v0 = all_345_0 | ~ (memberP(all_143_0, v0) = 0) |
% 139.76/19.80 | | | | | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (leq(all_345_0,
% 139.76/19.80 | | | | | v0) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 =
% 139.76/19.80 | | | | | 0))))
% 139.76/19.80 | | | | |
% 139.76/19.80 | | | | | ALPHA: (343) implies:
% 139.76/19.80 | | | | | (344) $i(all_345_0)
% 139.76/19.80 | | | | | (345) ssItem(all_345_0) = 0
% 139.76/19.80 | | | | | (346) cons(all_345_0, nil) = all_139_0
% 139.76/19.80 | | | | | (347) memberP(all_143_0, all_345_0) = 0
% 139.76/19.80 | | | | |
% 139.76/19.80 | | | | | REDUCE: (340), (347) imply:
% 139.76/19.80 | | | | | (348) memberP(nil, all_345_0) = 0
% 139.76/19.80 | | | | |
% 139.76/19.80 | | | | | BETA: splitting (43) gives:
% 139.76/19.80 | | | | |
% 139.76/19.80 | | | | | Case 1:
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | | (349) all_139_0 = nil
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | | REDUCE: (341), (349) imply:
% 139.76/19.80 | | | | | | (350) $false
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | | CLOSE: (350) is inconsistent.
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | Case 2:
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | | GROUND_INST: instantiating (40) with all_345_0, all_139_0,
% 139.76/19.80 | | | | | | simplifying with (344), (346) gives:
% 139.76/19.80 | | | | | | (351) ? [v0: any] : ? [v1: $i] : (tl(all_139_0) = v1 &
% 139.76/19.80 | | | | | | ssItem(all_345_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 139.76/19.80 | | | | | | nil))
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | | GROUND_INST: instantiating (41) with all_345_0, all_139_0,
% 139.76/19.80 | | | | | | simplifying with (344), (346) gives:
% 139.76/19.80 | | | | | | (352) ? [v0: any] : ? [v1: $i] : (hd(all_139_0) = v1 &
% 139.76/19.80 | | | | | | ssItem(all_345_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 139.76/19.80 | | | | | | all_345_0))
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | | GROUND_INST: instantiating (13) with all_345_0, all_139_0,
% 139.76/19.80 | | | | | | simplifying with (344), (346) gives:
% 139.76/19.80 | | | | | | (353) ? [v0: any] : ? [v1: any] : (equalelemsP(all_139_0) = v1
% 139.76/19.80 | | | | | | & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | | GROUND_INST: instantiating (12) with all_345_0, all_139_0,
% 139.76/19.80 | | | | | | simplifying with (344), (346) gives:
% 139.76/19.80 | | | | | | (354) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_139_0) =
% 139.76/19.80 | | | | | | v1 & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | | GROUND_INST: instantiating (11) with all_345_0, all_139_0,
% 139.76/19.80 | | | | | | simplifying with (344), (346) gives:
% 139.76/19.80 | | | | | | (355) ? [v0: any] : ? [v1: any] : (strictorderedP(all_139_0) =
% 139.76/19.80 | | | | | | v1 & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | | GROUND_INST: instantiating (10) with all_345_0, all_139_0,
% 139.76/19.80 | | | | | | simplifying with (344), (346) gives:
% 139.76/19.80 | | | | | | (356) ? [v0: any] : ? [v1: any] : (totalorderedP(all_139_0) =
% 139.76/19.80 | | | | | | v1 & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.80 | | | | | |
% 139.76/19.80 | | | | | | GROUND_INST: instantiating (9) with all_345_0, all_139_0,
% 139.76/19.80 | | | | | | simplifying with (344), (346) gives:
% 139.76/19.81 | | | | | | (357) ? [v0: any] : ? [v1: any] : (strictorderP(all_139_0) = v1
% 139.76/19.81 | | | | | | & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | GROUND_INST: instantiating (7) with all_345_0, all_139_0,
% 139.76/19.81 | | | | | | simplifying with (344), (346) gives:
% 139.76/19.81 | | | | | | (358) ? [v0: any] : ? [v1: any] : (totalorderP(all_139_0) = v1
% 139.76/19.81 | | | | | | & ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | GROUND_INST: instantiating (5) with all_345_0, all_139_0,
% 139.76/19.81 | | | | | | simplifying with (344), (346) gives:
% 139.76/19.81 | | | | | | (359) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_139_0) = v1 &
% 139.76/19.81 | | | | | | ssItem(all_345_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | GROUND_INST: instantiating (4) with all_345_0, simplifying with
% 139.76/19.81 | | | | | | (344), (348) gives:
% 139.76/19.81 | | | | | | (360) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_345_0) = v0)
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | DELTA: instantiating (360) with fresh symbol all_573_0 gives:
% 139.76/19.81 | | | | | | (361) ~ (all_573_0 = 0) & ssItem(all_345_0) = all_573_0
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | ALPHA: (361) implies:
% 139.76/19.81 | | | | | | (362) ~ (all_573_0 = 0)
% 139.76/19.81 | | | | | | (363) ssItem(all_345_0) = all_573_0
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | DELTA: instantiating (353) with fresh symbols all_575_0, all_575_1
% 139.76/19.81 | | | | | | gives:
% 139.76/19.81 | | | | | | (364) equalelemsP(all_139_0) = all_575_0 & ssItem(all_345_0) =
% 139.76/19.81 | | | | | | all_575_1 & ( ~ (all_575_1 = 0) | all_575_0 = 0)
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | ALPHA: (364) implies:
% 139.76/19.81 | | | | | | (365) ssItem(all_345_0) = all_575_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | DELTA: instantiating (359) with fresh symbols all_577_0, all_577_1
% 139.76/19.81 | | | | | | gives:
% 139.76/19.81 | | | | | | (366) cyclefreeP(all_139_0) = all_577_0 & ssItem(all_345_0) =
% 139.76/19.81 | | | | | | all_577_1 & ( ~ (all_577_1 = 0) | all_577_0 = 0)
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | ALPHA: (366) implies:
% 139.76/19.81 | | | | | | (367) ssItem(all_345_0) = all_577_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | DELTA: instantiating (358) with fresh symbols all_579_0, all_579_1
% 139.76/19.81 | | | | | | gives:
% 139.76/19.81 | | | | | | (368) totalorderP(all_139_0) = all_579_0 & ssItem(all_345_0) =
% 139.76/19.81 | | | | | | all_579_1 & ( ~ (all_579_1 = 0) | all_579_0 = 0)
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | ALPHA: (368) implies:
% 139.76/19.81 | | | | | | (369) ssItem(all_345_0) = all_579_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | DELTA: instantiating (357) with fresh symbols all_581_0, all_581_1
% 139.76/19.81 | | | | | | gives:
% 139.76/19.81 | | | | | | (370) strictorderP(all_139_0) = all_581_0 & ssItem(all_345_0) =
% 139.76/19.81 | | | | | | all_581_1 & ( ~ (all_581_1 = 0) | all_581_0 = 0)
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | ALPHA: (370) implies:
% 139.76/19.81 | | | | | | (371) ssItem(all_345_0) = all_581_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | DELTA: instantiating (356) with fresh symbols all_583_0, all_583_1
% 139.76/19.81 | | | | | | gives:
% 139.76/19.81 | | | | | | (372) totalorderedP(all_139_0) = all_583_0 & ssItem(all_345_0) =
% 139.76/19.81 | | | | | | all_583_1 & ( ~ (all_583_1 = 0) | all_583_0 = 0)
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | ALPHA: (372) implies:
% 139.76/19.81 | | | | | | (373) ssItem(all_345_0) = all_583_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | DELTA: instantiating (355) with fresh symbols all_585_0, all_585_1
% 139.76/19.81 | | | | | | gives:
% 139.76/19.81 | | | | | | (374) strictorderedP(all_139_0) = all_585_0 & ssItem(all_345_0) =
% 139.76/19.81 | | | | | | all_585_1 & ( ~ (all_585_1 = 0) | all_585_0 = 0)
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | ALPHA: (374) implies:
% 139.76/19.81 | | | | | | (375) ssItem(all_345_0) = all_585_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | DELTA: instantiating (354) with fresh symbols all_587_0, all_587_1
% 139.76/19.81 | | | | | | gives:
% 139.76/19.81 | | | | | | (376) duplicatefreeP(all_139_0) = all_587_0 & ssItem(all_345_0) =
% 139.76/19.81 | | | | | | all_587_1 & ( ~ (all_587_1 = 0) | all_587_0 = 0)
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | ALPHA: (376) implies:
% 139.76/19.81 | | | | | | (377) ssItem(all_345_0) = all_587_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | DELTA: instantiating (352) with fresh symbols all_589_0, all_589_1
% 139.76/19.81 | | | | | | gives:
% 139.76/19.81 | | | | | | (378) hd(all_139_0) = all_589_0 & ssItem(all_345_0) = all_589_1 &
% 139.76/19.81 | | | | | | $i(all_589_0) & ( ~ (all_589_1 = 0) | all_589_0 =
% 139.76/19.81 | | | | | | all_345_0)
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | ALPHA: (378) implies:
% 139.76/19.81 | | | | | | (379) ssItem(all_345_0) = all_589_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | DELTA: instantiating (351) with fresh symbols all_591_0, all_591_1
% 139.76/19.81 | | | | | | gives:
% 139.76/19.81 | | | | | | (380) tl(all_139_0) = all_591_0 & ssItem(all_345_0) = all_591_1 &
% 139.76/19.81 | | | | | | $i(all_591_0) & ( ~ (all_591_1 = 0) | all_591_0 = nil)
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | ALPHA: (380) implies:
% 139.76/19.81 | | | | | | (381) ssItem(all_345_0) = all_591_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | GROUND_INST: instantiating (17) with all_579_1, all_581_1,
% 139.76/19.81 | | | | | | all_345_0, simplifying with (369), (371) gives:
% 139.76/19.81 | | | | | | (382) all_581_1 = all_579_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | GROUND_INST: instantiating (17) with all_581_1, all_585_1,
% 139.76/19.81 | | | | | | all_345_0, simplifying with (371), (375) gives:
% 139.76/19.81 | | | | | | (383) all_585_1 = all_581_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | GROUND_INST: instantiating (17) with all_573_0, all_585_1,
% 139.76/19.81 | | | | | | all_345_0, simplifying with (363), (375) gives:
% 139.76/19.81 | | | | | | (384) all_585_1 = all_573_0
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | GROUND_INST: instantiating (17) with 0, all_587_1, all_345_0,
% 139.76/19.81 | | | | | | simplifying with (345), (377) gives:
% 139.76/19.81 | | | | | | (385) all_587_1 = 0
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | GROUND_INST: instantiating (17) with all_583_1, all_587_1,
% 139.76/19.81 | | | | | | all_345_0, simplifying with (373), (377) gives:
% 139.76/19.81 | | | | | | (386) all_587_1 = all_583_1
% 139.76/19.81 | | | | | |
% 139.76/19.81 | | | | | | GROUND_INST: instantiating (17) with all_587_1, all_589_1,
% 139.76/19.81 | | | | | | all_345_0, simplifying with (377), (379) gives:
% 139.76/19.81 | | | | | | (387) all_589_1 = all_587_1
% 139.76/19.81 | | | | | |
% 139.76/19.82 | | | | | | GROUND_INST: instantiating (17) with all_581_1, all_589_1,
% 139.76/19.82 | | | | | | all_345_0, simplifying with (371), (379) gives:
% 139.76/19.82 | | | | | | (388) all_589_1 = all_581_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | GROUND_INST: instantiating (17) with all_575_1, all_589_1,
% 139.76/19.82 | | | | | | all_345_0, simplifying with (365), (379) gives:
% 139.76/19.82 | | | | | | (389) all_589_1 = all_575_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | GROUND_INST: instantiating (17) with all_581_1, all_591_1,
% 139.76/19.82 | | | | | | all_345_0, simplifying with (371), (381) gives:
% 139.76/19.82 | | | | | | (390) all_591_1 = all_581_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | GROUND_INST: instantiating (17) with all_577_1, all_591_1,
% 139.76/19.82 | | | | | | all_345_0, simplifying with (367), (381) gives:
% 139.76/19.82 | | | | | | (391) all_591_1 = all_577_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (390), (391) imply:
% 139.76/19.82 | | | | | | (392) all_581_1 = all_577_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | SIMP: (392) implies:
% 139.76/19.82 | | | | | | (393) all_581_1 = all_577_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (387), (389) imply:
% 139.76/19.82 | | | | | | (394) all_587_1 = all_575_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | SIMP: (394) implies:
% 139.76/19.82 | | | | | | (395) all_587_1 = all_575_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (388), (389) imply:
% 139.76/19.82 | | | | | | (396) all_581_1 = all_575_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | SIMP: (396) implies:
% 139.76/19.82 | | | | | | (397) all_581_1 = all_575_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (385), (386) imply:
% 139.76/19.82 | | | | | | (398) all_583_1 = 0
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (386), (395) imply:
% 139.76/19.82 | | | | | | (399) all_583_1 = all_575_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (383), (384) imply:
% 139.76/19.82 | | | | | | (400) all_581_1 = all_573_0
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | SIMP: (400) implies:
% 139.76/19.82 | | | | | | (401) all_581_1 = all_573_0
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (398), (399) imply:
% 139.76/19.82 | | | | | | (402) all_575_1 = 0
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | SIMP: (402) implies:
% 139.76/19.82 | | | | | | (403) all_575_1 = 0
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (382), (397) imply:
% 139.76/19.82 | | | | | | (404) all_579_1 = all_575_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (382), (393) imply:
% 139.76/19.82 | | | | | | (405) all_579_1 = all_577_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (382), (401) imply:
% 139.76/19.82 | | | | | | (406) all_579_1 = all_573_0
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (405), (406) imply:
% 139.76/19.82 | | | | | | (407) all_577_1 = all_573_0
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (404), (405) imply:
% 139.76/19.82 | | | | | | (408) all_577_1 = all_575_1
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (407), (408) imply:
% 139.76/19.82 | | | | | | (409) all_575_1 = all_573_0
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | SIMP: (409) implies:
% 139.76/19.82 | | | | | | (410) all_575_1 = all_573_0
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | COMBINE_EQS: (403), (410) imply:
% 139.76/19.82 | | | | | | (411) all_573_0 = 0
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | SIMP: (411) implies:
% 139.76/19.82 | | | | | | (412) all_573_0 = 0
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | REDUCE: (362), (412) imply:
% 139.76/19.82 | | | | | | (413) $false
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | | CLOSE: (413) is inconsistent.
% 139.76/19.82 | | | | | |
% 139.76/19.82 | | | | | End of split
% 139.76/19.82 | | | | |
% 139.76/19.82 | | | | Case 2:
% 139.76/19.82 | | | | |
% 139.76/19.82 | | | | | (414) all_143_0 = nil & all_139_0 = nil
% 139.76/19.82 | | | | |
% 139.76/19.82 | | | | | ALPHA: (414) implies:
% 139.76/19.82 | | | | | (415) all_139_0 = nil
% 139.76/19.82 | | | | |
% 139.76/19.82 | | | | | REDUCE: (341), (415) imply:
% 139.76/19.82 | | | | | (416) $false
% 139.76/19.82 | | | | |
% 139.76/19.82 | | | | | CLOSE: (416) is inconsistent.
% 139.76/19.82 | | | | |
% 139.76/19.82 | | | | End of split
% 139.76/19.82 | | | |
% 139.76/19.82 | | | End of split
% 139.76/19.82 | | |
% 139.76/19.82 | | End of split
% 139.76/19.82 | |
% 139.76/19.82 | End of split
% 139.76/19.82 |
% 139.76/19.82 End of proof
% 139.76/19.82
% 139.76/19.82 Sub-proof #1 shows that the following formulas are inconsistent:
% 139.76/19.82 ----------------------------------------------------------------
% 139.76/19.82 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 139.76/19.82 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 139.76/19.82 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 139.76/19.82 (3) ssList(nil) = 0
% 139.76/19.82
% 139.76/19.82 Begin of proof
% 139.76/19.82 |
% 139.76/19.82 | DELTA: instantiating (1) with fresh symbol all_298_0 gives:
% 139.76/19.82 | (4) ~ (all_298_0 = 0) & ssList(nil) = all_298_0
% 139.76/19.82 |
% 139.76/19.82 | ALPHA: (4) implies:
% 139.76/19.82 | (5) ~ (all_298_0 = 0)
% 139.76/19.82 | (6) ssList(nil) = all_298_0
% 139.76/19.82 |
% 139.76/19.82 | DELTA: instantiating (1) with fresh symbol all_300_0 gives:
% 139.76/19.82 | (7) ~ (all_300_0 = 0) & ssList(nil) = all_300_0
% 139.76/19.82 |
% 139.76/19.82 | ALPHA: (7) implies:
% 139.76/19.82 | (8) ssList(nil) = all_300_0
% 139.76/19.82 |
% 139.76/19.82 | DELTA: instantiating (1) with fresh symbol all_302_0 gives:
% 139.76/19.82 | (9) ~ (all_302_0 = 0) & ssList(nil) = all_302_0
% 139.76/19.82 |
% 139.76/19.82 | ALPHA: (9) implies:
% 139.76/19.82 | (10) ssList(nil) = all_302_0
% 139.76/19.82 |
% 139.76/19.82 | DELTA: instantiating (1) with fresh symbol all_304_0 gives:
% 139.76/19.82 | (11) ~ (all_304_0 = 0) & ssList(nil) = all_304_0
% 139.76/19.82 |
% 139.76/19.82 | ALPHA: (11) implies:
% 139.76/19.82 | (12) ssList(nil) = all_304_0
% 139.76/19.82 |
% 139.76/19.82 | DELTA: instantiating (1) with fresh symbol all_306_0 gives:
% 139.76/19.83 | (13) ~ (all_306_0 = 0) & ssList(nil) = all_306_0
% 139.76/19.83 |
% 139.76/19.83 | ALPHA: (13) implies:
% 139.76/19.83 | (14) ssList(nil) = all_306_0
% 139.76/19.83 |
% 139.76/19.83 | DELTA: instantiating (1) with fresh symbol all_308_0 gives:
% 139.76/19.83 | (15) ~ (all_308_0 = 0) & ssList(nil) = all_308_0
% 139.76/19.83 |
% 139.76/19.83 | ALPHA: (15) implies:
% 139.76/19.83 | (16) ssList(nil) = all_308_0
% 139.76/19.83 |
% 139.76/19.83 | DELTA: instantiating (1) with fresh symbol all_310_0 gives:
% 139.76/19.83 | (17) ~ (all_310_0 = 0) & ssList(nil) = all_310_0
% 139.76/19.83 |
% 139.76/19.83 | ALPHA: (17) implies:
% 139.76/19.83 | (18) ssList(nil) = all_310_0
% 139.76/19.83 |
% 139.76/19.83 | GROUND_INST: instantiating (2) with all_300_0, all_302_0, nil, simplifying
% 139.76/19.83 | with (8), (10) gives:
% 139.76/19.83 | (19) all_302_0 = all_300_0
% 139.76/19.83 |
% 139.76/19.83 | GROUND_INST: instantiating (2) with all_300_0, all_304_0, nil, simplifying
% 139.76/19.83 | with (8), (12) gives:
% 139.76/19.83 | (20) all_304_0 = all_300_0
% 139.76/19.83 |
% 139.76/19.83 | GROUND_INST: instantiating (2) with 0, all_308_0, nil, simplifying with (3),
% 139.76/19.83 | (16) gives:
% 139.76/19.83 | (21) all_308_0 = 0
% 139.76/19.83 |
% 139.76/19.83 | GROUND_INST: instantiating (2) with all_306_0, all_308_0, nil, simplifying
% 139.76/19.83 | with (14), (16) gives:
% 139.76/19.83 | (22) all_308_0 = all_306_0
% 139.76/19.83 |
% 139.76/19.83 | GROUND_INST: instantiating (2) with all_302_0, all_308_0, nil, simplifying
% 139.76/19.83 | with (10), (16) gives:
% 139.76/19.83 | (23) all_308_0 = all_302_0
% 139.76/19.83 |
% 139.76/19.83 | GROUND_INST: instantiating (2) with all_304_0, all_310_0, nil, simplifying
% 139.76/19.83 | with (12), (18) gives:
% 139.76/19.83 | (24) all_310_0 = all_304_0
% 139.76/19.83 |
% 139.76/19.83 | GROUND_INST: instantiating (2) with all_298_0, all_310_0, nil, simplifying
% 139.76/19.83 | with (6), (18) gives:
% 139.76/19.83 | (25) all_310_0 = all_298_0
% 139.76/19.83 |
% 139.76/19.83 | COMBINE_EQS: (24), (25) imply:
% 139.76/19.83 | (26) all_304_0 = all_298_0
% 139.76/19.83 |
% 139.76/19.83 | SIMP: (26) implies:
% 139.76/19.83 | (27) all_304_0 = all_298_0
% 139.76/19.83 |
% 139.76/19.83 | COMBINE_EQS: (22), (23) imply:
% 139.76/19.83 | (28) all_306_0 = all_302_0
% 139.76/19.83 |
% 139.76/19.83 | COMBINE_EQS: (21), (22) imply:
% 139.76/19.83 | (29) all_306_0 = 0
% 139.76/19.83 |
% 139.76/19.83 | COMBINE_EQS: (28), (29) imply:
% 139.76/19.83 | (30) all_302_0 = 0
% 139.76/19.83 |
% 139.76/19.83 | SIMP: (30) implies:
% 139.76/19.83 | (31) all_302_0 = 0
% 139.76/19.83 |
% 139.76/19.83 | COMBINE_EQS: (20), (27) imply:
% 139.76/19.83 | (32) all_300_0 = all_298_0
% 139.76/19.83 |
% 139.76/19.83 | SIMP: (32) implies:
% 139.76/19.83 | (33) all_300_0 = all_298_0
% 139.76/19.83 |
% 139.76/19.83 | COMBINE_EQS: (19), (31) imply:
% 139.76/19.83 | (34) all_300_0 = 0
% 139.76/19.83 |
% 139.76/19.83 | SIMP: (34) implies:
% 139.76/19.83 | (35) all_300_0 = 0
% 139.76/19.83 |
% 139.76/19.83 | COMBINE_EQS: (33), (35) imply:
% 139.76/19.83 | (36) all_298_0 = 0
% 139.76/19.83 |
% 139.76/19.83 | SIMP: (36) implies:
% 139.76/19.83 | (37) all_298_0 = 0
% 139.76/19.83 |
% 139.76/19.83 | REDUCE: (5), (37) imply:
% 139.76/19.83 | (38) $false
% 139.76/19.83 |
% 139.76/19.83 | CLOSE: (38) is inconsistent.
% 139.76/19.83 |
% 139.76/19.83 End of proof
% 139.76/19.83 % SZS output end Proof for theBenchmark
% 139.76/19.83
% 139.76/19.83 19223ms
%------------------------------------------------------------------------------