TSTP Solution File: SWC019+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC019+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 20:49:13 EDT 2023
% Result : Theorem 54.88s 8.05s
% Output : Proof 61.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC019+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 18:59:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.24/1.41 Prover 1: Preprocessing ...
% 4.24/1.42 Prover 4: Preprocessing ...
% 5.33/1.44 Prover 2: Preprocessing ...
% 5.33/1.44 Prover 5: Preprocessing ...
% 5.33/1.44 Prover 6: Preprocessing ...
% 5.33/1.44 Prover 0: Preprocessing ...
% 5.33/1.44 Prover 3: Preprocessing ...
% 14.43/2.68 Prover 2: Proving ...
% 15.24/2.79 Prover 1: Constructing countermodel ...
% 15.24/2.81 Prover 5: Constructing countermodel ...
% 15.24/2.82 Prover 6: Proving ...
% 16.06/2.90 Prover 3: Constructing countermodel ...
% 21.34/3.59 Prover 4: Constructing countermodel ...
% 22.46/3.77 Prover 0: Proving ...
% 40.54/6.20 Prover 3: gave up
% 40.54/6.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 42.08/6.39 Prover 7: Preprocessing ...
% 43.70/6.59 Prover 7: Constructing countermodel ...
% 54.88/8.05 Prover 0: proved (7395ms)
% 54.88/8.05
% 54.88/8.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.88/8.05
% 54.88/8.07 Prover 6: stopped
% 54.88/8.07 Prover 2: stopped
% 54.88/8.07 Prover 5: stopped
% 54.88/8.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 54.88/8.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 54.88/8.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 54.88/8.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 56.32/8.23 Prover 8: Preprocessing ...
% 56.32/8.23 Prover 13: Preprocessing ...
% 56.32/8.25 Prover 11: Preprocessing ...
% 56.32/8.27 Prover 10: Preprocessing ...
% 57.81/8.44 Prover 10: Constructing countermodel ...
% 58.17/8.47 Prover 13: Constructing countermodel ...
% 58.60/8.51 Prover 8: Warning: ignoring some quantifiers
% 58.98/8.57 Prover 8: Constructing countermodel ...
% 58.98/8.64 Prover 4: Found proof (size 86)
% 58.98/8.64 Prover 4: proved (8018ms)
% 58.98/8.64 Prover 13: stopped
% 58.98/8.64 Prover 10: stopped
% 58.98/8.64 Prover 8: stopped
% 58.98/8.64 Prover 1: stopped
% 59.72/8.65 Prover 7: stopped
% 60.60/8.96 Prover 11: Constructing countermodel ...
% 60.60/8.98 Prover 11: stopped
% 60.60/8.98
% 60.60/8.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 60.60/8.98
% 60.60/9.00 % SZS output start Proof for theBenchmark
% 60.60/9.01 Assumptions after simplification:
% 60.60/9.01 ---------------------------------
% 60.60/9.01
% 60.60/9.01 (ax15)
% 61.30/9.06 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (ssList(v0)
% 61.30/9.06 = 0) | ~ (neq(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~
% 61.30/9.06 (v3 = 0) & ssList(v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (ssList(v1)
% 61.30/9.06 = 0) | ~ (ssList(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] :
% 61.30/9.06 (neq(v0, v1) = v2 & ( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))) & !
% 61.30/9.06 [v0: $i] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0) | ~ $i(v0))
% 61.30/9.06
% 61.30/9.06 (ax17)
% 61.30/9.06 ssList(nil) = 0 & $i(nil)
% 61.30/9.06
% 61.30/9.06 (ax2)
% 61.30/9.06 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & ssItem(v1) = 0 & ssItem(v0) = 0 &
% 61.30/9.06 $i(v1) & $i(v0))
% 61.30/9.06
% 61.30/9.06 (ax40)
% 61.30/9.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 61.30/9.08 (frontsegP(v0, v2) = v3) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0)
% 61.30/9.08 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: any] : (( ~ (v4
% 61.30/9.08 = 0) & ssList(v1) = v4) | (frontsegP(v1, v2) = v5 & ssList(v2) = v4 &
% 61.30/9.08 ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 61.30/9.08 : ( ~ (frontsegP(v1, v2) = 0) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) =
% 61.30/9.08 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: any] : ((
% 61.30/9.08 ~ (v3 = 0) & ssList(v1) = v3) | (frontsegP(v0, v2) = v4 & ssList(v2) =
% 61.30/9.08 v3 & ( ~ (v3 = 0) | v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 61.30/9.08 : ( ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v2) = 0) | ~ (ssList(v0) = 0) | ~
% 61.30/9.08 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: any] : (( ~ (v3 = 0)
% 61.30/9.08 & ssList(v1) = v3) | (frontsegP(v1, v2) = v3 & frontsegP(v0, v2) = v4 &
% 61.30/9.08 ( ~ (v3 = 0) | v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (ssList(v1)
% 61.30/9.08 = 0) | ~ (ssList(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] :
% 61.30/9.08 (frontsegP(v0, v1) = v2 & ! [v3: $i] : ! [v4: int] : ( ~ (v2 = 0) | v4 = 0
% 61.30/9.08 | ~ (frontsegP(v0, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any]
% 61.30/9.08 : (frontsegP(v1, v3) = v6 & ssList(v3) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 61.30/9.08 0)))) & ! [v3: $i] : ( ~ (v2 = 0) | ~ (frontsegP(v1, v3) = 0) |
% 61.30/9.08 ~ $i(v3) | ? [v4: any] : ? [v5: any] : (frontsegP(v0, v3) = v5 &
% 61.30/9.08 ssList(v3) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v3: $i] : ( ~ (v2 =
% 61.30/9.08 0) | ~ (ssList(v3) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] :
% 61.30/9.08 (frontsegP(v1, v3) = v4 & frontsegP(v0, v3) = v5 & ( ~ (v4 = 0) | v5 =
% 61.30/9.08 0)))))
% 61.30/9.08
% 61.30/9.08 (ax42)
% 61.30/9.08 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ~ $i(v0)
% 61.30/9.08 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0: $i] : ( ~
% 61.30/9.08 (ssList(v0) = 0) | ~ $i(v0) | frontsegP(v0, v0) = 0)
% 61.30/9.08
% 61.30/9.08 (ax43)
% 61.30/9.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (frontsegP(v0, v1)
% 61.30/9.08 = 0) | ~ (ssList(v0) = 0) | ~ (app(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 61.30/9.08 | ~ $i(v0) | ? [v4: int] : ? [v5: any] : (( ~ (v4 = 0) & ssList(v1) = v4)
% 61.30/9.08 | (frontsegP(v3, v1) = v5 & ssList(v2) = v4 & ( ~ (v4 = 0) | v5 = 0)))) &
% 61.30/9.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (frontsegP(v0, v1) = 0) | ~
% 61.30/9.08 (ssList(v2) = 0) | ~ (ssList(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 61.30/9.08 ? [v3: any] : ? [v4: int] : ((v4 = 0 & frontsegP(v3, v1) = 0 & app(v0, v2)
% 61.30/9.08 = v3 & $i(v3)) | ( ~ (v3 = 0) & ssList(v1) = v3))) & ! [v0: $i] : !
% 61.30/9.08 [v1: $i] : ( ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 61.30/9.08 | ? [v2: any] : (frontsegP(v0, v1) = v2 & ! [v3: $i] : ! [v4: $i] : ( ~
% 61.30/9.08 (v2 = 0) | ~ (app(v0, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6:
% 61.30/9.08 any] : (frontsegP(v4, v1) = v6 & ssList(v3) = v5 & ( ~ (v5 = 0) | v6 =
% 61.30/9.08 0))) & ! [v3: $i] : ( ~ (v2 = 0) | ~ (ssList(v3) = 0) | ~ $i(v3)
% 61.30/9.08 | ? [v4: $i] : (frontsegP(v4, v1) = 0 & app(v0, v3) = v4 & $i(v4)))))
% 61.30/9.08
% 61.30/9.08 (ax44)
% 61.58/9.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 61.58/9.09 any] : ( ~ (frontsegP(v2, v4) = v5) | ~ (cons(v0, v2) = v3) | ~
% 61.58/9.09 (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) |
% 61.58/9.09 ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: any] : (( ~ (v6 = 0) &
% 61.58/9.09 ssList(v2) = v6) | (frontsegP(v3, v7) = v8 & ssList(v4) = v6 & cons(v1,
% 61.58/9.09 v4) = v7 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v8 = 0) | (v5 = 0 & v1 = v0))
% 61.58/9.09 & ( ~ (v5 = 0) | ~ (v1 = v0) | v8 = 0)))))) & ! [v0: $i] : ! [v1:
% 61.58/9.09 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v1,
% 61.58/9.09 v4) = v5) | ~ (cons(v0, v2) = v3) | ~ (ssItem(v1) = 0) | ~
% 61.58/9.09 (ssItem(v0) = 0) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 61.58/9.09 int] : ? [v7: any] : ? [v8: any] : (( ~ (v6 = 0) & ssList(v2) = v6) |
% 61.58/9.09 (frontsegP(v3, v5) = v7 & frontsegP(v2, v4) = v8 & ssList(v4) = v6 & ( ~
% 61.58/9.09 (v6 = 0) | (( ~ (v8 = 0) | ~ (v1 = v0) | v7 = 0) & ( ~ (v7 = 0) | (v8
% 61.58/9.09 = 0 & v1 = v0))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 61.58/9.09 ! [v3: $i] : ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ (cons(v0, v2) = v3) | ~
% 61.58/9.09 (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) |
% 61.58/9.09 ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : (( ~ (v5 = 0) &
% 61.58/9.09 ssList(v2) = v5) | (frontsegP(v3, v5) = v6 & frontsegP(v2, v4) = v7 &
% 61.58/9.09 cons(v1, v4) = v5 & $i(v5) & ( ~ (v7 = 0) | ~ (v1 = v0) | v6 = 0) & ( ~
% 61.58/9.09 (v6 = 0) | (v7 = 0 & v1 = v0))))) & ! [v0: $i] : ! [v1: $i] : !
% 61.58/9.09 [v2: $i] : ( ~ (ssList(v2) = 0) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) |
% 61.58/9.09 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (cons(v0, v2) = v3 & $i(v3)
% 61.58/9.09 & ! [v4: $i] : ! [v5: any] : ( ~ (frontsegP(v2, v4) = v5) | ~ $i(v4) |
% 61.58/9.09 ? [v6: any] : ? [v7: $i] : ? [v8: any] : (frontsegP(v3, v7) = v8 &
% 61.58/9.09 ssList(v4) = v6 & cons(v1, v4) = v7 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v8
% 61.58/9.09 = 0) | (v5 = 0 & v1 = v0)) & ( ~ (v5 = 0) | ~ (v1 = v0) | v8
% 61.58/9.09 = 0))))) & ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v1, v4) = v5) |
% 61.58/9.09 ~ $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (frontsegP(v3,
% 61.58/9.09 v5) = v7 & frontsegP(v2, v4) = v8 & ssList(v4) = v6 & ( ~ (v6 = 0) |
% 61.58/9.09 (( ~ (v8 = 0) | ~ (v1 = v0) | v7 = 0) & ( ~ (v7 = 0) | (v8 = 0 & v1
% 61.58/9.09 = v0)))))) & ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) |
% 61.58/9.09 ? [v5: $i] : ? [v6: any] : ? [v7: any] : (frontsegP(v3, v5) = v6 &
% 61.58/9.09 frontsegP(v2, v4) = v7 & cons(v1, v4) = v5 & $i(v5) & ( ~ (v7 = 0) |
% 61.58/9.09 ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v7 = 0 & v1 = v0))))))
% 61.58/9.09
% 61.58/9.09 (ax5)
% 61.58/9.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~
% 61.58/9.10 (frontsegP(v0, v1) = v2) | ~ (ssList(v3) = 0) | ~ (ssList(v0) = 0) | ~
% 61.58/9.10 $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : (( ~ (v4 = v0) & app(v1, v3)
% 61.58/9.10 = v4 & $i(v4)) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0: $i] : !
% 61.58/9.10 [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ (frontsegP(v0, v1) = v2)
% 61.58/9.10 | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v0) | ~ $i(v3) | ~ $i(v1) | ~
% 61.58/9.10 $i(v0) | ? [v4: int] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) &
% 61.58/9.10 ssList(v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ (frontsegP(v0, v1)
% 61.58/9.10 = 0) | ~ (ssList(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ?
% 61.58/9.10 [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & ((v5 = v0 & v4 = 0 &
% 61.58/9.10 ssList(v3) = 0 & app(v1, v3) = v0) | ( ~ (v2 = 0) & ssList(v1) =
% 61.58/9.10 v2)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~
% 61.58/9.10 (ssList(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ?
% 61.58/9.10 [v4: int] : ? [v5: $i] : (frontsegP(v0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) |
% 61.58/9.10 (v5 = v0 & v4 = 0 & ssList(v3) = 0 & app(v1, v3) = v0)) & (v2 = 0 | ( !
% 61.58/9.10 [v6: $i] : ( ~ (ssList(v6) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 =
% 61.58/9.10 v0) & app(v1, v6) = v7 & $i(v7))) & ! [v6: $i] : ( ~ (app(v1,
% 61.58/9.10 v6) = v0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & ssList(v6)
% 61.58/9.10 = v7))))))
% 61.58/9.10
% 61.58/9.10 (co1)
% 61.58/9.10 $i(nil) & ? [v0: $i] : ( ~ (v0 = nil) & ssList(v0) = 0 & $i(v0) & ! [v1: $i]
% 61.58/9.10 : ( ~ (frontsegP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] :
% 61.58/9.10 (ssList(v1) = v2 & neq(v1, nil) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & !
% 61.58/9.10 [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] :
% 61.58/9.10 (frontsegP(v0, v1) = v3 & neq(v1, nil) = v2 & ( ~ (v3 = 0) | ~ (v2 =
% 61.58/9.10 0)))) & ! [v1: $i] : ( ~ (neq(v1, nil) = 0) | ~ $i(v1) | ? [v2:
% 61.58/9.10 any] : ? [v3: any] : (frontsegP(v0, v1) = v3 & ssList(v1) = v2 & ( ~
% 61.58/9.10 (v3 = 0) | ~ (v2 = 0)))))
% 61.58/9.10
% 61.58/9.10 (function-axioms)
% 61.58/9.11 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 61.58/9.11 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 61.58/9.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 61.58/9.11 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 61.58/9.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 61.58/9.11 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 61.58/9.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 61.58/9.11 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 61.58/9.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 61.58/9.11 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 61.58/9.11 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 61.58/9.11 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 61.58/9.11 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 61.58/9.11 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 61.58/9.11 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 61.58/9.11 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 61.58/9.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 61.58/9.11 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 61.58/9.11 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 61.58/9.11 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 61.58/9.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 61.58/9.11 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 61.58/9.11 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 61.58/9.11 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 61.58/9.11 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 61.58/9.11 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 61.58/9.11 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 61.58/9.11 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 61.58/9.11 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 61.58/9.11 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 61.58/9.11 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 61.58/9.11 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 61.58/9.11 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 61.58/9.11 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 61.58/9.11 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 61.58/9.11 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 61.58/9.11 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 61.58/9.11 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 61.58/9.11 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 61.58/9.11 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 61.58/9.11 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 61.58/9.11 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 61.58/9.11 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 61.58/9.11
% 61.58/9.11 Further assumptions not needed in the proof:
% 61.58/9.11 --------------------------------------------
% 61.58/9.11 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax20, ax21, ax22, ax23,
% 61.58/9.11 ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35,
% 61.58/9.11 ax36, ax37, ax38, ax39, ax4, ax41, ax45, ax46, ax47, ax48, ax49, ax50, ax51,
% 61.58/9.11 ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax63,
% 61.58/9.11 ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax72, ax73, ax74, ax75,
% 61.58/9.11 ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85, ax86, ax87,
% 61.58/9.11 ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 61.58/9.11
% 61.58/9.11 Those formulas are unsatisfiable:
% 61.58/9.11 ---------------------------------
% 61.58/9.11
% 61.58/9.11 Begin of proof
% 61.58/9.11 |
% 61.58/9.11 | ALPHA: (ax5) implies:
% 61.58/9.11 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0)
% 61.58/9.11 | | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: int] :
% 61.58/9.11 | ? [v5: $i] : (frontsegP(v0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | (v5 =
% 61.58/9.11 | v0 & v4 = 0 & ssList(v3) = 0 & app(v1, v3) = v0)) & (v2 = 0 | (
% 61.58/9.11 | ! [v6: $i] : ( ~ (ssList(v6) = 0) | ~ $i(v6) | ? [v7: $i] : (
% 61.58/9.11 | ~ (v7 = v0) & app(v1, v6) = v7 & $i(v7))) & ! [v6: $i] : (
% 61.58/9.11 | ~ (app(v1, v6) = v0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 =
% 61.58/9.11 | 0) & ssList(v6) = v7))))))
% 61.58/9.11 |
% 61.58/9.11 | ALPHA: (ax15) implies:
% 61.58/9.12 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0)
% 61.58/9.12 | | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : (neq(v0, v1) = v2 & ( ~ (v2
% 61.58/9.12 | = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))
% 61.58/9.12 |
% 61.58/9.12 | ALPHA: (ax17) implies:
% 61.58/9.12 | (3) ssList(nil) = 0
% 61.58/9.12 |
% 61.58/9.12 | ALPHA: (ax40) implies:
% 61.58/9.12 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0)
% 61.58/9.12 | | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : (frontsegP(v0, v1) = v2 & !
% 61.58/9.12 | [v3: $i] : ! [v4: int] : ( ~ (v2 = 0) | v4 = 0 | ~ (frontsegP(v0,
% 61.58/9.12 | v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] :
% 61.58/9.12 | (frontsegP(v1, v3) = v6 & ssList(v3) = v5 & ( ~ (v6 = 0) | ~ (v5
% 61.58/9.12 | = 0)))) & ! [v3: $i] : ( ~ (v2 = 0) | ~ (frontsegP(v1,
% 61.58/9.12 | v3) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] :
% 61.58/9.12 | (frontsegP(v0, v3) = v5 & ssList(v3) = v4 & ( ~ (v4 = 0) | v5 =
% 61.58/9.12 | 0))) & ! [v3: $i] : ( ~ (v2 = 0) | ~ (ssList(v3) = 0) | ~
% 61.58/9.12 | $i(v3) | ? [v4: any] : ? [v5: any] : (frontsegP(v1, v3) = v4 &
% 61.58/9.12 | frontsegP(v0, v3) = v5 & ( ~ (v4 = 0) | v5 = 0)))))
% 61.58/9.12 |
% 61.58/9.12 | ALPHA: (ax42) implies:
% 61.58/9.12 | (5) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | frontsegP(v0, v0) = 0)
% 61.58/9.12 |
% 61.58/9.12 | ALPHA: (ax43) implies:
% 61.58/9.12 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0)
% 61.58/9.12 | | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : (frontsegP(v0, v1) = v2 & !
% 61.58/9.12 | [v3: $i] : ! [v4: $i] : ( ~ (v2 = 0) | ~ (app(v0, v3) = v4) | ~
% 61.58/9.12 | $i(v3) | ? [v5: any] : ? [v6: any] : (frontsegP(v4, v1) = v6 &
% 61.58/9.12 | ssList(v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v3: $i] : ( ~
% 61.58/9.12 | (v2 = 0) | ~ (ssList(v3) = 0) | ~ $i(v3) | ? [v4: $i] :
% 61.58/9.12 | (frontsegP(v4, v1) = 0 & app(v0, v3) = v4 & $i(v4)))))
% 61.58/9.12 |
% 61.58/9.12 | ALPHA: (ax44) implies:
% 61.58/9.13 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~
% 61.58/9.13 | (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 61.58/9.13 | $i(v0) | ? [v3: $i] : (cons(v0, v2) = v3 & $i(v3) & ! [v4: $i] : !
% 61.58/9.13 | [v5: any] : ( ~ (frontsegP(v2, v4) = v5) | ~ $i(v4) | ? [v6: any]
% 61.58/9.13 | : ? [v7: $i] : ? [v8: any] : (frontsegP(v3, v7) = v8 &
% 61.58/9.13 | ssList(v4) = v6 & cons(v1, v4) = v7 & $i(v7) & ( ~ (v6 = 0) |
% 61.58/9.13 | (( ~ (v8 = 0) | (v5 = 0 & v1 = v0)) & ( ~ (v5 = 0) | ~ (v1 =
% 61.58/9.13 | v0) | v8 = 0))))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 61.58/9.13 | (cons(v1, v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] :
% 61.58/9.13 | ? [v8: any] : (frontsegP(v3, v5) = v7 & frontsegP(v2, v4) = v8 &
% 61.58/9.13 | ssList(v4) = v6 & ( ~ (v6 = 0) | (( ~ (v8 = 0) | ~ (v1 = v0) |
% 61.58/9.13 | v7 = 0) & ( ~ (v7 = 0) | (v8 = 0 & v1 = v0)))))) & !
% 61.58/9.13 | [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ? [v5: $i] : ? [v6:
% 61.58/9.13 | any] : ? [v7: any] : (frontsegP(v3, v5) = v6 & frontsegP(v2,
% 61.58/9.13 | v4) = v7 & cons(v1, v4) = v5 & $i(v5) & ( ~ (v7 = 0) | ~ (v1
% 61.58/9.13 | = v0) | v6 = 0) & ( ~ (v6 = 0) | (v7 = 0 & v1 = v0))))))
% 61.58/9.13 |
% 61.58/9.13 | ALPHA: (co1) implies:
% 61.58/9.13 | (8) $i(nil)
% 61.58/9.13 | (9) ? [v0: $i] : ( ~ (v0 = nil) & ssList(v0) = 0 & $i(v0) & ! [v1: $i] :
% 61.58/9.13 | ( ~ (frontsegP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any]
% 61.58/9.13 | : (ssList(v1) = v2 & neq(v1, nil) = v3 & ( ~ (v3 = 0) | ~ (v2 =
% 61.58/9.13 | 0)))) & ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ?
% 61.58/9.13 | [v2: any] : ? [v3: any] : (frontsegP(v0, v1) = v3 & neq(v1, nil) =
% 61.58/9.13 | v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v1: $i] : ( ~ (neq(v1,
% 61.58/9.13 | nil) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] :
% 61.58/9.13 | (frontsegP(v0, v1) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 =
% 61.58/9.13 | 0)))))
% 61.58/9.13 |
% 61.58/9.13 | ALPHA: (function-axioms) implies:
% 61.58/9.13 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 61.58/9.13 | : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 61.58/9.13 | v0))
% 61.58/9.13 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 61.58/9.13 | : ! [v3: $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~
% 61.58/9.13 | (frontsegP(v3, v2) = v0))
% 61.58/9.13 |
% 61.58/9.13 | DELTA: instantiating (ax2) with fresh symbols all_91_0, all_91_1 gives:
% 61.58/9.13 | (12) ~ (all_91_0 = all_91_1) & ssItem(all_91_0) = 0 & ssItem(all_91_1) = 0
% 61.58/9.13 | & $i(all_91_0) & $i(all_91_1)
% 61.58/9.13 |
% 61.58/9.13 | ALPHA: (12) implies:
% 61.58/9.13 | (13) $i(all_91_1)
% 61.58/9.13 | (14) $i(all_91_0)
% 61.58/9.13 | (15) ssItem(all_91_1) = 0
% 61.58/9.13 | (16) ssItem(all_91_0) = 0
% 61.58/9.13 |
% 61.58/9.13 | DELTA: instantiating (9) with fresh symbol all_93_0 gives:
% 61.58/9.13 | (17) ~ (all_93_0 = nil) & ssList(all_93_0) = 0 & $i(all_93_0) & ! [v0:
% 61.58/9.13 | $i] : ( ~ (frontsegP(all_93_0, v0) = 0) | ~ $i(v0) | ? [v1: any] :
% 61.58/9.13 | ? [v2: any] : (ssList(v0) = v1 & neq(v0, nil) = v2 & ( ~ (v2 = 0) |
% 61.58/9.13 | ~ (v1 = 0)))) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0)
% 61.58/9.13 | | ? [v1: any] : ? [v2: any] : (frontsegP(all_93_0, v0) = v2 &
% 61.58/9.13 | neq(v0, nil) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) & ! [v0: $i] :
% 61.58/9.13 | ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 61.58/9.13 | (frontsegP(all_93_0, v0) = v2 & ssList(v0) = v1 & ( ~ (v2 = 0) | ~
% 61.58/9.14 | (v1 = 0))))
% 61.58/9.14 |
% 61.58/9.14 | ALPHA: (17) implies:
% 61.58/9.14 | (18) ~ (all_93_0 = nil)
% 61.58/9.14 | (19) $i(all_93_0)
% 61.58/9.14 | (20) ssList(all_93_0) = 0
% 61.58/9.14 | (21) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 61.58/9.14 | [v2: any] : (frontsegP(all_93_0, v0) = v2 & neq(v0, nil) = v1 & ( ~
% 61.58/9.14 | (v2 = 0) | ~ (v1 = 0))))
% 61.58/9.14 |
% 61.84/9.14 | GROUND_INST: instantiating (1) with all_93_0, all_93_0, simplifying with (19),
% 61.84/9.14 | (20) gives:
% 61.84/9.14 | (22) ? [v0: any] : ? [v1: $i] : ? [v2: int] : ? [v3: int] :
% 61.84/9.14 | (frontsegP(all_93_0, all_93_0) = v0 & $i(v1) & ( ~ (v0 = 0) | (v3 =
% 61.84/9.14 | all_93_0 & v2 = 0 & ssList(v1) = 0 & app(all_93_0, v1) =
% 61.84/9.14 | all_93_0)) & (v0 = 0 | ( ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~
% 61.84/9.14 | $i(v4) | ? [v5: any] : ( ~ (v5 = all_93_0) & app(all_93_0,
% 61.84/9.14 | v4) = v5 & $i(v5))) & ! [v4: $i] : ( ~ (app(all_93_0, v4)
% 61.84/9.14 | = all_93_0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) &
% 61.84/9.14 | ssList(v4) = v5)))))
% 61.84/9.14 |
% 61.84/9.14 | GROUND_INST: instantiating (4) with all_93_0, all_93_0, simplifying with (19),
% 61.84/9.14 | (20) gives:
% 61.84/9.14 | (23) ? [v0: any] : (frontsegP(all_93_0, all_93_0) = v0 & ! [v1: $i] : !
% 61.84/9.14 | [v2: int] : ( ~ (v0 = 0) | v2 = 0 | ~ (frontsegP(all_93_0, v1) =
% 61.84/9.14 | v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] :
% 61.84/9.14 | (frontsegP(all_93_0, v1) = v4 & ssList(v1) = v3 & ( ~ (v4 = 0) |
% 61.84/9.14 | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (v0 = 0) | ~
% 61.84/9.14 | (frontsegP(all_93_0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3:
% 61.84/9.14 | any] : (frontsegP(all_93_0, v1) = v3 & ssList(v1) = v2 & ( ~ (v2
% 61.84/9.14 | = 0) | v3 = 0))) & ! [v1: $i] : ( ~ (v0 = 0) | ~
% 61.84/9.14 | (ssList(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] :
% 61.84/9.14 | (frontsegP(all_93_0, v1) = v3 & frontsegP(all_93_0, v1) = v2 & ( ~
% 61.84/9.14 | (v2 = 0) | v3 = 0))))
% 61.84/9.14 |
% 61.84/9.14 | GROUND_INST: instantiating (6) with all_93_0, all_93_0, simplifying with (19),
% 61.84/9.14 | (20) gives:
% 61.84/9.14 | (24) ? [v0: any] : (frontsegP(all_93_0, all_93_0) = v0 & ! [v1: $i] : !
% 61.84/9.14 | [v2: $i] : ( ~ (v0 = 0) | ~ (app(all_93_0, v1) = v2) | ~ $i(v1) |
% 61.84/9.14 | ? [v3: any] : ? [v4: any] : (frontsegP(v2, all_93_0) = v4 &
% 61.84/9.14 | ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~
% 61.84/9.14 | (v0 = 0) | ~ (ssList(v1) = 0) | ~ $i(v1) | ? [v2: $i] :
% 61.84/9.14 | (frontsegP(v2, all_93_0) = 0 & app(all_93_0, v1) = v2 & $i(v2))))
% 61.84/9.14 |
% 61.84/9.14 | GROUND_INST: instantiating (2) with all_93_0, nil, simplifying with (3), (8),
% 61.84/9.14 | (19), (20) gives:
% 61.84/9.14 | (25) ? [v0: any] : (neq(all_93_0, nil) = v0 & ( ~ (v0 = 0) | ~ (all_93_0
% 61.84/9.14 | = nil)) & (v0 = 0 | all_93_0 = nil))
% 61.84/9.14 |
% 61.84/9.14 | GROUND_INST: instantiating (7) with all_91_0, all_91_0, all_93_0, simplifying
% 61.84/9.14 | with (14), (16), (19), (20) gives:
% 61.84/9.15 | (26) ? [v0: $i] : (cons(all_91_0, all_93_0) = v0 & $i(v0) & ! [v1: $i] :
% 61.84/9.15 | ! [v2: any] : ( ~ (frontsegP(all_93_0, v1) = v2) | ~ $i(v1) | ?
% 61.84/9.15 | [v3: any] : ? [v4: $i] : ? [v5: any] : (frontsegP(v0, v4) = v5 &
% 61.84/9.15 | ssList(v1) = v3 & cons(all_91_0, v1) = v4 & $i(v4) & ( ~ (v3 =
% 61.84/9.15 | 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) &
% 61.84/9.15 | ! [v1: $i] : ! [v2: $i] : ( ~ (cons(all_91_0, v1) = v2) | ~ $i(v1)
% 61.84/9.15 | | ? [v3: any] : ? [v4: any] : ? [v5: any] : (frontsegP(v0, v2)
% 61.84/9.15 | = v4 & frontsegP(all_93_0, v1) = v5 & ssList(v1) = v3 & ( ~ (v3
% 61.84/9.15 | = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = 0)))))
% 61.84/9.15 | & ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ? [v2: $i] : ?
% 61.84/9.15 | [v3: any] : ? [v4: any] : (frontsegP(v0, v2) = v3 &
% 61.84/9.15 | frontsegP(all_93_0, v1) = v4 & cons(all_91_0, v1) = v2 & $i(v2)
% 61.84/9.15 | & ( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0))))
% 61.84/9.15 |
% 61.89/9.15 | GROUND_INST: instantiating (7) with all_91_1, all_91_0, all_93_0, simplifying
% 61.89/9.15 | with (13), (14), (15), (16), (19), (20) gives:
% 61.89/9.15 | (27) ? [v0: $i] : (cons(all_91_1, all_93_0) = v0 & $i(v0) & ! [v1: $i] :
% 61.89/9.15 | ! [v2: any] : ( ~ (frontsegP(all_93_0, v1) = v2) | ~ $i(v1) | ?
% 61.89/9.15 | [v3: any] : ? [v4: $i] : ? [v5: any] : (frontsegP(v0, v4) = v5 &
% 61.89/9.15 | ssList(v1) = v3 & cons(all_91_0, v1) = v4 & $i(v4) & ( ~ (v3 =
% 61.89/9.15 | 0) | (( ~ (v5 = 0) | (v2 = 0 & all_91_0 = all_91_1)) & ( ~
% 61.89/9.15 | (v2 = 0) | ~ (all_91_0 = all_91_1) | v5 = 0))))) & !
% 61.89/9.15 | [v1: $i] : ! [v2: $i] : ( ~ (cons(all_91_0, v1) = v2) | ~ $i(v1) |
% 61.89/9.15 | ? [v3: any] : ? [v4: any] : ? [v5: any] : (frontsegP(v0, v2) =
% 61.89/9.15 | v4 & frontsegP(all_93_0, v1) = v5 & ssList(v1) = v3 & ( ~ (v3 =
% 61.89/9.15 | 0) | (( ~ (v5 = 0) | ~ (all_91_0 = all_91_1) | v4 = 0) & (
% 61.89/9.15 | ~ (v4 = 0) | (v5 = 0 & all_91_0 = all_91_1)))))) & ! [v1:
% 61.89/9.15 | $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3:
% 61.89/9.15 | any] : ? [v4: any] : (frontsegP(v0, v2) = v3 &
% 61.89/9.15 | frontsegP(all_93_0, v1) = v4 & cons(all_91_0, v1) = v2 & $i(v2)
% 61.89/9.15 | & ( ~ (v4 = 0) | ~ (all_91_0 = all_91_1) | v3 = 0) & ( ~ (v3 =
% 61.89/9.15 | 0) | (v4 = 0 & all_91_0 = all_91_1)))))
% 61.89/9.15 |
% 61.89/9.15 | GROUND_INST: instantiating (7) with all_91_0, all_91_1, all_93_0, simplifying
% 61.89/9.15 | with (13), (14), (15), (16), (19), (20) gives:
% 61.89/9.15 | (28) ? [v0: $i] : (cons(all_91_0, all_93_0) = v0 & $i(v0) & ! [v1: $i] :
% 61.89/9.15 | ! [v2: any] : ( ~ (frontsegP(all_93_0, v1) = v2) | ~ $i(v1) | ?
% 61.89/9.15 | [v3: any] : ? [v4: $i] : ? [v5: any] : (frontsegP(v0, v4) = v5 &
% 61.89/9.15 | ssList(v1) = v3 & cons(all_91_1, v1) = v4 & $i(v4) & ( ~ (v3 =
% 61.89/9.15 | 0) | (( ~ (v5 = 0) | (v2 = 0 & all_91_0 = all_91_1)) & ( ~
% 61.89/9.15 | (v2 = 0) | ~ (all_91_0 = all_91_1) | v5 = 0))))) & !
% 61.89/9.15 | [v1: $i] : ! [v2: $i] : ( ~ (cons(all_91_1, v1) = v2) | ~ $i(v1) |
% 61.89/9.15 | ? [v3: any] : ? [v4: any] : ? [v5: any] : (frontsegP(v0, v2) =
% 61.89/9.15 | v4 & frontsegP(all_93_0, v1) = v5 & ssList(v1) = v3 & ( ~ (v3 =
% 61.89/9.15 | 0) | (( ~ (v5 = 0) | ~ (all_91_0 = all_91_1) | v4 = 0) & (
% 61.89/9.15 | ~ (v4 = 0) | (v5 = 0 & all_91_0 = all_91_1)))))) & ! [v1:
% 61.89/9.15 | $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3:
% 61.89/9.15 | any] : ? [v4: any] : (frontsegP(v0, v2) = v3 &
% 61.89/9.15 | frontsegP(all_93_0, v1) = v4 & cons(all_91_1, v1) = v2 & $i(v2)
% 61.89/9.15 | & ( ~ (v4 = 0) | ~ (all_91_0 = all_91_1) | v3 = 0) & ( ~ (v3 =
% 61.89/9.15 | 0) | (v4 = 0 & all_91_0 = all_91_1)))))
% 61.89/9.15 |
% 61.89/9.15 | GROUND_INST: instantiating (7) with all_91_1, all_91_1, all_93_0, simplifying
% 61.89/9.15 | with (13), (15), (19), (20) gives:
% 61.89/9.16 | (29) ? [v0: $i] : (cons(all_91_1, all_93_0) = v0 & $i(v0) & ! [v1: $i] :
% 61.89/9.16 | ! [v2: any] : ( ~ (frontsegP(all_93_0, v1) = v2) | ~ $i(v1) | ?
% 61.89/9.16 | [v3: any] : ? [v4: $i] : ? [v5: any] : (frontsegP(v0, v4) = v5 &
% 61.89/9.16 | ssList(v1) = v3 & cons(all_91_1, v1) = v4 & $i(v4) & ( ~ (v3 =
% 61.89/9.16 | 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) &
% 61.89/9.16 | ! [v1: $i] : ! [v2: $i] : ( ~ (cons(all_91_1, v1) = v2) | ~ $i(v1)
% 61.89/9.16 | | ? [v3: any] : ? [v4: any] : ? [v5: any] : (frontsegP(v0, v2)
% 61.89/9.16 | = v4 & frontsegP(all_93_0, v1) = v5 & ssList(v1) = v3 & ( ~ (v3
% 61.89/9.16 | = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = 0)))))
% 61.89/9.16 | & ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ? [v2: $i] : ?
% 61.89/9.16 | [v3: any] : ? [v4: any] : (frontsegP(v0, v2) = v3 &
% 61.89/9.16 | frontsegP(all_93_0, v1) = v4 & cons(all_91_1, v1) = v2 & $i(v2)
% 61.89/9.16 | & ( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0))))
% 61.89/9.16 |
% 61.89/9.16 | GROUND_INST: instantiating (5) with all_93_0, simplifying with (19), (20)
% 61.89/9.16 | gives:
% 61.89/9.16 | (30) frontsegP(all_93_0, all_93_0) = 0
% 61.89/9.16 |
% 61.89/9.16 | GROUND_INST: instantiating (21) with all_93_0, simplifying with (19), (20)
% 61.89/9.16 | gives:
% 61.89/9.16 | (31) ? [v0: any] : ? [v1: any] : (frontsegP(all_93_0, all_93_0) = v1 &
% 61.89/9.16 | neq(all_93_0, nil) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 61.89/9.16 |
% 61.89/9.16 | DELTA: instantiating (31) with fresh symbols all_198_0, all_198_1 gives:
% 61.89/9.16 | (32) frontsegP(all_93_0, all_93_0) = all_198_0 & neq(all_93_0, nil) =
% 61.89/9.16 | all_198_1 & ( ~ (all_198_0 = 0) | ~ (all_198_1 = 0))
% 61.89/9.16 |
% 61.89/9.16 | ALPHA: (32) implies:
% 61.89/9.16 | (33) neq(all_93_0, nil) = all_198_1
% 61.89/9.16 | (34) frontsegP(all_93_0, all_93_0) = all_198_0
% 61.89/9.16 | (35) ~ (all_198_0 = 0) | ~ (all_198_1 = 0)
% 61.89/9.16 |
% 61.89/9.16 | DELTA: instantiating (25) with fresh symbol all_228_0 gives:
% 61.89/9.16 | (36) neq(all_93_0, nil) = all_228_0 & ( ~ (all_228_0 = 0) | ~ (all_93_0 =
% 61.89/9.16 | nil)) & (all_228_0 = 0 | all_93_0 = nil)
% 61.89/9.16 |
% 61.89/9.16 | ALPHA: (36) implies:
% 61.89/9.16 | (37) neq(all_93_0, nil) = all_228_0
% 61.89/9.16 | (38) all_228_0 = 0 | all_93_0 = nil
% 61.89/9.16 |
% 61.89/9.16 | DELTA: instantiating (24) with fresh symbol all_342_0 gives:
% 61.89/9.16 | (39) frontsegP(all_93_0, all_93_0) = all_342_0 & ! [v0: $i] : ! [v1: $i]
% 61.89/9.16 | : ( ~ (all_342_0 = 0) | ~ (app(all_93_0, v0) = v1) | ~ $i(v0) | ?
% 61.89/9.16 | [v2: any] : ? [v3: any] : (frontsegP(v1, all_93_0) = v3 &
% 61.89/9.16 | ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 61.89/9.16 | (all_342_0 = 0) | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 61.89/9.16 | (frontsegP(v1, all_93_0) = 0 & app(all_93_0, v0) = v1 & $i(v1)))
% 61.89/9.16 |
% 61.89/9.16 | ALPHA: (39) implies:
% 61.89/9.16 | (40) frontsegP(all_93_0, all_93_0) = all_342_0
% 61.89/9.16 |
% 61.89/9.16 | DELTA: instantiating (22) with fresh symbols all_379_0, all_379_1, all_379_2,
% 61.89/9.16 | all_379_3 gives:
% 61.89/9.16 | (41) frontsegP(all_93_0, all_93_0) = all_379_3 & $i(all_379_2) & ( ~
% 61.89/9.16 | (all_379_3 = 0) | (all_379_0 = all_93_0 & all_379_1 = 0 &
% 61.89/9.16 | ssList(all_379_2) = 0 & app(all_93_0, all_379_2) = all_93_0)) &
% 61.89/9.16 | (all_379_3 = 0 | ( ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ?
% 61.89/9.16 | [v1: any] : ( ~ (v1 = all_93_0) & app(all_93_0, v0) = v1 &
% 61.89/9.16 | $i(v1))) & ! [v0: $i] : ( ~ (app(all_93_0, v0) = all_93_0) |
% 61.89/9.16 | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1))))
% 61.89/9.16 |
% 61.89/9.16 | ALPHA: (41) implies:
% 61.89/9.16 | (42) frontsegP(all_93_0, all_93_0) = all_379_3
% 61.89/9.16 |
% 61.89/9.16 | DELTA: instantiating (23) with fresh symbol all_485_0 gives:
% 61.89/9.16 | (43) frontsegP(all_93_0, all_93_0) = all_485_0 & ! [v0: $i] : ! [v1: int]
% 61.89/9.16 | : ( ~ (all_485_0 = 0) | v1 = 0 | ~ (frontsegP(all_93_0, v0) = v1) |
% 61.89/9.16 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (frontsegP(all_93_0, v0) =
% 61.89/9.16 | v3 & ssList(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i]
% 61.89/9.16 | : ( ~ (all_485_0 = 0) | ~ (frontsegP(all_93_0, v0) = 0) | ~ $i(v0) |
% 61.89/9.16 | ? [v1: any] : ? [v2: any] : (frontsegP(all_93_0, v0) = v2 &
% 61.89/9.16 | ssList(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0: $i] : ( ~
% 61.89/9.16 | (all_485_0 = 0) | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: any] :
% 61.89/9.16 | ? [v2: any] : (frontsegP(all_93_0, v0) = v2 & frontsegP(all_93_0,
% 61.89/9.16 | v0) = v1 & ( ~ (v1 = 0) | v2 = 0)))
% 61.89/9.16 |
% 61.89/9.16 | ALPHA: (43) implies:
% 61.89/9.16 | (44) frontsegP(all_93_0, all_93_0) = all_485_0
% 61.89/9.16 |
% 61.89/9.16 | DELTA: instantiating (26) with fresh symbol all_556_0 gives:
% 61.89/9.17 | (45) cons(all_91_0, all_93_0) = all_556_0 & $i(all_556_0) & ! [v0: $i] :
% 61.89/9.17 | ! [v1: any] : ( ~ (frontsegP(all_93_0, v0) = v1) | ~ $i(v0) | ? [v2:
% 61.89/9.17 | any] : ? [v3: $i] : ? [v4: any] : (frontsegP(all_556_0, v3) = v4
% 61.89/9.17 | & ssList(v0) = v2 & cons(all_91_0, v0) = v3 & $i(v3) & ( ~ (v2 =
% 61.89/9.17 | 0) | (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) | v4 = 0))))) & !
% 61.89/9.17 | [v0: $i] : ! [v1: $i] : ( ~ (cons(all_91_0, v0) = v1) | ~ $i(v0) |
% 61.89/9.17 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (frontsegP(all_556_0,
% 61.89/9.17 | v1) = v3 & frontsegP(all_93_0, v0) = v4 & ssList(v0) = v2 & ( ~
% 61.89/9.17 | (v2 = 0) | (( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0)))))
% 61.89/9.17 | & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 61.89/9.17 | [v2: any] : ? [v3: any] : (frontsegP(all_556_0, v1) = v2 &
% 61.89/9.17 | frontsegP(all_93_0, v0) = v3 & cons(all_91_0, v0) = v1 & $i(v1) &
% 61.89/9.17 | ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 61.89/9.17 |
% 61.89/9.17 | ALPHA: (45) implies:
% 61.89/9.17 | (46) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 61.89/9.17 | any] : ? [v3: any] : (frontsegP(all_556_0, v1) = v2 &
% 61.89/9.17 | frontsegP(all_93_0, v0) = v3 & cons(all_91_0, v0) = v1 & $i(v1) &
% 61.89/9.17 | ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 61.89/9.17 |
% 61.89/9.17 | GROUND_INST: instantiating (46) with all_93_0, simplifying with (19), (20)
% 61.89/9.17 | gives:
% 61.89/9.17 | (47) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (frontsegP(all_556_0, v0)
% 61.89/9.17 | = v1 & frontsegP(all_93_0, all_93_0) = v2 & cons(all_91_0, all_93_0)
% 61.89/9.17 | = v0 & $i(v0) & ( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0))
% 61.89/9.17 |
% 61.89/9.17 | DELTA: instantiating (29) with fresh symbol all_559_0 gives:
% 61.89/9.17 | (48) cons(all_91_1, all_93_0) = all_559_0 & $i(all_559_0) & ! [v0: $i] :
% 61.89/9.17 | ! [v1: any] : ( ~ (frontsegP(all_93_0, v0) = v1) | ~ $i(v0) | ? [v2:
% 61.89/9.17 | any] : ? [v3: $i] : ? [v4: any] : (frontsegP(all_559_0, v3) = v4
% 61.89/9.17 | & ssList(v0) = v2 & cons(all_91_1, v0) = v3 & $i(v3) & ( ~ (v2 =
% 61.89/9.17 | 0) | (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) | v4 = 0))))) & !
% 61.89/9.17 | [v0: $i] : ! [v1: $i] : ( ~ (cons(all_91_1, v0) = v1) | ~ $i(v0) |
% 61.89/9.17 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (frontsegP(all_559_0,
% 61.89/9.17 | v1) = v3 & frontsegP(all_93_0, v0) = v4 & ssList(v0) = v2 & ( ~
% 61.89/9.17 | (v2 = 0) | (( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0)))))
% 61.89/9.17 | & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 61.89/9.17 | [v2: any] : ? [v3: any] : (frontsegP(all_559_0, v1) = v2 &
% 61.89/9.17 | frontsegP(all_93_0, v0) = v3 & cons(all_91_1, v0) = v1 & $i(v1) &
% 61.89/9.17 | ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 61.89/9.17 |
% 61.89/9.17 | ALPHA: (48) implies:
% 61.89/9.17 | (49) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 61.89/9.17 | any] : ? [v3: any] : (frontsegP(all_559_0, v1) = v2 &
% 61.89/9.17 | frontsegP(all_93_0, v0) = v3 & cons(all_91_1, v0) = v1 & $i(v1) &
% 61.89/9.17 | ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 61.89/9.17 |
% 61.89/9.17 | GROUND_INST: instantiating (49) with all_93_0, simplifying with (19), (20)
% 61.89/9.17 | gives:
% 61.89/9.17 | (50) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (frontsegP(all_559_0, v0)
% 61.89/9.17 | = v1 & frontsegP(all_93_0, all_93_0) = v2 & cons(all_91_1, all_93_0)
% 61.89/9.17 | = v0 & $i(v0) & ( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0))
% 61.89/9.17 |
% 61.89/9.17 | DELTA: instantiating (27) with fresh symbol all_580_0 gives:
% 61.89/9.17 | (51) cons(all_91_1, all_93_0) = all_580_0 & $i(all_580_0) & ! [v0: $i] :
% 61.89/9.17 | ! [v1: any] : ( ~ (frontsegP(all_93_0, v0) = v1) | ~ $i(v0) | ? [v2:
% 61.89/9.17 | any] : ? [v3: $i] : ? [v4: any] : (frontsegP(all_580_0, v3) = v4
% 61.89/9.17 | & ssList(v0) = v2 & cons(all_91_0, v0) = v3 & $i(v3) & ( ~ (v2 =
% 61.89/9.17 | 0) | (( ~ (v4 = 0) | (v1 = 0 & all_91_0 = all_91_1)) & ( ~ (v1
% 61.89/9.17 | = 0) | ~ (all_91_0 = all_91_1) | v4 = 0))))) & ! [v0:
% 61.89/9.17 | $i] : ! [v1: $i] : ( ~ (cons(all_91_0, v0) = v1) | ~ $i(v0) | ?
% 61.89/9.17 | [v2: any] : ? [v3: any] : ? [v4: any] : (frontsegP(all_580_0, v1)
% 61.89/9.17 | = v3 & frontsegP(all_93_0, v0) = v4 & ssList(v0) = v2 & ( ~ (v2 =
% 61.89/9.17 | 0) | (( ~ (v4 = 0) | ~ (all_91_0 = all_91_1) | v3 = 0) & ( ~
% 61.89/9.17 | (v3 = 0) | (v4 = 0 & all_91_0 = all_91_1)))))) & ! [v0: $i]
% 61.89/9.17 | : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ?
% 61.89/9.17 | [v3: any] : (frontsegP(all_580_0, v1) = v2 & frontsegP(all_93_0, v0)
% 61.89/9.17 | = v3 & cons(all_91_0, v0) = v1 & $i(v1) & ( ~ (v3 = 0) | ~
% 61.89/9.17 | (all_91_0 = all_91_1) | v2 = 0) & ( ~ (v2 = 0) | (v3 = 0 &
% 61.89/9.17 | all_91_0 = all_91_1))))
% 61.89/9.17 |
% 61.89/9.17 | ALPHA: (51) implies:
% 61.89/9.17 | (52) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 61.89/9.17 | any] : ? [v3: any] : (frontsegP(all_580_0, v1) = v2 &
% 61.89/9.17 | frontsegP(all_93_0, v0) = v3 & cons(all_91_0, v0) = v1 & $i(v1) &
% 61.89/9.17 | ( ~ (v3 = 0) | ~ (all_91_0 = all_91_1) | v2 = 0) & ( ~ (v2 = 0) |
% 61.89/9.17 | (v3 = 0 & all_91_0 = all_91_1))))
% 61.89/9.17 |
% 61.89/9.17 | GROUND_INST: instantiating (52) with all_93_0, simplifying with (19), (20)
% 61.89/9.17 | gives:
% 61.89/9.17 | (53) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (frontsegP(all_580_0, v0)
% 61.89/9.17 | = v1 & frontsegP(all_93_0, all_93_0) = v2 & cons(all_91_0, all_93_0)
% 61.89/9.17 | = v0 & $i(v0) & ( ~ (v2 = 0) | ~ (all_91_0 = all_91_1) | v1 = 0) &
% 61.89/9.17 | ( ~ (v1 = 0) | (v2 = 0 & all_91_0 = all_91_1)))
% 61.89/9.17 |
% 61.89/9.17 | DELTA: instantiating (28) with fresh symbol all_586_0 gives:
% 61.89/9.18 | (54) cons(all_91_0, all_93_0) = all_586_0 & $i(all_586_0) & ! [v0: $i] :
% 61.89/9.18 | ! [v1: any] : ( ~ (frontsegP(all_93_0, v0) = v1) | ~ $i(v0) | ? [v2:
% 61.89/9.18 | any] : ? [v3: $i] : ? [v4: any] : (frontsegP(all_586_0, v3) = v4
% 61.89/9.18 | & ssList(v0) = v2 & cons(all_91_1, v0) = v3 & $i(v3) & ( ~ (v2 =
% 61.89/9.18 | 0) | (( ~ (v4 = 0) | (v1 = 0 & all_91_0 = all_91_1)) & ( ~ (v1
% 61.89/9.18 | = 0) | ~ (all_91_0 = all_91_1) | v4 = 0))))) & ! [v0:
% 61.89/9.18 | $i] : ! [v1: $i] : ( ~ (cons(all_91_1, v0) = v1) | ~ $i(v0) | ?
% 61.89/9.18 | [v2: any] : ? [v3: any] : ? [v4: any] : (frontsegP(all_586_0, v1)
% 61.89/9.18 | = v3 & frontsegP(all_93_0, v0) = v4 & ssList(v0) = v2 & ( ~ (v2 =
% 61.89/9.18 | 0) | (( ~ (v4 = 0) | ~ (all_91_0 = all_91_1) | v3 = 0) & ( ~
% 61.89/9.18 | (v3 = 0) | (v4 = 0 & all_91_0 = all_91_1)))))) & ! [v0: $i]
% 61.89/9.18 | : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ?
% 61.89/9.18 | [v3: any] : (frontsegP(all_586_0, v1) = v2 & frontsegP(all_93_0, v0)
% 61.89/9.18 | = v3 & cons(all_91_1, v0) = v1 & $i(v1) & ( ~ (v3 = 0) | ~
% 61.89/9.18 | (all_91_0 = all_91_1) | v2 = 0) & ( ~ (v2 = 0) | (v3 = 0 &
% 61.89/9.18 | all_91_0 = all_91_1))))
% 61.89/9.18 |
% 61.89/9.18 | ALPHA: (54) implies:
% 61.89/9.18 | (55) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 61.89/9.18 | any] : ? [v3: any] : (frontsegP(all_586_0, v1) = v2 &
% 61.89/9.18 | frontsegP(all_93_0, v0) = v3 & cons(all_91_1, v0) = v1 & $i(v1) &
% 61.89/9.18 | ( ~ (v3 = 0) | ~ (all_91_0 = all_91_1) | v2 = 0) & ( ~ (v2 = 0) |
% 61.89/9.18 | (v3 = 0 & all_91_0 = all_91_1))))
% 61.89/9.18 |
% 61.89/9.18 | GROUND_INST: instantiating (55) with all_93_0, simplifying with (19), (20)
% 61.89/9.18 | gives:
% 61.89/9.18 | (56) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (frontsegP(all_586_0, v0)
% 61.89/9.18 | = v1 & frontsegP(all_93_0, all_93_0) = v2 & cons(all_91_1, all_93_0)
% 61.89/9.18 | = v0 & $i(v0) & ( ~ (v2 = 0) | ~ (all_91_0 = all_91_1) | v1 = 0) &
% 61.89/9.18 | ( ~ (v1 = 0) | (v2 = 0 & all_91_0 = all_91_1)))
% 61.89/9.18 |
% 61.89/9.18 | DELTA: instantiating (47) with fresh symbols all_697_0, all_697_1, all_697_2
% 61.89/9.18 | gives:
% 61.89/9.18 | (57) frontsegP(all_556_0, all_697_2) = all_697_1 & frontsegP(all_93_0,
% 61.89/9.18 | all_93_0) = all_697_0 & cons(all_91_0, all_93_0) = all_697_2 &
% 61.89/9.18 | $i(all_697_2) & ( ~ (all_697_0 = 0) | all_697_1 = 0) & ( ~ (all_697_1
% 61.89/9.18 | = 0) | all_697_0 = 0)
% 61.89/9.18 |
% 61.89/9.18 | ALPHA: (57) implies:
% 61.89/9.18 | (58) frontsegP(all_93_0, all_93_0) = all_697_0
% 61.89/9.18 |
% 61.89/9.18 | DELTA: instantiating (50) with fresh symbols all_701_0, all_701_1, all_701_2
% 61.89/9.18 | gives:
% 61.89/9.18 | (59) frontsegP(all_559_0, all_701_2) = all_701_1 & frontsegP(all_93_0,
% 61.89/9.18 | all_93_0) = all_701_0 & cons(all_91_1, all_93_0) = all_701_2 &
% 61.89/9.18 | $i(all_701_2) & ( ~ (all_701_0 = 0) | all_701_1 = 0) & ( ~ (all_701_1
% 61.89/9.18 | = 0) | all_701_0 = 0)
% 61.89/9.18 |
% 61.89/9.18 | ALPHA: (59) implies:
% 61.89/9.18 | (60) frontsegP(all_93_0, all_93_0) = all_701_0
% 61.89/9.18 |
% 61.89/9.18 | DELTA: instantiating (53) with fresh symbols all_725_0, all_725_1, all_725_2
% 61.89/9.18 | gives:
% 61.89/9.18 | (61) frontsegP(all_580_0, all_725_2) = all_725_1 & frontsegP(all_93_0,
% 61.89/9.18 | all_93_0) = all_725_0 & cons(all_91_0, all_93_0) = all_725_2 &
% 61.89/9.18 | $i(all_725_2) & ( ~ (all_725_0 = 0) | ~ (all_91_0 = all_91_1) |
% 61.89/9.18 | all_725_1 = 0) & ( ~ (all_725_1 = 0) | (all_725_0 = 0 & all_91_0 =
% 61.89/9.18 | all_91_1))
% 61.89/9.18 |
% 61.89/9.18 | ALPHA: (61) implies:
% 61.89/9.18 | (62) frontsegP(all_93_0, all_93_0) = all_725_0
% 61.89/9.18 |
% 61.89/9.18 | DELTA: instantiating (56) with fresh symbols all_733_0, all_733_1, all_733_2
% 61.89/9.18 | gives:
% 61.89/9.18 | (63) frontsegP(all_586_0, all_733_2) = all_733_1 & frontsegP(all_93_0,
% 61.89/9.18 | all_93_0) = all_733_0 & cons(all_91_1, all_93_0) = all_733_2 &
% 61.89/9.18 | $i(all_733_2) & ( ~ (all_733_0 = 0) | ~ (all_91_0 = all_91_1) |
% 61.89/9.18 | all_733_1 = 0) & ( ~ (all_733_1 = 0) | (all_733_0 = 0 & all_91_0 =
% 61.89/9.18 | all_91_1))
% 61.89/9.18 |
% 61.89/9.18 | ALPHA: (63) implies:
% 61.89/9.18 | (64) frontsegP(all_93_0, all_93_0) = all_733_0
% 61.89/9.18 |
% 61.89/9.18 | BETA: splitting (38) gives:
% 61.89/9.18 |
% 61.89/9.18 | Case 1:
% 61.89/9.18 | |
% 61.89/9.18 | | (65) all_93_0 = nil
% 61.89/9.18 | |
% 61.89/9.18 | | REDUCE: (18), (65) imply:
% 61.89/9.18 | | (66) $false
% 61.89/9.18 | |
% 61.89/9.18 | | CLOSE: (66) is inconsistent.
% 61.89/9.18 | |
% 61.89/9.18 | Case 2:
% 61.89/9.18 | |
% 61.89/9.18 | | (67) all_228_0 = 0
% 61.89/9.18 | |
% 61.89/9.18 | | REDUCE: (37), (67) imply:
% 61.89/9.18 | | (68) neq(all_93_0, nil) = 0
% 61.89/9.18 | |
% 61.89/9.18 | | GROUND_INST: instantiating (10) with 0, all_198_1, nil, all_93_0,
% 61.89/9.18 | | simplifying with (33), (68) gives:
% 61.89/9.18 | | (69) all_198_1 = 0
% 61.89/9.18 | |
% 61.89/9.18 | | GROUND_INST: instantiating (11) with all_198_0, all_485_0, all_93_0,
% 61.89/9.18 | | all_93_0, simplifying with (34), (44) gives:
% 61.89/9.18 | | (70) all_485_0 = all_198_0
% 61.89/9.18 | |
% 61.89/9.18 | | GROUND_INST: instantiating (11) with all_485_0, all_697_0, all_93_0,
% 61.89/9.18 | | all_93_0, simplifying with (44), (58) gives:
% 61.89/9.18 | | (71) all_697_0 = all_485_0
% 61.89/9.18 | |
% 61.89/9.18 | | GROUND_INST: instantiating (11) with all_379_3, all_697_0, all_93_0,
% 61.89/9.18 | | all_93_0, simplifying with (42), (58) gives:
% 61.89/9.18 | | (72) all_697_0 = all_379_3
% 61.89/9.18 | |
% 61.89/9.18 | | GROUND_INST: instantiating (11) with all_342_0, all_697_0, all_93_0,
% 61.89/9.18 | | all_93_0, simplifying with (40), (58) gives:
% 61.89/9.18 | | (73) all_697_0 = all_342_0
% 61.89/9.18 | |
% 61.89/9.18 | | GROUND_INST: instantiating (11) with all_342_0, all_701_0, all_93_0,
% 61.89/9.18 | | all_93_0, simplifying with (40), (60) gives:
% 61.89/9.18 | | (74) all_701_0 = all_342_0
% 61.89/9.18 | |
% 61.89/9.19 | | GROUND_INST: instantiating (11) with all_701_0, all_725_0, all_93_0,
% 61.89/9.19 | | all_93_0, simplifying with (60), (62) gives:
% 61.89/9.19 | | (75) all_725_0 = all_701_0
% 61.89/9.19 | |
% 61.89/9.19 | | GROUND_INST: instantiating (11) with all_725_0, all_733_0, all_93_0,
% 61.89/9.19 | | all_93_0, simplifying with (62), (64) gives:
% 61.89/9.19 | | (76) all_733_0 = all_725_0
% 61.89/9.19 | |
% 61.89/9.19 | | GROUND_INST: instantiating (11) with 0, all_733_0, all_93_0, all_93_0,
% 61.89/9.19 | | simplifying with (30), (64) gives:
% 61.89/9.19 | | (77) all_733_0 = 0
% 61.89/9.19 | |
% 61.89/9.19 | | COMBINE_EQS: (76), (77) imply:
% 61.89/9.19 | | (78) all_725_0 = 0
% 61.89/9.19 | |
% 61.89/9.19 | | SIMP: (78) implies:
% 61.89/9.19 | | (79) all_725_0 = 0
% 61.89/9.19 | |
% 61.89/9.19 | | COMBINE_EQS: (75), (79) imply:
% 61.89/9.19 | | (80) all_701_0 = 0
% 61.89/9.19 | |
% 61.89/9.19 | | SIMP: (80) implies:
% 61.89/9.19 | | (81) all_701_0 = 0
% 61.89/9.19 | |
% 61.89/9.19 | | COMBINE_EQS: (74), (81) imply:
% 61.89/9.19 | | (82) all_342_0 = 0
% 61.89/9.19 | |
% 61.89/9.19 | | SIMP: (82) implies:
% 61.89/9.19 | | (83) all_342_0 = 0
% 61.89/9.19 | |
% 61.89/9.19 | | COMBINE_EQS: (72), (73) imply:
% 61.89/9.19 | | (84) all_379_3 = all_342_0
% 61.89/9.19 | |
% 61.89/9.19 | | COMBINE_EQS: (71), (72) imply:
% 61.89/9.19 | | (85) all_485_0 = all_379_3
% 61.89/9.19 | |
% 61.89/9.19 | | SIMP: (85) implies:
% 61.89/9.19 | | (86) all_485_0 = all_379_3
% 61.89/9.19 | |
% 61.89/9.19 | | COMBINE_EQS: (70), (86) imply:
% 61.89/9.19 | | (87) all_379_3 = all_198_0
% 61.89/9.19 | |
% 61.89/9.19 | | SIMP: (87) implies:
% 61.89/9.19 | | (88) all_379_3 = all_198_0
% 61.89/9.19 | |
% 61.89/9.19 | | COMBINE_EQS: (84), (88) imply:
% 61.89/9.19 | | (89) all_342_0 = all_198_0
% 61.89/9.19 | |
% 61.89/9.19 | | SIMP: (89) implies:
% 61.89/9.19 | | (90) all_342_0 = all_198_0
% 61.89/9.19 | |
% 61.89/9.19 | | COMBINE_EQS: (83), (90) imply:
% 61.89/9.19 | | (91) all_198_0 = 0
% 61.89/9.19 | |
% 61.89/9.19 | | BETA: splitting (35) gives:
% 61.89/9.19 | |
% 61.89/9.19 | | Case 1:
% 61.89/9.19 | | |
% 61.89/9.19 | | | (92) ~ (all_198_0 = 0)
% 61.89/9.19 | | |
% 61.89/9.19 | | | REDUCE: (91), (92) imply:
% 61.89/9.19 | | | (93) $false
% 61.89/9.19 | | |
% 61.89/9.19 | | | CLOSE: (93) is inconsistent.
% 61.89/9.19 | | |
% 61.89/9.19 | | Case 2:
% 61.89/9.19 | | |
% 61.89/9.19 | | | (94) ~ (all_198_1 = 0)
% 61.89/9.19 | | |
% 61.89/9.19 | | | REDUCE: (69), (94) imply:
% 61.89/9.19 | | | (95) $false
% 61.89/9.19 | | |
% 61.89/9.19 | | | CLOSE: (95) is inconsistent.
% 61.89/9.19 | | |
% 61.89/9.19 | | End of split
% 61.89/9.19 | |
% 61.89/9.19 | End of split
% 61.89/9.19 |
% 61.89/9.19 End of proof
% 61.89/9.19 % SZS output end Proof for theBenchmark
% 61.89/9.19
% 61.89/9.19 8587ms
%------------------------------------------------------------------------------