TSTP Solution File: SWC387+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC387+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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:51:10 EDT 2023
% Result : Theorem 33.68s 5.33s
% Output : Proof 87.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SWC387+1 : TPTP v8.1.2. Released v2.4.0.
% 0.02/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.31 % Computer : n003.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Aug 28 17:01:10 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.59 ________ _____
% 0.16/0.59 ___ __ \_________(_)________________________________
% 0.16/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.59
% 0.16/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.59 (2023-06-19)
% 0.16/0.59
% 0.16/0.59 (c) Philipp Rümmer, 2009-2023
% 0.16/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.59 Amanda Stjerna.
% 0.16/0.59 Free software under BSD-3-Clause.
% 0.16/0.59
% 0.16/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.59
% 0.16/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.61 Running up to 7 provers in parallel.
% 0.16/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.04/1.59 Prover 4: Preprocessing ...
% 6.49/1.67 Prover 6: Preprocessing ...
% 6.49/1.67 Prover 0: Preprocessing ...
% 6.49/1.67 Prover 5: Preprocessing ...
% 6.49/1.67 Prover 3: Preprocessing ...
% 6.49/1.67 Prover 2: Preprocessing ...
% 6.49/1.68 Prover 1: Preprocessing ...
% 19.86/3.44 Prover 1: Constructing countermodel ...
% 20.20/3.48 Prover 2: Proving ...
% 20.20/3.49 Prover 5: Constructing countermodel ...
% 20.20/3.52 Prover 6: Proving ...
% 21.32/3.64 Prover 3: Constructing countermodel ...
% 31.02/4.93 Prover 4: Constructing countermodel ...
% 31.27/5.08 Prover 0: Proving ...
% 33.68/5.32 Prover 3: proved (4690ms)
% 33.68/5.33
% 33.68/5.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.68/5.33
% 34.19/5.33 Prover 2: stopped
% 34.19/5.33 Prover 6: stopped
% 34.19/5.34 Prover 5: stopped
% 34.19/5.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 34.19/5.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 34.19/5.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 34.19/5.35 Prover 0: stopped
% 34.19/5.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 34.19/5.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 36.51/5.66 Prover 10: Preprocessing ...
% 36.51/5.70 Prover 7: Preprocessing ...
% 36.51/5.72 Prover 11: Preprocessing ...
% 36.51/5.75 Prover 13: Preprocessing ...
% 37.42/5.76 Prover 8: Preprocessing ...
% 38.98/6.00 Prover 10: Constructing countermodel ...
% 38.98/6.02 Prover 7: Constructing countermodel ...
% 41.31/6.31 Prover 13: Constructing countermodel ...
% 41.31/6.35 Prover 8: Warning: ignoring some quantifiers
% 41.31/6.40 Prover 8: Constructing countermodel ...
% 51.63/7.74 Prover 11: Constructing countermodel ...
% 72.39/10.33 Prover 13: stopped
% 72.39/10.33 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 74.44/10.51 Prover 16: Preprocessing ...
% 75.55/10.69 Prover 16: Constructing countermodel ...
% 86.83/12.10 Prover 1: Found proof (size 160)
% 86.83/12.10 Prover 1: proved (11484ms)
% 86.83/12.10 Prover 7: stopped
% 86.83/12.10 Prover 8: stopped
% 86.83/12.10 Prover 4: stopped
% 86.83/12.10 Prover 10: stopped
% 86.83/12.10 Prover 16: stopped
% 86.83/12.11 Prover 11: stopped
% 86.83/12.11
% 86.83/12.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 86.83/12.11
% 86.83/12.12 % SZS output start Proof for theBenchmark
% 86.83/12.13 Assumptions after simplification:
% 86.83/12.13 ---------------------------------
% 86.83/12.13
% 86.83/12.13 (ax15)
% 87.23/12.15 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 87.23/12.15 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 87.23/12.15 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 87.23/12.15
% 87.23/12.15 (ax17)
% 87.23/12.15 ssList(nil) = 0 & $i(nil)
% 87.23/12.15
% 87.23/12.15 (ax18)
% 87.23/12.15 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (cons(v1,
% 87.23/12.15 v0) = v0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v1) =
% 87.23/12.15 v2)))
% 87.23/12.15
% 87.23/12.15 (ax2)
% 87.23/12.16 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) &
% 87.23/12.16 ssItem(v1) = 0 & $i(v1)))
% 87.23/12.16
% 87.23/12.16 (ax20)
% 87.23/12.16 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1:
% 87.23/12.16 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 87.23/12.16 ssItem(v2) = 0 & $i(v2))))
% 87.23/12.16
% 87.23/12.16 (ax23)
% 87.23/12.16 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 87.23/12.16 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) =
% 87.23/12.16 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1))))
% 87.23/12.16
% 87.23/12.16 (ax25)
% 87.23/12.16 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 87.23/12.16 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) =
% 87.23/12.16 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0))))
% 87.23/12.16
% 87.23/12.16 (ax44)
% 87.23/12.16 ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1)
% 87.23/12.16 = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, v2) = v3) |
% 87.23/12.16 ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i]
% 87.23/12.16 : ! [v5: $i] : ! [v6: any] : ( ~ (frontsegP(v3, v5) = v6) | ~
% 87.23/12.16 (cons(v1, v4) = v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] :
% 87.23/12.16 (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 =
% 87.23/12.16 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 =
% 87.23/12.16 v0)))))))))
% 87.23/12.16
% 87.23/12.16 (ax59)
% 87.34/12.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 87.34/12.16 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 87.34/12.16 (v2 = 0) | v3 = 0)))
% 87.34/12.16
% 87.34/12.16 (ax61)
% 87.34/12.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 87.34/12.16 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 87.34/12.16 (v2 = 0) | v3 = 0)))
% 87.34/12.16
% 87.34/12.16 (ax63)
% 87.34/12.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 87.34/12.16 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 87.34/12.16 (v2 = 0) | v3 = 0)))
% 87.34/12.16
% 87.34/12.16 (ax65)
% 87.34/12.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 87.34/12.16 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 87.34/12.16 (v2 = 0) | v3 = 0)))
% 87.34/12.16
% 87.34/12.16 (ax68)
% 87.34/12.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 87.34/12.16 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & (
% 87.34/12.16 ~ (v2 = 0) | v3 = 0)))
% 87.34/12.16
% 87.34/12.16 (ax71)
% 87.34/12.17 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 87.34/12.17 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 87.34/12.17 ~ (v2 = 0) | v3 = 0)))
% 87.34/12.17
% 87.34/12.17 (ax73)
% 87.34/12.17 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 87.34/12.17 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 87.34/12.17 (v2 = 0) | v3 = 0)))
% 87.34/12.17
% 87.34/12.17 (co1)
% 87.34/12.17 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) =
% 87.34/12.17 0 & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: any] : (v2 =
% 87.34/12.17 v0 & neq(v1, nil) = v3 & ! [v4: $i] : ( ~ (cons(v4, nil) = v0) | ~
% 87.34/12.17 $i(v4) | ? [v5: any] : ? [v6: any] : (memberP(v1, v4) = v6 &
% 87.34/12.17 ssItem(v4) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ( ~ (v3 = 0) |
% 87.34/12.17 ? [v4: $i] : (memberP(v1, v4) = 0 & cons(v4, nil) = v0 & ssItem(v4)
% 87.34/12.17 = 0 & $i(v4))) & ( ~ (v1 = nil) | ~ (v0 = nil)) & ( ~ (v1 = nil)
% 87.34/12.17 | v0 = nil)))))
% 87.34/12.17
% 87.34/12.17 (function-axioms)
% 87.34/12.17 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 87.34/12.17 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 87.34/12.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 87.34/12.17 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 87.34/12.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 87.34/12.17 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 87.34/12.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 87.34/12.17 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 87.34/12.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 87.34/12.17 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 87.34/12.17 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 87.34/12.17 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 87.34/12.17 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 87.34/12.17 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 87.34/12.17 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 87.34/12.17 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 87.34/12.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 87.34/12.17 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 87.34/12.17 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 87.34/12.17 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 87.34/12.17 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 87.34/12.17 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 87.34/12.17 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 87.34/12.17 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 87.34/12.17 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 87.34/12.17 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.34/12.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 87.34/12.17 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.34/12.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 87.34/12.17 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.34/12.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 87.34/12.17 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.34/12.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 87.34/12.17 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.34/12.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 87.34/12.17 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.34/12.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 87.34/12.17 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.34/12.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 87.34/12.17 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.34/12.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 87.34/12.17 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 87.34/12.17 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 87.34/12.17
% 87.34/12.17 Further assumptions not needed in the proof:
% 87.34/12.17 --------------------------------------------
% 87.34/12.17 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax19, ax21, ax22, ax24, ax26, ax27,
% 87.34/12.17 ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39,
% 87.34/12.17 ax4, ax40, ax41, ax42, ax43, ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51,
% 87.34/12.17 ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax60, ax62, ax64, ax66, ax67,
% 87.34/12.17 ax69, ax7, ax70, ax72, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 87.34/12.17 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 87.34/12.17 ax94, ax95
% 87.34/12.17
% 87.34/12.17 Those formulas are unsatisfiable:
% 87.34/12.17 ---------------------------------
% 87.34/12.17
% 87.34/12.17 Begin of proof
% 87.34/12.17 |
% 87.34/12.18 | ALPHA: (ax17) implies:
% 87.34/12.18 | (1) ssList(nil) = 0
% 87.34/12.18 |
% 87.34/12.18 | ALPHA: (ax20) implies:
% 87.34/12.18 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 87.34/12.18 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 87.34/12.18 | ssItem(v2) = 0 & $i(v2))))
% 87.34/12.18 |
% 87.34/12.18 | ALPHA: (ax59) implies:
% 87.34/12.18 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 87.34/12.18 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 87.34/12.18 | ~ (v2 = 0) | v3 = 0)))
% 87.34/12.18 |
% 87.34/12.18 | ALPHA: (ax61) implies:
% 87.34/12.18 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 87.34/12.18 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 &
% 87.34/12.18 | ( ~ (v2 = 0) | v3 = 0)))
% 87.34/12.18 |
% 87.34/12.18 | ALPHA: (ax63) implies:
% 87.34/12.18 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 87.34/12.18 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 &
% 87.34/12.18 | ( ~ (v2 = 0) | v3 = 0)))
% 87.34/12.18 |
% 87.34/12.18 | ALPHA: (ax65) implies:
% 87.34/12.18 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 87.34/12.18 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2
% 87.34/12.18 | & ( ~ (v2 = 0) | v3 = 0)))
% 87.34/12.18 |
% 87.34/12.18 | ALPHA: (ax68) implies:
% 87.34/12.18 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 87.34/12.18 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2
% 87.34/12.18 | & ( ~ (v2 = 0) | v3 = 0)))
% 87.34/12.18 |
% 87.34/12.18 | ALPHA: (ax71) implies:
% 87.34/12.18 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 87.34/12.18 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2
% 87.34/12.18 | & ( ~ (v2 = 0) | v3 = 0)))
% 87.34/12.18 |
% 87.34/12.18 | ALPHA: (ax73) implies:
% 87.34/12.18 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 87.34/12.18 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 &
% 87.34/12.18 | ( ~ (v2 = 0) | v3 = 0)))
% 87.34/12.18 |
% 87.34/12.18 | ALPHA: (co1) implies:
% 87.34/12.18 | (10) $i(nil)
% 87.34/12.18 | (11) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0
% 87.34/12.18 | & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: any] :
% 87.34/12.18 | (v2 = v0 & neq(v1, nil) = v3 & ! [v4: $i] : ( ~ (cons(v4, nil)
% 87.34/12.18 | = v0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] :
% 87.34/12.18 | (memberP(v1, v4) = v6 & ssItem(v4) = v5 & ( ~ (v6 = 0) | ~
% 87.34/12.18 | (v5 = 0)))) & ( ~ (v3 = 0) | ? [v4: $i] : (memberP(v1,
% 87.34/12.18 | v4) = 0 & cons(v4, nil) = v0 & ssItem(v4) = 0 & $i(v4)))
% 87.34/12.18 | & ( ~ (v1 = nil) | ~ (v0 = nil)) & ( ~ (v1 = nil) | v0 =
% 87.34/12.18 | nil)))))
% 87.34/12.18 |
% 87.34/12.18 | ALPHA: (function-axioms) implies:
% 87.34/12.18 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.34/12.18 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 87.34/12.18 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.34/12.18 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 87.34/12.18 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.34/12.18 | : ! [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3,
% 87.34/12.18 | v2) = v0))
% 87.34/12.18 |
% 87.34/12.18 | DELTA: instantiating (ax2) with fresh symbol all_91_0 gives:
% 87.34/12.19 | (15) ssItem(all_91_0) = 0 & $i(all_91_0) & ? [v0: any] : ( ~ (v0 =
% 87.34/12.19 | all_91_0) & ssItem(v0) = 0 & $i(v0))
% 87.34/12.19 |
% 87.34/12.19 | ALPHA: (15) implies:
% 87.34/12.19 | (16) $i(all_91_0)
% 87.34/12.19 | (17) ssItem(all_91_0) = 0
% 87.34/12.19 |
% 87.34/12.19 | DELTA: instantiating (11) with fresh symbol all_93_0 gives:
% 87.34/12.19 | (18) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 &
% 87.34/12.19 | $i(v0) & ? [v1: $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: any] : (v1
% 87.34/12.19 | = all_93_0 & neq(v0, nil) = v2 & ! [v3: $i] : ( ~ (cons(v3,
% 87.34/12.19 | nil) = all_93_0) | ~ $i(v3) | ? [v4: any] : ? [v5: any]
% 87.34/12.19 | : (memberP(v0, v3) = v5 & ssItem(v3) = v4 & ( ~ (v5 = 0) | ~
% 87.34/12.19 | (v4 = 0)))) & ( ~ (v2 = 0) | ? [v3: $i] : (memberP(v0,
% 87.34/12.19 | v3) = 0 & cons(v3, nil) = all_93_0 & ssItem(v3) = 0 &
% 87.34/12.19 | $i(v3))) & ( ~ (v0 = nil) | ~ (all_93_0 = nil)) & ( ~ (v0 =
% 87.34/12.19 | nil) | all_93_0 = nil))))
% 87.34/12.19 |
% 87.34/12.19 | ALPHA: (18) implies:
% 87.34/12.19 | (19) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0
% 87.34/12.19 | & $i(v1) & ? [v2: any] : (v1 = all_93_0 & neq(v0, nil) = v2 & !
% 87.34/12.19 | [v3: $i] : ( ~ (cons(v3, nil) = all_93_0) | ~ $i(v3) | ? [v4:
% 87.34/12.19 | any] : ? [v5: any] : (memberP(v0, v3) = v5 & ssItem(v3) =
% 87.34/12.19 | v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ( ~ (v2 = 0) | ? [v3:
% 87.34/12.19 | $i] : (memberP(v0, v3) = 0 & cons(v3, nil) = all_93_0 &
% 87.34/12.19 | ssItem(v3) = 0 & $i(v3))) & ( ~ (v0 = nil) | ~ (all_93_0 =
% 87.34/12.19 | nil)) & ( ~ (v0 = nil) | all_93_0 = nil))))
% 87.34/12.19 |
% 87.34/12.19 | DELTA: instantiating (19) with fresh symbol all_97_0 gives:
% 87.34/12.19 | (20) ssList(all_97_0) = 0 & $i(all_97_0) & ? [v0: $i] : (ssList(v0) = 0 &
% 87.34/12.19 | $i(v0) & ? [v1: any] : (v0 = all_93_0 & neq(all_97_0, nil) = v1 &
% 87.34/12.19 | ! [v2: $i] : ( ~ (cons(v2, nil) = all_93_0) | ~ $i(v2) | ? [v3:
% 87.34/12.19 | any] : ? [v4: any] : (memberP(all_97_0, v2) = v4 & ssItem(v2)
% 87.34/12.19 | = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ( ~ (v1 = 0) | ? [v2:
% 87.34/12.19 | $i] : (memberP(all_97_0, v2) = 0 & cons(v2, nil) = all_93_0 &
% 87.34/12.19 | ssItem(v2) = 0 & $i(v2))) & ( ~ (all_97_0 = nil) | ~
% 87.34/12.19 | (all_93_0 = nil)) & ( ~ (all_97_0 = nil) | all_93_0 = nil)))
% 87.34/12.19 |
% 87.34/12.19 | ALPHA: (20) implies:
% 87.34/12.19 | (21) $i(all_97_0)
% 87.34/12.19 | (22) ssList(all_97_0) = 0
% 87.34/12.19 | (23) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: any] : (v0 = all_93_0
% 87.34/12.19 | & neq(all_97_0, nil) = v1 & ! [v2: $i] : ( ~ (cons(v2, nil) =
% 87.34/12.19 | all_93_0) | ~ $i(v2) | ? [v3: any] : ? [v4: any] :
% 87.34/12.19 | (memberP(all_97_0, v2) = v4 & ssItem(v2) = v3 & ( ~ (v4 = 0) |
% 87.34/12.19 | ~ (v3 = 0)))) & ( ~ (v1 = 0) | ? [v2: $i] :
% 87.34/12.19 | (memberP(all_97_0, v2) = 0 & cons(v2, nil) = all_93_0 &
% 87.34/12.19 | ssItem(v2) = 0 & $i(v2))) & ( ~ (all_97_0 = nil) | ~
% 87.34/12.19 | (all_93_0 = nil)) & ( ~ (all_97_0 = nil) | all_93_0 = nil)))
% 87.34/12.19 |
% 87.34/12.19 | DELTA: instantiating (23) with fresh symbol all_99_0 gives:
% 87.34/12.19 | (24) ssList(all_99_0) = 0 & $i(all_99_0) & ? [v0: any] : (all_99_0 =
% 87.34/12.19 | all_93_0 & neq(all_97_0, nil) = v0 & ! [v1: $i] : ( ~ (cons(v1,
% 87.34/12.19 | nil) = all_93_0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] :
% 87.34/12.19 | (memberP(all_97_0, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~
% 87.34/12.19 | (v2 = 0)))) & ( ~ (v0 = 0) | ? [v1: $i] : (memberP(all_97_0,
% 87.34/12.19 | v1) = 0 & cons(v1, nil) = all_93_0 & ssItem(v1) = 0 & $i(v1)))
% 87.34/12.19 | & ( ~ (all_97_0 = nil) | ~ (all_93_0 = nil)) & ( ~ (all_97_0 = nil)
% 87.34/12.19 | | all_93_0 = nil))
% 87.34/12.19 |
% 87.34/12.19 | ALPHA: (24) implies:
% 87.34/12.19 | (25) $i(all_99_0)
% 87.34/12.19 | (26) ssList(all_99_0) = 0
% 87.34/12.20 | (27) ? [v0: any] : (all_99_0 = all_93_0 & neq(all_97_0, nil) = v0 & !
% 87.34/12.20 | [v1: $i] : ( ~ (cons(v1, nil) = all_93_0) | ~ $i(v1) | ? [v2: any]
% 87.34/12.20 | : ? [v3: any] : (memberP(all_97_0, v1) = v3 & ssItem(v1) = v2 & (
% 87.34/12.20 | ~ (v3 = 0) | ~ (v2 = 0)))) & ( ~ (v0 = 0) | ? [v1: $i] :
% 87.34/12.20 | (memberP(all_97_0, v1) = 0 & cons(v1, nil) = all_93_0 & ssItem(v1)
% 87.34/12.20 | = 0 & $i(v1))) & ( ~ (all_97_0 = nil) | ~ (all_93_0 = nil)) & (
% 87.34/12.20 | ~ (all_97_0 = nil) | all_93_0 = nil))
% 87.34/12.20 |
% 87.34/12.20 | DELTA: instantiating (27) with fresh symbol all_101_0 gives:
% 87.34/12.20 | (28) all_99_0 = all_93_0 & neq(all_97_0, nil) = all_101_0 & ! [v0: $i] : (
% 87.34/12.20 | ~ (cons(v0, nil) = all_93_0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 87.34/12.20 | any] : (memberP(all_97_0, v0) = v2 & ssItem(v0) = v1 & ( ~ (v2 =
% 87.34/12.20 | 0) | ~ (v1 = 0)))) & ( ~ (all_101_0 = 0) | ? [v0: $i] :
% 87.34/12.20 | (memberP(all_97_0, v0) = 0 & cons(v0, nil) = all_93_0 & ssItem(v0) =
% 87.34/12.20 | 0 & $i(v0))) & ( ~ (all_97_0 = nil) | ~ (all_93_0 = nil)) & ( ~
% 87.34/12.20 | (all_97_0 = nil) | all_93_0 = nil)
% 87.34/12.20 |
% 87.34/12.20 | ALPHA: (28) implies:
% 87.34/12.20 | (29) all_99_0 = all_93_0
% 87.34/12.20 | (30) neq(all_97_0, nil) = all_101_0
% 87.34/12.20 | (31) ~ (all_97_0 = nil) | all_93_0 = nil
% 87.34/12.20 | (32) ~ (all_97_0 = nil) | ~ (all_93_0 = nil)
% 87.34/12.20 | (33) ~ (all_101_0 = 0) | ? [v0: $i] : (memberP(all_97_0, v0) = 0 &
% 87.34/12.20 | cons(v0, nil) = all_93_0 & ssItem(v0) = 0 & $i(v0))
% 87.34/12.20 | (34) ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_0) | ~ $i(v0) | ? [v1:
% 87.34/12.20 | any] : ? [v2: any] : (memberP(all_97_0, v0) = v2 & ssItem(v0) =
% 87.34/12.20 | v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 87.34/12.20 |
% 87.34/12.20 | REDUCE: (26), (29) imply:
% 87.34/12.20 | (35) ssList(all_93_0) = 0
% 87.34/12.20 |
% 87.34/12.20 | REDUCE: (25), (29) imply:
% 87.34/12.20 | (36) $i(all_93_0)
% 87.34/12.20 |
% 87.34/12.20 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (10) gives:
% 87.34/12.20 | (37) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 87.34/12.20 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 87.34/12.20 | ( ~ (v2 = 0) | v3 = nil)))
% 87.34/12.20 |
% 87.34/12.20 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (10) gives:
% 87.34/12.20 | (38) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 87.34/12.20 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 87.34/12.20 | ( ~ (v2 = 0) | v3 = v0)))
% 87.34/12.20 |
% 87.34/12.20 | GROUND_INST: instantiating (ax18) with nil, simplifying with (1), (10) gives:
% 87.34/12.20 | (39) ! [v0: $i] : ( ~ (cons(v0, nil) = nil) | ~ $i(v0) | ? [v1: int] : (
% 87.34/12.20 | ~ (v1 = 0) & ssItem(v0) = v1))
% 87.34/12.20 |
% 87.34/12.20 | GROUND_INST: instantiating (2) with all_93_0, simplifying with (35), (36)
% 87.34/12.20 | gives:
% 87.34/12.20 | (40) all_93_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i]
% 87.34/12.20 | : (cons(v1, v0) = all_93_0 & ssItem(v1) = 0 & $i(v1)))
% 87.34/12.20 |
% 87.34/12.20 | GROUND_INST: instantiating (ax15) with all_97_0, simplifying with (21), (22)
% 87.34/12.20 | gives:
% 87.34/12.20 | (41) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_0, v0) = v1) | ~ $i(v0)
% 87.34/12.20 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 87.34/12.20 | ~ (v0 = all_97_0)) & (v1 = 0 | v0 = all_97_0)))
% 87.34/12.20 |
% 87.34/12.20 | GROUND_INST: instantiating (41) with nil, all_101_0, simplifying with (10),
% 87.34/12.20 | (30) gives:
% 87.34/12.20 | (42) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_101_0 = 0)
% 87.34/12.20 | | ~ (all_97_0 = nil)) & (all_101_0 = 0 | all_97_0 = nil))
% 87.34/12.20 |
% 87.34/12.20 | BETA: splitting (31) gives:
% 87.34/12.20 |
% 87.34/12.21 | Case 1:
% 87.34/12.21 | |
% 87.34/12.21 | | (43) ~ (all_97_0 = nil)
% 87.34/12.21 | |
% 87.34/12.21 | | BETA: splitting (42) gives:
% 87.34/12.21 | |
% 87.34/12.21 | | Case 1:
% 87.34/12.21 | | |
% 87.34/12.21 | | | (44) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 87.34/12.21 | | |
% 87.34/12.21 | | | DELTA: instantiating (44) with fresh symbol all_279_0 gives:
% 87.34/12.21 | | | (45) ~ (all_279_0 = 0) & ssList(nil) = all_279_0
% 87.34/12.21 | | |
% 87.34/12.21 | | | ALPHA: (45) implies:
% 87.34/12.21 | | | (46) ~ (all_279_0 = 0)
% 87.34/12.21 | | | (47) ssList(nil) = all_279_0
% 87.34/12.21 | | |
% 87.34/12.21 | | | DELTA: instantiating (44) with fresh symbol all_281_0 gives:
% 87.34/12.21 | | | (48) ~ (all_281_0 = 0) & ssList(nil) = all_281_0
% 87.34/12.21 | | |
% 87.34/12.21 | | | ALPHA: (48) implies:
% 87.34/12.21 | | | (49) ssList(nil) = all_281_0
% 87.34/12.21 | | |
% 87.34/12.21 | | | GROUND_INST: instantiating (13) with 0, all_281_0, nil, simplifying with
% 87.34/12.21 | | | (1), (49) gives:
% 87.34/12.21 | | | (50) all_281_0 = 0
% 87.34/12.21 | | |
% 87.34/12.21 | | | GROUND_INST: instantiating (13) with all_279_0, all_281_0, nil,
% 87.34/12.21 | | | simplifying with (47), (49) gives:
% 87.34/12.21 | | | (51) all_281_0 = all_279_0
% 87.34/12.21 | | |
% 87.34/12.21 | | | COMBINE_EQS: (50), (51) imply:
% 87.34/12.21 | | | (52) all_279_0 = 0
% 87.34/12.21 | | |
% 87.34/12.21 | | | REDUCE: (46), (52) imply:
% 87.34/12.21 | | | (53) $false
% 87.34/12.21 | | |
% 87.34/12.21 | | | CLOSE: (53) is inconsistent.
% 87.34/12.21 | | |
% 87.34/12.21 | | Case 2:
% 87.34/12.21 | | |
% 87.34/12.21 | | | (54) ( ~ (all_101_0 = 0) | ~ (all_97_0 = nil)) & (all_101_0 = 0 |
% 87.34/12.21 | | | all_97_0 = nil)
% 87.34/12.21 | | |
% 87.34/12.21 | | | ALPHA: (54) implies:
% 87.34/12.21 | | | (55) all_101_0 = 0 | all_97_0 = nil
% 87.34/12.21 | | |
% 87.34/12.21 | | | BETA: splitting (55) gives:
% 87.34/12.21 | | |
% 87.34/12.21 | | | Case 1:
% 87.34/12.21 | | | |
% 87.34/12.21 | | | | (56) all_97_0 = nil
% 87.34/12.21 | | | |
% 87.34/12.21 | | | | REDUCE: (43), (56) imply:
% 87.34/12.21 | | | | (57) $false
% 87.34/12.21 | | | |
% 87.34/12.21 | | | | CLOSE: (57) is inconsistent.
% 87.34/12.21 | | | |
% 87.34/12.21 | | | Case 2:
% 87.34/12.21 | | | |
% 87.34/12.21 | | | | (58) all_101_0 = 0
% 87.34/12.21 | | | |
% 87.34/12.21 | | | | BETA: splitting (33) gives:
% 87.34/12.21 | | | |
% 87.34/12.21 | | | | Case 1:
% 87.34/12.21 | | | | |
% 87.34/12.21 | | | | | (59) ~ (all_101_0 = 0)
% 87.34/12.21 | | | | |
% 87.34/12.21 | | | | | REDUCE: (58), (59) imply:
% 87.34/12.21 | | | | | (60) $false
% 87.34/12.21 | | | | |
% 87.34/12.21 | | | | | CLOSE: (60) is inconsistent.
% 87.34/12.21 | | | | |
% 87.34/12.21 | | | | Case 2:
% 87.34/12.21 | | | | |
% 87.34/12.21 | | | | | (61) ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0, nil) =
% 87.34/12.21 | | | | | all_93_0 & ssItem(v0) = 0 & $i(v0))
% 87.34/12.21 | | | | |
% 87.34/12.21 | | | | | DELTA: instantiating (61) with fresh symbol all_317_0 gives:
% 87.34/12.21 | | | | | (62) memberP(all_97_0, all_317_0) = 0 & cons(all_317_0, nil) =
% 87.34/12.21 | | | | | all_93_0 & ssItem(all_317_0) = 0 & $i(all_317_0)
% 87.34/12.21 | | | | |
% 87.34/12.21 | | | | | ALPHA: (62) implies:
% 87.34/12.21 | | | | | (63) $i(all_317_0)
% 87.34/12.21 | | | | | (64) ssItem(all_317_0) = 0
% 87.34/12.21 | | | | | (65) cons(all_317_0, nil) = all_93_0
% 87.34/12.21 | | | | | (66) memberP(all_97_0, all_317_0) = 0
% 87.34/12.21 | | | | |
% 87.34/12.21 | | | | | BETA: splitting (40) gives:
% 87.34/12.21 | | | | |
% 87.34/12.21 | | | | | Case 1:
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | (67) all_93_0 = nil
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | REDUCE: (65), (67) imply:
% 87.34/12.21 | | | | | | (68) cons(all_317_0, nil) = nil
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | GROUND_INST: instantiating (39) with all_317_0, simplifying with
% 87.34/12.21 | | | | | | (63), (68) gives:
% 87.34/12.21 | | | | | | (69) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_317_0) = v0)
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | GROUND_INST: instantiating (37) with all_317_0, nil, simplifying
% 87.34/12.21 | | | | | | with (63), (68) gives:
% 87.34/12.21 | | | | | | (70) ? [v0: any] : ? [v1: $i] : (tl(nil) = v1 &
% 87.34/12.21 | | | | | | ssItem(all_317_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 87.34/12.21 | | | | | | nil))
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | GROUND_INST: instantiating (38) with all_317_0, nil, simplifying
% 87.34/12.21 | | | | | | with (63), (68) gives:
% 87.34/12.21 | | | | | | (71) ? [v0: any] : ? [v1: $i] : (hd(nil) = v1 &
% 87.34/12.21 | | | | | | ssItem(all_317_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 87.34/12.21 | | | | | | all_317_0))
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | DELTA: instantiating (69) with fresh symbol all_531_0 gives:
% 87.34/12.21 | | | | | | (72) ~ (all_531_0 = 0) & ssItem(all_317_0) = all_531_0
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | ALPHA: (72) implies:
% 87.34/12.21 | | | | | | (73) ~ (all_531_0 = 0)
% 87.34/12.21 | | | | | | (74) ssItem(all_317_0) = all_531_0
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | DELTA: instantiating (71) with fresh symbols all_533_0, all_533_1
% 87.34/12.21 | | | | | | gives:
% 87.34/12.21 | | | | | | (75) hd(nil) = all_533_0 & ssItem(all_317_0) = all_533_1 &
% 87.34/12.21 | | | | | | $i(all_533_0) & ( ~ (all_533_1 = 0) | all_533_0 = all_317_0)
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | ALPHA: (75) implies:
% 87.34/12.21 | | | | | | (76) ssItem(all_317_0) = all_533_1
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | DELTA: instantiating (70) with fresh symbols all_535_0, all_535_1
% 87.34/12.21 | | | | | | gives:
% 87.34/12.21 | | | | | | (77) tl(nil) = all_535_0 & ssItem(all_317_0) = all_535_1 &
% 87.34/12.21 | | | | | | $i(all_535_0) & ( ~ (all_535_1 = 0) | all_535_0 = nil)
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | ALPHA: (77) implies:
% 87.34/12.21 | | | | | | (78) ssItem(all_317_0) = all_535_1
% 87.34/12.21 | | | | | |
% 87.34/12.21 | | | | | | GROUND_INST: instantiating (12) with all_531_0, all_533_1,
% 87.34/12.21 | | | | | | all_317_0, simplifying with (74), (76) gives:
% 87.34/12.21 | | | | | | (79) all_533_1 = all_531_0
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | GROUND_INST: instantiating (12) with 0, all_535_1, all_317_0,
% 87.34/12.22 | | | | | | simplifying with (64), (78) gives:
% 87.34/12.22 | | | | | | (80) all_535_1 = 0
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | GROUND_INST: instantiating (12) with all_533_1, all_535_1,
% 87.34/12.22 | | | | | | all_317_0, simplifying with (76), (78) gives:
% 87.34/12.22 | | | | | | (81) all_535_1 = all_533_1
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | COMBINE_EQS: (80), (81) imply:
% 87.34/12.22 | | | | | | (82) all_533_1 = 0
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | SIMP: (82) implies:
% 87.34/12.22 | | | | | | (83) all_533_1 = 0
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | COMBINE_EQS: (79), (83) imply:
% 87.34/12.22 | | | | | | (84) all_531_0 = 0
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | SIMP: (84) implies:
% 87.34/12.22 | | | | | | (85) all_531_0 = 0
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | REDUCE: (73), (85) imply:
% 87.34/12.22 | | | | | | (86) $false
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | CLOSE: (86) is inconsistent.
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | Case 2:
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | (87) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] :
% 87.34/12.22 | | | | | | (cons(v1, v0) = all_93_0 & ssItem(v1) = 0 & $i(v1)))
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | DELTA: instantiating (87) with fresh symbol all_325_0 gives:
% 87.34/12.22 | | | | | | (88) ssList(all_325_0) = 0 & $i(all_325_0) & ? [v0: $i] :
% 87.34/12.22 | | | | | | (cons(v0, all_325_0) = all_93_0 & ssItem(v0) = 0 & $i(v0))
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | ALPHA: (88) implies:
% 87.34/12.22 | | | | | | (89) $i(all_325_0)
% 87.34/12.22 | | | | | | (90) ssList(all_325_0) = 0
% 87.34/12.22 | | | | | | (91) ? [v0: $i] : (cons(v0, all_325_0) = all_93_0 & ssItem(v0) =
% 87.34/12.22 | | | | | | 0 & $i(v0))
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | DELTA: instantiating (91) with fresh symbol all_327_0 gives:
% 87.34/12.22 | | | | | | (92) cons(all_327_0, all_325_0) = all_93_0 & ssItem(all_327_0) =
% 87.34/12.22 | | | | | | 0 & $i(all_327_0)
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | ALPHA: (92) implies:
% 87.34/12.22 | | | | | | (93) $i(all_327_0)
% 87.34/12.22 | | | | | | (94) ssItem(all_327_0) = 0
% 87.34/12.22 | | | | | | (95) cons(all_327_0, all_325_0) = all_93_0
% 87.34/12.22 | | | | | |
% 87.34/12.22 | | | | | | GROUND_INST: instantiating (ax44) with all_327_0, simplifying with
% 87.34/12.22 | | | | | | (93), (94) gives:
% 87.64/12.22 | | | | | | (96) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i]
% 87.64/12.22 | | | | | | : ! [v2: $i] : ( ~ (cons(all_327_0, v1) = v2) | ~ $i(v1)
% 87.64/12.22 | | | | | | | ? [v3: int] : ( ~ (v3 = 0) & ssList(v1) = v3) | !
% 87.64/12.22 | | | | | | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~
% 87.64/12.22 | | | | | | (frontsegP(v2, v4) = v5) | ~ (cons(v0, v3) = v4) | ~
% 87.64/12.22 | | | | | | $i(v3) | ? [v6: any] : ? [v7: any] : (frontsegP(v1,
% 87.64/12.22 | | | | | | v3) = v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~
% 87.64/12.22 | | | | | | (v7 = 0) | ~ (v0 = all_327_0) | v5 = 0) & ( ~
% 87.64/12.22 | | | | | | (v5 = 0) | (v7 = 0 & v0 = all_327_0))))))))
% 87.64/12.22 | | | | | |
% 87.64/12.22 | | | | | | GROUND_INST: instantiating (34) with all_317_0, simplifying with
% 87.64/12.22 | | | | | | (63), (65) gives:
% 87.64/12.22 | | | | | | (97) ? [v0: any] : ? [v1: any] : (memberP(all_97_0, all_317_0)
% 87.64/12.22 | | | | | | = v1 & ssItem(all_317_0) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 87.64/12.22 | | | | | | 0)))
% 87.64/12.22 | | | | | |
% 87.64/12.22 | | | | | | GROUND_INST: instantiating (37) with all_317_0, all_93_0,
% 87.64/12.22 | | | | | | simplifying with (63), (65) gives:
% 87.64/12.22 | | | | | | (98) ? [v0: any] : ? [v1: $i] : (tl(all_93_0) = v1 &
% 87.64/12.22 | | | | | | ssItem(all_317_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 87.64/12.22 | | | | | | nil))
% 87.64/12.22 | | | | | |
% 87.64/12.22 | | | | | | GROUND_INST: instantiating (38) with all_317_0, all_93_0,
% 87.64/12.22 | | | | | | simplifying with (63), (65) gives:
% 87.64/12.22 | | | | | | (99) ? [v0: any] : ? [v1: $i] : (hd(all_93_0) = v1 &
% 87.64/12.22 | | | | | | ssItem(all_317_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 87.64/12.22 | | | | | | all_317_0))
% 87.64/12.22 | | | | | |
% 87.64/12.22 | | | | | | GROUND_INST: instantiating (9) with all_317_0, all_93_0, simplifying
% 87.64/12.22 | | | | | | with (63), (65) gives:
% 87.64/12.22 | | | | | | (100) ? [v0: any] : ? [v1: any] : (equalelemsP(all_93_0) = v1 &
% 87.64/12.22 | | | | | | ssItem(all_317_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 87.64/12.22 | | | | | |
% 87.64/12.22 | | | | | | GROUND_INST: instantiating (8) with all_317_0, all_93_0, simplifying
% 87.64/12.22 | | | | | | with (63), (65) gives:
% 87.64/12.22 | | | | | | (101) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_93_0) =
% 87.64/12.22 | | | | | | v1 & ssItem(all_317_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 87.64/12.22 | | | | | |
% 87.64/12.22 | | | | | | GROUND_INST: instantiating (7) with all_317_0, all_93_0, simplifying
% 87.64/12.22 | | | | | | with (63), (65) gives:
% 87.64/12.22 | | | | | | (102) ? [v0: any] : ? [v1: any] : (strictorderedP(all_93_0) =
% 87.64/12.22 | | | | | | v1 & ssItem(all_317_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 87.64/12.22 | | | | | |
% 87.64/12.22 | | | | | | GROUND_INST: instantiating (6) with all_317_0, all_93_0, simplifying
% 87.64/12.22 | | | | | | with (63), (65) gives:
% 87.64/12.22 | | | | | | (103) ? [v0: any] : ? [v1: any] : (totalorderedP(all_93_0) = v1
% 87.64/12.22 | | | | | | & ssItem(all_317_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 87.64/12.22 | | | | | |
% 87.64/12.22 | | | | | | GROUND_INST: instantiating (5) with all_317_0, all_93_0, simplifying
% 87.64/12.22 | | | | | | with (63), (65) gives:
% 87.64/12.22 | | | | | | (104) ? [v0: any] : ? [v1: any] : (strictorderP(all_93_0) = v1
% 87.64/12.22 | | | | | | & ssItem(all_317_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 87.64/12.22 | | | | | |
% 87.64/12.22 | | | | | | GROUND_INST: instantiating (4) with all_317_0, all_93_0, simplifying
% 87.64/12.22 | | | | | | with (63), (65) gives:
% 87.64/12.22 | | | | | | (105) ? [v0: any] : ? [v1: any] : (totalorderP(all_93_0) = v1 &
% 87.64/12.22 | | | | | | ssItem(all_317_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 87.64/12.22 | | | | | |
% 87.64/12.22 | | | | | | GROUND_INST: instantiating (3) with all_317_0, all_93_0, simplifying
% 87.64/12.22 | | | | | | with (63), (65) gives:
% 87.64/12.22 | | | | | | (106) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_93_0) = v1 &
% 87.64/12.23 | | | | | | ssItem(all_317_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | GROUND_INST: instantiating (96) with all_91_0, simplifying with
% 87.64/12.23 | | | | | | (16), (17) gives:
% 87.64/12.23 | | | | | | (107) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_327_0, v0) = v1)
% 87.64/12.23 | | | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) =
% 87.64/12.23 | | | | | | v2) | ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 87.64/12.23 | | | | | | (frontsegP(v1, v3) = v4) | ~ (cons(all_91_0, v2) = v3)
% 87.64/12.23 | | | | | | | ~ $i(v2) | ? [v5: any] : ? [v6: any] :
% 87.64/12.23 | | | | | | (frontsegP(v0, v2) = v6 & ssList(v2) = v5 & ( ~ (v5 =
% 87.64/12.23 | | | | | | 0) | (( ~ (v6 = 0) | ~ (all_327_0 = all_91_0) |
% 87.64/12.23 | | | | | | v4 = 0) & ( ~ (v4 = 0) | (v6 = 0 & all_327_0 =
% 87.64/12.23 | | | | | | all_91_0)))))))
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | GROUND_INST: instantiating (107) with all_325_0, all_93_0,
% 87.64/12.23 | | | | | | simplifying with (89), (95) gives:
% 87.64/12.23 | | | | | | (108) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_325_0) = v0) | !
% 87.64/12.23 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 87.64/12.23 | | | | | | (frontsegP(all_93_0, v1) = v2) | ~ (cons(all_91_0, v0) =
% 87.64/12.23 | | | | | | v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 87.64/12.23 | | | | | | (frontsegP(all_325_0, v0) = v4 & ssList(v0) = v3 & ( ~
% 87.64/12.23 | | | | | | (v3 = 0) | (( ~ (v4 = 0) | ~ (all_327_0 = all_91_0)
% 87.64/12.23 | | | | | | | v2 = 0) & ( ~ (v2 = 0) | (v4 = 0 & all_327_0 =
% 87.64/12.23 | | | | | | all_91_0))))))
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | DELTA: instantiating (106) with fresh symbols all_766_0, all_766_1
% 87.64/12.23 | | | | | | gives:
% 87.64/12.23 | | | | | | (109) cyclefreeP(all_93_0) = all_766_0 & ssItem(all_317_0) =
% 87.64/12.23 | | | | | | all_766_1 & ( ~ (all_766_1 = 0) | all_766_0 = 0)
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | ALPHA: (109) implies:
% 87.64/12.23 | | | | | | (110) ssItem(all_317_0) = all_766_1
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | DELTA: instantiating (104) with fresh symbols all_768_0, all_768_1
% 87.64/12.23 | | | | | | gives:
% 87.64/12.23 | | | | | | (111) strictorderP(all_93_0) = all_768_0 & ssItem(all_317_0) =
% 87.64/12.23 | | | | | | all_768_1 & ( ~ (all_768_1 = 0) | all_768_0 = 0)
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | ALPHA: (111) implies:
% 87.64/12.23 | | | | | | (112) ssItem(all_317_0) = all_768_1
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | DELTA: instantiating (103) with fresh symbols all_770_0, all_770_1
% 87.64/12.23 | | | | | | gives:
% 87.64/12.23 | | | | | | (113) totalorderedP(all_93_0) = all_770_0 & ssItem(all_317_0) =
% 87.64/12.23 | | | | | | all_770_1 & ( ~ (all_770_1 = 0) | all_770_0 = 0)
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | ALPHA: (113) implies:
% 87.64/12.23 | | | | | | (114) ssItem(all_317_0) = all_770_1
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | DELTA: instantiating (97) with fresh symbols all_772_0, all_772_1
% 87.64/12.23 | | | | | | gives:
% 87.64/12.23 | | | | | | (115) memberP(all_97_0, all_317_0) = all_772_0 &
% 87.64/12.23 | | | | | | ssItem(all_317_0) = all_772_1 & ( ~ (all_772_0 = 0) | ~
% 87.64/12.23 | | | | | | (all_772_1 = 0))
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | ALPHA: (115) implies:
% 87.64/12.23 | | | | | | (116) ssItem(all_317_0) = all_772_1
% 87.64/12.23 | | | | | | (117) memberP(all_97_0, all_317_0) = all_772_0
% 87.64/12.23 | | | | | | (118) ~ (all_772_0 = 0) | ~ (all_772_1 = 0)
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | DELTA: instantiating (105) with fresh symbols all_774_0, all_774_1
% 87.64/12.23 | | | | | | gives:
% 87.64/12.23 | | | | | | (119) totalorderP(all_93_0) = all_774_0 & ssItem(all_317_0) =
% 87.64/12.23 | | | | | | all_774_1 & ( ~ (all_774_1 = 0) | all_774_0 = 0)
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | ALPHA: (119) implies:
% 87.64/12.23 | | | | | | (120) ssItem(all_317_0) = all_774_1
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | DELTA: instantiating (102) with fresh symbols all_776_0, all_776_1
% 87.64/12.23 | | | | | | gives:
% 87.64/12.23 | | | | | | (121) strictorderedP(all_93_0) = all_776_0 & ssItem(all_317_0) =
% 87.64/12.23 | | | | | | all_776_1 & ( ~ (all_776_1 = 0) | all_776_0 = 0)
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | ALPHA: (121) implies:
% 87.64/12.23 | | | | | | (122) ssItem(all_317_0) = all_776_1
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | DELTA: instantiating (100) with fresh symbols all_778_0, all_778_1
% 87.64/12.23 | | | | | | gives:
% 87.64/12.23 | | | | | | (123) equalelemsP(all_93_0) = all_778_0 & ssItem(all_317_0) =
% 87.64/12.23 | | | | | | all_778_1 & ( ~ (all_778_1 = 0) | all_778_0 = 0)
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | ALPHA: (123) implies:
% 87.64/12.23 | | | | | | (124) ssItem(all_317_0) = all_778_1
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | DELTA: instantiating (101) with fresh symbols all_780_0, all_780_1
% 87.64/12.23 | | | | | | gives:
% 87.64/12.23 | | | | | | (125) duplicatefreeP(all_93_0) = all_780_0 & ssItem(all_317_0) =
% 87.64/12.23 | | | | | | all_780_1 & ( ~ (all_780_1 = 0) | all_780_0 = 0)
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | ALPHA: (125) implies:
% 87.64/12.23 | | | | | | (126) ssItem(all_317_0) = all_780_1
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | DELTA: instantiating (98) with fresh symbols all_782_0, all_782_1
% 87.64/12.23 | | | | | | gives:
% 87.64/12.23 | | | | | | (127) tl(all_93_0) = all_782_0 & ssItem(all_317_0) = all_782_1 &
% 87.64/12.23 | | | | | | $i(all_782_0) & ( ~ (all_782_1 = 0) | all_782_0 = nil)
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | ALPHA: (127) implies:
% 87.64/12.23 | | | | | | (128) ssItem(all_317_0) = all_782_1
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | DELTA: instantiating (99) with fresh symbols all_784_0, all_784_1
% 87.64/12.23 | | | | | | gives:
% 87.64/12.23 | | | | | | (129) hd(all_93_0) = all_784_0 & ssItem(all_317_0) = all_784_1 &
% 87.64/12.23 | | | | | | $i(all_784_0) & ( ~ (all_784_1 = 0) | all_784_0 =
% 87.64/12.23 | | | | | | all_317_0)
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | ALPHA: (129) implies:
% 87.64/12.23 | | | | | | (130) ssItem(all_317_0) = all_784_1
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | BETA: splitting (108) gives:
% 87.64/12.23 | | | | | |
% 87.64/12.23 | | | | | | Case 1:
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | (131) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_325_0) = v0)
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | DELTA: instantiating (131) with fresh symbol all_819_0 gives:
% 87.64/12.23 | | | | | | | (132) ~ (all_819_0 = 0) & ssList(all_325_0) = all_819_0
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | ALPHA: (132) implies:
% 87.64/12.23 | | | | | | | (133) ~ (all_819_0 = 0)
% 87.64/12.23 | | | | | | | (134) ssList(all_325_0) = all_819_0
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | GROUND_INST: instantiating (13) with 0, all_819_0, all_325_0,
% 87.64/12.23 | | | | | | | simplifying with (90), (134) gives:
% 87.64/12.23 | | | | | | | (135) all_819_0 = 0
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | REDUCE: (133), (135) imply:
% 87.64/12.23 | | | | | | | (136) $false
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | CLOSE: (136) is inconsistent.
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | Case 2:
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | GROUND_INST: instantiating (12) with all_768_1, all_772_1,
% 87.64/12.23 | | | | | | | all_317_0, simplifying with (112), (116) gives:
% 87.64/12.23 | | | | | | | (137) all_772_1 = all_768_1
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | GROUND_INST: instantiating (12) with 0, all_774_1, all_317_0,
% 87.64/12.23 | | | | | | | simplifying with (64), (120) gives:
% 87.64/12.23 | | | | | | | (138) all_774_1 = 0
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | GROUND_INST: instantiating (12) with all_772_1, all_774_1,
% 87.64/12.23 | | | | | | | all_317_0, simplifying with (116), (120) gives:
% 87.64/12.23 | | | | | | | (139) all_774_1 = all_772_1
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | GROUND_INST: instantiating (12) with all_774_1, all_776_1,
% 87.64/12.23 | | | | | | | all_317_0, simplifying with (120), (122) gives:
% 87.64/12.23 | | | | | | | (140) all_776_1 = all_774_1
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | GROUND_INST: instantiating (12) with all_776_1, all_778_1,
% 87.64/12.23 | | | | | | | all_317_0, simplifying with (122), (124) gives:
% 87.64/12.23 | | | | | | | (141) all_778_1 = all_776_1
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | GROUND_INST: instantiating (12) with all_778_1, all_780_1,
% 87.64/12.23 | | | | | | | all_317_0, simplifying with (124), (126) gives:
% 87.64/12.23 | | | | | | | (142) all_780_1 = all_778_1
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | GROUND_INST: instantiating (12) with all_780_1, all_782_1,
% 87.64/12.23 | | | | | | | all_317_0, simplifying with (126), (128) gives:
% 87.64/12.23 | | | | | | | (143) all_782_1 = all_780_1
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | GROUND_INST: instantiating (12) with all_766_1, all_782_1,
% 87.64/12.23 | | | | | | | all_317_0, simplifying with (110), (128) gives:
% 87.64/12.23 | | | | | | | (144) all_782_1 = all_766_1
% 87.64/12.23 | | | | | | |
% 87.64/12.23 | | | | | | | GROUND_INST: instantiating (12) with all_774_1, all_784_1,
% 87.64/12.23 | | | | | | | all_317_0, simplifying with (120), (130) gives:
% 87.64/12.24 | | | | | | | (145) all_784_1 = all_774_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | GROUND_INST: instantiating (12) with all_770_1, all_784_1,
% 87.64/12.24 | | | | | | | all_317_0, simplifying with (114), (130) gives:
% 87.64/12.24 | | | | | | | (146) all_784_1 = all_770_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | GROUND_INST: instantiating (14) with 0, all_772_0, all_317_0,
% 87.64/12.24 | | | | | | | all_97_0, simplifying with (66), (117) gives:
% 87.64/12.24 | | | | | | | (147) all_772_0 = 0
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (145), (146) imply:
% 87.64/12.24 | | | | | | | (148) all_774_1 = all_770_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | SIMP: (148) implies:
% 87.64/12.24 | | | | | | | (149) all_774_1 = all_770_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (143), (144) imply:
% 87.64/12.24 | | | | | | | (150) all_780_1 = all_766_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | SIMP: (150) implies:
% 87.64/12.24 | | | | | | | (151) all_780_1 = all_766_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (142), (151) imply:
% 87.64/12.24 | | | | | | | (152) all_778_1 = all_766_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | SIMP: (152) implies:
% 87.64/12.24 | | | | | | | (153) all_778_1 = all_766_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (141), (153) imply:
% 87.64/12.24 | | | | | | | (154) all_776_1 = all_766_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | SIMP: (154) implies:
% 87.64/12.24 | | | | | | | (155) all_776_1 = all_766_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (140), (155) imply:
% 87.64/12.24 | | | | | | | (156) all_774_1 = all_766_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | SIMP: (156) implies:
% 87.64/12.24 | | | | | | | (157) all_774_1 = all_766_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (139), (149) imply:
% 87.64/12.24 | | | | | | | (158) all_772_1 = all_770_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | SIMP: (158) implies:
% 87.64/12.24 | | | | | | | (159) all_772_1 = all_770_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (138), (149) imply:
% 87.64/12.24 | | | | | | | (160) all_770_1 = 0
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (149), (157) imply:
% 87.64/12.24 | | | | | | | (161) all_770_1 = all_766_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (137), (159) imply:
% 87.64/12.24 | | | | | | | (162) all_770_1 = all_768_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | SIMP: (162) implies:
% 87.64/12.24 | | | | | | | (163) all_770_1 = all_768_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (160), (163) imply:
% 87.64/12.24 | | | | | | | (164) all_768_1 = 0
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (161), (163) imply:
% 87.64/12.24 | | | | | | | (165) all_768_1 = all_766_1
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (164), (165) imply:
% 87.64/12.24 | | | | | | | (166) all_766_1 = 0
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | COMBINE_EQS: (137), (164) imply:
% 87.64/12.24 | | | | | | | (167) all_772_1 = 0
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | BETA: splitting (118) gives:
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | | Case 1:
% 87.64/12.24 | | | | | | | |
% 87.64/12.24 | | | | | | | | (168) ~ (all_772_0 = 0)
% 87.64/12.24 | | | | | | | |
% 87.64/12.24 | | | | | | | | REDUCE: (147), (168) imply:
% 87.64/12.24 | | | | | | | | (169) $false
% 87.64/12.24 | | | | | | | |
% 87.64/12.24 | | | | | | | | CLOSE: (169) is inconsistent.
% 87.64/12.24 | | | | | | | |
% 87.64/12.24 | | | | | | | Case 2:
% 87.64/12.24 | | | | | | | |
% 87.64/12.24 | | | | | | | | (170) ~ (all_772_1 = 0)
% 87.64/12.24 | | | | | | | |
% 87.64/12.24 | | | | | | | | REDUCE: (167), (170) imply:
% 87.64/12.24 | | | | | | | | (171) $false
% 87.64/12.24 | | | | | | | |
% 87.64/12.24 | | | | | | | | CLOSE: (171) is inconsistent.
% 87.64/12.24 | | | | | | | |
% 87.64/12.24 | | | | | | | End of split
% 87.64/12.24 | | | | | | |
% 87.64/12.24 | | | | | | End of split
% 87.64/12.24 | | | | | |
% 87.64/12.24 | | | | | End of split
% 87.64/12.24 | | | | |
% 87.64/12.24 | | | | End of split
% 87.64/12.24 | | | |
% 87.64/12.24 | | | End of split
% 87.64/12.24 | | |
% 87.64/12.24 | | End of split
% 87.64/12.24 | |
% 87.64/12.24 | Case 2:
% 87.64/12.24 | |
% 87.64/12.24 | | (172) all_93_0 = nil
% 87.64/12.24 | | (173) all_97_0 = nil
% 87.64/12.24 | |
% 87.64/12.24 | | BETA: splitting (32) gives:
% 87.64/12.24 | |
% 87.64/12.24 | | Case 1:
% 87.64/12.24 | | |
% 87.64/12.24 | | | (174) ~ (all_97_0 = nil)
% 87.64/12.24 | | |
% 87.64/12.24 | | | REDUCE: (173), (174) imply:
% 87.64/12.24 | | | (175) $false
% 87.64/12.24 | | |
% 87.64/12.24 | | | CLOSE: (175) is inconsistent.
% 87.64/12.24 | | |
% 87.64/12.24 | | Case 2:
% 87.64/12.24 | | |
% 87.64/12.24 | | | (176) ~ (all_93_0 = nil)
% 87.64/12.24 | | |
% 87.64/12.24 | | | REDUCE: (172), (176) imply:
% 87.64/12.24 | | | (177) $false
% 87.64/12.24 | | |
% 87.64/12.24 | | | CLOSE: (177) is inconsistent.
% 87.64/12.24 | | |
% 87.64/12.24 | | End of split
% 87.64/12.24 | |
% 87.64/12.24 | End of split
% 87.64/12.24 |
% 87.64/12.24 End of proof
% 87.64/12.24 % SZS output end Proof for theBenchmark
% 87.64/12.24
% 87.64/12.24 11646ms
%------------------------------------------------------------------------------