TSTP Solution File: SWC067+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC067+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 : n024.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 20:49:29 EDT 2023
% Result : Theorem 148.10s 20.16s
% Output : Proof 219.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC067+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n024.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 16:54:08 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.60 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.27/1.39 Prover 1: Preprocessing ...
% 5.27/1.39 Prover 4: Preprocessing ...
% 5.43/1.42 Prover 6: Preprocessing ...
% 5.43/1.42 Prover 5: Preprocessing ...
% 5.43/1.42 Prover 0: Preprocessing ...
% 5.43/1.42 Prover 2: Preprocessing ...
% 5.55/1.43 Prover 3: Preprocessing ...
% 15.16/2.74 Prover 2: Proving ...
% 15.16/2.75 Prover 1: Constructing countermodel ...
% 15.60/2.79 Prover 6: Proving ...
% 15.60/2.80 Prover 3: Constructing countermodel ...
% 15.60/2.82 Prover 5: Constructing countermodel ...
% 20.63/3.44 Prover 4: Constructing countermodel ...
% 22.40/3.72 Prover 0: Proving ...
% 73.20/10.36 Prover 2: stopped
% 73.20/10.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 75.72/10.63 Prover 7: Preprocessing ...
% 77.58/10.87 Prover 7: Constructing countermodel ...
% 100.98/13.95 Prover 5: stopped
% 101.63/13.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 102.98/14.12 Prover 8: Preprocessing ...
% 105.14/14.42 Prover 8: Warning: ignoring some quantifiers
% 105.31/14.43 Prover 8: Constructing countermodel ...
% 116.88/15.95 Prover 1: stopped
% 116.88/15.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 118.03/16.09 Prover 9: Preprocessing ...
% 123.34/16.79 Prover 9: Constructing countermodel ...
% 131.13/17.86 Prover 6: stopped
% 131.13/17.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 132.15/17.98 Prover 10: Preprocessing ...
% 133.18/18.13 Prover 10: Constructing countermodel ...
% 148.10/20.16 Prover 9: proved (4194ms)
% 148.10/20.16
% 148.10/20.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 148.10/20.16
% 148.10/20.16 Prover 3: stopped
% 148.10/20.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 148.10/20.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 148.50/20.17 Prover 0: stopped
% 148.57/20.20 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 148.97/20.27 Prover 11: Preprocessing ...
% 148.97/20.30 Prover 13: Preprocessing ...
% 148.97/20.31 Prover 16: Preprocessing ...
% 150.17/20.42 Prover 16: Constructing countermodel ...
% 151.29/20.57 Prover 13: Constructing countermodel ...
% 154.99/21.06 Prover 11: Constructing countermodel ...
% 171.18/23.32 Prover 13: stopped
% 171.18/23.32 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 171.81/23.46 Prover 19: Preprocessing ...
% 176.44/24.02 Prover 19: Warning: ignoring some quantifiers
% 176.44/24.05 Prover 19: Constructing countermodel ...
% 178.88/24.36 Prover 16: stopped
% 193.46/26.46 Prover 19: stopped
% 201.16/27.94 Prover 4: stopped
% 211.10/30.22 Prover 7: stopped
% 218.22/32.28 Prover 10: Found proof (size 131)
% 218.22/32.28 Prover 10: proved (14419ms)
% 218.22/32.29 Prover 8: stopped
% 218.22/32.29 Prover 11: stopped
% 218.22/32.29
% 218.22/32.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 218.22/32.29
% 218.44/32.32 % SZS output start Proof for theBenchmark
% 218.44/32.33 Assumptions after simplification:
% 218.44/32.33 ---------------------------------
% 218.44/32.33
% 218.44/32.33 (ax15)
% 218.44/32.34 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) |
% 218.44/32.34 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~
% 218.44/32.34 neq(v0, v0))
% 218.44/32.34
% 218.44/32.34 (ax17)
% 218.44/32.34 $i(nil) & ssList(nil)
% 218.44/32.34
% 218.44/32.34 (ax26)
% 218.62/32.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) |
% 218.62/32.38 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 218.62/32.38
% 218.62/32.38 (ax28)
% 218.62/32.38 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 218.62/32.38 $i(v0) | ~ ssList(v0))
% 218.62/32.38
% 218.62/32.38 (ax42)
% 218.62/32.39 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0))
% 218.62/32.39
% 218.62/32.39 (ax45)
% 218.62/32.39 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 218.62/32.39
% 218.62/32.39 (ax46)
% 218.62/32.39 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 218.62/32.39 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 218.62/32.39
% 218.62/32.39 (ax5)
% 218.62/32.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 218.62/32.39 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 218.62/32.39 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 218.62/32.39 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 218.62/32.39 v2) = v0 & $i(v2) & ssList(v2)))
% 218.62/32.39
% 218.62/32.39 (ax51)
% 218.62/32.39 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 218.62/32.39
% 218.62/32.39 (ax52)
% 218.62/32.39 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~
% 218.62/32.39 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 218.62/32.39
% 218.62/32.39 (ax58)
% 218.62/32.39 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 218.62/32.39 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 218.62/32.39
% 218.62/32.39 (ax6)
% 218.62/32.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 218.62/32.40 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 218.62/32.40 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 218.62/32.40 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 218.62/32.40 v1) = v0 & $i(v2) & ssList(v2)))
% 218.62/32.40
% 218.62/32.40 (ax7)
% 218.62/32.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 218.62/32.40 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 218.62/32.40 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 218.62/32.40 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 218.62/32.40 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 218.62/32.40 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 218.62/32.40 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 218.62/32.40
% 218.62/32.40 (ax82)
% 218.62/32.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 218.62/32.40 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 218.62/32.40 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 218.62/32.40 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 218.62/32.40
% 218.62/32.40 (ax83)
% 218.62/32.40 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 218.62/32.40 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 218.62/32.40 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 218.62/32.40 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 218.62/32.40 v0) | ~ ssList(nil))
% 218.62/32.40
% 218.62/32.40 (ax84)
% 218.62/32.41 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 218.62/32.41 $i(v0) | ~ ssList(v0))
% 218.62/32.41
% 218.62/32.41 (co1)
% 218.62/32.41 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 218.62/32.41 : (app(v3, v4) = v1 & app(v2, v0) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 218.62/32.41 $i(v0) & strictorderedP(v0) & ssList(v4) & ssList(v2) & ssList(v1) &
% 218.62/32.41 ssList(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9:
% 218.62/32.41 $i] : ! [v10: $i] : ( ~ (cons(v8, nil) = v9) | ~ (cons(v5, nil) = v6) |
% 218.62/32.41 ~ (app(v10, v9) = v0) | ~ (app(v6, v7) = v4) | ~ $i(v10) | ~ $i(v8) |
% 218.62/32.41 ~ $i(v7) | ~ $i(v5) | ~ lt(v8, v5) | ~ ssList(v10) | ~ ssList(v7) | ~
% 218.62/32.41 ssItem(v8) | ~ ssItem(v5)) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 218.62/32.41 [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ (cons(v8, nil) = v9) | ~
% 218.62/32.41 (cons(v5, nil) = v6) | ~ (app(v9, v10) = v0) | ~ (app(v7, v6) = v2) | ~
% 218.62/32.41 $i(v10) | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ lt(v5, v8) | ~
% 218.62/32.41 ssList(v10) | ~ ssList(v7) | ~ ssItem(v8) | ~ ssItem(v5)) & ( ~ (v0 =
% 218.62/32.41 nil) | v1 = nil) & ((v1 = nil & ~ (v0 = nil)) | (neq(v1, nil) & ! [v5:
% 218.62/32.41 $i] : ( ~ $i(v5) | ~ segmentP(v1, v5) | ~ segmentP(v0, v5) | ~
% 218.62/32.41 ssList(v5) | ~ neq(v5, nil)))))
% 218.62/32.41
% 218.62/32.41 (function-axioms)
% 218.62/32.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 218.62/32.41 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 218.62/32.41 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 218.62/32.41 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 218.62/32.41 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 218.62/32.41 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 218.62/32.41
% 218.62/32.41 Further assumptions not needed in the proof:
% 218.62/32.41 --------------------------------------------
% 218.62/32.41 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 218.62/32.41 ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36,
% 218.62/32.41 ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax47, ax48, ax49, ax50, ax53,
% 218.62/32.41 ax54, ax55, ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67,
% 218.62/32.42 ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8,
% 218.62/32.42 ax80, ax81, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94,
% 218.62/32.42 ax95
% 218.62/32.42
% 218.62/32.42 Those formulas are unsatisfiable:
% 218.62/32.42 ---------------------------------
% 218.62/32.42
% 218.62/32.42 Begin of proof
% 218.62/32.42 |
% 218.62/32.42 | ALPHA: (ax5) implies:
% 218.62/32.42 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 218.62/32.42 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 218.62/32.42 | v0 & $i(v2) & ssList(v2)))
% 218.62/32.42 |
% 218.62/32.42 | ALPHA: (ax6) implies:
% 218.62/32.42 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 218.62/32.42 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 218.62/32.42 | v0 & $i(v2) & ssList(v2)))
% 218.62/32.42 |
% 218.62/32.42 | ALPHA: (ax7) implies:
% 218.62/32.42 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0,
% 218.62/32.42 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] :
% 218.62/32.42 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) &
% 218.62/32.42 | $i(v2) & ssList(v4) & ssList(v2)))
% 218.62/32.42 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 218.62/32.42 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2)
% 218.62/32.42 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~
% 218.62/32.42 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 218.62/32.42 |
% 218.62/32.42 | ALPHA: (ax15) implies:
% 218.62/32.42 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~ neq(v0, v0))
% 218.62/32.42 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 218.62/32.42 | ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 218.62/32.42 |
% 218.62/32.42 | ALPHA: (ax17) implies:
% 218.62/32.42 | (7) ssList(nil)
% 218.62/32.42 |
% 218.62/32.42 | ALPHA: (ax28) implies:
% 218.62/32.43 | (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 218.62/32.43 | $i(v0) | ~ ssList(v0))
% 218.62/32.43 |
% 218.62/32.43 | ALPHA: (ax45) implies:
% 218.62/32.43 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 218.62/32.43 |
% 218.62/32.43 | ALPHA: (ax46) implies:
% 218.62/32.43 | (10) ~ ssList(nil) | frontsegP(nil, nil)
% 218.62/32.43 |
% 218.62/32.43 | ALPHA: (ax51) implies:
% 218.62/32.43 | (11) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 218.62/32.43 |
% 218.62/32.43 | ALPHA: (ax52) implies:
% 218.62/32.43 | (12) ~ ssList(nil) | rearsegP(nil, nil)
% 218.62/32.43 |
% 218.62/32.43 | ALPHA: (ax58) implies:
% 218.62/32.43 | (13) ~ ssList(nil) | segmentP(nil, nil)
% 218.62/32.43 | (14) ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 218.62/32.43 | ssList(v0))
% 218.62/32.43 |
% 218.62/32.43 | ALPHA: (ax83) implies:
% 218.62/32.43 | (15) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 218.62/32.43 | (16) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 218.62/32.43 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 218.62/32.43 |
% 218.62/32.43 | ALPHA: (ax84) implies:
% 218.62/32.43 | (17) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 218.62/32.43 | $i(v0) | ~ ssList(v0))
% 218.62/32.43 |
% 218.62/32.43 | ALPHA: (co1) implies:
% 218.62/32.43 | (18) $i(nil)
% 218.62/32.43 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 218.62/32.43 | (app(v3, v4) = v1 & app(v2, v0) = v3 & $i(v4) & $i(v3) & $i(v2) &
% 218.62/32.43 | $i(v1) & $i(v0) & strictorderedP(v0) & ssList(v4) & ssList(v2) &
% 218.62/32.43 | ssList(v1) & ssList(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 218.62/32.43 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ (cons(v8, nil) = v9) |
% 218.62/32.43 | ~ (cons(v5, nil) = v6) | ~ (app(v10, v9) = v0) | ~ (app(v6, v7)
% 218.62/32.43 | = v4) | ~ $i(v10) | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~
% 218.62/32.43 | lt(v8, v5) | ~ ssList(v10) | ~ ssList(v7) | ~ ssItem(v8) | ~
% 218.62/32.43 | ssItem(v5)) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 218.62/32.43 | $i] : ! [v9: $i] : ! [v10: $i] : ( ~ (cons(v8, nil) = v9) | ~
% 218.62/32.43 | (cons(v5, nil) = v6) | ~ (app(v9, v10) = v0) | ~ (app(v7, v6) =
% 218.62/32.43 | v2) | ~ $i(v10) | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ lt(v5,
% 218.62/32.43 | v8) | ~ ssList(v10) | ~ ssList(v7) | ~ ssItem(v8) | ~
% 218.62/32.43 | ssItem(v5)) & ( ~ (v0 = nil) | v1 = nil) & ((v1 = nil & ~ (v0 =
% 218.62/32.43 | nil)) | (neq(v1, nil) & ! [v5: $i] : ( ~ $i(v5) | ~
% 218.62/32.43 | segmentP(v1, v5) | ~ segmentP(v0, v5) | ~ ssList(v5) | ~
% 218.62/32.43 | neq(v5, nil)))))
% 218.62/32.43 |
% 218.62/32.43 | ALPHA: (function-axioms) implies:
% 218.62/32.43 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 218.62/32.43 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 218.62/32.43 |
% 218.62/32.44 | DELTA: instantiating (19) with fresh symbols all_91_0, all_91_1, all_91_2,
% 218.62/32.44 | all_91_3, all_91_4 gives:
% 218.62/32.44 | (21) app(all_91_1, all_91_0) = all_91_3 & app(all_91_2, all_91_4) =
% 218.62/32.44 | all_91_1 & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 218.62/32.44 | $i(all_91_4) & strictorderedP(all_91_4) & ssList(all_91_0) &
% 218.62/32.44 | ssList(all_91_2) & ssList(all_91_3) & ssList(all_91_4) & ! [v0: $i] :
% 218.62/32.44 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 218.62/32.44 | ( ~ (cons(v3, nil) = v4) | ~ (cons(v0, nil) = v1) | ~ (app(v5, v4) =
% 218.62/32.44 | all_91_4) | ~ (app(v1, v2) = all_91_0) | ~ $i(v5) | ~ $i(v3) |
% 218.62/32.44 | ~ $i(v2) | ~ $i(v0) | ~ lt(v3, v0) | ~ ssList(v5) | ~ ssList(v2)
% 218.62/32.44 | | ~ ssItem(v3) | ~ ssItem(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 218.62/32.44 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v3,
% 218.62/32.44 | nil) = v4) | ~ (cons(v0, nil) = v1) | ~ (app(v4, v5) =
% 218.62/32.44 | all_91_4) | ~ (app(v2, v1) = all_91_2) | ~ $i(v5) | ~ $i(v3) |
% 218.62/32.44 | ~ $i(v2) | ~ $i(v0) | ~ lt(v0, v3) | ~ ssList(v5) | ~ ssList(v2)
% 218.62/32.44 | | ~ ssItem(v3) | ~ ssItem(v0)) & ( ~ (all_91_4 = nil) | all_91_3 =
% 218.62/32.44 | nil) & ((all_91_3 = nil & ~ (all_91_4 = nil)) | (neq(all_91_3, nil)
% 218.62/32.44 | & ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_3, v0) | ~
% 218.62/32.44 | segmentP(all_91_4, v0) | ~ ssList(v0) | ~ neq(v0, nil))))
% 218.62/32.44 |
% 218.62/32.44 | ALPHA: (21) implies:
% 218.62/32.44 | (22) ssList(all_91_4)
% 218.62/32.44 | (23) ssList(all_91_3)
% 218.62/32.44 | (24) ssList(all_91_2)
% 218.62/32.44 | (25) ssList(all_91_0)
% 218.62/32.44 | (26) $i(all_91_4)
% 218.62/32.44 | (27) $i(all_91_3)
% 218.62/32.44 | (28) $i(all_91_2)
% 218.62/32.44 | (29) $i(all_91_0)
% 218.62/32.44 | (30) app(all_91_2, all_91_4) = all_91_1
% 218.98/32.44 | (31) app(all_91_1, all_91_0) = all_91_3
% 218.98/32.44 | (32) (all_91_3 = nil & ~ (all_91_4 = nil)) | (neq(all_91_3, nil) & ! [v0:
% 218.98/32.44 | $i] : ( ~ $i(v0) | ~ segmentP(all_91_3, v0) | ~
% 218.98/32.44 | segmentP(all_91_4, v0) | ~ ssList(v0) | ~ neq(v0, nil)))
% 218.98/32.44 | (33) ~ (all_91_4 = nil) | all_91_3 = nil
% 218.98/32.44 |
% 218.98/32.44 | BETA: splitting (12) gives:
% 218.98/32.44 |
% 218.98/32.44 | Case 1:
% 218.98/32.44 | |
% 218.98/32.44 | | (34) ~ ssList(nil)
% 218.98/32.44 | |
% 218.98/32.44 | | PRED_UNIFY: (7), (34) imply:
% 218.98/32.44 | | (35) $false
% 218.98/32.44 | |
% 218.98/32.44 | | CLOSE: (35) is inconsistent.
% 218.98/32.44 | |
% 218.98/32.44 | Case 2:
% 218.98/32.44 | |
% 218.98/32.44 | | (36) rearsegP(nil, nil)
% 218.98/32.44 | |
% 218.98/32.44 | | BETA: splitting (10) gives:
% 218.98/32.44 | |
% 218.98/32.44 | | Case 1:
% 218.98/32.44 | | |
% 218.98/32.44 | | | (37) ~ ssList(nil)
% 218.98/32.44 | | |
% 218.98/32.44 | | | PRED_UNIFY: (7), (37) imply:
% 218.98/32.44 | | | (38) $false
% 218.98/32.44 | | |
% 218.98/32.44 | | | CLOSE: (38) is inconsistent.
% 218.98/32.44 | | |
% 218.98/32.44 | | Case 2:
% 218.98/32.44 | | |
% 218.98/32.44 | | | (39) frontsegP(nil, nil)
% 218.98/32.44 | | |
% 218.98/32.44 | | | BETA: splitting (13) gives:
% 218.98/32.44 | | |
% 218.98/32.44 | | | Case 1:
% 218.98/32.44 | | | |
% 218.98/32.44 | | | | (40) ~ ssList(nil)
% 218.98/32.44 | | | |
% 218.98/32.44 | | | | PRED_UNIFY: (7), (40) imply:
% 218.98/32.44 | | | | (41) $false
% 218.98/32.44 | | | |
% 218.98/32.44 | | | | CLOSE: (41) is inconsistent.
% 218.98/32.44 | | | |
% 218.98/32.44 | | | Case 2:
% 218.98/32.44 | | | |
% 218.98/32.45 | | | | (42) segmentP(nil, nil)
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | GROUND_INST: instantiating (11) with all_91_4, simplifying with (22),
% 218.98/32.45 | | | | (26) gives:
% 218.98/32.45 | | | | (43) rearsegP(all_91_4, nil)
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | GROUND_INST: instantiating (ax42) with all_91_4, simplifying with (22),
% 218.98/32.45 | | | | (26) gives:
% 218.98/32.45 | | | | (44) frontsegP(all_91_4, all_91_4)
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | GROUND_INST: instantiating (9) with all_91_4, simplifying with (22),
% 218.98/32.45 | | | | (26) gives:
% 218.98/32.45 | | | | (45) frontsegP(all_91_4, nil)
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | GROUND_INST: instantiating (11) with all_91_2, simplifying with (24),
% 218.98/32.45 | | | | (28) gives:
% 218.98/32.45 | | | | (46) rearsegP(all_91_2, nil)
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (7),
% 218.98/32.45 | | | | (18), (39) gives:
% 218.98/32.45 | | | | (47) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | GROUND_INST: instantiating (2) with nil, nil, simplifying with (7),
% 218.98/32.45 | | | | (18), (36) gives:
% 218.98/32.45 | | | | (48) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0))
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (7),
% 218.98/32.45 | | | | (18), (42) gives:
% 218.98/32.45 | | | | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil &
% 218.98/32.45 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) &
% 218.98/32.45 | | | | ssList(v0))
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | GROUND_INST: instantiating (4) with all_91_3, all_91_4, all_91_2,
% 218.98/32.45 | | | | all_91_1, all_91_0, simplifying with (22), (23), (24),
% 218.98/32.45 | | | | (25), (26), (27), (28), (29), (30), (31) gives:
% 218.98/32.45 | | | | (50) segmentP(all_91_3, all_91_4)
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | DELTA: instantiating (48) with fresh symbol all_112_0 gives:
% 218.98/32.45 | | | | (51) app(all_112_0, nil) = nil & $i(all_112_0) & ssList(all_112_0)
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | ALPHA: (51) implies:
% 218.98/32.45 | | | | (52) ssList(all_112_0)
% 218.98/32.45 | | | | (53) $i(all_112_0)
% 218.98/32.45 | | | | (54) app(all_112_0, nil) = nil
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | DELTA: instantiating (47) with fresh symbol all_114_0 gives:
% 218.98/32.45 | | | | (55) app(nil, all_114_0) = nil & $i(all_114_0) & ssList(all_114_0)
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | ALPHA: (55) implies:
% 218.98/32.45 | | | | (56) ssList(all_114_0)
% 218.98/32.45 | | | | (57) $i(all_114_0)
% 218.98/32.45 | | | | (58) app(nil, all_114_0) = nil
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | DELTA: instantiating (49) with fresh symbols all_118_0, all_118_1,
% 218.98/32.45 | | | | all_118_2 gives:
% 218.98/32.45 | | | | (59) app(all_118_1, all_118_0) = nil & app(all_118_2, nil) =
% 218.98/32.45 | | | | all_118_1 & $i(all_118_0) & $i(all_118_1) & $i(all_118_2) &
% 218.98/32.45 | | | | ssList(all_118_0) & ssList(all_118_2)
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | ALPHA: (59) implies:
% 218.98/32.45 | | | | (60) ssList(all_118_2)
% 218.98/32.45 | | | | (61) ssList(all_118_0)
% 218.98/32.45 | | | | (62) $i(all_118_2)
% 218.98/32.45 | | | | (63) $i(all_118_1)
% 218.98/32.45 | | | | (64) $i(all_118_0)
% 218.98/32.45 | | | | (65) app(all_118_2, nil) = all_118_1
% 218.98/32.45 | | | | (66) app(all_118_1, all_118_0) = nil
% 218.98/32.45 | | | |
% 218.98/32.45 | | | | GROUND_INST: instantiating (6) with all_91_4, all_118_0, simplifying
% 218.98/32.45 | | | | with (22), (26), (61), (64) gives:
% 218.98/32.45 | | | | (67) all_118_0 = all_91_4 | neq(all_91_4, all_118_0)
% 218.98/32.45 | | | |
% 218.98/32.46 | | | | GROUND_INST: instantiating (1) with all_91_4, nil, simplifying with (7),
% 218.98/32.46 | | | | (18), (22), (26), (45) gives:
% 218.98/32.46 | | | | (68) ? [v0: $i] : (app(nil, v0) = all_91_4 & $i(v0) & ssList(v0))
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | GROUND_INST: instantiating (1) with all_91_4, all_91_4, simplifying with
% 218.98/32.46 | | | | (22), (26), (44) gives:
% 218.98/32.46 | | | | (69) ? [v0: $i] : (app(all_91_4, v0) = all_91_4 & $i(v0) &
% 218.98/32.46 | | | | ssList(v0))
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | GROUND_INST: instantiating (2) with all_91_4, nil, simplifying with (7),
% 218.98/32.46 | | | | (18), (22), (26), (43) gives:
% 218.98/32.46 | | | | (70) ? [v0: $i] : (app(v0, nil) = all_91_4 & $i(v0) & ssList(v0))
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | GROUND_INST: instantiating (2) with all_91_2, nil, simplifying with (7),
% 218.98/32.46 | | | | (18), (24), (28), (46) gives:
% 218.98/32.46 | | | | (71) ? [v0: $i] : (app(v0, nil) = all_91_2 & $i(v0) & ssList(v0))
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | GROUND_INST: instantiating (ax82) with nil, all_114_0, nil, all_114_0,
% 218.98/32.46 | | | | nil, simplifying with (7), (18), (56), (57), (58) gives:
% 218.98/32.46 | | | | (72) ? [v0: $i] : (app(all_114_0, all_114_0) = v0 & app(nil, v0) =
% 218.98/32.46 | | | | nil & $i(v0))
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | GROUND_INST: instantiating (8) with all_114_0, nil, simplifying with
% 218.98/32.46 | | | | (56), (57), (58) gives:
% 218.98/32.46 | | | | (73) all_114_0 = nil
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | GROUND_INST: instantiating (17) with all_112_0, nil, simplifying with
% 218.98/32.46 | | | | (52), (53), (54) gives:
% 218.98/32.46 | | | | (74) all_112_0 = nil
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | GROUND_INST: instantiating (ax26) with all_118_2, nil, all_118_1,
% 218.98/32.46 | | | | simplifying with (7), (18), (60), (62), (65) gives:
% 218.98/32.46 | | | | (75) ssList(all_118_1)
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | GROUND_INST: instantiating (17) with all_118_2, all_118_1, simplifying
% 218.98/32.46 | | | | with (60), (62), (65) gives:
% 218.98/32.46 | | | | (76) all_118_1 = all_118_2
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | DELTA: instantiating (71) with fresh symbol all_140_0 gives:
% 218.98/32.46 | | | | (77) app(all_140_0, nil) = all_91_2 & $i(all_140_0) &
% 218.98/32.46 | | | | ssList(all_140_0)
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | ALPHA: (77) implies:
% 218.98/32.46 | | | | (78) ssList(all_140_0)
% 218.98/32.46 | | | | (79) $i(all_140_0)
% 218.98/32.46 | | | | (80) app(all_140_0, nil) = all_91_2
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | DELTA: instantiating (72) with fresh symbol all_142_0 gives:
% 218.98/32.46 | | | | (81) app(all_114_0, all_114_0) = all_142_0 & app(nil, all_142_0) =
% 218.98/32.46 | | | | nil & $i(all_142_0)
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | ALPHA: (81) implies:
% 218.98/32.46 | | | | (82) $i(all_142_0)
% 218.98/32.46 | | | | (83) app(all_114_0, all_114_0) = all_142_0
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | DELTA: instantiating (70) with fresh symbol all_164_0 gives:
% 218.98/32.46 | | | | (84) app(all_164_0, nil) = all_91_4 & $i(all_164_0) &
% 218.98/32.46 | | | | ssList(all_164_0)
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | ALPHA: (84) implies:
% 218.98/32.46 | | | | (85) ssList(all_164_0)
% 218.98/32.46 | | | | (86) $i(all_164_0)
% 218.98/32.46 | | | | (87) app(all_164_0, nil) = all_91_4
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | DELTA: instantiating (69) with fresh symbol all_166_0 gives:
% 218.98/32.46 | | | | (88) app(all_91_4, all_166_0) = all_91_4 & $i(all_166_0) &
% 218.98/32.46 | | | | ssList(all_166_0)
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | ALPHA: (88) implies:
% 218.98/32.46 | | | | (89) ssList(all_166_0)
% 218.98/32.46 | | | | (90) $i(all_166_0)
% 218.98/32.46 | | | | (91) app(all_91_4, all_166_0) = all_91_4
% 218.98/32.46 | | | |
% 218.98/32.46 | | | | DELTA: instantiating (68) with fresh symbol all_168_0 gives:
% 218.98/32.46 | | | | (92) app(nil, all_168_0) = all_91_4 & $i(all_168_0) &
% 218.98/32.47 | | | | ssList(all_168_0)
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | ALPHA: (92) implies:
% 218.98/32.47 | | | | (93) ssList(all_168_0)
% 218.98/32.47 | | | | (94) $i(all_168_0)
% 218.98/32.47 | | | | (95) app(nil, all_168_0) = all_91_4
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | REDUCE: (66), (76) imply:
% 218.98/32.47 | | | | (96) app(all_118_2, all_118_0) = nil
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | REDUCE: (73), (83) imply:
% 218.98/32.47 | | | | (97) app(nil, nil) = all_142_0
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | GROUND_INST: instantiating (15) with all_142_0, simplifying with (7),
% 218.98/32.47 | | | | (97) gives:
% 218.98/32.47 | | | | (98) all_142_0 = nil
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | REDUCE: (97), (98) imply:
% 218.98/32.47 | | | | (99) app(nil, nil) = nil
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_168_0,
% 218.98/32.47 | | | | all_91_4, simplifying with (7), (18), (93), (94), (95),
% 218.98/32.47 | | | | (99) gives:
% 218.98/32.47 | | | | (100) ? [v0: $i] : (app(nil, v0) = all_91_4 & app(nil, all_168_0) =
% 218.98/32.47 | | | | v0 & $i(v0) & $i(all_91_4))
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | GROUND_INST: instantiating (8) with all_168_0, all_91_4, simplifying
% 218.98/32.47 | | | | with (93), (94), (95) gives:
% 218.98/32.47 | | | | (101) all_168_0 = all_91_4
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | GROUND_INST: instantiating (4) with all_91_4, all_168_0, nil, all_91_4,
% 218.98/32.47 | | | | all_166_0, simplifying with (7), (18), (22), (26), (89),
% 218.98/32.47 | | | | (90), (91), (93), (94), (95) gives:
% 218.98/32.47 | | | | (102) segmentP(all_91_4, all_168_0)
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | GROUND_INST: instantiating (ax82) with nil, all_168_0, all_91_4,
% 218.98/32.47 | | | | all_166_0, all_91_4, simplifying with (7), (18), (89),
% 218.98/32.47 | | | | (90), (91), (93), (94), (95) gives:
% 218.98/32.47 | | | | (103) ? [v0: $i] : (app(all_168_0, all_166_0) = v0 & app(nil, v0) =
% 218.98/32.47 | | | | all_91_4 & $i(v0) & $i(all_91_4))
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | GROUND_INST: instantiating (ax82) with all_118_2, all_118_0, nil,
% 218.98/32.47 | | | | all_168_0, all_91_4, simplifying with (60), (61), (62),
% 218.98/32.47 | | | | (64), (93), (94), (95), (96) gives:
% 218.98/32.47 | | | | (104) ? [v0: $i] : (app(all_118_0, all_168_0) = v0 & app(all_118_2,
% 218.98/32.47 | | | | v0) = all_91_4 & $i(v0) & $i(all_91_4))
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | GROUND_INST: instantiating (16) with all_118_2, all_118_0, simplifying
% 218.98/32.47 | | | | with (60), (61), (62), (64), (96) gives:
% 218.98/32.47 | | | | (105) all_118_0 = nil
% 218.98/32.47 | | | |
% 218.98/32.47 | | | | GROUND_INST: instantiating (ax82) with all_140_0, nil, all_91_2,
% 218.98/32.47 | | | | all_91_4, all_91_1, simplifying with (7), (18), (22), (26),
% 218.98/32.47 | | | | (30), (78), (79), (80) gives:
% 218.98/32.48 | | | | (106) ? [v0: $i] : (app(all_140_0, v0) = all_91_1 & app(nil,
% 218.98/32.48 | | | | all_91_4) = v0 & $i(v0) & $i(all_91_1))
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | GROUND_INST: instantiating (ax82) with all_164_0, nil, all_91_4,
% 218.98/32.48 | | | | all_166_0, all_91_4, simplifying with (7), (18), (85),
% 218.98/32.48 | | | | (86), (87), (89), (90), (91) gives:
% 218.98/32.48 | | | | (107) ? [v0: $i] : (app(all_164_0, v0) = all_91_4 & app(nil,
% 218.98/32.48 | | | | all_166_0) = v0 & $i(v0) & $i(all_91_4))
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | GROUND_INST: instantiating (17) with all_164_0, all_91_4, simplifying
% 218.98/32.48 | | | | with (85), (86), (87) gives:
% 218.98/32.48 | | | | (108) all_164_0 = all_91_4
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | DELTA: instantiating (104) with fresh symbol all_264_0 gives:
% 218.98/32.48 | | | | (109) app(all_118_0, all_168_0) = all_264_0 & app(all_118_2,
% 218.98/32.48 | | | | all_264_0) = all_91_4 & $i(all_264_0) & $i(all_91_4)
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | ALPHA: (109) implies:
% 218.98/32.48 | | | | (110) $i(all_264_0)
% 218.98/32.48 | | | | (111) app(all_118_0, all_168_0) = all_264_0
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | DELTA: instantiating (106) with fresh symbol all_282_0 gives:
% 218.98/32.48 | | | | (112) app(all_140_0, all_282_0) = all_91_1 & app(nil, all_91_4) =
% 218.98/32.48 | | | | all_282_0 & $i(all_282_0) & $i(all_91_1)
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | ALPHA: (112) implies:
% 218.98/32.48 | | | | (113) app(nil, all_91_4) = all_282_0
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | DELTA: instantiating (103) with fresh symbol all_296_0 gives:
% 218.98/32.48 | | | | (114) app(all_168_0, all_166_0) = all_296_0 & app(nil, all_296_0) =
% 218.98/32.48 | | | | all_91_4 & $i(all_296_0) & $i(all_91_4)
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | ALPHA: (114) implies:
% 218.98/32.48 | | | | (115) app(all_168_0, all_166_0) = all_296_0
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | DELTA: instantiating (107) with fresh symbol all_300_0 gives:
% 218.98/32.48 | | | | (116) app(all_164_0, all_300_0) = all_91_4 & app(nil, all_166_0) =
% 218.98/32.48 | | | | all_300_0 & $i(all_300_0) & $i(all_91_4)
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | ALPHA: (116) implies:
% 218.98/32.48 | | | | (117) $i(all_300_0)
% 218.98/32.48 | | | | (118) app(nil, all_166_0) = all_300_0
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | DELTA: instantiating (100) with fresh symbol all_306_0 gives:
% 218.98/32.48 | | | | (119) app(nil, all_306_0) = all_91_4 & app(nil, all_168_0) =
% 218.98/32.48 | | | | all_306_0 & $i(all_306_0) & $i(all_91_4)
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | ALPHA: (119) implies:
% 218.98/32.48 | | | | (120) app(nil, all_168_0) = all_306_0
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | REDUCE: (101), (115) imply:
% 218.98/32.48 | | | | (121) app(all_91_4, all_166_0) = all_296_0
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | REDUCE: (101), (105), (111) imply:
% 218.98/32.48 | | | | (122) app(nil, all_91_4) = all_264_0
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | REDUCE: (101), (120) imply:
% 218.98/32.48 | | | | (123) app(nil, all_91_4) = all_306_0
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | REDUCE: (95), (101) imply:
% 218.98/32.48 | | | | (124) app(nil, all_91_4) = all_91_4
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | REDUCE: (101), (102) imply:
% 218.98/32.48 | | | | (125) segmentP(all_91_4, all_91_4)
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | GROUND_INST: instantiating (20) with all_264_0, all_282_0, all_91_4,
% 218.98/32.48 | | | | nil, simplifying with (113), (122) gives:
% 218.98/32.48 | | | | (126) all_282_0 = all_264_0
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | GROUND_INST: instantiating (20) with all_282_0, all_306_0, all_91_4,
% 218.98/32.48 | | | | nil, simplifying with (113), (123) gives:
% 218.98/32.48 | | | | (127) all_306_0 = all_282_0
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | GROUND_INST: instantiating (20) with all_91_4, all_306_0, all_91_4, nil,
% 218.98/32.48 | | | | simplifying with (123), (124) gives:
% 218.98/32.48 | | | | (128) all_306_0 = all_91_4
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | GROUND_INST: instantiating (20) with all_91_4, all_296_0, all_166_0,
% 218.98/32.48 | | | | all_91_4, simplifying with (91), (121) gives:
% 218.98/32.48 | | | | (129) all_296_0 = all_91_4
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | COMBINE_EQS: (127), (128) imply:
% 218.98/32.48 | | | | (130) all_282_0 = all_91_4
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | SIMP: (130) implies:
% 218.98/32.48 | | | | (131) all_282_0 = all_91_4
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | COMBINE_EQS: (126), (131) imply:
% 218.98/32.48 | | | | (132) all_264_0 = all_91_4
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | SIMP: (132) implies:
% 218.98/32.48 | | | | (133) all_264_0 = all_91_4
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | BETA: splitting (32) gives:
% 218.98/32.48 | | | |
% 218.98/32.48 | | | | Case 1:
% 218.98/32.48 | | | | |
% 218.98/32.48 | | | | | (134) all_91_3 = nil & ~ (all_91_4 = nil)
% 218.98/32.48 | | | | |
% 218.98/32.48 | | | | | ALPHA: (134) implies:
% 218.98/32.48 | | | | | (135) all_91_3 = nil
% 218.98/32.48 | | | | | (136) ~ (all_91_4 = nil)
% 218.98/32.48 | | | | |
% 218.98/32.48 | | | | | REDUCE: (50), (135) imply:
% 218.98/32.48 | | | | | (137) segmentP(nil, all_91_4)
% 218.98/32.48 | | | | |
% 218.98/32.48 | | | | | GROUND_INST: instantiating (14) with all_91_4, simplifying with (22),
% 218.98/32.48 | | | | | (26), (137) gives:
% 218.98/32.49 | | | | | (138) all_91_4 = nil
% 218.98/32.49 | | | | |
% 218.98/32.49 | | | | | REDUCE: (136), (138) imply:
% 218.98/32.49 | | | | | (139) $false
% 218.98/32.49 | | | | |
% 218.98/32.49 | | | | | CLOSE: (139) is inconsistent.
% 218.98/32.49 | | | | |
% 218.98/32.49 | | | | Case 2:
% 218.98/32.49 | | | | |
% 219.18/32.49 | | | | | (140) neq(all_91_3, nil) & ! [v0: $i] : ( ~ $i(v0) | ~
% 219.18/32.49 | | | | | segmentP(all_91_3, v0) | ~ segmentP(all_91_4, v0) | ~
% 219.18/32.49 | | | | | ssList(v0) | ~ neq(v0, nil))
% 219.18/32.49 | | | | |
% 219.18/32.49 | | | | | ALPHA: (140) implies:
% 219.18/32.49 | | | | | (141) neq(all_91_3, nil)
% 219.18/32.49 | | | | | (142) ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_3, v0) | ~
% 219.18/32.49 | | | | | segmentP(all_91_4, v0) | ~ ssList(v0) | ~ neq(v0, nil))
% 219.18/32.49 | | | | |
% 219.18/32.49 | | | | | BETA: splitting (33) gives:
% 219.18/32.49 | | | | |
% 219.18/32.49 | | | | | Case 1:
% 219.18/32.49 | | | | | |
% 219.18/32.49 | | | | | | (143) ~ (all_91_4 = nil)
% 219.18/32.49 | | | | | |
% 219.18/32.49 | | | | | | BETA: splitting (67) gives:
% 219.18/32.49 | | | | | |
% 219.18/32.49 | | | | | | Case 1:
% 219.18/32.49 | | | | | | |
% 219.18/32.49 | | | | | | | (144) neq(all_91_4, all_118_0)
% 219.18/32.49 | | | | | | |
% 219.18/32.49 | | | | | | | REDUCE: (105), (144) imply:
% 219.18/32.49 | | | | | | | (145) neq(all_91_4, nil)
% 219.18/32.49 | | | | | | |
% 219.18/32.49 | | | | | | | GROUND_INST: instantiating (142) with all_91_4, simplifying with
% 219.18/32.49 | | | | | | | (22), (26), (50), (125), (145) gives:
% 219.18/32.49 | | | | | | | (146) $false
% 219.18/32.49 | | | | | | |
% 219.18/32.49 | | | | | | | CLOSE: (146) is inconsistent.
% 219.18/32.49 | | | | | | |
% 219.18/32.49 | | | | | | Case 2:
% 219.18/32.49 | | | | | | |
% 219.18/32.49 | | | | | | | (147) all_118_0 = all_91_4
% 219.18/32.49 | | | | | | |
% 219.18/32.49 | | | | | | | COMBINE_EQS: (105), (147) imply:
% 219.18/32.49 | | | | | | | (148) all_91_4 = nil
% 219.18/32.49 | | | | | | |
% 219.18/32.49 | | | | | | | REDUCE: (143), (148) imply:
% 219.18/32.49 | | | | | | | (149) $false
% 219.18/32.49 | | | | | | |
% 219.18/32.49 | | | | | | | CLOSE: (149) is inconsistent.
% 219.18/32.49 | | | | | | |
% 219.18/32.49 | | | | | | End of split
% 219.18/32.49 | | | | | |
% 219.18/32.49 | | | | | Case 2:
% 219.18/32.49 | | | | | |
% 219.18/32.49 | | | | | | (150) all_91_4 = nil
% 219.18/32.49 | | | | | | (151) all_91_3 = nil
% 219.18/32.49 | | | | | |
% 219.18/32.49 | | | | | | REDUCE: (91), (150) imply:
% 219.18/32.49 | | | | | | (152) app(nil, all_166_0) = nil
% 219.18/32.49 | | | | | |
% 219.18/32.49 | | | | | | REDUCE: (141), (151) imply:
% 219.18/32.49 | | | | | | (153) neq(nil, nil)
% 219.18/32.49 | | | | | |
% 219.18/32.49 | | | | | | GROUND_INST: instantiating (20) with all_300_0, nil, all_166_0, nil,
% 219.18/32.49 | | | | | | simplifying with (118), (152) gives:
% 219.18/32.49 | | | | | | (154) all_300_0 = nil
% 219.18/32.49 | | | | | |
% 219.18/32.49 | | | | | | GROUND_INST: instantiating (5) with nil, simplifying with (7), (18),
% 219.18/32.49 | | | | | | (153) gives:
% 219.18/32.49 | | | | | | (155) $false
% 219.18/32.49 | | | | | |
% 219.18/32.49 | | | | | | CLOSE: (155) is inconsistent.
% 219.18/32.49 | | | | | |
% 219.18/32.49 | | | | | End of split
% 219.18/32.49 | | | | |
% 219.18/32.49 | | | | End of split
% 219.18/32.49 | | | |
% 219.18/32.49 | | | End of split
% 219.18/32.49 | | |
% 219.18/32.49 | | End of split
% 219.18/32.49 | |
% 219.18/32.49 | End of split
% 219.18/32.49 |
% 219.18/32.49 End of proof
% 219.18/32.49 % SZS output end Proof for theBenchmark
% 219.18/32.49
% 219.18/32.49 31903ms
%------------------------------------------------------------------------------