TSTP Solution File: SWC092+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC092+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 : n001.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 20:49:36 EDT 2023
% Result : Theorem 134.47s 18.77s
% Output : Proof 155.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC092+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 19:07:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.82/1.56 Prover 1: Preprocessing ...
% 5.82/1.57 Prover 4: Preprocessing ...
% 5.82/1.59 Prover 3: Preprocessing ...
% 5.82/1.59 Prover 5: Preprocessing ...
% 5.82/1.59 Prover 6: Preprocessing ...
% 5.82/1.60 Prover 2: Preprocessing ...
% 5.82/1.60 Prover 0: Preprocessing ...
% 15.94/2.98 Prover 2: Proving ...
% 16.54/3.07 Prover 1: Constructing countermodel ...
% 16.82/3.09 Prover 5: Constructing countermodel ...
% 16.82/3.12 Prover 6: Proving ...
% 17.20/3.13 Prover 3: Constructing countermodel ...
% 22.52/3.87 Prover 4: Constructing countermodel ...
% 23.95/4.05 Prover 0: Proving ...
% 71.02/10.36 Prover 2: stopped
% 71.50/10.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 72.52/10.54 Prover 7: Preprocessing ...
% 74.39/10.80 Prover 7: Constructing countermodel ...
% 98.13/14.01 Prover 5: stopped
% 98.13/14.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 100.38/14.19 Prover 8: Preprocessing ...
% 102.63/14.48 Prover 8: Warning: ignoring some quantifiers
% 102.63/14.49 Prover 8: Constructing countermodel ...
% 113.76/15.98 Prover 1: stopped
% 113.76/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 114.20/16.04 Prover 9: Preprocessing ...
% 119.34/16.72 Prover 9: Constructing countermodel ...
% 127.96/17.90 Prover 6: stopped
% 127.96/17.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 129.11/18.03 Prover 10: Preprocessing ...
% 130.24/18.19 Prover 10: Constructing countermodel ...
% 134.47/18.76 Prover 9: proved (2771ms)
% 134.47/18.76
% 134.47/18.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 134.47/18.77
% 134.91/18.79 Prover 3: stopped
% 134.91/18.80 Prover 0: stopped
% 134.91/18.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 134.91/18.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 134.91/18.82 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 135.47/18.87 Prover 11: Preprocessing ...
% 135.47/18.89 Prover 13: Preprocessing ...
% 135.47/18.93 Prover 16: Preprocessing ...
% 136.24/19.09 Prover 16: Constructing countermodel ...
% 136.95/19.15 Prover 13: Constructing countermodel ...
% 140.97/19.72 Prover 11: Constructing countermodel ...
% 155.57/21.65 Prover 7: Found proof (size 127)
% 155.57/21.65 Prover 7: proved (11193ms)
% 155.57/21.65 Prover 13: stopped
% 155.57/21.65 Prover 8: stopped
% 155.57/21.65 Prover 16: stopped
% 155.57/21.65 Prover 11: stopped
% 155.57/21.65 Prover 10: stopped
% 155.57/21.65 Prover 4: stopped
% 155.57/21.65
% 155.57/21.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 155.57/21.65
% 155.57/21.66 % SZS output start Proof for theBenchmark
% 155.57/21.67 Assumptions after simplification:
% 155.57/21.67 ---------------------------------
% 155.57/21.67
% 155.57/21.67 (ax15)
% 155.57/21.68 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) |
% 155.57/21.68 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~
% 155.57/21.68 neq(v0, v0))
% 155.57/21.68
% 155.57/21.68 (ax17)
% 155.57/21.68 $i(nil) & ssList(nil)
% 155.57/21.68
% 155.57/21.68 (ax26)
% 155.57/21.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) |
% 155.57/21.70 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 155.57/21.70
% 155.57/21.70 (ax28)
% 155.57/21.70 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 155.57/21.70 $i(v0) | ~ ssList(v0))
% 155.57/21.70
% 155.57/21.70 (ax45)
% 155.57/21.70 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 155.57/21.70
% 155.57/21.70 (ax46)
% 155.57/21.70 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 155.57/21.70 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 155.57/21.70
% 155.57/21.70 (ax5)
% 155.57/21.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 155.57/21.71 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 155.57/21.71 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 155.57/21.71 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 155.57/21.71 v2) = v0 & $i(v2) & ssList(v2)))
% 155.57/21.71
% 155.57/21.71 (ax51)
% 155.57/21.71 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 155.57/21.71
% 155.57/21.71 (ax55)
% 155.57/21.71 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, v0))
% 155.57/21.71
% 155.57/21.71 (ax58)
% 155.57/21.71 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 155.57/21.71 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 155.57/21.71
% 155.57/21.71 (ax6)
% 155.57/21.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 155.57/21.71 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 155.57/21.71 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 155.57/21.71 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 155.57/21.71 v1) = v0 & $i(v2) & ssList(v2)))
% 155.57/21.71
% 155.57/21.71 (ax7)
% 155.57/21.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 155.57/21.71 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 155.57/21.71 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 155.57/21.71 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 155.57/21.71 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 155.57/21.71 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 155.57/21.71 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 155.57/21.71
% 155.57/21.71 (ax82)
% 155.57/21.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 155.57/21.72 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 155.57/21.72 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 155.57/21.72 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : !
% 155.57/21.72 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (app(v1, v3) = v4) |
% 155.57/21.72 ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v3) |
% 155.57/21.72 ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : (app(v2, v3) = v5 & app(v0, v4)
% 155.57/21.72 = v5 & $i(v5)))
% 155.57/21.72
% 155.57/21.72 (ax83)
% 155.57/21.72 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 155.57/21.72 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 155.57/21.72 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 155.57/21.72 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 155.57/21.72 v0) | ~ ssList(nil))
% 155.57/21.72
% 155.57/21.72 (ax84)
% 155.57/21.72 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 155.57/21.72 $i(v0) | ~ ssList(v0))
% 155.57/21.72
% 155.57/21.72 (co1)
% 155.57/21.73 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2)
% 155.57/21.73 & $i(v1) & $i(v0) & strictorderedP(v0) & ssList(v2) & ssList(v1) &
% 155.57/21.73 ssList(v0) & neq(v1, nil) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 155.57/21.73 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v6, nil) = v7) | ~
% 155.57/21.73 (cons(v3, nil) = v4) | ~ (app(v8, v7) = v0) | ~ (app(v4, v5) = v2) | ~
% 155.57/21.73 $i(v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) | ~ lt(v6, v3) | ~ ssList(v8)
% 155.57/21.73 | ~ ssList(v5) | ~ ssItem(v6) | ~ ssItem(v3)) & ! [v3: $i] : ( ~
% 155.57/21.73 $i(v3) | ~ segmentP(v1, v3) | ~ segmentP(v0, v3) | ~ ssList(v3) | ~
% 155.57/21.73 neq(v3, nil)) & ( ~ (v0 = nil) | v1 = nil))
% 155.57/21.73
% 155.57/21.73 (function-axioms)
% 155.57/21.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.57/21.73 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 155.57/21.73 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 155.57/21.73 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 155.57/21.73 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 155.57/21.73 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 155.57/21.73
% 155.57/21.73 Further assumptions not needed in the proof:
% 155.57/21.73 --------------------------------------------
% 155.57/21.73 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 155.57/21.73 ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36,
% 155.57/21.73 ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax47, ax48, ax49, ax50,
% 155.57/21.73 ax52, ax53, ax54, ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66,
% 155.57/21.73 ax67, ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79,
% 155.57/21.73 ax8, ax80, ax81, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 155.57/21.73 ax94, ax95
% 155.57/21.73
% 155.57/21.73 Those formulas are unsatisfiable:
% 155.57/21.73 ---------------------------------
% 155.57/21.73
% 155.57/21.73 Begin of proof
% 155.57/21.73 |
% 155.57/21.73 | ALPHA: (ax5) implies:
% 155.57/21.73 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 155.57/21.73 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 155.57/21.73 | v0 & $i(v2) & ssList(v2)))
% 155.57/21.73 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~
% 155.57/21.73 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~
% 155.57/21.73 | ssList(v0) | frontsegP(v0, v1))
% 155.57/21.73 |
% 155.57/21.74 | ALPHA: (ax6) implies:
% 155.57/21.74 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 155.57/21.74 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 155.57/21.74 | v0 & $i(v2) & ssList(v2)))
% 155.57/21.74 |
% 155.57/21.74 | ALPHA: (ax7) implies:
% 155.57/21.74 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0,
% 155.57/21.74 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] :
% 155.57/21.74 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) &
% 155.57/21.74 | $i(v2) & ssList(v4) & ssList(v2)))
% 155.57/21.74 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 155.57/21.74 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2)
% 155.57/21.74 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~
% 155.57/21.74 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 155.57/21.74 |
% 155.57/21.74 | ALPHA: (ax15) implies:
% 155.57/21.74 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 155.57/21.74 | ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 155.57/21.74 |
% 155.57/21.74 | ALPHA: (ax17) implies:
% 155.57/21.74 | (7) ssList(nil)
% 155.57/21.74 |
% 155.57/21.74 | ALPHA: (ax28) implies:
% 155.57/21.74 | (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 155.57/21.74 | $i(v0) | ~ ssList(v0))
% 155.57/21.74 |
% 155.57/21.74 | ALPHA: (ax45) implies:
% 155.57/21.74 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 155.57/21.74 |
% 155.57/21.74 | ALPHA: (ax46) implies:
% 155.57/21.74 | (10) ~ ssList(nil) | frontsegP(nil, nil)
% 155.57/21.74 |
% 155.57/21.74 | ALPHA: (ax51) implies:
% 155.57/21.74 | (11) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 155.57/21.74 |
% 155.57/21.74 | ALPHA: (ax58) implies:
% 155.57/21.74 | (12) ~ ssList(nil) | segmentP(nil, nil)
% 155.57/21.74 |
% 155.57/21.74 | ALPHA: (ax82) implies:
% 155.57/21.74 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 155.57/21.74 | ( ~ (app(v1, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1)
% 155.57/21.74 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ?
% 155.57/21.74 | [v5: $i] : (app(v2, v3) = v5 & app(v0, v4) = v5 & $i(v5)))
% 155.57/21.75 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 155.57/21.75 | ( ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1)
% 155.57/21.75 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ?
% 155.57/21.75 | [v5: $i] : (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 155.57/21.75 |
% 155.57/21.75 | ALPHA: (ax83) implies:
% 155.57/21.75 | (15) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 155.57/21.75 | (16) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~
% 155.57/21.75 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 155.57/21.75 | (17) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 155.57/21.75 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 155.57/21.75 |
% 155.57/21.75 | ALPHA: (ax84) implies:
% 155.57/21.75 | (18) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 155.57/21.75 | $i(v0) | ~ ssList(v0))
% 155.57/21.75 |
% 155.57/21.75 | ALPHA: (co1) implies:
% 155.57/21.75 | (19) $i(nil)
% 155.57/21.75 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2) &
% 155.57/21.75 | $i(v1) & $i(v0) & strictorderedP(v0) & ssList(v2) & ssList(v1) &
% 155.57/21.75 | ssList(v0) & neq(v1, nil) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 155.57/21.75 | : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v6, nil) = v7)
% 155.57/21.75 | | ~ (cons(v3, nil) = v4) | ~ (app(v8, v7) = v0) | ~ (app(v4,
% 155.57/21.75 | v5) = v2) | ~ $i(v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) | ~
% 155.57/21.75 | lt(v6, v3) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v6) | ~
% 155.57/21.75 | ssItem(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ segmentP(v1, v3) | ~
% 155.57/21.75 | segmentP(v0, v3) | ~ ssList(v3) | ~ neq(v3, nil)) & ( ~ (v0 =
% 155.57/21.75 | nil) | v1 = nil))
% 155.57/21.75 |
% 155.57/21.75 | ALPHA: (function-axioms) implies:
% 155.57/21.75 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.57/21.75 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 155.57/21.75 |
% 155.57/21.75 | DELTA: instantiating (20) with fresh symbols all_91_0, all_91_1, all_91_2
% 155.57/21.75 | gives:
% 155.57/21.75 | (22) app(all_91_2, all_91_0) = all_91_1 & $i(all_91_0) & $i(all_91_1) &
% 155.57/21.75 | $i(all_91_2) & strictorderedP(all_91_2) & ssList(all_91_0) &
% 155.57/21.75 | ssList(all_91_1) & ssList(all_91_2) & neq(all_91_1, nil) & ! [v0: $i]
% 155.57/21.75 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 155.57/21.75 | : ( ~ (cons(v3, nil) = v4) | ~ (cons(v0, nil) = v1) | ~ (app(v5, v4)
% 155.57/21.75 | = all_91_2) | ~ (app(v1, v2) = all_91_0) | ~ $i(v5) | ~ $i(v3)
% 155.57/21.75 | | ~ $i(v2) | ~ $i(v0) | ~ lt(v3, v0) | ~ ssList(v5) | ~
% 155.57/21.75 | ssList(v2) | ~ ssItem(v3) | ~ ssItem(v0)) & ! [v0: $i] : ( ~
% 155.57/21.75 | $i(v0) | ~ segmentP(all_91_1, v0) | ~ segmentP(all_91_2, v0) | ~
% 155.57/21.75 | ssList(v0) | ~ neq(v0, nil)) & ( ~ (all_91_2 = nil) | all_91_1 =
% 155.57/21.75 | nil)
% 155.57/21.75 |
% 155.57/21.75 | ALPHA: (22) implies:
% 155.57/21.76 | (23) neq(all_91_1, nil)
% 155.57/21.76 | (24) ssList(all_91_2)
% 155.57/21.76 | (25) ssList(all_91_1)
% 155.57/21.76 | (26) ssList(all_91_0)
% 155.57/21.76 | (27) $i(all_91_2)
% 155.57/21.76 | (28) $i(all_91_1)
% 155.57/21.76 | (29) $i(all_91_0)
% 155.57/21.76 | (30) app(all_91_2, all_91_0) = all_91_1
% 155.57/21.76 | (31) ~ (all_91_2 = nil) | all_91_1 = nil
% 155.57/21.76 | (32) ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_1, v0) | ~
% 155.57/21.76 | segmentP(all_91_2, v0) | ~ ssList(v0) | ~ neq(v0, nil))
% 155.57/21.76 |
% 155.57/21.76 | BETA: splitting (10) gives:
% 155.57/21.76 |
% 155.57/21.76 | Case 1:
% 155.57/21.76 | |
% 155.57/21.76 | | (33) ~ ssList(nil)
% 155.57/21.76 | |
% 155.57/21.76 | | PRED_UNIFY: (7), (33) imply:
% 155.57/21.76 | | (34) $false
% 155.57/21.76 | |
% 155.57/21.76 | | CLOSE: (34) is inconsistent.
% 155.57/21.76 | |
% 155.57/21.76 | Case 2:
% 155.57/21.76 | |
% 155.57/21.76 | | (35) frontsegP(nil, nil)
% 155.57/21.76 | |
% 155.57/21.76 | | BETA: splitting (12) gives:
% 155.57/21.76 | |
% 155.57/21.76 | | Case 1:
% 155.57/21.76 | | |
% 155.57/21.76 | | | (36) ~ ssList(nil)
% 155.57/21.76 | | |
% 155.57/21.76 | | | PRED_UNIFY: (7), (36) imply:
% 155.57/21.76 | | | (37) $false
% 155.57/21.76 | | |
% 155.57/21.76 | | | CLOSE: (37) is inconsistent.
% 155.57/21.76 | | |
% 155.57/21.76 | | Case 2:
% 155.57/21.76 | | |
% 155.57/21.76 | | | (38) segmentP(nil, nil)
% 155.57/21.76 | | |
% 155.57/21.76 | | | GROUND_INST: instantiating (ax55) with all_91_2, simplifying with (24),
% 155.57/21.76 | | | (27) gives:
% 155.57/21.76 | | | (39) segmentP(all_91_2, all_91_2)
% 155.57/21.76 | | |
% 155.57/21.76 | | | GROUND_INST: instantiating (11) with all_91_2, simplifying with (24), (27)
% 155.57/21.76 | | | gives:
% 155.57/21.76 | | | (40) rearsegP(all_91_2, nil)
% 155.57/21.76 | | |
% 155.57/21.76 | | | GROUND_INST: instantiating (9) with all_91_2, simplifying with (24), (27)
% 155.57/21.76 | | | gives:
% 155.57/21.76 | | | (41) frontsegP(all_91_2, nil)
% 155.57/21.76 | | |
% 155.57/21.76 | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (7), (19),
% 155.57/21.76 | | | (35) gives:
% 155.57/21.76 | | | (42) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 155.57/21.76 | | |
% 155.57/21.76 | | | GROUND_INST: instantiating (4) with nil, nil, simplifying with (7), (19),
% 155.57/21.76 | | | (38) gives:
% 155.57/21.76 | | | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil &
% 155.57/21.76 | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) &
% 155.57/21.76 | | | ssList(v0))
% 155.57/21.76 | | |
% 155.57/21.76 | | | GROUND_INST: instantiating (2) with all_91_1, all_91_2, all_91_0,
% 155.57/21.76 | | | simplifying with (24), (25), (26), (27), (28), (29), (30)
% 155.57/21.76 | | | gives:
% 155.57/21.76 | | | (44) frontsegP(all_91_1, all_91_2)
% 155.57/21.76 | | |
% 155.57/21.76 | | | DELTA: instantiating (42) with fresh symbol all_114_0 gives:
% 155.57/21.76 | | | (45) app(nil, all_114_0) = nil & $i(all_114_0) & ssList(all_114_0)
% 155.57/21.77 | | |
% 155.57/21.77 | | | ALPHA: (45) implies:
% 155.57/21.77 | | | (46) ssList(all_114_0)
% 155.57/21.77 | | | (47) $i(all_114_0)
% 155.57/21.77 | | | (48) app(nil, all_114_0) = nil
% 155.57/21.77 | | |
% 155.57/21.77 | | | DELTA: instantiating (43) with fresh symbols all_116_0, all_116_1,
% 155.57/21.77 | | | all_116_2 gives:
% 155.57/21.77 | | | (49) app(all_116_1, all_116_0) = nil & app(all_116_2, nil) = all_116_1
% 155.57/21.77 | | | & $i(all_116_0) & $i(all_116_1) & $i(all_116_2) &
% 155.57/21.77 | | | ssList(all_116_0) & ssList(all_116_2)
% 155.57/21.77 | | |
% 155.57/21.77 | | | ALPHA: (49) implies:
% 155.57/21.77 | | | (50) ssList(all_116_2)
% 155.57/21.77 | | | (51) ssList(all_116_0)
% 155.57/21.77 | | | (52) $i(all_116_2)
% 155.57/21.77 | | | (53) $i(all_116_0)
% 155.57/21.77 | | | (54) app(all_116_2, nil) = all_116_1
% 155.57/21.77 | | | (55) app(all_116_1, all_116_0) = nil
% 155.57/21.77 | | |
% 155.57/21.77 | | | GROUND_INST: instantiating (1) with all_91_2, nil, simplifying with (7),
% 155.57/21.77 | | | (19), (24), (27), (41) gives:
% 155.57/21.77 | | | (56) ? [v0: $i] : (app(nil, v0) = all_91_2 & $i(v0) & ssList(v0))
% 155.57/21.77 | | |
% 155.57/21.77 | | | GROUND_INST: instantiating (1) with all_91_1, all_91_2, simplifying with
% 155.57/21.77 | | | (24), (25), (27), (28), (44) gives:
% 155.57/21.77 | | | (57) ? [v0: $i] : (app(all_91_2, v0) = all_91_1 & $i(v0) & ssList(v0))
% 155.57/21.77 | | |
% 155.57/21.77 | | | GROUND_INST: instantiating (3) with all_91_2, nil, simplifying with (7),
% 155.57/21.77 | | | (19), (24), (27), (40) gives:
% 155.57/21.77 | | | (58) ? [v0: $i] : (app(v0, nil) = all_91_2 & $i(v0) & ssList(v0))
% 155.57/21.77 | | |
% 155.57/21.77 | | | GROUND_INST: instantiating (32) with all_91_2, simplifying with (24),
% 155.57/21.77 | | | (27), (39) gives:
% 155.57/21.77 | | | (59) ~ segmentP(all_91_1, all_91_2) | ~ neq(all_91_2, nil)
% 155.57/21.77 | | |
% 155.57/21.77 | | | GROUND_INST: instantiating (14) with nil, nil, nil, nil, nil, simplifying
% 155.57/21.77 | | | with (7), (19) gives:
% 155.57/21.77 | | | (60) ~ (app(nil, nil) = nil) | ? [v0: $i] : (app(nil, v0) = nil &
% 155.57/21.77 | | | app(nil, nil) = v0 & $i(v0))
% 155.57/21.77 | | |
% 155.57/21.77 | | | GROUND_INST: instantiating (14) with nil, all_114_0, nil, all_114_0, nil,
% 155.57/21.77 | | | simplifying with (7), (19), (46), (47), (48) gives:
% 155.57/21.77 | | | (61) ? [v0: $i] : (app(all_114_0, all_114_0) = v0 & app(nil, v0) = nil
% 155.57/21.77 | | | & $i(v0))
% 155.57/21.77 | | |
% 155.57/21.77 | | | GROUND_INST: instantiating (8) with all_114_0, nil, simplifying with (46),
% 155.57/21.77 | | | (47), (48) gives:
% 155.57/21.77 | | | (62) all_114_0 = nil
% 155.57/21.77 | | |
% 155.57/21.77 | | | GROUND_INST: instantiating (14) with all_116_2, nil, all_116_2, nil,
% 155.57/21.77 | | | all_116_2, simplifying with (7), (19), (50), (52) gives:
% 155.57/21.77 | | | (63) ~ (app(all_116_2, nil) = all_116_2) | ? [v0: $i] :
% 155.57/21.77 | | | (app(all_116_2, v0) = all_116_2 & app(nil, nil) = v0 & $i(v0))
% 155.57/21.77 | | |
% 155.57/21.78 | | | GROUND_INST: instantiating (13) with all_116_2, nil, all_116_1, all_114_0,
% 155.57/21.78 | | | nil, simplifying with (7), (19), (46), (47), (48), (50),
% 155.57/21.78 | | | (52), (54) gives:
% 155.57/21.78 | | | (64) ? [v0: $i] : (app(all_116_1, all_114_0) = v0 & app(all_116_2,
% 155.57/21.78 | | | nil) = v0 & $i(v0))
% 155.57/21.78 | | |
% 155.57/21.78 | | | GROUND_INST: instantiating (ax26) with all_116_2, nil, all_116_1,
% 155.57/21.78 | | | simplifying with (7), (19), (50), (52), (54) gives:
% 155.57/21.78 | | | (65) ssList(all_116_1)
% 155.57/21.78 | | |
% 155.57/21.78 | | | GROUND_INST: instantiating (18) with all_116_2, all_116_1, simplifying
% 155.57/21.78 | | | with (50), (52), (54) gives:
% 155.57/21.78 | | | (66) all_116_1 = all_116_2
% 155.57/21.78 | | |
% 155.57/21.78 | | | GROUND_INST: instantiating (14) with all_116_2, nil, all_116_1, all_116_0,
% 155.57/21.78 | | | nil, simplifying with (7), (19), (50), (51), (52), (53),
% 155.57/21.78 | | | (54), (55) gives:
% 155.57/21.78 | | | (67) ? [v0: $i] : (app(all_116_2, v0) = nil & app(nil, all_116_0) = v0
% 155.57/21.78 | | | & $i(v0))
% 155.57/21.78 | | |
% 155.57/21.78 | | | GROUND_INST: instantiating (17) with all_116_2, all_116_0, simplifying
% 155.57/21.78 | | | with (50), (51), (52), (53) gives:
% 155.57/21.78 | | | (68) all_116_0 = nil | ~ (app(all_116_2, all_116_0) = nil)
% 155.57/21.78 | | |
% 155.57/21.78 | | | GROUND_INST: instantiating (16) with all_116_2, all_116_0, simplifying
% 155.57/21.78 | | | with (50), (51), (52), (53) gives:
% 155.57/21.78 | | | (69) all_116_2 = nil | ~ (app(all_116_2, all_116_0) = nil)
% 155.57/21.78 | | |
% 155.57/21.78 | | | DELTA: instantiating (64) with fresh symbol all_132_0 gives:
% 155.57/21.78 | | | (70) app(all_116_1, all_114_0) = all_132_0 & app(all_116_2, nil) =
% 155.57/21.78 | | | all_132_0 & $i(all_132_0)
% 155.57/21.78 | | |
% 155.57/21.78 | | | ALPHA: (70) implies:
% 155.57/21.78 | | | (71) $i(all_132_0)
% 155.57/21.78 | | | (72) app(all_116_1, all_114_0) = all_132_0
% 155.57/21.78 | | |
% 155.57/21.78 | | | DELTA: instantiating (61) with fresh symbol all_134_0 gives:
% 155.57/21.78 | | | (73) app(all_114_0, all_114_0) = all_134_0 & app(nil, all_134_0) = nil
% 155.57/21.78 | | | & $i(all_134_0)
% 155.57/21.78 | | |
% 155.57/21.78 | | | ALPHA: (73) implies:
% 155.57/21.78 | | | (74) app(all_114_0, all_114_0) = all_134_0
% 155.57/21.78 | | |
% 155.57/21.78 | | | DELTA: instantiating (57) with fresh symbol all_140_0 gives:
% 155.57/21.78 | | | (75) app(all_91_2, all_140_0) = all_91_1 & $i(all_140_0) &
% 155.57/21.78 | | | ssList(all_140_0)
% 155.57/21.78 | | |
% 155.57/21.78 | | | ALPHA: (75) implies:
% 155.57/21.78 | | | (76) ssList(all_140_0)
% 155.57/21.78 | | | (77) $i(all_140_0)
% 155.57/21.78 | | | (78) app(all_91_2, all_140_0) = all_91_1
% 155.57/21.78 | | |
% 155.57/21.78 | | | DELTA: instantiating (56) with fresh symbol all_146_0 gives:
% 155.57/21.78 | | | (79) app(nil, all_146_0) = all_91_2 & $i(all_146_0) & ssList(all_146_0)
% 155.57/21.78 | | |
% 155.57/21.78 | | | ALPHA: (79) implies:
% 155.57/21.78 | | | (80) ssList(all_146_0)
% 155.57/21.78 | | | (81) $i(all_146_0)
% 155.57/21.78 | | | (82) app(nil, all_146_0) = all_91_2
% 155.57/21.78 | | |
% 155.57/21.78 | | | DELTA: instantiating (67) with fresh symbol all_150_0 gives:
% 155.57/21.78 | | | (83) app(all_116_2, all_150_0) = nil & app(nil, all_116_0) = all_150_0
% 155.57/21.78 | | | & $i(all_150_0)
% 155.57/21.78 | | |
% 155.57/21.78 | | | ALPHA: (83) implies:
% 155.57/21.78 | | | (84) app(nil, all_116_0) = all_150_0
% 155.57/21.78 | | |
% 155.57/21.78 | | | DELTA: instantiating (58) with fresh symbol all_154_0 gives:
% 155.57/21.78 | | | (85) app(all_154_0, nil) = all_91_2 & $i(all_154_0) & ssList(all_154_0)
% 155.57/21.78 | | |
% 155.57/21.78 | | | ALPHA: (85) implies:
% 155.57/21.78 | | | (86) ssList(all_154_0)
% 155.57/21.78 | | | (87) $i(all_154_0)
% 155.57/21.78 | | | (88) app(all_154_0, nil) = all_91_2
% 155.57/21.78 | | |
% 155.57/21.78 | | | REDUCE: (55), (66) imply:
% 155.57/21.78 | | | (89) app(all_116_2, all_116_0) = nil
% 155.57/21.78 | | |
% 155.57/21.78 | | | REDUCE: (62), (66), (72) imply:
% 155.57/21.78 | | | (90) app(all_116_2, nil) = all_132_0
% 155.57/21.78 | | |
% 155.57/21.79 | | | REDUCE: (54), (66) imply:
% 155.57/21.79 | | | (91) app(all_116_2, nil) = all_116_2
% 155.57/21.79 | | |
% 155.57/21.79 | | | REDUCE: (62), (74) imply:
% 155.57/21.79 | | | (92) app(nil, nil) = all_134_0
% 155.57/21.79 | | |
% 155.57/21.79 | | | REDUCE: (48), (62) imply:
% 155.57/21.79 | | | (93) app(nil, nil) = nil
% 155.57/21.79 | | |
% 155.57/21.79 | | | BETA: splitting (63) gives:
% 155.57/21.79 | | |
% 155.57/21.79 | | | Case 1:
% 155.57/21.79 | | | |
% 155.57/21.79 | | | | (94) ~ (app(all_116_2, nil) = all_116_2)
% 155.57/21.79 | | | |
% 155.57/21.79 | | | | PRED_UNIFY: (91), (94) imply:
% 155.57/21.79 | | | | (95) $false
% 155.57/21.79 | | | |
% 155.57/21.79 | | | | CLOSE: (95) is inconsistent.
% 155.57/21.79 | | | |
% 155.57/21.79 | | | Case 2:
% 155.57/21.79 | | | |
% 155.57/21.79 | | | | (96) ? [v0: $i] : (app(all_116_2, v0) = all_116_2 & app(nil, nil) =
% 155.57/21.79 | | | | v0 & $i(v0))
% 155.57/21.79 | | | |
% 155.57/21.79 | | | | DELTA: instantiating (96) with fresh symbol all_182_0 gives:
% 155.57/21.79 | | | | (97) app(all_116_2, all_182_0) = all_116_2 & app(nil, nil) =
% 155.57/21.79 | | | | all_182_0 & $i(all_182_0)
% 155.57/21.79 | | | |
% 155.57/21.79 | | | | ALPHA: (97) implies:
% 155.57/21.79 | | | | (98) app(nil, nil) = all_182_0
% 155.57/21.79 | | | |
% 155.57/21.79 | | | | BETA: splitting (60) gives:
% 155.57/21.79 | | | |
% 155.57/21.79 | | | | Case 1:
% 155.57/21.79 | | | | |
% 155.57/21.79 | | | | | (99) ~ (app(nil, nil) = nil)
% 155.57/21.79 | | | | |
% 155.57/21.79 | | | | | PRED_UNIFY: (93), (99) imply:
% 155.57/21.79 | | | | | (100) $false
% 155.57/21.79 | | | | |
% 155.57/21.79 | | | | | CLOSE: (100) is inconsistent.
% 155.57/21.79 | | | | |
% 155.57/21.79 | | | | Case 2:
% 155.57/21.79 | | | | |
% 155.57/21.79 | | | | | (101) ? [v0: $i] : (app(nil, v0) = nil & app(nil, nil) = v0 &
% 155.57/21.79 | | | | | $i(v0))
% 155.57/21.79 | | | | |
% 155.57/21.79 | | | | | DELTA: instantiating (101) with fresh symbol all_188_0 gives:
% 155.57/21.79 | | | | | (102) app(nil, all_188_0) = nil & app(nil, nil) = all_188_0 &
% 155.57/21.79 | | | | | $i(all_188_0)
% 155.57/21.79 | | | | |
% 155.57/21.79 | | | | | ALPHA: (102) implies:
% 155.57/21.79 | | | | | (103) app(nil, nil) = all_188_0
% 155.57/21.79 | | | | |
% 155.57/21.79 | | | | | BETA: splitting (68) gives:
% 155.57/21.79 | | | | |
% 155.57/21.79 | | | | | Case 1:
% 155.57/21.79 | | | | | |
% 155.57/21.79 | | | | | | (104) ~ (app(all_116_2, all_116_0) = nil)
% 155.57/21.79 | | | | | |
% 155.57/21.79 | | | | | | PRED_UNIFY: (89), (104) imply:
% 155.57/21.79 | | | | | | (105) $false
% 155.57/21.79 | | | | | |
% 155.57/21.79 | | | | | | CLOSE: (105) is inconsistent.
% 155.57/21.79 | | | | | |
% 155.57/21.79 | | | | | Case 2:
% 155.57/21.79 | | | | | |
% 155.57/21.79 | | | | | | (106) all_116_0 = nil
% 155.57/21.79 | | | | | |
% 155.57/21.79 | | | | | | REDUCE: (84), (106) imply:
% 155.57/21.79 | | | | | | (107) app(nil, nil) = all_150_0
% 155.57/21.79 | | | | | |
% 155.57/21.79 | | | | | | BETA: splitting (69) gives:
% 155.57/21.79 | | | | | |
% 155.57/21.79 | | | | | | Case 1:
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | (108) ~ (app(all_116_2, all_116_0) = nil)
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | PRED_UNIFY: (89), (108) imply:
% 155.57/21.79 | | | | | | | (109) $false
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | CLOSE: (109) is inconsistent.
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | Case 2:
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | (110) all_116_2 = nil
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | REDUCE: (90), (110) imply:
% 155.57/21.79 | | | | | | | (111) app(nil, nil) = all_132_0
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | GROUND_INST: instantiating (21) with all_150_0, all_182_0, nil,
% 155.57/21.79 | | | | | | | nil, simplifying with (98), (107) gives:
% 155.57/21.79 | | | | | | | (112) all_182_0 = all_150_0
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | GROUND_INST: instantiating (21) with all_134_0, all_182_0, nil,
% 155.57/21.79 | | | | | | | nil, simplifying with (92), (98) gives:
% 155.57/21.79 | | | | | | | (113) all_182_0 = all_134_0
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | GROUND_INST: instantiating (21) with all_132_0, all_182_0, nil,
% 155.57/21.79 | | | | | | | nil, simplifying with (98), (111) gives:
% 155.57/21.79 | | | | | | | (114) all_182_0 = all_132_0
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | GROUND_INST: instantiating (21) with all_150_0, all_188_0, nil,
% 155.57/21.79 | | | | | | | nil, simplifying with (103), (107) gives:
% 155.57/21.79 | | | | | | | (115) all_188_0 = all_150_0
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | GROUND_INST: instantiating (15) with all_188_0, simplifying with
% 155.57/21.79 | | | | | | | (7), (103) gives:
% 155.57/21.79 | | | | | | | (116) all_188_0 = nil
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | COMBINE_EQS: (115), (116) imply:
% 155.57/21.79 | | | | | | | (117) all_150_0 = nil
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | SIMP: (117) implies:
% 155.57/21.79 | | | | | | | (118) all_150_0 = nil
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | COMBINE_EQS: (112), (113) imply:
% 155.57/21.79 | | | | | | | (119) all_150_0 = all_134_0
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | SIMP: (119) implies:
% 155.57/21.79 | | | | | | | (120) all_150_0 = all_134_0
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | COMBINE_EQS: (113), (114) imply:
% 155.57/21.79 | | | | | | | (121) all_134_0 = all_132_0
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | COMBINE_EQS: (118), (120) imply:
% 155.57/21.79 | | | | | | | (122) all_134_0 = nil
% 155.57/21.79 | | | | | | |
% 155.57/21.79 | | | | | | | SIMP: (122) implies:
% 155.57/21.79 | | | | | | | (123) all_134_0 = nil
% 155.57/21.79 | | | | | | |
% 155.57/21.80 | | | | | | | COMBINE_EQS: (121), (123) imply:
% 155.57/21.80 | | | | | | | (124) all_132_0 = nil
% 155.57/21.80 | | | | | | |
% 155.57/21.80 | | | | | | | SIMP: (124) implies:
% 155.57/21.80 | | | | | | | (125) all_132_0 = nil
% 155.57/21.80 | | | | | | |
% 155.57/21.80 | | | | | | | GROUND_INST: instantiating (6) with all_154_0, nil, simplifying
% 155.57/21.80 | | | | | | | with (7), (19), (86), (87) gives:
% 155.57/21.80 | | | | | | | (126) all_154_0 = nil | neq(all_154_0, nil)
% 155.57/21.80 | | | | | | |
% 155.57/21.80 | | | | | | | GROUND_INST: instantiating (8) with all_146_0, all_91_2,
% 155.57/21.80 | | | | | | | simplifying with (80), (81), (82) gives:
% 155.57/21.80 | | | | | | | (127) all_146_0 = all_91_2
% 155.57/21.80 | | | | | | |
% 155.57/21.80 | | | | | | | GROUND_INST: instantiating (5) with all_91_1, all_146_0, nil,
% 155.57/21.80 | | | | | | | all_91_2, all_140_0, simplifying with (7), (19),
% 155.57/21.80 | | | | | | | (25), (28), (76), (77), (78), (80), (81), (82) gives:
% 155.57/21.80 | | | | | | | (128) segmentP(all_91_1, all_146_0)
% 155.57/21.80 | | | | | | |
% 155.57/21.80 | | | | | | | GROUND_INST: instantiating (18) with all_154_0, all_91_2,
% 155.57/21.80 | | | | | | | simplifying with (86), (87), (88) gives:
% 155.57/21.80 | | | | | | | (129) all_154_0 = all_91_2
% 155.57/21.80 | | | | | | |
% 155.57/21.80 | | | | | | | REDUCE: (127), (128) imply:
% 155.57/21.80 | | | | | | | (130) segmentP(all_91_1, all_91_2)
% 155.57/21.80 | | | | | | |
% 155.57/21.80 | | | | | | | BETA: splitting (59) gives:
% 155.57/21.80 | | | | | | |
% 155.57/21.80 | | | | | | | Case 1:
% 155.57/21.80 | | | | | | | |
% 155.57/21.80 | | | | | | | | (131) ~ neq(all_91_2, nil)
% 155.57/21.80 | | | | | | | |
% 155.57/21.80 | | | | | | | | BETA: splitting (126) gives:
% 155.57/21.80 | | | | | | | |
% 155.57/21.80 | | | | | | | | Case 1:
% 155.57/21.80 | | | | | | | | |
% 155.57/21.80 | | | | | | | | | (132) neq(all_154_0, nil)
% 155.57/21.80 | | | | | | | | |
% 155.57/21.80 | | | | | | | | | REDUCE: (129), (132) imply:
% 155.57/21.80 | | | | | | | | | (133) neq(all_91_2, nil)
% 155.57/21.80 | | | | | | | | |
% 155.57/21.80 | | | | | | | | | PRED_UNIFY: (131), (133) imply:
% 155.57/21.80 | | | | | | | | | (134) $false
% 155.57/21.80 | | | | | | | | |
% 155.57/21.80 | | | | | | | | | CLOSE: (134) is inconsistent.
% 155.57/21.80 | | | | | | | | |
% 155.57/21.80 | | | | | | | | Case 2:
% 155.57/21.80 | | | | | | | | |
% 155.57/21.80 | | | | | | | | | (135) all_154_0 = nil
% 155.57/21.80 | | | | | | | | |
% 155.57/21.80 | | | | | | | | | COMBINE_EQS: (129), (135) imply:
% 155.57/21.80 | | | | | | | | | (136) all_91_2 = nil
% 155.57/21.80 | | | | | | | | |
% 155.57/21.80 | | | | | | | | | REDUCE: (131), (136) imply:
% 155.57/21.80 | | | | | | | | | (137) ~ neq(nil, nil)
% 155.57/21.80 | | | | | | | | |
% 155.57/21.80 | | | | | | | | | BETA: splitting (31) gives:
% 155.57/21.80 | | | | | | | | |
% 155.57/21.80 | | | | | | | | | Case 1:
% 155.57/21.80 | | | | | | | | | |
% 155.57/21.80 | | | | | | | | | | (138) ~ (all_91_2 = nil)
% 155.57/21.80 | | | | | | | | | |
% 155.57/21.80 | | | | | | | | | | REDUCE: (136), (138) imply:
% 155.57/21.80 | | | | | | | | | | (139) $false
% 155.57/21.80 | | | | | | | | | |
% 155.57/21.80 | | | | | | | | | | CLOSE: (139) is inconsistent.
% 155.57/21.80 | | | | | | | | | |
% 155.57/21.80 | | | | | | | | | Case 2:
% 155.57/21.80 | | | | | | | | | |
% 155.57/21.80 | | | | | | | | | | (140) all_91_1 = nil
% 155.57/21.80 | | | | | | | | | |
% 155.57/21.80 | | | | | | | | | | REDUCE: (23), (140) imply:
% 155.57/21.80 | | | | | | | | | | (141) neq(nil, nil)
% 155.57/21.80 | | | | | | | | | |
% 155.57/21.80 | | | | | | | | | | PRED_UNIFY: (137), (141) imply:
% 155.57/21.80 | | | | | | | | | | (142) $false
% 155.57/21.80 | | | | | | | | | |
% 155.57/21.80 | | | | | | | | | | CLOSE: (142) is inconsistent.
% 155.57/21.80 | | | | | | | | | |
% 155.57/21.80 | | | | | | | | | End of split
% 155.57/21.80 | | | | | | | | |
% 155.57/21.80 | | | | | | | | End of split
% 155.57/21.80 | | | | | | | |
% 155.57/21.80 | | | | | | | Case 2:
% 155.57/21.80 | | | | | | | |
% 155.57/21.80 | | | | | | | | (143) ~ segmentP(all_91_1, all_91_2)
% 155.57/21.80 | | | | | | | |
% 155.57/21.80 | | | | | | | | PRED_UNIFY: (130), (143) imply:
% 155.57/21.80 | | | | | | | | (144) $false
% 155.57/21.80 | | | | | | | |
% 155.57/21.80 | | | | | | | | CLOSE: (144) is inconsistent.
% 155.57/21.80 | | | | | | | |
% 155.57/21.80 | | | | | | | End of split
% 155.57/21.80 | | | | | | |
% 155.57/21.81 | | | | | | End of split
% 155.57/21.81 | | | | | |
% 155.57/21.81 | | | | | End of split
% 155.57/21.81 | | | | |
% 155.57/21.81 | | | | End of split
% 155.57/21.81 | | | |
% 155.57/21.81 | | | End of split
% 155.57/21.81 | | |
% 155.57/21.81 | | End of split
% 155.57/21.81 | |
% 155.57/21.81 | End of split
% 155.57/21.81 |
% 155.57/21.81 End of proof
% 155.57/21.81 % SZS output end Proof for theBenchmark
% 155.57/21.81
% 155.57/21.81 21190ms
%------------------------------------------------------------------------------