TSTP Solution File: SWC068+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC068+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 : n025.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 119.29s 16.44s
% Output : Proof 289.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC068+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.33 % Computer : n025.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon Aug 28 17:27:54 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 4.95/1.43 Prover 4: Preprocessing ...
% 4.95/1.44 Prover 1: Preprocessing ...
% 5.84/1.51 Prover 0: Preprocessing ...
% 5.84/1.51 Prover 2: Preprocessing ...
% 5.84/1.51 Prover 3: Preprocessing ...
% 5.84/1.51 Prover 6: Preprocessing ...
% 5.84/1.51 Prover 5: Preprocessing ...
% 15.99/2.92 Prover 2: Proving ...
% 16.69/2.97 Prover 5: Constructing countermodel ...
% 16.69/2.98 Prover 1: Constructing countermodel ...
% 17.00/2.99 Prover 6: Proving ...
% 17.00/3.03 Prover 3: Constructing countermodel ...
% 22.75/3.78 Prover 0: Proving ...
% 23.65/3.87 Prover 4: Constructing countermodel ...
% 72.24/10.32 Prover 2: stopped
% 72.24/10.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.54/10.51 Prover 7: Preprocessing ...
% 75.44/10.65 Prover 7: Constructing countermodel ...
% 77.09/10.84 Prover 3: gave up
% 77.09/10.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 77.72/10.96 Prover 8: Preprocessing ...
% 79.03/11.17 Prover 8: Warning: ignoring some quantifiers
% 79.03/11.17 Prover 8: Constructing countermodel ...
% 100.57/13.95 Prover 5: stopped
% 100.57/13.95 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 100.57/14.04 Prover 9: Preprocessing ...
% 108.42/14.96 Prover 9: Constructing countermodel ...
% 116.15/15.97 Prover 1: stopped
% 116.15/15.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 116.81/16.12 Prover 10: Preprocessing ...
% 116.81/16.22 Prover 10: Constructing countermodel ...
% 119.29/16.42 Prover 9: proved (2468ms)
% 119.29/16.44
% 119.29/16.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 119.29/16.44
% 119.29/16.44 Prover 0: stopped
% 119.29/16.45 Prover 6: stopped
% 119.79/16.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 119.79/16.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 119.79/16.47 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 120.12/16.53 Prover 11: Preprocessing ...
% 120.36/16.55 Prover 16: Preprocessing ...
% 121.07/16.63 Prover 13: Preprocessing ...
% 121.07/16.67 Prover 16: Constructing countermodel ...
% 122.13/16.77 Prover 13: Constructing countermodel ...
% 125.39/17.26 Prover 11: Constructing countermodel ...
% 146.48/20.06 Prover 13: stopped
% 146.48/20.06 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 147.43/20.16 Prover 19: Preprocessing ...
% 150.83/20.63 Prover 16: stopped
% 150.83/20.66 Prover 19: Warning: ignoring some quantifiers
% 151.24/20.69 Prover 19: Constructing countermodel ...
% 168.50/23.21 Prover 19: stopped
% 195.71/27.96 Prover 4: stopped
% 204.14/29.85 Prover 7: stopped
% 250.92/42.63 Prover 8: stopped
% 253.50/43.73 Prover 11: stopped
% 287.55/71.59 Prover 10: Found proof (size 400)
% 287.55/71.59 Prover 10: proved (55609ms)
% 287.55/71.59
% 287.55/71.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 287.55/71.59
% 288.04/71.80 % SZS output start Proof for theBenchmark
% 288.04/71.81 Assumptions after simplification:
% 288.04/71.81 ---------------------------------
% 288.04/71.81
% 288.04/71.81 (ax15)
% 288.04/71.81 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) |
% 288.04/71.81 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~
% 288.04/71.81 neq(v0, v0))
% 288.04/71.81
% 288.04/71.82 (ax17)
% 288.04/71.82 $i(nil) & ssList(nil)
% 288.04/71.82
% 288.04/71.82 (ax26)
% 288.04/71.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) |
% 288.04/71.84 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 288.04/71.84
% 288.04/71.84 (ax28)
% 288.04/71.84 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 288.04/71.84 $i(v0) | ~ ssList(v0))
% 288.04/71.84
% 288.04/71.84 (ax42)
% 288.04/71.85 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0))
% 288.04/71.85
% 288.04/71.85 (ax45)
% 288.04/71.85 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 288.04/71.85
% 288.04/71.85 (ax46)
% 288.04/71.85 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 288.04/71.85 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 288.04/71.85
% 288.04/71.85 (ax49)
% 288.04/71.85 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, v0))
% 288.04/71.85
% 288.04/71.85 (ax5)
% 288.04/71.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 288.04/71.85 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 288.04/71.85 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 288.04/71.85 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 288.04/71.85 v2) = v0 & $i(v2) & ssList(v2)))
% 288.04/71.85
% 288.04/71.85 (ax50)
% 288.04/71.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2, v0) = v3)
% 288.04/71.85 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, v1) | ~ ssList(v2) |
% 288.04/71.85 ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1))
% 288.04/71.85
% 288.04/71.85 (ax51)
% 288.04/71.85 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 288.04/71.85
% 288.04/71.85 (ax52)
% 288.04/71.85 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~
% 288.04/71.85 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 288.04/71.85
% 288.04/71.85 (ax56)
% 288.04/71.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 288.04/71.86 $i] : ( ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ~ $i(v4) | ~ $i(v2)
% 288.04/71.86 | ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v4) | ~
% 288.04/71.86 ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v5, v1))
% 288.04/71.86
% 288.04/71.86 (ax57)
% 288.04/71.86 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil))
% 288.04/71.86
% 288.04/71.86 (ax58)
% 288.04/71.86 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 288.04/71.86 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 288.04/71.86
% 288.04/71.86 (ax6)
% 288.04/71.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 288.04/71.86 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 288.04/71.86 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 288.04/71.86 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 288.04/71.86 v1) = v0 & $i(v2) & ssList(v2)))
% 288.04/71.86
% 288.04/71.86 (ax7)
% 288.04/71.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 288.04/71.86 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 288.04/71.86 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 288.04/71.86 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 288.04/71.86 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 288.04/71.86 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 288.04/71.86 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 288.04/71.86
% 288.04/71.86 (ax79)
% 288.04/71.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v3,
% 288.04/71.87 v1) = v2) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 288.04/71.87 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 288.04/71.87
% 288.04/71.87 (ax80)
% 288.04/71.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v1,
% 288.04/71.87 v3) = v2) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 288.04/71.87 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 288.04/71.87
% 288.04/71.87 (ax82)
% 288.04/71.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 288.04/71.87 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 288.04/71.87 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 288.04/71.87 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 288.04/71.87
% 288.04/71.87 (ax83)
% 288.04/71.87 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 288.04/71.87 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 288.04/71.87 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 288.04/71.87 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 288.04/71.87 v0) | ~ ssList(nil))
% 288.04/71.87
% 288.04/71.87 (ax84)
% 288.04/71.87 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 288.04/71.87 $i(v0) | ~ ssList(v0))
% 288.04/71.87
% 288.04/71.87 (co1)
% 288.04/71.88 $i(nil) & ? [v0: $i] : ? [v1: $i] : (app(v1, v1) = v0 & $i(v1) & $i(v0) &
% 288.04/71.88 ssList(v1) & ssList(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ segmentP(v1, v2) |
% 288.04/71.88 ~ segmentP(v0, v2) | ~ ssList(v2) | ~ neq(v2, nil)) & ( ~ (v1 = nil) |
% 288.04/71.88 ~ (v0 = nil)))
% 288.04/71.88
% 288.04/71.88 (function-axioms)
% 288.04/71.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 288.04/71.88 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 288.04/71.88 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 288.04/71.88 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 288.04/71.88 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 288.04/71.88 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 288.04/71.88
% 288.04/71.88 Further assumptions not needed in the proof:
% 288.04/71.88 --------------------------------------------
% 288.04/71.88 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 288.04/71.88 ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36,
% 288.04/71.88 ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax47, ax48, ax53, ax54, ax55,
% 288.04/71.88 ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax70, ax71,
% 288.04/71.88 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax8, ax81, ax85, ax86, ax87, ax88,
% 288.04/71.88 ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 288.04/71.88
% 288.04/71.88 Those formulas are unsatisfiable:
% 288.04/71.88 ---------------------------------
% 288.04/71.88
% 288.04/71.88 Begin of proof
% 288.04/71.88 |
% 288.04/71.88 | ALPHA: (ax5) implies:
% 288.04/71.88 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 288.04/71.88 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 288.04/71.88 | v0 & $i(v2) & ssList(v2)))
% 288.04/71.89 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~
% 288.04/71.89 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~
% 288.04/71.89 | ssList(v0) | frontsegP(v0, v1))
% 288.04/71.89 |
% 288.04/71.89 | ALPHA: (ax6) implies:
% 288.04/71.89 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 288.04/71.89 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 288.04/71.89 | v0 & $i(v2) & ssList(v2)))
% 288.04/71.89 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~
% 288.04/71.89 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~
% 288.04/71.89 | ssList(v0) | rearsegP(v0, v1))
% 288.04/71.89 |
% 288.04/71.89 | ALPHA: (ax7) implies:
% 288.04/71.89 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0,
% 288.04/71.89 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] :
% 288.04/71.89 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) &
% 288.04/71.89 | $i(v2) & ssList(v4) & ssList(v2)))
% 288.04/71.89 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 288.04/71.89 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2)
% 288.04/71.89 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~
% 288.04/71.89 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 288.04/71.89 |
% 288.04/71.89 | ALPHA: (ax15) implies:
% 288.04/71.89 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 288.04/71.89 | ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 288.04/71.89 |
% 288.04/71.89 | ALPHA: (ax17) implies:
% 288.04/71.89 | (8) ssList(nil)
% 288.04/71.89 |
% 288.04/71.89 | ALPHA: (ax28) implies:
% 288.04/71.89 | (9) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 288.04/71.89 | $i(v0) | ~ ssList(v0))
% 288.04/71.89 |
% 288.04/71.89 | ALPHA: (ax45) implies:
% 288.04/71.89 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 288.04/71.89 |
% 288.04/71.89 | ALPHA: (ax46) implies:
% 288.04/71.90 | (11) ~ ssList(nil) | frontsegP(nil, nil)
% 288.04/71.90 |
% 288.04/71.90 | ALPHA: (ax51) implies:
% 288.04/71.90 | (12) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 288.04/71.90 |
% 288.04/71.90 | ALPHA: (ax52) implies:
% 288.04/71.90 | (13) ~ ssList(nil) | rearsegP(nil, nil)
% 288.04/71.90 |
% 288.04/71.90 | ALPHA: (ax57) implies:
% 288.04/71.90 | (14) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil))
% 288.04/71.90 |
% 288.04/71.90 | ALPHA: (ax58) implies:
% 288.04/71.90 | (15) ~ ssList(nil) | segmentP(nil, nil)
% 288.04/71.90 |
% 288.04/71.90 | ALPHA: (ax83) implies:
% 288.04/71.90 | (16) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 288.04/71.90 | (17) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~
% 288.04/71.90 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 288.04/71.90 | (18) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 288.04/71.90 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 288.04/71.90 |
% 288.04/71.90 | ALPHA: (ax84) implies:
% 288.04/71.90 | (19) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 288.04/71.90 | $i(v0) | ~ ssList(v0))
% 288.04/71.90 |
% 288.04/71.90 | ALPHA: (co1) implies:
% 288.04/71.90 | (20) $i(nil)
% 288.04/71.90 | (21) ? [v0: $i] : ? [v1: $i] : (app(v1, v1) = v0 & $i(v1) & $i(v0) &
% 288.04/71.90 | ssList(v1) & ssList(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ segmentP(v1,
% 288.04/71.90 | v2) | ~ segmentP(v0, v2) | ~ ssList(v2) | ~ neq(v2, nil)) & (
% 288.04/71.90 | ~ (v1 = nil) | ~ (v0 = nil)))
% 288.04/71.90 |
% 288.04/71.90 | ALPHA: (function-axioms) implies:
% 288.04/71.90 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 288.04/71.90 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 288.04/71.90 |
% 288.04/71.90 | DELTA: instantiating (21) with fresh symbols all_91_0, all_91_1 gives:
% 288.04/71.90 | (23) app(all_91_0, all_91_0) = all_91_1 & $i(all_91_0) & $i(all_91_1) &
% 288.04/71.90 | ssList(all_91_0) & ssList(all_91_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 288.04/71.90 | segmentP(all_91_0, v0) | ~ segmentP(all_91_1, v0) | ~ ssList(v0) |
% 288.04/71.90 | ~ neq(v0, nil)) & ( ~ (all_91_0 = nil) | ~ (all_91_1 = nil))
% 288.04/71.90 |
% 288.04/71.90 | ALPHA: (23) implies:
% 288.04/71.90 | (24) ssList(all_91_1)
% 288.04/71.90 | (25) ssList(all_91_0)
% 288.04/71.90 | (26) $i(all_91_1)
% 288.04/71.91 | (27) $i(all_91_0)
% 288.04/71.91 | (28) app(all_91_0, all_91_0) = all_91_1
% 288.04/71.91 | (29) ~ (all_91_0 = nil) | ~ (all_91_1 = nil)
% 288.04/71.91 | (30) ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_0, v0) | ~
% 288.04/71.91 | segmentP(all_91_1, v0) | ~ ssList(v0) | ~ neq(v0, nil))
% 288.04/71.91 |
% 288.04/71.91 | BETA: splitting (13) gives:
% 288.04/71.91 |
% 288.04/71.91 | Case 1:
% 288.04/71.91 | |
% 288.04/71.91 | | (31) ~ ssList(nil)
% 288.04/71.91 | |
% 288.04/71.91 | | PRED_UNIFY: (8), (31) imply:
% 288.04/71.91 | | (32) $false
% 288.04/71.91 | |
% 288.04/71.91 | | CLOSE: (32) is inconsistent.
% 288.04/71.91 | |
% 288.04/71.91 | Case 2:
% 288.04/71.91 | |
% 288.04/71.91 | | (33) rearsegP(nil, nil)
% 288.04/71.91 | |
% 288.04/71.91 | | BETA: splitting (11) gives:
% 288.04/71.91 | |
% 288.04/71.91 | | Case 1:
% 288.04/71.91 | | |
% 288.04/71.91 | | | (34) ~ ssList(nil)
% 288.04/71.91 | | |
% 288.04/71.91 | | | PRED_UNIFY: (8), (34) imply:
% 288.04/71.91 | | | (35) $false
% 288.04/71.91 | | |
% 288.04/71.91 | | | CLOSE: (35) is inconsistent.
% 288.04/71.91 | | |
% 288.04/71.91 | | Case 2:
% 288.04/71.91 | | |
% 288.04/71.91 | | | (36) frontsegP(nil, nil)
% 288.04/71.91 | | |
% 288.04/71.91 | | | BETA: splitting (15) gives:
% 288.04/71.91 | | |
% 288.04/71.91 | | | Case 1:
% 288.04/71.91 | | | |
% 288.04/71.91 | | | | (37) ~ ssList(nil)
% 288.04/71.91 | | | |
% 288.04/71.91 | | | | PRED_UNIFY: (8), (37) imply:
% 288.04/71.91 | | | | (38) $false
% 288.04/71.91 | | | |
% 288.04/71.91 | | | | CLOSE: (38) is inconsistent.
% 288.04/71.91 | | | |
% 288.04/71.91 | | | Case 2:
% 288.04/71.91 | | | |
% 288.04/71.91 | | | | (39) segmentP(nil, nil)
% 288.04/71.91 | | | |
% 288.04/71.91 | | | | GROUND_INST: instantiating (ax49) with all_91_1, simplifying with (24),
% 288.04/71.91 | | | | (26) gives:
% 288.04/71.91 | | | | (40) rearsegP(all_91_1, all_91_1)
% 288.04/71.91 | | | |
% 288.04/71.91 | | | | GROUND_INST: instantiating (12) with all_91_1, simplifying with (24),
% 288.04/71.91 | | | | (26) gives:
% 288.04/71.92 | | | | (41) rearsegP(all_91_1, nil)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (ax42) with all_91_1, simplifying with (24),
% 288.04/71.92 | | | | (26) gives:
% 288.04/71.92 | | | | (42) frontsegP(all_91_1, all_91_1)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (10) with all_91_1, simplifying with (24),
% 288.04/71.92 | | | | (26) gives:
% 288.04/71.92 | | | | (43) frontsegP(all_91_1, nil)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (7) with all_91_0, nil, simplifying with (8),
% 288.04/71.92 | | | | (20), (25), (27) gives:
% 288.04/71.92 | | | | (44) all_91_0 = nil | neq(all_91_0, nil)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (14) with all_91_0, simplifying with (25),
% 288.04/71.92 | | | | (27) gives:
% 288.04/71.92 | | | | (45) segmentP(all_91_0, nil)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (ax49) with all_91_0, simplifying with (25),
% 288.04/71.92 | | | | (27) gives:
% 288.04/71.92 | | | | (46) rearsegP(all_91_0, all_91_0)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (12) with all_91_0, simplifying with (25),
% 288.04/71.92 | | | | (27) gives:
% 288.04/71.92 | | | | (47) rearsegP(all_91_0, nil)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (ax42) with all_91_0, simplifying with (25),
% 288.04/71.92 | | | | (27) gives:
% 288.04/71.92 | | | | (48) frontsegP(all_91_0, all_91_0)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (10) with all_91_0, simplifying with (25),
% 288.04/71.92 | | | | (27) gives:
% 288.04/71.92 | | | | (49) frontsegP(all_91_0, nil)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (8),
% 288.04/71.92 | | | | (20), (36) gives:
% 288.04/71.92 | | | | (50) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (5) with nil, nil, simplifying with (8),
% 288.04/71.92 | | | | (20), (39) gives:
% 288.04/71.92 | | | | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil &
% 288.04/71.92 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) &
% 288.04/71.92 | | | | ssList(v0))
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (2) with all_91_1, all_91_0, all_91_0,
% 288.04/71.92 | | | | simplifying with (24), (25), (26), (27), (28) gives:
% 288.04/71.92 | | | | (52) frontsegP(all_91_1, all_91_0)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (4) with all_91_1, all_91_0, all_91_0,
% 288.04/71.92 | | | | simplifying with (24), (25), (26), (27), (28) gives:
% 288.04/71.92 | | | | (53) rearsegP(all_91_1, all_91_0)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | DELTA: instantiating (50) with fresh symbol all_112_0 gives:
% 288.04/71.92 | | | | (54) app(nil, all_112_0) = nil & $i(all_112_0) & ssList(all_112_0)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | ALPHA: (54) implies:
% 288.04/71.92 | | | | (55) ssList(all_112_0)
% 288.04/71.92 | | | | (56) $i(all_112_0)
% 288.04/71.92 | | | | (57) app(nil, all_112_0) = nil
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | DELTA: instantiating (51) with fresh symbols all_116_0, all_116_1,
% 288.04/71.92 | | | | all_116_2 gives:
% 288.04/71.92 | | | | (58) app(all_116_1, all_116_0) = nil & app(all_116_2, nil) =
% 288.04/71.92 | | | | all_116_1 & $i(all_116_0) & $i(all_116_1) & $i(all_116_2) &
% 288.04/71.92 | | | | ssList(all_116_0) & ssList(all_116_2)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | ALPHA: (58) implies:
% 288.04/71.92 | | | | (59) ssList(all_116_2)
% 288.04/71.92 | | | | (60) ssList(all_116_0)
% 288.04/71.92 | | | | (61) $i(all_116_2)
% 288.04/71.92 | | | | (62) $i(all_116_1)
% 288.04/71.92 | | | | (63) $i(all_116_0)
% 288.04/71.92 | | | | (64) app(all_116_2, nil) = all_116_1
% 288.04/71.92 | | | | (65) app(all_116_1, all_116_0) = nil
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (ax49) with all_116_2, simplifying with (59),
% 288.04/71.92 | | | | (61) gives:
% 288.04/71.92 | | | | (66) rearsegP(all_116_2, all_116_2)
% 288.04/71.92 | | | |
% 288.04/71.92 | | | | GROUND_INST: instantiating (ax42) with all_116_2, simplifying with (59),
% 288.04/71.93 | | | | (61) gives:
% 288.04/71.93 | | | | (67) frontsegP(all_116_2, all_116_2)
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (10) with all_116_2, simplifying with (59),
% 288.04/71.93 | | | | (61) gives:
% 288.04/71.93 | | | | (68) frontsegP(all_116_2, nil)
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (ax49) with all_116_0, simplifying with (60),
% 288.04/71.93 | | | | (63) gives:
% 288.04/71.93 | | | | (69) rearsegP(all_116_0, all_116_0)
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (12) with all_116_0, simplifying with (60),
% 288.04/71.93 | | | | (63) gives:
% 288.04/71.93 | | | | (70) rearsegP(all_116_0, nil)
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (ax42) with all_116_0, simplifying with (60),
% 288.04/71.93 | | | | (63) gives:
% 288.04/71.93 | | | | (71) frontsegP(all_116_0, all_116_0)
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (10) with all_116_0, simplifying with (60),
% 288.04/71.93 | | | | (63) gives:
% 288.04/71.93 | | | | (72) frontsegP(all_116_0, nil)
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (1) with all_91_1, nil, simplifying with (8),
% 288.04/71.93 | | | | (20), (24), (26), (43) gives:
% 288.04/71.93 | | | | (73) ? [v0: $i] : (app(nil, v0) = all_91_1 & $i(v0) & ssList(v0))
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (1) with all_91_1, all_91_1, simplifying with
% 288.04/71.93 | | | | (24), (26), (42) gives:
% 288.04/71.93 | | | | (74) ? [v0: $i] : (app(all_91_1, v0) = all_91_1 & $i(v0) &
% 288.04/71.93 | | | | ssList(v0))
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (1) with all_91_1, all_91_0, simplifying with
% 288.04/71.93 | | | | (24), (25), (26), (27), (52) gives:
% 288.04/71.93 | | | | (75) ? [v0: $i] : (app(all_91_0, v0) = all_91_1 & $i(v0) &
% 288.04/71.93 | | | | ssList(v0))
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (1) with all_91_0, nil, simplifying with (8),
% 288.04/71.93 | | | | (20), (25), (27), (49) gives:
% 288.04/71.93 | | | | (76) ? [v0: $i] : (app(nil, v0) = all_91_0 & $i(v0) & ssList(v0))
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (1) with all_91_0, all_91_0, simplifying with
% 288.04/71.93 | | | | (25), (27), (48) gives:
% 288.04/71.93 | | | | (77) ? [v0: $i] : (app(all_91_0, v0) = all_91_0 & $i(v0) &
% 288.04/71.93 | | | | ssList(v0))
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (3) with all_91_1, nil, simplifying with (8),
% 288.04/71.93 | | | | (20), (24), (26), (41) gives:
% 288.04/71.93 | | | | (78) ? [v0: $i] : (app(v0, nil) = all_91_1 & $i(v0) & ssList(v0))
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (3) with all_91_1, all_91_1, simplifying with
% 288.04/71.93 | | | | (24), (26), (40) gives:
% 288.04/71.93 | | | | (79) ? [v0: $i] : (app(v0, all_91_1) = all_91_1 & $i(v0) &
% 288.04/71.93 | | | | ssList(v0))
% 288.04/71.93 | | | |
% 288.04/71.93 | | | | GROUND_INST: instantiating (3) with all_91_1, all_91_0, simplifying with
% 288.04/71.93 | | | | (24), (25), (26), (27), (53) gives:
% 288.04/71.93 | | | | (80) ? [v0: $i] : (app(v0, all_91_0) = all_91_1 & $i(v0) &
% 288.04/71.93 | | | | ssList(v0))
% 288.04/71.93 | | | |
% 288.04/71.94 | | | | GROUND_INST: instantiating (3) with all_91_0, nil, simplifying with (8),
% 288.04/71.94 | | | | (20), (25), (27), (47) gives:
% 288.04/71.94 | | | | (81) ? [v0: $i] : (app(v0, nil) = all_91_0 & $i(v0) & ssList(v0))
% 288.04/71.94 | | | |
% 288.04/71.94 | | | | GROUND_INST: instantiating (3) with all_91_0, all_91_0, simplifying with
% 288.04/71.94 | | | | (25), (27), (46) gives:
% 288.04/71.94 | | | | (82) ? [v0: $i] : (app(v0, all_91_0) = all_91_0 & $i(v0) &
% 288.04/71.94 | | | | ssList(v0))
% 288.04/71.94 | | | |
% 288.04/71.94 | | | | GROUND_INST: instantiating (5) with all_91_0, nil, simplifying with (8),
% 288.04/71.94 | | | | (20), (25), (27), (45) gives:
% 288.04/71.94 | | | | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) =
% 288.04/71.94 | | | | all_91_0 & app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 288.04/71.94 | | | | ssList(v2) & ssList(v0))
% 288.04/71.94 | | | |
% 288.04/71.94 | | | | GROUND_INST: instantiating (ax82) with nil, all_112_0, nil, all_112_0,
% 288.04/71.94 | | | | nil, simplifying with (8), (20), (55), (56), (57) gives:
% 288.04/71.94 | | | | (84) ? [v0: $i] : (app(all_112_0, all_112_0) = v0 & app(nil, v0) =
% 288.04/71.94 | | | | nil & $i(v0))
% 288.04/71.94 | | | |
% 288.04/71.94 | | | | GROUND_INST: instantiating (9) with all_112_0, nil, simplifying with
% 288.04/71.94 | | | | (55), (56), (57) gives:
% 288.04/71.94 | | | | (85) all_112_0 = nil
% 288.04/71.94 | | | |
% 288.04/71.94 | | | | GROUND_INST: instantiating (ax50) with nil, nil, all_116_2, all_116_1,
% 288.04/71.94 | | | | simplifying with (8), (20), (33), (59), (61), (64) gives:
% 288.04/71.94 | | | | (86) rearsegP(all_116_1, nil)
% 288.04/71.94 | | | |
% 288.04/71.94 | | | | GROUND_INST: instantiating (ax26) with all_116_2, nil, all_116_1,
% 288.04/71.94 | | | | simplifying with (8), (20), (59), (61), (64) gives:
% 288.04/71.94 | | | | (87) ssList(all_116_1)
% 288.04/71.94 | | | |
% 288.04/71.94 | | | | GROUND_INST: instantiating (19) with all_116_2, all_116_1, simplifying
% 288.04/71.94 | | | | with (59), (61), (64) gives:
% 288.04/71.94 | | | | (88) all_116_1 = all_116_2
% 288.04/71.94 | | | |
% 288.74/71.94 | | | | GROUND_INST: instantiating (ax82) with all_116_2, nil, all_116_1,
% 288.74/71.94 | | | | all_116_0, nil, simplifying with (8), (20), (59), (60),
% 288.74/71.94 | | | | (61), (63), (64), (65) gives:
% 288.74/71.94 | | | | (89) ? [v0: $i] : (app(all_116_2, v0) = nil & app(nil, all_116_0) =
% 288.74/71.94 | | | | v0 & $i(v0))
% 288.74/71.94 | | | |
% 288.74/71.94 | | | | DELTA: instantiating (76) with fresh symbol all_132_0 gives:
% 288.74/71.94 | | | | (90) app(nil, all_132_0) = all_91_0 & $i(all_132_0) &
% 288.74/71.94 | | | | ssList(all_132_0)
% 288.74/71.94 | | | |
% 288.74/71.94 | | | | ALPHA: (90) implies:
% 288.74/71.94 | | | | (91) ssList(all_132_0)
% 288.74/71.94 | | | | (92) $i(all_132_0)
% 288.74/71.94 | | | | (93) app(nil, all_132_0) = all_91_0
% 288.74/71.94 | | | |
% 288.74/71.94 | | | | DELTA: instantiating (75) with fresh symbol all_134_0 gives:
% 288.74/71.94 | | | | (94) app(all_91_0, all_134_0) = all_91_1 & $i(all_134_0) &
% 288.74/71.94 | | | | ssList(all_134_0)
% 288.74/71.94 | | | |
% 288.74/71.94 | | | | ALPHA: (94) implies:
% 288.74/71.94 | | | | (95) ssList(all_134_0)
% 288.74/71.94 | | | | (96) $i(all_134_0)
% 288.74/71.94 | | | | (97) app(all_91_0, all_134_0) = all_91_1
% 288.74/71.94 | | | |
% 288.74/71.94 | | | | DELTA: instantiating (82) with fresh symbol all_136_0 gives:
% 288.74/71.95 | | | | (98) app(all_136_0, all_91_0) = all_91_0 & $i(all_136_0) &
% 288.74/71.95 | | | | ssList(all_136_0)
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | ALPHA: (98) implies:
% 288.74/71.95 | | | | (99) ssList(all_136_0)
% 288.74/71.95 | | | | (100) $i(all_136_0)
% 288.74/71.95 | | | | (101) app(all_136_0, all_91_0) = all_91_0
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | DELTA: instantiating (84) with fresh symbol all_138_0 gives:
% 288.74/71.95 | | | | (102) app(all_112_0, all_112_0) = all_138_0 & app(nil, all_138_0) =
% 288.74/71.95 | | | | nil & $i(all_138_0)
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | ALPHA: (102) implies:
% 288.74/71.95 | | | | (103) $i(all_138_0)
% 288.74/71.95 | | | | (104) app(all_112_0, all_112_0) = all_138_0
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | DELTA: instantiating (89) with fresh symbol all_140_0 gives:
% 288.74/71.95 | | | | (105) app(all_116_2, all_140_0) = nil & app(nil, all_116_0) =
% 288.74/71.95 | | | | all_140_0 & $i(all_140_0)
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | ALPHA: (105) implies:
% 288.74/71.95 | | | | (106) app(nil, all_116_0) = all_140_0
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | DELTA: instantiating (81) with fresh symbol all_142_0 gives:
% 288.74/71.95 | | | | (107) app(all_142_0, nil) = all_91_0 & $i(all_142_0) &
% 288.74/71.95 | | | | ssList(all_142_0)
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | ALPHA: (107) implies:
% 288.74/71.95 | | | | (108) ssList(all_142_0)
% 288.74/71.95 | | | | (109) $i(all_142_0)
% 288.74/71.95 | | | | (110) app(all_142_0, nil) = all_91_0
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | DELTA: instantiating (74) with fresh symbol all_144_0 gives:
% 288.74/71.95 | | | | (111) app(all_91_1, all_144_0) = all_91_1 & $i(all_144_0) &
% 288.74/71.95 | | | | ssList(all_144_0)
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | ALPHA: (111) implies:
% 288.74/71.95 | | | | (112) ssList(all_144_0)
% 288.74/71.95 | | | | (113) $i(all_144_0)
% 288.74/71.95 | | | | (114) app(all_91_1, all_144_0) = all_91_1
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | DELTA: instantiating (73) with fresh symbol all_146_0 gives:
% 288.74/71.95 | | | | (115) app(nil, all_146_0) = all_91_1 & $i(all_146_0) &
% 288.74/71.95 | | | | ssList(all_146_0)
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | ALPHA: (115) implies:
% 288.74/71.95 | | | | (116) ssList(all_146_0)
% 288.74/71.95 | | | | (117) $i(all_146_0)
% 288.74/71.95 | | | | (118) app(nil, all_146_0) = all_91_1
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | DELTA: instantiating (80) with fresh symbol all_148_0 gives:
% 288.74/71.95 | | | | (119) app(all_148_0, all_91_0) = all_91_1 & $i(all_148_0) &
% 288.74/71.95 | | | | ssList(all_148_0)
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | ALPHA: (119) implies:
% 288.74/71.95 | | | | (120) ssList(all_148_0)
% 288.74/71.95 | | | | (121) $i(all_148_0)
% 288.74/71.95 | | | | (122) app(all_148_0, all_91_0) = all_91_1
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | DELTA: instantiating (79) with fresh symbol all_150_0 gives:
% 288.74/71.95 | | | | (123) app(all_150_0, all_91_1) = all_91_1 & $i(all_150_0) &
% 288.74/71.95 | | | | ssList(all_150_0)
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | ALPHA: (123) implies:
% 288.74/71.95 | | | | (124) ssList(all_150_0)
% 288.74/71.95 | | | | (125) $i(all_150_0)
% 288.74/71.95 | | | | (126) app(all_150_0, all_91_1) = all_91_1
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | DELTA: instantiating (78) with fresh symbol all_152_0 gives:
% 288.74/71.95 | | | | (127) app(all_152_0, nil) = all_91_1 & $i(all_152_0) &
% 288.74/71.95 | | | | ssList(all_152_0)
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | ALPHA: (127) implies:
% 288.74/71.95 | | | | (128) ssList(all_152_0)
% 288.74/71.95 | | | | (129) $i(all_152_0)
% 288.74/71.95 | | | | (130) app(all_152_0, nil) = all_91_1
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | DELTA: instantiating (77) with fresh symbol all_154_0 gives:
% 288.74/71.95 | | | | (131) app(all_91_0, all_154_0) = all_91_0 & $i(all_154_0) &
% 288.74/71.95 | | | | ssList(all_154_0)
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | ALPHA: (131) implies:
% 288.74/71.95 | | | | (132) ssList(all_154_0)
% 288.74/71.95 | | | | (133) $i(all_154_0)
% 288.74/71.95 | | | | (134) app(all_91_0, all_154_0) = all_91_0
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | DELTA: instantiating (83) with fresh symbols all_162_0, all_162_1,
% 288.74/71.95 | | | | all_162_2 gives:
% 288.74/71.95 | | | | (135) app(all_162_1, all_162_0) = all_91_0 & app(all_162_2, nil) =
% 288.74/71.95 | | | | all_162_1 & $i(all_162_0) & $i(all_162_1) & $i(all_162_2) &
% 288.74/71.95 | | | | ssList(all_162_0) & ssList(all_162_2)
% 288.74/71.95 | | | |
% 288.74/71.95 | | | | ALPHA: (135) implies:
% 288.74/71.95 | | | | (136) ssList(all_162_2)
% 288.74/71.96 | | | | (137) ssList(all_162_0)
% 288.74/71.96 | | | | (138) $i(all_162_2)
% 288.74/71.96 | | | | (139) $i(all_162_1)
% 288.74/71.96 | | | | (140) $i(all_162_0)
% 288.74/71.96 | | | | (141) app(all_162_2, nil) = all_162_1
% 288.74/71.96 | | | | (142) app(all_162_1, all_162_0) = all_91_0
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | REDUCE: (65), (88) imply:
% 288.74/71.96 | | | | (143) app(all_116_2, all_116_0) = nil
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | REDUCE: (85), (104) imply:
% 288.74/71.96 | | | | (144) app(nil, nil) = all_138_0
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | REDUCE: (86), (88) imply:
% 288.74/71.96 | | | | (145) rearsegP(all_116_2, nil)
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | GROUND_INST: instantiating (16) with all_138_0, simplifying with (8),
% 288.74/71.96 | | | | (144) gives:
% 288.74/71.96 | | | | (146) all_138_0 = nil
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | REDUCE: (144), (146) imply:
% 288.74/71.96 | | | | (147) app(nil, nil) = nil
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | GROUND_INST: instantiating (1) with all_116_2, nil, simplifying with
% 288.74/71.96 | | | | (8), (20), (59), (61), (68) gives:
% 288.74/71.96 | | | | (148) ? [v0: $i] : (app(nil, v0) = all_116_2 & $i(v0) & ssList(v0))
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | GROUND_INST: instantiating (1) with all_116_2, all_116_2, simplifying
% 288.74/71.96 | | | | with (59), (61), (67) gives:
% 288.74/71.96 | | | | (149) ? [v0: $i] : (app(all_116_2, v0) = all_116_2 & $i(v0) &
% 288.74/71.96 | | | | ssList(v0))
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | GROUND_INST: instantiating (1) with all_116_0, nil, simplifying with
% 288.74/71.96 | | | | (8), (20), (60), (63), (72) gives:
% 288.74/71.96 | | | | (150) ? [v0: $i] : (app(nil, v0) = all_116_0 & $i(v0) & ssList(v0))
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | GROUND_INST: instantiating (1) with all_116_0, all_116_0, simplifying
% 288.74/71.96 | | | | with (60), (63), (71) gives:
% 288.74/71.96 | | | | (151) ? [v0: $i] : (app(all_116_0, v0) = all_116_0 & $i(v0) &
% 288.74/71.96 | | | | ssList(v0))
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | GROUND_INST: instantiating (3) with all_116_2, nil, simplifying with
% 288.74/71.96 | | | | (8), (20), (59), (61), (145) gives:
% 288.74/71.96 | | | | (152) ? [v0: $i] : (app(v0, nil) = all_116_2 & $i(v0) & ssList(v0))
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | GROUND_INST: instantiating (3) with all_116_2, all_116_2, simplifying
% 288.74/71.96 | | | | with (59), (61), (66) gives:
% 288.74/71.96 | | | | (153) ? [v0: $i] : (app(v0, all_116_2) = all_116_2 & $i(v0) &
% 288.74/71.96 | | | | ssList(v0))
% 288.74/71.96 | | | |
% 288.74/71.96 | | | | GROUND_INST: instantiating (3) with all_116_0, nil, simplifying with
% 288.74/71.96 | | | | (8), (20), (60), (63), (70) gives:
% 288.74/71.96 | | | | (154) ? [v0: $i] : (app(v0, nil) = all_116_0 & $i(v0) & ssList(v0))
% 288.74/71.96 | | | |
% 288.74/71.97 | | | | GROUND_INST: instantiating (3) with all_116_0, all_116_0, simplifying
% 288.74/71.97 | | | | with (60), (63), (69) gives:
% 288.74/71.97 | | | | (155) ? [v0: $i] : (app(v0, all_116_0) = all_116_0 & $i(v0) &
% 288.74/71.97 | | | | ssList(v0))
% 288.74/71.97 | | | |
% 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_116_0,
% 288.74/71.97 | | | | all_140_0, simplifying with (8), (20), (60), (63), (106),
% 288.74/71.97 | | | | (147) gives:
% 288.74/71.97 | | | | (156) ? [v0: $i] : (app(nil, v0) = all_140_0 & app(nil, all_116_0) =
% 288.74/71.97 | | | | v0 & $i(v0) & $i(all_140_0))
% 288.74/71.97 | | | |
% 288.74/71.97 | | | | GROUND_INST: instantiating (9) with all_116_0, all_140_0, simplifying
% 288.74/71.97 | | | | with (60), (63), (106) gives:
% 288.74/71.97 | | | | (157) all_140_0 = all_116_0
% 288.74/71.97 | | | |
% 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with nil, all_132_0, all_91_0,
% 288.74/71.97 | | | | all_91_0, all_91_1, simplifying with (8), (20), (25), (27),
% 288.74/71.97 | | | | (28), (91), (92), (93) gives:
% 288.74/71.97 | | | | (158) ? [v0: $i] : (app(all_132_0, all_91_0) = v0 & app(nil, v0) =
% 288.74/71.97 | | | | all_91_1 & $i(v0) & $i(all_91_1))
% 288.74/71.97 | | | |
% 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_132_0,
% 288.74/71.97 | | | | all_91_0, simplifying with (8), (20), (91), (92), (93),
% 288.74/71.97 | | | | (147) gives:
% 288.74/71.97 | | | | (159) ? [v0: $i] : (app(nil, v0) = all_91_0 & app(nil, all_132_0) =
% 288.74/71.97 | | | | v0 & $i(v0) & $i(all_91_0))
% 288.74/71.97 | | | |
% 288.74/71.97 | | | | GROUND_INST: instantiating (9) with all_132_0, all_91_0, simplifying
% 288.74/71.97 | | | | with (91), (92), (93) gives:
% 288.74/71.97 | | | | (160) all_132_0 = all_91_0
% 288.74/71.97 | | | |
% 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_146_0,
% 288.74/71.97 | | | | all_91_1, simplifying with (8), (20), (116), (117), (118),
% 288.74/71.97 | | | | (147) gives:
% 288.74/71.97 | | | | (161) ? [v0: $i] : (app(nil, v0) = all_91_1 & app(nil, all_146_0) =
% 288.74/71.97 | | | | v0 & $i(v0) & $i(all_91_1))
% 288.74/71.97 | | | |
% 288.74/71.97 | | | | GROUND_INST: instantiating (9) with all_146_0, all_91_1, simplifying
% 288.74/71.97 | | | | with (116), (117), (118) gives:
% 288.74/71.97 | | | | (162) all_146_0 = all_91_1
% 288.74/71.97 | | | |
% 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_91_0, all_91_1,
% 288.74/71.97 | | | | all_144_0, all_91_1, simplifying with (25), (27), (28),
% 288.74/71.97 | | | | (112), (113), (114) gives:
% 288.74/71.97 | | | | (163) ? [v0: $i] : (app(all_91_0, v0) = all_91_1 & app(all_91_0,
% 288.74/71.97 | | | | all_144_0) = v0 & $i(v0) & $i(all_91_1))
% 288.74/71.97 | | | |
% 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with nil, all_146_0, all_91_1,
% 288.74/71.97 | | | | all_144_0, all_91_1, simplifying with (8), (20), (112),
% 288.74/71.97 | | | | (113), (114), (116), (117), (118) gives:
% 288.74/71.97 | | | | (164) ? [v0: $i] : (app(all_146_0, all_144_0) = v0 & app(nil, v0) =
% 288.74/71.97 | | | | all_91_1 & $i(v0) & $i(all_91_1))
% 288.74/71.97 | | | |
% 288.74/71.97 | | | | GROUND_INST: instantiating (ax80) with all_134_0, all_91_0, all_91_1,
% 288.74/71.97 | | | | all_91_0, simplifying with (25), (27), (28), (95), (96),
% 288.74/71.97 | | | | (97) gives:
% 288.74/71.97 | | | | (165) all_134_0 = all_91_0
% 288.74/71.97 | | | |
% 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_134_0, all_91_1,
% 288.74/71.98 | | | | all_144_0, all_91_1, simplifying with (25), (27), (95),
% 288.74/71.98 | | | | (96), (97), (112), (113), (114) gives:
% 288.74/71.98 | | | | (166) ? [v0: $i] : (app(all_134_0, all_144_0) = v0 & app(all_91_0,
% 288.74/71.98 | | | | v0) = all_91_1 & $i(v0) & $i(all_91_1))
% 288.74/71.98 | | | |
% 288.74/71.98 | | | | GROUND_INST: instantiating (6) with all_91_1, all_132_0, nil, all_91_0,
% 288.74/71.98 | | | | all_134_0, simplifying with (8), (20), (24), (26), (91),
% 288.74/71.98 | | | | (92), (93), (95), (96), (97) gives:
% 288.74/71.98 | | | | (167) segmentP(all_91_1, all_132_0)
% 288.74/71.98 | | | |
% 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with nil, all_132_0, all_91_0,
% 288.74/71.98 | | | | all_134_0, all_91_1, simplifying with (8), (20), (91),
% 288.74/71.98 | | | | (92), (93), (95), (96), (97) gives:
% 288.74/71.98 | | | | (168) ? [v0: $i] : (app(all_132_0, all_134_0) = v0 & app(nil, v0) =
% 288.74/71.98 | | | | all_91_1 & $i(v0) & $i(all_91_1))
% 288.74/71.98 | | | |
% 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_154_0, all_91_0,
% 288.74/71.98 | | | | all_91_0, all_91_1, simplifying with (25), (27), (28),
% 288.74/71.98 | | | | (132), (133), (134) gives:
% 288.74/71.98 | | | | (169) ? [v0: $i] : (app(all_154_0, all_91_0) = v0 & app(all_91_0,
% 288.74/71.98 | | | | v0) = all_91_1 & $i(v0) & $i(all_91_1))
% 288.74/71.98 | | | |
% 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_154_0, all_91_0,
% 288.74/71.98 | | | | all_134_0, all_91_1, simplifying with (25), (27), (95),
% 288.74/71.98 | | | | (96), (97), (132), (133), (134) gives:
% 288.74/71.98 | | | | (170) ? [v0: $i] : (app(all_154_0, all_134_0) = v0 & app(all_91_0,
% 288.74/71.98 | | | | v0) = all_91_1 & $i(v0) & $i(all_91_1))
% 288.74/71.98 | | | |
% 288.74/71.98 | | | | GROUND_INST: instantiating (6) with all_91_0, all_132_0, nil, all_91_0,
% 288.74/71.98 | | | | all_154_0, simplifying with (8), (20), (25), (27), (91),
% 288.74/71.98 | | | | (92), (93), (132), (133), (134) gives:
% 288.74/71.98 | | | | (171) segmentP(all_91_0, all_132_0)
% 288.74/71.98 | | | |
% 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with nil, all_132_0, all_91_0,
% 288.74/71.98 | | | | all_154_0, all_91_0, simplifying with (8), (20), (91),
% 288.74/71.98 | | | | (92), (93), (132), (133), (134) gives:
% 288.74/71.98 | | | | (172) ? [v0: $i] : (app(all_132_0, all_154_0) = v0 & app(nil, v0) =
% 288.74/71.98 | | | | all_91_0 & $i(v0) & $i(all_91_0))
% 288.74/71.98 | | | |
% 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil,
% 288.74/71.98 | | | | all_146_0, all_91_1, simplifying with (59), (60), (61),
% 288.74/71.98 | | | | (63), (116), (117), (118), (143) gives:
% 288.74/71.98 | | | | (173) ? [v0: $i] : (app(all_116_0, all_146_0) = v0 & app(all_116_2,
% 288.74/71.98 | | | | v0) = all_91_1 & $i(v0) & $i(all_91_1))
% 288.74/71.98 | | | |
% 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil,
% 288.74/71.98 | | | | all_132_0, all_91_0, simplifying with (59), (60), (61),
% 288.74/71.98 | | | | (63), (91), (92), (93), (143) gives:
% 288.74/71.98 | | | | (174) ? [v0: $i] : (app(all_116_0, all_132_0) = v0 & app(all_116_2,
% 288.74/71.98 | | | | v0) = all_91_0 & $i(v0) & $i(all_91_0))
% 288.74/71.98 | | | |
% 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil,
% 288.74/71.98 | | | | all_116_0, all_140_0, simplifying with (59), (60), (61),
% 288.74/71.98 | | | | (63), (106), (143) gives:
% 288.74/71.98 | | | | (175) ? [v0: $i] : (app(all_116_0, all_116_0) = v0 & app(all_116_2,
% 288.74/71.98 | | | | v0) = all_140_0 & $i(v0) & $i(all_140_0))
% 288.74/71.98 | | | |
% 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil, nil,
% 288.74/71.98 | | | | nil, simplifying with (8), (20), (59), (60), (61), (63),
% 288.74/71.98 | | | | (143), (147) gives:
% 288.74/71.98 | | | | (176) ? [v0: $i] : (app(all_116_0, nil) = v0 & app(all_116_2, v0) =
% 288.74/71.98 | | | | nil & $i(v0))
% 288.74/71.98 | | | |
% 288.74/71.99 | | | | GROUND_INST: instantiating (18) with all_116_2, all_116_0, simplifying
% 288.74/71.99 | | | | with (59), (60), (61), (63), (143) gives:
% 288.74/71.99 | | | | (177) all_116_0 = nil
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | GROUND_INST: instantiating (17) with all_116_2, all_116_0, simplifying
% 288.74/71.99 | | | | with (59), (60), (61), (63), (143) gives:
% 288.74/71.99 | | | | (178) all_116_2 = nil
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | GROUND_INST: instantiating (ax82) with all_136_0, all_91_0, all_91_0,
% 288.74/71.99 | | | | all_91_0, all_91_1, simplifying with (25), (27), (28),
% 288.74/71.99 | | | | (99), (100), (101) gives:
% 288.74/71.99 | | | | (179) ? [v0: $i] : (app(all_136_0, v0) = all_91_1 & app(all_91_0,
% 288.74/71.99 | | | | all_91_0) = v0 & $i(v0) & $i(all_91_1))
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | GROUND_INST: instantiating (ax82) with all_136_0, all_91_0, all_91_0,
% 288.74/71.99 | | | | all_134_0, all_91_1, simplifying with (25), (27), (95),
% 288.74/71.99 | | | | (96), (97), (99), (100), (101) gives:
% 288.74/71.99 | | | | (180) ? [v0: $i] : (app(all_136_0, v0) = all_91_1 & app(all_91_0,
% 288.74/71.99 | | | | all_134_0) = v0 & $i(v0) & $i(all_91_1))
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | GROUND_INST: instantiating (ax82) with all_142_0, nil, all_91_0,
% 288.74/71.99 | | | | all_91_0, all_91_1, simplifying with (8), (20), (25), (27),
% 288.74/71.99 | | | | (28), (108), (109), (110) gives:
% 288.74/71.99 | | | | (181) ? [v0: $i] : (app(all_142_0, v0) = all_91_1 & app(nil,
% 288.74/71.99 | | | | all_91_0) = v0 & $i(v0) & $i(all_91_1))
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | GROUND_INST: instantiating (ax82) with all_142_0, nil, all_91_0,
% 288.74/71.99 | | | | all_134_0, all_91_1, simplifying with (8), (20), (95),
% 288.74/71.99 | | | | (96), (97), (108), (109), (110) gives:
% 288.74/71.99 | | | | (182) ? [v0: $i] : (app(all_142_0, v0) = all_91_1 & app(nil,
% 288.74/71.99 | | | | all_134_0) = v0 & $i(v0) & $i(all_91_1))
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | GROUND_INST: instantiating (19) with all_142_0, all_91_0, simplifying
% 288.74/71.99 | | | | with (108), (109), (110) gives:
% 288.74/71.99 | | | | (183) all_142_0 = all_91_0
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | GROUND_INST: instantiating (ax82) with all_148_0, all_91_0, all_91_1,
% 288.74/71.99 | | | | all_144_0, all_91_1, simplifying with (25), (27), (112),
% 288.74/71.99 | | | | (113), (114), (120), (121), (122) gives:
% 288.74/71.99 | | | | (184) ? [v0: $i] : (app(all_148_0, v0) = all_91_1 & app(all_91_0,
% 288.74/71.99 | | | | all_144_0) = v0 & $i(v0) & $i(all_91_1))
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | GROUND_INST: instantiating (19) with all_152_0, all_91_1, simplifying
% 288.74/71.99 | | | | with (128), (129), (130) gives:
% 288.74/71.99 | | | | (185) all_152_0 = all_91_1
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | GROUND_INST: instantiating (ax26) with all_162_2, nil, all_162_1,
% 288.74/71.99 | | | | simplifying with (8), (20), (136), (138), (141) gives:
% 288.74/71.99 | | | | (186) ssList(all_162_1)
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | GROUND_INST: instantiating (19) with all_162_2, all_162_1, simplifying
% 288.74/71.99 | | | | with (136), (138), (141) gives:
% 288.74/71.99 | | | | (187) all_162_1 = all_162_2
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | COMBINE_EQS: (157), (177) imply:
% 288.74/71.99 | | | | (188) all_140_0 = nil
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | DELTA: instantiating (153) with fresh symbol all_174_0 gives:
% 288.74/71.99 | | | | (189) app(all_174_0, all_116_2) = all_116_2 & $i(all_174_0) &
% 288.74/71.99 | | | | ssList(all_174_0)
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | ALPHA: (189) implies:
% 288.74/71.99 | | | | (190) ssList(all_174_0)
% 288.74/71.99 | | | | (191) $i(all_174_0)
% 288.74/71.99 | | | | (192) app(all_174_0, all_116_2) = all_116_2
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | DELTA: instantiating (152) with fresh symbol all_176_0 gives:
% 288.74/71.99 | | | | (193) app(all_176_0, nil) = all_116_2 & $i(all_176_0) &
% 288.74/71.99 | | | | ssList(all_176_0)
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | ALPHA: (193) implies:
% 288.74/71.99 | | | | (194) ssList(all_176_0)
% 288.74/71.99 | | | | (195) $i(all_176_0)
% 288.74/71.99 | | | | (196) app(all_176_0, nil) = all_116_2
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | DELTA: instantiating (155) with fresh symbol all_178_0 gives:
% 288.74/71.99 | | | | (197) app(all_178_0, all_116_0) = all_116_0 & $i(all_178_0) &
% 288.74/71.99 | | | | ssList(all_178_0)
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | ALPHA: (197) implies:
% 288.74/71.99 | | | | (198) ssList(all_178_0)
% 288.74/71.99 | | | | (199) $i(all_178_0)
% 288.74/71.99 | | | | (200) app(all_178_0, all_116_0) = all_116_0
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | DELTA: instantiating (154) with fresh symbol all_180_0 gives:
% 288.74/71.99 | | | | (201) app(all_180_0, nil) = all_116_0 & $i(all_180_0) &
% 288.74/71.99 | | | | ssList(all_180_0)
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | ALPHA: (201) implies:
% 288.74/71.99 | | | | (202) ssList(all_180_0)
% 288.74/71.99 | | | | (203) $i(all_180_0)
% 288.74/71.99 | | | | (204) app(all_180_0, nil) = all_116_0
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | DELTA: instantiating (176) with fresh symbol all_184_0 gives:
% 288.74/71.99 | | | | (205) app(all_116_0, nil) = all_184_0 & app(all_116_2, all_184_0) =
% 288.74/71.99 | | | | nil & $i(all_184_0)
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | ALPHA: (205) implies:
% 288.74/71.99 | | | | (206) $i(all_184_0)
% 288.74/71.99 | | | | (207) app(all_116_0, nil) = all_184_0
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | DELTA: instantiating (151) with fresh symbol all_186_0 gives:
% 288.74/71.99 | | | | (208) app(all_116_0, all_186_0) = all_116_0 & $i(all_186_0) &
% 288.74/71.99 | | | | ssList(all_186_0)
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | ALPHA: (208) implies:
% 288.74/71.99 | | | | (209) ssList(all_186_0)
% 288.74/71.99 | | | | (210) $i(all_186_0)
% 288.74/71.99 | | | | (211) app(all_116_0, all_186_0) = all_116_0
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | DELTA: instantiating (150) with fresh symbol all_188_0 gives:
% 288.74/71.99 | | | | (212) app(nil, all_188_0) = all_116_0 & $i(all_188_0) &
% 288.74/71.99 | | | | ssList(all_188_0)
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | ALPHA: (212) implies:
% 288.74/71.99 | | | | (213) ssList(all_188_0)
% 288.74/71.99 | | | | (214) $i(all_188_0)
% 288.74/71.99 | | | | (215) app(nil, all_188_0) = all_116_0
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | DELTA: instantiating (149) with fresh symbol all_192_0 gives:
% 288.74/71.99 | | | | (216) app(all_116_2, all_192_0) = all_116_2 & $i(all_192_0) &
% 288.74/71.99 | | | | ssList(all_192_0)
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | ALPHA: (216) implies:
% 288.74/71.99 | | | | (217) ssList(all_192_0)
% 288.74/71.99 | | | | (218) $i(all_192_0)
% 288.74/71.99 | | | | (219) app(all_116_2, all_192_0) = all_116_2
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | DELTA: instantiating (148) with fresh symbol all_194_0 gives:
% 288.74/71.99 | | | | (220) app(nil, all_194_0) = all_116_2 & $i(all_194_0) &
% 288.74/71.99 | | | | ssList(all_194_0)
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | ALPHA: (220) implies:
% 288.74/71.99 | | | | (221) ssList(all_194_0)
% 288.74/71.99 | | | | (222) $i(all_194_0)
% 288.74/71.99 | | | | (223) app(nil, all_194_0) = all_116_2
% 288.74/71.99 | | | |
% 288.74/71.99 | | | | DELTA: instantiating (156) with fresh symbol all_202_0 gives:
% 288.74/72.00 | | | | (224) app(nil, all_202_0) = all_140_0 & app(nil, all_116_0) =
% 288.74/72.00 | | | | all_202_0 & $i(all_202_0) & $i(all_140_0)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (224) implies:
% 288.74/72.00 | | | | (225) app(nil, all_116_0) = all_202_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (179) with fresh symbol all_204_0 gives:
% 288.74/72.00 | | | | (226) app(all_136_0, all_204_0) = all_91_1 & app(all_91_0, all_91_0)
% 288.74/72.00 | | | | = all_204_0 & $i(all_204_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (226) implies:
% 288.74/72.00 | | | | (227) $i(all_204_0)
% 288.74/72.00 | | | | (228) app(all_91_0, all_91_0) = all_204_0
% 288.74/72.00 | | | | (229) app(all_136_0, all_204_0) = all_91_1
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (181) with fresh symbol all_208_0 gives:
% 288.74/72.00 | | | | (230) app(all_142_0, all_208_0) = all_91_1 & app(nil, all_91_0) =
% 288.74/72.00 | | | | all_208_0 & $i(all_208_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (230) implies:
% 288.74/72.00 | | | | (231) $i(all_208_0)
% 288.74/72.00 | | | | (232) app(nil, all_91_0) = all_208_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (184) with fresh symbol all_210_0 gives:
% 288.74/72.00 | | | | (233) app(all_148_0, all_210_0) = all_91_1 & app(all_91_0, all_144_0)
% 288.74/72.00 | | | | = all_210_0 & $i(all_210_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (233) implies:
% 288.74/72.00 | | | | (234) app(all_91_0, all_144_0) = all_210_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (175) with fresh symbol all_216_0 gives:
% 288.74/72.00 | | | | (235) app(all_116_0, all_116_0) = all_216_0 & app(all_116_2,
% 288.74/72.00 | | | | all_216_0) = all_140_0 & $i(all_216_0) & $i(all_140_0)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (235) implies:
% 288.74/72.00 | | | | (236) app(all_116_0, all_116_0) = all_216_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (173) with fresh symbol all_218_0 gives:
% 288.74/72.00 | | | | (237) app(all_116_0, all_146_0) = all_218_0 & app(all_116_2,
% 288.74/72.00 | | | | all_218_0) = all_91_1 & $i(all_218_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (237) implies:
% 288.74/72.00 | | | | (238) app(all_116_0, all_146_0) = all_218_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (174) with fresh symbol all_220_0 gives:
% 288.74/72.00 | | | | (239) app(all_116_0, all_132_0) = all_220_0 & app(all_116_2,
% 288.74/72.00 | | | | all_220_0) = all_91_0 & $i(all_220_0) & $i(all_91_0)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (239) implies:
% 288.74/72.00 | | | | (240) app(all_116_0, all_132_0) = all_220_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (182) with fresh symbol all_222_0 gives:
% 288.74/72.00 | | | | (241) app(all_142_0, all_222_0) = all_91_1 & app(nil, all_134_0) =
% 288.74/72.00 | | | | all_222_0 & $i(all_222_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (241) implies:
% 288.74/72.00 | | | | (242) app(nil, all_134_0) = all_222_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (163) with fresh symbol all_224_0 gives:
% 288.74/72.00 | | | | (243) app(all_91_0, all_224_0) = all_91_1 & app(all_91_0, all_144_0)
% 288.74/72.00 | | | | = all_224_0 & $i(all_224_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (243) implies:
% 288.74/72.00 | | | | (244) app(all_91_0, all_144_0) = all_224_0
% 288.74/72.00 | | | | (245) app(all_91_0, all_224_0) = all_91_1
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (161) with fresh symbol all_226_0 gives:
% 288.74/72.00 | | | | (246) app(nil, all_226_0) = all_91_1 & app(nil, all_146_0) =
% 288.74/72.00 | | | | all_226_0 & $i(all_226_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (246) implies:
% 288.74/72.00 | | | | (247) app(nil, all_146_0) = all_226_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (159) with fresh symbol all_228_0 gives:
% 288.74/72.00 | | | | (248) app(nil, all_228_0) = all_91_0 & app(nil, all_132_0) =
% 288.74/72.00 | | | | all_228_0 & $i(all_228_0) & $i(all_91_0)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (248) implies:
% 288.74/72.00 | | | | (249) app(nil, all_132_0) = all_228_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (170) with fresh symbol all_230_0 gives:
% 288.74/72.00 | | | | (250) app(all_154_0, all_134_0) = all_230_0 & app(all_91_0,
% 288.74/72.00 | | | | all_230_0) = all_91_1 & $i(all_230_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (250) implies:
% 288.74/72.00 | | | | (251) app(all_154_0, all_134_0) = all_230_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (164) with fresh symbol all_232_0 gives:
% 288.74/72.00 | | | | (252) app(all_146_0, all_144_0) = all_232_0 & app(nil, all_232_0) =
% 288.74/72.00 | | | | all_91_1 & $i(all_232_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (252) implies:
% 288.74/72.00 | | | | (253) app(all_146_0, all_144_0) = all_232_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (168) with fresh symbol all_234_0 gives:
% 288.74/72.00 | | | | (254) app(all_132_0, all_134_0) = all_234_0 & app(nil, all_234_0) =
% 288.74/72.00 | | | | all_91_1 & $i(all_234_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (254) implies:
% 288.74/72.00 | | | | (255) app(all_132_0, all_134_0) = all_234_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (166) with fresh symbol all_236_0 gives:
% 288.74/72.00 | | | | (256) app(all_134_0, all_144_0) = all_236_0 & app(all_91_0,
% 288.74/72.00 | | | | all_236_0) = all_91_1 & $i(all_236_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (256) implies:
% 288.74/72.00 | | | | (257) app(all_134_0, all_144_0) = all_236_0
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | DELTA: instantiating (180) with fresh symbol all_238_0 gives:
% 288.74/72.00 | | | | (258) app(all_136_0, all_238_0) = all_91_1 & app(all_91_0, all_134_0)
% 288.74/72.00 | | | | = all_238_0 & $i(all_238_0) & $i(all_91_1)
% 288.74/72.00 | | | |
% 288.74/72.00 | | | | ALPHA: (258) implies:
% 289.06/72.00 | | | | (259) app(all_91_0, all_134_0) = all_238_0
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | DELTA: instantiating (172) with fresh symbol all_240_0 gives:
% 289.06/72.00 | | | | (260) app(all_132_0, all_154_0) = all_240_0 & app(nil, all_240_0) =
% 289.06/72.00 | | | | all_91_0 & $i(all_240_0) & $i(all_91_0)
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | ALPHA: (260) implies:
% 289.06/72.00 | | | | (261) app(all_132_0, all_154_0) = all_240_0
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | DELTA: instantiating (169) with fresh symbol all_242_0 gives:
% 289.06/72.00 | | | | (262) app(all_154_0, all_91_0) = all_242_0 & app(all_91_0, all_242_0)
% 289.06/72.00 | | | | = all_91_1 & $i(all_242_0) & $i(all_91_1)
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | ALPHA: (262) implies:
% 289.06/72.00 | | | | (263) app(all_154_0, all_91_0) = all_242_0
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | DELTA: instantiating (158) with fresh symbol all_244_0 gives:
% 289.06/72.00 | | | | (264) app(all_132_0, all_91_0) = all_244_0 & app(nil, all_244_0) =
% 289.06/72.00 | | | | all_91_1 & $i(all_244_0) & $i(all_91_1)
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | ALPHA: (264) implies:
% 289.06/72.00 | | | | (265) app(all_132_0, all_91_0) = all_244_0
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | REDUCE: (177), (204) imply:
% 289.06/72.00 | | | | (266) app(all_180_0, nil) = nil
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | REDUCE: (177), (200) imply:
% 289.06/72.00 | | | | (267) app(all_178_0, nil) = nil
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | REDUCE: (178), (196) imply:
% 289.06/72.00 | | | | (268) app(all_176_0, nil) = nil
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | REDUCE: (178), (192) imply:
% 289.06/72.00 | | | | (269) app(all_174_0, nil) = nil
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | REDUCE: (142), (187) imply:
% 289.06/72.00 | | | | (270) app(all_162_2, all_162_0) = all_91_0
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | REDUCE: (165), (251) imply:
% 289.06/72.00 | | | | (271) app(all_154_0, all_91_0) = all_230_0
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | REDUCE: (130), (185) imply:
% 289.06/72.00 | | | | (272) app(all_91_1, nil) = all_91_1
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | REDUCE: (162), (253) imply:
% 289.06/72.00 | | | | (273) app(all_91_1, all_144_0) = all_232_0
% 289.06/72.00 | | | |
% 289.06/72.00 | | | | REDUCE: (110), (183) imply:
% 289.06/72.01 | | | | (274) app(all_91_0, nil) = all_91_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (165), (257) imply:
% 289.06/72.01 | | | | (275) app(all_91_0, all_144_0) = all_236_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (160), (261) imply:
% 289.06/72.01 | | | | (276) app(all_91_0, all_154_0) = all_240_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (160), (165), (255) imply:
% 289.06/72.01 | | | | (277) app(all_91_0, all_91_0) = all_234_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (160), (265) imply:
% 289.06/72.01 | | | | (278) app(all_91_0, all_91_0) = all_244_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (177), (211) imply:
% 289.06/72.01 | | | | (279) app(nil, all_186_0) = nil
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (162), (177), (238) imply:
% 289.06/72.01 | | | | (280) app(nil, all_91_1) = all_218_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (160), (177), (240) imply:
% 289.06/72.01 | | | | (281) app(nil, all_91_0) = all_220_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (177), (236) imply:
% 289.06/72.01 | | | | (282) app(nil, nil) = all_216_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (177), (207) imply:
% 289.06/72.01 | | | | (283) app(nil, nil) = all_184_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (178), (219) imply:
% 289.06/72.01 | | | | (284) app(nil, all_192_0) = nil
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (165), (259) imply:
% 289.06/72.01 | | | | (285) app(all_91_0, all_91_0) = all_238_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (178), (223) imply:
% 289.06/72.01 | | | | (286) app(nil, all_194_0) = nil
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (177), (215) imply:
% 289.06/72.01 | | | | (287) app(nil, all_188_0) = nil
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (162), (247) imply:
% 289.06/72.01 | | | | (288) app(nil, all_91_1) = all_226_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (118), (162) imply:
% 289.06/72.01 | | | | (289) app(nil, all_91_1) = all_91_1
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (165), (242) imply:
% 289.06/72.01 | | | | (290) app(nil, all_91_0) = all_222_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (160), (249) imply:
% 289.06/72.01 | | | | (291) app(nil, all_91_0) = all_228_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (93), (160) imply:
% 289.06/72.01 | | | | (292) app(nil, all_91_0) = all_91_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (177), (225) imply:
% 289.06/72.01 | | | | (293) app(nil, nil) = all_202_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (160), (171) imply:
% 289.06/72.01 | | | | (294) segmentP(all_91_0, all_91_0)
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | REDUCE: (160), (167) imply:
% 289.06/72.01 | | | | (295) segmentP(all_91_1, all_91_0)
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_184_0, all_202_0, nil, nil,
% 289.06/72.01 | | | | simplifying with (283), (293) gives:
% 289.06/72.01 | | | | (296) all_202_0 = all_184_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | GROUND_INST: instantiating (22) with nil, all_216_0, nil, nil,
% 289.06/72.01 | | | | simplifying with (147), (282) gives:
% 289.06/72.01 | | | | (297) all_216_0 = nil
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_202_0, all_216_0, nil, nil,
% 289.06/72.01 | | | | simplifying with (282), (293) gives:
% 289.06/72.01 | | | | (298) all_216_0 = all_202_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_218_0, all_226_0, all_91_1,
% 289.06/72.01 | | | | nil, simplifying with (280), (288) gives:
% 289.06/72.01 | | | | (299) all_226_0 = all_218_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_91_1, all_226_0, all_91_1, nil,
% 289.06/72.01 | | | | simplifying with (288), (289) gives:
% 289.06/72.01 | | | | (300) all_226_0 = all_91_1
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_91_0, all_220_0, all_91_0, nil,
% 289.06/72.01 | | | | simplifying with (281), (292) gives:
% 289.06/72.01 | | | | (301) all_220_0 = all_91_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_220_0, all_222_0, all_91_0,
% 289.06/72.01 | | | | nil, simplifying with (281), (290) gives:
% 289.06/72.01 | | | | (302) all_222_0 = all_220_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_222_0, all_228_0, all_91_0,
% 289.06/72.01 | | | | nil, simplifying with (290), (291) gives:
% 289.06/72.01 | | | | (303) all_228_0 = all_222_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_208_0, all_228_0, all_91_0,
% 289.06/72.01 | | | | nil, simplifying with (232), (291) gives:
% 289.06/72.01 | | | | (304) all_228_0 = all_208_0
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_91_1, all_232_0, all_144_0,
% 289.06/72.01 | | | | all_91_1, simplifying with (114), (273) gives:
% 289.06/72.01 | | | | (305) all_232_0 = all_91_1
% 289.06/72.01 | | | |
% 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_91_1, all_234_0, all_91_0,
% 289.06/72.01 | | | | all_91_0, simplifying with (28), (277) gives:
% 289.06/72.01 | | | | (306) all_234_0 = all_91_1
% 289.06/72.01 | | | |
% 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_238_0, all_244_0, all_91_0,
% 289.11/72.01 | | | | all_91_0, simplifying with (278), (285) gives:
% 289.11/72.01 | | | | (307) all_244_0 = all_238_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_234_0, all_244_0, all_91_0,
% 289.11/72.01 | | | | all_91_0, simplifying with (277), (278) gives:
% 289.11/72.01 | | | | (308) all_244_0 = all_234_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_204_0, all_244_0, all_91_0,
% 289.11/72.01 | | | | all_91_0, simplifying with (228), (278) gives:
% 289.11/72.01 | | | | (309) all_244_0 = all_204_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_224_0, all_236_0, all_144_0,
% 289.11/72.01 | | | | all_91_0, simplifying with (244), (275) gives:
% 289.11/72.01 | | | | (310) all_236_0 = all_224_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_210_0, all_236_0, all_144_0,
% 289.11/72.01 | | | | all_91_0, simplifying with (234), (275) gives:
% 289.11/72.01 | | | | (311) all_236_0 = all_210_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_91_0, all_240_0, all_154_0,
% 289.11/72.01 | | | | all_91_0, simplifying with (134), (276) gives:
% 289.11/72.01 | | | | (312) all_240_0 = all_91_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_230_0, all_242_0, all_91_0,
% 289.11/72.01 | | | | all_154_0, simplifying with (263), (271) gives:
% 289.11/72.01 | | | | (313) all_242_0 = all_230_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | COMBINE_EQS: (307), (309) imply:
% 289.11/72.01 | | | | (314) all_238_0 = all_204_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | COMBINE_EQS: (307), (308) imply:
% 289.11/72.01 | | | | (315) all_238_0 = all_234_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | COMBINE_EQS: (314), (315) imply:
% 289.11/72.01 | | | | (316) all_234_0 = all_204_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | SIMP: (316) implies:
% 289.11/72.01 | | | | (317) all_234_0 = all_204_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | COMBINE_EQS: (310), (311) imply:
% 289.11/72.01 | | | | (318) all_224_0 = all_210_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | COMBINE_EQS: (306), (317) imply:
% 289.11/72.01 | | | | (319) all_204_0 = all_91_1
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | COMBINE_EQS: (303), (304) imply:
% 289.11/72.01 | | | | (320) all_222_0 = all_208_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | SIMP: (320) implies:
% 289.11/72.01 | | | | (321) all_222_0 = all_208_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | COMBINE_EQS: (299), (300) imply:
% 289.11/72.01 | | | | (322) all_218_0 = all_91_1
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | SIMP: (322) implies:
% 289.11/72.01 | | | | (323) all_218_0 = all_91_1
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | COMBINE_EQS: (302), (321) imply:
% 289.11/72.01 | | | | (324) all_220_0 = all_208_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | SIMP: (324) implies:
% 289.11/72.01 | | | | (325) all_220_0 = all_208_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | COMBINE_EQS: (301), (325) imply:
% 289.11/72.01 | | | | (326) all_208_0 = all_91_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | SIMP: (326) implies:
% 289.11/72.01 | | | | (327) all_208_0 = all_91_0
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | COMBINE_EQS: (297), (298) imply:
% 289.11/72.01 | | | | (328) all_202_0 = nil
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | SIMP: (328) implies:
% 289.11/72.01 | | | | (329) all_202_0 = nil
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | COMBINE_EQS: (296), (329) imply:
% 289.11/72.01 | | | | (330) all_184_0 = nil
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | SIMP: (330) implies:
% 289.11/72.01 | | | | (331) all_184_0 = nil
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | REDUCE: (229), (319) imply:
% 289.11/72.01 | | | | (332) app(all_136_0, all_91_1) = all_91_1
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | REDUCE: (245), (318) imply:
% 289.11/72.01 | | | | (333) app(all_91_0, all_210_0) = all_91_1
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | GROUND_INST: instantiating (ax79) with nil, all_91_1, all_91_1,
% 289.11/72.01 | | | | all_150_0, simplifying with (8), (20), (24), (26), (124),
% 289.11/72.01 | | | | (125), (126), (289) gives:
% 289.11/72.01 | | | | (334) all_150_0 = nil
% 289.11/72.01 | | | |
% 289.11/72.01 | | | | GROUND_INST: instantiating (ax82) with nil, all_186_0, nil, all_91_0,
% 289.11/72.01 | | | | all_91_0, simplifying with (8), (20), (25), (27), (209),
% 289.11/72.01 | | | | (210), (279), (292) gives:
% 289.11/72.02 | | | | (335) ? [v0: $i] : (app(all_186_0, all_91_0) = v0 & app(nil, v0) =
% 289.11/72.02 | | | | all_91_0 & $i(v0))
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with nil, all_188_0, nil, all_91_0,
% 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (213),
% 289.11/72.02 | | | | (214), (287), (292) gives:
% 289.11/72.02 | | | | (336) ? [v0: $i] : (app(all_188_0, all_91_0) = v0 & app(nil, v0) =
% 289.11/72.02 | | | | all_91_0 & $i(v0))
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (9) with all_188_0, nil, simplifying with
% 289.11/72.02 | | | | (213), (214), (287) gives:
% 289.11/72.02 | | | | (337) all_188_0 = nil
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with nil, all_192_0, nil, all_91_0,
% 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (217),
% 289.11/72.02 | | | | (218), (284), (292) gives:
% 289.11/72.02 | | | | (338) ? [v0: $i] : (app(all_192_0, all_91_0) = v0 & app(nil, v0) =
% 289.11/72.02 | | | | all_91_0 & $i(v0))
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax80) with all_192_0, nil, nil, all_194_0,
% 289.11/72.02 | | | | simplifying with (8), (20), (217), (218), (221), (222),
% 289.11/72.02 | | | | (284), (286) gives:
% 289.11/72.02 | | | | (339) all_194_0 = all_192_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax80) with all_188_0, nil, nil, all_194_0,
% 289.11/72.02 | | | | simplifying with (8), (20), (213), (214), (221), (222),
% 289.11/72.02 | | | | (286), (287) gives:
% 289.11/72.02 | | | | (340) all_194_0 = all_188_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax80) with all_186_0, nil, nil, all_194_0,
% 289.11/72.02 | | | | simplifying with (8), (20), (209), (210), (221), (222),
% 289.11/72.02 | | | | (279), (286) gives:
% 289.11/72.02 | | | | (341) all_194_0 = all_186_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with nil, all_194_0, nil, all_91_0,
% 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (221),
% 289.11/72.02 | | | | (222), (286), (292) gives:
% 289.11/72.02 | | | | (342) ? [v0: $i] : (app(all_194_0, all_91_0) = v0 & app(nil, v0) =
% 289.11/72.02 | | | | all_91_0 & $i(v0))
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax80) with nil, all_91_1, all_91_1,
% 289.11/72.02 | | | | all_144_0, simplifying with (8), (20), (24), (26), (112),
% 289.11/72.02 | | | | (113), (114), (272) gives:
% 289.11/72.02 | | | | (343) all_144_0 = nil
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax80) with nil, all_91_0, all_91_0,
% 289.11/72.02 | | | | all_154_0, simplifying with (8), (20), (25), (27), (132),
% 289.11/72.02 | | | | (133), (134), (274) gives:
% 289.11/72.02 | | | | (344) all_154_0 = nil
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_136_0, all_91_0, all_91_0,
% 289.11/72.02 | | | | all_144_0, all_210_0, simplifying with (25), (27), (99),
% 289.11/72.02 | | | | (100), (101), (112), (113), (234) gives:
% 289.11/72.02 | | | | (345) ? [v0: $i] : (app(all_136_0, v0) = all_210_0 & app(all_91_0,
% 289.11/72.02 | | | | all_144_0) = v0 & $i(v0) & $i(all_210_0))
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax56) with all_91_0, all_91_0, nil,
% 289.11/72.02 | | | | all_91_0, all_144_0, all_210_0, simplifying with (8), (20),
% 289.11/72.02 | | | | (25), (27), (112), (113), (234), (292), (294) gives:
% 289.11/72.02 | | | | (346) segmentP(all_210_0, all_91_0)
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with nil, all_91_0, all_91_0,
% 289.11/72.02 | | | | all_144_0, all_210_0, simplifying with (8), (20), (25),
% 289.11/72.02 | | | | (27), (112), (113), (234), (292) gives:
% 289.11/72.02 | | | | (347) ? [v0: $i] : (app(all_91_0, all_144_0) = v0 & app(nil, v0) =
% 289.11/72.02 | | | | all_210_0 & $i(v0) & $i(all_210_0))
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax26) with all_91_0, all_144_0, all_210_0,
% 289.11/72.02 | | | | simplifying with (25), (27), (112), (113), (234) gives:
% 289.11/72.02 | | | | (348) ssList(all_210_0)
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax79) with all_136_0, all_91_1, all_91_1,
% 289.11/72.02 | | | | all_150_0, simplifying with (24), (26), (99), (100), (124),
% 289.11/72.02 | | | | (125), (126), (332) gives:
% 289.11/72.02 | | | | (349) all_150_0 = all_136_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_162_2, all_162_0, all_91_0,
% 289.11/72.02 | | | | all_144_0, all_210_0, simplifying with (112), (113), (136),
% 289.11/72.02 | | | | (137), (138), (140), (234), (270) gives:
% 289.11/72.02 | | | | (350) ? [v0: $i] : (app(all_162_0, all_144_0) = v0 & app(all_162_2,
% 289.11/72.02 | | | | v0) = all_210_0 & $i(v0) & $i(all_210_0))
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_174_0, nil, nil, all_91_0,
% 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (190),
% 289.11/72.02 | | | | (191), (269), (292) gives:
% 289.11/72.02 | | | | (351) ? [v0: $i] : (app(all_174_0, v0) = all_91_0 & app(nil,
% 289.11/72.02 | | | | all_91_0) = v0 & $i(v0))
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_176_0, nil, nil, all_91_0,
% 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (194),
% 289.11/72.02 | | | | (195), (268), (292) gives:
% 289.11/72.02 | | | | (352) ? [v0: $i] : (app(all_176_0, v0) = all_91_0 & app(nil,
% 289.11/72.02 | | | | all_91_0) = v0 & $i(v0))
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_178_0, nil, nil, all_91_0,
% 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (198),
% 289.11/72.02 | | | | (199), (267), (292) gives:
% 289.11/72.02 | | | | (353) ? [v0: $i] : (app(all_178_0, v0) = all_91_0 & app(nil,
% 289.11/72.02 | | | | all_91_0) = v0 & $i(v0))
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_180_0, nil, nil, all_91_0,
% 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (202),
% 289.11/72.02 | | | | (203), (266), (292) gives:
% 289.11/72.02 | | | | (354) ? [v0: $i] : (app(all_180_0, v0) = all_91_0 & app(nil,
% 289.11/72.02 | | | | all_91_0) = v0 & $i(v0))
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | COMBINE_EQS: (339), (340) imply:
% 289.11/72.02 | | | | (355) all_192_0 = all_188_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | COMBINE_EQS: (339), (341) imply:
% 289.11/72.02 | | | | (356) all_192_0 = all_186_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | COMBINE_EQS: (355), (356) imply:
% 289.11/72.02 | | | | (357) all_188_0 = all_186_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | SIMP: (357) implies:
% 289.11/72.02 | | | | (358) all_188_0 = all_186_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | COMBINE_EQS: (337), (358) imply:
% 289.11/72.02 | | | | (359) all_186_0 = nil
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | SIMP: (359) implies:
% 289.11/72.02 | | | | (360) all_186_0 = nil
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | COMBINE_EQS: (334), (349) imply:
% 289.11/72.02 | | | | (361) all_136_0 = nil
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | SIMP: (361) implies:
% 289.11/72.02 | | | | (362) all_136_0 = nil
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | COMBINE_EQS: (356), (360) imply:
% 289.11/72.02 | | | | (363) all_192_0 = nil
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | COMBINE_EQS: (339), (363) imply:
% 289.11/72.02 | | | | (364) all_194_0 = nil
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | DELTA: instantiating (335) with fresh symbol all_264_0 gives:
% 289.11/72.02 | | | | (365) app(all_186_0, all_91_0) = all_264_0 & app(nil, all_264_0) =
% 289.11/72.02 | | | | all_91_0 & $i(all_264_0)
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | ALPHA: (365) implies:
% 289.11/72.02 | | | | (366) app(all_186_0, all_91_0) = all_264_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | DELTA: instantiating (351) with fresh symbol all_294_0 gives:
% 289.11/72.02 | | | | (367) app(all_174_0, all_294_0) = all_91_0 & app(nil, all_91_0) =
% 289.11/72.02 | | | | all_294_0 & $i(all_294_0)
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | ALPHA: (367) implies:
% 289.11/72.02 | | | | (368) app(nil, all_91_0) = all_294_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | DELTA: instantiating (352) with fresh symbol all_296_0 gives:
% 289.11/72.02 | | | | (369) app(all_176_0, all_296_0) = all_91_0 & app(nil, all_91_0) =
% 289.11/72.02 | | | | all_296_0 & $i(all_296_0)
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | ALPHA: (369) implies:
% 289.11/72.02 | | | | (370) app(nil, all_91_0) = all_296_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | DELTA: instantiating (342) with fresh symbol all_304_0 gives:
% 289.11/72.02 | | | | (371) app(all_194_0, all_91_0) = all_304_0 & app(nil, all_304_0) =
% 289.11/72.02 | | | | all_91_0 & $i(all_304_0)
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | ALPHA: (371) implies:
% 289.11/72.02 | | | | (372) app(all_194_0, all_91_0) = all_304_0
% 289.11/72.02 | | | |
% 289.11/72.02 | | | | DELTA: instantiating (338) with fresh symbol all_306_0 gives:
% 289.11/72.02 | | | | (373) app(all_192_0, all_91_0) = all_306_0 & app(nil, all_306_0) =
% 289.11/72.02 | | | | all_91_0 & $i(all_306_0)
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | ALPHA: (373) implies:
% 289.11/72.03 | | | | (374) app(all_192_0, all_91_0) = all_306_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | DELTA: instantiating (354) with fresh symbol all_312_0 gives:
% 289.11/72.03 | | | | (375) app(all_180_0, all_312_0) = all_91_0 & app(nil, all_91_0) =
% 289.11/72.03 | | | | all_312_0 & $i(all_312_0)
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | ALPHA: (375) implies:
% 289.11/72.03 | | | | (376) app(nil, all_91_0) = all_312_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | DELTA: instantiating (353) with fresh symbol all_414_0 gives:
% 289.11/72.03 | | | | (377) app(all_178_0, all_414_0) = all_91_0 & app(nil, all_91_0) =
% 289.11/72.03 | | | | all_414_0 & $i(all_414_0)
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | ALPHA: (377) implies:
% 289.11/72.03 | | | | (378) app(nil, all_91_0) = all_414_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | DELTA: instantiating (336) with fresh symbol all_418_0 gives:
% 289.11/72.03 | | | | (379) app(all_188_0, all_91_0) = all_418_0 & app(nil, all_418_0) =
% 289.11/72.03 | | | | all_91_0 & $i(all_418_0)
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | ALPHA: (379) implies:
% 289.11/72.03 | | | | (380) app(all_188_0, all_91_0) = all_418_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | DELTA: instantiating (347) with fresh symbol all_562_0 gives:
% 289.11/72.03 | | | | (381) app(all_91_0, all_144_0) = all_562_0 & app(nil, all_562_0) =
% 289.11/72.03 | | | | all_210_0 & $i(all_562_0) & $i(all_210_0)
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | ALPHA: (381) implies:
% 289.11/72.03 | | | | (382) app(all_91_0, all_144_0) = all_562_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | DELTA: instantiating (345) with fresh symbol all_590_0 gives:
% 289.11/72.03 | | | | (383) app(all_136_0, all_590_0) = all_210_0 & app(all_91_0,
% 289.11/72.03 | | | | all_144_0) = all_590_0 & $i(all_590_0) & $i(all_210_0)
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | ALPHA: (383) implies:
% 289.11/72.03 | | | | (384) app(all_91_0, all_144_0) = all_590_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | DELTA: instantiating (350) with fresh symbol all_592_0 gives:
% 289.11/72.03 | | | | (385) app(all_162_0, all_144_0) = all_592_0 & app(all_162_2,
% 289.11/72.03 | | | | all_592_0) = all_210_0 & $i(all_592_0) & $i(all_210_0)
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | ALPHA: (385) implies:
% 289.11/72.03 | | | | (386) $i(all_210_0)
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | REDUCE: (364), (372) imply:
% 289.11/72.03 | | | | (387) app(nil, all_91_0) = all_304_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | REDUCE: (363), (374) imply:
% 289.11/72.03 | | | | (388) app(nil, all_91_0) = all_306_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | REDUCE: (337), (380) imply:
% 289.11/72.03 | | | | (389) app(nil, all_91_0) = all_418_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | REDUCE: (360), (366) imply:
% 289.11/72.03 | | | | (390) app(nil, all_91_0) = all_264_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | REDUCE: (271), (344) imply:
% 289.11/72.03 | | | | (391) app(nil, all_91_0) = all_230_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | REDUCE: (343), (384) imply:
% 289.11/72.03 | | | | (392) app(all_91_0, nil) = all_590_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | REDUCE: (343), (382) imply:
% 289.11/72.03 | | | | (393) app(all_91_0, nil) = all_562_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | REDUCE: (234), (343) imply:
% 289.11/72.03 | | | | (394) app(all_91_0, nil) = all_210_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_91_0, all_296_0, all_91_0, nil,
% 289.11/72.03 | | | | simplifying with (292), (370) gives:
% 289.11/72.03 | | | | (395) all_296_0 = all_91_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_264_0, all_296_0, all_91_0,
% 289.11/72.03 | | | | nil, simplifying with (370), (390) gives:
% 289.11/72.03 | | | | (396) all_296_0 = all_264_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_230_0, all_296_0, all_91_0,
% 289.11/72.03 | | | | nil, simplifying with (370), (391) gives:
% 289.11/72.03 | | | | (397) all_296_0 = all_230_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_296_0, all_304_0, all_91_0,
% 289.11/72.03 | | | | nil, simplifying with (370), (387) gives:
% 289.11/72.03 | | | | (398) all_304_0 = all_296_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_304_0, all_306_0, all_91_0,
% 289.11/72.03 | | | | nil, simplifying with (387), (388) gives:
% 289.11/72.03 | | | | (399) all_306_0 = all_304_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_306_0, all_312_0, all_91_0,
% 289.11/72.03 | | | | nil, simplifying with (376), (388) gives:
% 289.11/72.03 | | | | (400) all_312_0 = all_306_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_312_0, all_414_0, all_91_0,
% 289.11/72.03 | | | | nil, simplifying with (376), (378) gives:
% 289.11/72.03 | | | | (401) all_414_0 = all_312_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_414_0, all_418_0, all_91_0,
% 289.11/72.03 | | | | nil, simplifying with (378), (389) gives:
% 289.11/72.03 | | | | (402) all_418_0 = all_414_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_294_0, all_418_0, all_91_0,
% 289.11/72.03 | | | | nil, simplifying with (368), (389) gives:
% 289.11/72.03 | | | | (403) all_418_0 = all_294_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_91_0, all_562_0, nil, all_91_0,
% 289.11/72.03 | | | | simplifying with (274), (393) gives:
% 289.11/72.03 | | | | (404) all_562_0 = all_91_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_562_0, all_590_0, nil,
% 289.11/72.03 | | | | all_91_0, simplifying with (392), (393) gives:
% 289.11/72.03 | | | | (405) all_590_0 = all_562_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_210_0, all_590_0, nil,
% 289.11/72.03 | | | | all_91_0, simplifying with (392), (394) gives:
% 289.11/72.03 | | | | (406) all_590_0 = all_210_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (405), (406) imply:
% 289.11/72.03 | | | | (407) all_562_0 = all_210_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | SIMP: (407) implies:
% 289.11/72.03 | | | | (408) all_562_0 = all_210_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (404), (408) imply:
% 289.11/72.03 | | | | (409) all_210_0 = all_91_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (402), (403) imply:
% 289.11/72.03 | | | | (410) all_414_0 = all_294_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | SIMP: (410) implies:
% 289.11/72.03 | | | | (411) all_414_0 = all_294_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (401), (411) imply:
% 289.11/72.03 | | | | (412) all_312_0 = all_294_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | SIMP: (412) implies:
% 289.11/72.03 | | | | (413) all_312_0 = all_294_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (400), (413) imply:
% 289.11/72.03 | | | | (414) all_306_0 = all_294_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | SIMP: (414) implies:
% 289.11/72.03 | | | | (415) all_306_0 = all_294_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (399), (415) imply:
% 289.11/72.03 | | | | (416) all_304_0 = all_294_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | SIMP: (416) implies:
% 289.11/72.03 | | | | (417) all_304_0 = all_294_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (398), (417) imply:
% 289.11/72.03 | | | | (418) all_296_0 = all_294_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | SIMP: (418) implies:
% 289.11/72.03 | | | | (419) all_296_0 = all_294_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (395), (419) imply:
% 289.11/72.03 | | | | (420) all_294_0 = all_91_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (397), (419) imply:
% 289.11/72.03 | | | | (421) all_294_0 = all_230_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (396), (419) imply:
% 289.11/72.03 | | | | (422) all_294_0 = all_264_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (420), (422) imply:
% 289.11/72.03 | | | | (423) all_264_0 = all_91_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (421), (422) imply:
% 289.11/72.03 | | | | (424) all_264_0 = all_230_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | COMBINE_EQS: (423), (424) imply:
% 289.11/72.03 | | | | (425) all_230_0 = all_91_0
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | BETA: splitting (29) gives:
% 289.11/72.03 | | | |
% 289.11/72.03 | | | | Case 1:
% 289.11/72.03 | | | | |
% 289.11/72.03 | | | | | (426) ~ (all_91_0 = nil)
% 289.11/72.03 | | | | |
% 289.11/72.03 | | | | | BETA: splitting (44) gives:
% 289.11/72.03 | | | | |
% 289.11/72.03 | | | | | Case 1:
% 289.11/72.03 | | | | | |
% 289.11/72.03 | | | | | | (427) neq(all_91_0, nil)
% 289.11/72.03 | | | | | |
% 289.11/72.03 | | | | | | GROUND_INST: instantiating (30) with all_91_0, simplifying with
% 289.11/72.03 | | | | | | (25), (27), (294), (295), (427) gives:
% 289.11/72.03 | | | | | | (428) $false
% 289.11/72.03 | | | | | |
% 289.11/72.03 | | | | | | CLOSE: (428) is inconsistent.
% 289.11/72.03 | | | | | |
% 289.11/72.03 | | | | | Case 2:
% 289.11/72.03 | | | | | |
% 289.11/72.03 | | | | | | (429) all_91_0 = nil
% 289.11/72.03 | | | | | |
% 289.11/72.03 | | | | | | REDUCE: (426), (429) imply:
% 289.11/72.03 | | | | | | (430) $false
% 289.11/72.03 | | | | | |
% 289.11/72.03 | | | | | | CLOSE: (430) is inconsistent.
% 289.11/72.03 | | | | | |
% 289.11/72.03 | | | | | End of split
% 289.11/72.03 | | | | |
% 289.11/72.03 | | | | Case 2:
% 289.11/72.03 | | | | |
% 289.11/72.03 | | | | | (431) all_91_0 = nil
% 289.11/72.03 | | | | | (432) ~ (all_91_1 = nil)
% 289.11/72.03 | | | | |
% 289.11/72.03 | | | | | REDUCE: (28), (431) imply:
% 289.11/72.03 | | | | | (433) app(nil, nil) = all_91_1
% 289.11/72.03 | | | | |
% 289.11/72.03 | | | | | GROUND_INST: instantiating (22) with nil, all_91_1, nil, nil,
% 289.11/72.03 | | | | | simplifying with (147), (433) gives:
% 289.11/72.03 | | | | | (434) all_91_1 = nil
% 289.11/72.03 | | | | |
% 289.11/72.03 | | | | | REDUCE: (432), (434) imply:
% 289.11/72.03 | | | | | (435) $false
% 289.11/72.03 | | | | |
% 289.11/72.03 | | | | | CLOSE: (435) is inconsistent.
% 289.11/72.03 | | | | |
% 289.11/72.03 | | | | End of split
% 289.11/72.03 | | | |
% 289.11/72.04 | | | End of split
% 289.11/72.04 | | |
% 289.11/72.04 | | End of split
% 289.11/72.04 | |
% 289.11/72.04 | End of split
% 289.11/72.04 |
% 289.11/72.04 End of proof
% 289.11/72.04 % SZS output end Proof for theBenchmark
% 289.11/72.04
% 289.11/72.04 71437ms
%------------------------------------------------------------------------------