TSTP Solution File: SWC346+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC346+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 : n021.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 20:50:57 EDT 2023
% Result : Theorem 27.36s 4.37s
% Output : Proof 261.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC346+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 15:29:58 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.60 ________ _____
% 0.18/0.60 ___ __ \_________(_)________________________________
% 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.60
% 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.60 (2023-06-19)
% 0.18/0.60
% 0.18/0.60 (c) Philipp Rümmer, 2009-2023
% 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.60 Amanda Stjerna.
% 0.18/0.60 Free software under BSD-3-Clause.
% 0.18/0.60
% 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.60
% 0.18/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.62 Running up to 7 provers in parallel.
% 0.18/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.10/1.43 Prover 1: Preprocessing ...
% 5.10/1.45 Prover 4: Preprocessing ...
% 5.42/1.47 Prover 0: Preprocessing ...
% 5.42/1.47 Prover 3: Preprocessing ...
% 5.42/1.47 Prover 6: Preprocessing ...
% 5.42/1.47 Prover 5: Preprocessing ...
% 5.42/1.47 Prover 2: Preprocessing ...
% 14.66/2.71 Prover 2: Proving ...
% 14.72/2.77 Prover 5: Constructing countermodel ...
% 15.37/2.82 Prover 1: Constructing countermodel ...
% 15.37/2.84 Prover 6: Proving ...
% 15.37/2.88 Prover 3: Constructing countermodel ...
% 20.02/3.49 Prover 4: Constructing countermodel ...
% 22.06/3.69 Prover 0: Proving ...
% 26.61/4.37 Prover 3: proved (3739ms)
% 26.61/4.37
% 27.36/4.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.36/4.37
% 27.36/4.37 Prover 5: stopped
% 27.36/4.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 27.36/4.38 Prover 6: stopped
% 27.36/4.38 Prover 0: stopped
% 27.36/4.38 Prover 2: stopped
% 27.36/4.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 27.36/4.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 27.36/4.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 27.36/4.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 30.48/4.78 Prover 11: Preprocessing ...
% 30.48/4.81 Prover 13: Preprocessing ...
% 30.48/4.84 Prover 7: Preprocessing ...
% 30.48/4.85 Prover 10: Preprocessing ...
% 30.48/4.86 Prover 8: Preprocessing ...
% 31.83/5.05 Prover 7: Constructing countermodel ...
% 32.71/5.08 Prover 10: Constructing countermodel ...
% 32.71/5.11 Prover 13: Constructing countermodel ...
% 33.95/5.25 Prover 8: Warning: ignoring some quantifiers
% 34.24/5.27 Prover 8: Constructing countermodel ...
% 38.43/5.81 Prover 11: Constructing countermodel ...
% 68.09/9.68 Prover 13: stopped
% 68.09/9.68 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 68.85/9.83 Prover 16: Preprocessing ...
% 70.85/10.03 Prover 16: Constructing countermodel ...
% 112.12/15.48 Prover 16: stopped
% 112.12/15.50 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 112.92/15.64 Prover 19: Preprocessing ...
% 115.62/15.97 Prover 1: stopped
% 116.34/16.03 Prover 19: Warning: ignoring some quantifiers
% 116.34/16.08 Prover 19: Constructing countermodel ...
% 138.66/19.23 Prover 19: stopped
% 180.48/27.00 Prover 7: stopped
% 184.54/27.96 Prover 4: stopped
% 226.08/39.70 Prover 8: stopped
% 226.94/40.07 Prover 11: stopped
% 259.76/67.29 Prover 10: Found proof (size 337)
% 259.76/67.29 Prover 10: proved (62913ms)
% 259.76/67.29
% 259.76/67.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 259.76/67.29
% 260.20/67.43 % SZS output start Proof for theBenchmark
% 260.20/67.43 Assumptions after simplification:
% 260.20/67.43 ---------------------------------
% 260.20/67.44
% 260.20/67.44 (ax17)
% 260.20/67.44 $i(nil) & ssList(nil)
% 260.20/67.44
% 260.20/67.44 (ax26)
% 260.20/67.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) |
% 260.20/67.47 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 260.20/67.47
% 260.20/67.47 (ax28)
% 260.20/67.47 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 260.20/67.47 $i(v0) | ~ ssList(v0))
% 260.20/67.47
% 260.20/67.47 (ax42)
% 260.20/67.47 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0))
% 260.20/67.47
% 260.20/67.47 (ax45)
% 260.20/67.47 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 260.20/67.47
% 260.20/67.47 (ax46)
% 260.20/67.47 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 260.20/67.47 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 260.20/67.47
% 260.20/67.47 (ax49)
% 260.20/67.47 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, v0))
% 260.20/67.47
% 260.20/67.47 (ax5)
% 260.20/67.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 260.20/67.48 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 260.20/67.48 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 260.20/67.48 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 260.20/67.48 v2) = v0 & $i(v2) & ssList(v2)))
% 260.20/67.48
% 260.20/67.48 (ax50)
% 260.20/67.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2, v0) = v3)
% 260.20/67.48 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, v1) | ~ ssList(v2) |
% 260.20/67.48 ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1))
% 260.20/67.48
% 260.20/67.48 (ax51)
% 260.20/67.48 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 260.20/67.48
% 260.20/67.48 (ax52)
% 260.20/67.48 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~
% 260.20/67.48 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 260.20/67.48
% 260.20/67.48 (ax58)
% 260.20/67.48 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 260.20/67.48 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 260.20/67.48
% 260.20/67.48 (ax6)
% 260.20/67.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 260.20/67.48 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 260.20/67.48 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 260.20/67.48 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 260.20/67.48 v1) = v0 & $i(v2) & ssList(v2)))
% 260.20/67.48
% 260.20/67.48 (ax68)
% 260.20/67.48 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 260.20/67.48 ~ ssItem(v0) | strictorderedP(v1))
% 260.20/67.48
% 260.20/67.48 (ax69)
% 260.48/67.49 $i(nil) & strictorderedP(nil)
% 260.48/67.49
% 260.48/67.49 (ax7)
% 260.48/67.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.48/67.49 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 260.48/67.49 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 260.48/67.49 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 260.48/67.49 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 260.48/67.49 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 260.48/67.49 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 260.48/67.49
% 260.48/67.49 (ax79)
% 260.48/67.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v3,
% 260.48/67.49 v1) = v2) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 260.48/67.49 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 260.48/67.49
% 260.48/67.49 (ax80)
% 260.48/67.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v1,
% 260.48/67.49 v3) = v2) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 260.48/67.49 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 260.48/67.49
% 260.48/67.49 (ax82)
% 260.48/67.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.48/67.50 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 260.48/67.50 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 260.48/67.50 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 260.48/67.50
% 260.48/67.50 (ax83)
% 260.48/67.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 260.48/67.50 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 260.48/67.50 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 260.48/67.50 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 260.48/67.50 v0) | ~ ssList(nil))
% 260.48/67.50
% 260.48/67.50 (ax84)
% 260.48/67.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 260.48/67.50 $i(v0) | ~ ssList(v0))
% 260.48/67.50
% 260.48/67.50 (co1)
% 260.48/67.51 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 260.48/67.51 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v4) & $i(v2) & $i(v1)
% 260.48/67.51 & $i(v0) & ssList(v1) & ssList(v0) & ( ~ strictorderedP(v0) | ~
% 260.48/67.51 segmentP(v1, v0)) & ((v7 = v1 & v3 = v0 & cons(v2, nil) = v0 & app(v5, v6)
% 260.48/67.51 = v1 & app(v4, v0) = v5 & $i(v5) & ssList(v6) & ssList(v4) & ssItem(v2)
% 260.48/67.51 & ! [v8: $i] : ( ~ $i(v8) | ~ lt(v8, v2) | ~ memberP(v6, v8) | ~
% 260.48/67.51 ssItem(v8)) & ! [v8: $i] : ( ~ $i(v8) | ~ lt(v2, v8) | ~
% 260.48/67.51 memberP(v4, v8) | ~ ssItem(v8))) | (v1 = nil & v0 = nil)))
% 260.48/67.51
% 260.48/67.51 (function-axioms)
% 260.48/67.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 260.48/67.51 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 260.48/67.51 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 260.48/67.51 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 260.48/67.51 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 260.48/67.51 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 260.48/67.51
% 260.48/67.51 Further assumptions not needed in the proof:
% 260.48/67.51 --------------------------------------------
% 260.48/67.51 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 260.48/67.51 ax22, ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35,
% 260.48/67.51 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax47, ax48, ax53, ax54,
% 260.48/67.51 ax55, ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax70,
% 260.48/67.51 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax8, ax81, ax85, ax86, ax87,
% 260.48/67.51 ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 260.48/67.51
% 260.48/67.51 Those formulas are unsatisfiable:
% 260.48/67.51 ---------------------------------
% 260.48/67.51
% 260.48/67.51 Begin of proof
% 260.48/67.51 |
% 260.48/67.51 | ALPHA: (ax5) implies:
% 260.48/67.51 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 260.48/67.51 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 260.48/67.51 | v0 & $i(v2) & ssList(v2)))
% 260.48/67.51 |
% 260.48/67.51 | ALPHA: (ax6) implies:
% 260.48/67.52 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 260.48/67.52 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 260.48/67.52 | v0 & $i(v2) & ssList(v2)))
% 260.48/67.52 |
% 260.48/67.52 | ALPHA: (ax7) implies:
% 260.48/67.52 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0,
% 260.48/67.52 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] :
% 260.48/67.52 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) &
% 260.48/67.52 | $i(v2) & ssList(v4) & ssList(v2)))
% 260.48/67.52 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 260.48/67.52 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2)
% 260.48/67.52 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~
% 260.48/67.52 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 260.48/67.52 |
% 260.48/67.52 | ALPHA: (ax17) implies:
% 260.48/67.52 | (5) ssList(nil)
% 260.48/67.52 |
% 260.48/67.52 | ALPHA: (ax28) implies:
% 260.48/67.52 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 260.48/67.52 | $i(v0) | ~ ssList(v0))
% 260.48/67.52 |
% 260.48/67.52 | ALPHA: (ax45) implies:
% 260.48/67.52 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 260.48/67.52 |
% 260.48/67.52 | ALPHA: (ax46) implies:
% 260.48/67.52 | (8) ~ ssList(nil) | frontsegP(nil, nil)
% 260.48/67.52 |
% 260.48/67.52 | ALPHA: (ax51) implies:
% 260.48/67.52 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 260.48/67.52 |
% 260.48/67.52 | ALPHA: (ax52) implies:
% 260.48/67.52 | (10) ~ ssList(nil) | rearsegP(nil, nil)
% 260.48/67.52 |
% 260.48/67.52 | ALPHA: (ax58) implies:
% 260.48/67.52 | (11) ~ ssList(nil) | segmentP(nil, nil)
% 260.48/67.52 |
% 260.48/67.52 | ALPHA: (ax68) implies:
% 260.48/67.52 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ~
% 260.48/67.52 | ssItem(v0) | strictorderedP(v1))
% 260.48/67.52 |
% 260.48/67.52 | ALPHA: (ax69) implies:
% 260.48/67.52 | (13) strictorderedP(nil)
% 260.48/67.52 |
% 260.48/67.52 | ALPHA: (ax83) implies:
% 260.48/67.52 | (14) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 260.48/67.53 | (15) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~
% 260.48/67.53 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 260.48/67.53 | (16) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 260.48/67.53 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 260.48/67.53 |
% 260.48/67.53 | ALPHA: (ax84) implies:
% 260.48/67.53 | (17) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 260.48/67.53 | $i(v0) | ~ ssList(v0))
% 260.48/67.53 |
% 260.48/67.53 | ALPHA: (co1) implies:
% 260.48/67.53 | (18) $i(nil)
% 260.48/67.53 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 260.48/67.53 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v4) & $i(v2) &
% 260.48/67.53 | $i(v1) & $i(v0) & ssList(v1) & ssList(v0) & ( ~ strictorderedP(v0) |
% 260.48/67.53 | ~ segmentP(v1, v0)) & ((v7 = v1 & v3 = v0 & cons(v2, nil) = v0 &
% 260.48/67.53 | app(v5, v6) = v1 & app(v4, v0) = v5 & $i(v5) & ssList(v6) &
% 260.48/67.53 | ssList(v4) & ssItem(v2) & ! [v8: $i] : ( ~ $i(v8) | ~ lt(v8,
% 260.48/67.53 | v2) | ~ memberP(v6, v8) | ~ ssItem(v8)) & ! [v8: $i] : (
% 260.48/67.53 | ~ $i(v8) | ~ lt(v2, v8) | ~ memberP(v4, v8) | ~
% 260.48/67.53 | ssItem(v8))) | (v1 = nil & v0 = nil)))
% 260.48/67.53 |
% 260.48/67.53 | ALPHA: (function-axioms) implies:
% 260.48/67.53 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 260.48/67.53 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 260.48/67.53 |
% 260.48/67.53 | DELTA: instantiating (19) with fresh symbols all_91_0, all_91_1, all_91_2,
% 260.48/67.53 | all_91_3, all_91_4, all_91_5, all_91_6, all_91_7 gives:
% 260.48/67.53 | (21) $i(all_91_1) & $i(all_91_3) & $i(all_91_5) & $i(all_91_6) &
% 260.48/67.53 | $i(all_91_7) & ssList(all_91_6) & ssList(all_91_7) & ( ~
% 260.48/67.53 | strictorderedP(all_91_7) | ~ segmentP(all_91_6, all_91_7)) &
% 260.48/67.53 | ((all_91_0 = all_91_6 & all_91_4 = all_91_7 & cons(all_91_5, nil) =
% 260.48/67.53 | all_91_7 & app(all_91_2, all_91_1) = all_91_6 & app(all_91_3,
% 260.48/67.53 | all_91_7) = all_91_2 & $i(all_91_2) & ssList(all_91_1) &
% 260.48/67.53 | ssList(all_91_3) & ssItem(all_91_5) & ! [v0: $i] : ( ~ $i(v0) |
% 260.48/67.53 | ~ lt(v0, all_91_5) | ~ memberP(all_91_1, v0) | ~ ssItem(v0)) &
% 260.48/67.53 | ! [v0: $i] : ( ~ $i(v0) | ~ lt(all_91_5, v0) | ~
% 260.48/67.53 | memberP(all_91_3, v0) | ~ ssItem(v0))) | (all_91_6 = nil &
% 260.48/67.53 | all_91_7 = nil))
% 260.48/67.53 |
% 260.48/67.53 | ALPHA: (21) implies:
% 260.48/67.53 | (22) ssList(all_91_7)
% 260.48/67.53 | (23) ssList(all_91_6)
% 260.48/67.53 | (24) $i(all_91_7)
% 260.48/67.53 | (25) $i(all_91_6)
% 260.48/67.53 | (26) $i(all_91_5)
% 260.48/67.54 | (27) $i(all_91_3)
% 260.48/67.54 | (28) $i(all_91_1)
% 260.48/67.54 | (29) (all_91_0 = all_91_6 & all_91_4 = all_91_7 & cons(all_91_5, nil) =
% 260.48/67.54 | all_91_7 & app(all_91_2, all_91_1) = all_91_6 & app(all_91_3,
% 260.48/67.54 | all_91_7) = all_91_2 & $i(all_91_2) & ssList(all_91_1) &
% 260.48/67.54 | ssList(all_91_3) & ssItem(all_91_5) & ! [v0: $i] : ( ~ $i(v0) | ~
% 260.48/67.54 | lt(v0, all_91_5) | ~ memberP(all_91_1, v0) | ~ ssItem(v0)) & !
% 260.48/67.54 | [v0: $i] : ( ~ $i(v0) | ~ lt(all_91_5, v0) | ~ memberP(all_91_3,
% 260.48/67.54 | v0) | ~ ssItem(v0))) | (all_91_6 = nil & all_91_7 = nil)
% 260.48/67.54 | (30) ~ strictorderedP(all_91_7) | ~ segmentP(all_91_6, all_91_7)
% 260.48/67.54 |
% 260.48/67.54 | BETA: splitting (10) gives:
% 260.48/67.54 |
% 260.48/67.54 | Case 1:
% 260.48/67.54 | |
% 260.48/67.54 | | (31) ~ ssList(nil)
% 260.48/67.54 | |
% 260.48/67.54 | | PRED_UNIFY: (5), (31) imply:
% 260.48/67.54 | | (32) $false
% 260.48/67.54 | |
% 260.48/67.54 | | CLOSE: (32) is inconsistent.
% 260.48/67.54 | |
% 260.48/67.54 | Case 2:
% 260.48/67.54 | |
% 260.48/67.54 | | (33) rearsegP(nil, nil)
% 260.48/67.54 | |
% 260.48/67.54 | | BETA: splitting (8) gives:
% 260.48/67.54 | |
% 260.48/67.54 | | Case 1:
% 260.48/67.54 | | |
% 260.48/67.54 | | | (34) ~ ssList(nil)
% 260.48/67.54 | | |
% 260.48/67.54 | | | PRED_UNIFY: (5), (34) imply:
% 260.48/67.54 | | | (35) $false
% 260.48/67.54 | | |
% 260.48/67.54 | | | CLOSE: (35) is inconsistent.
% 260.48/67.54 | | |
% 260.48/67.54 | | Case 2:
% 260.48/67.54 | | |
% 260.48/67.54 | | | (36) frontsegP(nil, nil)
% 260.48/67.54 | | |
% 260.48/67.54 | | | BETA: splitting (11) gives:
% 260.48/67.54 | | |
% 260.48/67.54 | | | Case 1:
% 260.48/67.54 | | | |
% 260.48/67.54 | | | | (37) ~ ssList(nil)
% 260.48/67.54 | | | |
% 260.48/67.54 | | | | PRED_UNIFY: (5), (37) imply:
% 260.48/67.54 | | | | (38) $false
% 260.48/67.54 | | | |
% 260.48/67.54 | | | | CLOSE: (38) is inconsistent.
% 260.48/67.54 | | | |
% 260.48/67.54 | | | Case 2:
% 260.48/67.54 | | | |
% 260.48/67.54 | | | | (39) segmentP(nil, nil)
% 260.48/67.54 | | | |
% 260.48/67.54 | | | | GROUND_INST: instantiating (ax49) with all_91_7, simplifying with (22),
% 260.48/67.54 | | | | (24) gives:
% 260.48/67.54 | | | | (40) rearsegP(all_91_7, all_91_7)
% 260.48/67.54 | | | |
% 260.48/67.54 | | | | GROUND_INST: instantiating (9) with all_91_7, simplifying with (22),
% 260.48/67.54 | | | | (24) gives:
% 260.48/67.54 | | | | (41) rearsegP(all_91_7, nil)
% 260.48/67.54 | | | |
% 260.48/67.54 | | | | GROUND_INST: instantiating (ax42) with all_91_7, simplifying with (22),
% 260.48/67.54 | | | | (24) gives:
% 260.48/67.54 | | | | (42) frontsegP(all_91_7, all_91_7)
% 260.48/67.54 | | | |
% 260.48/67.54 | | | | GROUND_INST: instantiating (7) with all_91_7, simplifying with (22),
% 260.48/67.54 | | | | (24) gives:
% 260.48/67.54 | | | | (43) frontsegP(all_91_7, nil)
% 260.48/67.54 | | | |
% 260.48/67.54 | | | | GROUND_INST: instantiating (ax49) with all_91_6, simplifying with (23),
% 260.48/67.54 | | | | (25) gives:
% 260.48/67.54 | | | | (44) rearsegP(all_91_6, all_91_6)
% 260.48/67.54 | | | |
% 260.48/67.54 | | | | GROUND_INST: instantiating (9) with all_91_6, simplifying with (23),
% 260.48/67.54 | | | | (25) gives:
% 260.48/67.54 | | | | (45) rearsegP(all_91_6, nil)
% 260.48/67.54 | | | |
% 260.48/67.54 | | | | GROUND_INST: instantiating (7) with all_91_6, simplifying with (23),
% 260.48/67.54 | | | | (25) gives:
% 260.48/67.55 | | | | (46) frontsegP(all_91_6, nil)
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (5),
% 260.48/67.55 | | | | (18), (36) gives:
% 260.48/67.55 | | | | (47) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | GROUND_INST: instantiating (2) with nil, nil, simplifying with (5),
% 260.48/67.55 | | | | (18), (33) gives:
% 260.48/67.55 | | | | (48) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0))
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (5),
% 260.48/67.55 | | | | (18), (39) gives:
% 260.48/67.55 | | | | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil &
% 260.48/67.55 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) &
% 260.48/67.55 | | | | ssList(v0))
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | DELTA: instantiating (48) with fresh symbol all_111_0 gives:
% 260.48/67.55 | | | | (50) app(all_111_0, nil) = nil & $i(all_111_0) & ssList(all_111_0)
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | ALPHA: (50) implies:
% 260.48/67.55 | | | | (51) ssList(all_111_0)
% 260.48/67.55 | | | | (52) $i(all_111_0)
% 260.48/67.55 | | | | (53) app(all_111_0, nil) = nil
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | DELTA: instantiating (47) with fresh symbol all_113_0 gives:
% 260.48/67.55 | | | | (54) app(nil, all_113_0) = nil & $i(all_113_0) & ssList(all_113_0)
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | ALPHA: (54) implies:
% 260.48/67.55 | | | | (55) ssList(all_113_0)
% 260.48/67.55 | | | | (56) $i(all_113_0)
% 260.48/67.55 | | | | (57) app(nil, all_113_0) = nil
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | DELTA: instantiating (49) with fresh symbols all_115_0, all_115_1,
% 260.48/67.55 | | | | all_115_2 gives:
% 260.48/67.55 | | | | (58) app(all_115_1, all_115_0) = nil & app(all_115_2, nil) =
% 260.48/67.55 | | | | all_115_1 & $i(all_115_0) & $i(all_115_1) & $i(all_115_2) &
% 260.48/67.55 | | | | ssList(all_115_0) & ssList(all_115_2)
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | ALPHA: (58) implies:
% 260.48/67.55 | | | | (59) ssList(all_115_2)
% 260.48/67.55 | | | | (60) ssList(all_115_0)
% 260.48/67.55 | | | | (61) $i(all_115_2)
% 260.48/67.55 | | | | (62) $i(all_115_1)
% 260.48/67.55 | | | | (63) $i(all_115_0)
% 260.48/67.55 | | | | (64) app(all_115_2, nil) = all_115_1
% 260.48/67.55 | | | | (65) app(all_115_1, all_115_0) = nil
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | GROUND_INST: instantiating (ax49) with all_115_2, simplifying with (59),
% 260.48/67.55 | | | | (61) gives:
% 260.48/67.55 | | | | (66) rearsegP(all_115_2, all_115_2)
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | GROUND_INST: instantiating (ax42) with all_115_2, simplifying with (59),
% 260.48/67.55 | | | | (61) gives:
% 260.48/67.55 | | | | (67) frontsegP(all_115_2, all_115_2)
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | GROUND_INST: instantiating (7) with all_115_2, simplifying with (59),
% 260.48/67.55 | | | | (61) gives:
% 260.48/67.55 | | | | (68) frontsegP(all_115_2, nil)
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | GROUND_INST: instantiating (ax49) with all_115_0, simplifying with (60),
% 260.48/67.55 | | | | (63) gives:
% 260.48/67.55 | | | | (69) rearsegP(all_115_0, all_115_0)
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | GROUND_INST: instantiating (9) with all_115_0, simplifying with (60),
% 260.48/67.55 | | | | (63) gives:
% 260.48/67.55 | | | | (70) rearsegP(all_115_0, nil)
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | GROUND_INST: instantiating (ax42) with all_115_0, simplifying with (60),
% 260.48/67.55 | | | | (63) gives:
% 260.48/67.55 | | | | (71) frontsegP(all_115_0, all_115_0)
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | GROUND_INST: instantiating (7) with all_115_0, simplifying with (60),
% 260.48/67.55 | | | | (63) gives:
% 260.48/67.55 | | | | (72) frontsegP(all_115_0, nil)
% 260.48/67.55 | | | |
% 260.48/67.55 | | | | GROUND_INST: instantiating (1) with all_91_7, nil, simplifying with (5),
% 260.48/67.55 | | | | (18), (22), (24), (43) gives:
% 260.48/67.55 | | | | (73) ? [v0: $i] : (app(nil, v0) = all_91_7 & $i(v0) & ssList(v0))
% 260.48/67.55 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (1) with all_91_7, all_91_7, simplifying with
% 260.48/67.56 | | | | (22), (24), (42) gives:
% 260.48/67.56 | | | | (74) ? [v0: $i] : (app(all_91_7, v0) = all_91_7 & $i(v0) &
% 260.48/67.56 | | | | ssList(v0))
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (1) with all_91_6, nil, simplifying with (5),
% 260.48/67.56 | | | | (18), (23), (25), (46) gives:
% 260.48/67.56 | | | | (75) ? [v0: $i] : (app(nil, v0) = all_91_6 & $i(v0) & ssList(v0))
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (2) with all_91_7, nil, simplifying with (5),
% 260.48/67.56 | | | | (18), (22), (24), (41) gives:
% 260.48/67.56 | | | | (76) ? [v0: $i] : (app(v0, nil) = all_91_7 & $i(v0) & ssList(v0))
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (2) with all_91_7, all_91_7, simplifying with
% 260.48/67.56 | | | | (22), (24), (40) gives:
% 260.48/67.56 | | | | (77) ? [v0: $i] : (app(v0, all_91_7) = all_91_7 & $i(v0) &
% 260.48/67.56 | | | | ssList(v0))
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (2) with all_91_6, nil, simplifying with (5),
% 260.48/67.56 | | | | (18), (23), (25), (45) gives:
% 260.48/67.56 | | | | (78) ? [v0: $i] : (app(v0, nil) = all_91_6 & $i(v0) & ssList(v0))
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (2) with all_91_6, all_91_6, simplifying with
% 260.48/67.56 | | | | (23), (25), (44) gives:
% 260.48/67.56 | | | | (79) ? [v0: $i] : (app(v0, all_91_6) = all_91_6 & $i(v0) &
% 260.48/67.56 | | | | ssList(v0))
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (ax82) with nil, all_113_0, nil, all_113_0,
% 260.48/67.56 | | | | nil, simplifying with (5), (18), (55), (56), (57) gives:
% 260.48/67.56 | | | | (80) ? [v0: $i] : (app(all_113_0, all_113_0) = v0 & app(nil, v0) =
% 260.48/67.56 | | | | nil & $i(v0))
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (6) with all_113_0, nil, simplifying with
% 260.48/67.56 | | | | (55), (56), (57) gives:
% 260.48/67.56 | | | | (81) all_113_0 = nil
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (17) with all_111_0, nil, simplifying with
% 260.48/67.56 | | | | (51), (52), (53) gives:
% 260.48/67.56 | | | | (82) all_111_0 = nil
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (ax50) with nil, nil, all_115_2, all_115_1,
% 260.48/67.56 | | | | simplifying with (5), (18), (33), (59), (61), (64) gives:
% 260.48/67.56 | | | | (83) rearsegP(all_115_1, nil)
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (ax26) with all_115_2, nil, all_115_1,
% 260.48/67.56 | | | | simplifying with (5), (18), (59), (61), (64) gives:
% 260.48/67.56 | | | | (84) ssList(all_115_1)
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (17) with all_115_2, all_115_1, simplifying
% 260.48/67.56 | | | | with (59), (61), (64) gives:
% 260.48/67.56 | | | | (85) all_115_1 = all_115_2
% 260.48/67.56 | | | |
% 260.48/67.56 | | | | GROUND_INST: instantiating (ax82) with all_115_2, nil, all_115_1,
% 260.48/67.56 | | | | all_115_0, nil, simplifying with (5), (18), (59), (60),
% 260.48/67.56 | | | | (61), (63), (64), (65) gives:
% 260.48/67.57 | | | | (86) ? [v0: $i] : (app(all_115_2, v0) = nil & app(nil, all_115_0) =
% 260.48/67.57 | | | | v0 & $i(v0))
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | DELTA: instantiating (79) with fresh symbol all_131_0 gives:
% 260.48/67.57 | | | | (87) app(all_131_0, all_91_6) = all_91_6 & $i(all_131_0) &
% 260.48/67.57 | | | | ssList(all_131_0)
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | ALPHA: (87) implies:
% 260.48/67.57 | | | | (88) ssList(all_131_0)
% 260.48/67.57 | | | | (89) $i(all_131_0)
% 260.48/67.57 | | | | (90) app(all_131_0, all_91_6) = all_91_6
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | DELTA: instantiating (78) with fresh symbol all_133_0 gives:
% 260.48/67.57 | | | | (91) app(all_133_0, nil) = all_91_6 & $i(all_133_0) &
% 260.48/67.57 | | | | ssList(all_133_0)
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | ALPHA: (91) implies:
% 260.48/67.57 | | | | (92) ssList(all_133_0)
% 260.48/67.57 | | | | (93) $i(all_133_0)
% 260.48/67.57 | | | | (94) app(all_133_0, nil) = all_91_6
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | DELTA: instantiating (77) with fresh symbol all_135_0 gives:
% 260.48/67.57 | | | | (95) app(all_135_0, all_91_7) = all_91_7 & $i(all_135_0) &
% 260.48/67.57 | | | | ssList(all_135_0)
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | ALPHA: (95) implies:
% 260.48/67.57 | | | | (96) ssList(all_135_0)
% 260.48/67.57 | | | | (97) $i(all_135_0)
% 260.48/67.57 | | | | (98) app(all_135_0, all_91_7) = all_91_7
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | DELTA: instantiating (76) with fresh symbol all_137_0 gives:
% 260.48/67.57 | | | | (99) app(all_137_0, nil) = all_91_7 & $i(all_137_0) &
% 260.48/67.57 | | | | ssList(all_137_0)
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | ALPHA: (99) implies:
% 260.48/67.57 | | | | (100) ssList(all_137_0)
% 260.48/67.57 | | | | (101) $i(all_137_0)
% 260.48/67.57 | | | | (102) app(all_137_0, nil) = all_91_7
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | DELTA: instantiating (86) with fresh symbol all_139_0 gives:
% 260.48/67.57 | | | | (103) app(all_115_2, all_139_0) = nil & app(nil, all_115_0) =
% 260.48/67.57 | | | | all_139_0 & $i(all_139_0)
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | ALPHA: (103) implies:
% 260.48/67.57 | | | | (104) app(nil, all_115_0) = all_139_0
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | DELTA: instantiating (75) with fresh symbol all_143_0 gives:
% 260.48/67.57 | | | | (105) app(nil, all_143_0) = all_91_6 & $i(all_143_0) &
% 260.48/67.57 | | | | ssList(all_143_0)
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | ALPHA: (105) implies:
% 260.48/67.57 | | | | (106) ssList(all_143_0)
% 260.48/67.57 | | | | (107) $i(all_143_0)
% 260.48/67.57 | | | | (108) app(nil, all_143_0) = all_91_6
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | DELTA: instantiating (80) with fresh symbol all_145_0 gives:
% 260.48/67.57 | | | | (109) app(all_113_0, all_113_0) = all_145_0 & app(nil, all_145_0) =
% 260.48/67.57 | | | | nil & $i(all_145_0)
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | ALPHA: (109) implies:
% 260.48/67.57 | | | | (110) $i(all_145_0)
% 260.48/67.57 | | | | (111) app(all_113_0, all_113_0) = all_145_0
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | DELTA: instantiating (74) with fresh symbol all_147_0 gives:
% 260.48/67.57 | | | | (112) app(all_91_7, all_147_0) = all_91_7 & $i(all_147_0) &
% 260.48/67.57 | | | | ssList(all_147_0)
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | ALPHA: (112) implies:
% 260.48/67.57 | | | | (113) ssList(all_147_0)
% 260.48/67.57 | | | | (114) $i(all_147_0)
% 260.48/67.57 | | | | (115) app(all_91_7, all_147_0) = all_91_7
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | DELTA: instantiating (73) with fresh symbol all_149_0 gives:
% 260.48/67.57 | | | | (116) app(nil, all_149_0) = all_91_7 & $i(all_149_0) &
% 260.48/67.57 | | | | ssList(all_149_0)
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | ALPHA: (116) implies:
% 260.48/67.57 | | | | (117) ssList(all_149_0)
% 260.48/67.57 | | | | (118) $i(all_149_0)
% 260.48/67.57 | | | | (119) app(nil, all_149_0) = all_91_7
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | REDUCE: (65), (85) imply:
% 260.48/67.57 | | | | (120) app(all_115_2, all_115_0) = nil
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | REDUCE: (81), (111) imply:
% 260.48/67.57 | | | | (121) app(nil, nil) = all_145_0
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | REDUCE: (83), (85) imply:
% 260.48/67.57 | | | | (122) rearsegP(all_115_2, nil)
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | GROUND_INST: instantiating (14) with all_145_0, simplifying with (5),
% 260.48/67.57 | | | | (121) gives:
% 260.48/67.57 | | | | (123) all_145_0 = nil
% 260.48/67.57 | | | |
% 260.48/67.57 | | | | REDUCE: (121), (123) imply:
% 260.48/67.57 | | | | (124) app(nil, nil) = nil
% 260.48/67.57 | | | |
% 260.48/67.58 | | | | GROUND_INST: instantiating (1) with all_115_2, nil, simplifying with
% 260.48/67.58 | | | | (5), (18), (59), (61), (68) gives:
% 260.48/67.58 | | | | (125) ? [v0: $i] : (app(nil, v0) = all_115_2 & $i(v0) & ssList(v0))
% 260.48/67.58 | | | |
% 260.48/67.58 | | | | GROUND_INST: instantiating (1) with all_115_2, all_115_2, simplifying
% 260.48/67.58 | | | | with (59), (61), (67) gives:
% 260.48/67.58 | | | | (126) ? [v0: $i] : (app(all_115_2, v0) = all_115_2 & $i(v0) &
% 260.48/67.58 | | | | ssList(v0))
% 260.48/67.58 | | | |
% 260.48/67.58 | | | | GROUND_INST: instantiating (1) with all_115_0, nil, simplifying with
% 260.48/67.58 | | | | (5), (18), (60), (63), (72) gives:
% 260.48/67.58 | | | | (127) ? [v0: $i] : (app(nil, v0) = all_115_0 & $i(v0) & ssList(v0))
% 260.48/67.58 | | | |
% 260.48/67.58 | | | | GROUND_INST: instantiating (1) with all_115_0, all_115_0, simplifying
% 260.48/67.58 | | | | with (60), (63), (71) gives:
% 260.48/67.58 | | | | (128) ? [v0: $i] : (app(all_115_0, v0) = all_115_0 & $i(v0) &
% 260.48/67.58 | | | | ssList(v0))
% 260.48/67.58 | | | |
% 260.48/67.58 | | | | GROUND_INST: instantiating (2) with all_115_2, nil, simplifying with
% 260.48/67.58 | | | | (5), (18), (59), (61), (122) gives:
% 260.48/67.58 | | | | (129) ? [v0: $i] : (app(v0, nil) = all_115_2 & $i(v0) & ssList(v0))
% 260.48/67.58 | | | |
% 260.48/67.58 | | | | GROUND_INST: instantiating (2) with all_115_2, all_115_2, simplifying
% 260.48/67.58 | | | | with (59), (61), (66) gives:
% 260.48/67.58 | | | | (130) ? [v0: $i] : (app(v0, all_115_2) = all_115_2 & $i(v0) &
% 260.48/67.58 | | | | ssList(v0))
% 260.48/67.58 | | | |
% 260.48/67.58 | | | | GROUND_INST: instantiating (2) with all_115_0, nil, simplifying with
% 260.48/67.58 | | | | (5), (18), (60), (63), (70) gives:
% 260.48/67.58 | | | | (131) ? [v0: $i] : (app(v0, nil) = all_115_0 & $i(v0) & ssList(v0))
% 260.48/67.58 | | | |
% 260.48/67.58 | | | | GROUND_INST: instantiating (2) with all_115_0, all_115_0, simplifying
% 260.48/67.58 | | | | with (60), (63), (69) gives:
% 260.48/67.58 | | | | (132) ? [v0: $i] : (app(v0, all_115_0) = all_115_0 & $i(v0) &
% 260.48/67.58 | | | | ssList(v0))
% 260.48/67.58 | | | |
% 260.48/67.58 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_115_0,
% 260.48/67.58 | | | | all_139_0, simplifying with (5), (18), (60), (63), (104),
% 260.48/67.58 | | | | (124) gives:
% 260.48/67.58 | | | | (133) ? [v0: $i] : (app(nil, v0) = all_139_0 & app(nil, all_115_0) =
% 260.48/67.58 | | | | v0 & $i(v0) & $i(all_139_0))
% 260.48/67.58 | | | |
% 260.48/67.58 | | | | GROUND_INST: instantiating (6) with all_115_0, all_139_0, simplifying
% 260.48/67.58 | | | | with (60), (63), (104) gives:
% 260.48/67.58 | | | | (134) all_139_0 = all_115_0
% 260.48/67.58 | | | |
% 260.48/67.58 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_143_0,
% 260.48/67.58 | | | | all_91_6, simplifying with (5), (18), (106), (107), (108),
% 260.69/67.58 | | | | (124) gives:
% 260.69/67.58 | | | | (135) ? [v0: $i] : (app(nil, v0) = all_91_6 & app(nil, all_143_0) =
% 260.69/67.58 | | | | v0 & $i(v0) & $i(all_91_6))
% 260.69/67.58 | | | |
% 260.69/67.59 | | | | GROUND_INST: instantiating (6) with all_143_0, all_91_6, simplifying
% 260.69/67.59 | | | | with (106), (107), (108) gives:
% 260.69/67.59 | | | | (136) all_143_0 = all_91_6
% 260.69/67.59 | | | |
% 260.69/67.59 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_149_0,
% 260.69/67.59 | | | | all_91_7, simplifying with (5), (18), (117), (118), (119),
% 260.69/67.59 | | | | (124) gives:
% 260.69/67.59 | | | | (137) ? [v0: $i] : (app(nil, v0) = all_91_7 & app(nil, all_149_0) =
% 260.69/67.59 | | | | v0 & $i(v0) & $i(all_91_7))
% 260.69/67.59 | | | |
% 260.69/67.59 | | | | GROUND_INST: instantiating (6) with all_149_0, all_91_7, simplifying
% 260.69/67.59 | | | | with (117), (118), (119) gives:
% 260.69/67.59 | | | | (138) all_149_0 = all_91_7
% 260.69/67.59 | | | |
% 260.69/67.59 | | | | GROUND_INST: instantiating (4) with all_91_7, all_147_0, all_91_7,
% 260.69/67.59 | | | | all_91_7, all_147_0, simplifying with (22), (24), (113),
% 260.69/67.59 | | | | (114), (115) gives:
% 260.69/67.59 | | | | (139) segmentP(all_91_7, all_147_0)
% 260.69/67.59 | | | |
% 260.69/67.59 | | | | GROUND_INST: instantiating (ax82) with nil, all_149_0, all_91_7,
% 260.69/67.59 | | | | all_147_0, all_91_7, simplifying with (5), (18), (113),
% 260.69/67.59 | | | | (114), (115), (117), (118), (119) gives:
% 260.69/67.59 | | | | (140) ? [v0: $i] : (app(all_149_0, all_147_0) = v0 & app(nil, v0) =
% 260.69/67.59 | | | | all_91_7 & $i(v0) & $i(all_91_7))
% 260.69/67.59 | | | |
% 260.69/67.59 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil,
% 260.69/67.59 | | | | all_149_0, all_91_7, simplifying with (59), (60), (61),
% 260.69/67.59 | | | | (63), (117), (118), (119), (120) gives:
% 260.69/67.59 | | | | (141) ? [v0: $i] : (app(all_115_0, all_149_0) = v0 & app(all_115_2,
% 260.69/67.59 | | | | v0) = all_91_7 & $i(v0) & $i(all_91_7))
% 260.69/67.59 | | | |
% 260.69/67.59 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil,
% 260.69/67.59 | | | | all_143_0, all_91_6, simplifying with (59), (60), (61),
% 260.69/67.59 | | | | (63), (106), (107), (108), (120) gives:
% 260.69/67.59 | | | | (142) ? [v0: $i] : (app(all_115_0, all_143_0) = v0 & app(all_115_2,
% 260.69/67.59 | | | | v0) = all_91_6 & $i(v0) & $i(all_91_6))
% 260.69/67.59 | | | |
% 260.69/67.59 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil,
% 260.69/67.59 | | | | all_115_0, all_139_0, simplifying with (59), (60), (61),
% 260.69/67.59 | | | | (63), (104), (120) gives:
% 260.69/67.59 | | | | (143) ? [v0: $i] : (app(all_115_0, all_115_0) = v0 & app(all_115_2,
% 260.69/67.59 | | | | v0) = all_139_0 & $i(v0) & $i(all_139_0))
% 260.69/67.59 | | | |
% 260.69/67.59 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil, nil,
% 260.69/67.59 | | | | nil, simplifying with (5), (18), (59), (60), (61), (63),
% 260.69/67.59 | | | | (120), (124) gives:
% 260.69/67.59 | | | | (144) ? [v0: $i] : (app(all_115_0, nil) = v0 & app(all_115_2, v0) =
% 260.69/67.59 | | | | nil & $i(v0))
% 260.69/67.59 | | | |
% 260.69/67.59 | | | | GROUND_INST: instantiating (16) with all_115_2, all_115_0, simplifying
% 260.69/67.59 | | | | with (59), (60), (61), (63), (120) gives:
% 260.69/67.59 | | | | (145) all_115_0 = nil
% 260.69/67.59 | | | |
% 260.69/67.60 | | | | GROUND_INST: instantiating (15) with all_115_2, all_115_0, simplifying
% 260.69/67.60 | | | | with (59), (60), (61), (63), (120) gives:
% 260.69/67.60 | | | | (146) all_115_2 = nil
% 260.69/67.60 | | | |
% 260.69/67.60 | | | | GROUND_INST: instantiating (17) with all_133_0, all_91_6, simplifying
% 260.69/67.60 | | | | with (92), (93), (94) gives:
% 260.69/67.60 | | | | (147) all_133_0 = all_91_6
% 260.69/67.60 | | | |
% 260.69/67.60 | | | | GROUND_INST: instantiating (17) with all_137_0, all_91_7, simplifying
% 260.69/67.60 | | | | with (100), (101), (102) gives:
% 260.69/67.60 | | | | (148) all_137_0 = all_91_7
% 260.69/67.60 | | | |
% 260.69/67.60 | | | | COMBINE_EQS: (134), (145) imply:
% 260.69/67.60 | | | | (149) all_139_0 = nil
% 260.69/67.60 | | | |
% 260.69/67.60 | | | | DELTA: instantiating (144) with fresh symbol all_169_0 gives:
% 261.03/67.60 | | | | (150) app(all_115_0, nil) = all_169_0 & app(all_115_2, all_169_0) =
% 261.03/67.60 | | | | nil & $i(all_169_0)
% 261.03/67.60 | | | |
% 261.03/67.60 | | | | ALPHA: (150) implies:
% 261.03/67.60 | | | | (151) $i(all_169_0)
% 261.03/67.60 | | | | (152) app(all_115_0, nil) = all_169_0
% 261.03/67.60 | | | |
% 261.03/67.60 | | | | DELTA: instantiating (132) with fresh symbol all_171_0 gives:
% 261.03/67.60 | | | | (153) app(all_171_0, all_115_0) = all_115_0 & $i(all_171_0) &
% 261.03/67.60 | | | | ssList(all_171_0)
% 261.03/67.60 | | | |
% 261.03/67.60 | | | | ALPHA: (153) implies:
% 261.03/67.60 | | | | (154) ssList(all_171_0)
% 261.03/67.60 | | | | (155) $i(all_171_0)
% 261.03/67.60 | | | | (156) app(all_171_0, all_115_0) = all_115_0
% 261.03/67.60 | | | |
% 261.03/67.60 | | | | DELTA: instantiating (130) with fresh symbol all_173_0 gives:
% 261.03/67.60 | | | | (157) app(all_173_0, all_115_2) = all_115_2 & $i(all_173_0) &
% 261.03/67.60 | | | | ssList(all_173_0)
% 261.03/67.60 | | | |
% 261.03/67.60 | | | | ALPHA: (157) implies:
% 261.03/67.60 | | | | (158) ssList(all_173_0)
% 261.03/67.60 | | | | (159) $i(all_173_0)
% 261.03/67.60 | | | | (160) app(all_173_0, all_115_2) = all_115_2
% 261.03/67.60 | | | |
% 261.03/67.60 | | | | DELTA: instantiating (129) with fresh symbol all_175_0 gives:
% 261.03/67.60 | | | | (161) app(all_175_0, nil) = all_115_2 & $i(all_175_0) &
% 261.03/67.60 | | | | ssList(all_175_0)
% 261.03/67.60 | | | |
% 261.03/67.60 | | | | ALPHA: (161) implies:
% 261.03/67.60 | | | | (162) ssList(all_175_0)
% 261.05/67.60 | | | | (163) $i(all_175_0)
% 261.05/67.60 | | | | (164) app(all_175_0, nil) = all_115_2
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | DELTA: instantiating (131) with fresh symbol all_181_0 gives:
% 261.05/67.60 | | | | (165) app(all_181_0, nil) = all_115_0 & $i(all_181_0) &
% 261.05/67.60 | | | | ssList(all_181_0)
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | ALPHA: (165) implies:
% 261.05/67.60 | | | | (166) ssList(all_181_0)
% 261.05/67.60 | | | | (167) $i(all_181_0)
% 261.05/67.60 | | | | (168) app(all_181_0, nil) = all_115_0
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | DELTA: instantiating (128) with fresh symbol all_183_0 gives:
% 261.05/67.60 | | | | (169) app(all_115_0, all_183_0) = all_115_0 & $i(all_183_0) &
% 261.05/67.60 | | | | ssList(all_183_0)
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | ALPHA: (169) implies:
% 261.05/67.60 | | | | (170) ssList(all_183_0)
% 261.05/67.60 | | | | (171) $i(all_183_0)
% 261.05/67.60 | | | | (172) app(all_115_0, all_183_0) = all_115_0
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | DELTA: instantiating (127) with fresh symbol all_185_0 gives:
% 261.05/67.60 | | | | (173) app(nil, all_185_0) = all_115_0 & $i(all_185_0) &
% 261.05/67.60 | | | | ssList(all_185_0)
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | ALPHA: (173) implies:
% 261.05/67.60 | | | | (174) ssList(all_185_0)
% 261.05/67.60 | | | | (175) $i(all_185_0)
% 261.05/67.60 | | | | (176) app(nil, all_185_0) = all_115_0
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | DELTA: instantiating (126) with fresh symbol all_187_0 gives:
% 261.05/67.60 | | | | (177) app(all_115_2, all_187_0) = all_115_2 & $i(all_187_0) &
% 261.05/67.60 | | | | ssList(all_187_0)
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | ALPHA: (177) implies:
% 261.05/67.60 | | | | (178) ssList(all_187_0)
% 261.05/67.60 | | | | (179) $i(all_187_0)
% 261.05/67.60 | | | | (180) app(all_115_2, all_187_0) = all_115_2
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | DELTA: instantiating (125) with fresh symbol all_189_0 gives:
% 261.05/67.60 | | | | (181) app(nil, all_189_0) = all_115_2 & $i(all_189_0) &
% 261.05/67.60 | | | | ssList(all_189_0)
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | ALPHA: (181) implies:
% 261.05/67.60 | | | | (182) ssList(all_189_0)
% 261.05/67.60 | | | | (183) $i(all_189_0)
% 261.05/67.60 | | | | (184) app(nil, all_189_0) = all_115_2
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | DELTA: instantiating (140) with fresh symbol all_195_0 gives:
% 261.05/67.60 | | | | (185) app(all_149_0, all_147_0) = all_195_0 & app(nil, all_195_0) =
% 261.05/67.60 | | | | all_91_7 & $i(all_195_0) & $i(all_91_7)
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | ALPHA: (185) implies:
% 261.05/67.60 | | | | (186) $i(all_195_0)
% 261.05/67.60 | | | | (187) app(all_149_0, all_147_0) = all_195_0
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | DELTA: instantiating (143) with fresh symbol all_197_0 gives:
% 261.05/67.60 | | | | (188) app(all_115_0, all_115_0) = all_197_0 & app(all_115_2,
% 261.05/67.60 | | | | all_197_0) = all_139_0 & $i(all_197_0) & $i(all_139_0)
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | ALPHA: (188) implies:
% 261.05/67.60 | | | | (189) app(all_115_0, all_115_0) = all_197_0
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | DELTA: instantiating (137) with fresh symbol all_201_0 gives:
% 261.05/67.60 | | | | (190) app(nil, all_201_0) = all_91_7 & app(nil, all_149_0) =
% 261.05/67.60 | | | | all_201_0 & $i(all_201_0) & $i(all_91_7)
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | ALPHA: (190) implies:
% 261.05/67.60 | | | | (191) app(nil, all_149_0) = all_201_0
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | DELTA: instantiating (142) with fresh symbol all_205_0 gives:
% 261.05/67.60 | | | | (192) app(all_115_0, all_143_0) = all_205_0 & app(all_115_2,
% 261.05/67.60 | | | | all_205_0) = all_91_6 & $i(all_205_0) & $i(all_91_6)
% 261.05/67.60 | | | |
% 261.05/67.60 | | | | ALPHA: (192) implies:
% 261.05/67.60 | | | | (193) $i(all_205_0)
% 261.05/67.61 | | | | (194) app(all_115_0, all_143_0) = all_205_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | DELTA: instantiating (135) with fresh symbol all_209_0 gives:
% 261.05/67.61 | | | | (195) app(nil, all_209_0) = all_91_6 & app(nil, all_143_0) =
% 261.05/67.61 | | | | all_209_0 & $i(all_209_0) & $i(all_91_6)
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | ALPHA: (195) implies:
% 261.05/67.61 | | | | (196) app(nil, all_143_0) = all_209_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | DELTA: instantiating (141) with fresh symbol all_215_0 gives:
% 261.05/67.61 | | | | (197) app(all_115_0, all_149_0) = all_215_0 & app(all_115_2,
% 261.05/67.61 | | | | all_215_0) = all_91_7 & $i(all_215_0) & $i(all_91_7)
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | ALPHA: (197) implies:
% 261.05/67.61 | | | | (198) app(all_115_0, all_149_0) = all_215_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | DELTA: instantiating (133) with fresh symbol all_217_0 gives:
% 261.05/67.61 | | | | (199) app(nil, all_217_0) = all_139_0 & app(nil, all_115_0) =
% 261.05/67.61 | | | | all_217_0 & $i(all_217_0) & $i(all_139_0)
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | ALPHA: (199) implies:
% 261.05/67.61 | | | | (200) app(nil, all_115_0) = all_217_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (145), (168) imply:
% 261.05/67.61 | | | | (201) app(all_181_0, nil) = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (146), (164) imply:
% 261.05/67.61 | | | | (202) app(all_175_0, nil) = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (146), (160) imply:
% 261.05/67.61 | | | | (203) app(all_173_0, nil) = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (145), (156) imply:
% 261.05/67.61 | | | | (204) app(all_171_0, nil) = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (138), (187) imply:
% 261.05/67.61 | | | | (205) app(all_91_7, all_147_0) = all_195_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (102), (148) imply:
% 261.05/67.61 | | | | (206) app(all_91_7, nil) = all_91_7
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (145), (172) imply:
% 261.05/67.61 | | | | (207) app(nil, all_183_0) = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (138), (145), (198) imply:
% 261.05/67.61 | | | | (208) app(nil, all_91_7) = all_215_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (136), (145), (194) imply:
% 261.05/67.61 | | | | (209) app(nil, all_91_6) = all_205_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (145), (189) imply:
% 261.05/67.61 | | | | (210) app(nil, nil) = all_197_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (145), (152) imply:
% 261.05/67.61 | | | | (211) app(nil, nil) = all_169_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (146), (180) imply:
% 261.05/67.61 | | | | (212) app(nil, all_187_0) = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (146), (184) imply:
% 261.05/67.61 | | | | (213) app(nil, all_189_0) = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (145), (176) imply:
% 261.05/67.61 | | | | (214) app(nil, all_185_0) = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (138), (191) imply:
% 261.05/67.61 | | | | (215) app(nil, all_91_7) = all_201_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (119), (138) imply:
% 261.05/67.61 | | | | (216) app(nil, all_91_7) = all_91_7
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (136), (196) imply:
% 261.05/67.61 | | | | (217) app(nil, all_91_6) = all_209_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (108), (136) imply:
% 261.05/67.61 | | | | (218) app(nil, all_91_6) = all_91_6
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | REDUCE: (145), (200) imply:
% 261.05/67.61 | | | | (219) app(nil, nil) = all_217_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | GROUND_INST: instantiating (20) with nil, all_197_0, nil, nil,
% 261.05/67.61 | | | | simplifying with (124), (210) gives:
% 261.05/67.61 | | | | (220) all_197_0 = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | GROUND_INST: instantiating (20) with all_197_0, all_217_0, nil, nil,
% 261.05/67.61 | | | | simplifying with (210), (219) gives:
% 261.05/67.61 | | | | (221) all_217_0 = all_197_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | GROUND_INST: instantiating (20) with all_169_0, all_217_0, nil, nil,
% 261.05/67.61 | | | | simplifying with (211), (219) gives:
% 261.05/67.61 | | | | (222) all_217_0 = all_169_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | GROUND_INST: instantiating (20) with all_201_0, all_215_0, all_91_7,
% 261.05/67.61 | | | | nil, simplifying with (208), (215) gives:
% 261.05/67.61 | | | | (223) all_215_0 = all_201_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | GROUND_INST: instantiating (20) with all_91_7, all_215_0, all_91_7, nil,
% 261.05/67.61 | | | | simplifying with (208), (216) gives:
% 261.05/67.61 | | | | (224) all_215_0 = all_91_7
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | GROUND_INST: instantiating (20) with all_205_0, all_209_0, all_91_6,
% 261.05/67.61 | | | | nil, simplifying with (209), (217) gives:
% 261.05/67.61 | | | | (225) all_209_0 = all_205_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | GROUND_INST: instantiating (20) with all_91_6, all_209_0, all_91_6, nil,
% 261.05/67.61 | | | | simplifying with (217), (218) gives:
% 261.05/67.61 | | | | (226) all_209_0 = all_91_6
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | GROUND_INST: instantiating (20) with all_91_7, all_195_0, all_147_0,
% 261.05/67.61 | | | | all_91_7, simplifying with (115), (205) gives:
% 261.05/67.61 | | | | (227) all_195_0 = all_91_7
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | COMBINE_EQS: (221), (222) imply:
% 261.05/67.61 | | | | (228) all_197_0 = all_169_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | SIMP: (228) implies:
% 261.05/67.61 | | | | (229) all_197_0 = all_169_0
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | COMBINE_EQS: (223), (224) imply:
% 261.05/67.61 | | | | (230) all_201_0 = all_91_7
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | COMBINE_EQS: (225), (226) imply:
% 261.05/67.61 | | | | (231) all_205_0 = all_91_6
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | SIMP: (231) implies:
% 261.05/67.61 | | | | (232) all_205_0 = all_91_6
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | COMBINE_EQS: (220), (229) imply:
% 261.05/67.61 | | | | (233) all_169_0 = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | SIMP: (233) implies:
% 261.05/67.61 | | | | (234) all_169_0 = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | GROUND_INST: instantiating (ax79) with nil, all_91_7, all_91_7,
% 261.05/67.61 | | | | all_135_0, simplifying with (5), (18), (22), (24), (96),
% 261.05/67.61 | | | | (97), (98), (216) gives:
% 261.05/67.61 | | | | (235) all_135_0 = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | GROUND_INST: instantiating (ax79) with nil, all_91_6, all_91_6,
% 261.05/67.61 | | | | all_131_0, simplifying with (5), (18), (23), (25), (88),
% 261.05/67.61 | | | | (89), (90), (218) gives:
% 261.05/67.61 | | | | (236) all_131_0 = nil
% 261.05/67.61 | | | |
% 261.05/67.61 | | | | GROUND_INST: instantiating (ax82) with nil, all_183_0, nil, all_91_6,
% 261.05/67.61 | | | | all_91_6, simplifying with (5), (18), (23), (25), (170),
% 261.05/67.61 | | | | (171), (207), (218) gives:
% 261.05/67.62 | | | | (237) ? [v0: $i] : (app(all_183_0, all_91_6) = v0 & app(nil, v0) =
% 261.05/67.62 | | | | all_91_6 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with nil, all_183_0, nil, all_91_7,
% 261.05/67.62 | | | | all_91_7, simplifying with (5), (18), (22), (24), (170),
% 261.05/67.62 | | | | (171), (207), (216) gives:
% 261.05/67.62 | | | | (238) ? [v0: $i] : (app(all_183_0, all_91_7) = v0 & app(nil, v0) =
% 261.05/67.62 | | | | all_91_7 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with nil, all_185_0, nil, all_91_6,
% 261.05/67.62 | | | | all_91_6, simplifying with (5), (18), (23), (25), (174),
% 261.05/67.62 | | | | (175), (214), (218) gives:
% 261.05/67.62 | | | | (239) ? [v0: $i] : (app(all_185_0, all_91_6) = v0 & app(nil, v0) =
% 261.05/67.62 | | | | all_91_6 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with nil, all_185_0, nil, all_91_7,
% 261.05/67.62 | | | | all_91_7, simplifying with (5), (18), (22), (24), (174),
% 261.05/67.62 | | | | (175), (214), (216) gives:
% 261.05/67.62 | | | | (240) ? [v0: $i] : (app(all_185_0, all_91_7) = v0 & app(nil, v0) =
% 261.05/67.62 | | | | all_91_7 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (6) with all_185_0, nil, simplifying with
% 261.05/67.62 | | | | (174), (175), (214) gives:
% 261.05/67.62 | | | | (241) all_185_0 = nil
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax80) with all_185_0, nil, nil, all_187_0,
% 261.05/67.62 | | | | simplifying with (5), (18), (174), (175), (178), (179),
% 261.05/67.62 | | | | (212), (214) gives:
% 261.05/67.62 | | | | (242) all_187_0 = all_185_0
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with nil, all_187_0, nil, all_91_6,
% 261.05/67.62 | | | | all_91_6, simplifying with (5), (18), (23), (25), (178),
% 261.05/67.62 | | | | (179), (212), (218) gives:
% 261.05/67.62 | | | | (243) ? [v0: $i] : (app(all_187_0, all_91_6) = v0 & app(nil, v0) =
% 261.05/67.62 | | | | all_91_6 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with nil, all_187_0, nil, all_91_7,
% 261.05/67.62 | | | | all_91_7, simplifying with (5), (18), (22), (24), (178),
% 261.05/67.62 | | | | (179), (212), (216) gives:
% 261.05/67.62 | | | | (244) ? [v0: $i] : (app(all_187_0, all_91_7) = v0 & app(nil, v0) =
% 261.05/67.62 | | | | all_91_7 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax80) with all_187_0, nil, nil, all_189_0,
% 261.05/67.62 | | | | simplifying with (5), (18), (178), (179), (182), (183),
% 261.05/67.62 | | | | (212), (213) gives:
% 261.05/67.62 | | | | (245) all_189_0 = all_187_0
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax80) with all_183_0, nil, nil, all_189_0,
% 261.05/67.62 | | | | simplifying with (5), (18), (170), (171), (182), (183),
% 261.05/67.62 | | | | (207), (213) gives:
% 261.05/67.62 | | | | (246) all_189_0 = all_183_0
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with nil, all_189_0, nil, all_91_6,
% 261.05/67.62 | | | | all_91_6, simplifying with (5), (18), (23), (25), (182),
% 261.05/67.62 | | | | (183), (213), (218) gives:
% 261.05/67.62 | | | | (247) ? [v0: $i] : (app(all_189_0, all_91_6) = v0 & app(nil, v0) =
% 261.05/67.62 | | | | all_91_6 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with nil, all_189_0, nil, all_91_7,
% 261.05/67.62 | | | | all_91_7, simplifying with (5), (18), (22), (24), (182),
% 261.05/67.62 | | | | (183), (213), (216) gives:
% 261.05/67.62 | | | | (248) ? [v0: $i] : (app(all_189_0, all_91_7) = v0 & app(nil, v0) =
% 261.05/67.62 | | | | all_91_7 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax80) with nil, all_91_7, all_91_7,
% 261.05/67.62 | | | | all_147_0, simplifying with (5), (18), (22), (24), (113),
% 261.05/67.62 | | | | (114), (115), (206) gives:
% 261.05/67.62 | | | | (249) all_147_0 = nil
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with all_171_0, nil, nil, all_91_6,
% 261.05/67.62 | | | | all_91_6, simplifying with (5), (18), (23), (25), (154),
% 261.05/67.62 | | | | (155), (204), (218) gives:
% 261.05/67.62 | | | | (250) ? [v0: $i] : (app(all_171_0, v0) = all_91_6 & app(nil,
% 261.05/67.62 | | | | all_91_6) = v0 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with all_171_0, nil, nil, all_91_7,
% 261.05/67.62 | | | | all_91_7, simplifying with (5), (18), (22), (24), (154),
% 261.05/67.62 | | | | (155), (204), (216) gives:
% 261.05/67.62 | | | | (251) ? [v0: $i] : (app(all_171_0, v0) = all_91_7 & app(nil,
% 261.05/67.62 | | | | all_91_7) = v0 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with all_173_0, nil, nil, all_91_6,
% 261.05/67.62 | | | | all_91_6, simplifying with (5), (18), (23), (25), (158),
% 261.05/67.62 | | | | (159), (203), (218) gives:
% 261.05/67.62 | | | | (252) ? [v0: $i] : (app(all_173_0, v0) = all_91_6 & app(nil,
% 261.05/67.62 | | | | all_91_6) = v0 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with all_173_0, nil, nil, all_91_7,
% 261.05/67.62 | | | | all_91_7, simplifying with (5), (18), (22), (24), (158),
% 261.05/67.62 | | | | (159), (203), (216) gives:
% 261.05/67.62 | | | | (253) ? [v0: $i] : (app(all_173_0, v0) = all_91_7 & app(nil,
% 261.05/67.62 | | | | all_91_7) = v0 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with all_175_0, nil, nil, all_91_6,
% 261.05/67.62 | | | | all_91_6, simplifying with (5), (18), (23), (25), (162),
% 261.05/67.62 | | | | (163), (202), (218) gives:
% 261.05/67.62 | | | | (254) ? [v0: $i] : (app(all_175_0, v0) = all_91_6 & app(nil,
% 261.05/67.62 | | | | all_91_6) = v0 & $i(v0))
% 261.05/67.62 | | | |
% 261.05/67.62 | | | | GROUND_INST: instantiating (ax82) with all_175_0, nil, nil, all_91_7,
% 261.05/67.62 | | | | all_91_7, simplifying with (5), (18), (22), (24), (162),
% 261.05/67.62 | | | | (163), (202), (216) gives:
% 261.05/67.63 | | | | (255) ? [v0: $i] : (app(all_175_0, v0) = all_91_7 & app(nil,
% 261.05/67.63 | | | | all_91_7) = v0 & $i(v0))
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | GROUND_INST: instantiating (ax82) with all_181_0, nil, nil, all_91_6,
% 261.05/67.63 | | | | all_91_6, simplifying with (5), (18), (23), (25), (166),
% 261.05/67.63 | | | | (167), (201), (218) gives:
% 261.05/67.63 | | | | (256) ? [v0: $i] : (app(all_181_0, v0) = all_91_6 & app(nil,
% 261.05/67.63 | | | | all_91_6) = v0 & $i(v0))
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | GROUND_INST: instantiating (ax82) with all_181_0, nil, nil, all_91_7,
% 261.05/67.63 | | | | all_91_7, simplifying with (5), (18), (22), (24), (166),
% 261.05/67.63 | | | | (167), (201), (216) gives:
% 261.05/67.63 | | | | (257) ? [v0: $i] : (app(all_181_0, v0) = all_91_7 & app(nil,
% 261.05/67.63 | | | | all_91_7) = v0 & $i(v0))
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | COMBINE_EQS: (245), (246) imply:
% 261.05/67.63 | | | | (258) all_187_0 = all_183_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | SIMP: (258) implies:
% 261.05/67.63 | | | | (259) all_187_0 = all_183_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | COMBINE_EQS: (242), (259) imply:
% 261.05/67.63 | | | | (260) all_185_0 = all_183_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | SIMP: (260) implies:
% 261.05/67.63 | | | | (261) all_185_0 = all_183_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | COMBINE_EQS: (241), (261) imply:
% 261.05/67.63 | | | | (262) all_183_0 = nil
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | COMBINE_EQS: (259), (262) imply:
% 261.05/67.63 | | | | (263) all_187_0 = nil
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | COMBINE_EQS: (246), (262) imply:
% 261.05/67.63 | | | | (264) all_189_0 = nil
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (240) with fresh symbol all_239_0 gives:
% 261.05/67.63 | | | | (265) app(all_185_0, all_91_7) = all_239_0 & app(nil, all_239_0) =
% 261.05/67.63 | | | | all_91_7 & $i(all_239_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (265) implies:
% 261.05/67.63 | | | | (266) $i(all_239_0)
% 261.05/67.63 | | | | (267) app(all_185_0, all_91_7) = all_239_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (253) with fresh symbol all_253_0 gives:
% 261.05/67.63 | | | | (268) app(all_173_0, all_253_0) = all_91_7 & app(nil, all_91_7) =
% 261.05/67.63 | | | | all_253_0 & $i(all_253_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (268) implies:
% 261.05/67.63 | | | | (269) app(nil, all_91_7) = all_253_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (252) with fresh symbol all_255_0 gives:
% 261.05/67.63 | | | | (270) app(all_173_0, all_255_0) = all_91_6 & app(nil, all_91_6) =
% 261.05/67.63 | | | | all_255_0 & $i(all_255_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (270) implies:
% 261.05/67.63 | | | | (271) $i(all_255_0)
% 261.05/67.63 | | | | (272) app(nil, all_91_6) = all_255_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (256) with fresh symbol all_259_0 gives:
% 261.05/67.63 | | | | (273) app(all_181_0, all_259_0) = all_91_6 & app(nil, all_91_6) =
% 261.05/67.63 | | | | all_259_0 & $i(all_259_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (273) implies:
% 261.05/67.63 | | | | (274) app(nil, all_91_6) = all_259_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (257) with fresh symbol all_265_0 gives:
% 261.05/67.63 | | | | (275) app(all_181_0, all_265_0) = all_91_7 & app(nil, all_91_7) =
% 261.05/67.63 | | | | all_265_0 & $i(all_265_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (275) implies:
% 261.05/67.63 | | | | (276) app(nil, all_91_7) = all_265_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (243) with fresh symbol all_271_0 gives:
% 261.05/67.63 | | | | (277) app(all_187_0, all_91_6) = all_271_0 & app(nil, all_271_0) =
% 261.05/67.63 | | | | all_91_6 & $i(all_271_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (277) implies:
% 261.05/67.63 | | | | (278) app(all_187_0, all_91_6) = all_271_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (244) with fresh symbol all_273_0 gives:
% 261.05/67.63 | | | | (279) app(all_187_0, all_91_7) = all_273_0 & app(nil, all_273_0) =
% 261.05/67.63 | | | | all_91_7 & $i(all_273_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (279) implies:
% 261.05/67.63 | | | | (280) app(all_187_0, all_91_7) = all_273_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (237) with fresh symbol all_283_0 gives:
% 261.05/67.63 | | | | (281) app(all_183_0, all_91_6) = all_283_0 & app(nil, all_283_0) =
% 261.05/67.63 | | | | all_91_6 & $i(all_283_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (281) implies:
% 261.05/67.63 | | | | (282) app(all_183_0, all_91_6) = all_283_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (239) with fresh symbol all_301_0 gives:
% 261.05/67.63 | | | | (283) app(all_185_0, all_91_6) = all_301_0 & app(nil, all_301_0) =
% 261.05/67.63 | | | | all_91_6 & $i(all_301_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (283) implies:
% 261.05/67.63 | | | | (284) app(all_185_0, all_91_6) = all_301_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (251) with fresh symbol all_343_0 gives:
% 261.05/67.63 | | | | (285) app(all_171_0, all_343_0) = all_91_7 & app(nil, all_91_7) =
% 261.05/67.63 | | | | all_343_0 & $i(all_343_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (285) implies:
% 261.05/67.63 | | | | (286) app(nil, all_91_7) = all_343_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (248) with fresh symbol all_375_0 gives:
% 261.05/67.63 | | | | (287) app(all_189_0, all_91_7) = all_375_0 & app(nil, all_375_0) =
% 261.05/67.63 | | | | all_91_7 & $i(all_375_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (287) implies:
% 261.05/67.63 | | | | (288) app(all_189_0, all_91_7) = all_375_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (247) with fresh symbol all_377_0 gives:
% 261.05/67.63 | | | | (289) app(all_189_0, all_91_6) = all_377_0 & app(nil, all_377_0) =
% 261.05/67.63 | | | | all_91_6 & $i(all_377_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (289) implies:
% 261.05/67.63 | | | | (290) app(all_189_0, all_91_6) = all_377_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (238) with fresh symbol all_383_0 gives:
% 261.05/67.63 | | | | (291) app(all_183_0, all_91_7) = all_383_0 & app(nil, all_383_0) =
% 261.05/67.63 | | | | all_91_7 & $i(all_383_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (291) implies:
% 261.05/67.63 | | | | (292) app(all_183_0, all_91_7) = all_383_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (255) with fresh symbol all_393_0 gives:
% 261.05/67.63 | | | | (293) app(all_175_0, all_393_0) = all_91_7 & app(nil, all_91_7) =
% 261.05/67.63 | | | | all_393_0 & $i(all_393_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (293) implies:
% 261.05/67.63 | | | | (294) app(nil, all_91_7) = all_393_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (254) with fresh symbol all_407_0 gives:
% 261.05/67.63 | | | | (295) app(all_175_0, all_407_0) = all_91_6 & app(nil, all_91_6) =
% 261.05/67.63 | | | | all_407_0 & $i(all_407_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (295) implies:
% 261.05/67.63 | | | | (296) app(nil, all_91_6) = all_407_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | DELTA: instantiating (250) with fresh symbol all_419_0 gives:
% 261.05/67.63 | | | | (297) app(all_171_0, all_419_0) = all_91_6 & app(nil, all_91_6) =
% 261.05/67.63 | | | | all_419_0 & $i(all_419_0)
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | ALPHA: (297) implies:
% 261.05/67.63 | | | | (298) app(nil, all_91_6) = all_419_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | REDUCE: (264), (290) imply:
% 261.05/67.63 | | | | (299) app(nil, all_91_6) = all_377_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | REDUCE: (264), (288) imply:
% 261.05/67.63 | | | | (300) app(nil, all_91_7) = all_375_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | REDUCE: (263), (278) imply:
% 261.05/67.63 | | | | (301) app(nil, all_91_6) = all_271_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | REDUCE: (263), (280) imply:
% 261.05/67.63 | | | | (302) app(nil, all_91_7) = all_273_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | REDUCE: (241), (284) imply:
% 261.05/67.63 | | | | (303) app(nil, all_91_6) = all_301_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | REDUCE: (241), (267) imply:
% 261.05/67.63 | | | | (304) app(nil, all_91_7) = all_239_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | REDUCE: (262), (282) imply:
% 261.05/67.63 | | | | (305) app(nil, all_91_6) = all_283_0
% 261.05/67.63 | | | |
% 261.05/67.63 | | | | REDUCE: (262), (292) imply:
% 261.05/67.64 | | | | (306) app(nil, all_91_7) = all_383_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | REDUCE: (139), (249) imply:
% 261.05/67.64 | | | | (307) segmentP(all_91_7, nil)
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_91_7, all_253_0, all_91_7, nil,
% 261.05/67.64 | | | | simplifying with (216), (269) gives:
% 261.05/67.64 | | | | (308) all_253_0 = all_91_7
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_343_0, all_375_0, all_91_7,
% 261.05/67.64 | | | | nil, simplifying with (286), (300) gives:
% 261.05/67.64 | | | | (309) all_375_0 = all_343_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_265_0, all_375_0, all_91_7,
% 261.05/67.64 | | | | nil, simplifying with (276), (300) gives:
% 261.05/67.64 | | | | (310) all_375_0 = all_265_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_253_0, all_375_0, all_91_7,
% 261.05/67.64 | | | | nil, simplifying with (269), (300) gives:
% 261.05/67.64 | | | | (311) all_375_0 = all_253_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_375_0, all_383_0, all_91_7,
% 261.05/67.64 | | | | nil, simplifying with (300), (306) gives:
% 261.05/67.64 | | | | (312) all_383_0 = all_375_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_273_0, all_383_0, all_91_7,
% 261.05/67.64 | | | | nil, simplifying with (302), (306) gives:
% 261.05/67.64 | | | | (313) all_383_0 = all_273_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_343_0, all_393_0, all_91_7,
% 261.05/67.64 | | | | nil, simplifying with (286), (294) gives:
% 261.05/67.64 | | | | (314) all_393_0 = all_343_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_239_0, all_393_0, all_91_7,
% 261.05/67.64 | | | | nil, simplifying with (294), (304) gives:
% 261.05/67.64 | | | | (315) all_393_0 = all_239_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_91_6, all_271_0, all_91_6, nil,
% 261.05/67.64 | | | | simplifying with (218), (301) gives:
% 261.05/67.64 | | | | (316) all_271_0 = all_91_6
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_271_0, all_283_0, all_91_6,
% 261.05/67.64 | | | | nil, simplifying with (301), (305) gives:
% 261.05/67.64 | | | | (317) all_283_0 = all_271_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_283_0, all_301_0, all_91_6,
% 261.05/67.64 | | | | nil, simplifying with (303), (305) gives:
% 261.05/67.64 | | | | (318) all_301_0 = all_283_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_301_0, all_377_0, all_91_6,
% 261.05/67.64 | | | | nil, simplifying with (299), (303) gives:
% 261.05/67.64 | | | | (319) all_377_0 = all_301_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_255_0, all_377_0, all_91_6,
% 261.05/67.64 | | | | nil, simplifying with (272), (299) gives:
% 261.05/67.64 | | | | (320) all_377_0 = all_255_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_271_0, all_407_0, all_91_6,
% 261.05/67.64 | | | | nil, simplifying with (296), (301) gives:
% 261.05/67.64 | | | | (321) all_407_0 = all_271_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_407_0, all_419_0, all_91_6,
% 261.05/67.64 | | | | nil, simplifying with (296), (298) gives:
% 261.05/67.64 | | | | (322) all_419_0 = all_407_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | GROUND_INST: instantiating (20) with all_259_0, all_419_0, all_91_6,
% 261.05/67.64 | | | | nil, simplifying with (274), (298) gives:
% 261.05/67.64 | | | | (323) all_419_0 = all_259_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (322), (323) imply:
% 261.05/67.64 | | | | (324) all_407_0 = all_259_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | SIMP: (324) implies:
% 261.05/67.64 | | | | (325) all_407_0 = all_259_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (321), (325) imply:
% 261.05/67.64 | | | | (326) all_271_0 = all_259_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | SIMP: (326) implies:
% 261.05/67.64 | | | | (327) all_271_0 = all_259_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (314), (315) imply:
% 261.05/67.64 | | | | (328) all_343_0 = all_239_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | SIMP: (328) implies:
% 261.05/67.64 | | | | (329) all_343_0 = all_239_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (312), (313) imply:
% 261.05/67.64 | | | | (330) all_375_0 = all_273_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | SIMP: (330) implies:
% 261.05/67.64 | | | | (331) all_375_0 = all_273_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (319), (320) imply:
% 261.05/67.64 | | | | (332) all_301_0 = all_255_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | SIMP: (332) implies:
% 261.05/67.64 | | | | (333) all_301_0 = all_255_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (311), (331) imply:
% 261.05/67.64 | | | | (334) all_273_0 = all_253_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (309), (331) imply:
% 261.05/67.64 | | | | (335) all_343_0 = all_273_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | SIMP: (335) implies:
% 261.05/67.64 | | | | (336) all_343_0 = all_273_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (310), (331) imply:
% 261.05/67.64 | | | | (337) all_273_0 = all_265_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (329), (336) imply:
% 261.05/67.64 | | | | (338) all_273_0 = all_239_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | SIMP: (338) implies:
% 261.05/67.64 | | | | (339) all_273_0 = all_239_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (318), (333) imply:
% 261.05/67.64 | | | | (340) all_283_0 = all_255_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | SIMP: (340) implies:
% 261.05/67.64 | | | | (341) all_283_0 = all_255_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (317), (341) imply:
% 261.05/67.64 | | | | (342) all_271_0 = all_255_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | SIMP: (342) implies:
% 261.05/67.64 | | | | (343) all_271_0 = all_255_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (337), (339) imply:
% 261.05/67.64 | | | | (344) all_265_0 = all_239_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (334), (337) imply:
% 261.05/67.64 | | | | (345) all_265_0 = all_253_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (316), (327) imply:
% 261.05/67.64 | | | | (346) all_259_0 = all_91_6
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (327), (343) imply:
% 261.05/67.64 | | | | (347) all_259_0 = all_255_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (344), (345) imply:
% 261.05/67.64 | | | | (348) all_253_0 = all_239_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | SIMP: (348) implies:
% 261.05/67.64 | | | | (349) all_253_0 = all_239_0
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (346), (347) imply:
% 261.05/67.64 | | | | (350) all_255_0 = all_91_6
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | SIMP: (350) implies:
% 261.05/67.64 | | | | (351) all_255_0 = all_91_6
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | COMBINE_EQS: (308), (349) imply:
% 261.05/67.64 | | | | (352) all_239_0 = all_91_7
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | BETA: splitting (30) gives:
% 261.05/67.64 | | | |
% 261.05/67.64 | | | | Case 1:
% 261.05/67.64 | | | | |
% 261.05/67.64 | | | | | (353) ~ strictorderedP(all_91_7)
% 261.05/67.64 | | | | |
% 261.05/67.64 | | | | | BETA: splitting (29) gives:
% 261.05/67.64 | | | | |
% 261.05/67.64 | | | | | Case 1:
% 261.05/67.64 | | | | | |
% 261.05/67.64 | | | | | | (354) all_91_0 = all_91_6 & all_91_4 = all_91_7 & cons(all_91_5,
% 261.05/67.64 | | | | | | nil) = all_91_7 & app(all_91_2, all_91_1) = all_91_6 &
% 261.05/67.64 | | | | | | app(all_91_3, all_91_7) = all_91_2 & $i(all_91_2) &
% 261.05/67.64 | | | | | | ssList(all_91_1) & ssList(all_91_3) & ssItem(all_91_5) & !
% 261.05/67.64 | | | | | | [v0: $i] : ( ~ $i(v0) | ~ lt(v0, all_91_5) | ~
% 261.05/67.64 | | | | | | memberP(all_91_1, v0) | ~ ssItem(v0)) & ! [v0: $i] : (
% 261.05/67.64 | | | | | | ~ $i(v0) | ~ lt(all_91_5, v0) | ~ memberP(all_91_3, v0)
% 261.05/67.64 | | | | | | | ~ ssItem(v0))
% 261.05/67.64 | | | | | |
% 261.05/67.64 | | | | | | ALPHA: (354) implies:
% 261.05/67.64 | | | | | | (355) ssItem(all_91_5)
% 261.05/67.64 | | | | | | (356) cons(all_91_5, nil) = all_91_7
% 261.05/67.64 | | | | | |
% 261.05/67.64 | | | | | | GROUND_INST: instantiating (12) with all_91_5, all_91_7, simplifying
% 261.05/67.64 | | | | | | with (26), (353), (355), (356) gives:
% 261.05/67.64 | | | | | | (357) $false
% 261.05/67.64 | | | | | |
% 261.05/67.64 | | | | | | CLOSE: (357) is inconsistent.
% 261.05/67.64 | | | | | |
% 261.05/67.64 | | | | | Case 2:
% 261.05/67.64 | | | | | |
% 261.05/67.64 | | | | | | (358) all_91_6 = nil & all_91_7 = nil
% 261.05/67.64 | | | | | |
% 261.05/67.64 | | | | | | ALPHA: (358) implies:
% 261.05/67.64 | | | | | | (359) all_91_7 = nil
% 261.05/67.64 | | | | | |
% 261.05/67.64 | | | | | | REDUCE: (353), (359) imply:
% 261.05/67.64 | | | | | | (360) ~ strictorderedP(nil)
% 261.05/67.64 | | | | | |
% 261.05/67.64 | | | | | | PRED_UNIFY: (13), (360) imply:
% 261.05/67.64 | | | | | | (361) $false
% 261.05/67.64 | | | | | |
% 261.05/67.64 | | | | | | CLOSE: (361) is inconsistent.
% 261.05/67.64 | | | | | |
% 261.05/67.64 | | | | | End of split
% 261.05/67.64 | | | | |
% 261.05/67.64 | | | | Case 2:
% 261.05/67.64 | | | | |
% 261.05/67.64 | | | | | (362) ~ segmentP(all_91_6, all_91_7)
% 261.05/67.64 | | | | |
% 261.05/67.64 | | | | | BETA: splitting (29) gives:
% 261.05/67.64 | | | | |
% 261.05/67.64 | | | | | Case 1:
% 261.05/67.64 | | | | | |
% 261.05/67.65 | | | | | | (363) all_91_0 = all_91_6 & all_91_4 = all_91_7 & cons(all_91_5,
% 261.05/67.65 | | | | | | nil) = all_91_7 & app(all_91_2, all_91_1) = all_91_6 &
% 261.05/67.65 | | | | | | app(all_91_3, all_91_7) = all_91_2 & $i(all_91_2) &
% 261.05/67.65 | | | | | | ssList(all_91_1) & ssList(all_91_3) & ssItem(all_91_5) & !
% 261.05/67.65 | | | | | | [v0: $i] : ( ~ $i(v0) | ~ lt(v0, all_91_5) | ~
% 261.05/67.65 | | | | | | memberP(all_91_1, v0) | ~ ssItem(v0)) & ! [v0: $i] : (
% 261.05/67.65 | | | | | | ~ $i(v0) | ~ lt(all_91_5, v0) | ~ memberP(all_91_3, v0)
% 261.05/67.65 | | | | | | | ~ ssItem(v0))
% 261.05/67.65 | | | | | |
% 261.05/67.65 | | | | | | ALPHA: (363) implies:
% 261.05/67.65 | | | | | | (364) ssList(all_91_3)
% 261.05/67.65 | | | | | | (365) ssList(all_91_1)
% 261.05/67.65 | | | | | | (366) app(all_91_3, all_91_7) = all_91_2
% 261.05/67.65 | | | | | | (367) app(all_91_2, all_91_1) = all_91_6
% 261.05/67.65 | | | | | |
% 261.05/67.65 | | | | | | GROUND_INST: instantiating (4) with all_91_6, all_91_7, all_91_3,
% 261.05/67.65 | | | | | | all_91_2, all_91_1, simplifying with (22), (23), (24),
% 261.05/67.65 | | | | | | (25), (27), (28), (362), (364), (365), (366), (367)
% 261.05/67.65 | | | | | | gives:
% 261.05/67.65 | | | | | | (368) $false
% 261.05/67.65 | | | | | |
% 261.05/67.65 | | | | | | CLOSE: (368) is inconsistent.
% 261.05/67.65 | | | | | |
% 261.05/67.65 | | | | | Case 2:
% 261.05/67.65 | | | | | |
% 261.05/67.65 | | | | | | (369) all_91_6 = nil & all_91_7 = nil
% 261.05/67.65 | | | | | |
% 261.05/67.65 | | | | | | ALPHA: (369) implies:
% 261.05/67.65 | | | | | | (370) all_91_7 = nil
% 261.05/67.65 | | | | | | (371) all_91_6 = nil
% 261.05/67.65 | | | | | |
% 261.05/67.65 | | | | | | REDUCE: (362), (370), (371) imply:
% 261.05/67.65 | | | | | | (372) ~ segmentP(nil, nil)
% 261.05/67.65 | | | | | |
% 261.05/67.65 | | | | | | PRED_UNIFY: (39), (372) imply:
% 261.05/67.65 | | | | | | (373) $false
% 261.05/67.65 | | | | | |
% 261.05/67.65 | | | | | | CLOSE: (373) is inconsistent.
% 261.05/67.65 | | | | | |
% 261.05/67.65 | | | | | End of split
% 261.05/67.65 | | | | |
% 261.05/67.65 | | | | End of split
% 261.05/67.65 | | | |
% 261.05/67.65 | | | End of split
% 261.05/67.65 | | |
% 261.05/67.65 | | End of split
% 261.05/67.65 | |
% 261.05/67.65 | End of split
% 261.05/67.65 |
% 261.05/67.65 End of proof
% 261.05/67.65 % SZS output end Proof for theBenchmark
% 261.05/67.65
% 261.05/67.65 67046ms
%------------------------------------------------------------------------------