TSTP Solution File: SWC060+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC060+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 : n009.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 20:49:26 EDT 2023
% Result : Theorem 33.52s 5.12s
% Output : Proof 256.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC060+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 : n009.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 18:32:05 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.67/0.64 ________ _____
% 0.67/0.64 ___ __ \_________(_)________________________________
% 0.67/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.67/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.67/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.67/0.64
% 0.67/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.67/0.64 (2023-06-19)
% 0.67/0.64
% 0.67/0.64 (c) Philipp Rümmer, 2009-2023
% 0.67/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.67/0.64 Amanda Stjerna.
% 0.67/0.64 Free software under BSD-3-Clause.
% 0.67/0.64
% 0.67/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.67/0.64
% 0.67/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.66 Running up to 7 provers in parallel.
% 0.67/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.67/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.67/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.67/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.67/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.67/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.67/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 5.70/1.47 Prover 1: Preprocessing ...
% 5.70/1.47 Prover 4: Preprocessing ...
% 6.04/1.52 Prover 5: Preprocessing ...
% 6.04/1.52 Prover 3: Preprocessing ...
% 6.04/1.54 Prover 0: Preprocessing ...
% 6.04/1.54 Prover 6: Preprocessing ...
% 6.04/1.54 Prover 2: Preprocessing ...
% 15.00/2.75 Prover 2: Proving ...
% 15.67/2.80 Prover 5: Constructing countermodel ...
% 16.03/2.85 Prover 1: Constructing countermodel ...
% 16.03/2.86 Prover 6: Proving ...
% 16.03/2.90 Prover 3: Constructing countermodel ...
% 22.50/3.70 Prover 4: Constructing countermodel ...
% 23.71/3.87 Prover 0: Proving ...
% 33.52/5.12 Prover 3: proved (4446ms)
% 33.52/5.12
% 33.52/5.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.52/5.12
% 33.52/5.12 Prover 5: stopped
% 33.52/5.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 33.52/5.13 Prover 6: stopped
% 33.52/5.13 Prover 0: stopped
% 33.52/5.13 Prover 2: stopped
% 33.52/5.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 33.52/5.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 33.52/5.15 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 33.52/5.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 35.25/5.37 Prover 7: Preprocessing ...
% 35.25/5.39 Prover 8: Preprocessing ...
% 35.87/5.41 Prover 10: Preprocessing ...
% 35.87/5.42 Prover 11: Preprocessing ...
% 35.87/5.43 Prover 13: Preprocessing ...
% 36.93/5.59 Prover 10: Constructing countermodel ...
% 36.93/5.61 Prover 7: Constructing countermodel ...
% 37.65/5.66 Prover 13: Constructing countermodel ...
% 38.90/5.80 Prover 8: Warning: ignoring some quantifiers
% 38.90/5.83 Prover 8: Constructing countermodel ...
% 45.37/6.60 Prover 11: Constructing countermodel ...
% 73.16/10.20 Prover 13: stopped
% 73.47/10.21 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 73.80/10.32 Prover 16: Preprocessing ...
% 74.91/10.42 Prover 16: Constructing countermodel ...
% 115.61/15.73 Prover 16: stopped
% 115.61/15.74 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 116.36/15.85 Prover 19: Preprocessing ...
% 118.14/16.03 Prover 1: stopped
% 118.92/16.22 Prover 19: Warning: ignoring some quantifiers
% 119.58/16.25 Prover 19: Constructing countermodel ...
% 142.76/19.46 Prover 19: stopped
% 186.85/27.71 Prover 7: stopped
% 188.10/28.00 Prover 4: stopped
% 230.99/39.85 Prover 8: stopped
% 231.51/40.01 Prover 11: stopped
% 255.71/60.60 Prover 10: Found proof (size 253)
% 255.71/60.60 Prover 10: proved (55475ms)
% 255.71/60.60
% 255.71/60.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 255.71/60.60
% 256.28/60.75 % SZS output start Proof for theBenchmark
% 256.39/60.75 Assumptions after simplification:
% 256.39/60.75 ---------------------------------
% 256.39/60.75
% 256.39/60.75 (ax15)
% 256.39/60.76 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) |
% 256.39/60.76 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~
% 256.39/60.76 neq(v0, v0))
% 256.39/60.76
% 256.39/60.76 (ax17)
% 256.39/60.76 $i(nil) & ssList(nil)
% 256.39/60.76
% 256.39/60.76 (ax26)
% 256.39/60.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) |
% 256.39/60.79 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 256.39/60.79
% 256.39/60.79 (ax28)
% 256.39/60.79 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 256.39/60.79 $i(v0) | ~ ssList(v0))
% 256.39/60.79
% 256.39/60.79 (ax42)
% 256.39/60.79 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0))
% 256.39/60.79
% 256.39/60.79 (ax45)
% 256.39/60.79 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 256.39/60.79
% 256.39/60.79 (ax46)
% 256.39/60.79 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 256.39/60.79 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 256.39/60.79
% 256.39/60.79 (ax49)
% 256.39/60.79 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, v0))
% 256.39/60.79
% 256.39/60.79 (ax5)
% 256.39/60.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 256.39/60.79 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 256.39/60.79 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 256.39/60.79 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 256.39/60.79 v2) = v0 & $i(v2) & ssList(v2)))
% 256.39/60.79
% 256.39/60.79 (ax50)
% 256.39/60.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2, v0) = v3)
% 256.39/60.80 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, v1) | ~ ssList(v2) |
% 256.39/60.80 ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1))
% 256.39/60.80
% 256.39/60.80 (ax51)
% 256.39/60.80 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 256.39/60.80
% 256.39/60.80 (ax52)
% 256.39/60.80 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~
% 256.39/60.80 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 256.39/60.80
% 256.39/60.80 (ax58)
% 256.39/60.80 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 256.39/60.80 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 256.39/60.80
% 256.39/60.80 (ax6)
% 256.39/60.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 256.39/60.80 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 256.39/60.80 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 256.39/60.80 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 256.39/60.80 v1) = v0 & $i(v2) & ssList(v2)))
% 256.39/60.80
% 256.39/60.80 (ax7)
% 256.39/60.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 256.39/60.81 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 256.39/60.81 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 256.39/60.81 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 256.39/60.81 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 256.39/60.81 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 256.39/60.81 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 256.39/60.81
% 256.39/60.81 (ax79)
% 256.39/60.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v3,
% 256.39/60.81 v1) = v2) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 256.39/60.81 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 256.39/60.81
% 256.39/60.81 (ax80)
% 256.39/60.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v1,
% 256.39/60.81 v3) = v2) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 256.39/60.81 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 256.39/60.81
% 256.39/60.81 (ax82)
% 256.39/60.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 256.39/60.81 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 256.39/60.81 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 256.39/60.81 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 256.39/60.81
% 256.39/60.81 (ax83)
% 256.39/60.82 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 256.39/60.82 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 256.39/60.82 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 256.39/60.82 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 256.39/60.82 v0) | ~ ssList(nil))
% 256.39/60.82
% 256.39/60.82 (ax84)
% 256.39/60.82 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 256.39/60.82 $i(v0) | ~ ssList(v0))
% 256.39/60.82
% 256.39/60.82 (co1)
% 256.39/60.82 $i(nil) & ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ssList(v1) &
% 256.39/60.82 ssList(v0) & ((v1 = nil & v0 = nil) | (segmentP(v1, v0) & neq(v0, nil))) &
% 256.39/60.82 ((v1 = nil & ~ (v0 = nil)) | (neq(v1, nil) & ! [v2: $i] : ( ~ $i(v2) | ~
% 256.39/60.82 segmentP(v1, v2) | ~ segmentP(v0, v2) | ~ ssList(v2) | ~ neq(v2,
% 256.39/60.82 nil)))))
% 256.39/60.82
% 256.39/60.82 (function-axioms)
% 256.39/60.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 256.39/60.82 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 256.39/60.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 256.39/60.82 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 256.39/60.82 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 256.39/60.82 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 256.39/60.82
% 256.39/60.82 Further assumptions not needed in the proof:
% 256.39/60.82 --------------------------------------------
% 256.39/60.82 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 256.39/60.82 ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36,
% 256.39/60.82 ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax47, ax48, ax53, ax54, ax55,
% 256.39/60.82 ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69,
% 256.72/60.82 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax8, ax81, ax85, ax86,
% 256.72/60.82 ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 256.72/60.82
% 256.72/60.82 Those formulas are unsatisfiable:
% 256.72/60.82 ---------------------------------
% 256.72/60.82
% 256.72/60.82 Begin of proof
% 256.72/60.83 |
% 256.72/60.83 | ALPHA: (ax5) implies:
% 256.72/60.83 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 256.72/60.83 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 256.72/60.83 | v0 & $i(v2) & ssList(v2)))
% 256.72/60.83 |
% 256.72/60.83 | ALPHA: (ax6) implies:
% 256.72/60.83 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 256.72/60.83 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 256.72/60.83 | v0 & $i(v2) & ssList(v2)))
% 256.72/60.83 |
% 256.72/60.83 | ALPHA: (ax7) implies:
% 256.72/60.83 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0,
% 256.72/60.83 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] :
% 256.72/60.83 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) &
% 256.72/60.83 | $i(v2) & ssList(v4) & ssList(v2)))
% 256.72/60.83 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 256.72/60.83 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2)
% 256.72/60.83 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~
% 256.72/60.83 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 256.72/60.83 |
% 256.72/60.83 | ALPHA: (ax15) implies:
% 256.72/60.83 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~ neq(v0, v0))
% 256.72/60.83 |
% 256.72/60.83 | ALPHA: (ax17) implies:
% 256.72/60.83 | (6) ssList(nil)
% 256.72/60.83 |
% 256.72/60.83 | ALPHA: (ax28) implies:
% 256.72/60.84 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 256.72/60.84 | $i(v0) | ~ ssList(v0))
% 256.72/60.84 |
% 256.72/60.84 | ALPHA: (ax45) implies:
% 256.72/60.84 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 256.72/60.84 |
% 256.72/60.84 | ALPHA: (ax46) implies:
% 256.72/60.84 | (9) ~ ssList(nil) | frontsegP(nil, nil)
% 256.72/60.84 |
% 256.72/60.84 | ALPHA: (ax51) implies:
% 256.72/60.84 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 256.72/60.84 |
% 256.72/60.84 | ALPHA: (ax52) implies:
% 256.72/60.84 | (11) ~ ssList(nil) | rearsegP(nil, nil)
% 256.72/60.84 |
% 256.72/60.84 | ALPHA: (ax58) implies:
% 256.72/60.84 | (12) ~ ssList(nil) | segmentP(nil, nil)
% 256.72/60.84 | (13) ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 256.72/60.84 | ssList(v0))
% 256.72/60.84 |
% 256.72/60.84 | ALPHA: (ax83) implies:
% 256.72/60.84 | (14) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 256.72/60.84 | (15) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~
% 256.72/60.84 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 256.72/60.84 | (16) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 256.72/60.84 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 256.72/60.84 |
% 256.72/60.84 | ALPHA: (ax84) implies:
% 256.72/60.84 | (17) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 256.72/60.84 | $i(v0) | ~ ssList(v0))
% 256.72/60.84 |
% 256.72/60.84 | ALPHA: (co1) implies:
% 256.72/60.84 | (18) $i(nil)
% 256.72/60.84 | (19) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ssList(v1) & ssList(v0)
% 256.72/60.84 | & ((v1 = nil & v0 = nil) | (segmentP(v1, v0) & neq(v0, nil))) & ((v1
% 256.72/60.84 | = nil & ~ (v0 = nil)) | (neq(v1, nil) & ! [v2: $i] : ( ~
% 256.72/60.84 | $i(v2) | ~ segmentP(v1, v2) | ~ segmentP(v0, v2) | ~
% 256.72/60.84 | ssList(v2) | ~ neq(v2, nil)))))
% 256.72/60.84 |
% 256.72/60.84 | ALPHA: (function-axioms) implies:
% 256.72/60.84 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 256.72/60.84 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 256.72/60.84 |
% 256.72/60.85 | DELTA: instantiating (19) with fresh symbols all_91_0, all_91_1 gives:
% 256.72/60.85 | (21) $i(all_91_0) & $i(all_91_1) & ssList(all_91_0) & ssList(all_91_1) &
% 256.72/60.85 | ((all_91_0 = nil & all_91_1 = nil) | (segmentP(all_91_0, all_91_1) &
% 256.72/60.85 | neq(all_91_1, nil))) & ((all_91_0 = nil & ~ (all_91_1 = nil)) |
% 256.72/60.85 | (neq(all_91_0, nil) & ! [v0: $i] : ( ~ $i(v0) | ~
% 256.72/60.85 | segmentP(all_91_0, v0) | ~ segmentP(all_91_1, v0) | ~
% 256.72/60.85 | ssList(v0) | ~ neq(v0, nil))))
% 256.72/60.85 |
% 256.72/60.85 | ALPHA: (21) implies:
% 256.72/60.85 | (22) ssList(all_91_1)
% 256.72/60.85 | (23) $i(all_91_1)
% 256.72/60.85 | (24) (all_91_0 = nil & ~ (all_91_1 = nil)) | (neq(all_91_0, nil) & ! [v0:
% 256.72/60.85 | $i] : ( ~ $i(v0) | ~ segmentP(all_91_0, v0) | ~
% 256.72/60.85 | segmentP(all_91_1, v0) | ~ ssList(v0) | ~ neq(v0, nil)))
% 256.72/60.85 | (25) (all_91_0 = nil & all_91_1 = nil) | (segmentP(all_91_0, all_91_1) &
% 256.72/60.85 | neq(all_91_1, nil))
% 256.72/60.85 |
% 256.72/60.85 | BETA: splitting (11) gives:
% 256.72/60.85 |
% 256.72/60.85 | Case 1:
% 256.72/60.85 | |
% 256.72/60.85 | | (26) ~ ssList(nil)
% 256.72/60.85 | |
% 256.72/60.85 | | PRED_UNIFY: (6), (26) imply:
% 256.72/60.85 | | (27) $false
% 256.72/60.85 | |
% 256.72/60.85 | | CLOSE: (27) is inconsistent.
% 256.72/60.85 | |
% 256.72/60.85 | Case 2:
% 256.72/60.85 | |
% 256.72/60.85 | | (28) rearsegP(nil, nil)
% 256.72/60.85 | |
% 256.72/60.85 | | BETA: splitting (9) gives:
% 256.72/60.85 | |
% 256.72/60.85 | | Case 1:
% 256.72/60.85 | | |
% 256.72/60.85 | | | (29) ~ ssList(nil)
% 256.72/60.85 | | |
% 256.72/60.85 | | | PRED_UNIFY: (6), (29) imply:
% 256.72/60.85 | | | (30) $false
% 256.72/60.85 | | |
% 256.72/60.85 | | | CLOSE: (30) is inconsistent.
% 256.72/60.85 | | |
% 256.72/60.85 | | Case 2:
% 256.72/60.85 | | |
% 256.72/60.85 | | | (31) frontsegP(nil, nil)
% 256.72/60.85 | | |
% 256.72/60.85 | | | BETA: splitting (12) gives:
% 256.72/60.85 | | |
% 256.72/60.85 | | | Case 1:
% 256.72/60.85 | | | |
% 256.72/60.85 | | | | (32) ~ ssList(nil)
% 256.72/60.85 | | | |
% 256.72/60.85 | | | | PRED_UNIFY: (6), (32) imply:
% 256.72/60.85 | | | | (33) $false
% 256.72/60.85 | | | |
% 256.72/60.85 | | | | CLOSE: (33) is inconsistent.
% 256.72/60.85 | | | |
% 256.72/60.85 | | | Case 2:
% 256.72/60.85 | | | |
% 256.72/60.85 | | | | (34) segmentP(nil, nil)
% 256.72/60.85 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (ax49) with all_91_1, simplifying with (22),
% 256.72/60.86 | | | | (23) gives:
% 256.72/60.86 | | | | (35) rearsegP(all_91_1, all_91_1)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (10) with all_91_1, simplifying with (22),
% 256.72/60.86 | | | | (23) gives:
% 256.72/60.86 | | | | (36) rearsegP(all_91_1, nil)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (ax42) with all_91_1, simplifying with (22),
% 256.72/60.86 | | | | (23) gives:
% 256.72/60.86 | | | | (37) frontsegP(all_91_1, all_91_1)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (8) with all_91_1, simplifying with (22),
% 256.72/60.86 | | | | (23) gives:
% 256.72/60.86 | | | | (38) frontsegP(all_91_1, nil)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (6),
% 256.72/60.86 | | | | (18), (31) gives:
% 256.72/60.86 | | | | (39) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (2) with nil, nil, simplifying with (6),
% 256.72/60.86 | | | | (18), (28) gives:
% 256.72/60.86 | | | | (40) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0))
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (6),
% 256.72/60.86 | | | | (18), (34) gives:
% 256.72/60.86 | | | | (41) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil &
% 256.72/60.86 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) &
% 256.72/60.86 | | | | ssList(v0))
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | DELTA: instantiating (40) with fresh symbol all_111_0 gives:
% 256.72/60.86 | | | | (42) app(all_111_0, nil) = nil & $i(all_111_0) & ssList(all_111_0)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | ALPHA: (42) implies:
% 256.72/60.86 | | | | (43) ssList(all_111_0)
% 256.72/60.86 | | | | (44) $i(all_111_0)
% 256.72/60.86 | | | | (45) app(all_111_0, nil) = nil
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | DELTA: instantiating (39) with fresh symbol all_113_0 gives:
% 256.72/60.86 | | | | (46) app(nil, all_113_0) = nil & $i(all_113_0) & ssList(all_113_0)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | ALPHA: (46) implies:
% 256.72/60.86 | | | | (47) ssList(all_113_0)
% 256.72/60.86 | | | | (48) $i(all_113_0)
% 256.72/60.86 | | | | (49) app(nil, all_113_0) = nil
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | DELTA: instantiating (41) with fresh symbols all_115_0, all_115_1,
% 256.72/60.86 | | | | all_115_2 gives:
% 256.72/60.86 | | | | (50) app(all_115_1, all_115_0) = nil & app(all_115_2, nil) =
% 256.72/60.86 | | | | all_115_1 & $i(all_115_0) & $i(all_115_1) & $i(all_115_2) &
% 256.72/60.86 | | | | ssList(all_115_0) & ssList(all_115_2)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | ALPHA: (50) implies:
% 256.72/60.86 | | | | (51) ssList(all_115_2)
% 256.72/60.86 | | | | (52) ssList(all_115_0)
% 256.72/60.86 | | | | (53) $i(all_115_2)
% 256.72/60.86 | | | | (54) $i(all_115_1)
% 256.72/60.86 | | | | (55) $i(all_115_0)
% 256.72/60.86 | | | | (56) app(all_115_2, nil) = all_115_1
% 256.72/60.86 | | | | (57) app(all_115_1, all_115_0) = nil
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (ax49) with all_115_2, simplifying with (51),
% 256.72/60.86 | | | | (53) gives:
% 256.72/60.86 | | | | (58) rearsegP(all_115_2, all_115_2)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (ax42) with all_115_2, simplifying with (51),
% 256.72/60.86 | | | | (53) gives:
% 256.72/60.86 | | | | (59) frontsegP(all_115_2, all_115_2)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (8) with all_115_2, simplifying with (51),
% 256.72/60.86 | | | | (53) gives:
% 256.72/60.86 | | | | (60) frontsegP(all_115_2, nil)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (ax49) with all_115_0, simplifying with (52),
% 256.72/60.86 | | | | (55) gives:
% 256.72/60.86 | | | | (61) rearsegP(all_115_0, all_115_0)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (10) with all_115_0, simplifying with (52),
% 256.72/60.86 | | | | (55) gives:
% 256.72/60.86 | | | | (62) rearsegP(all_115_0, nil)
% 256.72/60.86 | | | |
% 256.72/60.86 | | | | GROUND_INST: instantiating (ax42) with all_115_0, simplifying with (52),
% 256.72/60.86 | | | | (55) gives:
% 256.72/60.87 | | | | (63) frontsegP(all_115_0, all_115_0)
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (8) with all_115_0, simplifying with (52),
% 256.72/60.87 | | | | (55) gives:
% 256.72/60.87 | | | | (64) frontsegP(all_115_0, nil)
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (1) with all_91_1, nil, simplifying with (6),
% 256.72/60.87 | | | | (18), (22), (23), (38) gives:
% 256.72/60.87 | | | | (65) ? [v0: $i] : (app(nil, v0) = all_91_1 & $i(v0) & ssList(v0))
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (1) with all_91_1, all_91_1, simplifying with
% 256.72/60.87 | | | | (22), (23), (37) gives:
% 256.72/60.87 | | | | (66) ? [v0: $i] : (app(all_91_1, v0) = all_91_1 & $i(v0) &
% 256.72/60.87 | | | | ssList(v0))
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (2) with all_91_1, nil, simplifying with (6),
% 256.72/60.87 | | | | (18), (22), (23), (36) gives:
% 256.72/60.87 | | | | (67) ? [v0: $i] : (app(v0, nil) = all_91_1 & $i(v0) & ssList(v0))
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (2) with all_91_1, all_91_1, simplifying with
% 256.72/60.87 | | | | (22), (23), (35) gives:
% 256.72/60.87 | | | | (68) ? [v0: $i] : (app(v0, all_91_1) = all_91_1 & $i(v0) &
% 256.72/60.87 | | | | ssList(v0))
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (ax82) with nil, all_113_0, nil, all_113_0,
% 256.72/60.87 | | | | nil, simplifying with (6), (18), (47), (48), (49) gives:
% 256.72/60.87 | | | | (69) ? [v0: $i] : (app(all_113_0, all_113_0) = v0 & app(nil, v0) =
% 256.72/60.87 | | | | nil & $i(v0))
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (7) with all_113_0, nil, simplifying with
% 256.72/60.87 | | | | (47), (48), (49) gives:
% 256.72/60.87 | | | | (70) all_113_0 = nil
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (17) with all_111_0, nil, simplifying with
% 256.72/60.87 | | | | (43), (44), (45) gives:
% 256.72/60.87 | | | | (71) all_111_0 = nil
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (ax50) with nil, nil, all_115_2, all_115_1,
% 256.72/60.87 | | | | simplifying with (6), (18), (28), (51), (53), (56) gives:
% 256.72/60.87 | | | | (72) rearsegP(all_115_1, nil)
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (ax26) with all_115_2, nil, all_115_1,
% 256.72/60.87 | | | | simplifying with (6), (18), (51), (53), (56) gives:
% 256.72/60.87 | | | | (73) ssList(all_115_1)
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (17) with all_115_2, all_115_1, simplifying
% 256.72/60.87 | | | | with (51), (53), (56) gives:
% 256.72/60.87 | | | | (74) all_115_1 = all_115_2
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | GROUND_INST: instantiating (ax82) with all_115_2, nil, all_115_1,
% 256.72/60.87 | | | | all_115_0, nil, simplifying with (6), (18), (51), (52),
% 256.72/60.87 | | | | (53), (55), (56), (57) gives:
% 256.72/60.87 | | | | (75) ? [v0: $i] : (app(all_115_2, v0) = nil & app(nil, all_115_0) =
% 256.72/60.87 | | | | v0 & $i(v0))
% 256.72/60.87 | | | |
% 256.72/60.87 | | | | DELTA: instantiating (68) with fresh symbol all_135_0 gives:
% 256.93/60.88 | | | | (76) app(all_135_0, all_91_1) = all_91_1 & $i(all_135_0) &
% 256.93/60.88 | | | | ssList(all_135_0)
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | ALPHA: (76) implies:
% 256.93/60.88 | | | | (77) ssList(all_135_0)
% 256.93/60.88 | | | | (78) $i(all_135_0)
% 256.93/60.88 | | | | (79) app(all_135_0, all_91_1) = all_91_1
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | DELTA: instantiating (67) with fresh symbol all_137_0 gives:
% 256.93/60.88 | | | | (80) app(all_137_0, nil) = all_91_1 & $i(all_137_0) &
% 256.93/60.88 | | | | ssList(all_137_0)
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | ALPHA: (80) implies:
% 256.93/60.88 | | | | (81) ssList(all_137_0)
% 256.93/60.88 | | | | (82) $i(all_137_0)
% 256.93/60.88 | | | | (83) app(all_137_0, nil) = all_91_1
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | DELTA: instantiating (75) with fresh symbol all_139_0 gives:
% 256.93/60.88 | | | | (84) app(all_115_2, all_139_0) = nil & app(nil, all_115_0) =
% 256.93/60.88 | | | | all_139_0 & $i(all_139_0)
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | ALPHA: (84) implies:
% 256.93/60.88 | | | | (85) app(nil, all_115_0) = all_139_0
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | DELTA: instantiating (69) with fresh symbol all_145_0 gives:
% 256.93/60.88 | | | | (86) app(all_113_0, all_113_0) = all_145_0 & app(nil, all_145_0) =
% 256.93/60.88 | | | | nil & $i(all_145_0)
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | ALPHA: (86) implies:
% 256.93/60.88 | | | | (87) $i(all_145_0)
% 256.93/60.88 | | | | (88) app(all_113_0, all_113_0) = all_145_0
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | DELTA: instantiating (66) with fresh symbol all_147_0 gives:
% 256.93/60.88 | | | | (89) app(all_91_1, all_147_0) = all_91_1 & $i(all_147_0) &
% 256.93/60.88 | | | | ssList(all_147_0)
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | ALPHA: (89) implies:
% 256.93/60.88 | | | | (90) ssList(all_147_0)
% 256.93/60.88 | | | | (91) $i(all_147_0)
% 256.93/60.88 | | | | (92) app(all_91_1, all_147_0) = all_91_1
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | DELTA: instantiating (65) with fresh symbol all_149_0 gives:
% 256.93/60.88 | | | | (93) app(nil, all_149_0) = all_91_1 & $i(all_149_0) &
% 256.93/60.88 | | | | ssList(all_149_0)
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | ALPHA: (93) implies:
% 256.93/60.88 | | | | (94) ssList(all_149_0)
% 256.93/60.88 | | | | (95) $i(all_149_0)
% 256.93/60.88 | | | | (96) app(nil, all_149_0) = all_91_1
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | REDUCE: (57), (74) imply:
% 256.93/60.88 | | | | (97) app(all_115_2, all_115_0) = nil
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | REDUCE: (70), (88) imply:
% 256.93/60.88 | | | | (98) app(nil, nil) = all_145_0
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | REDUCE: (72), (74) imply:
% 256.93/60.88 | | | | (99) rearsegP(all_115_2, nil)
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | GROUND_INST: instantiating (14) with all_145_0, simplifying with (6),
% 256.93/60.88 | | | | (98) gives:
% 256.93/60.88 | | | | (100) all_145_0 = nil
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | REDUCE: (98), (100) imply:
% 256.93/60.88 | | | | (101) app(nil, nil) = nil
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | GROUND_INST: instantiating (1) with all_115_2, nil, simplifying with
% 256.93/60.88 | | | | (6), (18), (51), (53), (60) gives:
% 256.93/60.88 | | | | (102) ? [v0: $i] : (app(nil, v0) = all_115_2 & $i(v0) & ssList(v0))
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | GROUND_INST: instantiating (1) with all_115_2, all_115_2, simplifying
% 256.93/60.88 | | | | with (51), (53), (59) gives:
% 256.93/60.88 | | | | (103) ? [v0: $i] : (app(all_115_2, v0) = all_115_2 & $i(v0) &
% 256.93/60.88 | | | | ssList(v0))
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | GROUND_INST: instantiating (1) with all_115_0, nil, simplifying with
% 256.93/60.88 | | | | (6), (18), (52), (55), (64) gives:
% 256.93/60.88 | | | | (104) ? [v0: $i] : (app(nil, v0) = all_115_0 & $i(v0) & ssList(v0))
% 256.93/60.88 | | | |
% 256.93/60.88 | | | | GROUND_INST: instantiating (1) with all_115_0, all_115_0, simplifying
% 256.93/60.88 | | | | with (52), (55), (63) gives:
% 256.93/60.89 | | | | (105) ? [v0: $i] : (app(all_115_0, v0) = all_115_0 & $i(v0) &
% 256.93/60.89 | | | | ssList(v0))
% 256.93/60.89 | | | |
% 256.93/60.89 | | | | GROUND_INST: instantiating (2) with all_115_2, nil, simplifying with
% 256.93/60.89 | | | | (6), (18), (51), (53), (99) gives:
% 256.93/60.89 | | | | (106) ? [v0: $i] : (app(v0, nil) = all_115_2 & $i(v0) & ssList(v0))
% 256.93/60.89 | | | |
% 256.93/60.89 | | | | GROUND_INST: instantiating (2) with all_115_2, all_115_2, simplifying
% 256.93/60.89 | | | | with (51), (53), (58) gives:
% 256.93/60.89 | | | | (107) ? [v0: $i] : (app(v0, all_115_2) = all_115_2 & $i(v0) &
% 256.93/60.89 | | | | ssList(v0))
% 256.93/60.89 | | | |
% 256.93/60.89 | | | | GROUND_INST: instantiating (2) with all_115_0, nil, simplifying with
% 256.93/60.89 | | | | (6), (18), (52), (55), (62) gives:
% 256.93/60.89 | | | | (108) ? [v0: $i] : (app(v0, nil) = all_115_0 & $i(v0) & ssList(v0))
% 256.93/60.89 | | | |
% 256.93/60.89 | | | | GROUND_INST: instantiating (2) with all_115_0, all_115_0, simplifying
% 256.93/60.89 | | | | with (52), (55), (61) gives:
% 256.93/60.89 | | | | (109) ? [v0: $i] : (app(v0, all_115_0) = all_115_0 & $i(v0) &
% 256.93/60.89 | | | | ssList(v0))
% 256.93/60.89 | | | |
% 256.93/60.89 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_115_0,
% 256.93/60.89 | | | | all_139_0, simplifying with (6), (18), (52), (55), (85),
% 256.93/60.89 | | | | (101) gives:
% 256.93/60.89 | | | | (110) ? [v0: $i] : (app(nil, v0) = all_139_0 & app(nil, all_115_0) =
% 256.93/60.89 | | | | v0 & $i(v0) & $i(all_139_0))
% 256.93/60.89 | | | |
% 256.93/60.89 | | | | GROUND_INST: instantiating (7) with all_115_0, all_139_0, simplifying
% 256.93/60.89 | | | | with (52), (55), (85) gives:
% 256.93/60.89 | | | | (111) all_139_0 = all_115_0
% 256.93/60.89 | | | |
% 256.93/60.89 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_149_0,
% 256.93/60.89 | | | | all_91_1, simplifying with (6), (18), (94), (95), (96),
% 256.93/60.89 | | | | (101) gives:
% 256.93/60.89 | | | | (112) ? [v0: $i] : (app(nil, v0) = all_91_1 & app(nil, all_149_0) =
% 256.93/60.89 | | | | v0 & $i(v0) & $i(all_91_1))
% 256.93/60.89 | | | |
% 256.93/60.89 | | | | GROUND_INST: instantiating (7) with all_149_0, all_91_1, simplifying
% 256.93/60.89 | | | | with (94), (95), (96) gives:
% 256.93/60.89 | | | | (113) all_149_0 = all_91_1
% 256.93/60.89 | | | |
% 256.93/60.89 | | | | GROUND_INST: instantiating (4) with all_91_1, all_149_0, nil, all_91_1,
% 256.93/60.89 | | | | all_147_0, simplifying with (6), (18), (22), (23), (90),
% 256.93/60.89 | | | | (91), (92), (94), (95), (96) gives:
% 256.93/60.89 | | | | (114) segmentP(all_91_1, all_149_0)
% 256.93/60.89 | | | |
% 256.93/60.90 | | | | GROUND_INST: instantiating (ax82) with nil, all_149_0, all_91_1,
% 256.93/60.90 | | | | all_147_0, all_91_1, simplifying with (6), (18), (90),
% 256.93/60.90 | | | | (91), (92), (94), (95), (96) gives:
% 256.93/60.90 | | | | (115) ? [v0: $i] : (app(all_149_0, all_147_0) = v0 & app(nil, v0) =
% 256.93/60.90 | | | | all_91_1 & $i(v0) & $i(all_91_1))
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil,
% 256.93/60.90 | | | | all_149_0, all_91_1, simplifying with (51), (52), (53),
% 256.93/60.90 | | | | (55), (94), (95), (96), (97) gives:
% 256.93/60.90 | | | | (116) ? [v0: $i] : (app(all_115_0, all_149_0) = v0 & app(all_115_2,
% 256.93/60.90 | | | | v0) = all_91_1 & $i(v0) & $i(all_91_1))
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil,
% 256.93/60.90 | | | | all_115_0, all_139_0, simplifying with (51), (52), (53),
% 256.93/60.90 | | | | (55), (85), (97) gives:
% 256.93/60.90 | | | | (117) ? [v0: $i] : (app(all_115_0, all_115_0) = v0 & app(all_115_2,
% 256.93/60.90 | | | | v0) = all_139_0 & $i(v0) & $i(all_139_0))
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil, nil,
% 256.93/60.90 | | | | nil, simplifying with (6), (18), (51), (52), (53), (55),
% 256.93/60.90 | | | | (97), (101) gives:
% 256.93/60.90 | | | | (118) ? [v0: $i] : (app(all_115_0, nil) = v0 & app(all_115_2, v0) =
% 256.93/60.90 | | | | nil & $i(v0))
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | GROUND_INST: instantiating (16) with all_115_2, all_115_0, simplifying
% 256.93/60.90 | | | | with (51), (52), (53), (55), (97) gives:
% 256.93/60.90 | | | | (119) all_115_0 = nil
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | GROUND_INST: instantiating (15) with all_115_2, all_115_0, simplifying
% 256.93/60.90 | | | | with (51), (52), (53), (55), (97) gives:
% 256.93/60.90 | | | | (120) all_115_2 = nil
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | GROUND_INST: instantiating (17) with all_137_0, all_91_1, simplifying
% 256.93/60.90 | | | | with (81), (82), (83) gives:
% 256.93/60.90 | | | | (121) all_137_0 = all_91_1
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | COMBINE_EQS: (111), (119) imply:
% 256.93/60.90 | | | | (122) all_139_0 = nil
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | DELTA: instantiating (118) with fresh symbol all_169_0 gives:
% 256.93/60.90 | | | | (123) app(all_115_0, nil) = all_169_0 & app(all_115_2, all_169_0) =
% 256.93/60.90 | | | | nil & $i(all_169_0)
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | ALPHA: (123) implies:
% 256.93/60.90 | | | | (124) $i(all_169_0)
% 256.93/60.90 | | | | (125) app(all_115_0, nil) = all_169_0
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | DELTA: instantiating (109) with fresh symbol all_171_0 gives:
% 256.93/60.90 | | | | (126) app(all_171_0, all_115_0) = all_115_0 & $i(all_171_0) &
% 256.93/60.90 | | | | ssList(all_171_0)
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | ALPHA: (126) implies:
% 256.93/60.90 | | | | (127) ssList(all_171_0)
% 256.93/60.90 | | | | (128) $i(all_171_0)
% 256.93/60.90 | | | | (129) app(all_171_0, all_115_0) = all_115_0
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | DELTA: instantiating (107) with fresh symbol all_173_0 gives:
% 256.93/60.90 | | | | (130) app(all_173_0, all_115_2) = all_115_2 & $i(all_173_0) &
% 256.93/60.90 | | | | ssList(all_173_0)
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | ALPHA: (130) implies:
% 256.93/60.90 | | | | (131) ssList(all_173_0)
% 256.93/60.90 | | | | (132) $i(all_173_0)
% 256.93/60.90 | | | | (133) app(all_173_0, all_115_2) = all_115_2
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | DELTA: instantiating (106) with fresh symbol all_175_0 gives:
% 256.93/60.90 | | | | (134) app(all_175_0, nil) = all_115_2 & $i(all_175_0) &
% 256.93/60.90 | | | | ssList(all_175_0)
% 256.93/60.90 | | | |
% 256.93/60.90 | | | | ALPHA: (134) implies:
% 256.93/60.90 | | | | (135) ssList(all_175_0)
% 256.93/60.91 | | | | (136) $i(all_175_0)
% 256.93/60.91 | | | | (137) app(all_175_0, nil) = all_115_2
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | DELTA: instantiating (108) with fresh symbol all_181_0 gives:
% 256.93/60.91 | | | | (138) app(all_181_0, nil) = all_115_0 & $i(all_181_0) &
% 256.93/60.91 | | | | ssList(all_181_0)
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | ALPHA: (138) implies:
% 256.93/60.91 | | | | (139) ssList(all_181_0)
% 256.93/60.91 | | | | (140) $i(all_181_0)
% 256.93/60.91 | | | | (141) app(all_181_0, nil) = all_115_0
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | DELTA: instantiating (105) with fresh symbol all_183_0 gives:
% 256.93/60.91 | | | | (142) app(all_115_0, all_183_0) = all_115_0 & $i(all_183_0) &
% 256.93/60.91 | | | | ssList(all_183_0)
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | ALPHA: (142) implies:
% 256.93/60.91 | | | | (143) ssList(all_183_0)
% 256.93/60.91 | | | | (144) $i(all_183_0)
% 256.93/60.91 | | | | (145) app(all_115_0, all_183_0) = all_115_0
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | DELTA: instantiating (104) with fresh symbol all_185_0 gives:
% 256.93/60.91 | | | | (146) app(nil, all_185_0) = all_115_0 & $i(all_185_0) &
% 256.93/60.91 | | | | ssList(all_185_0)
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | ALPHA: (146) implies:
% 256.93/60.91 | | | | (147) ssList(all_185_0)
% 256.93/60.91 | | | | (148) $i(all_185_0)
% 256.93/60.91 | | | | (149) app(nil, all_185_0) = all_115_0
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | DELTA: instantiating (103) with fresh symbol all_187_0 gives:
% 256.93/60.91 | | | | (150) app(all_115_2, all_187_0) = all_115_2 & $i(all_187_0) &
% 256.93/60.91 | | | | ssList(all_187_0)
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | ALPHA: (150) implies:
% 256.93/60.91 | | | | (151) ssList(all_187_0)
% 256.93/60.91 | | | | (152) $i(all_187_0)
% 256.93/60.91 | | | | (153) app(all_115_2, all_187_0) = all_115_2
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | DELTA: instantiating (102) with fresh symbol all_189_0 gives:
% 256.93/60.91 | | | | (154) app(nil, all_189_0) = all_115_2 & $i(all_189_0) &
% 256.93/60.91 | | | | ssList(all_189_0)
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | ALPHA: (154) implies:
% 256.93/60.91 | | | | (155) ssList(all_189_0)
% 256.93/60.91 | | | | (156) $i(all_189_0)
% 256.93/60.91 | | | | (157) app(nil, all_189_0) = all_115_2
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | DELTA: instantiating (115) with fresh symbol all_195_0 gives:
% 256.93/60.91 | | | | (158) app(all_149_0, all_147_0) = all_195_0 & app(nil, all_195_0) =
% 256.93/60.91 | | | | all_91_1 & $i(all_195_0) & $i(all_91_1)
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | ALPHA: (158) implies:
% 256.93/60.91 | | | | (159) $i(all_195_0)
% 256.93/60.91 | | | | (160) app(all_149_0, all_147_0) = all_195_0
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | DELTA: instantiating (117) with fresh symbol all_197_0 gives:
% 256.93/60.91 | | | | (161) app(all_115_0, all_115_0) = all_197_0 & app(all_115_2,
% 256.93/60.91 | | | | all_197_0) = all_139_0 & $i(all_197_0) & $i(all_139_0)
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | ALPHA: (161) implies:
% 256.93/60.91 | | | | (162) app(all_115_0, all_115_0) = all_197_0
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | DELTA: instantiating (112) with fresh symbol all_201_0 gives:
% 256.93/60.91 | | | | (163) app(nil, all_201_0) = all_91_1 & app(nil, all_149_0) =
% 256.93/60.91 | | | | all_201_0 & $i(all_201_0) & $i(all_91_1)
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | ALPHA: (163) implies:
% 256.93/60.91 | | | | (164) app(nil, all_149_0) = all_201_0
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | DELTA: instantiating (116) with fresh symbol all_215_0 gives:
% 256.93/60.91 | | | | (165) app(all_115_0, all_149_0) = all_215_0 & app(all_115_2,
% 256.93/60.91 | | | | all_215_0) = all_91_1 & $i(all_215_0) & $i(all_91_1)
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | ALPHA: (165) implies:
% 256.93/60.91 | | | | (166) app(all_115_0, all_149_0) = all_215_0
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | DELTA: instantiating (110) with fresh symbol all_217_0 gives:
% 256.93/60.91 | | | | (167) app(nil, all_217_0) = all_139_0 & app(nil, all_115_0) =
% 256.93/60.91 | | | | all_217_0 & $i(all_217_0) & $i(all_139_0)
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | ALPHA: (167) implies:
% 256.93/60.91 | | | | (168) app(nil, all_115_0) = all_217_0
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | REDUCE: (119), (141) imply:
% 256.93/60.91 | | | | (169) app(all_181_0, nil) = nil
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | REDUCE: (120), (137) imply:
% 256.93/60.91 | | | | (170) app(all_175_0, nil) = nil
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | REDUCE: (120), (133) imply:
% 256.93/60.91 | | | | (171) app(all_173_0, nil) = nil
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | REDUCE: (119), (129) imply:
% 256.93/60.91 | | | | (172) app(all_171_0, nil) = nil
% 256.93/60.91 | | | |
% 256.93/60.91 | | | | REDUCE: (113), (160) imply:
% 256.93/60.91 | | | | (173) app(all_91_1, all_147_0) = all_195_0
% 256.93/60.91 | | | |
% 256.93/60.92 | | | | REDUCE: (119), (145) imply:
% 256.93/60.92 | | | | (174) app(nil, all_183_0) = nil
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | REDUCE: (113), (119), (166) imply:
% 256.93/60.92 | | | | (175) app(nil, all_91_1) = all_215_0
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | REDUCE: (119), (162) imply:
% 256.93/60.92 | | | | (176) app(nil, nil) = all_197_0
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | REDUCE: (119), (125) imply:
% 256.93/60.92 | | | | (177) app(nil, nil) = all_169_0
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | REDUCE: (120), (153) imply:
% 256.93/60.92 | | | | (178) app(nil, all_187_0) = nil
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | REDUCE: (120), (157) imply:
% 256.93/60.92 | | | | (179) app(nil, all_189_0) = nil
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | REDUCE: (119), (149) imply:
% 256.93/60.92 | | | | (180) app(nil, all_185_0) = nil
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | REDUCE: (113), (164) imply:
% 256.93/60.92 | | | | (181) app(nil, all_91_1) = all_201_0
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | REDUCE: (96), (113) imply:
% 256.93/60.92 | | | | (182) app(nil, all_91_1) = all_91_1
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | REDUCE: (119), (168) imply:
% 256.93/60.92 | | | | (183) app(nil, nil) = all_217_0
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | REDUCE: (113), (114) imply:
% 256.93/60.92 | | | | (184) segmentP(all_91_1, all_91_1)
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | GROUND_INST: instantiating (20) with nil, all_197_0, nil, nil,
% 256.93/60.92 | | | | simplifying with (101), (176) gives:
% 256.93/60.92 | | | | (185) all_197_0 = nil
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | GROUND_INST: instantiating (20) with all_197_0, all_217_0, nil, nil,
% 256.93/60.92 | | | | simplifying with (176), (183) gives:
% 256.93/60.92 | | | | (186) all_217_0 = all_197_0
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | GROUND_INST: instantiating (20) with all_169_0, all_217_0, nil, nil,
% 256.93/60.92 | | | | simplifying with (177), (183) gives:
% 256.93/60.92 | | | | (187) all_217_0 = all_169_0
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | GROUND_INST: instantiating (20) with all_201_0, all_215_0, all_91_1,
% 256.93/60.92 | | | | nil, simplifying with (175), (181) gives:
% 256.93/60.92 | | | | (188) all_215_0 = all_201_0
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | GROUND_INST: instantiating (20) with all_91_1, all_215_0, all_91_1, nil,
% 256.93/60.92 | | | | simplifying with (175), (182) gives:
% 256.93/60.92 | | | | (189) all_215_0 = all_91_1
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | GROUND_INST: instantiating (20) with all_91_1, all_195_0, all_147_0,
% 256.93/60.92 | | | | all_91_1, simplifying with (92), (173) gives:
% 256.93/60.92 | | | | (190) all_195_0 = all_91_1
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | COMBINE_EQS: (186), (187) imply:
% 256.93/60.92 | | | | (191) all_197_0 = all_169_0
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | SIMP: (191) implies:
% 256.93/60.92 | | | | (192) all_197_0 = all_169_0
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | COMBINE_EQS: (188), (189) imply:
% 256.93/60.92 | | | | (193) all_201_0 = all_91_1
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | COMBINE_EQS: (185), (192) imply:
% 256.93/60.92 | | | | (194) all_169_0 = nil
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | SIMP: (194) implies:
% 256.93/60.92 | | | | (195) all_169_0 = nil
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | GROUND_INST: instantiating (ax79) with nil, all_91_1, all_91_1,
% 256.93/60.92 | | | | all_135_0, simplifying with (6), (18), (22), (23), (77),
% 256.93/60.92 | | | | (78), (79), (182) gives:
% 256.93/60.92 | | | | (196) all_135_0 = nil
% 256.93/60.92 | | | |
% 256.93/60.92 | | | | GROUND_INST: instantiating (ax82) with nil, all_183_0, nil, all_91_1,
% 256.93/60.92 | | | | all_91_1, simplifying with (6), (18), (22), (23), (143),
% 256.93/60.92 | | | | (144), (174), (182) gives:
% 256.93/60.92 | | | | (197) ? [v0: $i] : (app(all_183_0, all_91_1) = v0 & app(nil, v0) =
% 256.93/60.92 | | | | all_91_1 & $i(v0))
% 256.93/60.92 | | | |
% 256.93/60.93 | | | | GROUND_INST: instantiating (ax82) with nil, all_185_0, nil, all_91_1,
% 256.93/60.93 | | | | all_91_1, simplifying with (6), (18), (22), (23), (147),
% 256.93/60.93 | | | | (148), (180), (182) gives:
% 256.93/60.93 | | | | (198) ? [v0: $i] : (app(all_185_0, all_91_1) = v0 & app(nil, v0) =
% 256.93/60.93 | | | | all_91_1 & $i(v0))
% 256.93/60.93 | | | |
% 256.93/60.93 | | | | GROUND_INST: instantiating (7) with all_185_0, nil, simplifying with
% 256.93/60.93 | | | | (147), (148), (180) gives:
% 256.93/60.93 | | | | (199) all_185_0 = nil
% 256.93/60.93 | | | |
% 256.93/60.93 | | | | GROUND_INST: instantiating (ax80) with all_185_0, nil, nil, all_187_0,
% 256.93/60.93 | | | | simplifying with (6), (18), (147), (148), (151), (152),
% 256.93/60.93 | | | | (178), (180) gives:
% 256.93/60.93 | | | | (200) all_187_0 = all_185_0
% 256.93/60.93 | | | |
% 256.93/60.93 | | | | GROUND_INST: instantiating (ax82) with nil, all_187_0, nil, all_91_1,
% 256.93/60.93 | | | | all_91_1, simplifying with (6), (18), (22), (23), (151),
% 256.93/60.93 | | | | (152), (178), (182) gives:
% 256.93/60.93 | | | | (201) ? [v0: $i] : (app(all_187_0, all_91_1) = v0 & app(nil, v0) =
% 256.93/60.93 | | | | all_91_1 & $i(v0))
% 256.93/60.93 | | | |
% 256.93/60.93 | | | | GROUND_INST: instantiating (ax80) with all_187_0, nil, nil, all_189_0,
% 256.93/60.93 | | | | simplifying with (6), (18), (151), (152), (155), (156),
% 256.93/60.93 | | | | (178), (179) gives:
% 256.93/60.93 | | | | (202) all_189_0 = all_187_0
% 256.93/60.93 | | | |
% 256.93/60.93 | | | | GROUND_INST: instantiating (ax80) with all_183_0, nil, nil, all_189_0,
% 256.93/60.93 | | | | simplifying with (6), (18), (143), (144), (155), (156),
% 256.93/60.93 | | | | (174), (179) gives:
% 256.93/60.93 | | | | (203) all_189_0 = all_183_0
% 256.93/60.93 | | | |
% 256.93/60.93 | | | | GROUND_INST: instantiating (ax82) with nil, all_189_0, nil, all_91_1,
% 256.93/60.93 | | | | all_91_1, simplifying with (6), (18), (22), (23), (155),
% 256.93/60.93 | | | | (156), (179), (182) gives:
% 256.93/60.93 | | | | (204) ? [v0: $i] : (app(all_189_0, all_91_1) = v0 & app(nil, v0) =
% 256.93/60.93 | | | | all_91_1 & $i(v0))
% 256.93/60.93 | | | |
% 256.93/60.93 | | | | GROUND_INST: instantiating (ax82) with all_171_0, nil, nil, all_91_1,
% 256.93/60.93 | | | | all_91_1, simplifying with (6), (18), (22), (23), (127),
% 256.93/60.93 | | | | (128), (172), (182) gives:
% 256.93/60.93 | | | | (205) ? [v0: $i] : (app(all_171_0, v0) = all_91_1 & app(nil,
% 256.93/60.93 | | | | all_91_1) = v0 & $i(v0))
% 256.93/60.93 | | | |
% 256.93/60.94 | | | | GROUND_INST: instantiating (ax82) with all_173_0, nil, nil, all_91_1,
% 256.93/60.94 | | | | all_91_1, simplifying with (6), (18), (22), (23), (131),
% 256.93/60.94 | | | | (132), (171), (182) gives:
% 256.93/60.94 | | | | (206) ? [v0: $i] : (app(all_173_0, v0) = all_91_1 & app(nil,
% 256.93/60.94 | | | | all_91_1) = v0 & $i(v0))
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | GROUND_INST: instantiating (ax82) with all_175_0, nil, nil, all_91_1,
% 256.93/60.94 | | | | all_91_1, simplifying with (6), (18), (22), (23), (135),
% 256.93/60.94 | | | | (136), (170), (182) gives:
% 256.93/60.94 | | | | (207) ? [v0: $i] : (app(all_175_0, v0) = all_91_1 & app(nil,
% 256.93/60.94 | | | | all_91_1) = v0 & $i(v0))
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | GROUND_INST: instantiating (ax82) with all_181_0, nil, nil, all_91_1,
% 256.93/60.94 | | | | all_91_1, simplifying with (6), (18), (22), (23), (139),
% 256.93/60.94 | | | | (140), (169), (182) gives:
% 256.93/60.94 | | | | (208) ? [v0: $i] : (app(all_181_0, v0) = all_91_1 & app(nil,
% 256.93/60.94 | | | | all_91_1) = v0 & $i(v0))
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | COMBINE_EQS: (202), (203) imply:
% 256.93/60.94 | | | | (209) all_187_0 = all_183_0
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | SIMP: (209) implies:
% 256.93/60.94 | | | | (210) all_187_0 = all_183_0
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | COMBINE_EQS: (200), (210) imply:
% 256.93/60.94 | | | | (211) all_185_0 = all_183_0
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | SIMP: (211) implies:
% 256.93/60.94 | | | | (212) all_185_0 = all_183_0
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | COMBINE_EQS: (199), (212) imply:
% 256.93/60.94 | | | | (213) all_183_0 = nil
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | COMBINE_EQS: (210), (213) imply:
% 256.93/60.94 | | | | (214) all_187_0 = nil
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | COMBINE_EQS: (203), (213) imply:
% 256.93/60.94 | | | | (215) all_189_0 = nil
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | DELTA: instantiating (198) with fresh symbol all_239_0 gives:
% 256.93/60.94 | | | | (216) app(all_185_0, all_91_1) = all_239_0 & app(nil, all_239_0) =
% 256.93/60.94 | | | | all_91_1 & $i(all_239_0)
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | ALPHA: (216) implies:
% 256.93/60.94 | | | | (217) $i(all_239_0)
% 256.93/60.94 | | | | (218) app(all_185_0, all_91_1) = all_239_0
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | DELTA: instantiating (206) with fresh symbol all_253_0 gives:
% 256.93/60.94 | | | | (219) app(all_173_0, all_253_0) = all_91_1 & app(nil, all_91_1) =
% 256.93/60.94 | | | | all_253_0 & $i(all_253_0)
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | ALPHA: (219) implies:
% 256.93/60.94 | | | | (220) app(nil, all_91_1) = all_253_0
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | DELTA: instantiating (208) with fresh symbol all_265_0 gives:
% 256.93/60.94 | | | | (221) app(all_181_0, all_265_0) = all_91_1 & app(nil, all_91_1) =
% 256.93/60.94 | | | | all_265_0 & $i(all_265_0)
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | ALPHA: (221) implies:
% 256.93/60.94 | | | | (222) app(nil, all_91_1) = all_265_0
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | DELTA: instantiating (201) with fresh symbol all_273_0 gives:
% 256.93/60.94 | | | | (223) app(all_187_0, all_91_1) = all_273_0 & app(nil, all_273_0) =
% 256.93/60.94 | | | | all_91_1 & $i(all_273_0)
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | ALPHA: (223) implies:
% 256.93/60.94 | | | | (224) app(all_187_0, all_91_1) = all_273_0
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | DELTA: instantiating (205) with fresh symbol all_343_0 gives:
% 256.93/60.94 | | | | (225) app(all_171_0, all_343_0) = all_91_1 & app(nil, all_91_1) =
% 256.93/60.94 | | | | all_343_0 & $i(all_343_0)
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | ALPHA: (225) implies:
% 256.93/60.94 | | | | (226) app(nil, all_91_1) = all_343_0
% 256.93/60.94 | | | |
% 256.93/60.94 | | | | DELTA: instantiating (204) with fresh symbol all_375_0 gives:
% 256.93/60.95 | | | | (227) app(all_189_0, all_91_1) = all_375_0 & app(nil, all_375_0) =
% 256.93/60.95 | | | | all_91_1 & $i(all_375_0)
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | ALPHA: (227) implies:
% 256.93/60.95 | | | | (228) app(all_189_0, all_91_1) = all_375_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | DELTA: instantiating (197) with fresh symbol all_383_0 gives:
% 256.93/60.95 | | | | (229) app(all_183_0, all_91_1) = all_383_0 & app(nil, all_383_0) =
% 256.93/60.95 | | | | all_91_1 & $i(all_383_0)
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | ALPHA: (229) implies:
% 256.93/60.95 | | | | (230) app(all_183_0, all_91_1) = all_383_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | DELTA: instantiating (207) with fresh symbol all_393_0 gives:
% 256.93/60.95 | | | | (231) app(all_175_0, all_393_0) = all_91_1 & app(nil, all_91_1) =
% 256.93/60.95 | | | | all_393_0 & $i(all_393_0)
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | ALPHA: (231) implies:
% 256.93/60.95 | | | | (232) app(nil, all_91_1) = all_393_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | REDUCE: (215), (228) imply:
% 256.93/60.95 | | | | (233) app(nil, all_91_1) = all_375_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | REDUCE: (214), (224) imply:
% 256.93/60.95 | | | | (234) app(nil, all_91_1) = all_273_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | REDUCE: (199), (218) imply:
% 256.93/60.95 | | | | (235) app(nil, all_91_1) = all_239_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | REDUCE: (213), (230) imply:
% 256.93/60.95 | | | | (236) app(nil, all_91_1) = all_383_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_91_1, all_253_0, all_91_1, nil,
% 256.93/60.95 | | | | simplifying with (182), (220) gives:
% 256.93/60.95 | | | | (237) all_253_0 = all_91_1
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_343_0, all_375_0, all_91_1,
% 256.93/60.95 | | | | nil, simplifying with (226), (233) gives:
% 256.93/60.95 | | | | (238) all_375_0 = all_343_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_265_0, all_375_0, all_91_1,
% 256.93/60.95 | | | | nil, simplifying with (222), (233) gives:
% 256.93/60.95 | | | | (239) all_375_0 = all_265_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_253_0, all_375_0, all_91_1,
% 256.93/60.95 | | | | nil, simplifying with (220), (233) gives:
% 256.93/60.95 | | | | (240) all_375_0 = all_253_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_375_0, all_383_0, all_91_1,
% 256.93/60.95 | | | | nil, simplifying with (233), (236) gives:
% 256.93/60.95 | | | | (241) all_383_0 = all_375_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_273_0, all_383_0, all_91_1,
% 256.93/60.95 | | | | nil, simplifying with (234), (236) gives:
% 256.93/60.95 | | | | (242) all_383_0 = all_273_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_343_0, all_393_0, all_91_1,
% 256.93/60.95 | | | | nil, simplifying with (226), (232) gives:
% 256.93/60.95 | | | | (243) all_393_0 = all_343_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_239_0, all_393_0, all_91_1,
% 256.93/60.95 | | | | nil, simplifying with (232), (235) gives:
% 256.93/60.95 | | | | (244) all_393_0 = all_239_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | COMBINE_EQS: (243), (244) imply:
% 256.93/60.95 | | | | (245) all_343_0 = all_239_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | SIMP: (245) implies:
% 256.93/60.95 | | | | (246) all_343_0 = all_239_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | COMBINE_EQS: (241), (242) imply:
% 256.93/60.95 | | | | (247) all_375_0 = all_273_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | SIMP: (247) implies:
% 256.93/60.95 | | | | (248) all_375_0 = all_273_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | COMBINE_EQS: (240), (248) imply:
% 256.93/60.95 | | | | (249) all_273_0 = all_253_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | COMBINE_EQS: (238), (248) imply:
% 256.93/60.95 | | | | (250) all_343_0 = all_273_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | SIMP: (250) implies:
% 256.93/60.95 | | | | (251) all_343_0 = all_273_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | COMBINE_EQS: (239), (248) imply:
% 256.93/60.95 | | | | (252) all_273_0 = all_265_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | COMBINE_EQS: (246), (251) imply:
% 256.93/60.95 | | | | (253) all_273_0 = all_239_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | SIMP: (253) implies:
% 256.93/60.95 | | | | (254) all_273_0 = all_239_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | COMBINE_EQS: (252), (254) imply:
% 256.93/60.95 | | | | (255) all_265_0 = all_239_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | COMBINE_EQS: (249), (252) imply:
% 256.93/60.95 | | | | (256) all_265_0 = all_253_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | COMBINE_EQS: (255), (256) imply:
% 256.93/60.95 | | | | (257) all_253_0 = all_239_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | SIMP: (257) implies:
% 256.93/60.95 | | | | (258) all_253_0 = all_239_0
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | COMBINE_EQS: (237), (258) imply:
% 256.93/60.95 | | | | (259) all_239_0 = all_91_1
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | BETA: splitting (24) gives:
% 256.93/60.95 | | | |
% 256.93/60.95 | | | | Case 1:
% 256.93/60.95 | | | | |
% 256.93/60.95 | | | | | (260) all_91_0 = nil & ~ (all_91_1 = nil)
% 256.93/60.95 | | | | |
% 256.93/60.95 | | | | | ALPHA: (260) implies:
% 256.93/60.95 | | | | | (261) all_91_0 = nil
% 256.93/60.95 | | | | | (262) ~ (all_91_1 = nil)
% 256.93/60.95 | | | | |
% 256.93/60.95 | | | | | BETA: splitting (25) gives:
% 256.93/60.95 | | | | |
% 256.93/60.95 | | | | | Case 1:
% 256.93/60.95 | | | | | |
% 256.93/60.95 | | | | | | (263) all_91_0 = nil & all_91_1 = nil
% 256.93/60.95 | | | | | |
% 256.93/60.95 | | | | | | ALPHA: (263) implies:
% 256.93/60.96 | | | | | | (264) all_91_1 = nil
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | REDUCE: (262), (264) imply:
% 256.93/60.96 | | | | | | (265) $false
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | CLOSE: (265) is inconsistent.
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | Case 2:
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | (266) segmentP(all_91_0, all_91_1) & neq(all_91_1, nil)
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | ALPHA: (266) implies:
% 256.93/60.96 | | | | | | (267) segmentP(all_91_0, all_91_1)
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | REDUCE: (261), (267) imply:
% 256.93/60.96 | | | | | | (268) segmentP(nil, all_91_1)
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | GROUND_INST: instantiating (13) with all_91_1, simplifying with
% 256.93/60.96 | | | | | | (22), (23), (268) gives:
% 256.93/60.96 | | | | | | (269) all_91_1 = nil
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | REDUCE: (262), (269) imply:
% 256.93/60.96 | | | | | | (270) $false
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | CLOSE: (270) is inconsistent.
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | End of split
% 256.93/60.96 | | | | |
% 256.93/60.96 | | | | Case 2:
% 256.93/60.96 | | | | |
% 256.93/60.96 | | | | | (271) neq(all_91_0, nil) & ! [v0: $i] : ( ~ $i(v0) | ~
% 256.93/60.96 | | | | | segmentP(all_91_0, v0) | ~ segmentP(all_91_1, v0) | ~
% 256.93/60.96 | | | | | ssList(v0) | ~ neq(v0, nil))
% 256.93/60.96 | | | | |
% 256.93/60.96 | | | | | ALPHA: (271) implies:
% 256.93/60.96 | | | | | (272) neq(all_91_0, nil)
% 256.93/60.96 | | | | | (273) ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_0, v0) | ~
% 256.93/60.96 | | | | | segmentP(all_91_1, v0) | ~ ssList(v0) | ~ neq(v0, nil))
% 256.93/60.96 | | | | |
% 256.93/60.96 | | | | | BETA: splitting (25) gives:
% 256.93/60.96 | | | | |
% 256.93/60.96 | | | | | Case 1:
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | (274) all_91_0 = nil & all_91_1 = nil
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | ALPHA: (274) implies:
% 256.93/60.96 | | | | | | (275) all_91_1 = nil
% 256.93/60.96 | | | | | | (276) all_91_0 = nil
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | REDUCE: (272), (276) imply:
% 256.93/60.96 | | | | | | (277) neq(nil, nil)
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | GROUND_INST: instantiating (5) with nil, simplifying with (6), (18),
% 256.93/60.96 | | | | | | (277) gives:
% 256.93/60.96 | | | | | | (278) $false
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | CLOSE: (278) is inconsistent.
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | Case 2:
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | (279) segmentP(all_91_0, all_91_1) & neq(all_91_1, nil)
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | ALPHA: (279) implies:
% 256.93/60.96 | | | | | | (280) neq(all_91_1, nil)
% 256.93/60.96 | | | | | | (281) segmentP(all_91_0, all_91_1)
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | GROUND_INST: instantiating (273) with all_91_1, simplifying with
% 256.93/60.96 | | | | | | (22), (23), (184), (280), (281) gives:
% 256.93/60.96 | | | | | | (282) $false
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | | CLOSE: (282) is inconsistent.
% 256.93/60.96 | | | | | |
% 256.93/60.96 | | | | | End of split
% 256.93/60.96 | | | | |
% 256.93/60.96 | | | | End of split
% 256.93/60.96 | | | |
% 256.93/60.96 | | | End of split
% 256.93/60.96 | | |
% 256.93/60.96 | | End of split
% 256.93/60.96 | |
% 256.93/60.96 | End of split
% 256.93/60.96 |
% 256.93/60.96 End of proof
% 256.93/60.96 % SZS output end Proof for theBenchmark
% 256.93/60.96
% 256.93/60.96 60325ms
%------------------------------------------------------------------------------