TSTP Solution File: SWC059+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC059+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 : n032.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 35.55s 5.37s
% Output : Proof 242.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SWC059+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Mon Aug 28 16:48:00 EDT 2023
% 0.11/0.30 % CPUTime :
% 0.16/0.50 ________ _____
% 0.16/0.50 ___ __ \_________(_)________________________________
% 0.16/0.50 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.50 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.50 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.50
% 0.16/0.50 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.50 (2023-06-19)
% 0.16/0.50
% 0.16/0.50 (c) Philipp Rümmer, 2009-2023
% 0.16/0.50 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.50 Amanda Stjerna.
% 0.16/0.50 Free software under BSD-3-Clause.
% 0.16/0.51
% 0.16/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.51
% 0.16/0.51 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.52 Running up to 7 provers in parallel.
% 0.16/0.53 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.53 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.53 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.53 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.53 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.16/0.53 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 5.04/1.31 Prover 1: Preprocessing ...
% 5.04/1.34 Prover 4: Preprocessing ...
% 5.51/1.35 Prover 3: Preprocessing ...
% 5.51/1.35 Prover 5: Preprocessing ...
% 5.51/1.36 Prover 2: Preprocessing ...
% 5.51/1.36 Prover 6: Preprocessing ...
% 5.51/1.36 Prover 0: Preprocessing ...
% 15.78/2.72 Prover 2: Proving ...
% 16.28/2.80 Prover 5: Constructing countermodel ...
% 16.97/2.88 Prover 6: Proving ...
% 16.97/2.91 Prover 3: Constructing countermodel ...
% 17.35/2.94 Prover 1: Constructing countermodel ...
% 24.32/3.87 Prover 4: Constructing countermodel ...
% 24.32/3.90 Prover 0: Proving ...
% 35.55/5.37 Prover 3: proved (4842ms)
% 35.55/5.37
% 35.55/5.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.55/5.37
% 35.55/5.37 Prover 5: stopped
% 35.55/5.37 Prover 6: stopped
% 35.55/5.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 35.55/5.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 35.55/5.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 35.55/5.38 Prover 2: stopped
% 35.55/5.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 36.27/5.44 Prover 0: stopped
% 36.27/5.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 37.45/5.58 Prover 10: Preprocessing ...
% 37.45/5.60 Prover 8: Preprocessing ...
% 37.45/5.61 Prover 13: Preprocessing ...
% 37.45/5.63 Prover 11: Preprocessing ...
% 37.45/5.64 Prover 7: Preprocessing ...
% 38.72/5.83 Prover 10: Constructing countermodel ...
% 39.45/5.84 Prover 13: Constructing countermodel ...
% 39.45/5.88 Prover 7: Constructing countermodel ...
% 40.36/5.96 Prover 8: Warning: ignoring some quantifiers
% 40.42/5.97 Prover 8: Constructing countermodel ...
% 46.53/6.78 Prover 11: Constructing countermodel ...
% 75.34/10.46 Prover 13: stopped
% 75.34/10.47 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 76.12/10.60 Prover 16: Preprocessing ...
% 77.72/10.77 Prover 16: Constructing countermodel ...
% 116.68/15.87 Prover 1: stopped
% 117.20/15.89 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 117.20/15.95 Prover 16: stopped
% 118.06/16.04 Prover 19: Preprocessing ...
% 120.59/16.38 Prover 19: Warning: ignoring some quantifiers
% 121.24/16.42 Prover 19: Constructing countermodel ...
% 142.17/19.47 Prover 19: stopped
% 187.15/27.84 Prover 7: stopped
% 187.15/27.86 Prover 4: stopped
% 225.84/38.76 Prover 11: stopped
% 228.60/39.96 Prover 8: stopped
% 241.57/51.17 Prover 10: Found proof (size 252)
% 241.57/51.17 Prover 10: proved (45795ms)
% 241.57/51.17
% 241.57/51.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 241.57/51.17
% 241.92/51.24 % SZS output start Proof for theBenchmark
% 241.92/51.25 Assumptions after simplification:
% 241.92/51.25 ---------------------------------
% 241.92/51.25
% 241.92/51.25 (ax17)
% 241.92/51.25 $i(nil) & ssList(nil)
% 241.92/51.25
% 241.92/51.25 (ax26)
% 241.92/51.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) |
% 241.92/51.28 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 241.92/51.28
% 241.92/51.28 (ax28)
% 241.92/51.28 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 241.92/51.28 $i(v0) | ~ ssList(v0))
% 241.92/51.28
% 241.92/51.28 (ax42)
% 241.92/51.28 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0))
% 241.92/51.28
% 241.92/51.28 (ax45)
% 241.92/51.28 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 241.92/51.28
% 241.92/51.28 (ax46)
% 241.92/51.29 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 241.92/51.29 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 241.92/51.29
% 241.92/51.29 (ax49)
% 241.92/51.29 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, v0))
% 241.92/51.29
% 241.92/51.29 (ax5)
% 241.92/51.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 241.92/51.29 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 241.92/51.29 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 241.92/51.29 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 241.92/51.29 v2) = v0 & $i(v2) & ssList(v2)))
% 241.92/51.29
% 241.92/51.29 (ax50)
% 241.92/51.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2, v0) = v3)
% 241.92/51.29 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, v1) | ~ ssList(v2) |
% 241.92/51.29 ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1))
% 241.92/51.29
% 241.92/51.29 (ax51)
% 241.92/51.29 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 241.92/51.29
% 241.92/51.29 (ax52)
% 241.92/51.29 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~
% 241.92/51.29 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 241.92/51.29
% 241.92/51.29 (ax58)
% 241.92/51.29 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 241.92/51.29 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 241.92/51.30
% 241.92/51.30 (ax6)
% 241.92/51.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 241.92/51.30 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 241.92/51.30 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 241.92/51.30 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 241.92/51.30 v1) = v0 & $i(v2) & ssList(v2)))
% 241.92/51.30
% 241.92/51.30 (ax7)
% 241.92/51.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 241.92/51.30 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 241.92/51.30 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 241.92/51.30 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 241.92/51.30 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 241.92/51.30 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 241.92/51.30 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 241.92/51.30
% 241.92/51.30 (ax79)
% 241.92/51.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v3,
% 241.92/51.30 v1) = v2) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 241.92/51.30 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 241.92/51.30
% 241.92/51.30 (ax80)
% 241.92/51.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v1,
% 241.92/51.31 v3) = v2) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 241.92/51.31 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 241.92/51.31
% 241.92/51.31 (ax82)
% 241.92/51.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 241.92/51.31 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 241.92/51.31 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 241.92/51.31 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 241.92/51.31
% 241.92/51.31 (ax83)
% 242.26/51.31 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 242.26/51.31 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 242.26/51.31 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 242.26/51.31 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 242.26/51.31 v0) | ~ ssList(nil))
% 242.26/51.31
% 242.26/51.31 (ax84)
% 242.26/51.31 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 242.26/51.31 $i(v0) | ~ ssList(v0))
% 242.26/51.31
% 242.26/51.31 (co1)
% 242.26/51.31 $i(nil) & ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ssList(v1) &
% 242.26/51.31 ssList(v0) & ( ~ (v1 = nil) | v0 = nil) & ( ~ neq(v1, nil) | (segmentP(v1,
% 242.26/51.31 v0) & neq(v0, nil))) & ((v1 = nil & ~ (v0 = nil)) | (neq(v1, nil) &
% 242.26/51.31 ! [v2: $i] : ( ~ $i(v2) | ~ segmentP(v1, v2) | ~ segmentP(v0, v2) | ~
% 242.26/51.31 ssList(v2) | ~ neq(v2, nil)))))
% 242.26/51.31
% 242.26/51.31 (function-axioms)
% 242.26/51.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 242.26/51.31 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 242.26/51.31 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 242.26/51.31 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 242.26/51.31 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 242.26/51.31 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 242.26/51.31
% 242.26/51.31 Further assumptions not needed in the proof:
% 242.26/51.31 --------------------------------------------
% 242.26/51.32 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 242.26/51.32 ax22, ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35,
% 242.26/51.32 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax47, ax48, ax53, ax54,
% 242.26/51.32 ax55, ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68,
% 242.26/51.32 ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax8, ax81, ax85,
% 242.26/51.32 ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 242.26/51.32
% 242.26/51.32 Those formulas are unsatisfiable:
% 242.26/51.32 ---------------------------------
% 242.26/51.32
% 242.26/51.32 Begin of proof
% 242.26/51.32 |
% 242.26/51.32 | ALPHA: (ax5) implies:
% 242.26/51.32 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 242.26/51.32 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 242.26/51.32 | v0 & $i(v2) & ssList(v2)))
% 242.26/51.32 |
% 242.26/51.32 | ALPHA: (ax6) implies:
% 242.26/51.32 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 242.26/51.32 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 242.26/51.32 | v0 & $i(v2) & ssList(v2)))
% 242.26/51.32 |
% 242.26/51.32 | ALPHA: (ax7) implies:
% 242.26/51.32 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0,
% 242.26/51.32 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] :
% 242.26/51.32 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) &
% 242.26/51.32 | $i(v2) & ssList(v4) & ssList(v2)))
% 242.26/51.32 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 242.26/51.32 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2)
% 242.26/51.32 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~
% 242.26/51.32 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 242.26/51.32 |
% 242.26/51.32 | ALPHA: (ax17) implies:
% 242.26/51.32 | (5) ssList(nil)
% 242.26/51.32 |
% 242.26/51.32 | ALPHA: (ax28) implies:
% 242.26/51.32 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 242.26/51.32 | $i(v0) | ~ ssList(v0))
% 242.26/51.32 |
% 242.26/51.32 | ALPHA: (ax45) implies:
% 242.26/51.32 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 242.26/51.32 |
% 242.26/51.32 | ALPHA: (ax46) implies:
% 242.26/51.32 | (8) ~ ssList(nil) | frontsegP(nil, nil)
% 242.26/51.32 |
% 242.26/51.32 | ALPHA: (ax51) implies:
% 242.26/51.32 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 242.26/51.32 |
% 242.26/51.32 | ALPHA: (ax52) implies:
% 242.26/51.32 | (10) ~ ssList(nil) | rearsegP(nil, nil)
% 242.26/51.33 |
% 242.26/51.33 | ALPHA: (ax58) implies:
% 242.26/51.33 | (11) ~ ssList(nil) | segmentP(nil, nil)
% 242.26/51.33 |
% 242.26/51.33 | ALPHA: (ax83) implies:
% 242.26/51.33 | (12) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 242.26/51.33 | (13) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~
% 242.26/51.33 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 242.26/51.33 | (14) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 242.26/51.33 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 242.26/51.33 |
% 242.26/51.33 | ALPHA: (ax84) implies:
% 242.26/51.33 | (15) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 242.26/51.33 | $i(v0) | ~ ssList(v0))
% 242.26/51.33 |
% 242.26/51.33 | ALPHA: (co1) implies:
% 242.26/51.33 | (16) $i(nil)
% 242.26/51.33 | (17) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ssList(v1) & ssList(v0)
% 242.26/51.33 | & ( ~ (v1 = nil) | v0 = nil) & ( ~ neq(v1, nil) | (segmentP(v1, v0)
% 242.26/51.33 | & neq(v0, nil))) & ((v1 = nil & ~ (v0 = nil)) | (neq(v1, nil) &
% 242.26/51.33 | ! [v2: $i] : ( ~ $i(v2) | ~ segmentP(v1, v2) | ~ segmentP(v0,
% 242.26/51.33 | v2) | ~ ssList(v2) | ~ neq(v2, nil)))))
% 242.26/51.33 |
% 242.26/51.33 | ALPHA: (function-axioms) implies:
% 242.26/51.33 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 242.26/51.33 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 242.26/51.33 |
% 242.26/51.33 | DELTA: instantiating (17) with fresh symbols all_91_0, all_91_1 gives:
% 242.26/51.33 | (19) $i(all_91_0) & $i(all_91_1) & ssList(all_91_0) & ssList(all_91_1) & (
% 242.26/51.33 | ~ (all_91_0 = nil) | all_91_1 = nil) & ( ~ neq(all_91_0, nil) |
% 242.26/51.33 | (segmentP(all_91_0, all_91_1) & neq(all_91_1, nil))) & ((all_91_0 =
% 242.26/51.33 | nil & ~ (all_91_1 = nil)) | (neq(all_91_0, nil) & ! [v0: $i] : (
% 242.26/51.33 | ~ $i(v0) | ~ segmentP(all_91_0, v0) | ~ segmentP(all_91_1, v0)
% 242.26/51.33 | | ~ ssList(v0) | ~ neq(v0, nil))))
% 242.26/51.33 |
% 242.26/51.33 | ALPHA: (19) implies:
% 242.26/51.33 | (20) ssList(all_91_1)
% 242.26/51.33 | (21) $i(all_91_1)
% 242.26/51.33 | (22) (all_91_0 = nil & ~ (all_91_1 = nil)) | (neq(all_91_0, nil) & ! [v0:
% 242.26/51.34 | $i] : ( ~ $i(v0) | ~ segmentP(all_91_0, v0) | ~
% 242.26/51.34 | segmentP(all_91_1, v0) | ~ ssList(v0) | ~ neq(v0, nil)))
% 242.26/51.34 | (23) ~ neq(all_91_0, nil) | (segmentP(all_91_0, all_91_1) & neq(all_91_1,
% 242.26/51.34 | nil))
% 242.26/51.34 | (24) ~ (all_91_0 = nil) | all_91_1 = nil
% 242.26/51.34 |
% 242.26/51.34 | BETA: splitting (8) gives:
% 242.26/51.34 |
% 242.26/51.34 | Case 1:
% 242.26/51.34 | |
% 242.26/51.34 | | (25) ~ ssList(nil)
% 242.26/51.34 | |
% 242.26/51.34 | | PRED_UNIFY: (5), (25) imply:
% 242.26/51.34 | | (26) $false
% 242.26/51.34 | |
% 242.26/51.34 | | CLOSE: (26) is inconsistent.
% 242.26/51.34 | |
% 242.26/51.34 | Case 2:
% 242.26/51.34 | |
% 242.26/51.34 | | (27) frontsegP(nil, nil)
% 242.26/51.34 | |
% 242.26/51.34 | | BETA: splitting (11) gives:
% 242.26/51.34 | |
% 242.26/51.34 | | Case 1:
% 242.26/51.34 | | |
% 242.26/51.34 | | | (28) ~ ssList(nil)
% 242.26/51.34 | | |
% 242.26/51.34 | | | PRED_UNIFY: (5), (28) imply:
% 242.26/51.34 | | | (29) $false
% 242.26/51.34 | | |
% 242.26/51.34 | | | CLOSE: (29) is inconsistent.
% 242.26/51.34 | | |
% 242.26/51.34 | | Case 2:
% 242.26/51.34 | | |
% 242.26/51.34 | | | (30) segmentP(nil, nil)
% 242.26/51.34 | | |
% 242.26/51.34 | | | BETA: splitting (10) gives:
% 242.26/51.34 | | |
% 242.26/51.34 | | | Case 1:
% 242.26/51.34 | | | |
% 242.26/51.34 | | | | (31) ~ ssList(nil)
% 242.26/51.34 | | | |
% 242.26/51.34 | | | | PRED_UNIFY: (5), (31) imply:
% 242.26/51.34 | | | | (32) $false
% 242.26/51.34 | | | |
% 242.26/51.34 | | | | CLOSE: (32) is inconsistent.
% 242.26/51.34 | | | |
% 242.26/51.34 | | | Case 2:
% 242.26/51.34 | | | |
% 242.26/51.34 | | | | (33) rearsegP(nil, nil)
% 242.26/51.34 | | | |
% 242.26/51.34 | | | | GROUND_INST: instantiating (ax49) with all_91_1, simplifying with (20),
% 242.26/51.34 | | | | (21) gives:
% 242.26/51.34 | | | | (34) rearsegP(all_91_1, all_91_1)
% 242.26/51.34 | | | |
% 242.26/51.34 | | | | GROUND_INST: instantiating (9) with all_91_1, simplifying with (20),
% 242.26/51.34 | | | | (21) gives:
% 242.26/51.34 | | | | (35) rearsegP(all_91_1, nil)
% 242.26/51.34 | | | |
% 242.26/51.34 | | | | GROUND_INST: instantiating (ax42) with all_91_1, simplifying with (20),
% 242.26/51.34 | | | | (21) gives:
% 242.26/51.34 | | | | (36) frontsegP(all_91_1, all_91_1)
% 242.26/51.34 | | | |
% 242.26/51.34 | | | | GROUND_INST: instantiating (7) with all_91_1, simplifying with (20),
% 242.26/51.34 | | | | (21) gives:
% 242.26/51.34 | | | | (37) frontsegP(all_91_1, nil)
% 242.26/51.34 | | | |
% 242.26/51.34 | | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (5),
% 242.26/51.34 | | | | (16), (27) gives:
% 242.26/51.34 | | | | (38) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 242.26/51.34 | | | |
% 242.26/51.34 | | | | GROUND_INST: instantiating (2) with nil, nil, simplifying with (5),
% 242.26/51.34 | | | | (16), (33) gives:
% 242.26/51.34 | | | | (39) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0))
% 242.26/51.34 | | | |
% 242.26/51.35 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (5),
% 242.26/51.35 | | | | (16), (30) gives:
% 242.26/51.35 | | | | (40) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil &
% 242.26/51.35 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) &
% 242.26/51.35 | | | | ssList(v0))
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | DELTA: instantiating (39) with fresh symbol all_111_0 gives:
% 242.26/51.35 | | | | (41) app(all_111_0, nil) = nil & $i(all_111_0) & ssList(all_111_0)
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | ALPHA: (41) implies:
% 242.26/51.35 | | | | (42) ssList(all_111_0)
% 242.26/51.35 | | | | (43) $i(all_111_0)
% 242.26/51.35 | | | | (44) app(all_111_0, nil) = nil
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | DELTA: instantiating (38) with fresh symbol all_113_0 gives:
% 242.26/51.35 | | | | (45) app(nil, all_113_0) = nil & $i(all_113_0) & ssList(all_113_0)
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | ALPHA: (45) implies:
% 242.26/51.35 | | | | (46) ssList(all_113_0)
% 242.26/51.35 | | | | (47) $i(all_113_0)
% 242.26/51.35 | | | | (48) app(nil, all_113_0) = nil
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | DELTA: instantiating (40) with fresh symbols all_115_0, all_115_1,
% 242.26/51.35 | | | | all_115_2 gives:
% 242.26/51.35 | | | | (49) app(all_115_1, all_115_0) = nil & app(all_115_2, nil) =
% 242.26/51.35 | | | | all_115_1 & $i(all_115_0) & $i(all_115_1) & $i(all_115_2) &
% 242.26/51.35 | | | | ssList(all_115_0) & ssList(all_115_2)
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | ALPHA: (49) implies:
% 242.26/51.35 | | | | (50) ssList(all_115_2)
% 242.26/51.35 | | | | (51) ssList(all_115_0)
% 242.26/51.35 | | | | (52) $i(all_115_2)
% 242.26/51.35 | | | | (53) $i(all_115_1)
% 242.26/51.35 | | | | (54) $i(all_115_0)
% 242.26/51.35 | | | | (55) app(all_115_2, nil) = all_115_1
% 242.26/51.35 | | | | (56) app(all_115_1, all_115_0) = nil
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | GROUND_INST: instantiating (ax49) with all_115_2, simplifying with (50),
% 242.26/51.35 | | | | (52) gives:
% 242.26/51.35 | | | | (57) rearsegP(all_115_2, all_115_2)
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | GROUND_INST: instantiating (ax42) with all_115_2, simplifying with (50),
% 242.26/51.35 | | | | (52) gives:
% 242.26/51.35 | | | | (58) frontsegP(all_115_2, all_115_2)
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | GROUND_INST: instantiating (7) with all_115_2, simplifying with (50),
% 242.26/51.35 | | | | (52) gives:
% 242.26/51.35 | | | | (59) frontsegP(all_115_2, nil)
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | GROUND_INST: instantiating (ax49) with all_115_0, simplifying with (51),
% 242.26/51.35 | | | | (54) gives:
% 242.26/51.35 | | | | (60) rearsegP(all_115_0, all_115_0)
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | GROUND_INST: instantiating (9) with all_115_0, simplifying with (51),
% 242.26/51.35 | | | | (54) gives:
% 242.26/51.35 | | | | (61) rearsegP(all_115_0, nil)
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | GROUND_INST: instantiating (ax42) with all_115_0, simplifying with (51),
% 242.26/51.35 | | | | (54) gives:
% 242.26/51.35 | | | | (62) frontsegP(all_115_0, all_115_0)
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | GROUND_INST: instantiating (7) with all_115_0, simplifying with (51),
% 242.26/51.35 | | | | (54) gives:
% 242.26/51.35 | | | | (63) frontsegP(all_115_0, nil)
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | GROUND_INST: instantiating (1) with all_91_1, nil, simplifying with (5),
% 242.26/51.35 | | | | (16), (20), (21), (37) gives:
% 242.26/51.35 | | | | (64) ? [v0: $i] : (app(nil, v0) = all_91_1 & $i(v0) & ssList(v0))
% 242.26/51.35 | | | |
% 242.26/51.35 | | | | GROUND_INST: instantiating (1) with all_91_1, all_91_1, simplifying with
% 242.26/51.35 | | | | (20), (21), (36) gives:
% 242.26/51.35 | | | | (65) ? [v0: $i] : (app(all_91_1, v0) = all_91_1 & $i(v0) &
% 242.26/51.35 | | | | ssList(v0))
% 242.26/51.35 | | | |
% 242.26/51.36 | | | | GROUND_INST: instantiating (2) with all_91_1, nil, simplifying with (5),
% 242.26/51.36 | | | | (16), (20), (21), (35) gives:
% 242.26/51.36 | | | | (66) ? [v0: $i] : (app(v0, nil) = all_91_1 & $i(v0) & ssList(v0))
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | GROUND_INST: instantiating (2) with all_91_1, all_91_1, simplifying with
% 242.26/51.36 | | | | (20), (21), (34) gives:
% 242.26/51.36 | | | | (67) ? [v0: $i] : (app(v0, all_91_1) = all_91_1 & $i(v0) &
% 242.26/51.36 | | | | ssList(v0))
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | GROUND_INST: instantiating (ax82) with nil, all_113_0, nil, all_113_0,
% 242.26/51.36 | | | | nil, simplifying with (5), (16), (46), (47), (48) gives:
% 242.26/51.36 | | | | (68) ? [v0: $i] : (app(all_113_0, all_113_0) = v0 & app(nil, v0) =
% 242.26/51.36 | | | | nil & $i(v0))
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | GROUND_INST: instantiating (6) with all_113_0, nil, simplifying with
% 242.26/51.36 | | | | (46), (47), (48) gives:
% 242.26/51.36 | | | | (69) all_113_0 = nil
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | GROUND_INST: instantiating (15) with all_111_0, nil, simplifying with
% 242.26/51.36 | | | | (42), (43), (44) gives:
% 242.26/51.36 | | | | (70) all_111_0 = nil
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | GROUND_INST: instantiating (ax50) with nil, nil, all_115_2, all_115_1,
% 242.26/51.36 | | | | simplifying with (5), (16), (33), (50), (52), (55) gives:
% 242.26/51.36 | | | | (71) rearsegP(all_115_1, nil)
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | GROUND_INST: instantiating (ax26) with all_115_2, nil, all_115_1,
% 242.26/51.36 | | | | simplifying with (5), (16), (50), (52), (55) gives:
% 242.26/51.36 | | | | (72) ssList(all_115_1)
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | GROUND_INST: instantiating (15) with all_115_2, all_115_1, simplifying
% 242.26/51.36 | | | | with (50), (52), (55) gives:
% 242.26/51.36 | | | | (73) all_115_1 = all_115_2
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | GROUND_INST: instantiating (ax82) with all_115_2, nil, all_115_1,
% 242.26/51.36 | | | | all_115_0, nil, simplifying with (5), (16), (50), (51),
% 242.26/51.36 | | | | (52), (54), (55), (56) gives:
% 242.26/51.36 | | | | (74) ? [v0: $i] : (app(all_115_2, v0) = nil & app(nil, all_115_0) =
% 242.26/51.36 | | | | v0 & $i(v0))
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | DELTA: instantiating (67) with fresh symbol all_135_0 gives:
% 242.26/51.36 | | | | (75) app(all_135_0, all_91_1) = all_91_1 & $i(all_135_0) &
% 242.26/51.36 | | | | ssList(all_135_0)
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | ALPHA: (75) implies:
% 242.26/51.36 | | | | (76) ssList(all_135_0)
% 242.26/51.36 | | | | (77) $i(all_135_0)
% 242.26/51.36 | | | | (78) app(all_135_0, all_91_1) = all_91_1
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | DELTA: instantiating (66) with fresh symbol all_137_0 gives:
% 242.26/51.36 | | | | (79) app(all_137_0, nil) = all_91_1 & $i(all_137_0) &
% 242.26/51.36 | | | | ssList(all_137_0)
% 242.26/51.36 | | | |
% 242.26/51.36 | | | | ALPHA: (79) implies:
% 242.26/51.36 | | | | (80) ssList(all_137_0)
% 242.26/51.36 | | | | (81) $i(all_137_0)
% 242.26/51.37 | | | | (82) app(all_137_0, nil) = all_91_1
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | DELTA: instantiating (74) with fresh symbol all_139_0 gives:
% 242.26/51.37 | | | | (83) app(all_115_2, all_139_0) = nil & app(nil, all_115_0) =
% 242.26/51.37 | | | | all_139_0 & $i(all_139_0)
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | ALPHA: (83) implies:
% 242.26/51.37 | | | | (84) app(nil, all_115_0) = all_139_0
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | DELTA: instantiating (68) with fresh symbol all_145_0 gives:
% 242.26/51.37 | | | | (85) app(all_113_0, all_113_0) = all_145_0 & app(nil, all_145_0) =
% 242.26/51.37 | | | | nil & $i(all_145_0)
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | ALPHA: (85) implies:
% 242.26/51.37 | | | | (86) $i(all_145_0)
% 242.26/51.37 | | | | (87) app(all_113_0, all_113_0) = all_145_0
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | DELTA: instantiating (65) with fresh symbol all_147_0 gives:
% 242.26/51.37 | | | | (88) app(all_91_1, all_147_0) = all_91_1 & $i(all_147_0) &
% 242.26/51.37 | | | | ssList(all_147_0)
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | ALPHA: (88) implies:
% 242.26/51.37 | | | | (89) ssList(all_147_0)
% 242.26/51.37 | | | | (90) $i(all_147_0)
% 242.26/51.37 | | | | (91) app(all_91_1, all_147_0) = all_91_1
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | DELTA: instantiating (64) with fresh symbol all_149_0 gives:
% 242.26/51.37 | | | | (92) app(nil, all_149_0) = all_91_1 & $i(all_149_0) &
% 242.26/51.37 | | | | ssList(all_149_0)
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | ALPHA: (92) implies:
% 242.26/51.37 | | | | (93) ssList(all_149_0)
% 242.26/51.37 | | | | (94) $i(all_149_0)
% 242.26/51.37 | | | | (95) app(nil, all_149_0) = all_91_1
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | REDUCE: (56), (73) imply:
% 242.26/51.37 | | | | (96) app(all_115_2, all_115_0) = nil
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | REDUCE: (69), (87) imply:
% 242.26/51.37 | | | | (97) app(nil, nil) = all_145_0
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | REDUCE: (71), (73) imply:
% 242.26/51.37 | | | | (98) rearsegP(all_115_2, nil)
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | GROUND_INST: instantiating (12) with all_145_0, simplifying with (5),
% 242.26/51.37 | | | | (97) gives:
% 242.26/51.37 | | | | (99) all_145_0 = nil
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | REDUCE: (97), (99) imply:
% 242.26/51.37 | | | | (100) app(nil, nil) = nil
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | GROUND_INST: instantiating (1) with all_115_2, nil, simplifying with
% 242.26/51.37 | | | | (5), (16), (50), (52), (59) gives:
% 242.26/51.37 | | | | (101) ? [v0: $i] : (app(nil, v0) = all_115_2 & $i(v0) & ssList(v0))
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | GROUND_INST: instantiating (1) with all_115_2, all_115_2, simplifying
% 242.26/51.37 | | | | with (50), (52), (58) gives:
% 242.26/51.37 | | | | (102) ? [v0: $i] : (app(all_115_2, v0) = all_115_2 & $i(v0) &
% 242.26/51.37 | | | | ssList(v0))
% 242.26/51.37 | | | |
% 242.26/51.37 | | | | GROUND_INST: instantiating (1) with all_115_0, nil, simplifying with
% 242.26/51.37 | | | | (5), (16), (51), (54), (63) gives:
% 242.26/51.38 | | | | (103) ? [v0: $i] : (app(nil, v0) = all_115_0 & $i(v0) & ssList(v0))
% 242.26/51.38 | | | |
% 242.26/51.38 | | | | GROUND_INST: instantiating (1) with all_115_0, all_115_0, simplifying
% 242.26/51.38 | | | | with (51), (54), (62) gives:
% 242.26/51.38 | | | | (104) ? [v0: $i] : (app(all_115_0, v0) = all_115_0 & $i(v0) &
% 242.26/51.38 | | | | ssList(v0))
% 242.26/51.38 | | | |
% 242.26/51.38 | | | | GROUND_INST: instantiating (2) with all_115_2, nil, simplifying with
% 242.26/51.38 | | | | (5), (16), (50), (52), (98) gives:
% 242.26/51.38 | | | | (105) ? [v0: $i] : (app(v0, nil) = all_115_2 & $i(v0) & ssList(v0))
% 242.26/51.38 | | | |
% 242.26/51.38 | | | | GROUND_INST: instantiating (2) with all_115_2, all_115_2, simplifying
% 242.26/51.38 | | | | with (50), (52), (57) gives:
% 242.26/51.38 | | | | (106) ? [v0: $i] : (app(v0, all_115_2) = all_115_2 & $i(v0) &
% 242.26/51.38 | | | | ssList(v0))
% 242.26/51.38 | | | |
% 242.26/51.38 | | | | GROUND_INST: instantiating (2) with all_115_0, nil, simplifying with
% 242.26/51.38 | | | | (5), (16), (51), (54), (61) gives:
% 242.26/51.38 | | | | (107) ? [v0: $i] : (app(v0, nil) = all_115_0 & $i(v0) & ssList(v0))
% 242.26/51.38 | | | |
% 242.26/51.38 | | | | GROUND_INST: instantiating (2) with all_115_0, all_115_0, simplifying
% 242.26/51.38 | | | | with (51), (54), (60) gives:
% 242.26/51.38 | | | | (108) ? [v0: $i] : (app(v0, all_115_0) = all_115_0 & $i(v0) &
% 242.26/51.38 | | | | ssList(v0))
% 242.26/51.38 | | | |
% 242.26/51.38 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_115_0,
% 242.26/51.38 | | | | all_139_0, simplifying with (5), (16), (51), (54), (84),
% 242.26/51.38 | | | | (100) gives:
% 242.26/51.38 | | | | (109) ? [v0: $i] : (app(nil, v0) = all_139_0 & app(nil, all_115_0) =
% 242.26/51.38 | | | | v0 & $i(v0) & $i(all_139_0))
% 242.26/51.38 | | | |
% 242.26/51.38 | | | | GROUND_INST: instantiating (6) with all_115_0, all_139_0, simplifying
% 242.26/51.38 | | | | with (51), (54), (84) gives:
% 242.26/51.38 | | | | (110) all_139_0 = all_115_0
% 242.26/51.38 | | | |
% 242.26/51.38 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_149_0,
% 242.26/51.38 | | | | all_91_1, simplifying with (5), (16), (93), (94), (95),
% 242.26/51.38 | | | | (100) gives:
% 242.26/51.38 | | | | (111) ? [v0: $i] : (app(nil, v0) = all_91_1 & app(nil, all_149_0) =
% 242.26/51.38 | | | | v0 & $i(v0) & $i(all_91_1))
% 242.26/51.38 | | | |
% 242.26/51.38 | | | | GROUND_INST: instantiating (6) with all_149_0, all_91_1, simplifying
% 242.26/51.38 | | | | with (93), (94), (95) gives:
% 242.26/51.38 | | | | (112) all_149_0 = all_91_1
% 242.26/51.38 | | | |
% 242.26/51.39 | | | | GROUND_INST: instantiating (4) with all_91_1, all_149_0, nil, all_91_1,
% 242.26/51.39 | | | | all_147_0, simplifying with (5), (16), (20), (21), (89),
% 242.26/51.39 | | | | (90), (91), (93), (94), (95) gives:
% 242.26/51.39 | | | | (113) segmentP(all_91_1, all_149_0)
% 242.26/51.39 | | | |
% 242.26/51.39 | | | | GROUND_INST: instantiating (ax82) with nil, all_149_0, all_91_1,
% 242.26/51.39 | | | | all_147_0, all_91_1, simplifying with (5), (16), (89),
% 242.26/51.39 | | | | (90), (91), (93), (94), (95) gives:
% 242.26/51.39 | | | | (114) ? [v0: $i] : (app(all_149_0, all_147_0) = v0 & app(nil, v0) =
% 242.26/51.39 | | | | all_91_1 & $i(v0) & $i(all_91_1))
% 242.26/51.39 | | | |
% 242.26/51.39 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil,
% 242.26/51.39 | | | | all_149_0, all_91_1, simplifying with (50), (51), (52),
% 242.26/51.39 | | | | (54), (93), (94), (95), (96) gives:
% 242.26/51.39 | | | | (115) ? [v0: $i] : (app(all_115_0, all_149_0) = v0 & app(all_115_2,
% 242.26/51.39 | | | | v0) = all_91_1 & $i(v0) & $i(all_91_1))
% 242.26/51.39 | | | |
% 242.26/51.39 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil,
% 242.26/51.39 | | | | all_115_0, all_139_0, simplifying with (50), (51), (52),
% 242.26/51.39 | | | | (54), (84), (96) gives:
% 242.26/51.39 | | | | (116) ? [v0: $i] : (app(all_115_0, all_115_0) = v0 & app(all_115_2,
% 242.26/51.39 | | | | v0) = all_139_0 & $i(v0) & $i(all_139_0))
% 242.26/51.39 | | | |
% 242.67/51.39 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil, nil,
% 242.67/51.39 | | | | nil, simplifying with (5), (16), (50), (51), (52), (54),
% 242.67/51.39 | | | | (96), (100) gives:
% 242.67/51.39 | | | | (117) ? [v0: $i] : (app(all_115_0, nil) = v0 & app(all_115_2, v0) =
% 242.67/51.39 | | | | nil & $i(v0))
% 242.67/51.39 | | | |
% 242.67/51.39 | | | | GROUND_INST: instantiating (14) with all_115_2, all_115_0, simplifying
% 242.67/51.39 | | | | with (50), (51), (52), (54), (96) gives:
% 242.67/51.39 | | | | (118) all_115_0 = nil
% 242.67/51.39 | | | |
% 242.67/51.39 | | | | GROUND_INST: instantiating (13) with all_115_2, all_115_0, simplifying
% 242.67/51.39 | | | | with (50), (51), (52), (54), (96) gives:
% 242.67/51.39 | | | | (119) all_115_2 = nil
% 242.67/51.39 | | | |
% 242.67/51.39 | | | | GROUND_INST: instantiating (15) with all_137_0, all_91_1, simplifying
% 242.67/51.39 | | | | with (80), (81), (82) gives:
% 242.67/51.39 | | | | (120) all_137_0 = all_91_1
% 242.67/51.39 | | | |
% 242.67/51.39 | | | | COMBINE_EQS: (110), (118) imply:
% 242.67/51.39 | | | | (121) all_139_0 = nil
% 242.67/51.39 | | | |
% 242.67/51.39 | | | | DELTA: instantiating (117) with fresh symbol all_169_0 gives:
% 242.67/51.39 | | | | (122) app(all_115_0, nil) = all_169_0 & app(all_115_2, all_169_0) =
% 242.67/51.39 | | | | nil & $i(all_169_0)
% 242.67/51.39 | | | |
% 242.67/51.39 | | | | ALPHA: (122) implies:
% 242.67/51.39 | | | | (123) $i(all_169_0)
% 242.67/51.39 | | | | (124) app(all_115_0, nil) = all_169_0
% 242.67/51.39 | | | |
% 242.67/51.39 | | | | DELTA: instantiating (108) with fresh symbol all_171_0 gives:
% 242.67/51.39 | | | | (125) app(all_171_0, all_115_0) = all_115_0 & $i(all_171_0) &
% 242.67/51.39 | | | | ssList(all_171_0)
% 242.67/51.39 | | | |
% 242.67/51.39 | | | | ALPHA: (125) implies:
% 242.67/51.39 | | | | (126) ssList(all_171_0)
% 242.67/51.39 | | | | (127) $i(all_171_0)
% 242.67/51.39 | | | | (128) app(all_171_0, all_115_0) = all_115_0
% 242.67/51.39 | | | |
% 242.67/51.39 | | | | DELTA: instantiating (106) with fresh symbol all_173_0 gives:
% 242.67/51.39 | | | | (129) app(all_173_0, all_115_2) = all_115_2 & $i(all_173_0) &
% 242.67/51.39 | | | | ssList(all_173_0)
% 242.67/51.39 | | | |
% 242.67/51.39 | | | | ALPHA: (129) implies:
% 242.67/51.39 | | | | (130) ssList(all_173_0)
% 242.67/51.39 | | | | (131) $i(all_173_0)
% 242.67/51.39 | | | | (132) app(all_173_0, all_115_2) = all_115_2
% 242.67/51.39 | | | |
% 242.67/51.39 | | | | DELTA: instantiating (105) with fresh symbol all_175_0 gives:
% 242.67/51.40 | | | | (133) app(all_175_0, nil) = all_115_2 & $i(all_175_0) &
% 242.67/51.40 | | | | ssList(all_175_0)
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | ALPHA: (133) implies:
% 242.67/51.40 | | | | (134) ssList(all_175_0)
% 242.67/51.40 | | | | (135) $i(all_175_0)
% 242.67/51.40 | | | | (136) app(all_175_0, nil) = all_115_2
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | DELTA: instantiating (107) with fresh symbol all_181_0 gives:
% 242.67/51.40 | | | | (137) app(all_181_0, nil) = all_115_0 & $i(all_181_0) &
% 242.67/51.40 | | | | ssList(all_181_0)
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | ALPHA: (137) implies:
% 242.67/51.40 | | | | (138) ssList(all_181_0)
% 242.67/51.40 | | | | (139) $i(all_181_0)
% 242.67/51.40 | | | | (140) app(all_181_0, nil) = all_115_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | DELTA: instantiating (104) with fresh symbol all_183_0 gives:
% 242.67/51.40 | | | | (141) app(all_115_0, all_183_0) = all_115_0 & $i(all_183_0) &
% 242.67/51.40 | | | | ssList(all_183_0)
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | ALPHA: (141) implies:
% 242.67/51.40 | | | | (142) ssList(all_183_0)
% 242.67/51.40 | | | | (143) $i(all_183_0)
% 242.67/51.40 | | | | (144) app(all_115_0, all_183_0) = all_115_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | DELTA: instantiating (103) with fresh symbol all_185_0 gives:
% 242.67/51.40 | | | | (145) app(nil, all_185_0) = all_115_0 & $i(all_185_0) &
% 242.67/51.40 | | | | ssList(all_185_0)
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | ALPHA: (145) implies:
% 242.67/51.40 | | | | (146) ssList(all_185_0)
% 242.67/51.40 | | | | (147) $i(all_185_0)
% 242.67/51.40 | | | | (148) app(nil, all_185_0) = all_115_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | DELTA: instantiating (102) with fresh symbol all_187_0 gives:
% 242.67/51.40 | | | | (149) app(all_115_2, all_187_0) = all_115_2 & $i(all_187_0) &
% 242.67/51.40 | | | | ssList(all_187_0)
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | ALPHA: (149) implies:
% 242.67/51.40 | | | | (150) ssList(all_187_0)
% 242.67/51.40 | | | | (151) $i(all_187_0)
% 242.67/51.40 | | | | (152) app(all_115_2, all_187_0) = all_115_2
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | DELTA: instantiating (101) with fresh symbol all_189_0 gives:
% 242.67/51.40 | | | | (153) app(nil, all_189_0) = all_115_2 & $i(all_189_0) &
% 242.67/51.40 | | | | ssList(all_189_0)
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | ALPHA: (153) implies:
% 242.67/51.40 | | | | (154) ssList(all_189_0)
% 242.67/51.40 | | | | (155) $i(all_189_0)
% 242.67/51.40 | | | | (156) app(nil, all_189_0) = all_115_2
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | DELTA: instantiating (114) with fresh symbol all_195_0 gives:
% 242.67/51.40 | | | | (157) app(all_149_0, all_147_0) = all_195_0 & app(nil, all_195_0) =
% 242.67/51.40 | | | | all_91_1 & $i(all_195_0) & $i(all_91_1)
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | ALPHA: (157) implies:
% 242.67/51.40 | | | | (158) $i(all_195_0)
% 242.67/51.40 | | | | (159) app(all_149_0, all_147_0) = all_195_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | DELTA: instantiating (116) with fresh symbol all_197_0 gives:
% 242.67/51.40 | | | | (160) app(all_115_0, all_115_0) = all_197_0 & app(all_115_2,
% 242.67/51.40 | | | | all_197_0) = all_139_0 & $i(all_197_0) & $i(all_139_0)
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | ALPHA: (160) implies:
% 242.67/51.40 | | | | (161) app(all_115_0, all_115_0) = all_197_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | DELTA: instantiating (111) with fresh symbol all_201_0 gives:
% 242.67/51.40 | | | | (162) app(nil, all_201_0) = all_91_1 & app(nil, all_149_0) =
% 242.67/51.40 | | | | all_201_0 & $i(all_201_0) & $i(all_91_1)
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | ALPHA: (162) implies:
% 242.67/51.40 | | | | (163) app(nil, all_149_0) = all_201_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | DELTA: instantiating (115) with fresh symbol all_215_0 gives:
% 242.67/51.40 | | | | (164) app(all_115_0, all_149_0) = all_215_0 & app(all_115_2,
% 242.67/51.40 | | | | all_215_0) = all_91_1 & $i(all_215_0) & $i(all_91_1)
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | ALPHA: (164) implies:
% 242.67/51.40 | | | | (165) app(all_115_0, all_149_0) = all_215_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | DELTA: instantiating (109) with fresh symbol all_217_0 gives:
% 242.67/51.40 | | | | (166) app(nil, all_217_0) = all_139_0 & app(nil, all_115_0) =
% 242.67/51.40 | | | | all_217_0 & $i(all_217_0) & $i(all_139_0)
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | ALPHA: (166) implies:
% 242.67/51.40 | | | | (167) app(nil, all_115_0) = all_217_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | REDUCE: (118), (140) imply:
% 242.67/51.40 | | | | (168) app(all_181_0, nil) = nil
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | REDUCE: (119), (136) imply:
% 242.67/51.40 | | | | (169) app(all_175_0, nil) = nil
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | REDUCE: (119), (132) imply:
% 242.67/51.40 | | | | (170) app(all_173_0, nil) = nil
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | REDUCE: (118), (128) imply:
% 242.67/51.40 | | | | (171) app(all_171_0, nil) = nil
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | REDUCE: (112), (159) imply:
% 242.67/51.40 | | | | (172) app(all_91_1, all_147_0) = all_195_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | REDUCE: (118), (144) imply:
% 242.67/51.40 | | | | (173) app(nil, all_183_0) = nil
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | REDUCE: (112), (118), (165) imply:
% 242.67/51.40 | | | | (174) app(nil, all_91_1) = all_215_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | REDUCE: (118), (161) imply:
% 242.67/51.40 | | | | (175) app(nil, nil) = all_197_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | REDUCE: (118), (124) imply:
% 242.67/51.40 | | | | (176) app(nil, nil) = all_169_0
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | REDUCE: (119), (152) imply:
% 242.67/51.40 | | | | (177) app(nil, all_187_0) = nil
% 242.67/51.40 | | | |
% 242.67/51.40 | | | | REDUCE: (119), (156) imply:
% 242.67/51.40 | | | | (178) app(nil, all_189_0) = nil
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | REDUCE: (118), (148) imply:
% 242.67/51.41 | | | | (179) app(nil, all_185_0) = nil
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | REDUCE: (112), (163) imply:
% 242.67/51.41 | | | | (180) app(nil, all_91_1) = all_201_0
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | REDUCE: (95), (112) imply:
% 242.67/51.41 | | | | (181) app(nil, all_91_1) = all_91_1
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | REDUCE: (118), (167) imply:
% 242.67/51.41 | | | | (182) app(nil, nil) = all_217_0
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | REDUCE: (112), (113) imply:
% 242.67/51.41 | | | | (183) segmentP(all_91_1, all_91_1)
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (18) with nil, all_197_0, nil, nil,
% 242.67/51.41 | | | | simplifying with (100), (175) gives:
% 242.67/51.41 | | | | (184) all_197_0 = nil
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (18) with all_197_0, all_217_0, nil, nil,
% 242.67/51.41 | | | | simplifying with (175), (182) gives:
% 242.67/51.41 | | | | (185) all_217_0 = all_197_0
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (18) with all_169_0, all_217_0, nil, nil,
% 242.67/51.41 | | | | simplifying with (176), (182) gives:
% 242.67/51.41 | | | | (186) all_217_0 = all_169_0
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (18) with all_201_0, all_215_0, all_91_1,
% 242.67/51.41 | | | | nil, simplifying with (174), (180) gives:
% 242.67/51.41 | | | | (187) all_215_0 = all_201_0
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (18) with all_91_1, all_215_0, all_91_1, nil,
% 242.67/51.41 | | | | simplifying with (174), (181) gives:
% 242.67/51.41 | | | | (188) all_215_0 = all_91_1
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (18) with all_91_1, all_195_0, all_147_0,
% 242.67/51.41 | | | | all_91_1, simplifying with (91), (172) gives:
% 242.67/51.41 | | | | (189) all_195_0 = all_91_1
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | COMBINE_EQS: (185), (186) imply:
% 242.67/51.41 | | | | (190) all_197_0 = all_169_0
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | SIMP: (190) implies:
% 242.67/51.41 | | | | (191) all_197_0 = all_169_0
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | COMBINE_EQS: (187), (188) imply:
% 242.67/51.41 | | | | (192) all_201_0 = all_91_1
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | COMBINE_EQS: (184), (191) imply:
% 242.67/51.41 | | | | (193) all_169_0 = nil
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | SIMP: (193) implies:
% 242.67/51.41 | | | | (194) all_169_0 = nil
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (ax79) with nil, all_91_1, all_91_1,
% 242.67/51.41 | | | | all_135_0, simplifying with (5), (16), (20), (21), (76),
% 242.67/51.41 | | | | (77), (78), (181) gives:
% 242.67/51.41 | | | | (195) all_135_0 = nil
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (ax82) with nil, all_183_0, nil, all_91_1,
% 242.67/51.41 | | | | all_91_1, simplifying with (5), (16), (20), (21), (142),
% 242.67/51.41 | | | | (143), (173), (181) gives:
% 242.67/51.41 | | | | (196) ? [v0: $i] : (app(all_183_0, all_91_1) = v0 & app(nil, v0) =
% 242.67/51.41 | | | | all_91_1 & $i(v0))
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (ax82) with nil, all_185_0, nil, all_91_1,
% 242.67/51.41 | | | | all_91_1, simplifying with (5), (16), (20), (21), (146),
% 242.67/51.41 | | | | (147), (179), (181) gives:
% 242.67/51.41 | | | | (197) ? [v0: $i] : (app(all_185_0, all_91_1) = v0 & app(nil, v0) =
% 242.67/51.41 | | | | all_91_1 & $i(v0))
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (6) with all_185_0, nil, simplifying with
% 242.67/51.41 | | | | (146), (147), (179) gives:
% 242.67/51.41 | | | | (198) all_185_0 = nil
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (ax80) with all_185_0, nil, nil, all_187_0,
% 242.67/51.41 | | | | simplifying with (5), (16), (146), (147), (150), (151),
% 242.67/51.41 | | | | (177), (179) gives:
% 242.67/51.41 | | | | (199) all_187_0 = all_185_0
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (ax82) with nil, all_187_0, nil, all_91_1,
% 242.67/51.41 | | | | all_91_1, simplifying with (5), (16), (20), (21), (150),
% 242.67/51.41 | | | | (151), (177), (181) gives:
% 242.67/51.41 | | | | (200) ? [v0: $i] : (app(all_187_0, all_91_1) = v0 & app(nil, v0) =
% 242.67/51.41 | | | | all_91_1 & $i(v0))
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (ax80) with all_187_0, nil, nil, all_189_0,
% 242.67/51.41 | | | | simplifying with (5), (16), (150), (151), (154), (155),
% 242.67/51.41 | | | | (177), (178) gives:
% 242.67/51.41 | | | | (201) all_189_0 = all_187_0
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (ax80) with all_183_0, nil, nil, all_189_0,
% 242.67/51.41 | | | | simplifying with (5), (16), (142), (143), (154), (155),
% 242.67/51.41 | | | | (173), (178) gives:
% 242.67/51.41 | | | | (202) all_189_0 = all_183_0
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (ax82) with nil, all_189_0, nil, all_91_1,
% 242.67/51.41 | | | | all_91_1, simplifying with (5), (16), (20), (21), (154),
% 242.67/51.41 | | | | (155), (178), (181) gives:
% 242.67/51.41 | | | | (203) ? [v0: $i] : (app(all_189_0, all_91_1) = v0 & app(nil, v0) =
% 242.67/51.41 | | | | all_91_1 & $i(v0))
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (ax82) with all_171_0, nil, nil, all_91_1,
% 242.67/51.41 | | | | all_91_1, simplifying with (5), (16), (20), (21), (126),
% 242.67/51.41 | | | | (127), (171), (181) gives:
% 242.67/51.41 | | | | (204) ? [v0: $i] : (app(all_171_0, v0) = all_91_1 & app(nil,
% 242.67/51.41 | | | | all_91_1) = v0 & $i(v0))
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (ax82) with all_173_0, nil, nil, all_91_1,
% 242.67/51.41 | | | | all_91_1, simplifying with (5), (16), (20), (21), (130),
% 242.67/51.41 | | | | (131), (170), (181) gives:
% 242.67/51.41 | | | | (205) ? [v0: $i] : (app(all_173_0, v0) = all_91_1 & app(nil,
% 242.67/51.41 | | | | all_91_1) = v0 & $i(v0))
% 242.67/51.41 | | | |
% 242.67/51.41 | | | | GROUND_INST: instantiating (ax82) with all_175_0, nil, nil, all_91_1,
% 242.67/51.41 | | | | all_91_1, simplifying with (5), (16), (20), (21), (134),
% 242.67/51.41 | | | | (135), (169), (181) gives:
% 242.67/51.42 | | | | (206) ? [v0: $i] : (app(all_175_0, v0) = all_91_1 & app(nil,
% 242.67/51.42 | | | | all_91_1) = v0 & $i(v0))
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | GROUND_INST: instantiating (ax82) with all_181_0, nil, nil, all_91_1,
% 242.67/51.42 | | | | all_91_1, simplifying with (5), (16), (20), (21), (138),
% 242.67/51.42 | | | | (139), (168), (181) gives:
% 242.67/51.42 | | | | (207) ? [v0: $i] : (app(all_181_0, v0) = all_91_1 & app(nil,
% 242.67/51.42 | | | | all_91_1) = v0 & $i(v0))
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (201), (202) imply:
% 242.67/51.42 | | | | (208) all_187_0 = all_183_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | SIMP: (208) implies:
% 242.67/51.42 | | | | (209) all_187_0 = all_183_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (199), (209) imply:
% 242.67/51.42 | | | | (210) all_185_0 = all_183_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | SIMP: (210) implies:
% 242.67/51.42 | | | | (211) all_185_0 = all_183_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (198), (211) imply:
% 242.67/51.42 | | | | (212) all_183_0 = nil
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (209), (212) imply:
% 242.67/51.42 | | | | (213) all_187_0 = nil
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (202), (212) imply:
% 242.67/51.42 | | | | (214) all_189_0 = nil
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | DELTA: instantiating (197) with fresh symbol all_239_0 gives:
% 242.67/51.42 | | | | (215) app(all_185_0, all_91_1) = all_239_0 & app(nil, all_239_0) =
% 242.67/51.42 | | | | all_91_1 & $i(all_239_0)
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | ALPHA: (215) implies:
% 242.67/51.42 | | | | (216) $i(all_239_0)
% 242.67/51.42 | | | | (217) app(all_185_0, all_91_1) = all_239_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | DELTA: instantiating (205) with fresh symbol all_253_0 gives:
% 242.67/51.42 | | | | (218) app(all_173_0, all_253_0) = all_91_1 & app(nil, all_91_1) =
% 242.67/51.42 | | | | all_253_0 & $i(all_253_0)
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | ALPHA: (218) implies:
% 242.67/51.42 | | | | (219) app(nil, all_91_1) = all_253_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | DELTA: instantiating (207) with fresh symbol all_265_0 gives:
% 242.67/51.42 | | | | (220) app(all_181_0, all_265_0) = all_91_1 & app(nil, all_91_1) =
% 242.67/51.42 | | | | all_265_0 & $i(all_265_0)
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | ALPHA: (220) implies:
% 242.67/51.42 | | | | (221) app(nil, all_91_1) = all_265_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | DELTA: instantiating (200) with fresh symbol all_273_0 gives:
% 242.67/51.42 | | | | (222) app(all_187_0, all_91_1) = all_273_0 & app(nil, all_273_0) =
% 242.67/51.42 | | | | all_91_1 & $i(all_273_0)
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | ALPHA: (222) implies:
% 242.67/51.42 | | | | (223) app(all_187_0, all_91_1) = all_273_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | DELTA: instantiating (204) with fresh symbol all_343_0 gives:
% 242.67/51.42 | | | | (224) app(all_171_0, all_343_0) = all_91_1 & app(nil, all_91_1) =
% 242.67/51.42 | | | | all_343_0 & $i(all_343_0)
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | ALPHA: (224) implies:
% 242.67/51.42 | | | | (225) app(nil, all_91_1) = all_343_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | DELTA: instantiating (203) with fresh symbol all_375_0 gives:
% 242.67/51.42 | | | | (226) app(all_189_0, all_91_1) = all_375_0 & app(nil, all_375_0) =
% 242.67/51.42 | | | | all_91_1 & $i(all_375_0)
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | ALPHA: (226) implies:
% 242.67/51.42 | | | | (227) app(all_189_0, all_91_1) = all_375_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | DELTA: instantiating (196) with fresh symbol all_383_0 gives:
% 242.67/51.42 | | | | (228) app(all_183_0, all_91_1) = all_383_0 & app(nil, all_383_0) =
% 242.67/51.42 | | | | all_91_1 & $i(all_383_0)
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | ALPHA: (228) implies:
% 242.67/51.42 | | | | (229) app(all_183_0, all_91_1) = all_383_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | DELTA: instantiating (206) with fresh symbol all_393_0 gives:
% 242.67/51.42 | | | | (230) app(all_175_0, all_393_0) = all_91_1 & app(nil, all_91_1) =
% 242.67/51.42 | | | | all_393_0 & $i(all_393_0)
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | ALPHA: (230) implies:
% 242.67/51.42 | | | | (231) app(nil, all_91_1) = all_393_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | REDUCE: (214), (227) imply:
% 242.67/51.42 | | | | (232) app(nil, all_91_1) = all_375_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | REDUCE: (213), (223) imply:
% 242.67/51.42 | | | | (233) app(nil, all_91_1) = all_273_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | REDUCE: (198), (217) imply:
% 242.67/51.42 | | | | (234) app(nil, all_91_1) = all_239_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | REDUCE: (212), (229) imply:
% 242.67/51.42 | | | | (235) app(nil, all_91_1) = all_383_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | GROUND_INST: instantiating (18) with all_91_1, all_253_0, all_91_1, nil,
% 242.67/51.42 | | | | simplifying with (181), (219) gives:
% 242.67/51.42 | | | | (236) all_253_0 = all_91_1
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | GROUND_INST: instantiating (18) with all_343_0, all_375_0, all_91_1,
% 242.67/51.42 | | | | nil, simplifying with (225), (232) gives:
% 242.67/51.42 | | | | (237) all_375_0 = all_343_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | GROUND_INST: instantiating (18) with all_265_0, all_375_0, all_91_1,
% 242.67/51.42 | | | | nil, simplifying with (221), (232) gives:
% 242.67/51.42 | | | | (238) all_375_0 = all_265_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | GROUND_INST: instantiating (18) with all_253_0, all_375_0, all_91_1,
% 242.67/51.42 | | | | nil, simplifying with (219), (232) gives:
% 242.67/51.42 | | | | (239) all_375_0 = all_253_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | GROUND_INST: instantiating (18) with all_375_0, all_383_0, all_91_1,
% 242.67/51.42 | | | | nil, simplifying with (232), (235) gives:
% 242.67/51.42 | | | | (240) all_383_0 = all_375_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | GROUND_INST: instantiating (18) with all_273_0, all_383_0, all_91_1,
% 242.67/51.42 | | | | nil, simplifying with (233), (235) gives:
% 242.67/51.42 | | | | (241) all_383_0 = all_273_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | GROUND_INST: instantiating (18) with all_343_0, all_393_0, all_91_1,
% 242.67/51.42 | | | | nil, simplifying with (225), (231) gives:
% 242.67/51.42 | | | | (242) all_393_0 = all_343_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | GROUND_INST: instantiating (18) with all_239_0, all_393_0, all_91_1,
% 242.67/51.42 | | | | nil, simplifying with (231), (234) gives:
% 242.67/51.42 | | | | (243) all_393_0 = all_239_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (242), (243) imply:
% 242.67/51.42 | | | | (244) all_343_0 = all_239_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | SIMP: (244) implies:
% 242.67/51.42 | | | | (245) all_343_0 = all_239_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (240), (241) imply:
% 242.67/51.42 | | | | (246) all_375_0 = all_273_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | SIMP: (246) implies:
% 242.67/51.42 | | | | (247) all_375_0 = all_273_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (239), (247) imply:
% 242.67/51.42 | | | | (248) all_273_0 = all_253_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (237), (247) imply:
% 242.67/51.42 | | | | (249) all_343_0 = all_273_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | SIMP: (249) implies:
% 242.67/51.42 | | | | (250) all_343_0 = all_273_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (238), (247) imply:
% 242.67/51.42 | | | | (251) all_273_0 = all_265_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (245), (250) imply:
% 242.67/51.42 | | | | (252) all_273_0 = all_239_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | SIMP: (252) implies:
% 242.67/51.42 | | | | (253) all_273_0 = all_239_0
% 242.67/51.42 | | | |
% 242.67/51.42 | | | | COMBINE_EQS: (251), (253) imply:
% 242.67/51.43 | | | | (254) all_265_0 = all_239_0
% 242.67/51.43 | | | |
% 242.67/51.43 | | | | COMBINE_EQS: (248), (251) imply:
% 242.67/51.43 | | | | (255) all_265_0 = all_253_0
% 242.67/51.43 | | | |
% 242.67/51.43 | | | | COMBINE_EQS: (254), (255) imply:
% 242.67/51.43 | | | | (256) all_253_0 = all_239_0
% 242.67/51.43 | | | |
% 242.67/51.43 | | | | SIMP: (256) implies:
% 242.67/51.43 | | | | (257) all_253_0 = all_239_0
% 242.67/51.43 | | | |
% 242.67/51.43 | | | | COMBINE_EQS: (236), (257) imply:
% 242.67/51.43 | | | | (258) all_239_0 = all_91_1
% 242.67/51.43 | | | |
% 242.67/51.43 | | | | BETA: splitting (23) gives:
% 242.67/51.43 | | | |
% 242.67/51.43 | | | | Case 1:
% 242.67/51.43 | | | | |
% 242.67/51.43 | | | | | (259) ~ neq(all_91_0, nil)
% 242.67/51.43 | | | | |
% 242.67/51.43 | | | | | BETA: splitting (22) gives:
% 242.67/51.43 | | | | |
% 242.67/51.43 | | | | | Case 1:
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | (260) all_91_0 = nil & ~ (all_91_1 = nil)
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | ALPHA: (260) implies:
% 242.67/51.43 | | | | | | (261) all_91_0 = nil
% 242.67/51.43 | | | | | | (262) ~ (all_91_1 = nil)
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | REF_CLOSE: (24), (261), (262) are inconsistent by sub-proof #1.
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | Case 2:
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | (263) neq(all_91_0, nil) & ! [v0: $i] : ( ~ $i(v0) | ~
% 242.67/51.43 | | | | | | segmentP(all_91_0, v0) | ~ segmentP(all_91_1, v0) | ~
% 242.67/51.43 | | | | | | ssList(v0) | ~ neq(v0, nil))
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | ALPHA: (263) implies:
% 242.67/51.43 | | | | | | (264) neq(all_91_0, nil)
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | PRED_UNIFY: (259), (264) imply:
% 242.67/51.43 | | | | | | (265) $false
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | CLOSE: (265) is inconsistent.
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | End of split
% 242.67/51.43 | | | | |
% 242.67/51.43 | | | | Case 2:
% 242.67/51.43 | | | | |
% 242.67/51.43 | | | | | (266) segmentP(all_91_0, all_91_1) & neq(all_91_1, nil)
% 242.67/51.43 | | | | |
% 242.67/51.43 | | | | | ALPHA: (266) implies:
% 242.67/51.43 | | | | | (267) neq(all_91_1, nil)
% 242.67/51.43 | | | | | (268) segmentP(all_91_0, all_91_1)
% 242.67/51.43 | | | | |
% 242.67/51.43 | | | | | BETA: splitting (22) gives:
% 242.67/51.43 | | | | |
% 242.67/51.43 | | | | | Case 1:
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | (269) all_91_0 = nil & ~ (all_91_1 = nil)
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | ALPHA: (269) implies:
% 242.67/51.43 | | | | | | (270) all_91_0 = nil
% 242.67/51.43 | | | | | | (271) ~ (all_91_1 = nil)
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | REF_CLOSE: (24), (270), (271) are inconsistent by sub-proof #1.
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | Case 2:
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | (272) neq(all_91_0, nil) & ! [v0: $i] : ( ~ $i(v0) | ~
% 242.67/51.43 | | | | | | segmentP(all_91_0, v0) | ~ segmentP(all_91_1, v0) | ~
% 242.67/51.43 | | | | | | ssList(v0) | ~ neq(v0, nil))
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | ALPHA: (272) implies:
% 242.67/51.43 | | | | | | (273) ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_0, v0) | ~
% 242.67/51.43 | | | | | | segmentP(all_91_1, v0) | ~ ssList(v0) | ~ neq(v0, nil))
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | GROUND_INST: instantiating (273) with all_91_1, simplifying with
% 242.67/51.43 | | | | | | (20), (21), (183), (267), (268) gives:
% 242.67/51.43 | | | | | | (274) $false
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | | CLOSE: (274) is inconsistent.
% 242.67/51.43 | | | | | |
% 242.67/51.43 | | | | | End of split
% 242.67/51.43 | | | | |
% 242.67/51.43 | | | | End of split
% 242.67/51.43 | | | |
% 242.67/51.43 | | | End of split
% 242.67/51.43 | | |
% 242.67/51.43 | | End of split
% 242.67/51.43 | |
% 242.67/51.43 | End of split
% 242.67/51.43 |
% 242.67/51.43 End of proof
% 242.67/51.43
% 242.67/51.43 Sub-proof #1 shows that the following formulas are inconsistent:
% 242.67/51.43 ----------------------------------------------------------------
% 242.67/51.43 (1) ~ (all_91_0 = nil) | all_91_1 = nil
% 242.67/51.43 (2) all_91_0 = nil
% 242.67/51.43 (3) ~ (all_91_1 = nil)
% 242.67/51.43
% 242.67/51.43 Begin of proof
% 242.67/51.43 |
% 242.67/51.43 | BETA: splitting (1) gives:
% 242.67/51.43 |
% 242.67/51.43 | Case 1:
% 242.67/51.43 | |
% 242.67/51.43 | | (4) ~ (all_91_0 = nil)
% 242.67/51.43 | |
% 242.67/51.43 | | REDUCE: (2), (4) imply:
% 242.67/51.43 | | (5) $false
% 242.67/51.43 | |
% 242.67/51.43 | | CLOSE: (5) is inconsistent.
% 242.67/51.43 | |
% 242.67/51.43 | Case 2:
% 242.67/51.43 | |
% 242.67/51.43 | | (6) all_91_1 = nil
% 242.67/51.43 | |
% 242.67/51.43 | | REDUCE: (3), (6) imply:
% 242.67/51.43 | | (7) $false
% 242.67/51.43 | |
% 242.67/51.43 | | CLOSE: (7) is inconsistent.
% 242.67/51.43 | |
% 242.67/51.43 | End of split
% 242.67/51.43 |
% 242.67/51.43 End of proof
% 242.67/51.43 % SZS output end Proof for theBenchmark
% 242.67/51.43
% 242.67/51.43 50928ms
%------------------------------------------------------------------------------