Princess---230619.THM-Prf.s

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz
%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC012+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 : n002.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 20:49:10 EDT 2023

% Result   : Theorem 47.86s 7.04s
% Output   : Proof 104.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWC012+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.33  % Computer : n002.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 300
% 0.14/0.33  % DateTime : Mon Aug 28 16:34:04 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.60  ________       _____
% 0.20/0.60  ___  __ \_________(_)________________________________
% 0.20/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60  
% 0.20/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60  (2023-06-19)
% 0.20/0.60  
% 0.20/0.60  (c) Philipp Rümmer, 2009-2023
% 0.20/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60                Amanda Stjerna.
% 0.20/0.60  Free software under BSD-3-Clause.
% 0.20/0.60  
% 0.20/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60  
% 0.20/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61  Running up to 7 provers in parallel.
% 0.20/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.60/1.48  Prover 1: Preprocessing ...
% 5.60/1.49  Prover 4: Preprocessing ...
% 5.83/1.51  Prover 0: Preprocessing ...
% 5.83/1.51  Prover 2: Preprocessing ...
% 5.83/1.51  Prover 5: Preprocessing ...
% 5.83/1.51  Prover 6: Preprocessing ...
% 5.83/1.51  Prover 3: Preprocessing ...
% 15.48/2.81  Prover 2: Proving ...
% 16.04/2.88  Prover 5: Constructing countermodel ...
% 16.04/2.89  Prover 6: Proving ...
% 16.04/2.89  Prover 1: Constructing countermodel ...
% 16.28/2.92  Prover 3: Constructing countermodel ...
% 21.86/3.63  Prover 4: Constructing countermodel ...
% 23.26/3.85  Prover 0: Proving ...
% 47.86/7.04  Prover 5: proved (6418ms)
% 47.86/7.04  
% 47.86/7.04  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.86/7.04  
% 47.86/7.05  Prover 6: stopped
% 47.86/7.05  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 47.86/7.05  Prover 2: stopped
% 47.86/7.06  Prover 0: stopped
% 47.86/7.07  Prover 3: stopped
% 48.26/7.09  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 48.26/7.09  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 48.26/7.09  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 48.26/7.09  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 50.20/7.35  Prover 8: Preprocessing ...
% 50.20/7.36  Prover 7: Preprocessing ...
% 50.20/7.36  Prover 11: Preprocessing ...
% 50.20/7.37  Prover 10: Preprocessing ...
% 50.20/7.37  Prover 13: Preprocessing ...
% 51.74/7.59  Prover 7: Constructing countermodel ...
% 51.74/7.61  Prover 10: Constructing countermodel ...
% 52.26/7.65  Prover 13: Constructing countermodel ...
% 52.95/7.77  Prover 8: Warning: ignoring some quantifiers
% 53.65/7.79  Prover 8: Constructing countermodel ...
% 57.39/8.32  Prover 11: Constructing countermodel ...
% 83.94/11.70  Prover 13: stopped
% 83.94/11.72  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 84.49/11.83  Prover 16: Preprocessing ...
% 85.59/11.97  Prover 16: Constructing countermodel ...
% 103.42/14.26  Prover 10: Found proof (size 285)
% 103.42/14.26  Prover 10: proved (7196ms)
% 103.42/14.26  Prover 7: stopped
% 103.42/14.26  Prover 16: stopped
% 103.42/14.26  Prover 1: stopped
% 103.42/14.26  Prover 8: stopped
% 103.42/14.26  Prover 11: stopped
% 103.42/14.26  Prover 4: stopped
% 103.42/14.26  
% 103.42/14.26  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 103.42/14.26  
% 103.71/14.32  % SZS output start Proof for theBenchmark
% 103.71/14.33  Assumptions after simplification:
% 103.71/14.33  ---------------------------------
% 103.71/14.33  
% 103.71/14.33    (ax16)
% 103.82/14.35     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (cons(v1, v0) = v2) |  ~ $i(v1)
% 103.82/14.36      |  ~ $i(v0) |  ~ ssList(v0) |  ~ ssItem(v1) | ssList(v2))
% 103.82/14.36  
% 103.82/14.36    (ax17)
% 103.82/14.36    $i(nil) & ssList(nil)
% 103.82/14.36  
% 103.82/14.36    (ax23)
% 103.82/14.36     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (cons(v1, v0) = v2) |  ~ $i(v1)
% 103.82/14.36      |  ~ $i(v0) |  ~ ssList(v0) |  ~ ssItem(v1) | hd(v2) = v1)
% 103.82/14.36  
% 103.82/14.36    (ax25)
% 103.82/14.36     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (cons(v1, v0) = v2) |  ~ $i(v1)
% 103.82/14.36      |  ~ $i(v0) |  ~ ssList(v0) |  ~ ssItem(v1) | tl(v2) = v0)
% 103.82/14.36  
% 103.82/14.36    (ax26)
% 103.82/14.36     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (app(v0, v1) = v2) |  ~ $i(v1) |
% 103.82/14.36       ~ $i(v0) |  ~ ssList(v1) |  ~ ssList(v0) | ssList(v2))
% 103.82/14.36  
% 103.82/14.36    (ax27)
% 103.82/14.36     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~
% 103.82/14.36      (cons(v3, v2) = v4) |  ~ (app(v1, v0) = v2) |  ~ $i(v3) |  ~ $i(v1) |  ~
% 103.82/14.36      $i(v0) |  ~ ssList(v1) |  ~ ssList(v0) |  ~ ssItem(v3) |  ? [v5: $i] :
% 103.82/14.36      (cons(v3, v1) = v5 & app(v5, v0) = v4 & $i(v5) & $i(v4)))
% 103.82/14.36  
% 103.82/14.36    (ax28)
% 103.82/14.36    $i(nil) &  ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (app(nil, v0) = v1) |  ~
% 103.82/14.36      $i(v0) |  ~ ssList(v0))
% 103.82/14.36  
% 103.82/14.36    (ax31)
% 103.82/14.36     ! [v0: $i] : ( ~ $i(v0) |  ~ ssItem(v0) | leq(v0, v0))
% 103.82/14.36  
% 103.82/14.36    (ax4)
% 103.82/14.37    $i(nil) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (cons(v1, nil) = v0) |  ~ $i(v1) | 
% 103.82/14.37      ~ $i(v0) |  ~ ssList(v0) |  ~ ssItem(v1) | singletonP(v0)) &  ! [v0: $i] : (
% 103.82/14.37      ~ $i(v0) |  ~ singletonP(v0) |  ~ ssList(v0) |  ? [v1: $i] : (cons(v1, nil)
% 103.82/14.37        = v0 & $i(v1) & ssItem(v1)))
% 103.82/14.37  
% 103.82/14.37    (ax42)
% 103.82/14.37     ! [v0: $i] : ( ~ $i(v0) |  ~ ssList(v0) | frontsegP(v0, v0))
% 103.82/14.37  
% 103.82/14.37    (ax44)
% 103.82/14.37     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 103.82/14.37      $i] : (v1 = v0 |  ~ (cons(v1, v4) = v5) |  ~ (cons(v0, v2) = v3) |  ~ $i(v4)
% 103.82/14.37      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ frontsegP(v3, v5) |  ~ ssList(v4) |
% 103.82/14.37       ~ ssList(v2) |  ~ ssItem(v1) |  ~ ssItem(v0)) &  ! [v0: $i] :  ! [v1: $i] :
% 103.82/14.37     ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : ( ~ (cons(v1, v4) =
% 103.82/14.37        v5) |  ~ (cons(v0, v2) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 103.82/14.37      $i(v0) |  ~ frontsegP(v3, v5) |  ~ ssList(v4) |  ~ ssList(v2) |  ~
% 103.82/14.37      ssItem(v1) |  ~ ssItem(v0) | frontsegP(v2, v4)) &  ! [v0: $i] :  ! [v1: $i]
% 103.82/14.37    :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~ (cons(v0, v3) = v4) |  ~
% 103.82/14.37      (cons(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v1) |  ~ $i(v0) |  ~ frontsegP(v1,
% 103.82/14.37        v3) |  ~ ssList(v3) |  ~ ssList(v1) |  ~ ssItem(v0) | frontsegP(v2, v4))
% 103.82/14.37  
% 103.82/14.37    (ax45)
% 103.82/14.37    $i(nil) &  ! [v0: $i] : ( ~ $i(v0) |  ~ ssList(v0) | frontsegP(v0, nil))
% 103.82/14.37  
% 103.82/14.37    (ax46)
% 103.82/14.37    $i(nil) &  ! [v0: $i] : (v0 = nil |  ~ $i(v0) |  ~ frontsegP(nil, v0) |  ~
% 103.82/14.37      ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 103.82/14.37  
% 103.82/14.37    (ax49)
% 103.82/14.38     ! [v0: $i] : ( ~ $i(v0) |  ~ ssList(v0) | rearsegP(v0, v0))
% 103.82/14.38  
% 103.82/14.38    (ax5)
% 103.82/14.38     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (app(v1, v2) = v0) |  ~ $i(v2) |
% 103.82/14.38       ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~ ssList(v0) |
% 103.82/14.38      frontsegP(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 103.82/14.38      frontsegP(v0, v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] : (app(v1,
% 103.82/14.38          v2) = v0 & $i(v2) & ssList(v2)))
% 103.82/14.38  
% 103.82/14.38    (ax51)
% 103.82/14.38    $i(nil) &  ! [v0: $i] : ( ~ $i(v0) |  ~ ssList(v0) | rearsegP(v0, nil))
% 103.82/14.38  
% 103.82/14.38    (ax52)
% 103.82/14.38    $i(nil) &  ! [v0: $i] : (v0 = nil |  ~ $i(v0) |  ~ rearsegP(nil, v0) |  ~
% 103.82/14.38      ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 103.82/14.38  
% 103.82/14.38    (ax58)
% 103.82/14.38    $i(nil) &  ! [v0: $i] : (v0 = nil |  ~ $i(v0) |  ~ segmentP(nil, v0) |  ~
% 103.82/14.38      ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 103.82/14.38  
% 103.82/14.38    (ax6)
% 103.82/14.38     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (app(v2, v1) = v0) |  ~ $i(v2) |
% 103.82/14.38       ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~ ssList(v0) |
% 103.82/14.38      rearsegP(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 103.82/14.38      rearsegP(v0, v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] : (app(v2,
% 103.82/14.38          v1) = v0 & $i(v2) & ssList(v2)))
% 103.82/14.38  
% 103.82/14.38    (ax65)
% 103.82/14.38    $i(nil) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (cons(v0, nil) = v1) |  ~ $i(v0) | 
% 103.82/14.38      ~ ssItem(v0) | totalorderedP(v1))
% 103.82/14.38  
% 103.82/14.38    (ax67)
% 103.82/14.38    $i(nil) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (hd(v1) = v2) |  ~
% 103.82/14.38      $i(v1) |  ~ $i(v0) |  ~ ssList(v1) |  ~ ssItem(v0) |  ? [v3: $i] : ((v1 =
% 103.82/14.38          nil | (cons(v0, v1) = v3 & $i(v3) &  ~ totalorderedP(v3)) |
% 103.82/14.38          (totalorderedP(v1) & leq(v0, v2))) & (( ~ (v1 = nil) & ( ~
% 103.82/14.38              totalorderedP(v1) |  ~ leq(v0, v2))) | (cons(v0, v1) = v3 & $i(v3) &
% 103.82/14.38            totalorderedP(v3)))))
% 103.82/14.38  
% 103.82/14.38    (ax7)
% 103.82/14.39     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~
% 103.82/14.39      (app(v3, v4) = v0) |  ~ (app(v2, v1) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~
% 103.82/14.39      $i(v1) |  ~ $i(v0) |  ~ ssList(v4) |  ~ ssList(v2) |  ~ ssList(v1) |  ~
% 103.82/14.39      ssList(v0) | segmentP(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~
% 103.82/14.39      $i(v0) |  ~ segmentP(v0, v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] :
% 103.82/14.39       ? [v3: $i] :  ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 103.82/14.39        $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 103.82/14.39  
% 103.82/14.39    (ax77)
% 103.82/14.39    $i(nil) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (tl(v0) = v1) |  ~ $i(v0) |  ~
% 103.82/14.39      ssList(v0) |  ? [v2: $i] : (hd(v0) = v2 & $i(v2) &  ! [v3: $i] : (v3 = v0 |
% 103.82/14.39          v3 = nil | v0 = nil |  ~ (tl(v3) = v1) |  ~ $i(v3) |  ~ ssList(v3) |  ?
% 103.82/14.39          [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 & $i(v4)))))
% 103.82/14.39  
% 103.82/14.39    (ax79)
% 103.82/14.39     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v0 |  ~ (app(v3,
% 103.82/14.39          v1) = v2) |  ~ (app(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v1) |  ~ $i(v0) | 
% 103.82/14.39      ~ ssList(v3) |  ~ ssList(v1) |  ~ ssList(v0))
% 103.82/14.39  
% 103.82/14.39    (ax80)
% 103.82/14.39     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v0 |  ~ (app(v1,
% 103.82/14.39          v3) = v2) |  ~ (app(v1, v0) = v2) |  ~ $i(v3) |  ~ $i(v1) |  ~ $i(v0) | 
% 103.82/14.39      ~ ssList(v3) |  ~ ssList(v1) |  ~ ssList(v0))
% 103.82/14.39  
% 103.82/14.39    (ax81)
% 103.82/14.39    $i(nil) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 103.82/14.39      (cons(v1, nil) = v2) |  ~ (app(v2, v0) = v3) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 103.82/14.39      ssList(v0) |  ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3)))
% 103.82/14.39  
% 103.82/14.39    (ax82)
% 103.82/14.39     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~
% 103.82/14.39      (app(v2, v3) = v4) |  ~ (app(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v1) |  ~
% 103.82/14.39      $i(v0) |  ~ ssList(v3) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v5: $i] :
% 103.82/14.39      (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 103.82/14.39  
% 103.82/14.39    (ax83)
% 103.82/14.39    $i(nil) &  ! [v0: $i] :  ! [v1: $i] : (v1 = nil |  ~ (app(v0, v1) = nil) |  ~
% 103.82/14.39      $i(v1) |  ~ $i(v0) |  ~ ssList(v1) |  ~ ssList(v0)) &  ! [v0: $i] :  ! [v1:
% 103.82/14.39      $i] : (v0 = nil |  ~ (app(v0, v1) = nil) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 103.82/14.39      ssList(v1) |  ~ ssList(v0)) &  ! [v0: $i] : (v0 = nil |  ~ (app(nil, nil) =
% 103.82/14.39        v0) |  ~ ssList(nil))
% 103.82/14.39  
% 103.82/14.39    (ax84)
% 103.82/14.39    $i(nil) &  ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (app(v0, nil) = v1) |  ~
% 103.82/14.39      $i(v0) |  ~ ssList(v0))
% 103.82/14.39  
% 103.82/14.39    (co1)
% 103.82/14.39    $i(nil) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : (cons(v2,
% 103.82/14.39        nil) = v3 & app(v0, v3) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 103.82/14.39      ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) &  ! [v4: $i] :  ! [v5:
% 103.82/14.39        $i] :  ! [v6: $i] :  ! [v7: $i] :  ! [v8: $i] : ( ~ (cons(v4, nil) = v5) |
% 103.82/14.39         ~ (app(v7, v8) = v1) |  ~ (app(v6, v5) = v7) |  ~ $i(v8) |  ~ $i(v6) |  ~
% 103.82/14.39        $i(v4) |  ~ ssList(v8) |  ~ ssList(v6) |  ~ ssItem(v4) |  ? [v9: $i] : ( ~
% 103.82/14.40          (v9 = v0) & app(v6, v8) = v9 & $i(v9))))
% 103.82/14.40  
% 103.82/14.40    (function-axioms)
% 103.82/14.40     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 103.82/14.40      (cons(v3, v2) = v1) |  ~ (cons(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 103.82/14.40    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (app(v3, v2) = v1) |  ~ (app(v3, v2)
% 103.82/14.40        = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (tl(v2) =
% 103.82/14.40        v1) |  ~ (tl(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 =
% 103.82/14.40      v0 |  ~ (hd(v2) = v1) |  ~ (hd(v2) = v0))
% 103.82/14.40  
% 103.82/14.40  Further assumptions not needed in the proof:
% 103.82/14.40  --------------------------------------------
% 103.82/14.40  ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax18, ax19, ax2, ax20, ax21, ax22,
% 103.82/14.40  ax24, ax29, ax3, ax30, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax40,
% 103.82/14.40  ax41, ax43, ax47, ax48, ax50, ax53, ax54, ax55, ax56, ax57, ax59, ax60, ax61,
% 103.82/14.40  ax62, ax63, ax64, ax66, ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76,
% 103.82/14.40  ax78, ax8, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 103.82/14.40  
% 103.82/14.40  Those formulas are unsatisfiable:
% 103.82/14.40  ---------------------------------
% 103.82/14.40  
% 103.82/14.40  Begin of proof
% 103.82/14.40  | 
% 103.82/14.40  | ALPHA: (ax4) implies:
% 103.82/14.40  |   (1)   ! [v0: $i] : ( ~ $i(v0) |  ~ singletonP(v0) |  ~ ssList(v0) |  ? [v1:
% 103.82/14.40  |            $i] : (cons(v1, nil) = v0 & $i(v1) & ssItem(v1)))
% 103.82/14.40  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (cons(v1, nil) = v0) |  ~ $i(v1) |  ~
% 103.82/14.40  |          $i(v0) |  ~ ssList(v0) |  ~ ssItem(v1) | singletonP(v0))
% 103.82/14.40  | 
% 103.82/14.40  | ALPHA: (ax5) implies:
% 103.82/14.40  |   (3)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ frontsegP(v0,
% 103.82/14.40  |            v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] : (app(v1, v2) =
% 103.82/14.40  |            v0 & $i(v2) & ssList(v2)))
% 103.82/14.40  | 
% 103.82/14.40  | ALPHA: (ax6) implies:
% 103.82/14.40  |   (4)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ rearsegP(v0,
% 103.82/14.40  |            v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] : (app(v2, v1) =
% 103.82/14.40  |            v0 & $i(v2) & ssList(v2)))
% 103.82/14.40  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (app(v2, v1) = v0) |  ~
% 103.82/14.40  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~
% 103.82/14.40  |          ssList(v0) | rearsegP(v0, v1))
% 103.82/14.40  | 
% 103.82/14.40  | ALPHA: (ax7) implies:
% 103.82/14.40  |   (6)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ segmentP(v0,
% 103.82/14.40  |            v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] :  ? [v3: $i] : 
% 103.82/14.40  |          ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) &
% 103.82/14.40  |            $i(v2) & ssList(v4) & ssList(v2)))
% 103.82/14.40  | 
% 103.82/14.40  | ALPHA: (ax17) implies:
% 103.82/14.40  |   (7)  ssList(nil)
% 103.82/14.40  | 
% 103.82/14.40  | ALPHA: (ax28) implies:
% 103.82/14.41  |   (8)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (app(nil, v0) = v1) |  ~
% 103.82/14.41  |          $i(v0) |  ~ ssList(v0))
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax44) implies:
% 103.82/14.41  |   (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (
% 103.82/14.41  |          ~ (cons(v0, v3) = v4) |  ~ (cons(v0, v1) = v2) |  ~ $i(v3) |  ~
% 103.82/14.41  |          $i(v1) |  ~ $i(v0) |  ~ frontsegP(v1, v3) |  ~ ssList(v3) |  ~
% 103.82/14.41  |          ssList(v1) |  ~ ssItem(v0) | frontsegP(v2, v4))
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax45) implies:
% 103.82/14.41  |   (10)   ! [v0: $i] : ( ~ $i(v0) |  ~ ssList(v0) | frontsegP(v0, nil))
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax46) implies:
% 103.82/14.41  |   (11)   ~ ssList(nil) | frontsegP(nil, nil)
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax51) implies:
% 103.82/14.41  |   (12)   ! [v0: $i] : ( ~ $i(v0) |  ~ ssList(v0) | rearsegP(v0, nil))
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax52) implies:
% 103.82/14.41  |   (13)   ~ ssList(nil) | rearsegP(nil, nil)
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax58) implies:
% 103.82/14.41  |   (14)   ~ ssList(nil) | segmentP(nil, nil)
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax65) implies:
% 103.82/14.41  |   (15)   ! [v0: $i] :  ! [v1: $i] : ( ~ (cons(v0, nil) = v1) |  ~ $i(v0) |  ~
% 103.82/14.41  |           ssItem(v0) | totalorderedP(v1))
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax67) implies:
% 103.82/14.41  |   (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (hd(v1) = v2) |  ~
% 103.82/14.41  |           $i(v1) |  ~ $i(v0) |  ~ ssList(v1) |  ~ ssItem(v0) |  ? [v3: $i] :
% 103.82/14.41  |           ((v1 = nil | (cons(v0, v1) = v3 & $i(v3) &  ~ totalorderedP(v3)) |
% 103.82/14.41  |               (totalorderedP(v1) & leq(v0, v2))) & (( ~ (v1 = nil) & ( ~
% 103.82/14.41  |                   totalorderedP(v1) |  ~ leq(v0, v2))) | (cons(v0, v1) = v3 &
% 103.82/14.41  |                 $i(v3) & totalorderedP(v3)))))
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax77) implies:
% 103.82/14.41  |   (17)   ! [v0: $i] :  ! [v1: $i] : ( ~ (tl(v0) = v1) |  ~ $i(v0) |  ~
% 103.82/14.41  |           ssList(v0) |  ? [v2: $i] : (hd(v0) = v2 & $i(v2) &  ! [v3: $i] : (v3
% 103.82/14.41  |               = v0 | v3 = nil | v0 = nil |  ~ (tl(v3) = v1) |  ~ $i(v3) |  ~
% 103.82/14.41  |               ssList(v3) |  ? [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 &
% 103.82/14.41  |                 $i(v4)))))
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax81) implies:
% 103.82/14.41  |   (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (cons(v1,
% 103.82/14.41  |               nil) = v2) |  ~ (app(v2, v0) = v3) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 103.82/14.41  |           ssList(v0) |  ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3)))
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax83) implies:
% 103.82/14.41  |   (19)   ! [v0: $i] : (v0 = nil |  ~ (app(nil, nil) = v0) |  ~ ssList(nil))
% 103.82/14.41  |   (20)   ! [v0: $i] :  ! [v1: $i] : (v0 = nil |  ~ (app(v0, v1) = nil) |  ~
% 103.82/14.41  |           $i(v1) |  ~ $i(v0) |  ~ ssList(v1) |  ~ ssList(v0))
% 103.82/14.41  |   (21)   ! [v0: $i] :  ! [v1: $i] : (v1 = nil |  ~ (app(v0, v1) = nil) |  ~
% 103.82/14.41  |           $i(v1) |  ~ $i(v0) |  ~ ssList(v1) |  ~ ssList(v0))
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (ax84) implies:
% 103.82/14.41  |   (22)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (app(v0, nil) = v1) |  ~
% 103.82/14.41  |           $i(v0) |  ~ ssList(v0))
% 103.82/14.41  | 
% 103.82/14.41  | ALPHA: (co1) implies:
% 103.82/14.41  |   (23)  $i(nil)
% 103.82/14.42  |   (24)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : (cons(v2, nil)
% 103.82/14.42  |           = v3 & app(v0, v3) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 103.82/14.42  |           ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) &  ! [v4: $i] : 
% 103.82/14.42  |           ! [v5: $i] :  ! [v6: $i] :  ! [v7: $i] :  ! [v8: $i] : ( ~ (cons(v4,
% 103.82/14.42  |                 nil) = v5) |  ~ (app(v7, v8) = v1) |  ~ (app(v6, v5) = v7) | 
% 103.82/14.42  |             ~ $i(v8) |  ~ $i(v6) |  ~ $i(v4) |  ~ ssList(v8) |  ~ ssList(v6) |
% 103.82/14.42  |              ~ ssItem(v4) |  ? [v9: $i] : ( ~ (v9 = v0) & app(v6, v8) = v9 &
% 103.82/14.42  |               $i(v9))))
% 103.82/14.42  | 
% 103.82/14.42  | ALPHA: (function-axioms) implies:
% 103.82/14.42  |   (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (hd(v2) = v1)
% 103.82/14.42  |           |  ~ (hd(v2) = v0))
% 103.82/14.42  |   (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 103.82/14.42  |           (app(v3, v2) = v1) |  ~ (app(v3, v2) = v0))
% 103.82/14.42  |   (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 103.82/14.42  |           (cons(v3, v2) = v1) |  ~ (cons(v3, v2) = v0))
% 103.82/14.42  | 
% 103.82/14.42  | DELTA: instantiating (24) with fresh symbols all_91_0, all_91_1, all_91_2,
% 103.82/14.42  |        all_91_3 gives:
% 103.82/14.42  |   (28)  cons(all_91_1, nil) = all_91_0 & app(all_91_3, all_91_0) = all_91_2 &
% 103.82/14.42  |         $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 103.82/14.42  |         ssList(all_91_2) & ssList(all_91_3) & neq(all_91_2, nil) &
% 103.82/14.42  |         ssItem(all_91_1) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 103.82/14.42  |           $i] :  ! [v4: $i] : ( ~ (cons(v0, nil) = v1) |  ~ (app(v3, v4) =
% 103.82/14.42  |             all_91_2) |  ~ (app(v2, v1) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~
% 103.82/14.42  |           $i(v0) |  ~ ssList(v4) |  ~ ssList(v2) |  ~ ssItem(v0) |  ? [v5:
% 103.82/14.42  |             any] : ( ~ (v5 = all_91_3) & app(v2, v4) = v5 & $i(v5)))
% 103.82/14.42  | 
% 103.82/14.42  | ALPHA: (28) implies:
% 103.82/14.42  |   (29)  ssItem(all_91_1)
% 103.82/14.42  |   (30)  ssList(all_91_3)
% 103.82/14.42  |   (31)  ssList(all_91_2)
% 103.82/14.42  |   (32)  $i(all_91_3)
% 103.82/14.42  |   (33)  $i(all_91_2)
% 104.24/14.42  |   (34)  $i(all_91_1)
% 104.24/14.42  |   (35)  $i(all_91_0)
% 104.24/14.42  |   (36)  app(all_91_3, all_91_0) = all_91_2
% 104.24/14.42  |   (37)  cons(all_91_1, nil) = all_91_0
% 104.24/14.42  |   (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 104.24/14.42  |         ( ~ (cons(v0, nil) = v1) |  ~ (app(v3, v4) = all_91_2) |  ~ (app(v2,
% 104.24/14.42  |               v1) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~ $i(v0) |  ~ ssList(v4) | 
% 104.24/14.42  |           ~ ssList(v2) |  ~ ssItem(v0) |  ? [v5: any] : ( ~ (v5 = all_91_3) &
% 104.24/14.42  |             app(v2, v4) = v5 & $i(v5)))
% 104.24/14.42  | 
% 104.24/14.42  | BETA: splitting (11) gives:
% 104.24/14.42  | 
% 104.24/14.42  | Case 1:
% 104.24/14.42  | | 
% 104.24/14.42  | |   (39)   ~ ssList(nil)
% 104.24/14.42  | | 
% 104.24/14.43  | | PRED_UNIFY: (7), (39) imply:
% 104.24/14.43  | |   (40)  $false
% 104.24/14.43  | | 
% 104.24/14.43  | | CLOSE: (40) is inconsistent.
% 104.24/14.43  | | 
% 104.24/14.43  | Case 2:
% 104.24/14.43  | | 
% 104.24/14.43  | |   (41)  frontsegP(nil, nil)
% 104.24/14.43  | | 
% 104.24/14.43  | | BETA: splitting (13) gives:
% 104.24/14.43  | | 
% 104.24/14.43  | | Case 1:
% 104.24/14.43  | | | 
% 104.24/14.43  | | |   (42)   ~ ssList(nil)
% 104.24/14.43  | | | 
% 104.24/14.43  | | | PRED_UNIFY: (7), (42) imply:
% 104.24/14.43  | | |   (43)  $false
% 104.24/14.43  | | | 
% 104.24/14.43  | | | CLOSE: (43) is inconsistent.
% 104.24/14.43  | | | 
% 104.24/14.43  | | Case 2:
% 104.24/14.43  | | | 
% 104.24/14.43  | | |   (44)  rearsegP(nil, nil)
% 104.24/14.43  | | | 
% 104.24/14.43  | | | BETA: splitting (14) gives:
% 104.24/14.43  | | | 
% 104.24/14.43  | | | Case 1:
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | |   (45)   ~ ssList(nil)
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | PRED_UNIFY: (7), (45) imply:
% 104.24/14.43  | | | |   (46)  $false
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | CLOSE: (46) is inconsistent.
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | Case 2:
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | |   (47)  segmentP(nil, nil)
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (ax31) with all_91_1, simplifying with (29),
% 104.24/14.43  | | | |              (34) gives:
% 104.24/14.43  | | | |   (48)  leq(all_91_1, all_91_1)
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (ax49) with all_91_3, simplifying with (30),
% 104.24/14.43  | | | |              (32) gives:
% 104.24/14.43  | | | |   (49)  rearsegP(all_91_3, all_91_3)
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (12) with all_91_3, simplifying with (30),
% 104.24/14.43  | | | |              (32) gives:
% 104.24/14.43  | | | |   (50)  rearsegP(all_91_3, nil)
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (ax42) with all_91_3, simplifying with (30),
% 104.24/14.43  | | | |              (32) gives:
% 104.24/14.43  | | | |   (51)  frontsegP(all_91_3, all_91_3)
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (10) with all_91_3, simplifying with (30),
% 104.24/14.43  | | | |              (32) gives:
% 104.24/14.43  | | | |   (52)  frontsegP(all_91_3, nil)
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (12) with all_91_2, simplifying with (31),
% 104.24/14.43  | | | |              (33) gives:
% 104.24/14.43  | | | |   (53)  rearsegP(all_91_2, nil)
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (ax42) with all_91_2, simplifying with (31),
% 104.24/14.43  | | | |              (33) gives:
% 104.24/14.43  | | | |   (54)  frontsegP(all_91_2, all_91_2)
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (10) with all_91_2, simplifying with (31),
% 104.24/14.43  | | | |              (33) gives:
% 104.24/14.43  | | | |   (55)  frontsegP(all_91_2, nil)
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (7),
% 104.24/14.43  | | | |              (23), (41) gives:
% 104.24/14.43  | | | |   (56)   ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (4) with nil, nil, simplifying with (7),
% 104.24/14.43  | | | |              (23), (44) gives:
% 104.24/14.43  | | | |   (57)   ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0))
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (6) with nil, nil, simplifying with (7),
% 104.24/14.43  | | | |              (23), (47) gives:
% 104.24/14.43  | | | |   (58)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (app(v1, v2) = nil &
% 104.24/14.43  | | | |           app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) &
% 104.24/14.43  | | | |           ssList(v0))
% 104.24/14.43  | | | | 
% 104.24/14.43  | | | | GROUND_INST: instantiating (9) with all_91_1, nil, all_91_0, nil,
% 104.24/14.43  | | | |              all_91_0, simplifying with (7), (23), (29), (34), (37),
% 104.24/14.44  | | | |              (41) gives:
% 104.24/14.44  | | | |   (59)  frontsegP(all_91_0, all_91_0)
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | GROUND_INST: instantiating (ax25) with nil, all_91_1, all_91_0,
% 104.24/14.44  | | | |              simplifying with (7), (23), (29), (34), (37) gives:
% 104.24/14.44  | | | |   (60)  tl(all_91_0) = nil
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | GROUND_INST: instantiating (ax23) with nil, all_91_1, all_91_0,
% 104.24/14.44  | | | |              simplifying with (7), (23), (29), (34), (37) gives:
% 104.24/14.44  | | | |   (61)  hd(all_91_0) = all_91_1
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | GROUND_INST: instantiating (ax16) with nil, all_91_1, all_91_0,
% 104.24/14.44  | | | |              simplifying with (7), (23), (29), (34), (37) gives:
% 104.24/14.44  | | | |   (62)  ssList(all_91_0)
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | GROUND_INST: instantiating (15) with all_91_1, all_91_0, simplifying
% 104.24/14.44  | | | |              with (29), (34), (37) gives:
% 104.24/14.44  | | | |   (63)  totalorderedP(all_91_0)
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | DELTA: instantiating (57) with fresh symbol all_112_0 gives:
% 104.24/14.44  | | | |   (64)  app(all_112_0, nil) = nil & $i(all_112_0) & ssList(all_112_0)
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | ALPHA: (64) implies:
% 104.24/14.44  | | | |   (65)  ssList(all_112_0)
% 104.24/14.44  | | | |   (66)  $i(all_112_0)
% 104.24/14.44  | | | |   (67)  app(all_112_0, nil) = nil
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | DELTA: instantiating (56) with fresh symbol all_114_0 gives:
% 104.24/14.44  | | | |   (68)  app(nil, all_114_0) = nil & $i(all_114_0) & ssList(all_114_0)
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | ALPHA: (68) implies:
% 104.24/14.44  | | | |   (69)  ssList(all_114_0)
% 104.24/14.44  | | | |   (70)  $i(all_114_0)
% 104.24/14.44  | | | |   (71)  app(nil, all_114_0) = nil
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | DELTA: instantiating (58) with fresh symbols all_116_0, all_116_1,
% 104.24/14.44  | | | |        all_116_2 gives:
% 104.24/14.44  | | | |   (72)  app(all_116_1, all_116_0) = nil & app(all_116_2, nil) =
% 104.24/14.44  | | | |         all_116_1 & $i(all_116_0) & $i(all_116_1) & $i(all_116_2) &
% 104.24/14.44  | | | |         ssList(all_116_0) & ssList(all_116_2)
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | ALPHA: (72) implies:
% 104.24/14.44  | | | |   (73)  ssList(all_116_2)
% 104.24/14.44  | | | |   (74)  ssList(all_116_0)
% 104.24/14.44  | | | |   (75)  $i(all_116_2)
% 104.24/14.44  | | | |   (76)  $i(all_116_1)
% 104.24/14.44  | | | |   (77)  $i(all_116_0)
% 104.24/14.44  | | | |   (78)  app(all_116_2, nil) = all_116_1
% 104.24/14.44  | | | |   (79)  app(all_116_1, all_116_0) = nil
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | GROUND_INST: instantiating (2) with all_91_0, all_91_1, simplifying with
% 104.24/14.44  | | | |              (29), (34), (35), (37), (62) gives:
% 104.24/14.44  | | | |   (80)  singletonP(all_91_0)
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | GROUND_INST: instantiating (5) with all_91_2, all_91_0, all_91_3,
% 104.24/14.44  | | | |              simplifying with (30), (31), (32), (33), (35), (36), (62)
% 104.24/14.44  | | | |              gives:
% 104.24/14.44  | | | |   (81)  rearsegP(all_91_2, all_91_0)
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | GROUND_INST: instantiating (3) with all_91_3, nil, simplifying with (7),
% 104.24/14.44  | | | |              (23), (30), (32), (52) gives:
% 104.24/14.44  | | | |   (82)   ? [v0: $i] : (app(nil, v0) = all_91_3 & $i(v0) & ssList(v0))
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | GROUND_INST: instantiating (3) with all_91_3, all_91_3, simplifying with
% 104.24/14.44  | | | |              (30), (32), (51) gives:
% 104.24/14.44  | | | |   (83)   ? [v0: $i] : (app(all_91_3, v0) = all_91_3 & $i(v0) &
% 104.24/14.44  | | | |           ssList(v0))
% 104.24/14.44  | | | | 
% 104.24/14.44  | | | | GROUND_INST: instantiating (3) with all_91_2, nil, simplifying with (7),
% 104.24/14.44  | | | |              (23), (31), (33), (55) gives:
% 104.24/14.45  | | | |   (84)   ? [v0: $i] : (app(nil, v0) = all_91_2 & $i(v0) & ssList(v0))
% 104.24/14.45  | | | | 
% 104.24/14.45  | | | | GROUND_INST: instantiating (3) with all_91_2, all_91_2, simplifying with
% 104.24/14.45  | | | |              (31), (33), (54) gives:
% 104.24/14.45  | | | |   (85)   ? [v0: $i] : (app(all_91_2, v0) = all_91_2 & $i(v0) &
% 104.24/14.45  | | | |           ssList(v0))
% 104.24/14.45  | | | | 
% 104.24/14.45  | | | | GROUND_INST: instantiating (3) with all_91_0, all_91_0, simplifying with
% 104.24/14.45  | | | |              (35), (59), (62) gives:
% 104.24/14.45  | | | |   (86)   ? [v0: $i] : (app(all_91_0, v0) = all_91_0 & $i(v0) &
% 104.24/14.45  | | | |           ssList(v0))
% 104.24/14.45  | | | | 
% 104.24/14.45  | | | | GROUND_INST: instantiating (4) with all_91_3, nil, simplifying with (7),
% 104.24/14.45  | | | |              (23), (30), (32), (50) gives:
% 104.24/14.45  | | | |   (87)   ? [v0: $i] : (app(v0, nil) = all_91_3 & $i(v0) & ssList(v0))
% 104.24/14.45  | | | | 
% 104.24/14.45  | | | | GROUND_INST: instantiating (4) with all_91_3, all_91_3, simplifying with
% 104.24/14.45  | | | |              (30), (32), (49) gives:
% 104.24/14.45  | | | |   (88)   ? [v0: $i] : (app(v0, all_91_3) = all_91_3 & $i(v0) &
% 104.24/14.45  | | | |           ssList(v0))
% 104.24/14.45  | | | | 
% 104.24/14.45  | | | | GROUND_INST: instantiating (4) with all_91_2, nil, simplifying with (7),
% 104.24/14.45  | | | |              (23), (31), (33), (53) gives:
% 104.24/14.45  | | | |   (89)   ? [v0: $i] : (app(v0, nil) = all_91_2 & $i(v0) & ssList(v0))
% 104.24/14.45  | | | | 
% 104.24/14.45  | | | | GROUND_INST: instantiating (ax27) with all_114_0, nil, nil, all_91_1,
% 104.24/14.45  | | | |              all_91_0, simplifying with (7), (23), (29), (34), (37),
% 104.24/14.45  | | | |              (69), (70), (71) gives:
% 104.24/14.45  | | | |   (90)   ? [v0: $i] : (cons(all_91_1, nil) = v0 & app(v0, all_114_0) =
% 104.24/14.45  | | | |           all_91_0 & $i(v0) & $i(all_91_0))
% 104.24/14.45  | | | | 
% 104.24/14.45  | | | | GROUND_INST: instantiating (ax82) with nil, all_114_0, nil, all_114_0,
% 104.24/14.45  | | | |              nil, simplifying with (7), (23), (69), (70), (71) gives:
% 104.24/14.45  | | | |   (91)   ? [v0: $i] : (app(all_114_0, all_114_0) = v0 & app(nil, v0) =
% 104.24/14.45  | | | |           nil & $i(v0))
% 104.24/14.45  | | | | 
% 104.24/14.45  | | | | GROUND_INST: instantiating (8) with all_114_0, nil, simplifying with
% 104.24/14.45  | | | |              (69), (70), (71) gives:
% 104.24/14.45  | | | |   (92)  all_114_0 = nil
% 104.24/14.45  | | | | 
% 104.24/14.45  | | | | GROUND_INST: instantiating (ax27) with nil, all_112_0, nil, all_91_1,
% 104.24/14.45  | | | |              all_91_0, simplifying with (7), (23), (29), (34), (37),
% 104.24/14.45  | | | |              (65), (66), (67) gives:
% 104.24/14.45  | | | |   (93)   ? [v0: $i] : (cons(all_91_1, all_112_0) = v0 & app(v0, nil) =
% 104.24/14.45  | | | |           all_91_0 & $i(v0) & $i(all_91_0))
% 104.24/14.45  | | | | 
% 104.24/14.45  | | | | GROUND_INST: instantiating (22) with all_112_0, nil, simplifying with
% 104.24/14.45  | | | |              (65), (66), (67) gives:
% 104.24/14.45  | | | |   (94)  all_112_0 = nil
% 104.24/14.45  | | | | 
% 104.24/14.46  | | | | GROUND_INST: instantiating (ax26) with all_116_2, nil, all_116_1,
% 104.24/14.46  | | | |              simplifying with (7), (23), (73), (75), (78) gives:
% 104.24/14.46  | | | |   (95)  ssList(all_116_1)
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | GROUND_INST: instantiating (22) with all_116_2, all_116_1, simplifying
% 104.24/14.46  | | | |              with (73), (75), (78) gives:
% 104.24/14.46  | | | |   (96)  all_116_1 = all_116_2
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | GROUND_INST: instantiating (ax82) with all_116_2, nil, all_116_1,
% 104.24/14.46  | | | |              all_116_0, nil, simplifying with (7), (23), (73), (74),
% 104.24/14.46  | | | |              (75), (77), (78), (79) gives:
% 104.24/14.46  | | | |   (97)   ? [v0: $i] : (app(all_116_2, v0) = nil & app(nil, all_116_0) =
% 104.24/14.46  | | | |           v0 & $i(v0))
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | GROUND_INST: instantiating (16) with all_91_1, all_91_0, all_91_1,
% 104.24/14.46  | | | |              simplifying with (29), (34), (35), (61), (62) gives:
% 104.24/14.46  | | | |   (98)   ? [v0: $i] : ((all_91_0 = nil | (cons(all_91_1, all_91_0) = v0
% 104.24/14.46  | | | |               & $i(v0) &  ~ totalorderedP(v0)) |
% 104.24/14.46  | | | |             (totalorderedP(all_91_0) & leq(all_91_1, all_91_1))) & (( ~
% 104.24/14.46  | | | |               (all_91_0 = nil) & ( ~ totalorderedP(all_91_0) |  ~
% 104.24/14.46  | | | |                 leq(all_91_1, all_91_1))) | (cons(all_91_1, all_91_0) =
% 104.24/14.46  | | | |               v0 & $i(v0) & totalorderedP(v0))))
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | GROUND_INST: instantiating (17) with all_91_0, nil, simplifying with
% 104.24/14.46  | | | |              (35), (60), (62) gives:
% 104.24/14.46  | | | |   (99)   ? [v0: $i] : (hd(all_91_0) = v0 & $i(v0) &  ! [v1: any] : (v1 =
% 104.24/14.46  | | | |             all_91_0 | v1 = nil | all_91_0 = nil |  ~ (tl(v1) = nil) | 
% 104.24/14.46  | | | |             ~ $i(v1) |  ~ ssList(v1) |  ? [v2: $i] : ( ~ (v2 = v0) &
% 104.24/14.46  | | | |               hd(v1) = v2 & $i(v2))))
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | DELTA: instantiating (97) with fresh symbol all_132_0 gives:
% 104.24/14.46  | | | |   (100)  app(all_116_2, all_132_0) = nil & app(nil, all_116_0) =
% 104.24/14.46  | | | |          all_132_0 & $i(all_132_0)
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | ALPHA: (100) implies:
% 104.24/14.46  | | | |   (101)  app(nil, all_116_0) = all_132_0
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | DELTA: instantiating (84) with fresh symbol all_134_0 gives:
% 104.24/14.46  | | | |   (102)  app(nil, all_134_0) = all_91_2 & $i(all_134_0) &
% 104.24/14.46  | | | |          ssList(all_134_0)
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | ALPHA: (102) implies:
% 104.24/14.46  | | | |   (103)  ssList(all_134_0)
% 104.24/14.46  | | | |   (104)  $i(all_134_0)
% 104.24/14.46  | | | |   (105)  app(nil, all_134_0) = all_91_2
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | DELTA: instantiating (82) with fresh symbol all_136_0 gives:
% 104.24/14.46  | | | |   (106)  app(nil, all_136_0) = all_91_3 & $i(all_136_0) &
% 104.24/14.46  | | | |          ssList(all_136_0)
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | ALPHA: (106) implies:
% 104.24/14.46  | | | |   (107)  ssList(all_136_0)
% 104.24/14.46  | | | |   (108)  $i(all_136_0)
% 104.24/14.46  | | | |   (109)  app(nil, all_136_0) = all_91_3
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | DELTA: instantiating (83) with fresh symbol all_138_0 gives:
% 104.24/14.46  | | | |   (110)  app(all_91_3, all_138_0) = all_91_3 & $i(all_138_0) &
% 104.24/14.46  | | | |          ssList(all_138_0)
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | ALPHA: (110) implies:
% 104.24/14.46  | | | |   (111)  ssList(all_138_0)
% 104.24/14.46  | | | |   (112)  $i(all_138_0)
% 104.24/14.46  | | | |   (113)  app(all_91_3, all_138_0) = all_91_3
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | DELTA: instantiating (91) with fresh symbol all_140_0 gives:
% 104.24/14.46  | | | |   (114)  app(all_114_0, all_114_0) = all_140_0 & app(nil, all_140_0) =
% 104.24/14.46  | | | |          nil & $i(all_140_0)
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | ALPHA: (114) implies:
% 104.24/14.46  | | | |   (115)  $i(all_140_0)
% 104.24/14.46  | | | |   (116)  app(all_114_0, all_114_0) = all_140_0
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | DELTA: instantiating (89) with fresh symbol all_144_0 gives:
% 104.24/14.46  | | | |   (117)  app(all_144_0, nil) = all_91_2 & $i(all_144_0) &
% 104.24/14.46  | | | |          ssList(all_144_0)
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | ALPHA: (117) implies:
% 104.24/14.46  | | | |   (118)  ssList(all_144_0)
% 104.24/14.46  | | | |   (119)  $i(all_144_0)
% 104.24/14.46  | | | |   (120)  app(all_144_0, nil) = all_91_2
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | DELTA: instantiating (88) with fresh symbol all_146_0 gives:
% 104.24/14.46  | | | |   (121)  app(all_146_0, all_91_3) = all_91_3 & $i(all_146_0) &
% 104.24/14.46  | | | |          ssList(all_146_0)
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | ALPHA: (121) implies:
% 104.24/14.46  | | | |   (122)  ssList(all_146_0)
% 104.24/14.46  | | | |   (123)  $i(all_146_0)
% 104.24/14.46  | | | |   (124)  app(all_146_0, all_91_3) = all_91_3
% 104.24/14.46  | | | | 
% 104.24/14.46  | | | | DELTA: instantiating (87) with fresh symbol all_148_0 gives:
% 104.24/14.46  | | | |   (125)  app(all_148_0, nil) = all_91_3 & $i(all_148_0) &
% 104.24/14.46  | | | |          ssList(all_148_0)
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | ALPHA: (125) implies:
% 104.24/14.47  | | | |   (126)  ssList(all_148_0)
% 104.24/14.47  | | | |   (127)  $i(all_148_0)
% 104.24/14.47  | | | |   (128)  app(all_148_0, nil) = all_91_3
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | DELTA: instantiating (86) with fresh symbol all_150_0 gives:
% 104.24/14.47  | | | |   (129)  app(all_91_0, all_150_0) = all_91_0 & $i(all_150_0) &
% 104.24/14.47  | | | |          ssList(all_150_0)
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | ALPHA: (129) implies:
% 104.24/14.47  | | | |   (130)  ssList(all_150_0)
% 104.24/14.47  | | | |   (131)  $i(all_150_0)
% 104.24/14.47  | | | |   (132)  app(all_91_0, all_150_0) = all_91_0
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | DELTA: instantiating (85) with fresh symbol all_152_0 gives:
% 104.24/14.47  | | | |   (133)  app(all_91_2, all_152_0) = all_91_2 & $i(all_152_0) &
% 104.24/14.47  | | | |          ssList(all_152_0)
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | ALPHA: (133) implies:
% 104.24/14.47  | | | |   (134)  ssList(all_152_0)
% 104.24/14.47  | | | |   (135)  $i(all_152_0)
% 104.24/14.47  | | | |   (136)  app(all_91_2, all_152_0) = all_91_2
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | DELTA: instantiating (93) with fresh symbol all_154_0 gives:
% 104.24/14.47  | | | |   (137)  cons(all_91_1, all_112_0) = all_154_0 & app(all_154_0, nil) =
% 104.24/14.47  | | | |          all_91_0 & $i(all_154_0) & $i(all_91_0)
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | ALPHA: (137) implies:
% 104.24/14.47  | | | |   (138)  $i(all_154_0)
% 104.24/14.47  | | | |   (139)  app(all_154_0, nil) = all_91_0
% 104.24/14.47  | | | |   (140)  cons(all_91_1, all_112_0) = all_154_0
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | DELTA: instantiating (90) with fresh symbol all_156_0 gives:
% 104.24/14.47  | | | |   (141)  cons(all_91_1, nil) = all_156_0 & app(all_156_0, all_114_0) =
% 104.24/14.47  | | | |          all_91_0 & $i(all_156_0) & $i(all_91_0)
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | ALPHA: (141) implies:
% 104.24/14.47  | | | |   (142)  cons(all_91_1, nil) = all_156_0
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | DELTA: instantiating (99) with fresh symbol all_170_0 gives:
% 104.24/14.47  | | | |   (143)  hd(all_91_0) = all_170_0 & $i(all_170_0) &  ! [v0: any] : (v0 =
% 104.24/14.47  | | | |            all_91_0 | v0 = nil | all_91_0 = nil |  ~ (tl(v0) = nil) |  ~
% 104.24/14.47  | | | |            $i(v0) |  ~ ssList(v0) |  ? [v1: any] : ( ~ (v1 = all_170_0)
% 104.24/14.47  | | | |              & hd(v0) = v1 & $i(v1)))
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | ALPHA: (143) implies:
% 104.24/14.47  | | | |   (144)  $i(all_170_0)
% 104.24/14.47  | | | |   (145)  hd(all_91_0) = all_170_0
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | DELTA: instantiating (98) with fresh symbol all_173_0 gives:
% 104.24/14.47  | | | |   (146)  (all_91_0 = nil | (cons(all_91_1, all_91_0) = all_173_0 &
% 104.24/14.47  | | | |              $i(all_173_0) &  ~ totalorderedP(all_173_0)) |
% 104.24/14.47  | | | |            (totalorderedP(all_91_0) & leq(all_91_1, all_91_1))) & (( ~
% 104.24/14.47  | | | |              (all_91_0 = nil) & ( ~ totalorderedP(all_91_0) |  ~
% 104.24/14.47  | | | |                leq(all_91_1, all_91_1))) | (cons(all_91_1, all_91_0) =
% 104.24/14.47  | | | |              all_173_0 & $i(all_173_0) & totalorderedP(all_173_0)))
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | ALPHA: (146) implies:
% 104.24/14.47  | | | |   (147)  ( ~ (all_91_0 = nil) & ( ~ totalorderedP(all_91_0) |  ~
% 104.24/14.47  | | | |              leq(all_91_1, all_91_1))) | (cons(all_91_1, all_91_0) =
% 104.24/14.47  | | | |            all_173_0 & $i(all_173_0) & totalorderedP(all_173_0))
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | REDUCE: (94), (140) imply:
% 104.24/14.47  | | | |   (148)  cons(all_91_1, nil) = all_154_0
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | REDUCE: (79), (96) imply:
% 104.24/14.47  | | | |   (149)  app(all_116_2, all_116_0) = nil
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | REDUCE: (92), (116) imply:
% 104.24/14.47  | | | |   (150)  app(nil, nil) = all_140_0
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | BETA: splitting (147) gives:
% 104.24/14.47  | | | | 
% 104.24/14.47  | | | | Case 1:
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | |   (151)   ~ (all_91_0 = nil) & ( ~ totalorderedP(all_91_0) |  ~
% 104.24/14.47  | | | | |            leq(all_91_1, all_91_1))
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | ALPHA: (151) implies:
% 104.24/14.47  | | | | |   (152)   ~ totalorderedP(all_91_0) |  ~ leq(all_91_1, all_91_1)
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | BETA: splitting (152) gives:
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | Case 1:
% 104.24/14.47  | | | | | | 
% 104.24/14.47  | | | | | |   (153)   ~ totalorderedP(all_91_0)
% 104.24/14.47  | | | | | | 
% 104.24/14.47  | | | | | | PRED_UNIFY: (63), (153) imply:
% 104.24/14.47  | | | | | |   (154)  $false
% 104.24/14.47  | | | | | | 
% 104.24/14.47  | | | | | | CLOSE: (154) is inconsistent.
% 104.24/14.47  | | | | | | 
% 104.24/14.47  | | | | | Case 2:
% 104.24/14.47  | | | | | | 
% 104.24/14.47  | | | | | |   (155)   ~ leq(all_91_1, all_91_1)
% 104.24/14.47  | | | | | | 
% 104.24/14.47  | | | | | | PRED_UNIFY: (48), (155) imply:
% 104.24/14.47  | | | | | |   (156)  $false
% 104.24/14.47  | | | | | | 
% 104.24/14.47  | | | | | | CLOSE: (156) is inconsistent.
% 104.24/14.47  | | | | | | 
% 104.24/14.47  | | | | | End of split
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | Case 2:
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | GROUND_INST: instantiating (19) with all_140_0, simplifying with (7),
% 104.24/14.47  | | | | |              (150) gives:
% 104.24/14.47  | | | | |   (157)  all_140_0 = nil
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | GROUND_INST: instantiating (27) with all_91_0, all_156_0, nil,
% 104.24/14.47  | | | | |              all_91_1, simplifying with (37), (142) gives:
% 104.24/14.47  | | | | |   (158)  all_156_0 = all_91_0
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | GROUND_INST: instantiating (27) with all_154_0, all_156_0, nil,
% 104.24/14.47  | | | | |              all_91_1, simplifying with (142), (148) gives:
% 104.24/14.47  | | | | |   (159)  all_156_0 = all_154_0
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | GROUND_INST: instantiating (25) with all_91_1, all_170_0, all_91_0,
% 104.24/14.47  | | | | |              simplifying with (61), (145) gives:
% 104.24/14.47  | | | | |   (160)  all_170_0 = all_91_1
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | COMBINE_EQS: (158), (159) imply:
% 104.24/14.47  | | | | |   (161)  all_154_0 = all_91_0
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | REDUCE: (139), (161) imply:
% 104.24/14.47  | | | | |   (162)  app(all_91_0, nil) = all_91_0
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | REDUCE: (150), (157) imply:
% 104.24/14.47  | | | | |   (163)  app(nil, nil) = nil
% 104.24/14.47  | | | | | 
% 104.24/14.47  | | | | | GROUND_INST: instantiating (1) with all_91_0, simplifying with (35),
% 104.24/14.47  | | | | |              (62), (80) gives:
% 104.24/14.48  | | | | |   (164)   ? [v0: $i] : (cons(v0, nil) = all_91_0 & $i(v0) &
% 104.24/14.48  | | | | |            ssItem(v0))
% 104.24/14.48  | | | | | 
% 104.24/14.48  | | | | | GROUND_INST: instantiating (4) with all_91_2, all_91_0, simplifying
% 104.24/14.48  | | | | |              with (31), (33), (35), (62), (81) gives:
% 104.24/14.48  | | | | |   (165)   ? [v0: $i] : (app(v0, all_91_0) = all_91_2 & $i(v0) &
% 104.24/14.48  | | | | |            ssList(v0))
% 104.24/14.48  | | | | | 
% 104.24/14.48  | | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_116_0,
% 104.24/14.48  | | | | |              all_132_0, simplifying with (7), (23), (74), (77), (101),
% 104.24/14.48  | | | | |              (163) gives:
% 104.24/14.48  | | | | |   (166)   ? [v0: $i] : (app(nil, v0) = all_132_0 & app(nil, all_116_0)
% 104.24/14.48  | | | | |            = v0 & $i(v0) & $i(all_132_0))
% 104.24/14.48  | | | | | 
% 104.24/14.48  | | | | | GROUND_INST: instantiating (8) with all_116_0, all_132_0, simplifying
% 104.24/14.48  | | | | |              with (74), (77), (101) gives:
% 104.24/14.48  | | | | |   (167)  all_132_0 = all_116_0
% 104.24/14.48  | | | | | 
% 104.24/14.48  | | | | | GROUND_INST: instantiating (8) with all_134_0, all_91_2, simplifying
% 104.24/14.48  | | | | |              with (103), (104), (105) gives:
% 104.24/14.48  | | | | |   (168)  all_134_0 = all_91_2
% 104.24/14.48  | | | | | 
% 104.24/14.48  | | | | | GROUND_INST: instantiating (ax82) with nil, all_136_0, all_91_3,
% 104.24/14.48  | | | | |              all_91_0, all_91_2, simplifying with (7), (23), (35),
% 104.24/14.48  | | | | |              (36), (62), (107), (108), (109) gives:
% 104.24/14.48  | | | | |   (169)   ? [v0: $i] : (app(all_136_0, all_91_0) = v0 & app(nil, v0) =
% 104.24/14.48  | | | | |            all_91_2 & $i(v0) & $i(all_91_2))
% 104.24/14.48  | | | | | 
% 104.24/14.48  | | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_136_0,
% 104.24/14.48  | | | | |              all_91_3, simplifying with (7), (23), (107), (108),
% 104.24/14.48  | | | | |              (109), (163) gives:
% 104.24/14.48  | | | | |   (170)   ? [v0: $i] : (app(nil, v0) = all_91_3 & app(nil, all_136_0)
% 104.24/14.48  | | | | |            = v0 & $i(v0) & $i(all_91_3))
% 104.24/14.48  | | | | | 
% 104.24/14.48  | | | | | GROUND_INST: instantiating (8) with all_136_0, all_91_3, simplifying
% 104.24/14.48  | | | | |              with (107), (108), (109) gives:
% 104.24/14.48  | | | | |   (171)  all_136_0 = all_91_3
% 104.24/14.48  | | | | | 
% 104.24/14.48  | | | | | GROUND_INST: instantiating (ax82) with nil, all_136_0, all_91_3,
% 104.24/14.48  | | | | |              all_138_0, all_91_3, simplifying with (7), (23), (107),
% 104.24/14.48  | | | | |              (108), (109), (111), (112), (113) gives:
% 104.24/14.48  | | | | |   (172)   ? [v0: $i] : (app(all_136_0, all_138_0) = v0 & app(nil, v0)
% 104.24/14.48  | | | | |            = all_91_3 & $i(v0) & $i(all_91_3))
% 104.24/14.48  | | | | | 
% 104.24/14.48  | | | | | GROUND_INST: instantiating (ax82) with nil, all_134_0, all_91_2,
% 104.24/14.48  | | | | |              all_152_0, all_91_2, simplifying with (7), (23), (103),
% 104.24/14.48  | | | | |              (104), (105), (134), (135), (136) gives:
% 104.24/14.48  | | | | |   (173)   ? [v0: $i] : (app(all_134_0, all_152_0) = v0 & app(nil, v0)
% 104.24/14.48  | | | | |            = all_91_2 & $i(v0) & $i(all_91_2))
% 104.24/14.48  | | | | | 
% 104.24/14.48  | | | | | GROUND_INST: instantiating (38) with all_91_1, all_91_0, all_91_3,
% 104.24/14.48  | | | | |              all_91_2, all_152_0, simplifying with (29), (30), (32),
% 104.24/14.48  | | | | |              (34), (36), (37), (134), (135), (136) gives:
% 104.53/14.48  | | | | |   (174)   ? [v0: any] : ( ~ (v0 = all_91_3) & app(all_91_3, all_152_0)
% 104.53/14.48  | | | | |            = v0 & $i(v0))
% 104.53/14.48  | | | | | 
% 104.53/14.48  | | | | | GROUND_INST: instantiating (18) with all_150_0, all_91_1, all_91_0,
% 104.53/14.48  | | | | |              all_91_0, simplifying with (29), (34), (37), (130),
% 104.53/14.48  | | | | |              (131), (132) gives:
% 104.53/14.48  | | | | |   (175)  cons(all_91_1, all_150_0) = all_91_0 & $i(all_91_0)
% 104.53/14.48  | | | | | 
% 104.53/14.48  | | | | | ALPHA: (175) implies:
% 104.53/14.48  | | | | |   (176)  cons(all_91_1, all_150_0) = all_91_0
% 104.53/14.48  | | | | | 
% 104.53/14.48  | | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_150_0, all_91_0,
% 104.53/14.48  | | | | |              all_150_0, all_91_0, simplifying with (35), (62), (130),
% 104.53/14.48  | | | | |              (131), (132) gives:
% 104.53/14.48  | | | | |   (177)   ? [v0: $i] : (app(all_150_0, all_150_0) = v0 & app(all_91_0,
% 104.53/14.48  | | | | |              v0) = all_91_0 & $i(v0))
% 104.53/14.48  | | | | | 
% 104.53/14.48  | | | | | GROUND_INST: instantiating (ax80) with all_150_0, all_91_0, all_91_0,
% 104.53/14.48  | | | | |              nil, simplifying with (7), (23), (35), (62), (130),
% 104.53/14.48  | | | | |              (131), (132), (162) gives:
% 104.53/14.48  | | | | |   (178)  all_150_0 = nil
% 104.53/14.48  | | | | | 
% 104.53/14.48  | | | | | GROUND_INST: instantiating (ax82) with all_91_0, nil, all_91_0,
% 104.53/14.48  | | | | |              all_150_0, all_91_0, simplifying with (7), (23), (35),
% 104.53/14.48  | | | | |              (62), (130), (131), (132), (162) gives:
% 104.53/14.48  | | | | |   (179)   ? [v0: $i] : (app(all_91_0, v0) = all_91_0 & app(nil,
% 104.53/14.48  | | | | |              all_150_0) = v0 & $i(v0))
% 104.53/14.48  | | | | | 
% 104.53/14.48  | | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_150_0, all_91_0,
% 104.53/14.48  | | | | |              nil, all_91_0, simplifying with (7), (23), (35), (62),
% 104.53/14.48  | | | | |              (130), (131), (132), (162) gives:
% 104.53/14.48  | | | | |   (180)   ? [v0: $i] : (app(all_150_0, nil) = v0 & app(all_91_0, v0) =
% 104.53/14.48  | | | | |            all_91_0 & $i(v0))
% 104.53/14.48  | | | | | 
% 104.53/14.48  | | | | | GROUND_INST: instantiating (ax27) with all_116_0, all_116_2, nil,
% 104.53/14.48  | | | | |              all_91_1, all_91_0, simplifying with (29), (34), (37),
% 104.53/14.48  | | | | |              (73), (74), (75), (77), (149) gives:
% 104.53/14.48  | | | | |   (181)   ? [v0: $i] : (cons(all_91_1, all_116_2) = v0 & app(v0,
% 104.53/14.48  | | | | |              all_116_0) = all_91_0 & $i(v0) & $i(all_91_0))
% 104.53/14.48  | | | | | 
% 104.53/14.48  | | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil,
% 104.53/14.48  | | | | |              all_136_0, all_91_3, simplifying with (73), (74), (75),
% 104.53/14.48  | | | | |              (77), (107), (108), (109), (149) gives:
% 104.53/14.49  | | | | |   (182)   ? [v0: $i] : (app(all_116_0, all_136_0) = v0 &
% 104.53/14.49  | | | | |            app(all_116_2, v0) = all_91_3 & $i(v0) & $i(all_91_3))
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil,
% 104.53/14.49  | | | | |              all_116_0, all_132_0, simplifying with (73), (74), (75),
% 104.53/14.49  | | | | |              (77), (101), (149) gives:
% 104.53/14.49  | | | | |   (183)   ? [v0: $i] : (app(all_116_0, all_116_0) = v0 &
% 104.53/14.49  | | | | |            app(all_116_2, v0) = all_132_0 & $i(v0) & $i(all_132_0))
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil, nil,
% 104.53/14.49  | | | | |              nil, simplifying with (7), (23), (73), (74), (75), (77),
% 104.53/14.49  | | | | |              (149), (163) gives:
% 104.53/14.49  | | | | |   (184)   ? [v0: $i] : (app(all_116_0, nil) = v0 & app(all_116_2, v0)
% 104.53/14.49  | | | | |            = nil & $i(v0))
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | GROUND_INST: instantiating (21) with all_116_2, all_116_0, simplifying
% 104.53/14.49  | | | | |              with (73), (74), (75), (77), (149) gives:
% 104.53/14.49  | | | | |   (185)  all_116_0 = nil
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | GROUND_INST: instantiating (20) with all_116_2, all_116_0, simplifying
% 104.53/14.49  | | | | |              with (73), (74), (75), (77), (149) gives:
% 104.53/14.49  | | | | |   (186)  all_116_2 = nil
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | GROUND_INST: instantiating (22) with all_144_0, all_91_2, simplifying
% 104.53/14.49  | | | | |              with (118), (119), (120) gives:
% 104.53/14.49  | | | | |   (187)  all_144_0 = all_91_2
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | GROUND_INST: instantiating (ax82) with all_146_0, all_91_3, all_91_3,
% 104.53/14.49  | | | | |              all_91_0, all_91_2, simplifying with (30), (32), (35),
% 104.53/14.49  | | | | |              (36), (62), (122), (123), (124) gives:
% 104.53/14.49  | | | | |   (188)   ? [v0: $i] : (app(all_146_0, v0) = all_91_2 & app(all_91_3,
% 104.53/14.49  | | | | |              all_91_0) = v0 & $i(v0) & $i(all_91_2))
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | GROUND_INST: instantiating (22) with all_148_0, all_91_3, simplifying
% 104.53/14.49  | | | | |              with (126), (127), (128) gives:
% 104.53/14.49  | | | | |   (189)  all_148_0 = all_91_3
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | COMBINE_EQS: (167), (185) imply:
% 104.53/14.49  | | | | |   (190)  all_132_0 = nil
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (177) with fresh symbol all_193_0 gives:
% 104.53/14.49  | | | | |   (191)  app(all_150_0, all_150_0) = all_193_0 & app(all_91_0,
% 104.53/14.49  | | | | |            all_193_0) = all_91_0 & $i(all_193_0)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (191) implies:
% 104.53/14.49  | | | | |   (192)  $i(all_193_0)
% 104.53/14.49  | | | | |   (193)  app(all_150_0, all_150_0) = all_193_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (174) with fresh symbol all_197_0 gives:
% 104.53/14.49  | | | | |   (194)   ~ (all_197_0 = all_91_3) & app(all_91_3, all_152_0) =
% 104.53/14.49  | | | | |          all_197_0 & $i(all_197_0)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (194) implies:
% 104.53/14.49  | | | | |   (195)   ~ (all_197_0 = all_91_3)
% 104.53/14.49  | | | | |   (196)  app(all_91_3, all_152_0) = all_197_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (165) with fresh symbol all_205_0 gives:
% 104.53/14.49  | | | | |   (197)  app(all_205_0, all_91_0) = all_91_2 & $i(all_205_0) &
% 104.53/14.49  | | | | |          ssList(all_205_0)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (197) implies:
% 104.53/14.49  | | | | |   (198)  ssList(all_205_0)
% 104.53/14.49  | | | | |   (199)  $i(all_205_0)
% 104.53/14.49  | | | | |   (200)  app(all_205_0, all_91_0) = all_91_2
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (164) with fresh symbol all_213_0 gives:
% 104.53/14.49  | | | | |   (201)  cons(all_213_0, nil) = all_91_0 & $i(all_213_0) &
% 104.53/14.49  | | | | |          ssItem(all_213_0)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (201) implies:
% 104.53/14.49  | | | | |   (202)  ssItem(all_213_0)
% 104.53/14.49  | | | | |   (203)  $i(all_213_0)
% 104.53/14.49  | | | | |   (204)  cons(all_213_0, nil) = all_91_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (180) with fresh symbol all_217_0 gives:
% 104.53/14.49  | | | | |   (205)  app(all_150_0, nil) = all_217_0 & app(all_91_0, all_217_0) =
% 104.53/14.49  | | | | |          all_91_0 & $i(all_217_0)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (205) implies:
% 104.53/14.49  | | | | |   (206)  app(all_150_0, nil) = all_217_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (184) with fresh symbol all_219_0 gives:
% 104.53/14.49  | | | | |   (207)  app(all_116_0, nil) = all_219_0 & app(all_116_2, all_219_0) =
% 104.53/14.49  | | | | |          nil & $i(all_219_0)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (207) implies:
% 104.53/14.49  | | | | |   (208)  app(all_116_0, nil) = all_219_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (179) with fresh symbol all_229_0 gives:
% 104.53/14.49  | | | | |   (209)  app(all_91_0, all_229_0) = all_91_0 & app(nil, all_150_0) =
% 104.53/14.49  | | | | |          all_229_0 & $i(all_229_0)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (209) implies:
% 104.53/14.49  | | | | |   (210)  app(nil, all_150_0) = all_229_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (183) with fresh symbol all_247_0 gives:
% 104.53/14.49  | | | | |   (211)  app(all_116_0, all_116_0) = all_247_0 & app(all_116_2,
% 104.53/14.49  | | | | |            all_247_0) = all_132_0 & $i(all_247_0) & $i(all_132_0)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (211) implies:
% 104.53/14.49  | | | | |   (212)  app(all_116_0, all_116_0) = all_247_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (173) with fresh symbol all_253_0 gives:
% 104.53/14.49  | | | | |   (213)  app(all_134_0, all_152_0) = all_253_0 & app(nil, all_253_0) =
% 104.53/14.49  | | | | |          all_91_2 & $i(all_253_0) & $i(all_91_2)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (213) implies:
% 104.53/14.49  | | | | |   (214)  $i(all_253_0)
% 104.53/14.49  | | | | |   (215)  app(all_134_0, all_152_0) = all_253_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (188) with fresh symbol all_257_0 gives:
% 104.53/14.49  | | | | |   (216)  app(all_146_0, all_257_0) = all_91_2 & app(all_91_3,
% 104.53/14.49  | | | | |            all_91_0) = all_257_0 & $i(all_257_0) & $i(all_91_2)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (216) implies:
% 104.53/14.49  | | | | |   (217)  app(all_91_3, all_91_0) = all_257_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (166) with fresh symbol all_259_0 gives:
% 104.53/14.49  | | | | |   (218)  app(nil, all_259_0) = all_132_0 & app(nil, all_116_0) =
% 104.53/14.49  | | | | |          all_259_0 & $i(all_259_0) & $i(all_132_0)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (218) implies:
% 104.53/14.49  | | | | |   (219)  app(nil, all_116_0) = all_259_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (182) with fresh symbol all_269_0 gives:
% 104.53/14.49  | | | | |   (220)  app(all_116_0, all_136_0) = all_269_0 & app(all_116_2,
% 104.53/14.49  | | | | |            all_269_0) = all_91_3 & $i(all_269_0) & $i(all_91_3)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (220) implies:
% 104.53/14.49  | | | | |   (221)  $i(all_269_0)
% 104.53/14.49  | | | | |   (222)  app(all_116_0, all_136_0) = all_269_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (172) with fresh symbol all_271_0 gives:
% 104.53/14.49  | | | | |   (223)  app(all_136_0, all_138_0) = all_271_0 & app(nil, all_271_0) =
% 104.53/14.49  | | | | |          all_91_3 & $i(all_271_0) & $i(all_91_3)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (223) implies:
% 104.53/14.49  | | | | |   (224)  app(all_136_0, all_138_0) = all_271_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (181) with fresh symbol all_273_0 gives:
% 104.53/14.49  | | | | |   (225)  cons(all_91_1, all_116_2) = all_273_0 & app(all_273_0,
% 104.53/14.49  | | | | |            all_116_0) = all_91_0 & $i(all_273_0) & $i(all_91_0)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (225) implies:
% 104.53/14.49  | | | | |   (226)  $i(all_273_0)
% 104.53/14.49  | | | | |   (227)  cons(all_91_1, all_116_2) = all_273_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (170) with fresh symbol all_275_0 gives:
% 104.53/14.49  | | | | |   (228)  app(nil, all_275_0) = all_91_3 & app(nil, all_136_0) =
% 104.53/14.49  | | | | |          all_275_0 & $i(all_275_0) & $i(all_91_3)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (228) implies:
% 104.53/14.49  | | | | |   (229)  app(nil, all_136_0) = all_275_0
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | DELTA: instantiating (169) with fresh symbol all_277_0 gives:
% 104.53/14.49  | | | | |   (230)  app(all_136_0, all_91_0) = all_277_0 & app(nil, all_277_0) =
% 104.53/14.49  | | | | |          all_91_2 & $i(all_277_0) & $i(all_91_2)
% 104.53/14.49  | | | | | 
% 104.53/14.49  | | | | | ALPHA: (230) implies:
% 104.53/14.50  | | | | |   (231)  app(all_136_0, all_91_0) = all_277_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (186), (227) imply:
% 104.53/14.50  | | | | |   (232)  cons(all_91_1, nil) = all_273_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (178), (193) imply:
% 104.53/14.50  | | | | |   (233)  app(nil, nil) = all_193_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (178), (206) imply:
% 104.53/14.50  | | | | |   (234)  app(nil, nil) = all_217_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (128), (189) imply:
% 104.53/14.50  | | | | |   (235)  app(all_91_3, nil) = all_91_3
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (120), (187) imply:
% 104.53/14.50  | | | | |   (236)  app(all_91_2, nil) = all_91_2
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (171), (224) imply:
% 104.53/14.50  | | | | |   (237)  app(all_91_3, all_138_0) = all_271_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (171), (231) imply:
% 104.53/14.50  | | | | |   (238)  app(all_91_3, all_91_0) = all_277_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (168), (215) imply:
% 104.53/14.50  | | | | |   (239)  app(all_91_2, all_152_0) = all_253_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (171), (185), (222) imply:
% 104.53/14.50  | | | | |   (240)  app(nil, all_91_3) = all_269_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (185), (212) imply:
% 104.53/14.50  | | | | |   (241)  app(nil, nil) = all_247_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (185), (208) imply:
% 104.53/14.50  | | | | |   (242)  app(nil, nil) = all_219_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (178), (210) imply:
% 104.53/14.50  | | | | |   (243)  app(nil, nil) = all_229_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (171), (229) imply:
% 104.53/14.50  | | | | |   (244)  app(nil, all_91_3) = all_275_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (109), (171) imply:
% 104.53/14.50  | | | | |   (245)  app(nil, all_91_3) = all_91_3
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | REDUCE: (185), (219) imply:
% 104.53/14.50  | | | | |   (246)  app(nil, nil) = all_259_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with nil, all_217_0, nil, nil,
% 104.53/14.50  | | | | |              simplifying with (163), (234) gives:
% 104.53/14.50  | | | | |   (247)  all_217_0 = nil
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with all_217_0, all_229_0, nil, nil,
% 104.53/14.50  | | | | |              simplifying with (234), (243) gives:
% 104.53/14.50  | | | | |   (248)  all_229_0 = all_217_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with all_193_0, all_229_0, nil, nil,
% 104.53/14.50  | | | | |              simplifying with (233), (243) gives:
% 104.53/14.50  | | | | |   (249)  all_229_0 = all_193_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with all_229_0, all_247_0, nil, nil,
% 104.53/14.50  | | | | |              simplifying with (241), (243) gives:
% 104.53/14.50  | | | | |   (250)  all_247_0 = all_229_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with all_247_0, all_259_0, nil, nil,
% 104.53/14.50  | | | | |              simplifying with (241), (246) gives:
% 104.53/14.50  | | | | |   (251)  all_259_0 = all_247_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with all_219_0, all_259_0, nil, nil,
% 104.53/14.50  | | | | |              simplifying with (242), (246) gives:
% 104.53/14.50  | | | | |   (252)  all_259_0 = all_219_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with all_269_0, all_275_0, all_91_3,
% 104.53/14.50  | | | | |              nil, simplifying with (240), (244) gives:
% 104.53/14.50  | | | | |   (253)  all_275_0 = all_269_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with all_91_3, all_275_0, all_91_3,
% 104.53/14.50  | | | | |              nil, simplifying with (244), (245) gives:
% 104.53/14.50  | | | | |   (254)  all_275_0 = all_91_3
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with all_91_2, all_277_0, all_91_0,
% 104.53/14.50  | | | | |              all_91_3, simplifying with (36), (238) gives:
% 104.53/14.50  | | | | |   (255)  all_277_0 = all_91_2
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with all_257_0, all_277_0, all_91_0,
% 104.53/14.50  | | | | |              all_91_3, simplifying with (217), (238) gives:
% 104.53/14.50  | | | | |   (256)  all_277_0 = all_257_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with all_91_3, all_271_0, all_138_0,
% 104.53/14.50  | | | | |              all_91_3, simplifying with (113), (237) gives:
% 104.53/14.50  | | | | |   (257)  all_271_0 = all_91_3
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (26) with all_91_2, all_253_0, all_152_0,
% 104.53/14.50  | | | | |              all_91_2, simplifying with (136), (239) gives:
% 104.53/14.50  | | | | |   (258)  all_253_0 = all_91_2
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (27) with all_91_0, all_273_0, nil,
% 104.53/14.50  | | | | |              all_91_1, simplifying with (37), (232) gives:
% 104.53/14.50  | | | | |   (259)  all_273_0 = all_91_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | COMBINE_EQS: (255), (256) imply:
% 104.53/14.50  | | | | |   (260)  all_257_0 = all_91_2
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | COMBINE_EQS: (253), (254) imply:
% 104.53/14.50  | | | | |   (261)  all_269_0 = all_91_3
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | SIMP: (261) implies:
% 104.53/14.50  | | | | |   (262)  all_269_0 = all_91_3
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | COMBINE_EQS: (251), (252) imply:
% 104.53/14.50  | | | | |   (263)  all_247_0 = all_219_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | SIMP: (263) implies:
% 104.53/14.50  | | | | |   (264)  all_247_0 = all_219_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | COMBINE_EQS: (250), (264) imply:
% 104.53/14.50  | | | | |   (265)  all_229_0 = all_219_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | SIMP: (265) implies:
% 104.53/14.50  | | | | |   (266)  all_229_0 = all_219_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | COMBINE_EQS: (248), (266) imply:
% 104.53/14.50  | | | | |   (267)  all_219_0 = all_217_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | COMBINE_EQS: (249), (266) imply:
% 104.53/14.50  | | | | |   (268)  all_219_0 = all_193_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | COMBINE_EQS: (267), (268) imply:
% 104.53/14.50  | | | | |   (269)  all_217_0 = all_193_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | SIMP: (269) implies:
% 104.53/14.50  | | | | |   (270)  all_217_0 = all_193_0
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | COMBINE_EQS: (247), (270) imply:
% 104.53/14.50  | | | | |   (271)  all_193_0 = nil
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | SIMP: (271) implies:
% 104.53/14.50  | | | | |   (272)  all_193_0 = nil
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (ax80) with nil, all_91_3, all_91_3,
% 104.53/14.50  | | | | |              all_138_0, simplifying with (7), (23), (30), (32), (111),
% 104.53/14.50  | | | | |              (112), (113), (235) gives:
% 104.53/14.50  | | | | |   (273)  all_138_0 = nil
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (ax82) with all_146_0, all_91_3, all_91_3,
% 104.53/14.50  | | | | |              all_152_0, all_197_0, simplifying with (30), (32), (122),
% 104.53/14.50  | | | | |              (123), (124), (134), (135), (196) gives:
% 104.53/14.50  | | | | |   (274)   ? [v0: $i] : (app(all_146_0, v0) = all_197_0 & app(all_91_3,
% 104.53/14.50  | | | | |              all_152_0) = v0 & $i(v0) & $i(all_197_0))
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (ax82) with nil, all_91_3, all_91_3,
% 104.53/14.50  | | | | |              all_152_0, all_197_0, simplifying with (7), (23), (30),
% 104.53/14.50  | | | | |              (32), (134), (135), (196), (245) gives:
% 104.53/14.50  | | | | |   (275)   ? [v0: $i] : (app(all_91_3, all_152_0) = v0 & app(nil, v0) =
% 104.53/14.50  | | | | |            all_197_0 & $i(v0) & $i(all_197_0))
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (ax80) with nil, all_91_2, all_91_2,
% 104.53/14.50  | | | | |              all_152_0, simplifying with (7), (23), (31), (33), (134),
% 104.53/14.50  | | | | |              (135), (136), (236) gives:
% 104.53/14.50  | | | | |   (276)  all_152_0 = nil
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (ax79) with all_205_0, all_91_0, all_91_2,
% 104.53/14.50  | | | | |              all_91_3, simplifying with (30), (32), (35), (36), (62),
% 104.53/14.50  | | | | |              (198), (199), (200) gives:
% 104.53/14.50  | | | | |   (277)  all_205_0 = all_91_3
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (38) with all_213_0, all_91_0, all_205_0,
% 104.53/14.50  | | | | |              all_91_2, all_152_0, simplifying with (134), (135),
% 104.53/14.50  | | | | |              (136), (198), (199), (200), (202), (203), (204) gives:
% 104.53/14.50  | | | | |   (278)   ? [v0: any] : ( ~ (v0 = all_91_3) & app(all_205_0,
% 104.53/14.50  | | | | |              all_152_0) = v0 & $i(v0))
% 104.53/14.50  | | | | | 
% 104.53/14.50  | | | | | GROUND_INST: instantiating (38) with all_213_0, all_91_0, all_91_3,
% 104.53/14.50  | | | | |              all_91_2, nil, simplifying with (7), (23), (30), (32),
% 104.53/14.50  | | | | |              (36), (202), (203), (204), (236) gives:
% 104.53/14.50  | | | | |   (279)   ? [v0: any] : ( ~ (v0 = all_91_3) & app(all_91_3, nil) = v0
% 104.53/14.50  | | | | |            & $i(v0))
% 104.53/14.50  | | | | | 
% 104.53/14.51  | | | | | GROUND_INST: instantiating (38) with all_213_0, all_91_0, all_205_0,
% 104.53/14.51  | | | | |              all_91_2, nil, simplifying with (7), (23), (198), (199),
% 104.53/14.51  | | | | |              (200), (202), (203), (204), (236) gives:
% 104.53/14.51  | | | | |   (280)   ? [v0: any] : ( ~ (v0 = all_91_3) & app(all_205_0, nil) = v0
% 104.53/14.51  | | | | |            & $i(v0))
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | DELTA: instantiating (280) with fresh symbol all_323_0 gives:
% 104.53/14.51  | | | | |   (281)   ~ (all_323_0 = all_91_3) & app(all_205_0, nil) = all_323_0 &
% 104.53/14.51  | | | | |          $i(all_323_0)
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | ALPHA: (281) implies:
% 104.53/14.51  | | | | |   (282)  app(all_205_0, nil) = all_323_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | DELTA: instantiating (279) with fresh symbol all_347_0 gives:
% 104.53/14.51  | | | | |   (283)   ~ (all_347_0 = all_91_3) & app(all_91_3, nil) = all_347_0 &
% 104.53/14.51  | | | | |          $i(all_347_0)
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | ALPHA: (283) implies:
% 104.53/14.51  | | | | |   (284)  app(all_91_3, nil) = all_347_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | DELTA: instantiating (278) with fresh symbol all_349_0 gives:
% 104.53/14.51  | | | | |   (285)   ~ (all_349_0 = all_91_3) & app(all_205_0, all_152_0) =
% 104.53/14.51  | | | | |          all_349_0 & $i(all_349_0)
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | ALPHA: (285) implies:
% 104.53/14.51  | | | | |   (286)  app(all_205_0, all_152_0) = all_349_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | DELTA: instantiating (275) with fresh symbol all_745_0 gives:
% 104.53/14.51  | | | | |   (287)  app(all_91_3, all_152_0) = all_745_0 & app(nil, all_745_0) =
% 104.53/14.51  | | | | |          all_197_0 & $i(all_745_0) & $i(all_197_0)
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | ALPHA: (287) implies:
% 104.53/14.51  | | | | |   (288)  app(all_91_3, all_152_0) = all_745_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | DELTA: instantiating (274) with fresh symbol all_747_0 gives:
% 104.53/14.51  | | | | |   (289)  app(all_146_0, all_747_0) = all_197_0 & app(all_91_3,
% 104.53/14.51  | | | | |            all_152_0) = all_747_0 & $i(all_747_0) & $i(all_197_0)
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | ALPHA: (289) implies:
% 104.53/14.51  | | | | |   (290)  app(all_91_3, all_152_0) = all_747_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | REDUCE: (276), (277), (286) imply:
% 104.53/14.51  | | | | |   (291)  app(all_91_3, nil) = all_349_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | REDUCE: (277), (282) imply:
% 104.53/14.51  | | | | |   (292)  app(all_91_3, nil) = all_323_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | REDUCE: (276), (290) imply:
% 104.53/14.51  | | | | |   (293)  app(all_91_3, nil) = all_747_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | REDUCE: (276), (288) imply:
% 104.53/14.51  | | | | |   (294)  app(all_91_3, nil) = all_745_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | REDUCE: (196), (276) imply:
% 104.53/14.51  | | | | |   (295)  app(all_91_3, nil) = all_197_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | GROUND_INST: instantiating (26) with all_347_0, all_349_0, nil,
% 104.53/14.51  | | | | |              all_91_3, simplifying with (284), (291) gives:
% 104.53/14.51  | | | | |   (296)  all_349_0 = all_347_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | GROUND_INST: instantiating (26) with all_323_0, all_349_0, nil,
% 104.53/14.51  | | | | |              all_91_3, simplifying with (291), (292) gives:
% 104.53/14.51  | | | | |   (297)  all_349_0 = all_323_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | GROUND_INST: instantiating (26) with all_347_0, all_745_0, nil,
% 104.53/14.51  | | | | |              all_91_3, simplifying with (284), (294) gives:
% 104.53/14.51  | | | | |   (298)  all_745_0 = all_347_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | GROUND_INST: instantiating (26) with all_197_0, all_745_0, nil,
% 104.53/14.51  | | | | |              all_91_3, simplifying with (294), (295) gives:
% 104.53/14.51  | | | | |   (299)  all_745_0 = all_197_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | GROUND_INST: instantiating (26) with all_91_3, all_747_0, nil,
% 104.53/14.51  | | | | |              all_91_3, simplifying with (235), (293) gives:
% 104.53/14.51  | | | | |   (300)  all_747_0 = all_91_3
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | GROUND_INST: instantiating (26) with all_349_0, all_747_0, nil,
% 104.53/14.51  | | | | |              all_91_3, simplifying with (291), (293) gives:
% 104.53/14.51  | | | | |   (301)  all_747_0 = all_349_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | COMBINE_EQS: (300), (301) imply:
% 104.53/14.51  | | | | |   (302)  all_349_0 = all_91_3
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | SIMP: (302) implies:
% 104.53/14.51  | | | | |   (303)  all_349_0 = all_91_3
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | COMBINE_EQS: (298), (299) imply:
% 104.53/14.51  | | | | |   (304)  all_347_0 = all_197_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | SIMP: (304) implies:
% 104.53/14.51  | | | | |   (305)  all_347_0 = all_197_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | COMBINE_EQS: (297), (303) imply:
% 104.53/14.51  | | | | |   (306)  all_323_0 = all_91_3
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | COMBINE_EQS: (296), (297) imply:
% 104.53/14.51  | | | | |   (307)  all_347_0 = all_323_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | SIMP: (307) implies:
% 104.53/14.51  | | | | |   (308)  all_347_0 = all_323_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | COMBINE_EQS: (305), (308) imply:
% 104.53/14.51  | | | | |   (309)  all_323_0 = all_197_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | SIMP: (309) implies:
% 104.53/14.51  | | | | |   (310)  all_323_0 = all_197_0
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | COMBINE_EQS: (306), (310) imply:
% 104.53/14.51  | | | | |   (311)  all_197_0 = all_91_3
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | REDUCE: (195), (311) imply:
% 104.53/14.51  | | | | |   (312)  $false
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | | CLOSE: (312) is inconsistent.
% 104.53/14.51  | | | | | 
% 104.53/14.51  | | | | End of split
% 104.53/14.51  | | | | 
% 104.53/14.51  | | | End of split
% 104.53/14.51  | | | 
% 104.53/14.51  | | End of split
% 104.53/14.51  | | 
% 104.53/14.51  | End of split
% 104.53/14.51  | 
% 104.53/14.51  End of proof
% 104.53/14.51  % SZS output end Proof for theBenchmark
% 104.53/14.51  
% 104.53/14.51  13914ms
%------------------------------------------------------------------------------