TSTP Solution File: SWC274+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC274+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 20:50:35 EDT 2023

% Result   : Theorem 143.50s 19.43s
% Output   : Proof 143.86s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SWC274+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.08  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.07/0.26  % Computer : n032.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Mon Aug 28 17:28:01 EDT 2023
% 0.07/0.26  % CPUTime  : 
% 0.12/0.50  ________       _____
% 0.12/0.50  ___  __ \_________(_)________________________________
% 0.12/0.50  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.12/0.50  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.12/0.50  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.12/0.50  
% 0.12/0.50  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.12/0.50  (2023-06-19)
% 0.12/0.50  
% 0.12/0.50  (c) Philipp Rümmer, 2009-2023
% 0.12/0.50  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.12/0.50                Amanda Stjerna.
% 0.12/0.50  Free software under BSD-3-Clause.
% 0.12/0.50  
% 0.12/0.50  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.12/0.50  
% 0.12/0.50  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.12/0.51  Running up to 7 provers in parallel.
% 0.12/0.52  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.12/0.52  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.12/0.52  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.12/0.52  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.12/0.52  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.12/0.52  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.12/0.52  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.36/1.29  Prover 1: Preprocessing ...
% 4.36/1.29  Prover 4: Preprocessing ...
% 5.02/1.33  Prover 2: Preprocessing ...
% 5.02/1.33  Prover 5: Preprocessing ...
% 5.02/1.33  Prover 3: Preprocessing ...
% 5.02/1.33  Prover 0: Preprocessing ...
% 5.02/1.33  Prover 6: Preprocessing ...
% 15.29/2.68  Prover 2: Proving ...
% 15.67/2.72  Prover 6: Proving ...
% 15.67/2.73  Prover 5: Constructing countermodel ...
% 15.81/2.73  Prover 1: Constructing countermodel ...
% 15.81/2.74  Prover 3: Constructing countermodel ...
% 22.42/3.66  Prover 4: Constructing countermodel ...
% 24.21/3.84  Prover 0: Proving ...
% 73.16/10.20  Prover 2: stopped
% 73.59/10.22  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.54/10.39  Prover 7: Preprocessing ...
% 76.83/10.62  Prover 7: Constructing countermodel ...
% 102.18/13.90  Prover 5: stopped
% 102.18/13.90  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 102.18/14.04  Prover 8: Preprocessing ...
% 105.27/14.34  Prover 8: Warning: ignoring some quantifiers
% 105.27/14.35  Prover 8: Constructing countermodel ...
% 116.92/15.86  Prover 1: stopped
% 116.92/15.87  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 118.22/16.02  Prover 9: Preprocessing ...
% 125.20/16.93  Prover 9: Constructing countermodel ...
% 130.55/17.77  Prover 6: stopped
% 130.55/17.77  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 132.21/17.91  Prover 10: Preprocessing ...
% 132.98/18.05  Prover 10: Constructing countermodel ...
% 143.50/19.40  Prover 10: Found proof (size 20)
% 143.50/19.41  Prover 10: proved (1638ms)
% 143.50/19.41  Prover 3: stopped
% 143.50/19.41  Prover 7: stopped
% 143.50/19.41  Prover 8: stopped
% 143.50/19.41  Prover 9: stopped
% 143.50/19.41  Prover 4: stopped
% 143.50/19.43  Prover 0: stopped
% 143.50/19.43  
% 143.50/19.43  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 143.50/19.43  
% 143.50/19.43  % SZS output start Proof for theBenchmark
% 143.50/19.43  Assumptions after simplification:
% 143.50/19.43  ---------------------------------
% 143.50/19.43  
% 143.50/19.43    (ax11)
% 143.50/19.46     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 143.50/19.46      $i] :  ! [v6: $i] :  ! [v7: $i] :  ! [v8: $i] : ( ~ (cons(v2, v7) = v8) |  ~
% 143.50/19.47      (cons(v1, v4) = v5) |  ~ (app(v6, v8) = v0) |  ~ (app(v3, v5) = v6) |  ~
% 143.50/19.47      $i(v7) |  ~ $i(v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 143.50/19.47      totalorderedP(v0) |  ~ ssList(v7) |  ~ ssList(v4) |  ~ ssList(v3) |  ~
% 143.50/19.47      ssList(v0) |  ~ ssItem(v2) |  ~ ssItem(v1) | leq(v1, v2)) &  ! [v0: $i] : (
% 143.50/19.47      ~ $i(v0) |  ~ ssList(v0) | totalorderedP(v0) |  ? [v1: $i] :  ? [v2: $i] : 
% 143.50/19.47      ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 143.50/19.47        $i] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3,
% 143.50/19.47          v5) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 143.50/19.47        & $i(v1) & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1)
% 143.50/19.47        &  ~ leq(v1, v2)))
% 143.50/19.47  
% 143.50/19.47    (ax12)
% 143.50/19.47     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 143.50/19.47      $i] :  ! [v6: $i] :  ! [v7: $i] :  ! [v8: $i] : ( ~ (cons(v2, v7) = v8) |  ~
% 143.50/19.47      (cons(v1, v4) = v5) |  ~ (app(v6, v8) = v0) |  ~ (app(v3, v5) = v6) |  ~
% 143.50/19.47      $i(v7) |  ~ $i(v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 143.50/19.47      strictorderedP(v0) |  ~ ssList(v7) |  ~ ssList(v4) |  ~ ssList(v3) |  ~
% 143.50/19.47      ssList(v0) |  ~ ssItem(v2) |  ~ ssItem(v1) | lt(v1, v2)) &  ! [v0: $i] : ( ~
% 143.50/19.47      $i(v0) |  ~ ssList(v0) | strictorderedP(v0) |  ? [v1: $i] :  ? [v2: $i] :  ?
% 143.50/19.47      [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 143.50/19.47        $i] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3,
% 143.50/19.47          v5) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 143.50/19.47        & $i(v1) & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1)
% 143.50/19.47        &  ~ lt(v1, v2)))
% 143.50/19.47  
% 143.50/19.47    (ax17)
% 143.50/19.47    $i(nil) & ssList(nil)
% 143.50/19.47  
% 143.50/19.47    (ax58)
% 143.50/19.47    $i(nil) &  ! [v0: $i] : (v0 = nil |  ~ $i(v0) |  ~ segmentP(nil, v0) |  ~
% 143.50/19.47      ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 143.50/19.47  
% 143.86/19.47    (ax93)
% 143.86/19.48     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v0, v1)
% 143.86/19.48      |  ~ ssItem(v1) |  ~ ssItem(v0) | lt(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] :
% 143.86/19.48    ( ~ $i(v1) |  ~ $i(v0) |  ~ lt(v0, v1) |  ~ ssItem(v1) |  ~ ssItem(v0) |
% 143.86/19.48      leq(v0, v1)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ lt(v0, v0) |  ~ ssItem(v0))
% 143.86/19.48  
% 143.86/19.48    (co1)
% 143.86/19.48    $i(nil) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i]
% 143.86/19.48    : (app(v3, v4) = v1 & app(v2, v0) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 143.86/19.48      $i(v0) & strictorderedP(v0) & ssList(v4) & ssList(v2) & ssList(v1) &
% 143.86/19.48      ssList(v0) &  ~ totalorderedP(v0) &  ! [v5: $i] :  ! [v6: $i] :  ! [v7: $i]
% 143.86/19.48      :  ! [v8: $i] :  ! [v9: $i] :  ! [v10: $i] : ( ~ (cons(v8, nil) = v9) |  ~
% 143.86/19.48        (cons(v5, nil) = v6) |  ~ (app(v10, v9) = v0) |  ~ (app(v6, v7) = v4) |  ~
% 143.86/19.48        $i(v10) |  ~ $i(v8) |  ~ $i(v7) |  ~ $i(v5) |  ~ lt(v8, v5) |  ~
% 143.86/19.48        ssList(v10) |  ~ ssList(v7) |  ~ ssItem(v8) |  ~ ssItem(v5)) &  ! [v5: $i]
% 143.86/19.48      :  ! [v6: $i] :  ! [v7: $i] :  ! [v8: $i] :  ! [v9: $i] :  ! [v10: $i] : ( ~
% 143.86/19.48        (cons(v8, nil) = v9) |  ~ (cons(v5, nil) = v6) |  ~ (app(v9, v10) = v0) | 
% 143.86/19.48        ~ (app(v7, v6) = v2) |  ~ $i(v10) |  ~ $i(v8) |  ~ $i(v7) |  ~ $i(v5) |  ~
% 143.86/19.48        lt(v5, v8) |  ~ ssList(v10) |  ~ ssList(v7) |  ~ ssItem(v8) |  ~
% 143.86/19.48        ssItem(v5)) & ( ~ (v0 = nil) | v1 = nil))
% 143.86/19.48  
% 143.86/19.48  Further assumptions not needed in the proof:
% 143.86/19.48  --------------------------------------------
% 143.86/19.48  ax1, ax10, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21, ax22, ax23,
% 143.86/19.48  ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35,
% 143.86/19.48  ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47,
% 143.86/19.48  ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6,
% 143.86/19.48  ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71,
% 143.86/19.48  ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83,
% 143.86/19.48  ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax94, ax95
% 143.86/19.48  
% 143.86/19.48  Those formulas are unsatisfiable:
% 143.86/19.48  ---------------------------------
% 143.86/19.48  
% 143.86/19.48  Begin of proof
% 143.86/19.49  | 
% 143.86/19.49  | ALPHA: (ax11) implies:
% 143.86/19.49  |   (1)   ! [v0: $i] : ( ~ $i(v0) |  ~ ssList(v0) | totalorderedP(v0) |  ? [v1:
% 143.86/19.49  |            $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ?
% 143.86/19.49  |          [v6: $i] :  ? [v7: $i] :  ? [v8: $i] : (cons(v2, v7) = v8 & cons(v1,
% 143.86/19.49  |              v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & $i(v8) & $i(v7)
% 143.86/19.49  |            & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & ssList(v7)
% 143.86/19.49  |            & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) &  ~ leq(v1,
% 143.86/19.49  |              v2)))
% 143.86/19.49  | 
% 143.86/19.49  | ALPHA: (ax12) implies:
% 143.86/19.49  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : 
% 143.86/19.49  |        ! [v5: $i] :  ! [v6: $i] :  ! [v7: $i] :  ! [v8: $i] : ( ~ (cons(v2,
% 143.86/19.49  |              v7) = v8) |  ~ (cons(v1, v4) = v5) |  ~ (app(v6, v8) = v0) |  ~
% 143.86/19.49  |          (app(v3, v5) = v6) |  ~ $i(v7) |  ~ $i(v4) |  ~ $i(v3) |  ~ $i(v2) | 
% 143.86/19.49  |          ~ $i(v1) |  ~ $i(v0) |  ~ strictorderedP(v0) |  ~ ssList(v7) |  ~
% 143.86/19.49  |          ssList(v4) |  ~ ssList(v3) |  ~ ssList(v0) |  ~ ssItem(v2) |  ~
% 143.86/19.49  |          ssItem(v1) | lt(v1, v2))
% 143.86/19.49  | 
% 143.86/19.49  | ALPHA: (ax17) implies:
% 143.86/19.49  |   (3)  ssList(nil)
% 143.86/19.49  | 
% 143.86/19.49  | ALPHA: (ax58) implies:
% 143.86/19.49  |   (4)   ~ ssList(nil) | segmentP(nil, nil)
% 143.86/19.49  | 
% 143.86/19.49  | ALPHA: (ax93) implies:
% 143.86/19.50  |   (5)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ lt(v0, v1) |  ~
% 143.86/19.50  |          ssItem(v1) |  ~ ssItem(v0) | leq(v0, v1))
% 143.86/19.50  | 
% 143.86/19.50  | ALPHA: (co1) implies:
% 143.86/19.50  |   (6)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :
% 143.86/19.50  |        (app(v3, v4) = v1 & app(v2, v0) = v3 & $i(v4) & $i(v3) & $i(v2) &
% 143.86/19.50  |          $i(v1) & $i(v0) & strictorderedP(v0) & ssList(v4) & ssList(v2) &
% 143.86/19.50  |          ssList(v1) & ssList(v0) &  ~ totalorderedP(v0) &  ! [v5: $i] :  !
% 143.86/19.50  |          [v6: $i] :  ! [v7: $i] :  ! [v8: $i] :  ! [v9: $i] :  ! [v10: $i] : (
% 143.86/19.50  |            ~ (cons(v8, nil) = v9) |  ~ (cons(v5, nil) = v6) |  ~ (app(v10, v9)
% 143.86/19.50  |              = v0) |  ~ (app(v6, v7) = v4) |  ~ $i(v10) |  ~ $i(v8) |  ~
% 143.86/19.50  |            $i(v7) |  ~ $i(v5) |  ~ lt(v8, v5) |  ~ ssList(v10) |  ~ ssList(v7)
% 143.86/19.50  |            |  ~ ssItem(v8) |  ~ ssItem(v5)) &  ! [v5: $i] :  ! [v6: $i] :  !
% 143.86/19.50  |          [v7: $i] :  ! [v8: $i] :  ! [v9: $i] :  ! [v10: $i] : ( ~ (cons(v8,
% 143.86/19.50  |                nil) = v9) |  ~ (cons(v5, nil) = v6) |  ~ (app(v9, v10) = v0) |
% 143.86/19.50  |             ~ (app(v7, v6) = v2) |  ~ $i(v10) |  ~ $i(v8) |  ~ $i(v7) |  ~
% 143.86/19.50  |            $i(v5) |  ~ lt(v5, v8) |  ~ ssList(v10) |  ~ ssList(v7) |  ~
% 143.86/19.50  |            ssItem(v8) |  ~ ssItem(v5)) & ( ~ (v0 = nil) | v1 = nil))
% 143.86/19.50  | 
% 143.86/19.50  | DELTA: instantiating (6) with fresh symbols all_91_0, all_91_1, all_91_2,
% 143.86/19.50  |        all_91_3, all_91_4 gives:
% 143.86/19.51  |   (7)  app(all_91_1, all_91_0) = all_91_3 & app(all_91_2, all_91_4) = all_91_1
% 143.86/19.51  |        & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 143.86/19.51  |        $i(all_91_4) & strictorderedP(all_91_4) & ssList(all_91_0) &
% 143.86/19.51  |        ssList(all_91_2) & ssList(all_91_3) & ssList(all_91_4) &  ~
% 143.86/19.51  |        totalorderedP(all_91_4) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 143.86/19.51  |        [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : ( ~ (cons(v3, nil) = v4) |  ~
% 143.86/19.51  |          (cons(v0, nil) = v1) |  ~ (app(v5, v4) = all_91_4) |  ~ (app(v1, v2)
% 143.86/19.51  |            = all_91_0) |  ~ $i(v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v0) |  ~
% 143.86/19.51  |          lt(v3, v0) |  ~ ssList(v5) |  ~ ssList(v2) |  ~ ssItem(v3) |  ~
% 143.86/19.51  |          ssItem(v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :
% 143.86/19.51  |         ! [v4: $i] :  ! [v5: $i] : ( ~ (cons(v3, nil) = v4) |  ~ (cons(v0,
% 143.86/19.51  |              nil) = v1) |  ~ (app(v4, v5) = all_91_4) |  ~ (app(v2, v1) =
% 143.86/19.51  |            all_91_2) |  ~ $i(v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v0) |  ~
% 143.86/19.51  |          lt(v0, v3) |  ~ ssList(v5) |  ~ ssList(v2) |  ~ ssItem(v3) |  ~
% 143.86/19.51  |          ssItem(v0)) & ( ~ (all_91_4 = nil) | all_91_3 = nil)
% 143.86/19.51  | 
% 143.86/19.51  | ALPHA: (7) implies:
% 143.86/19.51  |   (8)   ~ totalorderedP(all_91_4)
% 143.86/19.51  |   (9)  ssList(all_91_4)
% 143.86/19.51  |   (10)  strictorderedP(all_91_4)
% 143.86/19.51  |   (11)  $i(all_91_4)
% 143.86/19.51  | 
% 143.86/19.51  | BETA: splitting (4) gives:
% 143.86/19.51  | 
% 143.86/19.51  | Case 1:
% 143.86/19.51  | | 
% 143.86/19.51  | |   (12)   ~ ssList(nil)
% 143.86/19.51  | | 
% 143.86/19.51  | | PRED_UNIFY: (3), (12) imply:
% 143.86/19.51  | |   (13)  $false
% 143.86/19.51  | | 
% 143.86/19.51  | | CLOSE: (13) is inconsistent.
% 143.86/19.51  | | 
% 143.86/19.51  | Case 2:
% 143.86/19.51  | | 
% 143.86/19.51  | | 
% 143.86/19.51  | | GROUND_INST: instantiating (1) with all_91_4, simplifying with (8), (9),
% 143.86/19.51  | |              (11) gives:
% 143.86/19.52  | |   (14)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i]
% 143.86/19.52  | |         :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] : (cons(v1, v6) = v7 &
% 143.86/19.52  | |           cons(v0, v3) = v4 & app(v5, v7) = all_91_4 & app(v2, v4) = v5 &
% 143.86/19.52  | |           $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 143.86/19.52  | |           $i(v0) & ssList(v6) & ssList(v3) & ssList(v2) & ssItem(v1) &
% 143.86/19.52  | |           ssItem(v0) &  ~ leq(v0, v1))
% 143.86/19.52  | | 
% 143.86/19.52  | | DELTA: instantiating (14) with fresh symbols all_120_0, all_120_1,
% 143.86/19.52  | |        all_120_2, all_120_3, all_120_4, all_120_5, all_120_6, all_120_7
% 143.86/19.52  | |        gives:
% 143.86/19.52  | |   (15)  cons(all_120_6, all_120_1) = all_120_0 & cons(all_120_7, all_120_4)
% 143.86/19.52  | |         = all_120_3 & app(all_120_2, all_120_0) = all_91_4 & app(all_120_5,
% 143.86/19.52  | |           all_120_3) = all_120_2 & $i(all_120_0) & $i(all_120_1) &
% 143.86/19.52  | |         $i(all_120_2) & $i(all_120_3) & $i(all_120_4) & $i(all_120_5) &
% 143.86/19.52  | |         $i(all_120_6) & $i(all_120_7) & ssList(all_120_1) &
% 143.86/19.52  | |         ssList(all_120_4) & ssList(all_120_5) & ssItem(all_120_6) &
% 143.86/19.52  | |         ssItem(all_120_7) &  ~ leq(all_120_7, all_120_6)
% 143.86/19.52  | | 
% 143.86/19.52  | | ALPHA: (15) implies:
% 143.86/19.52  | |   (16)   ~ leq(all_120_7, all_120_6)
% 143.86/19.52  | |   (17)  ssItem(all_120_7)
% 143.86/19.52  | |   (18)  ssItem(all_120_6)
% 143.86/19.52  | |   (19)  ssList(all_120_5)
% 143.86/19.52  | |   (20)  ssList(all_120_4)
% 143.86/19.52  | |   (21)  ssList(all_120_1)
% 143.86/19.52  | |   (22)  $i(all_120_7)
% 143.86/19.52  | |   (23)  $i(all_120_6)
% 143.86/19.52  | |   (24)  $i(all_120_5)
% 143.86/19.52  | |   (25)  $i(all_120_4)
% 143.86/19.52  | |   (26)  $i(all_120_1)
% 143.86/19.52  | |   (27)  app(all_120_5, all_120_3) = all_120_2
% 143.86/19.52  | |   (28)  app(all_120_2, all_120_0) = all_91_4
% 143.86/19.52  | |   (29)  cons(all_120_7, all_120_4) = all_120_3
% 143.86/19.52  | |   (30)  cons(all_120_6, all_120_1) = all_120_0
% 143.86/19.52  | | 
% 143.86/19.52  | | GROUND_INST: instantiating (2) with all_91_4, all_120_7, all_120_6,
% 143.86/19.52  | |              all_120_5, all_120_4, all_120_3, all_120_2, all_120_1,
% 143.86/19.52  | |              all_120_0, simplifying with (9), (10), (11), (17), (18), (19),
% 143.86/19.52  | |              (20), (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 143.86/19.52  | |              (30) gives:
% 143.86/19.52  | |   (31)  lt(all_120_7, all_120_6)
% 143.86/19.52  | | 
% 143.86/19.52  | | GROUND_INST: instantiating (5) with all_120_7, all_120_6, simplifying with
% 143.86/19.52  | |              (16), (17), (18), (22), (23), (31) gives:
% 143.86/19.52  | |   (32)  $false
% 143.86/19.52  | | 
% 143.86/19.52  | | CLOSE: (32) is inconsistent.
% 143.86/19.52  | | 
% 143.86/19.52  | End of split
% 143.86/19.52  | 
% 143.86/19.52  End of proof
% 143.86/19.53  % SZS output end Proof for theBenchmark
% 143.86/19.53  
% 143.86/19.53  19024ms
%------------------------------------------------------------------------------