TSTP Solution File: SWC399+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC399+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:51:14 EDT 2023

% Result   : Theorem 136.60s 18.40s
% Output   : Proof 136.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWC399+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Aug 28 16:39:50 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.60  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 0.20/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.62  Running up to 7 provers in parallel.
% 0.73/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.73/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.73/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.73/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.73/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.73/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.73/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.04/1.50  Prover 1: Preprocessing ...
% 6.04/1.52  Prover 4: Preprocessing ...
% 6.04/1.53  Prover 3: Preprocessing ...
% 6.04/1.53  Prover 2: Preprocessing ...
% 6.33/1.54  Prover 5: Preprocessing ...
% 6.33/1.54  Prover 0: Preprocessing ...
% 6.33/1.54  Prover 6: Preprocessing ...
% 15.74/2.86  Prover 2: Proving ...
% 15.74/2.88  Prover 5: Constructing countermodel ...
% 16.29/2.90  Prover 6: Proving ...
% 16.29/2.91  Prover 1: Constructing countermodel ...
% 16.29/2.91  Prover 3: Constructing countermodel ...
% 21.53/3.58  Prover 4: Constructing countermodel ...
% 22.21/3.69  Prover 0: Proving ...
% 73.73/10.30  Prover 2: stopped
% 73.73/10.30  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.53/10.42  Prover 7: Preprocessing ...
% 76.11/10.61  Prover 7: Constructing countermodel ...
% 101.82/13.97  Prover 5: stopped
% 102.62/13.99  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 104.17/14.20  Prover 8: Preprocessing ...
% 106.51/14.52  Prover 8: Warning: ignoring some quantifiers
% 106.51/14.53  Prover 8: Constructing countermodel ...
% 117.77/15.97  Prover 1: stopped
% 117.77/15.97  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 118.53/16.07  Prover 9: Preprocessing ...
% 124.26/16.81  Prover 9: Constructing countermodel ...
% 132.09/17.87  Prover 6: stopped
% 132.09/17.89  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 133.72/18.03  Prover 10: Preprocessing ...
% 134.49/18.14  Prover 10: Constructing countermodel ...
% 136.49/18.38  Prover 10: Found proof (size 16)
% 136.60/18.39  Prover 10: proved (497ms)
% 136.60/18.39  Prover 9: stopped
% 136.60/18.39  Prover 3: stopped
% 136.60/18.39  Prover 8: stopped
% 136.60/18.39  Prover 0: stopped
% 136.60/18.39  Prover 7: stopped
% 136.60/18.40  Prover 4: stopped
% 136.60/18.40  
% 136.60/18.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 136.60/18.40  
% 136.60/18.40  % SZS output start Proof for theBenchmark
% 136.60/18.41  Assumptions after simplification:
% 136.60/18.41  ---------------------------------
% 136.60/18.41  
% 136.60/18.41    (ax17)
% 136.70/18.41    $i(nil) & ssList(nil)
% 136.70/18.41  
% 136.70/18.41    (ax26)
% 136.73/18.44     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (app(v0, v1) = v2) |  ~ $i(v1) |
% 136.73/18.44       ~ $i(v0) |  ~ ssList(v1) |  ~ ssList(v0) | ssList(v2))
% 136.73/18.44  
% 136.73/18.44    (ax36)
% 136.73/18.44     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (app(v1, v2) = v3)
% 136.73/18.44      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ memberP(v3, v0) |  ~ ssList(v2) | 
% 136.73/18.44      ~ ssList(v1) |  ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0)) &  ! [v0:
% 136.73/18.44      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (app(v1, v2) = v3) |  ~
% 136.73/18.44      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ memberP(v2, v0) |  ~ ssList(v2) |  ~
% 136.73/18.44      ssList(v1) |  ~ ssItem(v0) | memberP(v3, v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 136.73/18.44    ! [v2: $i] :  ! [v3: $i] : ( ~ (app(v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 136.73/18.44      $i(v0) |  ~ memberP(v1, v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~ ssItem(v0)
% 136.73/18.44      | memberP(v3, v0))
% 136.73/18.44  
% 136.73/18.44    (ax58)
% 136.73/18.44    $i(nil) &  ! [v0: $i] : (v0 = nil |  ~ $i(v0) |  ~ segmentP(nil, v0) |  ~
% 136.73/18.44      ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 136.73/18.44  
% 136.73/18.44    (co1)
% 136.73/18.45    $i(nil) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i]
% 136.73/18.45    :  ? [v5: $i] : (app(v4, v5) = v1 & app(v3, v0) = v4 & $i(v5) & $i(v4) &
% 136.73/18.45      $i(v3) & $i(v2) & $i(v1) & $i(v0) & equalelemsP(v0) & memberP(v0, v2) &
% 136.73/18.45      ssList(v5) & ssList(v3) & ssList(v1) & ssList(v0) & ssItem(v2) &  ~
% 136.73/18.45      memberP(v1, v2) &  ! [v6: $i] :  ! [v7: $i] :  ! [v8: $i] :  ! [v9: $i] : (
% 136.73/18.45        ~ (cons(v6, nil) = v7) |  ~ (app(v9, v7) = v0) |  ~ (app(v7, v8) = v5) | 
% 136.73/18.45        ~ $i(v9) |  ~ $i(v8) |  ~ $i(v6) |  ~ ssList(v9) |  ~ ssList(v8) |  ~
% 136.73/18.45        ssItem(v6)) &  ! [v6: $i] :  ! [v7: $i] :  ! [v8: $i] :  ! [v9: $i] : ( ~
% 136.73/18.45        (cons(v6, nil) = v7) |  ~ (app(v8, v7) = v3) |  ~ (app(v7, v9) = v0) |  ~
% 136.73/18.45        $i(v9) |  ~ $i(v8) |  ~ $i(v6) |  ~ ssList(v9) |  ~ ssList(v8) |  ~
% 136.73/18.45        ssItem(v6)) & ( ~ (v0 = nil) | v1 = nil))
% 136.73/18.45  
% 136.73/18.45  Further assumptions not needed in the proof:
% 136.73/18.45  --------------------------------------------
% 136.73/18.45  ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 136.73/18.45  ax22, ax23, ax24, ax25, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 136.73/18.45  ax35, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47,
% 136.73/18.45  ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6,
% 136.73/18.45  ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71,
% 136.73/18.45  ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83,
% 136.73/18.45  ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 136.73/18.45  
% 136.73/18.45  Those formulas are unsatisfiable:
% 136.73/18.45  ---------------------------------
% 136.73/18.45  
% 136.73/18.45  Begin of proof
% 136.73/18.45  | 
% 136.73/18.45  | ALPHA: (ax17) implies:
% 136.73/18.45  |   (1)  ssList(nil)
% 136.73/18.45  | 
% 136.73/18.45  | ALPHA: (ax36) implies:
% 136.73/18.46  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (app(v1,
% 136.73/18.46  |              v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ memberP(v1,
% 136.73/18.46  |            v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~ ssItem(v0) | memberP(v3,
% 136.73/18.46  |            v0))
% 136.73/18.46  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (app(v1,
% 136.73/18.46  |              v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ memberP(v2,
% 136.73/18.46  |            v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~ ssItem(v0) | memberP(v3,
% 136.73/18.46  |            v0))
% 136.73/18.46  | 
% 136.73/18.46  | ALPHA: (ax58) implies:
% 136.73/18.46  |   (4)   ~ ssList(nil) | segmentP(nil, nil)
% 136.73/18.46  | 
% 136.73/18.46  | ALPHA: (co1) implies:
% 136.73/18.46  |   (5)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 136.73/18.46  |        ? [v5: $i] : (app(v4, v5) = v1 & app(v3, v0) = v4 & $i(v5) & $i(v4) &
% 136.73/18.46  |          $i(v3) & $i(v2) & $i(v1) & $i(v0) & equalelemsP(v0) & memberP(v0, v2)
% 136.73/18.46  |          & ssList(v5) & ssList(v3) & ssList(v1) & ssList(v0) & ssItem(v2) &  ~
% 136.73/18.46  |          memberP(v1, v2) &  ! [v6: $i] :  ! [v7: $i] :  ! [v8: $i] :  ! [v9:
% 136.73/18.46  |            $i] : ( ~ (cons(v6, nil) = v7) |  ~ (app(v9, v7) = v0) |  ~
% 136.73/18.46  |            (app(v7, v8) = v5) |  ~ $i(v9) |  ~ $i(v8) |  ~ $i(v6) |  ~
% 136.73/18.46  |            ssList(v9) |  ~ ssList(v8) |  ~ ssItem(v6)) &  ! [v6: $i] :  ! [v7:
% 136.73/18.46  |            $i] :  ! [v8: $i] :  ! [v9: $i] : ( ~ (cons(v6, nil) = v7) |  ~
% 136.73/18.46  |            (app(v8, v7) = v3) |  ~ (app(v7, v9) = v0) |  ~ $i(v9) |  ~ $i(v8)
% 136.73/18.46  |            |  ~ $i(v6) |  ~ ssList(v9) |  ~ ssList(v8) |  ~ ssItem(v6)) & ( ~
% 136.73/18.46  |            (v0 = nil) | v1 = nil))
% 136.73/18.46  | 
% 136.73/18.46  | DELTA: instantiating (5) with fresh symbols all_91_0, all_91_1, all_91_2,
% 136.73/18.46  |        all_91_3, all_91_4, all_91_5 gives:
% 136.73/18.47  |   (6)  app(all_91_1, all_91_0) = all_91_4 & app(all_91_2, all_91_5) = all_91_1
% 136.73/18.47  |        & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 136.73/18.47  |        $i(all_91_4) & $i(all_91_5) & equalelemsP(all_91_5) & memberP(all_91_5,
% 136.73/18.47  |          all_91_3) & ssList(all_91_0) & ssList(all_91_2) & ssList(all_91_4) &
% 136.73/18.47  |        ssList(all_91_5) & ssItem(all_91_3) &  ~ memberP(all_91_4, all_91_3) & 
% 136.73/18.47  |        ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (cons(v0,
% 136.73/18.47  |              nil) = v1) |  ~ (app(v3, v1) = all_91_5) |  ~ (app(v1, v2) =
% 136.73/18.47  |            all_91_0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v0) |  ~ ssList(v3) |  ~
% 136.73/18.47  |          ssList(v2) |  ~ ssItem(v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 136.73/18.47  |        :  ! [v3: $i] : ( ~ (cons(v0, nil) = v1) |  ~ (app(v2, v1) = all_91_2)
% 136.73/18.47  |          |  ~ (app(v1, v3) = all_91_5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v0) | 
% 136.73/18.47  |          ~ ssList(v3) |  ~ ssList(v2) |  ~ ssItem(v0)) & ( ~ (all_91_5 = nil)
% 136.73/18.47  |          | all_91_4 = nil)
% 136.73/18.47  | 
% 136.73/18.47  | ALPHA: (6) implies:
% 136.73/18.47  |   (7)   ~ memberP(all_91_4, all_91_3)
% 136.73/18.47  |   (8)  ssItem(all_91_3)
% 136.73/18.47  |   (9)  ssList(all_91_5)
% 136.73/18.47  |   (10)  ssList(all_91_2)
% 136.73/18.47  |   (11)  ssList(all_91_0)
% 136.73/18.47  |   (12)  memberP(all_91_5, all_91_3)
% 136.73/18.47  |   (13)  $i(all_91_5)
% 136.73/18.47  |   (14)  $i(all_91_3)
% 136.73/18.47  |   (15)  $i(all_91_2)
% 136.73/18.47  |   (16)  $i(all_91_1)
% 136.73/18.47  |   (17)  $i(all_91_0)
% 136.73/18.47  |   (18)  app(all_91_2, all_91_5) = all_91_1
% 136.73/18.47  |   (19)  app(all_91_1, all_91_0) = all_91_4
% 136.73/18.47  | 
% 136.73/18.47  | BETA: splitting (4) gives:
% 136.73/18.47  | 
% 136.73/18.47  | Case 1:
% 136.73/18.47  | | 
% 136.73/18.47  | |   (20)   ~ ssList(nil)
% 136.73/18.47  | | 
% 136.73/18.47  | | PRED_UNIFY: (1), (20) imply:
% 136.73/18.47  | |   (21)  $false
% 136.73/18.47  | | 
% 136.73/18.47  | | CLOSE: (21) is inconsistent.
% 136.73/18.47  | | 
% 136.73/18.47  | Case 2:
% 136.73/18.47  | | 
% 136.73/18.47  | | 
% 136.73/18.47  | | GROUND_INST: instantiating (3) with all_91_3, all_91_2, all_91_5, all_91_1,
% 136.73/18.47  | |              simplifying with (8), (9), (10), (12), (13), (14), (15), (18)
% 136.73/18.47  | |              gives:
% 136.73/18.47  | |   (22)  memberP(all_91_1, all_91_3)
% 136.73/18.47  | | 
% 136.73/18.47  | | GROUND_INST: instantiating (ax26) with all_91_2, all_91_5, all_91_1,
% 136.73/18.47  | |              simplifying with (9), (10), (13), (15), (18) gives:
% 136.73/18.47  | |   (23)  ssList(all_91_1)
% 136.73/18.47  | | 
% 136.73/18.47  | | GROUND_INST: instantiating (2) with all_91_3, all_91_1, all_91_0, all_91_4,
% 136.73/18.47  | |              simplifying with (7), (8), (11), (14), (16), (17), (19), (22),
% 136.73/18.47  | |              (23) gives:
% 136.73/18.47  | |   (24)  $false
% 136.73/18.47  | | 
% 136.73/18.47  | | CLOSE: (24) is inconsistent.
% 136.73/18.47  | | 
% 136.73/18.47  | End of split
% 136.73/18.47  | 
% 136.73/18.47  End of proof
% 136.73/18.47  % SZS output end Proof for theBenchmark
% 136.73/18.48  
% 136.73/18.48  17868ms
%------------------------------------------------------------------------------