TSTP Solution File: SWC179+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC179+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 : n023.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 20:50:06 EDT 2023

% Result   : Theorem 21.23s 3.58s
% Output   : Proof 41.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWC179+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.33  % CPULimit : 300
% 0.18/0.33  % WCLimit  : 300
% 0.18/0.33  % DateTime : Mon Aug 28 16:56:40 EDT 2023
% 0.18/0.33  % CPUTime  : 
% 0.62/0.62  ________       _____
% 0.62/0.62  ___  __ \_________(_)________________________________
% 0.62/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.62/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.62/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.62/0.62  
% 0.62/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.62/0.62  (2023-06-19)
% 0.62/0.62  
% 0.62/0.62  (c) Philipp Rümmer, 2009-2023
% 0.62/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.62/0.62                Amanda Stjerna.
% 0.62/0.62  Free software under BSD-3-Clause.
% 0.62/0.62  
% 0.62/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.62/0.62  
% 0.62/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.63  Running up to 7 provers in parallel.
% 0.72/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.72/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.72/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.72/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.72/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.72/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.72/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.06/1.45  Prover 1: Preprocessing ...
% 5.06/1.45  Prover 4: Preprocessing ...
% 5.68/1.48  Prover 5: Preprocessing ...
% 5.68/1.48  Prover 3: Preprocessing ...
% 5.68/1.48  Prover 2: Preprocessing ...
% 5.68/1.48  Prover 0: Preprocessing ...
% 5.68/1.49  Prover 6: Preprocessing ...
% 15.01/2.71  Prover 2: Proving ...
% 15.83/2.86  Prover 5: Constructing countermodel ...
% 15.83/2.87  Prover 1: Constructing countermodel ...
% 15.83/2.88  Prover 3: Constructing countermodel ...
% 16.57/2.91  Prover 6: Proving ...
% 21.23/3.57  Prover 6: proved (2925ms)
% 21.23/3.57  
% 21.23/3.58  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.23/3.58  
% 21.23/3.58  Prover 5: stopped
% 21.23/3.58  Prover 2: stopped
% 21.79/3.59  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.79/3.59  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.79/3.59  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.79/3.61  Prover 3: stopped
% 21.79/3.61  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.89/3.74  Prover 4: Constructing countermodel ...
% 23.53/3.82  Prover 10: Preprocessing ...
% 24.10/3.89  Prover 11: Preprocessing ...
% 24.10/3.89  Prover 0: Proving ...
% 24.10/3.93  Prover 0: stopped
% 24.10/3.93  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.10/3.93  Prover 8: Preprocessing ...
% 24.10/3.95  Prover 7: Preprocessing ...
% 25.20/4.04  Prover 13: Preprocessing ...
% 25.79/4.10  Prover 10: Constructing countermodel ...
% 26.31/4.18  Prover 7: Constructing countermodel ...
% 26.31/4.25  Prover 8: Warning: ignoring some quantifiers
% 26.31/4.26  Prover 8: Constructing countermodel ...
% 27.21/4.30  Prover 13: Constructing countermodel ...
% 32.09/4.96  Prover 11: Constructing countermodel ...
% 41.22/6.14  Prover 7: Found proof (size 14)
% 41.22/6.15  Prover 7: proved (2569ms)
% 41.22/6.15  Prover 11: stopped
% 41.22/6.15  Prover 8: stopped
% 41.22/6.15  Prover 1: stopped
% 41.22/6.15  Prover 10: stopped
% 41.22/6.15  Prover 4: stopped
% 41.22/6.15  Prover 13: stopped
% 41.22/6.15  
% 41.22/6.15  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.22/6.15  
% 41.22/6.15  % SZS output start Proof for theBenchmark
% 41.22/6.16  Assumptions after simplification:
% 41.22/6.16  ---------------------------------
% 41.22/6.16  
% 41.22/6.16    (ax71)
% 41.22/6.18    $i(nil) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (cons(v0, nil) = v1) |  ~ $i(v0) | 
% 41.22/6.18      ~ ssItem(v0) | duplicatefreeP(v1))
% 41.22/6.18  
% 41.22/6.18    (ax72)
% 41.22/6.18    $i(nil) & duplicatefreeP(nil)
% 41.22/6.18  
% 41.22/6.18    (co1)
% 41.22/6.18    $i(nil) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i]
% 41.22/6.18    :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] : ($i(v6) & $i(v4) & $i(v2) & $i(v1)
% 41.22/6.18      & $i(v0) & ssList(v1) & ssList(v0) &  ~ duplicatefreeP(v0) & ((v7 = v1 & v3
% 41.22/6.18          = v0 & cons(v2, nil) = v0 & app(v5, v6) = v1 & app(v4, v0) = v5 & $i(v5)
% 41.22/6.18          & ssList(v6) & ssList(v4) & ssItem(v2) &  ! [v8: $i] : ( ~ $i(v8) |  ~
% 41.22/6.18            lt(v8, v2) |  ~ memberP(v6, v8) |  ~ ssItem(v8)) &  ! [v8: $i] : ( ~
% 41.22/6.18            $i(v8) |  ~ lt(v2, v8) |  ~ memberP(v4, v8) |  ~ ssItem(v8))) | (v1 =
% 41.22/6.18          nil & v0 = nil)))
% 41.22/6.18  
% 41.22/6.18  Further assumptions not needed in the proof:
% 41.22/6.18  --------------------------------------------
% 41.22/6.19  ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20,
% 41.22/6.19  ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32,
% 41.22/6.19  ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44,
% 41.22/6.19  ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56,
% 41.22/6.19  ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68,
% 41.22/6.19  ax69, ax7, ax70, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 41.22/6.19  ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 41.22/6.19  ax94, ax95
% 41.22/6.19  
% 41.22/6.19  Those formulas are unsatisfiable:
% 41.22/6.19  ---------------------------------
% 41.22/6.19  
% 41.22/6.19  Begin of proof
% 41.22/6.19  | 
% 41.22/6.19  | ALPHA: (ax71) implies:
% 41.22/6.19  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (cons(v0, nil) = v1) |  ~ $i(v0) |  ~
% 41.85/6.19  |          ssItem(v0) | duplicatefreeP(v1))
% 41.85/6.19  | 
% 41.85/6.19  | ALPHA: (ax72) implies:
% 41.85/6.19  |   (2)  duplicatefreeP(nil)
% 41.85/6.19  | 
% 41.85/6.19  | ALPHA: (co1) implies:
% 41.85/6.19  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 41.85/6.19  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] : ($i(v6) & $i(v4) & $i(v2) &
% 41.85/6.19  |          $i(v1) & $i(v0) & ssList(v1) & ssList(v0) &  ~ duplicatefreeP(v0) &
% 41.85/6.19  |          ((v7 = v1 & v3 = v0 & cons(v2, nil) = v0 & app(v5, v6) = v1 & app(v4,
% 41.85/6.19  |                v0) = v5 & $i(v5) & ssList(v6) & ssList(v4) & ssItem(v2) &  !
% 41.85/6.19  |              [v8: $i] : ( ~ $i(v8) |  ~ lt(v8, v2) |  ~ memberP(v6, v8) |  ~
% 41.85/6.19  |                ssItem(v8)) &  ! [v8: $i] : ( ~ $i(v8) |  ~ lt(v2, v8) |  ~
% 41.85/6.19  |                memberP(v4, v8) |  ~ ssItem(v8))) | (v1 = nil & v0 = nil)))
% 41.85/6.19  | 
% 41.85/6.19  | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2,
% 41.85/6.19  |        all_91_3, all_91_4, all_91_5, all_91_6, all_91_7 gives:
% 41.87/6.19  |   (4)  $i(all_91_1) & $i(all_91_3) & $i(all_91_5) & $i(all_91_6) &
% 41.87/6.19  |        $i(all_91_7) & ssList(all_91_6) & ssList(all_91_7) &  ~
% 41.87/6.19  |        duplicatefreeP(all_91_7) & ((all_91_0 = all_91_6 & all_91_4 = all_91_7
% 41.87/6.19  |            & cons(all_91_5, nil) = all_91_7 & app(all_91_2, all_91_1) =
% 41.87/6.19  |            all_91_6 & app(all_91_3, all_91_7) = all_91_2 & $i(all_91_2) &
% 41.87/6.19  |            ssList(all_91_1) & ssList(all_91_3) & ssItem(all_91_5) &  ! [v0:
% 41.87/6.19  |              $i] : ( ~ $i(v0) |  ~ lt(v0, all_91_5) |  ~ memberP(all_91_1, v0)
% 41.87/6.19  |              |  ~ ssItem(v0)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ lt(all_91_5, v0)
% 41.87/6.19  |              |  ~ memberP(all_91_3, v0) |  ~ ssItem(v0))) | (all_91_6 = nil &
% 41.87/6.19  |            all_91_7 = nil))
% 41.87/6.19  | 
% 41.87/6.19  | ALPHA: (4) implies:
% 41.87/6.20  |   (5)   ~ duplicatefreeP(all_91_7)
% 41.87/6.20  |   (6)  $i(all_91_5)
% 41.87/6.20  |   (7)  (all_91_0 = all_91_6 & all_91_4 = all_91_7 & cons(all_91_5, nil) =
% 41.87/6.20  |          all_91_7 & app(all_91_2, all_91_1) = all_91_6 & app(all_91_3,
% 41.87/6.20  |            all_91_7) = all_91_2 & $i(all_91_2) & ssList(all_91_1) &
% 41.87/6.20  |          ssList(all_91_3) & ssItem(all_91_5) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 41.87/6.20  |            lt(v0, all_91_5) |  ~ memberP(all_91_1, v0) |  ~ ssItem(v0)) &  !
% 41.87/6.20  |          [v0: $i] : ( ~ $i(v0) |  ~ lt(all_91_5, v0) |  ~ memberP(all_91_3,
% 41.87/6.20  |              v0) |  ~ ssItem(v0))) | (all_91_6 = nil & all_91_7 = nil)
% 41.87/6.20  | 
% 41.87/6.20  | PRED_UNIFY: (2), (5) imply:
% 41.87/6.20  |   (8)   ~ (all_91_7 = nil)
% 41.87/6.20  | 
% 41.87/6.20  | BETA: splitting (7) gives:
% 41.87/6.20  | 
% 41.87/6.20  | Case 1:
% 41.87/6.20  | | 
% 41.87/6.20  | |   (9)  all_91_0 = all_91_6 & all_91_4 = all_91_7 & cons(all_91_5, nil) =
% 41.87/6.20  | |        all_91_7 & app(all_91_2, all_91_1) = all_91_6 & app(all_91_3,
% 41.87/6.20  | |          all_91_7) = all_91_2 & $i(all_91_2) & ssList(all_91_1) &
% 41.87/6.20  | |        ssList(all_91_3) & ssItem(all_91_5) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 41.87/6.20  | |          lt(v0, all_91_5) |  ~ memberP(all_91_1, v0) |  ~ ssItem(v0)) &  !
% 41.87/6.20  | |        [v0: $i] : ( ~ $i(v0) |  ~ lt(all_91_5, v0) |  ~ memberP(all_91_3,
% 41.87/6.20  | |            v0) |  ~ ssItem(v0))
% 41.87/6.20  | | 
% 41.87/6.20  | | ALPHA: (9) implies:
% 41.87/6.20  | |   (10)  ssItem(all_91_5)
% 41.87/6.20  | |   (11)  cons(all_91_5, nil) = all_91_7
% 41.87/6.20  | | 
% 41.87/6.20  | | GROUND_INST: instantiating (1) with all_91_5, all_91_7, simplifying with
% 41.87/6.20  | |              (5), (6), (10), (11) gives:
% 41.87/6.20  | |   (12)  $false
% 41.87/6.20  | | 
% 41.87/6.20  | | CLOSE: (12) is inconsistent.
% 41.87/6.20  | | 
% 41.87/6.20  | Case 2:
% 41.87/6.20  | | 
% 41.87/6.20  | |   (13)  all_91_6 = nil & all_91_7 = nil
% 41.87/6.20  | | 
% 41.87/6.20  | | ALPHA: (13) implies:
% 41.87/6.20  | |   (14)  all_91_7 = nil
% 41.87/6.20  | | 
% 41.87/6.20  | | REDUCE: (8), (14) imply:
% 41.87/6.20  | |   (15)  $false
% 41.87/6.20  | | 
% 41.87/6.20  | | CLOSE: (15) is inconsistent.
% 41.87/6.20  | | 
% 41.87/6.20  | End of split
% 41.87/6.20  | 
% 41.87/6.20  End of proof
% 41.87/6.20  % SZS output end Proof for theBenchmark
% 41.87/6.20  
% 41.87/6.20  5584ms
%------------------------------------------------------------------------------