TSTP Solution File: SWC241+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC241+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 : n029.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 20:50:24 EDT 2023

% Result   : Theorem 31.85s 4.86s
% Output   : Proof 40.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWC241+1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n029.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
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Aug 28 19:25:26 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.57/0.59  ________       _____
% 0.57/0.59  ___  __ \_________(_)________________________________
% 0.57/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.57/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.57/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.57/0.60  
% 0.57/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.57/0.60  (2023-06-19)
% 0.57/0.60  
% 0.57/0.60  (c) Philipp Rümmer, 2009-2023
% 0.57/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.57/0.60                Amanda Stjerna.
% 0.57/0.60  Free software under BSD-3-Clause.
% 0.57/0.60  
% 0.57/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.57/0.60  
% 0.57/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.57/0.61  Running up to 7 provers in parallel.
% 0.57/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.57/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.57/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.57/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.57/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.57/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.57/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.09/1.44  Prover 1: Preprocessing ...
% 5.09/1.44  Prover 4: Preprocessing ...
% 5.72/1.48  Prover 2: Preprocessing ...
% 5.72/1.48  Prover 5: Preprocessing ...
% 5.96/1.48  Prover 6: Preprocessing ...
% 5.96/1.49  Prover 0: Preprocessing ...
% 5.96/1.49  Prover 3: Preprocessing ...
% 16.27/2.87  Prover 2: Proving ...
% 16.70/2.95  Prover 5: Constructing countermodel ...
% 17.22/2.97  Prover 3: Constructing countermodel ...
% 17.22/2.98  Prover 6: Proving ...
% 17.55/3.01  Prover 1: Constructing countermodel ...
% 21.27/3.49  Prover 4: Constructing countermodel ...
% 22.59/3.67  Prover 0: Proving ...
% 31.85/4.86  Prover 3: proved (4239ms)
% 31.85/4.86  
% 31.85/4.86  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.85/4.86  
% 31.85/4.86  Prover 5: stopped
% 31.85/4.86  Prover 6: stopped
% 31.85/4.88  Prover 2: stopped
% 31.85/4.88  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 31.85/4.88  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 31.85/4.88  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 31.85/4.89  Prover 0: stopped
% 31.85/4.89  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 31.85/4.89  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 33.94/5.11  Prover 7: Preprocessing ...
% 34.08/5.14  Prover 13: Preprocessing ...
% 34.08/5.19  Prover 11: Preprocessing ...
% 34.08/5.19  Prover 10: Preprocessing ...
% 34.08/5.20  Prover 8: Preprocessing ...
% 35.90/5.36  Prover 10: Constructing countermodel ...
% 35.90/5.37  Prover 13: Constructing countermodel ...
% 36.03/5.40  Prover 7: Constructing countermodel ...
% 37.70/5.63  Prover 8: Warning: ignoring some quantifiers
% 37.70/5.65  Prover 8: Constructing countermodel ...
% 38.57/5.72  Prover 10: Found proof (size 17)
% 38.57/5.72  Prover 10: proved (838ms)
% 38.57/5.72  Prover 13: stopped
% 38.57/5.72  Prover 7: stopped
% 38.57/5.72  Prover 1: stopped
% 38.57/5.72  Prover 8: stopped
% 38.57/5.72  Prover 4: stopped
% 40.05/6.07  Prover 11: Constructing countermodel ...
% 40.05/6.09  Prover 11: stopped
% 40.05/6.10  
% 40.05/6.10  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.05/6.10  
% 40.05/6.10  % SZS output start Proof for theBenchmark
% 40.05/6.11  Assumptions after simplification:
% 40.05/6.11  ---------------------------------
% 40.05/6.11  
% 40.05/6.11    (ax17)
% 40.05/6.12    $i(nil) & ssList(nil)
% 40.05/6.12  
% 40.05/6.12    (ax58)
% 40.05/6.12    $i(nil) &  ! [v0: $i] : (v0 = nil |  ~ $i(v0) |  ~ segmentP(nil, v0) |  ~
% 40.05/6.12      ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 40.05/6.12  
% 40.05/6.12    (ax93)
% 40.05/6.12     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v0, v1)
% 40.05/6.12      |  ~ ssItem(v1) |  ~ ssItem(v0) | lt(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] :
% 40.05/6.12    ( ~ $i(v1) |  ~ $i(v0) |  ~ lt(v0, v1) |  ~ ssItem(v1) |  ~ ssItem(v0) |
% 40.05/6.12      leq(v0, v1)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ lt(v0, v0) |  ~ ssItem(v0))
% 40.05/6.12  
% 40.05/6.13    (co1)
% 40.45/6.17    $i(nil) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i]
% 40.45/6.17    :  ? [v5: $i] :  ? [v6: $i] : ( ~ (v0 = nil) & cons(v2, nil) = v3 & app(v5,
% 40.45/6.17        v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 40.45/6.17      $i(v1) & $i(v0) & ssList(v6) & ssList(v4) & ssList(v1) & ssList(v0) &
% 40.45/6.17      ssItem(v2) &  ! [v7: $i] :  ! [v8: $i] :  ! [v9: $i] :  ! [v10: $i] :  !
% 40.45/6.17      [v11: $i] : ( ~ (cons(v7, nil) = v8) |  ~ (app(v10, v11) = v0) |  ~ (app(v9,
% 40.45/6.17            v8) = v10) |  ~ $i(v11) |  ~ $i(v9) |  ~ $i(v7) |  ~ ssList(v11) |  ~
% 40.45/6.17        ssList(v9) |  ~ ssItem(v7) |  ? [v12: $i] : ($i(v12) & lt(v7, v12) &
% 40.45/6.17          memberP(v11, v12) & memberP(v9, v12) & ssItem(v12) &  ~ leq(v7, v12))) &
% 40.45/6.17       ! [v7: $i] : ( ~ $i(v7) |  ~ leq(v2, v7) |  ~ memberP(v6, v7) |  ~
% 40.45/6.17        memberP(v4, v7) |  ~ ssItem(v7) | leq(v7, v2)))
% 40.45/6.17  
% 40.45/6.17  Further assumptions not needed in the proof:
% 40.45/6.17  --------------------------------------------
% 40.45/6.17  ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 40.45/6.17  ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 40.45/6.17  ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45,
% 40.45/6.17  ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57,
% 40.45/6.17  ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 40.45/6.17  ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 40.45/6.17  ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax94,
% 40.45/6.17  ax95
% 40.45/6.17  
% 40.45/6.17  Those formulas are unsatisfiable:
% 40.45/6.17  ---------------------------------
% 40.45/6.17  
% 40.45/6.17  Begin of proof
% 40.45/6.17  | 
% 40.45/6.17  | ALPHA: (ax17) implies:
% 40.45/6.17  |   (1)  ssList(nil)
% 40.45/6.17  | 
% 40.45/6.17  | ALPHA: (ax58) implies:
% 40.45/6.17  |   (2)   ~ ssList(nil) | segmentP(nil, nil)
% 40.45/6.17  | 
% 40.45/6.17  | ALPHA: (ax93) implies:
% 40.45/6.17  |   (3)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ lt(v0, v1) |  ~
% 40.45/6.17  |          ssItem(v1) |  ~ ssItem(v0) | leq(v0, v1))
% 40.45/6.17  | 
% 40.45/6.17  | ALPHA: (co1) implies:
% 40.45/6.18  |   (4)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 40.45/6.18  |        ? [v5: $i] :  ? [v6: $i] : ( ~ (v0 = nil) & cons(v2, nil) = v3 &
% 40.45/6.18  |          app(v5, v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) &
% 40.45/6.18  |          $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v6) & ssList(v4) &
% 40.45/6.18  |          ssList(v1) & ssList(v0) & ssItem(v2) &  ! [v7: $i] :  ! [v8: $i] :  !
% 40.45/6.18  |          [v9: $i] :  ! [v10: $i] :  ! [v11: $i] : ( ~ (cons(v7, nil) = v8) | 
% 40.45/6.18  |            ~ (app(v10, v11) = v0) |  ~ (app(v9, v8) = v10) |  ~ $i(v11) |  ~
% 40.45/6.18  |            $i(v9) |  ~ $i(v7) |  ~ ssList(v11) |  ~ ssList(v9) |  ~ ssItem(v7)
% 40.45/6.18  |            |  ? [v12: $i] : ($i(v12) & lt(v7, v12) & memberP(v11, v12) &
% 40.45/6.18  |              memberP(v9, v12) & ssItem(v12) &  ~ leq(v7, v12))) &  ! [v7: $i]
% 40.45/6.18  |          : ( ~ $i(v7) |  ~ leq(v2, v7) |  ~ memberP(v6, v7) |  ~ memberP(v4,
% 40.45/6.18  |              v7) |  ~ ssItem(v7) | leq(v7, v2)))
% 40.45/6.18  | 
% 40.45/6.18  | DELTA: instantiating (4) with fresh symbols all_91_0, all_91_1, all_91_2,
% 40.45/6.18  |        all_91_3, all_91_4, all_91_5, all_91_6 gives:
% 40.45/6.18  |   (5)   ~ (all_91_6 = nil) & cons(all_91_4, nil) = all_91_3 & app(all_91_1,
% 40.45/6.18  |          all_91_0) = all_91_6 & app(all_91_2, all_91_3) = all_91_1 &
% 40.45/6.18  |        $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 40.45/6.18  |        $i(all_91_4) & $i(all_91_5) & $i(all_91_6) & ssList(all_91_0) &
% 40.45/6.18  |        ssList(all_91_2) & ssList(all_91_5) & ssList(all_91_6) &
% 40.45/6.18  |        ssItem(all_91_4) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 40.45/6.18  |          $i] :  ! [v4: $i] : ( ~ (cons(v0, nil) = v1) |  ~ (app(v3, v4) =
% 40.45/6.18  |            all_91_6) |  ~ (app(v2, v1) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~
% 40.45/6.18  |          $i(v0) |  ~ ssList(v4) |  ~ ssList(v2) |  ~ ssItem(v0) |  ? [v5: $i]
% 40.45/6.18  |          : ($i(v5) & lt(v0, v5) & memberP(v4, v5) & memberP(v2, v5) &
% 40.45/6.18  |            ssItem(v5) &  ~ leq(v0, v5))) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 40.45/6.18  |          leq(all_91_4, v0) |  ~ memberP(all_91_0, v0) |  ~ memberP(all_91_2,
% 40.45/6.18  |            v0) |  ~ ssItem(v0) | leq(v0, all_91_4))
% 40.45/6.18  | 
% 40.45/6.18  | ALPHA: (5) implies:
% 40.45/6.18  |   (6)  ssItem(all_91_4)
% 40.45/6.18  |   (7)  ssList(all_91_2)
% 40.45/6.18  |   (8)  ssList(all_91_0)
% 40.45/6.18  |   (9)  $i(all_91_4)
% 40.45/6.18  |   (10)  $i(all_91_2)
% 40.45/6.18  |   (11)  $i(all_91_0)
% 40.45/6.18  |   (12)  app(all_91_2, all_91_3) = all_91_1
% 40.45/6.18  |   (13)  app(all_91_1, all_91_0) = all_91_6
% 40.45/6.18  |   (14)  cons(all_91_4, nil) = all_91_3
% 40.45/6.18  |   (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 40.45/6.18  |         ( ~ (cons(v0, nil) = v1) |  ~ (app(v3, v4) = all_91_6) |  ~ (app(v2,
% 40.45/6.18  |               v1) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~ $i(v0) |  ~ ssList(v4) | 
% 40.45/6.18  |           ~ ssList(v2) |  ~ ssItem(v0) |  ? [v5: $i] : ($i(v5) & lt(v0, v5) &
% 40.45/6.18  |             memberP(v4, v5) & memberP(v2, v5) & ssItem(v5) &  ~ leq(v0, v5)))
% 40.45/6.18  | 
% 40.45/6.18  | BETA: splitting (2) gives:
% 40.45/6.18  | 
% 40.45/6.18  | Case 1:
% 40.45/6.18  | | 
% 40.45/6.18  | |   (16)   ~ ssList(nil)
% 40.45/6.18  | | 
% 40.45/6.18  | | PRED_UNIFY: (1), (16) imply:
% 40.45/6.19  | |   (17)  $false
% 40.45/6.19  | | 
% 40.45/6.19  | | CLOSE: (17) is inconsistent.
% 40.45/6.19  | | 
% 40.45/6.19  | Case 2:
% 40.45/6.19  | | 
% 40.45/6.19  | | 
% 40.45/6.19  | | GROUND_INST: instantiating (15) with all_91_4, all_91_3, all_91_2, all_91_1,
% 40.45/6.19  | |              all_91_0, simplifying with (6), (7), (8), (9), (10), (11),
% 40.45/6.19  | |              (12), (13), (14) gives:
% 40.45/6.19  | |   (18)   ? [v0: $i] : ($i(v0) & lt(all_91_4, v0) & memberP(all_91_0, v0) &
% 40.45/6.19  | |           memberP(all_91_2, v0) & ssItem(v0) &  ~ leq(all_91_4, v0))
% 40.45/6.19  | | 
% 40.45/6.19  | | DELTA: instantiating (18) with fresh symbol all_116_0 gives:
% 40.45/6.19  | |   (19)  $i(all_116_0) & lt(all_91_4, all_116_0) & memberP(all_91_0,
% 40.45/6.19  | |           all_116_0) & memberP(all_91_2, all_116_0) & ssItem(all_116_0) &  ~
% 40.45/6.19  | |         leq(all_91_4, all_116_0)
% 40.45/6.19  | | 
% 40.45/6.19  | | ALPHA: (19) implies:
% 40.45/6.19  | |   (20)   ~ leq(all_91_4, all_116_0)
% 40.45/6.19  | |   (21)  ssItem(all_116_0)
% 40.45/6.19  | |   (22)  lt(all_91_4, all_116_0)
% 40.45/6.19  | |   (23)  $i(all_116_0)
% 40.45/6.19  | | 
% 40.45/6.19  | | GROUND_INST: instantiating (3) with all_91_4, all_116_0, simplifying with
% 40.45/6.19  | |              (6), (9), (20), (21), (22), (23) gives:
% 40.45/6.19  | |   (24)  $false
% 40.45/6.19  | | 
% 40.45/6.19  | | CLOSE: (24) is inconsistent.
% 40.45/6.19  | | 
% 40.45/6.19  | End of split
% 40.45/6.19  | 
% 40.45/6.19  End of proof
% 40.45/6.19  % SZS output end Proof for theBenchmark
% 40.45/6.19  
% 40.45/6.19  5594ms
%------------------------------------------------------------------------------