TSTP Solution File: SWC011+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC011+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 : n018.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 31.81s 5.22s
% Output   : Proof 46.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem  : SWC011+1 : TPTP v8.1.2. Released v2.4.0.
% 0.05/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33  % Computer : n018.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Mon Aug 28 14:58:02 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.17/0.62  ________       _____
% 0.17/0.62  ___  __ \_________(_)________________________________
% 0.17/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.17/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.17/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.17/0.62  
% 0.17/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.62  (2023-06-19)
% 0.17/0.62  
% 0.17/0.62  (c) Philipp Rümmer, 2009-2023
% 0.17/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.62                Amanda Stjerna.
% 0.17/0.62  Free software under BSD-3-Clause.
% 0.17/0.62  
% 0.17/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.62  
% 0.17/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.64  Running up to 7 provers in parallel.
% 0.17/0.66  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.66  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.66  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.66  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.66  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.66  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.66  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.46/1.68  Prover 1: Preprocessing ...
% 6.46/1.68  Prover 4: Preprocessing ...
% 6.46/1.74  Prover 3: Preprocessing ...
% 6.46/1.74  Prover 5: Preprocessing ...
% 6.46/1.74  Prover 6: Preprocessing ...
% 6.46/1.74  Prover 2: Preprocessing ...
% 6.46/1.74  Prover 0: Preprocessing ...
% 21.05/3.66  Prover 2: Proving ...
% 21.72/3.78  Prover 5: Constructing countermodel ...
% 22.20/3.81  Prover 1: Constructing countermodel ...
% 22.20/3.83  Prover 6: Proving ...
% 22.20/3.90  Prover 3: Constructing countermodel ...
% 31.41/5.05  Prover 0: Proving ...
% 31.41/5.06  Prover 4: Constructing countermodel ...
% 31.81/5.21  Prover 0: proved (4562ms)
% 31.81/5.21  
% 31.81/5.22  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.81/5.22  
% 31.81/5.22  Prover 5: stopped
% 31.81/5.23  Prover 3: stopped
% 33.00/5.23  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 33.00/5.23  Prover 6: stopped
% 33.00/5.27  Prover 2: stopped
% 33.00/5.27  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 33.00/5.27  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 33.00/5.27  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 33.00/5.27  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 35.56/5.61  Prover 10: Preprocessing ...
% 35.56/5.61  Prover 7: Preprocessing ...
% 35.56/5.64  Prover 13: Preprocessing ...
% 35.56/5.64  Prover 8: Preprocessing ...
% 35.98/5.66  Prover 11: Preprocessing ...
% 38.16/5.99  Prover 7: Constructing countermodel ...
% 38.82/6.02  Prover 10: Constructing countermodel ...
% 39.36/6.16  Prover 13: Constructing countermodel ...
% 41.06/6.32  Prover 8: Warning: ignoring some quantifiers
% 41.06/6.34  Prover 8: Constructing countermodel ...
% 41.59/6.44  Prover 10: Found proof (size 18)
% 41.59/6.45  Prover 10: proved (1210ms)
% 41.59/6.45  Prover 7: stopped
% 41.59/6.45  Prover 4: stopped
% 41.59/6.45  Prover 13: stopped
% 41.59/6.45  Prover 1: stopped
% 41.59/6.45  Prover 8: stopped
% 45.50/7.32  Prover 11: Constructing countermodel ...
% 45.80/7.37  Prover 11: stopped
% 45.80/7.38  
% 45.80/7.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.80/7.38  
% 45.80/7.38  % SZS output start Proof for theBenchmark
% 45.80/7.39  Assumptions after simplification:
% 45.80/7.39  ---------------------------------
% 45.80/7.39  
% 45.80/7.39    (ax17)
% 45.80/7.39    $i(nil) & ssList(nil)
% 45.80/7.39  
% 45.80/7.39    (ax58)
% 45.80/7.40    $i(nil) &  ! [v0: $i] : (v0 = nil |  ~ $i(v0) |  ~ segmentP(nil, v0) |  ~
% 45.80/7.40      ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 45.80/7.40  
% 45.80/7.40    (co1)
% 45.99/7.43    $i(nil) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i]
% 45.99/7.43    :  ? [v5: $i] :  ? [v6: $i] : (cons(v2, nil) = v3 & app(v5, v6) = v1 & app(v4,
% 45.99/7.43        v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 45.99/7.43      $i(v1) & $i(v0) & ssList(v6) & ssList(v4) & ssList(v1) & ssList(v0) &
% 45.99/7.43      neq(v1, nil) & ssItem(v2) &  ! [v7: $i] :  ! [v8: $i] :  ! [v9: $i] :  !
% 45.99/7.43      [v10: $i] :  ! [v11: $i] : ( ~ (cons(v7, nil) = v8) |  ~ (app(v10, v11) =
% 45.99/7.43          v1) |  ~ (app(v9, v8) = v10) |  ~ $i(v11) |  ~ $i(v9) |  ~ $i(v7) |  ~
% 45.99/7.43        ssList(v11) |  ~ ssList(v9) |  ~ ssItem(v7) |  ? [v12: $i] : ( ~ (v12 =
% 45.99/7.43            v0) & app(v9, v11) = v12 & $i(v12))))
% 45.99/7.43  
% 45.99/7.43    (function-axioms)
% 45.99/7.43     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 45.99/7.43      (cons(v3, v2) = v1) |  ~ (cons(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 45.99/7.43    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (app(v3, v2) = v1) |  ~ (app(v3, v2)
% 45.99/7.43        = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (tl(v2) =
% 45.99/7.43        v1) |  ~ (tl(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 =
% 45.99/7.43      v0 |  ~ (hd(v2) = v1) |  ~ (hd(v2) = v0))
% 45.99/7.43  
% 45.99/7.43  Further assumptions not needed in the proof:
% 45.99/7.43  --------------------------------------------
% 45.99/7.43  ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 45.99/7.43  ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 45.99/7.43  ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45,
% 45.99/7.43  ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57,
% 45.99/7.43  ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 45.99/7.43  ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 45.99/7.43  ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 45.99/7.43  ax94, ax95
% 45.99/7.43  
% 45.99/7.43  Those formulas are unsatisfiable:
% 45.99/7.43  ---------------------------------
% 45.99/7.43  
% 45.99/7.43  Begin of proof
% 45.99/7.43  | 
% 45.99/7.43  | ALPHA: (ax17) implies:
% 45.99/7.43  |   (1)  ssList(nil)
% 45.99/7.43  | 
% 45.99/7.43  | ALPHA: (ax58) implies:
% 45.99/7.43  |   (2)   ~ ssList(nil) | segmentP(nil, nil)
% 45.99/7.43  | 
% 45.99/7.43  | ALPHA: (co1) implies:
% 45.99/7.44  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 45.99/7.44  |        ? [v5: $i] :  ? [v6: $i] : (cons(v2, nil) = v3 & app(v5, v6) = v1 &
% 45.99/7.44  |          app(v4, v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) &
% 45.99/7.44  |          $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v6) & ssList(v4) &
% 45.99/7.44  |          ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) &  ! [v7: $i] : 
% 45.99/7.44  |          ! [v8: $i] :  ! [v9: $i] :  ! [v10: $i] :  ! [v11: $i] : ( ~
% 45.99/7.44  |            (cons(v7, nil) = v8) |  ~ (app(v10, v11) = v1) |  ~ (app(v9, v8) =
% 45.99/7.44  |              v10) |  ~ $i(v11) |  ~ $i(v9) |  ~ $i(v7) |  ~ ssList(v11) |  ~
% 45.99/7.44  |            ssList(v9) |  ~ ssItem(v7) |  ? [v12: $i] : ( ~ (v12 = v0) &
% 45.99/7.44  |              app(v9, v11) = v12 & $i(v12))))
% 46.15/7.44  | 
% 46.15/7.44  | ALPHA: (function-axioms) implies:
% 46.15/7.44  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 46.15/7.44  |          (app(v3, v2) = v1) |  ~ (app(v3, v2) = v0))
% 46.15/7.44  | 
% 46.15/7.44  | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2,
% 46.15/7.44  |        all_91_3, all_91_4, all_91_5, all_91_6 gives:
% 46.15/7.44  |   (5)  cons(all_91_4, nil) = all_91_3 & app(all_91_1, all_91_0) = all_91_5 &
% 46.15/7.44  |        app(all_91_2, all_91_0) = all_91_6 & app(all_91_2, all_91_3) = all_91_1
% 46.15/7.44  |        & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 46.15/7.44  |        $i(all_91_4) & $i(all_91_5) & $i(all_91_6) & ssList(all_91_0) &
% 46.15/7.44  |        ssList(all_91_2) & ssList(all_91_5) & ssList(all_91_6) & neq(all_91_5,
% 46.15/7.44  |          nil) & ssItem(all_91_4) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 46.15/7.44  |        ! [v3: $i] :  ! [v4: $i] : ( ~ (cons(v0, nil) = v1) |  ~ (app(v3, v4) =
% 46.15/7.44  |            all_91_5) |  ~ (app(v2, v1) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~
% 46.15/7.44  |          $i(v0) |  ~ ssList(v4) |  ~ ssList(v2) |  ~ ssItem(v0) |  ? [v5: any]
% 46.15/7.44  |          : ( ~ (v5 = all_91_6) & app(v2, v4) = v5 & $i(v5)))
% 46.15/7.44  | 
% 46.15/7.44  | ALPHA: (5) implies:
% 46.15/7.45  |   (6)  ssItem(all_91_4)
% 46.15/7.45  |   (7)  ssList(all_91_2)
% 46.15/7.45  |   (8)  ssList(all_91_0)
% 46.15/7.45  |   (9)  $i(all_91_4)
% 46.15/7.45  |   (10)  $i(all_91_2)
% 46.15/7.45  |   (11)  $i(all_91_0)
% 46.15/7.45  |   (12)  app(all_91_2, all_91_3) = all_91_1
% 46.15/7.45  |   (13)  app(all_91_2, all_91_0) = all_91_6
% 46.15/7.45  |   (14)  app(all_91_1, all_91_0) = all_91_5
% 46.15/7.45  |   (15)  cons(all_91_4, nil) = all_91_3
% 46.15/7.45  |   (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 46.15/7.45  |         ( ~ (cons(v0, nil) = v1) |  ~ (app(v3, v4) = all_91_5) |  ~ (app(v2,
% 46.15/7.45  |               v1) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~ $i(v0) |  ~ ssList(v4) | 
% 46.15/7.45  |           ~ ssList(v2) |  ~ ssItem(v0) |  ? [v5: any] : ( ~ (v5 = all_91_6) &
% 46.15/7.45  |             app(v2, v4) = v5 & $i(v5)))
% 46.15/7.45  | 
% 46.15/7.45  | BETA: splitting (2) gives:
% 46.15/7.45  | 
% 46.15/7.45  | Case 1:
% 46.15/7.45  | | 
% 46.15/7.45  | |   (17)   ~ ssList(nil)
% 46.15/7.45  | | 
% 46.15/7.45  | | PRED_UNIFY: (1), (17) imply:
% 46.15/7.45  | |   (18)  $false
% 46.15/7.45  | | 
% 46.15/7.45  | | CLOSE: (18) is inconsistent.
% 46.15/7.45  | | 
% 46.15/7.45  | Case 2:
% 46.15/7.45  | | 
% 46.15/7.45  | | 
% 46.15/7.45  | | GROUND_INST: instantiating (16) with all_91_4, all_91_3, all_91_2, all_91_1,
% 46.15/7.45  | |              all_91_0, simplifying with (6), (7), (8), (9), (10), (11),
% 46.15/7.45  | |              (12), (14), (15) gives:
% 46.15/7.45  | |   (19)   ? [v0: any] : ( ~ (v0 = all_91_6) & app(all_91_2, all_91_0) = v0 &
% 46.15/7.45  | |           $i(v0))
% 46.15/7.46  | | 
% 46.15/7.46  | | DELTA: instantiating (19) with fresh symbol all_112_0 gives:
% 46.15/7.46  | |   (20)   ~ (all_112_0 = all_91_6) & app(all_91_2, all_91_0) = all_112_0 &
% 46.15/7.46  | |         $i(all_112_0)
% 46.15/7.46  | | 
% 46.15/7.46  | | ALPHA: (20) implies:
% 46.15/7.46  | |   (21)   ~ (all_112_0 = all_91_6)
% 46.15/7.46  | |   (22)  app(all_91_2, all_91_0) = all_112_0
% 46.15/7.46  | | 
% 46.15/7.46  | | GROUND_INST: instantiating (4) with all_91_6, all_112_0, all_91_0, all_91_2,
% 46.15/7.46  | |              simplifying with (13), (22) gives:
% 46.15/7.46  | |   (23)  all_112_0 = all_91_6
% 46.15/7.46  | | 
% 46.15/7.46  | | REDUCE: (21), (23) imply:
% 46.15/7.46  | |   (24)  $false
% 46.15/7.46  | | 
% 46.15/7.46  | | CLOSE: (24) is inconsistent.
% 46.15/7.46  | | 
% 46.15/7.46  | End of split
% 46.15/7.46  | 
% 46.15/7.46  End of proof
% 46.15/7.46  % SZS output end Proof for theBenchmark
% 46.15/7.46  
% 46.15/7.46  6835ms
%------------------------------------------------------------------------------