TSTP Solution File: SWC101+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC101+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 : n008.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 20:49:39 EDT 2023

% Result   : Theorem 21.87s 3.78s
% Output   : Proof 31.37s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC101+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Aug 28 17:11:32 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.22/0.62  ________       _____
% 0.22/0.62  ___  __ \_________(_)________________________________
% 0.22/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.22/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.22/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.22/0.62  
% 0.22/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.62  (2023-06-19)
% 0.22/0.62  
% 0.22/0.62  (c) Philipp Rümmer, 2009-2023
% 0.22/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.62                Amanda Stjerna.
% 0.22/0.62  Free software under BSD-3-Clause.
% 0.22/0.62  
% 0.22/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.62  
% 0.22/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.63  Running up to 7 provers in parallel.
% 0.22/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.85/1.50  Prover 4: Preprocessing ...
% 4.85/1.50  Prover 1: Preprocessing ...
% 4.85/1.53  Prover 2: Preprocessing ...
% 4.85/1.53  Prover 3: Preprocessing ...
% 4.85/1.53  Prover 5: Preprocessing ...
% 4.85/1.53  Prover 0: Preprocessing ...
% 4.85/1.53  Prover 6: Preprocessing ...
% 14.49/2.88  Prover 2: Proving ...
% 14.49/2.91  Prover 5: Constructing countermodel ...
% 15.84/2.94  Prover 1: Constructing countermodel ...
% 15.84/2.95  Prover 3: Constructing countermodel ...
% 15.84/2.97  Prover 6: Proving ...
% 21.29/3.69  Prover 4: Constructing countermodel ...
% 21.87/3.78  Prover 3: proved (3138ms)
% 21.87/3.78  
% 21.87/3.78  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.87/3.78  
% 21.87/3.78  Prover 6: stopped
% 21.87/3.79  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.87/3.79  Prover 5: stopped
% 21.87/3.79  Prover 2: stopped
% 21.87/3.79  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.87/3.79  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.87/3.79  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.43/3.84  Prover 0: Proving ...
% 22.43/3.84  Prover 0: stopped
% 22.43/3.86  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.25/4.20  Prover 11: Preprocessing ...
% 24.25/4.22  Prover 13: Preprocessing ...
% 24.25/4.22  Prover 7: Preprocessing ...
% 24.25/4.23  Prover 10: Preprocessing ...
% 24.25/4.25  Prover 8: Preprocessing ...
% 27.29/4.48  Prover 7: Constructing countermodel ...
% 27.29/4.48  Prover 10: Constructing countermodel ...
% 27.67/4.56  Prover 13: Constructing countermodel ...
% 28.35/4.67  Prover 8: Warning: ignoring some quantifiers
% 28.35/4.68  Prover 10: Found proof (size 23)
% 28.35/4.68  Prover 10: proved (883ms)
% 28.35/4.68  Prover 13: stopped
% 28.35/4.68  Prover 4: stopped
% 28.35/4.68  Prover 1: stopped
% 28.35/4.68  Prover 7: stopped
% 28.93/4.69  Prover 8: Constructing countermodel ...
% 28.93/4.70  Prover 8: stopped
% 31.11/5.21  Prover 11: Constructing countermodel ...
% 31.11/5.23  Prover 11: stopped
% 31.11/5.24  
% 31.11/5.24  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.11/5.24  
% 31.11/5.24  % SZS output start Proof for theBenchmark
% 31.11/5.25  Assumptions after simplification:
% 31.11/5.25  ---------------------------------
% 31.11/5.25  
% 31.11/5.25    (ax15)
% 31.11/5.26     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v1) |
% 31.11/5.27       ~ ssList(v0) | neq(v0, v1)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ ssList(v0) |  ~
% 31.11/5.27      neq(v0, v0))
% 31.11/5.27  
% 31.11/5.27    (ax17)
% 31.11/5.27    $i(nil) & ssList(nil)
% 31.11/5.27  
% 31.11/5.27    (ax5)
% 31.37/5.31     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (app(v1, v2) = v0) |  ~ $i(v2) |
% 31.37/5.31       ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~ ssList(v0) |
% 31.37/5.31      frontsegP(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 31.37/5.31      frontsegP(v0, v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] : (app(v1,
% 31.37/5.31          v2) = v0 & $i(v2) & ssList(v2)))
% 31.37/5.31  
% 31.37/5.31    (co1)
% 31.37/5.32    $i(nil) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (app(v0, v2) = v1 & $i(v2)
% 31.37/5.32      & $i(v1) & $i(v0) & equalelemsP(v0) & ssList(v2) & ssList(v1) & ssList(v0) &
% 31.37/5.32       ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] :  ! [v6: $i] : ( ~ (cons(v3, nil) =
% 31.37/5.32          v4) |  ~ (app(v6, v4) = v0) |  ~ (app(v4, v5) = v2) |  ~ $i(v6) |  ~
% 31.37/5.32        $i(v5) |  ~ $i(v3) |  ~ ssList(v6) |  ~ ssList(v5) |  ~ ssItem(v3)) & ( ~
% 31.37/5.32        (v1 = nil) |  ~ (v0 = nil)) & ( ~ (v0 = nil) | v1 = nil) & ( ~
% 31.37/5.32        frontsegP(v1, v0) |  ~ neq(v0, nil)))
% 31.37/5.32  
% 31.37/5.32  Further assumptions not needed in the proof:
% 31.37/5.32  --------------------------------------------
% 31.37/5.32  ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 31.37/5.32  ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 31.37/5.32  ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46,
% 31.37/5.32  ax47, ax48, ax49, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59,
% 31.37/5.32  ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70,
% 31.37/5.32  ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82,
% 31.37/5.32  ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94,
% 31.37/5.32  ax95
% 31.37/5.32  
% 31.37/5.32  Those formulas are unsatisfiable:
% 31.37/5.32  ---------------------------------
% 31.37/5.32  
% 31.37/5.32  Begin of proof
% 31.37/5.32  | 
% 31.37/5.32  | ALPHA: (ax5) implies:
% 31.37/5.32  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (app(v1, v2) = v0) |  ~
% 31.37/5.32  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~
% 31.37/5.32  |          ssList(v0) | frontsegP(v0, v1))
% 31.37/5.32  | 
% 31.37/5.32  | ALPHA: (ax15) implies:
% 31.37/5.33  |   (2)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 31.37/5.33  |          ssList(v1) |  ~ ssList(v0) | neq(v0, v1))
% 31.37/5.33  | 
% 31.37/5.33  | ALPHA: (ax17) implies:
% 31.37/5.33  |   (3)  ssList(nil)
% 31.37/5.33  | 
% 31.37/5.33  | ALPHA: (co1) implies:
% 31.37/5.33  |   (4)  $i(nil)
% 31.37/5.33  |   (5)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (app(v0, v2) = v1 & $i(v2) &
% 31.37/5.33  |          $i(v1) & $i(v0) & equalelemsP(v0) & ssList(v2) & ssList(v1) &
% 31.37/5.33  |          ssList(v0) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] :  ! [v6: $i] :
% 31.37/5.33  |          ( ~ (cons(v3, nil) = v4) |  ~ (app(v6, v4) = v0) |  ~ (app(v4, v5) =
% 31.37/5.33  |              v2) |  ~ $i(v6) |  ~ $i(v5) |  ~ $i(v3) |  ~ ssList(v6) |  ~
% 31.37/5.33  |            ssList(v5) |  ~ ssItem(v3)) & ( ~ (v1 = nil) |  ~ (v0 = nil)) & ( ~
% 31.37/5.33  |            (v0 = nil) | v1 = nil) & ( ~ frontsegP(v1, v0) |  ~ neq(v0, nil)))
% 31.37/5.33  | 
% 31.37/5.33  | DELTA: instantiating (5) with fresh symbols all_91_0, all_91_1, all_91_2
% 31.37/5.33  |        gives:
% 31.37/5.34  |   (6)  app(all_91_2, all_91_0) = all_91_1 & $i(all_91_0) & $i(all_91_1) &
% 31.37/5.34  |        $i(all_91_2) & equalelemsP(all_91_2) & ssList(all_91_0) &
% 31.37/5.34  |        ssList(all_91_1) & ssList(all_91_2) &  ! [v0: $i] :  ! [v1: $i] :  !
% 31.37/5.34  |        [v2: $i] :  ! [v3: $i] : ( ~ (cons(v0, nil) = v1) |  ~ (app(v3, v1) =
% 31.37/5.34  |            all_91_2) |  ~ (app(v1, v2) = all_91_0) |  ~ $i(v3) |  ~ $i(v2) | 
% 31.37/5.34  |          ~ $i(v0) |  ~ ssList(v3) |  ~ ssList(v2) |  ~ ssItem(v0)) & ( ~
% 31.37/5.34  |          (all_91_1 = nil) |  ~ (all_91_2 = nil)) & ( ~ (all_91_2 = nil) |
% 31.37/5.34  |          all_91_1 = nil) & ( ~ frontsegP(all_91_1, all_91_2) |  ~
% 31.37/5.34  |          neq(all_91_2, nil))
% 31.37/5.34  | 
% 31.37/5.34  | ALPHA: (6) implies:
% 31.37/5.34  |   (7)  ssList(all_91_2)
% 31.37/5.34  |   (8)  ssList(all_91_1)
% 31.37/5.34  |   (9)  ssList(all_91_0)
% 31.37/5.34  |   (10)  $i(all_91_2)
% 31.37/5.34  |   (11)  $i(all_91_1)
% 31.37/5.34  |   (12)  $i(all_91_0)
% 31.37/5.34  |   (13)  app(all_91_2, all_91_0) = all_91_1
% 31.37/5.34  |   (14)   ~ frontsegP(all_91_1, all_91_2) |  ~ neq(all_91_2, nil)
% 31.37/5.34  |   (15)   ~ (all_91_2 = nil) | all_91_1 = nil
% 31.37/5.34  |   (16)   ~ (all_91_1 = nil) |  ~ (all_91_2 = nil)
% 31.37/5.34  | 
% 31.37/5.34  | GROUND_INST: instantiating (2) with all_91_2, nil, simplifying with (3), (4),
% 31.37/5.34  |              (7), (10) gives:
% 31.37/5.34  |   (17)  all_91_2 = nil | neq(all_91_2, nil)
% 31.37/5.34  | 
% 31.37/5.34  | GROUND_INST: instantiating (1) with all_91_1, all_91_2, all_91_0, simplifying
% 31.37/5.34  |              with (7), (8), (9), (10), (11), (12), (13) gives:
% 31.37/5.35  |   (18)  frontsegP(all_91_1, all_91_2)
% 31.37/5.35  | 
% 31.37/5.35  | BETA: splitting (14) gives:
% 31.37/5.35  | 
% 31.37/5.35  | Case 1:
% 31.37/5.35  | | 
% 31.37/5.35  | |   (19)   ~ neq(all_91_2, nil)
% 31.37/5.35  | | 
% 31.37/5.35  | | BETA: splitting (17) gives:
% 31.37/5.35  | | 
% 31.37/5.35  | | Case 1:
% 31.37/5.35  | | | 
% 31.37/5.35  | | |   (20)  neq(all_91_2, nil)
% 31.37/5.35  | | | 
% 31.37/5.35  | | | PRED_UNIFY: (19), (20) imply:
% 31.37/5.35  | | |   (21)  $false
% 31.37/5.35  | | | 
% 31.37/5.35  | | | CLOSE: (21) is inconsistent.
% 31.37/5.35  | | | 
% 31.37/5.35  | | Case 2:
% 31.37/5.35  | | | 
% 31.37/5.35  | | |   (22)  all_91_2 = nil
% 31.37/5.35  | | | 
% 31.37/5.35  | | | BETA: splitting (15) gives:
% 31.37/5.35  | | | 
% 31.37/5.35  | | | Case 1:
% 31.37/5.35  | | | | 
% 31.37/5.35  | | | |   (23)   ~ (all_91_2 = nil)
% 31.37/5.35  | | | | 
% 31.37/5.35  | | | | REDUCE: (22), (23) imply:
% 31.37/5.35  | | | |   (24)  $false
% 31.37/5.35  | | | | 
% 31.37/5.35  | | | | CLOSE: (24) is inconsistent.
% 31.37/5.35  | | | | 
% 31.37/5.35  | | | Case 2:
% 31.37/5.35  | | | | 
% 31.37/5.35  | | | |   (25)  all_91_1 = nil
% 31.37/5.35  | | | | 
% 31.37/5.35  | | | | BETA: splitting (16) gives:
% 31.37/5.35  | | | | 
% 31.37/5.35  | | | | Case 1:
% 31.37/5.35  | | | | | 
% 31.37/5.35  | | | | |   (26)   ~ (all_91_1 = nil)
% 31.37/5.35  | | | | | 
% 31.37/5.35  | | | | | REDUCE: (25), (26) imply:
% 31.37/5.35  | | | | |   (27)  $false
% 31.37/5.35  | | | | | 
% 31.37/5.35  | | | | | CLOSE: (27) is inconsistent.
% 31.37/5.35  | | | | | 
% 31.37/5.35  | | | | Case 2:
% 31.37/5.35  | | | | | 
% 31.37/5.35  | | | | |   (28)   ~ (all_91_2 = nil)
% 31.37/5.35  | | | | | 
% 31.37/5.35  | | | | | REDUCE: (22), (28) imply:
% 31.37/5.35  | | | | |   (29)  $false
% 31.37/5.35  | | | | | 
% 31.37/5.35  | | | | | CLOSE: (29) is inconsistent.
% 31.37/5.35  | | | | | 
% 31.37/5.35  | | | | End of split
% 31.37/5.35  | | | | 
% 31.37/5.35  | | | End of split
% 31.37/5.35  | | | 
% 31.37/5.35  | | End of split
% 31.37/5.35  | | 
% 31.37/5.35  | Case 2:
% 31.37/5.35  | | 
% 31.37/5.35  | |   (30)   ~ frontsegP(all_91_1, all_91_2)
% 31.37/5.35  | | 
% 31.37/5.35  | | PRED_UNIFY: (18), (30) imply:
% 31.37/5.35  | |   (31)  $false
% 31.37/5.35  | | 
% 31.37/5.35  | | CLOSE: (31) is inconsistent.
% 31.37/5.35  | | 
% 31.37/5.35  | End of split
% 31.37/5.35  | 
% 31.37/5.35  End of proof
% 31.37/5.35  % SZS output end Proof for theBenchmark
% 31.37/5.35  
% 31.37/5.35  4731ms
%------------------------------------------------------------------------------