TSTP Solution File: SWC122+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC122+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 : n017.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 20:49:46 EDT 2023

% Result   : Theorem 123.27s 16.82s
% Output   : Proof 123.27s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SWC122+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35  % Computer : n017.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 18:25:12 EDT 2023
% 0.14/0.36  % 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  
% 0.22/0.63  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.64  Running up to 7 provers in parallel.
% 0.22/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.22/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 4.68/1.42  Prover 3: Preprocessing ...
% 4.68/1.42  Prover 5: Preprocessing ...
% 4.68/1.42  Prover 0: Preprocessing ...
% 4.68/1.42  Prover 2: Preprocessing ...
% 4.68/1.43  Prover 4: Preprocessing ...
% 4.68/1.43  Prover 6: Preprocessing ...
% 4.68/1.43  Prover 1: Preprocessing ...
% 14.57/2.68  Prover 2: Proving ...
% 15.02/2.73  Prover 5: Constructing countermodel ...
% 15.33/2.80  Prover 1: Constructing countermodel ...
% 15.90/2.86  Prover 6: Proving ...
% 16.19/2.92  Prover 3: Constructing countermodel ...
% 21.80/3.63  Prover 4: Constructing countermodel ...
% 21.80/3.71  Prover 0: Proving ...
% 72.85/10.28  Prover 2: stopped
% 72.85/10.29  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.47/10.45  Prover 7: Preprocessing ...
% 75.67/10.67  Prover 7: Constructing countermodel ...
% 101.13/13.98  Prover 5: stopped
% 101.13/13.98  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 103.17/14.23  Prover 8: Preprocessing ...
% 103.17/14.26  Prover 3: gave up
% 103.17/14.26  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 104.12/14.35  Prover 9: Preprocessing ...
% 105.01/14.55  Prover 8: Warning: ignoring some quantifiers
% 105.92/14.57  Prover 8: Constructing countermodel ...
% 109.73/15.10  Prover 9: Constructing countermodel ...
% 116.92/15.99  Prover 1: stopped
% 116.92/15.99  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 117.70/16.07  Prover 10: Preprocessing ...
% 118.68/16.22  Prover 10: Constructing countermodel ...
% 123.19/16.80  Prover 10: Found proof (size 23)
% 123.19/16.80  Prover 10: proved (810ms)
% 123.19/16.80  Prover 0: stopped
% 123.19/16.80  Prover 7: stopped
% 123.19/16.81  Prover 8: stopped
% 123.19/16.81  Prover 6: stopped
% 123.27/16.81  Prover 4: stopped
% 123.27/16.82  Prover 9: stopped
% 123.27/16.82  
% 123.27/16.82  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 123.27/16.82  
% 123.27/16.82  % SZS output start Proof for theBenchmark
% 123.27/16.83  Assumptions after simplification:
% 123.27/16.83  ---------------------------------
% 123.27/16.83  
% 123.27/16.83    (ax17)
% 123.27/16.83    $i(nil) & ssList(nil)
% 123.27/16.83  
% 123.27/16.83    (ax42)
% 123.27/16.83     ! [v0: $i] : ( ~ $i(v0) |  ~ ssList(v0) | frontsegP(v0, v0))
% 123.27/16.83  
% 123.27/16.83    (ax5)
% 123.27/16.85     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (app(v1, v2) = v0) |  ~ $i(v2) |
% 123.27/16.85       ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~ ssList(v0) |
% 123.27/16.85      frontsegP(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 123.27/16.85      frontsegP(v0, v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] : (app(v1,
% 123.27/16.85          v2) = v0 & $i(v2) & ssList(v2)))
% 123.27/16.85  
% 123.27/16.85    (ax58)
% 123.27/16.86    $i(nil) &  ! [v0: $i] : (v0 = nil |  ~ $i(v0) |  ~ segmentP(nil, v0) |  ~
% 123.27/16.86      ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 123.27/16.86  
% 123.27/16.86    (ax6)
% 123.27/16.86     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (app(v2, v1) = v0) |  ~ $i(v2) |
% 123.27/16.86       ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~ ssList(v0) |
% 123.27/16.86      rearsegP(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 123.27/16.86      rearsegP(v0, v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] : (app(v2,
% 123.27/16.86          v1) = v0 & $i(v2) & ssList(v2)))
% 123.27/16.86  
% 123.27/16.86    (ax7)
% 123.27/16.86     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~
% 123.27/16.86      (app(v3, v4) = v0) |  ~ (app(v2, v1) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~
% 123.27/16.86      $i(v1) |  ~ $i(v0) |  ~ ssList(v4) |  ~ ssList(v2) |  ~ ssList(v1) |  ~
% 123.27/16.86      ssList(v0) | segmentP(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~
% 123.27/16.86      $i(v0) |  ~ segmentP(v0, v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] :
% 123.27/16.86       ? [v3: $i] :  ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 123.27/16.86        $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 123.27/16.86  
% 123.27/16.86    (co1)
% 123.27/16.86    $i(nil) &  ? [v0: $i] :  ? [v1: $i] : ($i(v1) & $i(v0) & rearsegP(v1, v0) &
% 123.27/16.86      ssList(v1) & ssList(v0) & neq(v1, nil) & neq(v0, nil) &  ~ segmentP(v1, v0)
% 123.27/16.86      & ( ~ (v1 = nil) | v0 = nil))
% 123.27/16.86  
% 123.27/16.86  Further assumptions not needed in the proof:
% 123.27/16.86  --------------------------------------------
% 123.27/16.86  ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 123.27/16.87  ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 123.27/16.87  ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax45, ax46,
% 123.27/16.87  ax47, ax48, ax49, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax60,
% 123.27/16.87  ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax70, ax71, ax72, ax73,
% 123.27/16.87  ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85,
% 123.27/16.87  ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 123.27/16.87  
% 123.27/16.87  Those formulas are unsatisfiable:
% 123.27/16.87  ---------------------------------
% 123.27/16.87  
% 123.27/16.87  Begin of proof
% 123.27/16.87  | 
% 123.27/16.87  | ALPHA: (ax5) implies:
% 123.27/16.87  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ frontsegP(v0,
% 123.27/16.87  |            v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] : (app(v1, v2) =
% 123.27/16.87  |            v0 & $i(v2) & ssList(v2)))
% 123.27/16.87  | 
% 123.27/16.87  | ALPHA: (ax6) implies:
% 123.27/16.87  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ rearsegP(v0,
% 123.27/16.87  |            v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] : (app(v2, v1) =
% 123.27/16.87  |            v0 & $i(v2) & ssList(v2)))
% 123.27/16.87  | 
% 123.27/16.87  | ALPHA: (ax7) implies:
% 123.27/16.87  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (
% 123.27/16.87  |          ~ (app(v3, v4) = v0) |  ~ (app(v2, v1) = v3) |  ~ $i(v4) |  ~ $i(v2)
% 123.27/16.87  |          |  ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v4) |  ~ ssList(v2) |  ~
% 123.27/16.87  |          ssList(v1) |  ~ ssList(v0) | segmentP(v0, v1))
% 123.27/16.87  | 
% 123.27/16.87  | ALPHA: (ax17) implies:
% 123.27/16.87  |   (4)  ssList(nil)
% 123.27/16.87  | 
% 123.27/16.87  | ALPHA: (ax58) implies:
% 123.27/16.87  |   (5)   ~ ssList(nil) | segmentP(nil, nil)
% 123.27/16.87  | 
% 123.27/16.87  | ALPHA: (co1) implies:
% 123.27/16.87  |   (6)   ? [v0: $i] :  ? [v1: $i] : ($i(v1) & $i(v0) & rearsegP(v1, v0) &
% 123.27/16.87  |          ssList(v1) & ssList(v0) & neq(v1, nil) & neq(v0, nil) &  ~
% 123.27/16.87  |          segmentP(v1, v0) & ( ~ (v1 = nil) | v0 = nil))
% 123.27/16.87  | 
% 123.27/16.88  | DELTA: instantiating (6) with fresh symbols all_91_0, all_91_1 gives:
% 123.27/16.88  |   (7)  $i(all_91_0) & $i(all_91_1) & rearsegP(all_91_0, all_91_1) &
% 123.27/16.88  |        ssList(all_91_0) & ssList(all_91_1) & neq(all_91_0, nil) &
% 123.27/16.88  |        neq(all_91_1, nil) &  ~ segmentP(all_91_0, all_91_1) & ( ~ (all_91_0 =
% 123.27/16.88  |            nil) | all_91_1 = nil)
% 123.27/16.88  | 
% 123.27/16.88  | ALPHA: (7) implies:
% 123.27/16.88  |   (8)   ~ segmentP(all_91_0, all_91_1)
% 123.27/16.88  |   (9)  ssList(all_91_1)
% 123.27/16.88  |   (10)  ssList(all_91_0)
% 123.27/16.88  |   (11)  rearsegP(all_91_0, all_91_1)
% 123.27/16.88  |   (12)  $i(all_91_1)
% 123.27/16.88  |   (13)  $i(all_91_0)
% 123.27/16.88  | 
% 123.27/16.88  | BETA: splitting (5) gives:
% 123.27/16.88  | 
% 123.27/16.88  | Case 1:
% 123.27/16.88  | | 
% 123.27/16.88  | |   (14)   ~ ssList(nil)
% 123.27/16.88  | | 
% 123.27/16.88  | | PRED_UNIFY: (4), (14) imply:
% 123.27/16.88  | |   (15)  $false
% 123.27/16.88  | | 
% 123.27/16.88  | | CLOSE: (15) is inconsistent.
% 123.27/16.88  | | 
% 123.27/16.88  | Case 2:
% 123.27/16.88  | | 
% 123.27/16.88  | | 
% 123.27/16.88  | | GROUND_INST: instantiating (ax42) with all_91_0, simplifying with (10), (13)
% 123.27/16.88  | |              gives:
% 123.27/16.88  | |   (16)  frontsegP(all_91_0, all_91_0)
% 123.27/16.88  | | 
% 123.27/16.88  | | GROUND_INST: instantiating (2) with all_91_0, all_91_1, simplifying with
% 123.27/16.88  | |              (9), (10), (11), (12), (13) gives:
% 123.27/16.88  | |   (17)   ? [v0: $i] : (app(v0, all_91_1) = all_91_0 & $i(v0) & ssList(v0))
% 123.27/16.88  | | 
% 123.27/16.88  | | DELTA: instantiating (17) with fresh symbol all_111_0 gives:
% 123.27/16.88  | |   (18)  app(all_111_0, all_91_1) = all_91_0 & $i(all_111_0) &
% 123.27/16.88  | |         ssList(all_111_0)
% 123.27/16.88  | | 
% 123.27/16.88  | | ALPHA: (18) implies:
% 123.27/16.88  | |   (19)  ssList(all_111_0)
% 123.27/16.88  | |   (20)  $i(all_111_0)
% 123.27/16.88  | |   (21)  app(all_111_0, all_91_1) = all_91_0
% 123.27/16.88  | | 
% 123.27/16.88  | | GROUND_INST: instantiating (1) with all_91_0, all_91_0, simplifying with
% 123.27/16.88  | |              (10), (13), (16) gives:
% 123.27/16.88  | |   (22)   ? [v0: $i] : (app(all_91_0, v0) = all_91_0 & $i(v0) & ssList(v0))
% 123.27/16.88  | | 
% 123.27/16.88  | | DELTA: instantiating (22) with fresh symbol all_143_0 gives:
% 123.27/16.88  | |   (23)  app(all_91_0, all_143_0) = all_91_0 & $i(all_143_0) &
% 123.27/16.88  | |         ssList(all_143_0)
% 123.27/16.88  | | 
% 123.27/16.88  | | ALPHA: (23) implies:
% 123.27/16.88  | |   (24)  ssList(all_143_0)
% 123.27/16.88  | |   (25)  $i(all_143_0)
% 123.27/16.88  | |   (26)  app(all_91_0, all_143_0) = all_91_0
% 123.27/16.88  | | 
% 123.27/16.89  | | GROUND_INST: instantiating (3) with all_91_0, all_91_1, all_111_0, all_91_0,
% 123.27/16.89  | |              all_143_0, simplifying with (8), (9), (10), (12), (13), (19),
% 123.27/16.89  | |              (20), (21), (24), (25), (26) gives:
% 123.27/16.89  | |   (27)  $false
% 123.27/16.89  | | 
% 123.27/16.89  | | CLOSE: (27) is inconsistent.
% 123.27/16.89  | | 
% 123.27/16.89  | End of split
% 123.27/16.89  | 
% 123.27/16.89  End of proof
% 123.27/16.89  % SZS output end Proof for theBenchmark
% 123.27/16.89  
% 123.27/16.89  16262ms
%------------------------------------------------------------------------------