TSTP Solution File: SWC095+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC095+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 : n028.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 20:49:37 EDT 2023

% Result   : Theorem 26.26s 4.13s
% Output   : Proof 35.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWC095+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Mon Aug 28 15:00:39 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.19/0.58  ________       _____
% 0.19/0.58  ___  __ \_________(_)________________________________
% 0.19/0.58  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.58  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.58  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58  (2023-06-19)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2023
% 0.19/0.58  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58                Amanda Stjerna.
% 0.19/0.58  Free software under BSD-3-Clause.
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58  
% 0.19/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60  Running up to 7 provers in parallel.
% 0.19/0.61  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.61  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 6.93/1.59  Prover 4: Preprocessing ...
% 6.93/1.60  Prover 1: Preprocessing ...
% 7.14/1.63  Prover 3: Preprocessing ...
% 7.14/1.63  Prover 0: Preprocessing ...
% 7.14/1.63  Prover 2: Preprocessing ...
% 7.14/1.63  Prover 5: Preprocessing ...
% 7.14/1.63  Prover 6: Preprocessing ...
% 16.61/2.91  Prover 2: Proving ...
% 17.41/3.03  Prover 1: Constructing countermodel ...
% 17.87/3.05  Prover 5: Constructing countermodel ...
% 17.87/3.06  Prover 6: Proving ...
% 18.25/3.12  Prover 3: Constructing countermodel ...
% 22.49/3.74  Prover 4: Constructing countermodel ...
% 24.66/3.95  Prover 0: Proving ...
% 26.26/4.12  Prover 0: proved (3522ms)
% 26.26/4.13  
% 26.26/4.13  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.26/4.13  
% 26.26/4.13  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 26.26/4.13  Prover 2: stopped
% 26.26/4.14  Prover 5: stopped
% 26.26/4.15  Prover 3: stopped
% 26.26/4.16  Prover 6: stopped
% 26.26/4.17  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 26.26/4.17  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 26.26/4.17  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 26.26/4.17  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 27.47/4.37  Prover 13: Preprocessing ...
% 27.47/4.37  Prover 10: Preprocessing ...
% 27.47/4.38  Prover 8: Preprocessing ...
% 27.47/4.39  Prover 7: Preprocessing ...
% 28.72/4.47  Prover 11: Preprocessing ...
% 30.43/4.71  Prover 10: Constructing countermodel ...
% 30.43/4.73  Prover 7: Constructing countermodel ...
% 30.43/4.74  Prover 13: Constructing countermodel ...
% 31.07/4.77  Prover 8: Warning: ignoring some quantifiers
% 31.26/4.79  Prover 8: Constructing countermodel ...
% 33.08/5.09  Prover 10: Found proof (size 17)
% 33.08/5.09  Prover 10: proved (946ms)
% 33.08/5.09  Prover 4: stopped
% 33.08/5.09  Prover 7: stopped
% 33.08/5.09  Prover 8: stopped
% 33.08/5.09  Prover 1: stopped
% 33.08/5.09  Prover 13: stopped
% 34.91/5.46  Prover 11: Constructing countermodel ...
% 34.91/5.48  Prover 11: stopped
% 35.24/5.48  
% 35.24/5.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.24/5.48  
% 35.24/5.49  % SZS output start Proof for theBenchmark
% 35.24/5.49  Assumptions after simplification:
% 35.24/5.49  ---------------------------------
% 35.24/5.49  
% 35.24/5.49    (ax17)
% 35.24/5.50    $i(nil) & ssList(nil)
% 35.24/5.50  
% 35.24/5.50    (ax58)
% 35.24/5.50    $i(nil) &  ! [v0: $i] : (v0 = nil |  ~ $i(v0) |  ~ segmentP(nil, v0) |  ~
% 35.24/5.50      ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 35.24/5.50  
% 35.24/5.50    (co1)
% 35.24/5.55     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 35.24/5.55      $i] : (app(v4, v5) = v0 & app(v2, v5) = v1 & app(v2, v3) = v4 & $i(v5) &
% 35.24/5.55      $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v5) & ssList(v3) &
% 35.24/5.55      ssList(v2) & ssList(v1) & ssList(v0) &  ! [v6: $i] :  ! [v7: $i] :  ! [v8:
% 35.24/5.55        $i] :  ! [v9: $i] : ( ~ (app(v8, v9) = v0) |  ~ (app(v6, v7) = v8) |  ~
% 35.24/5.55        $i(v9) |  ~ $i(v7) |  ~ $i(v6) |  ~ ssList(v9) |  ~ ssList(v7) |  ~
% 35.24/5.55        ssList(v6) |  ? [v10: $i] : ( ~ (v10 = v1) & app(v6, v9) = v10 &
% 35.24/5.55          $i(v10))))
% 35.24/5.55  
% 35.24/5.55    (function-axioms)
% 35.24/5.55     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 35.24/5.55      (cons(v3, v2) = v1) |  ~ (cons(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 35.24/5.55    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (app(v3, v2) = v1) |  ~ (app(v3, v2)
% 35.24/5.55        = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (tl(v2) =
% 35.24/5.55        v1) |  ~ (tl(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 =
% 35.24/5.55      v0 |  ~ (hd(v2) = v1) |  ~ (hd(v2) = v0))
% 35.24/5.55  
% 35.24/5.55  Further assumptions not needed in the proof:
% 35.24/5.55  --------------------------------------------
% 35.24/5.55  ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 35.24/5.55  ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 35.24/5.55  ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45,
% 35.24/5.55  ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57,
% 35.24/5.55  ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 35.24/5.55  ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 35.24/5.55  ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 35.24/5.55  ax94, ax95
% 35.24/5.55  
% 35.24/5.55  Those formulas are unsatisfiable:
% 35.24/5.55  ---------------------------------
% 35.24/5.55  
% 35.24/5.55  Begin of proof
% 35.24/5.55  | 
% 35.24/5.55  | ALPHA: (ax17) implies:
% 35.24/5.56  |   (1)  ssList(nil)
% 35.24/5.56  | 
% 35.24/5.56  | ALPHA: (ax58) implies:
% 35.24/5.56  |   (2)   ~ ssList(nil) | segmentP(nil, nil)
% 35.24/5.56  | 
% 35.24/5.56  | ALPHA: (function-axioms) implies:
% 35.24/5.56  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 35.24/5.56  |          (app(v3, v2) = v1) |  ~ (app(v3, v2) = v0))
% 35.24/5.56  | 
% 35.24/5.56  | DELTA: instantiating (co1) with fresh symbols all_91_0, all_91_1, all_91_2,
% 35.24/5.56  |        all_91_3, all_91_4, all_91_5 gives:
% 35.24/5.56  |   (4)  app(all_91_1, all_91_0) = all_91_5 & app(all_91_3, all_91_0) = all_91_4
% 35.24/5.56  |        & app(all_91_3, all_91_2) = all_91_1 & $i(all_91_0) & $i(all_91_1) &
% 35.24/5.56  |        $i(all_91_2) & $i(all_91_3) & $i(all_91_4) & $i(all_91_5) &
% 35.24/5.56  |        ssList(all_91_0) & ssList(all_91_2) & ssList(all_91_3) &
% 35.24/5.56  |        ssList(all_91_4) & ssList(all_91_5) &  ! [v0: $i] :  ! [v1: $i] :  !
% 35.24/5.56  |        [v2: $i] :  ! [v3: $i] : ( ~ (app(v2, v3) = all_91_5) |  ~ (app(v0, v1)
% 35.24/5.56  |            = v2) |  ~ $i(v3) |  ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v3) |  ~
% 35.24/5.56  |          ssList(v1) |  ~ ssList(v0) |  ? [v4: any] : ( ~ (v4 = all_91_4) &
% 35.24/5.56  |            app(v0, v3) = v4 & $i(v4)))
% 35.24/5.56  | 
% 35.24/5.56  | ALPHA: (4) implies:
% 35.24/5.56  |   (5)  ssList(all_91_3)
% 35.24/5.57  |   (6)  ssList(all_91_2)
% 35.24/5.57  |   (7)  ssList(all_91_0)
% 35.24/5.57  |   (8)  $i(all_91_3)
% 35.24/5.57  |   (9)  $i(all_91_2)
% 35.24/5.57  |   (10)  $i(all_91_0)
% 35.24/5.57  |   (11)  app(all_91_3, all_91_2) = all_91_1
% 35.24/5.57  |   (12)  app(all_91_3, all_91_0) = all_91_4
% 35.24/5.57  |   (13)  app(all_91_1, all_91_0) = all_91_5
% 35.24/5.57  |   (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (app(v2,
% 35.24/5.57  |               v3) = all_91_5) |  ~ (app(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v1)
% 35.24/5.57  |           |  ~ $i(v0) |  ~ ssList(v3) |  ~ ssList(v1) |  ~ ssList(v0) |  ?
% 35.24/5.57  |           [v4: any] : ( ~ (v4 = all_91_4) & app(v0, v3) = v4 & $i(v4)))
% 35.24/5.57  | 
% 35.24/5.57  | BETA: splitting (2) gives:
% 35.24/5.57  | 
% 35.24/5.57  | Case 1:
% 35.24/5.57  | | 
% 35.24/5.57  | |   (15)   ~ ssList(nil)
% 35.24/5.57  | | 
% 35.24/5.57  | | PRED_UNIFY: (1), (15) imply:
% 35.24/5.57  | |   (16)  $false
% 35.24/5.57  | | 
% 35.24/5.57  | | CLOSE: (16) is inconsistent.
% 35.24/5.57  | | 
% 35.24/5.57  | Case 2:
% 35.24/5.57  | | 
% 35.24/5.57  | | 
% 35.24/5.57  | | GROUND_INST: instantiating (14) with all_91_3, all_91_2, all_91_1, all_91_0,
% 35.24/5.57  | |              simplifying with (5), (6), (7), (8), (9), (10), (11), (13)
% 35.24/5.57  | |              gives:
% 35.24/5.57  | |   (17)   ? [v0: any] : ( ~ (v0 = all_91_4) & app(all_91_3, all_91_0) = v0 &
% 35.24/5.57  | |           $i(v0))
% 35.24/5.57  | | 
% 35.24/5.57  | | DELTA: instantiating (17) with fresh symbol all_114_0 gives:
% 35.67/5.57  | |   (18)   ~ (all_114_0 = all_91_4) & app(all_91_3, all_91_0) = all_114_0 &
% 35.67/5.57  | |         $i(all_114_0)
% 35.67/5.57  | | 
% 35.67/5.57  | | ALPHA: (18) implies:
% 35.67/5.58  | |   (19)   ~ (all_114_0 = all_91_4)
% 35.67/5.58  | |   (20)  app(all_91_3, all_91_0) = all_114_0
% 35.67/5.58  | | 
% 35.67/5.58  | | GROUND_INST: instantiating (3) with all_91_4, all_114_0, all_91_0, all_91_3,
% 35.67/5.58  | |              simplifying with (12), (20) gives:
% 35.67/5.58  | |   (21)  all_114_0 = all_91_4
% 35.67/5.58  | | 
% 35.67/5.58  | | REDUCE: (19), (21) imply:
% 35.67/5.58  | |   (22)  $false
% 35.67/5.58  | | 
% 35.67/5.58  | | CLOSE: (22) is inconsistent.
% 35.67/5.58  | | 
% 35.67/5.58  | End of split
% 35.67/5.58  | 
% 35.67/5.58  End of proof
% 35.67/5.58  % SZS output end Proof for theBenchmark
% 35.67/5.58  
% 35.67/5.58  4993ms
%------------------------------------------------------------------------------