TSTP Solution File: SWC242+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC242+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 : n002.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 20:50:25 EDT 2023

% Result   : Theorem 28.01s 4.41s
% Output   : Proof 36.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC242+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.21/0.34  % WCLimit  : 300
% 0.21/0.34  % DateTime : Mon Aug 28 16:09:19 EDT 2023
% 0.21/0.34  % CPUTime  : 
% 0.21/0.62  ________       _____
% 0.21/0.62  ___  __ \_________(_)________________________________
% 0.21/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62  
% 0.21/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62  (2023-06-19)
% 0.21/0.62  
% 0.21/0.62  (c) Philipp Rümmer, 2009-2023
% 0.21/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62                Amanda Stjerna.
% 0.21/0.62  Free software under BSD-3-Clause.
% 0.21/0.62  
% 0.21/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62  
% 0.21/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63  Running up to 7 provers in parallel.
% 0.21/0.66  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.16/1.40  Prover 1: Preprocessing ...
% 5.21/1.41  Prover 4: Preprocessing ...
% 5.21/1.44  Prover 6: Preprocessing ...
% 5.21/1.44  Prover 3: Preprocessing ...
% 5.21/1.44  Prover 0: Preprocessing ...
% 5.21/1.44  Prover 2: Preprocessing ...
% 5.21/1.44  Prover 5: Preprocessing ...
% 15.93/2.84  Prover 2: Proving ...
% 15.93/2.88  Prover 1: Constructing countermodel ...
% 15.93/2.89  Prover 5: Constructing countermodel ...
% 16.63/2.95  Prover 3: Constructing countermodel ...
% 16.63/2.97  Prover 6: Proving ...
% 24.82/4.01  Prover 4: Constructing countermodel ...
% 24.82/4.04  Prover 0: Proving ...
% 28.01/4.41  Prover 0: proved (3766ms)
% 28.01/4.41  
% 28.01/4.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.01/4.41  
% 28.01/4.41  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 28.01/4.41  Prover 2: stopped
% 28.01/4.42  Prover 3: stopped
% 28.01/4.43  Prover 5: stopped
% 28.01/4.44  Prover 6: stopped
% 28.01/4.44  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 28.01/4.44  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 28.01/4.44  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 28.01/4.44  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 29.56/4.63  Prover 7: Preprocessing ...
% 29.56/4.64  Prover 8: Preprocessing ...
% 29.56/4.65  Prover 13: Preprocessing ...
% 29.56/4.67  Prover 11: Preprocessing ...
% 30.02/4.69  Prover 10: Preprocessing ...
% 31.32/4.89  Prover 10: Constructing countermodel ...
% 31.32/4.90  Prover 7: Constructing countermodel ...
% 31.92/4.95  Prover 13: Constructing countermodel ...
% 32.38/5.00  Prover 8: Warning: ignoring some quantifiers
% 32.38/5.01  Prover 8: Constructing countermodel ...
% 35.78/5.42  Prover 10: Found proof (size 16)
% 35.86/5.42  Prover 10: proved (977ms)
% 35.86/5.42  Prover 7: stopped
% 35.86/5.42  Prover 8: stopped
% 35.86/5.42  Prover 13: stopped
% 35.86/5.42  Prover 4: stopped
% 35.86/5.42  Prover 1: stopped
% 36.51/5.63  Prover 11: Constructing countermodel ...
% 36.51/5.65  Prover 11: stopped
% 36.51/5.65  
% 36.51/5.66  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.51/5.66  
% 36.51/5.66  % SZS output start Proof for theBenchmark
% 36.51/5.67  Assumptions after simplification:
% 36.51/5.67  ---------------------------------
% 36.51/5.67  
% 36.51/5.67    (ax17)
% 36.89/5.67    $i(nil) & ssList(nil)
% 36.89/5.67  
% 36.89/5.67    (ax58)
% 36.89/5.68    $i(nil) &  ! [v0: $i] : (v0 = nil |  ~ $i(v0) |  ~ segmentP(nil, v0) |  ~
% 36.89/5.68      ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 36.89/5.68  
% 36.89/5.68    (co1)
% 36.96/5.72    $i(nil) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i]
% 36.96/5.72    :  ? [v5: $i] :  ? [v6: $i] : ( ~ (v0 = nil) & cons(v2, nil) = v3 & app(v5,
% 36.96/5.72        v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 36.96/5.72      $i(v1) & $i(v0) & ssList(v6) & ssList(v4) & ssList(v1) & ssList(v0) &
% 36.96/5.72      ssItem(v2) &  ! [v7: $i] :  ! [v8: $i] :  ! [v9: $i] :  ! [v10: $i] :  !
% 36.96/5.72      [v11: $i] : ( ~ (cons(v7, nil) = v8) |  ~ (app(v10, v11) = v0) |  ~ (app(v9,
% 36.96/5.72            v8) = v10) |  ~ $i(v11) |  ~ $i(v9) |  ~ $i(v7) |  ~ ssList(v11) |  ~
% 36.96/5.72        ssList(v9) |  ~ ssItem(v7) |  ? [v12: $i] : ($i(v12) & lt(v7, v12) &
% 36.96/5.72          memberP(v11, v12) & memberP(v9, v12) & ssItem(v12) &  ~ leq(v7, v12))) &
% 36.96/5.72       ! [v7: $i] : ( ~ $i(v7) |  ~ lt(v2, v7) |  ~ memberP(v6, v7) |  ~
% 36.96/5.72        memberP(v4, v7) |  ~ ssItem(v7) | leq(v2, v7)))
% 36.96/5.72  
% 36.96/5.72  Further assumptions not needed in the proof:
% 36.96/5.72  --------------------------------------------
% 36.96/5.72  ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 36.96/5.72  ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 36.96/5.72  ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45,
% 36.96/5.72  ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57,
% 36.96/5.72  ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 36.96/5.72  ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 36.96/5.72  ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 36.96/5.72  ax94, ax95
% 36.96/5.72  
% 36.96/5.72  Those formulas are unsatisfiable:
% 36.96/5.72  ---------------------------------
% 36.96/5.72  
% 36.96/5.72  Begin of proof
% 36.96/5.72  | 
% 36.96/5.72  | ALPHA: (ax17) implies:
% 36.96/5.72  |   (1)  ssList(nil)
% 36.96/5.72  | 
% 36.96/5.72  | ALPHA: (ax58) implies:
% 36.96/5.72  |   (2)   ~ ssList(nil) | segmentP(nil, nil)
% 36.96/5.72  | 
% 36.96/5.72  | ALPHA: (co1) implies:
% 36.96/5.73  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 36.96/5.73  |        ? [v5: $i] :  ? [v6: $i] : ( ~ (v0 = nil) & cons(v2, nil) = v3 &
% 36.96/5.73  |          app(v5, v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) &
% 36.96/5.73  |          $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v6) & ssList(v4) &
% 36.96/5.73  |          ssList(v1) & ssList(v0) & ssItem(v2) &  ! [v7: $i] :  ! [v8: $i] :  !
% 36.96/5.73  |          [v9: $i] :  ! [v10: $i] :  ! [v11: $i] : ( ~ (cons(v7, nil) = v8) | 
% 36.96/5.73  |            ~ (app(v10, v11) = v0) |  ~ (app(v9, v8) = v10) |  ~ $i(v11) |  ~
% 36.96/5.73  |            $i(v9) |  ~ $i(v7) |  ~ ssList(v11) |  ~ ssList(v9) |  ~ ssItem(v7)
% 36.96/5.73  |            |  ? [v12: $i] : ($i(v12) & lt(v7, v12) & memberP(v11, v12) &
% 36.96/5.73  |              memberP(v9, v12) & ssItem(v12) &  ~ leq(v7, v12))) &  ! [v7: $i]
% 36.96/5.73  |          : ( ~ $i(v7) |  ~ lt(v2, v7) |  ~ memberP(v6, v7) |  ~ memberP(v4,
% 36.96/5.73  |              v7) |  ~ ssItem(v7) | leq(v2, v7)))
% 36.96/5.73  | 
% 36.96/5.73  | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2,
% 36.96/5.73  |        all_91_3, all_91_4, all_91_5, all_91_6 gives:
% 36.96/5.73  |   (4)   ~ (all_91_6 = nil) & cons(all_91_4, nil) = all_91_3 & app(all_91_1,
% 36.96/5.73  |          all_91_0) = all_91_6 & app(all_91_2, all_91_3) = all_91_1 &
% 36.96/5.73  |        $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 36.96/5.73  |        $i(all_91_4) & $i(all_91_5) & $i(all_91_6) & ssList(all_91_0) &
% 36.96/5.73  |        ssList(all_91_2) & ssList(all_91_5) & ssList(all_91_6) &
% 36.96/5.73  |        ssItem(all_91_4) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 36.96/5.73  |          $i] :  ! [v4: $i] : ( ~ (cons(v0, nil) = v1) |  ~ (app(v3, v4) =
% 36.96/5.73  |            all_91_6) |  ~ (app(v2, v1) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~
% 36.96/5.73  |          $i(v0) |  ~ ssList(v4) |  ~ ssList(v2) |  ~ ssItem(v0) |  ? [v5: $i]
% 36.96/5.73  |          : ($i(v5) & lt(v0, v5) & memberP(v4, v5) & memberP(v2, v5) &
% 36.96/5.73  |            ssItem(v5) &  ~ leq(v0, v5))) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 36.96/5.73  |          lt(all_91_4, v0) |  ~ memberP(all_91_0, v0) |  ~ memberP(all_91_2,
% 36.96/5.73  |            v0) |  ~ ssItem(v0) | leq(all_91_4, v0))
% 36.96/5.73  | 
% 36.96/5.73  | ALPHA: (4) implies:
% 36.96/5.73  |   (5)  ssItem(all_91_4)
% 36.96/5.73  |   (6)  ssList(all_91_2)
% 36.96/5.73  |   (7)  ssList(all_91_0)
% 36.96/5.73  |   (8)  $i(all_91_4)
% 36.96/5.73  |   (9)  $i(all_91_2)
% 36.96/5.73  |   (10)  $i(all_91_0)
% 36.96/5.73  |   (11)  app(all_91_2, all_91_3) = all_91_1
% 36.96/5.73  |   (12)  app(all_91_1, all_91_0) = all_91_6
% 36.96/5.73  |   (13)  cons(all_91_4, nil) = all_91_3
% 36.96/5.73  |   (14)   ! [v0: $i] : ( ~ $i(v0) |  ~ lt(all_91_4, v0) |  ~ memberP(all_91_0,
% 36.96/5.73  |             v0) |  ~ memberP(all_91_2, v0) |  ~ ssItem(v0) | leq(all_91_4,
% 36.96/5.73  |             v0))
% 36.96/5.74  |   (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 36.96/5.74  |         ( ~ (cons(v0, nil) = v1) |  ~ (app(v3, v4) = all_91_6) |  ~ (app(v2,
% 36.96/5.74  |               v1) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~ $i(v0) |  ~ ssList(v4) | 
% 36.96/5.74  |           ~ ssList(v2) |  ~ ssItem(v0) |  ? [v5: $i] : ($i(v5) & lt(v0, v5) &
% 36.96/5.74  |             memberP(v4, v5) & memberP(v2, v5) & ssItem(v5) &  ~ leq(v0, v5)))
% 36.96/5.74  | 
% 36.96/5.74  | BETA: splitting (2) gives:
% 36.96/5.74  | 
% 36.96/5.74  | Case 1:
% 36.96/5.74  | | 
% 36.96/5.74  | |   (16)   ~ ssList(nil)
% 36.96/5.74  | | 
% 36.96/5.74  | | PRED_UNIFY: (1), (16) imply:
% 36.96/5.74  | |   (17)  $false
% 36.96/5.74  | | 
% 36.96/5.74  | | CLOSE: (17) is inconsistent.
% 36.96/5.74  | | 
% 36.96/5.74  | Case 2:
% 36.96/5.74  | | 
% 36.96/5.74  | | 
% 36.96/5.74  | | GROUND_INST: instantiating (15) with all_91_4, all_91_3, all_91_2, all_91_1,
% 36.96/5.74  | |              all_91_0, simplifying with (5), (6), (7), (8), (9), (10), (11),
% 36.96/5.74  | |              (12), (13) gives:
% 36.96/5.74  | |   (18)   ? [v0: $i] : ($i(v0) & lt(all_91_4, v0) & memberP(all_91_0, v0) &
% 36.96/5.74  | |           memberP(all_91_2, v0) & ssItem(v0) &  ~ leq(all_91_4, v0))
% 36.96/5.74  | | 
% 36.96/5.74  | | DELTA: instantiating (18) with fresh symbol all_116_0 gives:
% 36.96/5.74  | |   (19)  $i(all_116_0) & lt(all_91_4, all_116_0) & memberP(all_91_0,
% 36.96/5.74  | |           all_116_0) & memberP(all_91_2, all_116_0) & ssItem(all_116_0) &  ~
% 36.96/5.74  | |         leq(all_91_4, all_116_0)
% 36.96/5.74  | | 
% 36.96/5.74  | | ALPHA: (19) implies:
% 36.96/5.74  | |   (20)   ~ leq(all_91_4, all_116_0)
% 36.96/5.74  | |   (21)  ssItem(all_116_0)
% 36.96/5.74  | |   (22)  memberP(all_91_2, all_116_0)
% 36.96/5.74  | |   (23)  memberP(all_91_0, all_116_0)
% 36.96/5.74  | |   (24)  lt(all_91_4, all_116_0)
% 36.96/5.74  | |   (25)  $i(all_116_0)
% 36.96/5.74  | | 
% 36.96/5.74  | | GROUND_INST: instantiating (14) with all_116_0, simplifying with (20), (21),
% 36.96/5.74  | |              (22), (23), (24), (25) gives:
% 36.96/5.74  | |   (26)  $false
% 36.96/5.74  | | 
% 36.96/5.74  | | CLOSE: (26) is inconsistent.
% 36.96/5.74  | | 
% 36.96/5.74  | End of split
% 36.96/5.74  | 
% 36.96/5.74  End of proof
% 36.96/5.74  % SZS output end Proof for theBenchmark
% 36.96/5.74  
% 36.96/5.74  5120ms
%------------------------------------------------------------------------------