TSTP Solution File: SWC102+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC102+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 : n020.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 27.45s 4.55s
% Output   : Proof 39.92s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC102+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n020.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Mon Aug 28 16:40:44 EDT 2023
% 0.14/0.34  % 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 ...
% 0.21/0.64  Running up to 7 provers in parallel.
% 0.21/0.67  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 7.56/1.86  Prover 1: Preprocessing ...
% 7.56/1.93  Prover 4: Preprocessing ...
% 7.56/1.97  Prover 6: Preprocessing ...
% 7.56/1.97  Prover 0: Preprocessing ...
% 7.56/1.97  Prover 3: Preprocessing ...
% 7.56/1.98  Prover 5: Preprocessing ...
% 7.56/1.98  Prover 2: Preprocessing ...
% 21.29/3.74  Prover 2: Proving ...
% 21.29/3.77  Prover 1: Constructing countermodel ...
% 22.04/3.80  Prover 5: Constructing countermodel ...
% 22.04/3.84  Prover 6: Proving ...
% 23.46/3.99  Prover 3: Constructing countermodel ...
% 27.38/4.49  Prover 6: proved (3821ms)
% 27.45/4.54  
% 27.45/4.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.45/4.55  
% 27.45/4.55  Prover 5: stopped
% 27.45/4.55  Prover 3: stopped
% 27.45/4.56  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 27.45/4.56  Prover 2: stopped
% 27.45/4.57  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 27.45/4.57  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 27.45/4.58  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 29.76/4.84  Prover 8: Preprocessing ...
% 29.76/4.89  Prover 11: Preprocessing ...
% 30.47/4.94  Prover 4: Constructing countermodel ...
% 30.47/4.97  Prover 7: Preprocessing ...
% 31.11/5.07  Prover 10: Preprocessing ...
% 32.29/5.23  Prover 0: Proving ...
% 32.29/5.25  Prover 0: stopped
% 32.29/5.26  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 33.34/5.32  Prover 7: Constructing countermodel ...
% 34.34/5.46  Prover 8: Warning: ignoring some quantifiers
% 34.34/5.47  Prover 13: Preprocessing ...
% 34.34/5.48  Prover 8: Constructing countermodel ...
% 35.03/5.54  Prover 10: Constructing countermodel ...
% 35.66/5.66  Prover 1: Found proof (size 16)
% 35.66/5.66  Prover 1: proved (5003ms)
% 35.66/5.66  Prover 4: stopped
% 35.66/5.66  Prover 7: stopped
% 35.66/5.66  Prover 8: stopped
% 35.66/5.66  Prover 10: stopped
% 35.66/5.66  Prover 13: stopped
% 39.12/6.44  Prover 11: Constructing countermodel ...
% 39.63/6.50  Prover 11: stopped
% 39.63/6.50  
% 39.63/6.50  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.63/6.50  
% 39.63/6.50  % SZS output start Proof for theBenchmark
% 39.63/6.51  Assumptions after simplification:
% 39.63/6.51  ---------------------------------
% 39.63/6.51  
% 39.63/6.51    (ax42)
% 39.63/6.55     ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (frontsegP(v0, v0) = v1) |  ~ $i(v0)
% 39.63/6.56      |  ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 39.63/6.56  
% 39.63/6.56    (co1)
% 39.63/6.56    $i(nil) &  ? [v0: $i] :  ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 39.63/6.56      $i(v0) &  ? [v2: int] : (v1 = 0 &  ~ (v2 = 0) & frontsegP(v0, v0) = v2))
% 39.63/6.56  
% 39.63/6.56    (function-axioms)
% 39.92/6.58     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 39.92/6.58    [v3: $i] : (v1 = v0 |  ~ (gt(v3, v2) = v1) |  ~ (gt(v3, v2) = v0)) &  ! [v0:
% 39.92/6.58      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 39.92/6.58    : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0:
% 39.92/6.58      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 39.92/6.58    : (v1 = v0 |  ~ (lt(v3, v2) = v1) |  ~ (lt(v3, v2) = v0)) &  ! [v0:
% 39.92/6.58      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 39.92/6.58    : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0:
% 39.92/6.58      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 39.92/6.58    : (v1 = v0 |  ~ (segmentP(v3, v2) = v1) |  ~ (segmentP(v3, v2) = v0)) &  !
% 39.92/6.58    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 39.92/6.58      $i] : (v1 = v0 |  ~ (rearsegP(v3, v2) = v1) |  ~ (rearsegP(v3, v2) = v0)) & 
% 39.92/6.58    ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 39.92/6.58      $i] : (v1 = v0 |  ~ (frontsegP(v3, v2) = v1) |  ~ (frontsegP(v3, v2) = v0))
% 39.92/6.58    &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 39.92/6.58    [v3: $i] : (v1 = v0 |  ~ (memberP(v3, v2) = v1) |  ~ (memberP(v3, v2) = v0)) &
% 39.92/6.58     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 39.92/6.58      (cons(v3, v2) = v1) |  ~ (cons(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 39.92/6.58    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (app(v3, v2) = v1) |  ~ (app(v3, v2)
% 39.92/6.58        = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 39.92/6.59      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (neq(v3, v2) = v1) |  ~ (neq(v3, v2) =
% 39.92/6.59        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (tl(v2) =
% 39.92/6.59        v1) |  ~ (tl(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 =
% 39.92/6.59      v0 |  ~ (hd(v2) = v1) |  ~ (hd(v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 39.92/6.59    [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (equalelemsP(v2) = v1) |
% 39.92/6.59       ~ (equalelemsP(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 39.92/6.59      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (duplicatefreeP(v2) = v1) |
% 39.92/6.59       ~ (duplicatefreeP(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 39.92/6.59      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (strictorderedP(v2) = v1) |
% 39.92/6.59       ~ (strictorderedP(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 39.92/6.59      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (totalorderedP(v2) = v1) | 
% 39.92/6.59      ~ (totalorderedP(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 39.92/6.59      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (strictorderP(v2) = v1) | 
% 39.92/6.59      ~ (strictorderP(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 39.92/6.59      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (totalorderP(v2) = v1) |  ~
% 39.92/6.59      (totalorderP(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 39.92/6.59      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (cyclefreeP(v2) = v1) |  ~
% 39.92/6.59      (cyclefreeP(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 39.92/6.59      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (singletonP(v2) = v1) |  ~
% 39.92/6.59      (singletonP(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 39.92/6.59      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (ssList(v2) = v1) |  ~
% 39.92/6.59      (ssList(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool]
% 39.92/6.59    :  ! [v2: $i] : (v1 = v0 |  ~ (ssItem(v2) = v1) |  ~ (ssItem(v2) = v0))
% 39.92/6.59  
% 39.92/6.59  Further assumptions not needed in the proof:
% 39.92/6.59  --------------------------------------------
% 39.92/6.59  ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20,
% 39.92/6.59  ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32,
% 39.92/6.59  ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax45,
% 39.92/6.59  ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57,
% 39.92/6.59  ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69,
% 39.92/6.59  ax7, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80,
% 39.92/6.59  ax81, ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92,
% 39.92/6.59  ax93, ax94, ax95
% 39.92/6.59  
% 39.92/6.59  Those formulas are unsatisfiable:
% 39.92/6.59  ---------------------------------
% 39.92/6.59  
% 39.92/6.59  Begin of proof
% 39.92/6.59  | 
% 39.92/6.59  | ALPHA: (co1) implies:
% 39.92/6.59  |   (1)   ? [v0: $i] :  ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 39.92/6.59  |          $i(v0) &  ? [v2: int] : (v1 = 0 &  ~ (v2 = 0) & frontsegP(v0, v0) =
% 39.92/6.59  |            v2))
% 39.92/6.59  | 
% 39.92/6.59  | ALPHA: (function-axioms) implies:
% 39.92/6.59  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 39.92/6.59  |        (v1 = v0 |  ~ (ssList(v2) = v1) |  ~ (ssList(v2) = v0))
% 39.92/6.59  | 
% 39.92/6.59  | DELTA: instantiating (1) with fresh symbols all_93_0, all_93_1 gives:
% 39.92/6.60  |   (3)  ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) & 
% 39.92/6.60  |        ? [v0: int] : (all_93_0 = 0 &  ~ (v0 = 0) & frontsegP(all_93_1,
% 39.92/6.60  |            all_93_1) = v0)
% 39.92/6.60  | 
% 39.92/6.60  | ALPHA: (3) implies:
% 39.92/6.60  |   (4)  $i(all_93_1)
% 39.92/6.60  |   (5)  ssList(all_93_1) = 0
% 39.92/6.60  |   (6)   ? [v0: int] : (all_93_0 = 0 &  ~ (v0 = 0) & frontsegP(all_93_1,
% 39.92/6.60  |            all_93_1) = v0)
% 39.92/6.60  | 
% 39.92/6.60  | DELTA: instantiating (6) with fresh symbol all_97_0 gives:
% 39.92/6.60  |   (7)  all_93_0 = 0 &  ~ (all_97_0 = 0) & frontsegP(all_93_1, all_93_1) =
% 39.92/6.60  |        all_97_0
% 39.92/6.60  | 
% 39.92/6.60  | ALPHA: (7) implies:
% 39.92/6.60  |   (8)   ~ (all_97_0 = 0)
% 39.92/6.60  |   (9)  frontsegP(all_93_1, all_93_1) = all_97_0
% 39.92/6.60  | 
% 39.92/6.60  | GROUND_INST: instantiating (ax42) with all_93_1, all_97_0, simplifying with
% 39.92/6.60  |              (4), (9) gives:
% 39.92/6.60  |   (10)  all_97_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0)
% 39.92/6.60  | 
% 39.92/6.60  | BETA: splitting (10) gives:
% 39.92/6.60  | 
% 39.92/6.60  | Case 1:
% 39.92/6.60  | | 
% 39.92/6.60  | |   (11)  all_97_0 = 0
% 39.92/6.60  | | 
% 39.92/6.60  | | REDUCE: (8), (11) imply:
% 39.92/6.60  | |   (12)  $false
% 39.92/6.61  | | 
% 39.92/6.61  | | CLOSE: (12) is inconsistent.
% 39.92/6.61  | | 
% 39.92/6.61  | Case 2:
% 39.92/6.61  | | 
% 39.92/6.61  | |   (13)   ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0)
% 39.92/6.61  | | 
% 39.92/6.61  | | DELTA: instantiating (13) with fresh symbol all_245_0 gives:
% 39.92/6.61  | |   (14)   ~ (all_245_0 = 0) & ssList(all_93_1) = all_245_0
% 39.92/6.61  | | 
% 39.92/6.61  | | ALPHA: (14) implies:
% 39.92/6.61  | |   (15)   ~ (all_245_0 = 0)
% 39.92/6.61  | |   (16)  ssList(all_93_1) = all_245_0
% 39.92/6.61  | | 
% 39.92/6.61  | | GROUND_INST: instantiating (2) with 0, all_245_0, all_93_1, simplifying with
% 39.92/6.61  | |              (5), (16) gives:
% 39.92/6.61  | |   (17)  all_245_0 = 0
% 39.92/6.61  | | 
% 39.92/6.61  | | REDUCE: (15), (17) imply:
% 39.92/6.61  | |   (18)  $false
% 39.92/6.61  | | 
% 39.92/6.61  | | CLOSE: (18) is inconsistent.
% 39.92/6.61  | | 
% 39.92/6.61  | End of split
% 39.92/6.61  | 
% 39.92/6.61  End of proof
% 39.92/6.61  % SZS output end Proof for theBenchmark
% 39.92/6.61  
% 39.92/6.61  5992ms
%------------------------------------------------------------------------------