TSTP Solution File: SWC106+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWC106+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 20:49:41 EDT 2023

% Result   : Theorem 38.87s 5.94s
% Output   : Proof 47.07s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC106+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12  % 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 15:34:39 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.18/0.58  ________       _____
% 0.18/0.58  ___  __ \_________(_)________________________________
% 0.18/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.18/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.18/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59  
% 0.18/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59  (2023-06-19)
% 0.18/0.59  
% 0.18/0.59  (c) Philipp Rümmer, 2009-2023
% 0.18/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59                Amanda Stjerna.
% 0.18/0.59  Free software under BSD-3-Clause.
% 0.18/0.59  
% 0.18/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59  
% 0.18/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.60  Running up to 7 provers in parallel.
% 0.18/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.74/1.36  Prover 4: Preprocessing ...
% 4.74/1.36  Prover 1: Preprocessing ...
% 5.16/1.41  Prover 5: Preprocessing ...
% 5.16/1.41  Prover 6: Preprocessing ...
% 5.16/1.41  Prover 2: Preprocessing ...
% 5.16/1.41  Prover 3: Preprocessing ...
% 5.16/1.41  Prover 0: Preprocessing ...
% 14.28/2.64  Prover 2: Proving ...
% 15.33/2.82  Prover 6: Proving ...
% 15.33/2.82  Prover 5: Constructing countermodel ...
% 15.98/2.84  Prover 1: Constructing countermodel ...
% 16.36/2.91  Prover 3: Constructing countermodel ...
% 22.06/3.67  Prover 4: Constructing countermodel ...
% 23.23/3.81  Prover 0: Proving ...
% 38.87/5.94  Prover 3: proved (5324ms)
% 38.87/5.94  
% 38.87/5.94  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.87/5.94  
% 38.87/5.94  Prover 5: stopped
% 38.87/5.95  Prover 0: stopped
% 38.87/5.96  Prover 2: stopped
% 40.07/5.96  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 40.07/5.96  Prover 6: stopped
% 40.07/5.97  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 40.07/5.97  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 40.07/5.97  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 40.07/5.97  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 41.01/6.11  Prover 7: Preprocessing ...
% 41.46/6.17  Prover 11: Preprocessing ...
% 41.46/6.19  Prover 8: Preprocessing ...
% 41.46/6.21  Prover 13: Preprocessing ...
% 42.06/6.23  Prover 10: Preprocessing ...
% 43.36/6.39  Prover 10: Constructing countermodel ...
% 43.36/6.41  Prover 7: Constructing countermodel ...
% 43.81/6.54  Prover 13: Constructing countermodel ...
% 44.76/6.57  Prover 8: Warning: ignoring some quantifiers
% 44.76/6.59  Prover 8: Constructing countermodel ...
% 44.76/6.60  Prover 10: Found proof (size 27)
% 44.76/6.60  Prover 10: proved (631ms)
% 44.76/6.61  Prover 13: stopped
% 44.76/6.61  Prover 4: stopped
% 44.76/6.61  Prover 1: stopped
% 44.76/6.61  Prover 8: stopped
% 44.76/6.61  Prover 7: stopped
% 46.73/7.04  Prover 11: Constructing countermodel ...
% 46.73/7.06  Prover 11: stopped
% 46.73/7.06  
% 46.73/7.06  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.73/7.06  
% 46.73/7.07  % SZS output start Proof for theBenchmark
% 46.73/7.08  Assumptions after simplification:
% 46.73/7.08  ---------------------------------
% 46.73/7.08  
% 46.73/7.08    (ax15)
% 47.07/7.09     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v1) |
% 47.07/7.09       ~ ssList(v0) | neq(v0, v1)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ ssList(v0) |  ~
% 47.07/7.09      neq(v0, v0))
% 47.07/7.09  
% 47.07/7.09    (ax17)
% 47.07/7.09    $i(nil) & ssList(nil)
% 47.07/7.09  
% 47.07/7.09    (ax39)
% 47.07/7.09    $i(nil) &  ~ singletonP(nil)
% 47.07/7.09  
% 47.07/7.09    (ax4)
% 47.07/7.13    $i(nil) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (cons(v1, nil) = v0) |  ~ $i(v1) | 
% 47.07/7.13      ~ $i(v0) |  ~ ssList(v0) |  ~ ssItem(v1) | singletonP(v0)) &  ! [v0: $i] : (
% 47.07/7.13      ~ $i(v0) |  ~ singletonP(v0) |  ~ ssList(v0) |  ? [v1: $i] : (cons(v1, nil)
% 47.07/7.13        = v0 & $i(v1) & ssItem(v1)))
% 47.07/7.13  
% 47.07/7.13    (ax58)
% 47.07/7.13    $i(nil) &  ! [v0: $i] : (v0 = nil |  ~ $i(v0) |  ~ segmentP(nil, v0) |  ~
% 47.07/7.13      ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 47.07/7.13  
% 47.07/7.13    (ax6)
% 47.07/7.13     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (app(v2, v1) = v0) |  ~ $i(v2) |
% 47.07/7.13       ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~ ssList(v0) |
% 47.07/7.14      rearsegP(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 47.07/7.14      rearsegP(v0, v1) |  ~ ssList(v1) |  ~ ssList(v0) |  ? [v2: $i] : (app(v2,
% 47.07/7.14          v1) = v0 & $i(v2) & ssList(v2)))
% 47.07/7.14  
% 47.07/7.14    (co1)
% 47.07/7.14    $i(nil) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : (cons(v2,
% 47.07/7.14        nil) = v0 & app(v3, v0) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 47.07/7.14      ssList(v3) & ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ( ~
% 47.07/7.14        rearsegP(v1, v0) |  ~ neq(v0, nil)))
% 47.07/7.14  
% 47.07/7.14  Further assumptions not needed in the proof:
% 47.07/7.14  --------------------------------------------
% 47.07/7.14  ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 47.07/7.14  ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 47.07/7.14  ax35, ax36, ax37, ax38, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48,
% 47.07/7.14  ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax60, ax61,
% 47.07/7.14  ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax72, ax73,
% 47.07/7.14  ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85,
% 47.07/7.14  ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 47.07/7.14  
% 47.07/7.14  Those formulas are unsatisfiable:
% 47.07/7.14  ---------------------------------
% 47.07/7.14  
% 47.07/7.14  Begin of proof
% 47.07/7.14  | 
% 47.07/7.14  | ALPHA: (ax4) implies:
% 47.07/7.14  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (cons(v1, nil) = v0) |  ~ $i(v1) |  ~
% 47.07/7.14  |          $i(v0) |  ~ ssList(v0) |  ~ ssItem(v1) | singletonP(v0))
% 47.07/7.14  | 
% 47.07/7.14  | ALPHA: (ax6) implies:
% 47.07/7.14  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (app(v2, v1) = v0) |  ~
% 47.07/7.14  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ ssList(v2) |  ~ ssList(v1) |  ~
% 47.07/7.14  |          ssList(v0) | rearsegP(v0, v1))
% 47.07/7.15  | 
% 47.07/7.15  | ALPHA: (ax15) implies:
% 47.07/7.15  |   (3)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 47.07/7.15  |          ssList(v1) |  ~ ssList(v0) | neq(v0, v1))
% 47.07/7.15  | 
% 47.07/7.15  | ALPHA: (ax17) implies:
% 47.07/7.15  |   (4)  ssList(nil)
% 47.07/7.15  | 
% 47.07/7.15  | ALPHA: (ax39) implies:
% 47.07/7.15  |   (5)   ~ singletonP(nil)
% 47.07/7.15  | 
% 47.07/7.15  | ALPHA: (ax58) implies:
% 47.07/7.15  |   (6)   ~ ssList(nil) | segmentP(nil, nil)
% 47.07/7.15  | 
% 47.07/7.15  | ALPHA: (co1) implies:
% 47.07/7.15  |   (7)  $i(nil)
% 47.07/7.15  |   (8)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : (cons(v2, nil)
% 47.07/7.15  |          = v0 & app(v3, v0) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 47.07/7.15  |          ssList(v3) & ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & (
% 47.07/7.15  |            ~ rearsegP(v1, v0) |  ~ neq(v0, nil)))
% 47.07/7.15  | 
% 47.07/7.15  | DELTA: instantiating (8) with fresh symbols all_91_0, all_91_1, all_91_2,
% 47.07/7.15  |        all_91_3 gives:
% 47.07/7.15  |   (9)  cons(all_91_1, nil) = all_91_3 & app(all_91_0, all_91_3) = all_91_2 &
% 47.07/7.15  |        $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 47.07/7.15  |        ssList(all_91_0) & ssList(all_91_2) & ssList(all_91_3) & neq(all_91_2,
% 47.07/7.15  |          nil) & ssItem(all_91_1) & ( ~ rearsegP(all_91_2, all_91_3) |  ~
% 47.07/7.15  |          neq(all_91_3, nil))
% 47.07/7.15  | 
% 47.07/7.15  | ALPHA: (9) implies:
% 47.07/7.15  |   (10)  ssItem(all_91_1)
% 47.07/7.15  |   (11)  ssList(all_91_3)
% 47.07/7.15  |   (12)  ssList(all_91_2)
% 47.07/7.15  |   (13)  ssList(all_91_0)
% 47.07/7.15  |   (14)  $i(all_91_3)
% 47.07/7.15  |   (15)  $i(all_91_2)
% 47.07/7.15  |   (16)  $i(all_91_1)
% 47.07/7.15  |   (17)  $i(all_91_0)
% 47.07/7.15  |   (18)  app(all_91_0, all_91_3) = all_91_2
% 47.07/7.15  |   (19)  cons(all_91_1, nil) = all_91_3
% 47.07/7.16  |   (20)   ~ rearsegP(all_91_2, all_91_3) |  ~ neq(all_91_3, nil)
% 47.07/7.16  | 
% 47.07/7.16  | BETA: splitting (6) gives:
% 47.07/7.16  | 
% 47.07/7.16  | Case 1:
% 47.07/7.16  | | 
% 47.07/7.16  | |   (21)   ~ ssList(nil)
% 47.07/7.16  | | 
% 47.07/7.16  | | PRED_UNIFY: (4), (21) imply:
% 47.07/7.16  | |   (22)  $false
% 47.07/7.16  | | 
% 47.07/7.16  | | CLOSE: (22) is inconsistent.
% 47.07/7.16  | | 
% 47.07/7.16  | Case 2:
% 47.07/7.16  | | 
% 47.07/7.16  | | 
% 47.07/7.16  | | GROUND_INST: instantiating (3) with all_91_3, nil, simplifying with (4),
% 47.07/7.16  | |              (7), (11), (14) gives:
% 47.07/7.16  | |   (23)  all_91_3 = nil | neq(all_91_3, nil)
% 47.07/7.16  | | 
% 47.07/7.16  | | GROUND_INST: instantiating (2) with all_91_2, all_91_3, all_91_0,
% 47.07/7.16  | |              simplifying with (11), (12), (13), (14), (15), (17), (18)
% 47.07/7.16  | |              gives:
% 47.07/7.16  | |   (24)  rearsegP(all_91_2, all_91_3)
% 47.07/7.16  | | 
% 47.07/7.16  | | GROUND_INST: instantiating (1) with all_91_3, all_91_1, simplifying with
% 47.07/7.16  | |              (10), (11), (14), (16), (19) gives:
% 47.07/7.16  | |   (25)  singletonP(all_91_3)
% 47.07/7.16  | | 
% 47.07/7.16  | | BETA: splitting (20) gives:
% 47.07/7.16  | | 
% 47.07/7.16  | | Case 1:
% 47.07/7.16  | | | 
% 47.07/7.16  | | |   (26)   ~ neq(all_91_3, nil)
% 47.07/7.16  | | | 
% 47.07/7.16  | | | BETA: splitting (23) gives:
% 47.07/7.16  | | | 
% 47.07/7.16  | | | Case 1:
% 47.07/7.16  | | | | 
% 47.07/7.16  | | | |   (27)  neq(all_91_3, nil)
% 47.07/7.16  | | | | 
% 47.07/7.16  | | | | PRED_UNIFY: (26), (27) imply:
% 47.07/7.16  | | | |   (28)  $false
% 47.07/7.16  | | | | 
% 47.07/7.16  | | | | CLOSE: (28) is inconsistent.
% 47.07/7.16  | | | | 
% 47.07/7.16  | | | Case 2:
% 47.07/7.16  | | | | 
% 47.07/7.16  | | | |   (29)  all_91_3 = nil
% 47.07/7.16  | | | | 
% 47.07/7.16  | | | | REDUCE: (25), (29) imply:
% 47.07/7.16  | | | |   (30)  singletonP(nil)
% 47.07/7.16  | | | | 
% 47.07/7.16  | | | | PRED_UNIFY: (5), (30) imply:
% 47.07/7.16  | | | |   (31)  $false
% 47.07/7.16  | | | | 
% 47.07/7.16  | | | | CLOSE: (31) is inconsistent.
% 47.07/7.16  | | | | 
% 47.07/7.16  | | | End of split
% 47.07/7.16  | | | 
% 47.07/7.16  | | Case 2:
% 47.07/7.16  | | | 
% 47.07/7.16  | | |   (32)   ~ rearsegP(all_91_2, all_91_3)
% 47.07/7.16  | | | 
% 47.07/7.16  | | | PRED_UNIFY: (24), (32) imply:
% 47.07/7.17  | | |   (33)  $false
% 47.07/7.17  | | | 
% 47.07/7.17  | | | CLOSE: (33) is inconsistent.
% 47.07/7.17  | | | 
% 47.07/7.17  | | End of split
% 47.07/7.17  | | 
% 47.07/7.17  | End of split
% 47.07/7.17  | 
% 47.07/7.17  End of proof
% 47.07/7.17  % SZS output end Proof for theBenchmark
% 47.07/7.17  
% 47.07/7.17  6579ms
%------------------------------------------------------------------------------