TSTP Solution File: COM012+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : COM012+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n004.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 : Wed Aug 30 18:44:15 EDT 2023

% Result   : Theorem 4.96s 1.53s
% Output   : Proof 7.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : COM012+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n004.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 : Tue Aug 29 13:23:22 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.21/0.61  ________       _____
% 0.21/0.61  ___  __ \_________(_)________________________________
% 0.21/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61  
% 0.21/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61  (2023-06-19)
% 0.21/0.61  
% 0.21/0.61  (c) Philipp Rümmer, 2009-2023
% 0.21/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61                Amanda Stjerna.
% 0.21/0.61  Free software under BSD-3-Clause.
% 0.21/0.61  
% 0.21/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61  
% 0.21/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62  Running up to 7 provers in parallel.
% 0.21/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.05/1.07  Prover 4: Preprocessing ...
% 2.60/1.08  Prover 1: Preprocessing ...
% 2.60/1.11  Prover 6: Preprocessing ...
% 2.60/1.11  Prover 3: Preprocessing ...
% 2.60/1.11  Prover 0: Preprocessing ...
% 2.60/1.11  Prover 5: Preprocessing ...
% 2.60/1.11  Prover 2: Preprocessing ...
% 3.59/1.29  Prover 5: Constructing countermodel ...
% 3.59/1.29  Prover 2: Constructing countermodel ...
% 4.30/1.34  Prover 1: Constructing countermodel ...
% 4.30/1.36  Prover 3: Constructing countermodel ...
% 4.30/1.36  Prover 6: Proving ...
% 4.30/1.45  Prover 4: Constructing countermodel ...
% 4.96/1.52  Prover 2: proved (884ms)
% 4.96/1.52  
% 4.96/1.53  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.96/1.53  
% 4.96/1.53  Prover 3: stopped
% 4.96/1.53  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.96/1.54  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.96/1.54  Prover 6: stopped
% 5.76/1.55  Prover 5: stopped
% 5.76/1.55  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.76/1.56  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.76/1.57  Prover 0: Proving ...
% 5.76/1.57  Prover 0: stopped
% 5.76/1.58  Prover 7: Preprocessing ...
% 5.76/1.58  Prover 8: Preprocessing ...
% 5.76/1.58  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.76/1.58  Prover 10: Preprocessing ...
% 5.76/1.61  Prover 11: Preprocessing ...
% 5.76/1.61  Prover 7: Constructing countermodel ...
% 5.76/1.61  Prover 13: Preprocessing ...
% 5.76/1.61  Prover 10: Constructing countermodel ...
% 6.53/1.64  Prover 13: Constructing countermodel ...
% 6.53/1.65  Prover 8: Warning: ignoring some quantifiers
% 6.53/1.65  Prover 8: Constructing countermodel ...
% 6.92/1.72  Prover 10: Found proof (size 16)
% 6.92/1.72  Prover 10: proved (174ms)
% 6.92/1.72  Prover 8: stopped
% 6.92/1.72  Prover 1: stopped
% 6.92/1.72  Prover 7: stopped
% 6.92/1.72  Prover 13: stopped
% 6.92/1.72  Prover 4: stopped
% 7.22/1.78  Prover 11: Constructing countermodel ...
% 7.22/1.78  Prover 11: stopped
% 7.22/1.78  
% 7.22/1.78  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.22/1.78  
% 7.22/1.79  % SZS output start Proof for theBenchmark
% 7.22/1.79  Assumptions after simplification:
% 7.22/1.79  ---------------------------------
% 7.22/1.79  
% 7.22/1.79    (mTCRDef)
% 7.22/1.80     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ $i(v2) |  ~ $i(v1) | 
% 7.22/1.80      ~ $i(v0) |  ~ sdtmndtasgtdt0(v0, v1, v2) |  ~ aRewritingSystem0(v1) |  ~
% 7.22/1.80      aElement0(v2) |  ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2)) &  ! [v0: $i]
% 7.22/1.80    :  ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 7.22/1.80      sdtmndtplgtdt0(v0, v1, v2) |  ~ aRewritingSystem0(v1) |  ~ aElement0(v2) | 
% 7.22/1.80      ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, v2)) &  ! [v0: $i] :  ! [v1: $i] :
% 7.22/1.80    ( ~ $i(v1) |  ~ $i(v0) |  ~ aRewritingSystem0(v1) |  ~ aElement0(v0) |
% 7.22/1.80      sdtmndtasgtdt0(v0, v1, v0))
% 7.22/1.80  
% 7.22/1.80    (mTCTrans)
% 7.22/1.80     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2)
% 7.22/1.80      |  ~ $i(v1) |  ~ $i(v0) |  ~ sdtmndtplgtdt0(v2, v1, v3) |  ~
% 7.22/1.80      sdtmndtplgtdt0(v0, v1, v2) |  ~ aRewritingSystem0(v1) |  ~ aElement0(v3) | 
% 7.22/1.80      ~ aElement0(v2) |  ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v3))
% 7.22/1.80  
% 7.22/1.80    (m__)
% 7.22/1.80    $i(xz) & $i(xy) & $i(xR) & $i(xx) & sdtmndtasgtdt0(xy, xR, xz) &
% 7.22/1.80    sdtmndtasgtdt0(xx, xR, xy) &  ~ sdtmndtasgtdt0(xx, xR, xz)
% 7.22/1.80  
% 7.22/1.80    (m__349)
% 7.22/1.80    $i(xz) & $i(xy) & $i(xR) & $i(xx) & aRewritingSystem0(xR) & aElement0(xz) &
% 7.22/1.80    aElement0(xy) & aElement0(xx)
% 7.22/1.80  
% 7.22/1.80  Further assumptions not needed in the proof:
% 7.22/1.80  --------------------------------------------
% 7.22/1.80  mElmSort, mReduct, mRelSort, mTCDef, mTCbr, mWFOrd
% 7.22/1.80  
% 7.22/1.80  Those formulas are unsatisfiable:
% 7.22/1.81  ---------------------------------
% 7.22/1.81  
% 7.22/1.81  Begin of proof
% 7.22/1.81  | 
% 7.22/1.81  | ALPHA: (m__) implies:
% 7.22/1.81  |   (1)   ~ sdtmndtasgtdt0(xx, xR, xz)
% 7.22/1.81  |   (2)  sdtmndtasgtdt0(xx, xR, xy)
% 7.22/1.81  |   (3)  sdtmndtasgtdt0(xy, xR, xz)
% 7.22/1.81  | 
% 7.22/1.81  | ALPHA: (m__349) implies:
% 7.22/1.81  |   (4)  aElement0(xx)
% 7.22/1.81  |   (5)  aElement0(xy)
% 7.22/1.81  |   (6)  aElement0(xz)
% 7.22/1.81  |   (7)  aRewritingSystem0(xR)
% 7.22/1.81  |   (8)  $i(xx)
% 7.22/1.81  |   (9)  $i(xR)
% 7.22/1.81  |   (10)  $i(xy)
% 7.22/1.81  |   (11)  $i(xz)
% 7.22/1.81  | 
% 7.22/1.81  | ALPHA: (mTCRDef) implies:
% 7.22/1.81  |   (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~
% 7.22/1.81  |           $i(v0) |  ~ sdtmndtplgtdt0(v0, v1, v2) |  ~ aRewritingSystem0(v1) | 
% 7.22/1.81  |           ~ aElement0(v2) |  ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, v2))
% 7.22/1.81  |   (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ $i(v2) |  ~
% 7.22/1.81  |           $i(v1) |  ~ $i(v0) |  ~ sdtmndtasgtdt0(v0, v1, v2) |  ~
% 7.22/1.81  |           aRewritingSystem0(v1) |  ~ aElement0(v2) |  ~ aElement0(v0) |
% 7.22/1.81  |           sdtmndtplgtdt0(v0, v1, v2))
% 7.22/1.81  | 
% 7.22/1.81  | GROUND_INST: instantiating (13) with xx, xR, xy, simplifying with (2), (4),
% 7.22/1.81  |              (5), (7), (8), (9), (10) gives:
% 7.22/1.82  |   (14)  xy = xx | sdtmndtplgtdt0(xx, xR, xy)
% 7.22/1.82  | 
% 7.22/1.82  | GROUND_INST: instantiating (13) with xy, xR, xz, simplifying with (3), (5),
% 7.22/1.82  |              (6), (7), (9), (10), (11) gives:
% 7.22/1.82  |   (15)  xz = xy | sdtmndtplgtdt0(xy, xR, xz)
% 7.22/1.82  | 
% 7.22/1.82  | BETA: splitting (15) gives:
% 7.22/1.82  | 
% 7.22/1.82  | Case 1:
% 7.22/1.82  | | 
% 7.22/1.82  | |   (16)  sdtmndtplgtdt0(xy, xR, xz)
% 7.22/1.82  | | 
% 7.22/1.82  | | BETA: splitting (14) gives:
% 7.22/1.82  | | 
% 7.22/1.82  | | Case 1:
% 7.22/1.82  | | | 
% 7.22/1.82  | | |   (17)  sdtmndtplgtdt0(xx, xR, xy)
% 7.22/1.82  | | | 
% 7.22/1.82  | | | GROUND_INST: instantiating (mTCTrans) with xx, xR, xy, xz, simplifying
% 7.22/1.82  | | |              with (4), (5), (6), (7), (8), (9), (10), (11), (16), (17)
% 7.22/1.82  | | |              gives:
% 7.22/1.82  | | |   (18)  sdtmndtplgtdt0(xx, xR, xz)
% 7.22/1.82  | | | 
% 7.22/1.82  | | | GROUND_INST: instantiating (12) with xx, xR, xz, simplifying with (1),
% 7.22/1.82  | | |              (4), (6), (7), (8), (9), (11), (18) gives:
% 7.22/1.82  | | |   (19)  $false
% 7.22/1.82  | | | 
% 7.22/1.82  | | | CLOSE: (19) is inconsistent.
% 7.22/1.82  | | | 
% 7.22/1.82  | | Case 2:
% 7.22/1.82  | | | 
% 7.22/1.82  | | |   (20)  xy = xx
% 7.22/1.82  | | | 
% 7.22/1.82  | | | REDUCE: (3), (20) imply:
% 7.22/1.82  | | |   (21)  sdtmndtasgtdt0(xx, xR, xz)
% 7.22/1.82  | | | 
% 7.22/1.82  | | | PRED_UNIFY: (1), (21) imply:
% 7.22/1.82  | | |   (22)  $false
% 7.22/1.82  | | | 
% 7.22/1.82  | | | CLOSE: (22) is inconsistent.
% 7.22/1.82  | | | 
% 7.22/1.82  | | End of split
% 7.22/1.82  | | 
% 7.22/1.82  | Case 2:
% 7.22/1.82  | | 
% 7.22/1.82  | |   (23)  xz = xy
% 7.22/1.82  | | 
% 7.22/1.82  | | REDUCE: (1), (23) imply:
% 7.22/1.82  | |   (24)   ~ sdtmndtasgtdt0(xx, xR, xy)
% 7.22/1.82  | | 
% 7.22/1.82  | | PRED_UNIFY: (2), (24) imply:
% 7.22/1.82  | |   (25)  $false
% 7.22/1.82  | | 
% 7.22/1.82  | | CLOSE: (25) is inconsistent.
% 7.22/1.82  | | 
% 7.22/1.82  | End of split
% 7.22/1.82  | 
% 7.22/1.82  End of proof
% 7.22/1.82  % SZS output end Proof for theBenchmark
% 7.22/1.82  
% 7.22/1.82  1211ms
%------------------------------------------------------------------------------