TSTP Solution File: COM012+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n015.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 4.64s 1.38s
% Output   : Proof 7.30s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n015.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
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 29 13:46:11 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.60  ________       _____
% 0.19/0.60  ___  __ \_________(_)________________________________
% 0.19/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60  
% 0.19/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60  (2023-06-19)
% 0.19/0.60  
% 0.19/0.60  (c) Philipp Rümmer, 2009-2023
% 0.19/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60                Amanda Stjerna.
% 0.19/0.60  Free software under BSD-3-Clause.
% 0.19/0.60  
% 0.19/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60  
% 0.19/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61  Running up to 7 provers in parallel.
% 0.19/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.50/1.01  Prover 4: Preprocessing ...
% 2.50/1.01  Prover 1: Preprocessing ...
% 2.50/1.05  Prover 2: Preprocessing ...
% 2.50/1.05  Prover 0: Preprocessing ...
% 2.50/1.05  Prover 6: Preprocessing ...
% 2.50/1.05  Prover 5: Preprocessing ...
% 2.50/1.05  Prover 3: Preprocessing ...
% 3.87/1.21  Prover 5: Constructing countermodel ...
% 3.94/1.23  Prover 2: Constructing countermodel ...
% 3.94/1.28  Prover 1: Constructing countermodel ...
% 4.64/1.32  Prover 3: Constructing countermodel ...
% 4.64/1.33  Prover 6: Proving ...
% 4.64/1.37  Prover 2: proved (745ms)
% 4.64/1.38  
% 4.64/1.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.64/1.38  
% 4.64/1.38  Prover 5: stopped
% 4.64/1.39  Prover 3: stopped
% 4.64/1.40  Prover 6: stopped
% 4.64/1.41  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.64/1.41  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.64/1.41  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.64/1.41  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.64/1.42  Prover 8: Preprocessing ...
% 4.64/1.43  Prover 4: Constructing countermodel ...
% 4.64/1.45  Prover 7: Preprocessing ...
% 4.64/1.45  Prover 10: Preprocessing ...
% 4.64/1.48  Prover 11: Preprocessing ...
% 5.68/1.52  Prover 7: Constructing countermodel ...
% 5.68/1.52  Prover 10: Constructing countermodel ...
% 5.68/1.53  Prover 8: Warning: ignoring some quantifiers
% 5.68/1.54  Prover 0: Proving ...
% 5.68/1.54  Prover 8: Constructing countermodel ...
% 5.68/1.54  Prover 0: stopped
% 5.68/1.55  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.68/1.59  Prover 13: Preprocessing ...
% 6.70/1.63  Prover 13: Constructing countermodel ...
% 6.70/1.68  Prover 7: Found proof (size 16)
% 6.70/1.68  Prover 7: proved (297ms)
% 6.70/1.68  Prover 4: stopped
% 6.70/1.68  Prover 1: stopped
% 6.70/1.68  Prover 8: stopped
% 6.70/1.68  Prover 10: Found proof (size 16)
% 6.70/1.68  Prover 10: proved (279ms)
% 6.70/1.68  Prover 13: stopped
% 7.30/1.71  Prover 11: Constructing countermodel ...
% 7.30/1.72  Prover 11: stopped
% 7.30/1.72  
% 7.30/1.72  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.30/1.72  
% 7.30/1.73  % SZS output start Proof for theBenchmark
% 7.30/1.73  Assumptions after simplification:
% 7.30/1.73  ---------------------------------
% 7.30/1.73  
% 7.30/1.73    (mTCTrans)
% 7.30/1.74     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2)
% 7.30/1.74      |  ~ $i(v1) |  ~ $i(v0) |  ~ sdtmndtplgtdt0(v2, v1, v3) |  ~
% 7.30/1.74      sdtmndtplgtdt0(v0, v1, v2) |  ~ aRewritingSystem0(v1) |  ~ aElement0(v3) | 
% 7.30/1.74      ~ aElement0(v2) |  ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v3))
% 7.30/1.74  
% 7.30/1.74    (m__)
% 7.30/1.74    $i(xz) & $i(xy) & $i(xR) & $i(xx) &  ? [v0: $i] :  ? [v1: $i] : ( ~ (xz = xx)
% 7.30/1.74      & $i(v1) & $i(v0) & sdtmndtasgtdt0(xy, xR, xz) & sdtmndtasgtdt0(xx, xR, xy)
% 7.30/1.74      &  ~ sdtmndtasgtdt0(xx, xR, xz) &  ~ sdtmndtplgtdt0(xx, xR, xz) &  ~
% 7.30/1.74      aReductOfIn0(xz, xx, xR) &  ! [v2: $i] : ( ~ $i(v2) |  ~ sdtmndtplgtdt0(v2,
% 7.30/1.74          xR, xz) |  ~ aReductOfIn0(v2, xx, xR) |  ~ aElement0(v2)) & (xz = xy |
% 7.30/1.74        (sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) |
% 7.30/1.74            (sdtmndtplgtdt0(v0, xR, xz) & aReductOfIn0(v0, xy, xR) &
% 7.30/1.74              aElement0(v0))))) & (xy = xx | (sdtmndtplgtdt0(xx, xR, xy) &
% 7.30/1.74          (aReductOfIn0(xy, xx, xR) | (sdtmndtplgtdt0(v1, xR, xy) &
% 7.30/1.74              aReductOfIn0(v1, xx, xR) & aElement0(v1))))))
% 7.30/1.74  
% 7.30/1.74    (m__349)
% 7.30/1.74    $i(xz) & $i(xy) & $i(xR) & $i(xx) & aRewritingSystem0(xR) & aElement0(xz) &
% 7.30/1.74    aElement0(xy) & aElement0(xx)
% 7.30/1.74  
% 7.30/1.74  Further assumptions not needed in the proof:
% 7.30/1.74  --------------------------------------------
% 7.30/1.74  mElmSort, mReduct, mRelSort, mTCDef, mTCRDef, mTCbr, mWFOrd
% 7.30/1.74  
% 7.30/1.74  Those formulas are unsatisfiable:
% 7.30/1.74  ---------------------------------
% 7.30/1.74  
% 7.30/1.74  Begin of proof
% 7.30/1.74  | 
% 7.30/1.75  | ALPHA: (m__) implies:
% 7.30/1.75  |   (1)   ? [v0: $i] :  ? [v1: $i] : ( ~ (xz = xx) & $i(v1) & $i(v0) &
% 7.30/1.75  |          sdtmndtasgtdt0(xy, xR, xz) & sdtmndtasgtdt0(xx, xR, xy) &  ~
% 7.30/1.75  |          sdtmndtasgtdt0(xx, xR, xz) &  ~ sdtmndtplgtdt0(xx, xR, xz) &  ~
% 7.30/1.75  |          aReductOfIn0(xz, xx, xR) &  ! [v2: $i] : ( ~ $i(v2) |  ~
% 7.30/1.75  |            sdtmndtplgtdt0(v2, xR, xz) |  ~ aReductOfIn0(v2, xx, xR) |  ~
% 7.30/1.75  |            aElement0(v2)) & (xz = xy | (sdtmndtplgtdt0(xy, xR, xz) &
% 7.30/1.75  |              (aReductOfIn0(xz, xy, xR) | (sdtmndtplgtdt0(v0, xR, xz) &
% 7.30/1.75  |                  aReductOfIn0(v0, xy, xR) & aElement0(v0))))) & (xy = xx |
% 7.30/1.75  |            (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) |
% 7.30/1.75  |                (sdtmndtplgtdt0(v1, xR, xy) & aReductOfIn0(v1, xx, xR) &
% 7.30/1.75  |                  aElement0(v1))))))
% 7.30/1.75  | 
% 7.30/1.75  | ALPHA: (m__349) implies:
% 7.30/1.75  |   (2)  aElement0(xx)
% 7.30/1.75  |   (3)  aElement0(xy)
% 7.30/1.75  |   (4)  aElement0(xz)
% 7.30/1.75  |   (5)  aRewritingSystem0(xR)
% 7.30/1.75  |   (6)  $i(xx)
% 7.30/1.75  |   (7)  $i(xR)
% 7.30/1.75  |   (8)  $i(xy)
% 7.30/1.75  |   (9)  $i(xz)
% 7.30/1.75  | 
% 7.30/1.75  | DELTA: instantiating (1) with fresh symbols all_7_0, all_7_1 gives:
% 7.30/1.75  |   (10)   ~ (xz = xx) & $i(all_7_0) & $i(all_7_1) & sdtmndtasgtdt0(xy, xR, xz)
% 7.30/1.75  |         & sdtmndtasgtdt0(xx, xR, xy) &  ~ sdtmndtasgtdt0(xx, xR, xz) &  ~
% 7.30/1.75  |         sdtmndtplgtdt0(xx, xR, xz) &  ~ aReductOfIn0(xz, xx, xR) &  ! [v0: $i]
% 7.30/1.75  |         : ( ~ $i(v0) |  ~ sdtmndtplgtdt0(v0, xR, xz) |  ~ aReductOfIn0(v0, xx,
% 7.30/1.75  |             xR) |  ~ aElement0(v0)) & (xz = xy | (sdtmndtplgtdt0(xy, xR, xz) &
% 7.30/1.75  |             (aReductOfIn0(xz, xy, xR) | (sdtmndtplgtdt0(all_7_1, xR, xz) &
% 7.30/1.75  |                 aReductOfIn0(all_7_1, xy, xR) & aElement0(all_7_1))))) & (xy =
% 7.30/1.75  |           xx | (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) |
% 7.30/1.75  |               (sdtmndtplgtdt0(all_7_0, xR, xy) & aReductOfIn0(all_7_0, xx, xR)
% 7.30/1.75  |                 & aElement0(all_7_0)))))
% 7.30/1.76  | 
% 7.30/1.76  | ALPHA: (10) implies:
% 7.30/1.76  |   (11)   ~ sdtmndtplgtdt0(xx, xR, xz)
% 7.30/1.76  |   (12)   ~ sdtmndtasgtdt0(xx, xR, xz)
% 7.30/1.76  |   (13)  sdtmndtasgtdt0(xx, xR, xy)
% 7.30/1.76  |   (14)  sdtmndtasgtdt0(xy, xR, xz)
% 7.30/1.76  |   (15)  xy = xx | (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) |
% 7.30/1.76  |             (sdtmndtplgtdt0(all_7_0, xR, xy) & aReductOfIn0(all_7_0, xx, xR) &
% 7.30/1.76  |               aElement0(all_7_0))))
% 7.30/1.76  |   (16)  xz = xy | (sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) |
% 7.30/1.76  |             (sdtmndtplgtdt0(all_7_1, xR, xz) & aReductOfIn0(all_7_1, xy, xR) &
% 7.30/1.76  |               aElement0(all_7_1))))
% 7.30/1.76  | 
% 7.30/1.76  | PRED_UNIFY: (12), (14) imply:
% 7.30/1.76  |   (17)   ~ (xy = xx)
% 7.30/1.76  | 
% 7.30/1.76  | PRED_UNIFY: (12), (13) imply:
% 7.30/1.76  |   (18)   ~ (xz = xy)
% 7.30/1.76  | 
% 7.30/1.76  | BETA: splitting (15) gives:
% 7.30/1.76  | 
% 7.30/1.76  | Case 1:
% 7.30/1.76  | | 
% 7.30/1.76  | |   (19)  xy = xx
% 7.30/1.76  | | 
% 7.30/1.76  | | REDUCE: (17), (19) imply:
% 7.30/1.76  | |   (20)  $false
% 7.30/1.76  | | 
% 7.30/1.76  | | CLOSE: (20) is inconsistent.
% 7.30/1.76  | | 
% 7.30/1.76  | Case 2:
% 7.30/1.76  | | 
% 7.30/1.76  | |   (21)  sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) |
% 7.30/1.76  | |           (sdtmndtplgtdt0(all_7_0, xR, xy) & aReductOfIn0(all_7_0, xx, xR) &
% 7.30/1.76  | |             aElement0(all_7_0)))
% 7.30/1.76  | | 
% 7.30/1.76  | | ALPHA: (21) implies:
% 7.30/1.76  | |   (22)  sdtmndtplgtdt0(xx, xR, xy)
% 7.30/1.76  | | 
% 7.30/1.76  | | BETA: splitting (16) gives:
% 7.30/1.76  | | 
% 7.30/1.76  | | Case 1:
% 7.30/1.76  | | | 
% 7.30/1.76  | | |   (23)  xz = xy
% 7.30/1.76  | | | 
% 7.30/1.76  | | | REDUCE: (18), (23) imply:
% 7.30/1.76  | | |   (24)  $false
% 7.30/1.76  | | | 
% 7.30/1.76  | | | CLOSE: (24) is inconsistent.
% 7.30/1.76  | | | 
% 7.30/1.76  | | Case 2:
% 7.30/1.76  | | | 
% 7.30/1.76  | | |   (25)  sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) |
% 7.30/1.76  | | |           (sdtmndtplgtdt0(all_7_1, xR, xz) & aReductOfIn0(all_7_1, xy, xR)
% 7.30/1.76  | | |             & aElement0(all_7_1)))
% 7.30/1.76  | | | 
% 7.30/1.76  | | | ALPHA: (25) implies:
% 7.30/1.76  | | |   (26)  sdtmndtplgtdt0(xy, xR, xz)
% 7.30/1.76  | | | 
% 7.30/1.77  | | | GROUND_INST: instantiating (mTCTrans) with xx, xR, xy, xz, simplifying
% 7.30/1.77  | | |              with (2), (3), (4), (5), (6), (7), (8), (9), (11), (22), (26)
% 7.30/1.77  | | |              gives:
% 7.30/1.77  | | |   (27)  $false
% 7.30/1.77  | | | 
% 7.30/1.77  | | | CLOSE: (27) is inconsistent.
% 7.30/1.77  | | | 
% 7.30/1.77  | | End of split
% 7.30/1.77  | | 
% 7.30/1.77  | End of split
% 7.30/1.77  | 
% 7.30/1.77  End of proof
% 7.30/1.77  % SZS output end Proof for theBenchmark
% 7.30/1.77  
% 7.30/1.77  1163ms
%------------------------------------------------------------------------------