TSTP Solution File: RNG087+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : RNG087+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n009.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 13:57:47 EDT 2023

% Result   : Theorem 9.78s 1.99s
% Output   : Proof 13.57s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : RNG087+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.32  % Computer : n009.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.32  % CPULimit : 300
% 0.17/0.32  % WCLimit  : 300
% 0.17/0.32  % DateTime : Sun Aug 27 02:13:20 EDT 2023
% 0.17/0.32  % CPUTime  : 
% 0.65/0.60  ________       _____
% 0.65/0.60  ___  __ \_________(_)________________________________
% 0.65/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.65/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.65/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.65/0.60  
% 0.65/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.65/0.60  (2023-06-19)
% 0.65/0.60  
% 0.65/0.60  (c) Philipp Rümmer, 2009-2023
% 0.65/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.65/0.60                Amanda Stjerna.
% 0.65/0.60  Free software under BSD-3-Clause.
% 0.65/0.60  
% 0.65/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.65/0.60  
% 0.65/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.62  Running up to 7 provers in parallel.
% 0.69/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.69/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.10/1.14  Prover 4: Preprocessing ...
% 3.10/1.14  Prover 1: Preprocessing ...
% 3.74/1.18  Prover 5: Preprocessing ...
% 3.74/1.18  Prover 3: Preprocessing ...
% 3.74/1.18  Prover 0: Preprocessing ...
% 3.74/1.18  Prover 6: Preprocessing ...
% 3.74/1.18  Prover 2: Preprocessing ...
% 7.62/1.73  Prover 1: Constructing countermodel ...
% 7.62/1.74  Prover 3: Constructing countermodel ...
% 7.62/1.74  Prover 6: Proving ...
% 8.69/1.84  Prover 4: Constructing countermodel ...
% 8.69/1.86  Prover 2: Proving ...
% 8.69/1.88  Prover 5: Proving ...
% 9.78/1.98  Prover 0: Proving ...
% 9.78/1.98  Prover 3: proved (1357ms)
% 9.78/1.99  
% 9.78/1.99  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.78/1.99  
% 9.78/1.99  Prover 2: stopped
% 9.78/1.99  Prover 6: stopped
% 9.78/1.99  Prover 5: stopped
% 9.78/1.99  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.78/1.99  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.78/1.99  Prover 0: stopped
% 9.78/1.99  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.78/1.99  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.78/1.99  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.95/2.20  Prover 7: Preprocessing ...
% 10.95/2.21  Prover 8: Preprocessing ...
% 10.95/2.21  Prover 10: Preprocessing ...
% 11.64/2.22  Prover 13: Preprocessing ...
% 11.64/2.22  Prover 11: Preprocessing ...
% 12.17/2.32  Prover 1: Found proof (size 14)
% 12.17/2.32  Prover 1: proved (1698ms)
% 12.17/2.32  Prover 4: stopped
% 12.17/2.33  Prover 10: Constructing countermodel ...
% 12.17/2.34  Prover 10: stopped
% 12.17/2.36  Prover 8: Warning: ignoring some quantifiers
% 12.17/2.37  Prover 8: Constructing countermodel ...
% 12.17/2.37  Prover 7: Constructing countermodel ...
% 12.87/2.38  Prover 13: Warning: ignoring some quantifiers
% 12.87/2.38  Prover 8: stopped
% 12.95/2.39  Prover 7: stopped
% 12.95/2.39  Prover 13: Constructing countermodel ...
% 12.95/2.40  Prover 13: stopped
% 13.13/2.45  Prover 11: Constructing countermodel ...
% 13.13/2.46  Prover 11: stopped
% 13.13/2.46  
% 13.13/2.46  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.13/2.46  
% 13.13/2.47  % SZS output start Proof for theBenchmark
% 13.13/2.47  Assumptions after simplification:
% 13.13/2.47  ---------------------------------
% 13.13/2.47  
% 13.13/2.47    (m__)
% 13.13/2.50    $i(xy) & $i(xJ) & $i(xI) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (aElementOf0(v1,
% 13.13/2.50          xJ) = 0) |  ~ (aElementOf0(v0, xI) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 13.13/2.50      [v2: $i] : ( ~ (v2 = xy) & sdtpldt0(v0, v1) = v2 & $i(v2)))
% 13.13/2.50  
% 13.13/2.50    (m__901)
% 13.13/2.50    $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) &  ? [v0: $i] : (sdtpldt1(xI, xJ) =
% 13.13/2.50      v0 & aElementOf0(xy, v0) = 0 & aElementOf0(xx, v0) = 0 & aElement0(xz) = 0 &
% 13.13/2.50      $i(v0) &  ? [v1: $i] :  ? [v2: $i] : (aElementOf0(v2, xJ) = 0 &
% 13.13/2.50        aElementOf0(v1, xI) = 0 & sdtpldt0(v1, v2) = xy & $i(v2) & $i(v1)) &  ?
% 13.13/2.50      [v1: $i] :  ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0
% 13.13/2.50        & sdtpldt0(v1, v2) = xx & $i(v2) & $i(v1)))
% 13.13/2.50  
% 13.13/2.50    (function-axioms)
% 13.13/2.50     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 13.13/2.50      (sdtasasdt0(v3, v2) = v1) |  ~ (sdtasasdt0(v3, v2) = v0)) &  ! [v0: $i] :  !
% 13.13/2.50    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtpldt1(v3, v2) = v1) |
% 13.13/2.50       ~ (sdtpldt1(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 13.13/2.50      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 13.13/2.50      (aElementOf0(v3, v2) = v1) |  ~ (aElementOf0(v3, v2) = v0)) &  ! [v0: $i] : 
% 13.13/2.50    ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtasdt0(v3, v2) = v1)
% 13.13/2.50      |  ~ (sdtasdt0(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 13.13/2.50    [v3: $i] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0))
% 13.13/2.50    &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1
% 13.13/2.50      = v0 |  ~ (aIdeal0(v2) = v1) |  ~ (aIdeal0(v2) = v0)) &  ! [v0:
% 13.13/2.50      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 13.13/2.50      ~ (aSet0(v2) = v1) |  ~ (aSet0(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 13.13/2.50    [v2: $i] : (v1 = v0 |  ~ (smndt0(v2) = v1) |  ~ (smndt0(v2) = v0)) &  ! [v0:
% 13.13/2.50      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 13.13/2.51      ~ (aElement0(v2) = v1) |  ~ (aElement0(v2) = v0))
% 13.13/2.51  
% 13.13/2.51  Further assumptions not needed in the proof:
% 13.13/2.51  --------------------------------------------
% 13.13/2.51  mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefIdeal, mDefSInt,
% 13.13/2.51  mDefSSum, mEOfElem, mElmSort, mMulAsso, mMulComm, mMulMnOne, mMulUnit, mMulZero,
% 13.13/2.51  mSetEq, mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr,
% 13.13/2.51  m__870, m__934
% 13.13/2.51  
% 13.13/2.51  Those formulas are unsatisfiable:
% 13.13/2.51  ---------------------------------
% 13.13/2.51  
% 13.13/2.51  Begin of proof
% 13.13/2.51  | 
% 13.57/2.51  | ALPHA: (m__901) implies:
% 13.57/2.51  |   (1)   ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & aElementOf0(xy, v0) = 0 &
% 13.57/2.51  |          aElementOf0(xx, v0) = 0 & aElement0(xz) = 0 & $i(v0) &  ? [v1: $i] : 
% 13.57/2.51  |          ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0 &
% 13.57/2.51  |            sdtpldt0(v1, v2) = xy & $i(v2) & $i(v1)) &  ? [v1: $i] :  ? [v2:
% 13.57/2.51  |            $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0 &
% 13.57/2.51  |            sdtpldt0(v1, v2) = xx & $i(v2) & $i(v1)))
% 13.57/2.51  | 
% 13.57/2.51  | ALPHA: (m__) implies:
% 13.57/2.51  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (aElementOf0(v1, xJ) = 0) |  ~
% 13.57/2.51  |          (aElementOf0(v0, xI) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: $i] : ( ~
% 13.57/2.51  |            (v2 = xy) & sdtpldt0(v0, v1) = v2 & $i(v2)))
% 13.57/2.51  | 
% 13.57/2.51  | ALPHA: (function-axioms) implies:
% 13.57/2.51  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 13.57/2.51  |          (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0))
% 13.57/2.51  | 
% 13.57/2.51  | DELTA: instantiating (1) with fresh symbol all_27_0 gives:
% 13.57/2.51  |   (4)  sdtpldt1(xI, xJ) = all_27_0 & aElementOf0(xy, all_27_0) = 0 &
% 13.57/2.51  |        aElementOf0(xx, all_27_0) = 0 & aElement0(xz) = 0 & $i(all_27_0) &  ?
% 13.57/2.51  |        [v0: $i] :  ? [v1: $i] : (aElementOf0(v1, xJ) = 0 & aElementOf0(v0, xI)
% 13.57/2.51  |          = 0 & sdtpldt0(v0, v1) = xy & $i(v1) & $i(v0)) &  ? [v0: $i] :  ?
% 13.57/2.51  |        [v1: $i] : (aElementOf0(v1, xJ) = 0 & aElementOf0(v0, xI) = 0 &
% 13.57/2.51  |          sdtpldt0(v0, v1) = xx & $i(v1) & $i(v0))
% 13.57/2.51  | 
% 13.57/2.51  | ALPHA: (4) implies:
% 13.57/2.51  |   (5)   ? [v0: $i] :  ? [v1: $i] : (aElementOf0(v1, xJ) = 0 & aElementOf0(v0,
% 13.57/2.51  |            xI) = 0 & sdtpldt0(v0, v1) = xy & $i(v1) & $i(v0))
% 13.57/2.51  | 
% 13.57/2.51  | DELTA: instantiating (5) with fresh symbols all_29_0, all_29_1 gives:
% 13.57/2.51  |   (6)  aElementOf0(all_29_0, xJ) = 0 & aElementOf0(all_29_1, xI) = 0 &
% 13.57/2.51  |        sdtpldt0(all_29_1, all_29_0) = xy & $i(all_29_0) & $i(all_29_1)
% 13.57/2.51  | 
% 13.57/2.51  | ALPHA: (6) implies:
% 13.57/2.52  |   (7)  $i(all_29_1)
% 13.57/2.52  |   (8)  $i(all_29_0)
% 13.57/2.52  |   (9)  sdtpldt0(all_29_1, all_29_0) = xy
% 13.57/2.52  |   (10)  aElementOf0(all_29_1, xI) = 0
% 13.57/2.52  |   (11)  aElementOf0(all_29_0, xJ) = 0
% 13.57/2.52  | 
% 13.57/2.52  | GROUND_INST: instantiating (2) with all_29_1, all_29_0, simplifying with (7),
% 13.57/2.52  |              (8), (10), (11) gives:
% 13.57/2.52  |   (12)   ? [v0: $i] : ( ~ (v0 = xy) & sdtpldt0(all_29_1, all_29_0) = v0 &
% 13.57/2.52  |           $i(v0))
% 13.57/2.52  | 
% 13.57/2.52  | DELTA: instantiating (12) with fresh symbol all_71_0 gives:
% 13.57/2.52  |   (13)   ~ (all_71_0 = xy) & sdtpldt0(all_29_1, all_29_0) = all_71_0 &
% 13.57/2.52  |         $i(all_71_0)
% 13.57/2.52  | 
% 13.57/2.52  | ALPHA: (13) implies:
% 13.57/2.52  |   (14)   ~ (all_71_0 = xy)
% 13.57/2.52  |   (15)  sdtpldt0(all_29_1, all_29_0) = all_71_0
% 13.57/2.52  | 
% 13.57/2.52  | GROUND_INST: instantiating (3) with xy, all_71_0, all_29_0, all_29_1,
% 13.57/2.52  |              simplifying with (9), (15) gives:
% 13.57/2.52  |   (16)  all_71_0 = xy
% 13.57/2.52  | 
% 13.57/2.52  | REDUCE: (14), (16) imply:
% 13.57/2.52  |   (17)  $false
% 13.57/2.52  | 
% 13.57/2.52  | CLOSE: (17) is inconsistent.
% 13.57/2.52  | 
% 13.57/2.52  End of proof
% 13.57/2.52  % SZS output end Proof for theBenchmark
% 13.57/2.52  
% 13.57/2.52  1916ms
%------------------------------------------------------------------------------