TSTP Solution File: RNG102+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : RNG102+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 : 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 13:57:52 EDT 2023

% Result   : Theorem 23.42s 3.79s
% Output   : Proof 23.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : RNG102+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Aug 27 02:06:35 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.66/0.63  ________       _____
% 0.66/0.63  ___  __ \_________(_)________________________________
% 0.66/0.63  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.66/0.63  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.66/0.63  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.66/0.63  
% 0.66/0.63  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.66/0.63  (2023-06-19)
% 0.66/0.63  
% 0.66/0.63  (c) Philipp Rümmer, 2009-2023
% 0.66/0.63  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.66/0.63                Amanda Stjerna.
% 0.66/0.63  Free software under BSD-3-Clause.
% 0.66/0.63  
% 0.66/0.63  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.66/0.63  
% 0.66/0.64  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.65  Running up to 7 provers in parallel.
% 0.66/0.66  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.66/0.66  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.66/0.66  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.66/0.66  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.66/0.66  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.66/0.66  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.66/0.66  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.36/1.17  Prover 1: Preprocessing ...
% 3.36/1.17  Prover 4: Preprocessing ...
% 3.55/1.22  Prover 2: Preprocessing ...
% 3.55/1.22  Prover 6: Preprocessing ...
% 3.55/1.22  Prover 3: Preprocessing ...
% 3.55/1.22  Prover 5: Preprocessing ...
% 3.92/1.24  Prover 0: Preprocessing ...
% 9.53/2.00  Prover 1: Constructing countermodel ...
% 9.53/2.04  Prover 3: Constructing countermodel ...
% 10.23/2.11  Prover 5: Proving ...
% 10.56/2.11  Prover 6: Proving ...
% 10.80/2.21  Prover 2: Proving ...
% 11.87/2.32  Prover 4: Constructing countermodel ...
% 12.44/2.38  Prover 0: Proving ...
% 14.20/2.62  Prover 3: gave up
% 14.20/2.62  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.77/2.69  Prover 7: Preprocessing ...
% 15.15/2.74  Prover 1: gave up
% 15.15/2.74  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.43/2.78  Prover 8: Preprocessing ...
% 16.49/2.93  Prover 7: Constructing countermodel ...
% 16.98/3.00  Prover 8: Warning: ignoring some quantifiers
% 17.40/3.04  Prover 8: Constructing countermodel ...
% 23.14/3.78  Prover 7: Found proof (size 12)
% 23.14/3.78  Prover 7: proved (1154ms)
% 23.14/3.78  Prover 8: stopped
% 23.14/3.78  Prover 4: stopped
% 23.14/3.78  Prover 0: stopped
% 23.14/3.78  Prover 6: stopped
% 23.14/3.78  Prover 5: stopped
% 23.42/3.79  Prover 2: stopped
% 23.42/3.79  
% 23.42/3.79  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.42/3.79  
% 23.42/3.79  % SZS output start Proof for theBenchmark
% 23.42/3.80  Assumptions after simplification:
% 23.42/3.80  ---------------------------------
% 23.42/3.80  
% 23.42/3.80    (mDefPrIdeal)
% 23.42/3.83     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (slsdtgt0(v0) =
% 23.42/3.83        v1) |  ~ (sdtasdt0(v0, v3) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 23.42/3.83      $i(v0) |  ~ aElement0(v3) |  ~ aElement0(v0) | aElementOf0(v2, v1)) &  !
% 23.42/3.83    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ (slsdtgt0(v0) = v1) |  ~
% 23.42/3.83      $i(v2) |  ~ $i(v0) |  ~ aSet0(v2) |  ~ aElement0(v0) |  ? [v3: $i] :  ? [v4:
% 23.42/3.83        $i] :  ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) |  ! [v6:
% 23.42/3.83            $i] : ( ~ (sdtasdt0(v0, v6) = v3) |  ~ $i(v6) |  ~ aElement0(v6))) &
% 23.42/3.83        (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 &
% 23.42/3.83            aElement0(v4))))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 23.42/3.83      (slsdtgt0(v0) = v1) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v2,
% 23.42/3.83        v1) |  ~ aElement0(v0) |  ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 23.42/3.83        aElement0(v3))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) |  ~
% 23.42/3.83      $i(v1) |  ~ $i(v0) |  ~ aElement0(v0) | aSet0(v1))
% 23.42/3.83  
% 23.42/3.83    (m__)
% 23.42/3.83    $i(xy) & $i(xc) &  ! [v0: $i] : ( ~ (sdtasdt0(xc, v0) = xy) |  ~ $i(v0) |  ~
% 23.42/3.83      aElement0(v0))
% 23.42/3.83  
% 23.42/3.83    (m__1905)
% 23.42/3.83    $i(xc) & aElement0(xc)
% 23.42/3.83  
% 23.42/3.83    (m__1933)
% 23.42/3.83    $i(xz) & $i(xy) & $i(xx) & $i(xc) &  ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0)
% 23.42/3.83      & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz))
% 23.42/3.83  
% 23.42/3.83  Further assumptions not needed in the proof:
% 23.42/3.83  --------------------------------------------
% 23.42/3.83  mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder,
% 23.42/3.83  mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDefSSum,
% 23.42/3.83  mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulComm,
% 23.42/3.83  mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mSetEq, mSetSort, mSortsB,
% 23.42/3.83  mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__1956
% 23.42/3.83  
% 23.42/3.83  Those formulas are unsatisfiable:
% 23.42/3.83  ---------------------------------
% 23.42/3.83  
% 23.42/3.83  Begin of proof
% 23.42/3.83  | 
% 23.42/3.83  | ALPHA: (mDefPrIdeal) implies:
% 23.42/3.83  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) |  ~
% 23.42/3.83  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v2, v1) |  ~
% 23.42/3.83  |          aElement0(v0) |  ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 23.42/3.83  |            aElement0(v3)))
% 23.42/3.83  | 
% 23.42/3.83  | ALPHA: (m__1905) implies:
% 23.42/3.83  |   (2)  aElement0(xc)
% 23.42/3.83  | 
% 23.42/3.83  | ALPHA: (m__1933) implies:
% 23.42/3.83  |   (3)   ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) & aElementOf0(xy, v0) &
% 23.42/3.83  |          aElementOf0(xx, v0) & aElement0(xz))
% 23.42/3.83  | 
% 23.42/3.83  | ALPHA: (m__) implies:
% 23.42/3.83  |   (4)  $i(xc)
% 23.42/3.83  |   (5)  $i(xy)
% 23.42/3.84  |   (6)   ! [v0: $i] : ( ~ (sdtasdt0(xc, v0) = xy) |  ~ $i(v0) |  ~
% 23.42/3.84  |          aElement0(v0))
% 23.42/3.84  | 
% 23.42/3.84  | DELTA: instantiating (3) with fresh symbol all_34_0 gives:
% 23.42/3.84  |   (7)  slsdtgt0(xc) = all_34_0 & $i(all_34_0) & aElementOf0(xy, all_34_0) &
% 23.42/3.84  |        aElementOf0(xx, all_34_0) & aElement0(xz)
% 23.42/3.84  | 
% 23.42/3.84  | ALPHA: (7) implies:
% 23.42/3.84  |   (8)  aElementOf0(xy, all_34_0)
% 23.42/3.84  |   (9)  $i(all_34_0)
% 23.42/3.84  |   (10)  slsdtgt0(xc) = all_34_0
% 23.42/3.84  | 
% 23.42/3.84  | GROUND_INST: instantiating (1) with xc, all_34_0, xy, simplifying with (2),
% 23.42/3.84  |              (4), (5), (8), (9), (10) gives:
% 23.42/3.84  |   (11)   ? [v0: $i] : (sdtasdt0(xc, v0) = xy & $i(v0) & aElement0(v0))
% 23.42/3.84  | 
% 23.42/3.84  | DELTA: instantiating (11) with fresh symbol all_47_0 gives:
% 23.42/3.84  |   (12)  sdtasdt0(xc, all_47_0) = xy & $i(all_47_0) & aElement0(all_47_0)
% 23.42/3.84  | 
% 23.42/3.84  | ALPHA: (12) implies:
% 23.42/3.84  |   (13)  aElement0(all_47_0)
% 23.42/3.84  |   (14)  $i(all_47_0)
% 23.42/3.84  |   (15)  sdtasdt0(xc, all_47_0) = xy
% 23.42/3.84  | 
% 23.42/3.84  | GROUND_INST: instantiating (6) with all_47_0, simplifying with (13), (14),
% 23.42/3.84  |              (15) gives:
% 23.42/3.84  |   (16)  $false
% 23.42/3.84  | 
% 23.42/3.84  | CLOSE: (16) is inconsistent.
% 23.42/3.84  | 
% 23.42/3.84  End of proof
% 23.42/3.84  % SZS output end Proof for theBenchmark
% 23.42/3.84  
% 23.42/3.84  3204ms
%------------------------------------------------------------------------------