TSTP Solution File: RNG101+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : RNG101+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 : 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 : Thu Aug 31 13:57:52 EDT 2023

% Result   : Theorem 19.21s 3.30s
% Output   : Proof 19.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG101+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Aug 27 01:59:23 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.62  ________       _____
% 0.20/0.62  ___  __ \_________(_)________________________________
% 0.20/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62  
% 0.20/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62  (2023-06-19)
% 0.20/0.62  
% 0.20/0.62  (c) Philipp Rümmer, 2009-2023
% 0.20/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62                Amanda Stjerna.
% 0.20/0.62  Free software under BSD-3-Clause.
% 0.20/0.62  
% 0.20/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62  
% 0.20/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.85/1.21  Prover 1: Preprocessing ...
% 3.85/1.21  Prover 4: Preprocessing ...
% 3.85/1.25  Prover 6: Preprocessing ...
% 3.85/1.25  Prover 3: Preprocessing ...
% 3.85/1.25  Prover 5: Preprocessing ...
% 3.85/1.25  Prover 0: Preprocessing ...
% 3.85/1.25  Prover 2: Preprocessing ...
% 9.24/1.96  Prover 5: Proving ...
% 9.24/1.99  Prover 3: Constructing countermodel ...
% 9.24/2.00  Prover 1: Constructing countermodel ...
% 9.24/2.00  Prover 6: Proving ...
% 9.24/2.10  Prover 2: Proving ...
% 11.25/2.27  Prover 4: Constructing countermodel ...
% 12.09/2.37  Prover 0: Proving ...
% 12.49/2.41  Prover 3: gave up
% 12.49/2.41  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.82/2.49  Prover 7: Preprocessing ...
% 13.54/2.58  Prover 1: gave up
% 13.87/2.59  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.35/2.68  Prover 8: Preprocessing ...
% 14.35/2.74  Prover 7: Constructing countermodel ...
% 16.19/2.93  Prover 8: Warning: ignoring some quantifiers
% 16.19/2.94  Prover 8: Constructing countermodel ...
% 18.51/3.29  Prover 7: Found proof (size 11)
% 18.51/3.29  Prover 7: proved (874ms)
% 18.51/3.29  Prover 4: stopped
% 18.51/3.29  Prover 6: stopped
% 18.51/3.29  Prover 0: stopped
% 18.51/3.29  Prover 2: stopped
% 19.21/3.29  Prover 5: stopped
% 19.21/3.30  Prover 8: stopped
% 19.21/3.30  
% 19.21/3.30  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.21/3.30  
% 19.21/3.30  % SZS output start Proof for theBenchmark
% 19.21/3.30  Assumptions after simplification:
% 19.21/3.30  ---------------------------------
% 19.21/3.30  
% 19.21/3.30    (mDefPrIdeal)
% 19.21/3.33     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (slsdtgt0(v0) =
% 19.21/3.33        v1) |  ~ (sdtasdt0(v0, v3) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 19.21/3.33      $i(v0) |  ~ aElement0(v3) |  ~ aElement0(v0) | aElementOf0(v2, v1)) &  !
% 19.21/3.33    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ (slsdtgt0(v0) = v1) |  ~
% 19.21/3.33      $i(v2) |  ~ $i(v0) |  ~ aSet0(v2) |  ~ aElement0(v0) |  ? [v3: $i] :  ? [v4:
% 19.21/3.33        $i] :  ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) |  ! [v6:
% 19.21/3.33            $i] : ( ~ (sdtasdt0(v0, v6) = v3) |  ~ $i(v6) |  ~ aElement0(v6))) &
% 19.21/3.33        (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 &
% 19.21/3.33            aElement0(v4))))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 19.21/3.33      (slsdtgt0(v0) = v1) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v2,
% 19.21/3.33        v1) |  ~ aElement0(v0) |  ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 19.21/3.33        aElement0(v3))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) |  ~
% 19.21/3.33      $i(v1) |  ~ $i(v0) |  ~ aElement0(v0) | aSet0(v1))
% 19.21/3.33  
% 19.21/3.33    (m__)
% 19.21/3.33    $i(xx) & $i(xc) &  ! [v0: $i] : ( ~ (sdtasdt0(xc, v0) = xx) |  ~ $i(v0) |  ~
% 19.21/3.33      aElement0(v0))
% 19.21/3.33  
% 19.21/3.33    (m__1905)
% 19.21/3.33    $i(xc) & aElement0(xc)
% 19.21/3.33  
% 19.21/3.33    (m__1933)
% 19.21/3.34    $i(xz) & $i(xy) & $i(xx) & $i(xc) &  ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0)
% 19.21/3.34      & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz))
% 19.21/3.34  
% 19.21/3.34  Further assumptions not needed in the proof:
% 19.21/3.34  --------------------------------------------
% 19.21/3.34  mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder,
% 19.21/3.34  mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDefSSum,
% 19.21/3.34  mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulComm,
% 19.21/3.34  mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mSetEq, mSetSort, mSortsB,
% 19.21/3.34  mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr
% 19.21/3.34  
% 19.21/3.34  Those formulas are unsatisfiable:
% 19.21/3.34  ---------------------------------
% 19.21/3.34  
% 19.21/3.34  Begin of proof
% 19.21/3.34  | 
% 19.21/3.34  | ALPHA: (mDefPrIdeal) implies:
% 19.21/3.34  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) |  ~
% 19.21/3.34  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v2, v1) |  ~
% 19.21/3.34  |          aElement0(v0) |  ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 19.21/3.34  |            aElement0(v3)))
% 19.21/3.34  | 
% 19.21/3.34  | ALPHA: (m__1905) implies:
% 19.21/3.34  |   (2)  aElement0(xc)
% 19.21/3.34  | 
% 19.21/3.34  | ALPHA: (m__1933) implies:
% 19.21/3.34  |   (3)   ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) & aElementOf0(xy, v0) &
% 19.21/3.34  |          aElementOf0(xx, v0) & aElement0(xz))
% 19.21/3.34  | 
% 19.21/3.34  | ALPHA: (m__) implies:
% 19.21/3.34  |   (4)  $i(xc)
% 19.21/3.34  |   (5)  $i(xx)
% 19.21/3.34  |   (6)   ! [v0: $i] : ( ~ (sdtasdt0(xc, v0) = xx) |  ~ $i(v0) |  ~
% 19.21/3.34  |          aElement0(v0))
% 19.21/3.34  | 
% 19.21/3.34  | DELTA: instantiating (3) with fresh symbol all_34_0 gives:
% 19.21/3.34  |   (7)  slsdtgt0(xc) = all_34_0 & $i(all_34_0) & aElementOf0(xy, all_34_0) &
% 19.21/3.34  |        aElementOf0(xx, all_34_0) & aElement0(xz)
% 19.21/3.34  | 
% 19.21/3.34  | ALPHA: (7) implies:
% 19.21/3.34  |   (8)  aElementOf0(xx, all_34_0)
% 19.21/3.34  |   (9)  $i(all_34_0)
% 19.21/3.34  |   (10)  slsdtgt0(xc) = all_34_0
% 19.21/3.34  | 
% 19.21/3.34  | GROUND_INST: instantiating (1) with xc, all_34_0, xx, simplifying with (2),
% 19.21/3.34  |              (4), (5), (8), (9), (10) gives:
% 19.21/3.34  |   (11)   ? [v0: $i] : (sdtasdt0(xc, v0) = xx & $i(v0) & aElement0(v0))
% 19.21/3.34  | 
% 19.21/3.34  | DELTA: instantiating (11) with fresh symbol all_45_0 gives:
% 19.21/3.35  |   (12)  sdtasdt0(xc, all_45_0) = xx & $i(all_45_0) & aElement0(all_45_0)
% 19.21/3.35  | 
% 19.21/3.35  | ALPHA: (12) implies:
% 19.21/3.35  |   (13)  aElement0(all_45_0)
% 19.21/3.35  |   (14)  $i(all_45_0)
% 19.21/3.35  |   (15)  sdtasdt0(xc, all_45_0) = xx
% 19.21/3.35  | 
% 19.21/3.35  | GROUND_INST: instantiating (6) with all_45_0, simplifying with (13), (14),
% 19.21/3.35  |              (15) gives:
% 19.21/3.35  |   (16)  $false
% 19.21/3.35  | 
% 19.21/3.35  | CLOSE: (16) is inconsistent.
% 19.21/3.35  | 
% 19.21/3.35  End of proof
% 19.21/3.35  % SZS output end Proof for theBenchmark
% 19.21/3.35  
% 19.21/3.35  2726ms
%------------------------------------------------------------------------------