TSTP Solution File: NUM613+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM613+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 11:48:58 EDT 2023

% Result   : Theorem 19.26s 3.42s
% Output   : Proof 28.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : NUM613+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33  % Computer : n015.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Fri Aug 25 13:53:07 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.20/0.59  ________       _____
% 0.20/0.59  ___  __ \_________(_)________________________________
% 0.20/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59  
% 0.20/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59  (2023-06-19)
% 0.20/0.59  
% 0.20/0.59  (c) Philipp Rümmer, 2009-2023
% 0.20/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59                Amanda Stjerna.
% 0.20/0.59  Free software under BSD-3-Clause.
% 0.20/0.59  
% 0.20/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59  
% 0.20/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61  Running up to 7 provers in parallel.
% 0.20/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.39/1.48  Prover 1: Preprocessing ...
% 5.56/1.50  Prover 4: Preprocessing ...
% 5.82/1.53  Prover 2: Preprocessing ...
% 5.82/1.53  Prover 0: Preprocessing ...
% 5.82/1.53  Prover 6: Preprocessing ...
% 5.82/1.54  Prover 3: Preprocessing ...
% 5.82/1.54  Prover 5: Preprocessing ...
% 14.62/2.76  Prover 1: Constructing countermodel ...
% 14.62/2.79  Prover 3: Constructing countermodel ...
% 14.62/2.79  Prover 6: Proving ...
% 16.37/2.93  Prover 5: Proving ...
% 16.37/3.00  Prover 2: Proving ...
% 19.26/3.41  Prover 3: proved (2783ms)
% 19.26/3.41  
% 19.26/3.42  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.26/3.42  
% 19.26/3.43  Prover 5: stopped
% 19.26/3.43  Prover 6: stopped
% 19.26/3.44  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.26/3.44  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 19.26/3.44  Prover 2: stopped
% 19.26/3.45  Prover 4: Constructing countermodel ...
% 19.26/3.45  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 19.26/3.45  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.55/3.63  Prover 8: Preprocessing ...
% 21.55/3.65  Prover 0: Proving ...
% 21.55/3.69  Prover 0: stopped
% 21.55/3.70  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 21.55/3.72  Prover 7: Preprocessing ...
% 22.29/3.74  Prover 11: Preprocessing ...
% 22.29/3.74  Prover 10: Preprocessing ...
% 23.48/3.89  Prover 13: Preprocessing ...
% 23.89/3.97  Prover 8: Warning: ignoring some quantifiers
% 23.89/3.99  Prover 8: Constructing countermodel ...
% 23.89/3.99  Prover 10: Constructing countermodel ...
% 24.65/4.04  Prover 7: Constructing countermodel ...
% 25.20/4.23  Prover 13: Warning: ignoring some quantifiers
% 25.20/4.25  Prover 13: Constructing countermodel ...
% 26.75/4.32  Prover 10: Found proof (size 19)
% 26.75/4.32  Prover 10: proved (875ms)
% 26.75/4.32  Prover 4: stopped
% 26.75/4.32  Prover 7: stopped
% 26.75/4.33  Prover 8: stopped
% 26.75/4.33  Prover 1: stopped
% 26.75/4.33  Prover 13: stopped
% 28.02/4.63  Prover 11: Constructing countermodel ...
% 28.19/4.67  Prover 11: stopped
% 28.19/4.67  
% 28.19/4.67  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.19/4.67  
% 28.19/4.68  % SZS output start Proof for theBenchmark
% 28.19/4.69  Assumptions after simplification:
% 28.19/4.69  ---------------------------------
% 28.19/4.69  
% 28.19/4.69    (mSuccEquSucc)
% 28.56/4.73    $i(szNzAzT0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 28.56/4.74      (szszuzczcdt0(v1) = v2) |  ~ (szszuzczcdt0(v0) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 28.56/4.74      |  ~ aElementOf0(v1, szNzAzT0) |  ~ aElementOf0(v0, szNzAzT0))
% 28.56/4.74  
% 28.56/4.74    (m__)
% 28.56/4.74    $i(xP) & $i(xk) &  ? [v0: $i] : ( ~ (v0 = xk) & sbrdtbr0(xP) = v0 & $i(v0))
% 28.56/4.74  
% 28.56/4.74    (m__3533)
% 28.56/4.74    szszuzczcdt0(xk) = xK & $i(xk) & $i(xK) & $i(szNzAzT0) & aElementOf0(xk,
% 28.56/4.74      szNzAzT0)
% 28.56/4.74  
% 28.56/4.74    (m__5255)
% 28.56/4.74    $i(xP) & $i(xQ) & $i(xk) & $i(szNzAzT0) &  ? [v0: $i] :  ? [v1: $i] :
% 28.56/4.74    (sbrdtbr0(xP) = v1 & sbrdtbr0(xQ) = v0 & szszuzczcdt0(v1) = v0 &
% 28.56/4.74      szszuzczcdt0(xk) = v0 & $i(v1) & $i(v0) & aElementOf0(v1, szNzAzT0))
% 28.56/4.74  
% 28.56/4.74    (function-axioms)
% 28.56/4.76     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 28.56/4.76      (sdtexdt0(v3, v2) = v1) |  ~ (sdtexdt0(v3, v2) = v0)) &  ! [v0: $i] :  !
% 28.56/4.76    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtlcdtrc0(v3, v2) = v1)
% 28.56/4.76      |  ~ (sdtlcdtrc0(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 28.56/4.76    ! [v3: $i] : (v1 = v0 |  ~ (sdtlbdtrb0(v3, v2) = v1) |  ~ (sdtlbdtrb0(v3, v2)
% 28.56/4.76        = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0
% 28.56/4.76      |  ~ (sdtlpdtrp0(v3, v2) = v1) |  ~ (sdtlpdtrp0(v3, v2) = v0)) &  ! [v0: $i]
% 28.56/4.76    :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (slbdtsldtrb0(v3,
% 28.56/4.76          v2) = v1) |  ~ (slbdtsldtrb0(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i]
% 28.56/4.76    :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtmndt0(v3, v2) = v1) |  ~
% 28.56/4.76      (sdtmndt0(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 28.56/4.76      $i] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0)) & 
% 28.56/4.76    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (szDzizrdt0(v2) = v1) |
% 28.56/4.76       ~ (szDzizrdt0(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 =
% 28.56/4.76      v0 |  ~ (szDzozmdt0(v2) = v1) |  ~ (szDzozmdt0(v2) = v0)) &  ! [v0: $i] :  !
% 28.56/4.76    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (slbdtrb0(v2) = v1) |  ~ (slbdtrb0(v2)
% 28.56/4.76        = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 28.56/4.76      (szmzazxdt0(v2) = v1) |  ~ (szmzazxdt0(v2) = v0)) &  ! [v0: $i] :  ! [v1:
% 28.56/4.76      $i] :  ! [v2: $i] : (v1 = v0 |  ~ (szmzizndt0(v2) = v1) |  ~ (szmzizndt0(v2)
% 28.56/4.76        = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 28.56/4.76      (sbrdtbr0(v2) = v1) |  ~ (sbrdtbr0(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 28.56/4.76    ! [v2: $i] : (v1 = v0 |  ~ (szszuzczcdt0(v2) = v1) |  ~ (szszuzczcdt0(v2) =
% 28.56/4.76        v0))
% 28.56/4.76  
% 28.56/4.76  Further assumptions not needed in the proof:
% 28.56/4.76  --------------------------------------------
% 28.56/4.76  mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 28.56/4.76  mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 28.56/4.76  mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 28.56/4.76  mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 28.56/4.76  mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 28.56/4.76  mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 28.56/4.76  mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr,
% 28.56/4.76  mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet,
% 28.56/4.76  mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans,
% 28.56/4.76  mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435,
% 28.56/4.76  m__3453, m__3462, m__3520, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151,
% 28.56/4.76  m__4182, m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4891,
% 28.56/4.76  m__4908, m__4982, m__4998, m__5078, m__5093, m__5106, m__5116, m__5147, m__5164,
% 28.56/4.76  m__5173, m__5182, m__5195, m__5208
% 28.56/4.76  
% 28.56/4.76  Those formulas are unsatisfiable:
% 28.56/4.76  ---------------------------------
% 28.56/4.76  
% 28.56/4.76  Begin of proof
% 28.56/4.76  | 
% 28.56/4.76  | ALPHA: (mSuccEquSucc) implies:
% 28.56/4.76  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 28.56/4.76  |          (szszuzczcdt0(v1) = v2) |  ~ (szszuzczcdt0(v0) = v2) |  ~ $i(v1) |  ~
% 28.56/4.76  |          $i(v0) |  ~ aElementOf0(v1, szNzAzT0) |  ~ aElementOf0(v0, szNzAzT0))
% 28.56/4.76  | 
% 28.56/4.76  | ALPHA: (m__3533) implies:
% 28.56/4.77  |   (2)  aElementOf0(xk, szNzAzT0)
% 28.56/4.77  |   (3)  szszuzczcdt0(xk) = xK
% 28.56/4.77  | 
% 28.56/4.77  | ALPHA: (m__5255) implies:
% 28.56/4.77  |   (4)   ? [v0: $i] :  ? [v1: $i] : (sbrdtbr0(xP) = v1 & sbrdtbr0(xQ) = v0 &
% 28.56/4.77  |          szszuzczcdt0(v1) = v0 & szszuzczcdt0(xk) = v0 & $i(v1) & $i(v0) &
% 28.56/4.77  |          aElementOf0(v1, szNzAzT0))
% 28.56/4.77  | 
% 28.56/4.77  | ALPHA: (m__) implies:
% 28.56/4.77  |   (5)  $i(xk)
% 28.56/4.77  |   (6)   ? [v0: $i] : ( ~ (v0 = xk) & sbrdtbr0(xP) = v0 & $i(v0))
% 28.56/4.77  | 
% 28.56/4.77  | ALPHA: (function-axioms) implies:
% 28.56/4.77  |   (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 28.56/4.77  |          (szszuzczcdt0(v2) = v1) |  ~ (szszuzczcdt0(v2) = v0))
% 28.56/4.77  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (sbrdtbr0(v2) =
% 28.56/4.77  |            v1) |  ~ (sbrdtbr0(v2) = v0))
% 28.56/4.77  | 
% 28.56/4.77  | DELTA: instantiating (6) with fresh symbol all_76_0 gives:
% 28.56/4.77  |   (9)   ~ (all_76_0 = xk) & sbrdtbr0(xP) = all_76_0 & $i(all_76_0)
% 28.56/4.77  | 
% 28.56/4.77  | ALPHA: (9) implies:
% 28.56/4.77  |   (10)   ~ (all_76_0 = xk)
% 28.56/4.77  |   (11)  sbrdtbr0(xP) = all_76_0
% 28.56/4.77  | 
% 28.56/4.77  | DELTA: instantiating (4) with fresh symbols all_90_0, all_90_1 gives:
% 28.56/4.77  |   (12)  sbrdtbr0(xP) = all_90_0 & sbrdtbr0(xQ) = all_90_1 &
% 28.56/4.77  |         szszuzczcdt0(all_90_0) = all_90_1 & szszuzczcdt0(xk) = all_90_1 &
% 28.56/4.77  |         $i(all_90_0) & $i(all_90_1) & aElementOf0(all_90_0, szNzAzT0)
% 28.56/4.77  | 
% 28.56/4.77  | ALPHA: (12) implies:
% 28.56/4.77  |   (13)  aElementOf0(all_90_0, szNzAzT0)
% 28.56/4.77  |   (14)  $i(all_90_0)
% 28.56/4.77  |   (15)  szszuzczcdt0(xk) = all_90_1
% 28.56/4.77  |   (16)  szszuzczcdt0(all_90_0) = all_90_1
% 28.56/4.77  |   (17)  sbrdtbr0(xP) = all_90_0
% 28.56/4.77  | 
% 28.56/4.77  | GROUND_INST: instantiating (7) with xK, all_90_1, xk, simplifying with (3),
% 28.56/4.77  |              (15) gives:
% 28.56/4.78  |   (18)  all_90_1 = xK
% 28.56/4.78  | 
% 28.56/4.78  | GROUND_INST: instantiating (8) with all_76_0, all_90_0, xP, simplifying with
% 28.56/4.78  |              (11), (17) gives:
% 28.56/4.78  |   (19)  all_90_0 = all_76_0
% 28.56/4.78  | 
% 28.56/4.78  | REDUCE: (16), (18), (19) imply:
% 28.56/4.78  |   (20)  szszuzczcdt0(all_76_0) = xK
% 28.56/4.78  | 
% 28.56/4.78  | REDUCE: (14), (19) imply:
% 28.56/4.78  |   (21)  $i(all_76_0)
% 28.56/4.78  | 
% 28.56/4.78  | REDUCE: (13), (19) imply:
% 28.56/4.78  |   (22)  aElementOf0(all_76_0, szNzAzT0)
% 28.56/4.78  | 
% 28.56/4.78  | GROUND_INST: instantiating (1) with xk, all_76_0, xK, simplifying with (2),
% 28.56/4.78  |              (3), (5), (20), (21), (22) gives:
% 28.56/4.78  |   (23)  all_76_0 = xk
% 28.56/4.78  | 
% 28.56/4.78  | REDUCE: (10), (23) imply:
% 28.56/4.78  |   (24)  $false
% 28.56/4.78  | 
% 28.56/4.78  | CLOSE: (24) is inconsistent.
% 28.56/4.78  | 
% 28.56/4.78  End of proof
% 28.56/4.78  % SZS output end Proof for theBenchmark
% 28.56/4.78  
% 28.56/4.78  4189ms
%------------------------------------------------------------------------------