TSTP Solution File: NUM540+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM540+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 : n002.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 11:48:29 EDT 2023

% Result   : Theorem 78.52s 11.04s
% Output   : Proof 79.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM540+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n002.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Fri Aug 25 10:45:47 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.60  ________       _____
% 0.20/0.60  ___  __ \_________(_)________________________________
% 0.20/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60  
% 0.20/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60  (2023-06-19)
% 0.20/0.60  
% 0.20/0.60  (c) Philipp Rümmer, 2009-2023
% 0.20/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60                Amanda Stjerna.
% 0.20/0.60  Free software under BSD-3-Clause.
% 0.20/0.60  
% 0.20/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60  
% 0.20/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61  Running up to 7 provers in parallel.
% 0.20/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.34/1.19  Prover 1: Preprocessing ...
% 3.34/1.19  Prover 4: Preprocessing ...
% 3.66/1.22  Prover 0: Preprocessing ...
% 3.66/1.22  Prover 6: Preprocessing ...
% 3.66/1.22  Prover 3: Preprocessing ...
% 3.66/1.22  Prover 2: Preprocessing ...
% 3.66/1.23  Prover 5: Preprocessing ...
% 8.97/2.06  Prover 1: Constructing countermodel ...
% 8.97/2.07  Prover 5: Constructing countermodel ...
% 8.97/2.08  Prover 3: Constructing countermodel ...
% 9.52/2.13  Prover 2: Proving ...
% 10.55/2.18  Prover 6: Proving ...
% 12.27/2.44  Prover 4: Constructing countermodel ...
% 13.53/2.61  Prover 0: Proving ...
% 73.85/10.36  Prover 2: stopped
% 73.85/10.38  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.25/10.45  Prover 7: Preprocessing ...
% 74.80/10.56  Prover 7: Constructing countermodel ...
% 78.16/10.96  Prover 7: Found proof (size 21)
% 78.52/11.02  Prover 7: proved (626ms)
% 78.52/11.02  Prover 0: stopped
% 78.52/11.02  Prover 3: stopped
% 78.52/11.02  Prover 5: stopped
% 78.52/11.03  Prover 1: stopped
% 78.52/11.03  Prover 4: stopped
% 78.52/11.03  Prover 6: stopped
% 78.52/11.03  
% 78.52/11.04  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 78.52/11.04  
% 78.52/11.04  % SZS output start Proof for theBenchmark
% 78.52/11.04  Assumptions after simplification:
% 78.52/11.04  ---------------------------------
% 79.02/11.04  
% 79.02/11.04    (mDefEmp)
% 79.02/11.05    $i(slcrc0) & aSet0(slcrc0) &  ! [v0: $i] : (v0 = slcrc0 |  ~ $i(v0) |  ~
% 79.02/11.05      aSet0(v0) |  ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) &  ! [v0: $i] : (
% 79.02/11.05      ~ $i(v0) |  ~ aElementOf0(v0, slcrc0))
% 79.02/11.05  
% 79.02/11.05    (mDefSeg)
% 79.14/11.08    $i(szNzAzT0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 79.14/11.08      (slbdtrb0(v0) = v1) |  ~ (szszuzczcdt0(v2) = v3) |  ~ $i(v2) |  ~ $i(v1) | 
% 79.14/11.08      ~ $i(v0) |  ~ sdtlseqdt0(v3, v0) |  ~ aElementOf0(v2, szNzAzT0) |  ~
% 79.14/11.08      aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) &  ! [v0: $i] :  ! [v1: $i]
% 79.14/11.08    :  ! [v2: $i] :  ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) |  ~ (szszuzczcdt0(v2) =
% 79.14/11.08        v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v2, v1) |  ~
% 79.14/11.08      aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) &  ! [v0: $i] :  ! [v1: $i]
% 79.14/11.08    :  ! [v2: $i] :  ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) |  ~ (szszuzczcdt0(v2) =
% 79.14/11.08        v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v2, v1) |  ~
% 79.14/11.08      aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) &  ! [v0: $i] :  !
% 79.14/11.08    [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ (slbdtrb0(v0) = v1) |  ~ $i(v2) |  ~
% 79.14/11.08      $i(v0) |  ~ aElementOf0(v0, szNzAzT0) |  ~ aSet0(v2) |  ? [v3: $i] :  ? [v4:
% 79.14/11.08        $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) |  ~ aElementOf0(v3, szNzAzT0) |
% 79.14/11.08          (szszuzczcdt0(v3) = v4 & $i(v4) &  ~ sdtlseqdt0(v4, v0))) &
% 79.14/11.08        (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4,
% 79.14/11.08              v0) & aElementOf0(v3, szNzAzT0))))) &  ! [v0: $i] :  ! [v1: $i] : (
% 79.14/11.08      ~ (slbdtrb0(v0) = v1) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v0, szNzAzT0)
% 79.14/11.08      | aSet0(v1))
% 79.14/11.08  
% 79.14/11.08    (mNoScLessZr)
% 79.14/11.08    $i(sz00) & $i(szNzAzT0) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 79.14/11.08        v1) |  ~ $i(v0) |  ~ sdtlseqdt0(v1, sz00) |  ~ aElementOf0(v0, szNzAzT0))
% 79.14/11.08  
% 79.14/11.08    (mZeroNum)
% 79.14/11.08    $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 79.14/11.08  
% 79.14/11.08    (m__)
% 79.14/11.08    $i(sz00) & $i(slcrc0) &  ? [v0: $i] : ( ~ (v0 = slcrc0) & slbdtrb0(sz00) = v0
% 79.14/11.08      & $i(v0))
% 79.14/11.08  
% 79.14/11.08  Further assumptions not needed in the proof:
% 79.14/11.08  --------------------------------------------
% 79.14/11.08  mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 79.14/11.08  mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons,
% 79.14/11.08  mDefDiff, mDefMax, mDefMin, mDefSub, mDiffCons, mEOfElem, mElmSort, mEmpFin,
% 79.14/11.08  mFConsSet, mFDiffSet, mFinRel, mIH, mIHSort, mLessASymm, mLessRefl, mLessRel,
% 79.14/11.08  mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc,
% 79.14/11.08  mSegFin, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc,
% 79.14/11.08  mSuccLess, mSuccNum, mZeroLess
% 79.14/11.08  
% 79.14/11.08  Those formulas are unsatisfiable:
% 79.14/11.08  ---------------------------------
% 79.14/11.08  
% 79.14/11.08  Begin of proof
% 79.14/11.08  | 
% 79.14/11.08  | ALPHA: (mDefEmp) implies:
% 79.14/11.08  |   (1)  aSet0(slcrc0)
% 79.14/11.08  |   (2)   ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, slcrc0))
% 79.14/11.08  | 
% 79.14/11.08  | ALPHA: (mZeroNum) implies:
% 79.14/11.08  |   (3)  aElementOf0(sz00, szNzAzT0)
% 79.14/11.08  | 
% 79.14/11.08  | ALPHA: (mNoScLessZr) implies:
% 79.14/11.08  |   (4)   ! [v0: $i] :  ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) |  ~ $i(v0) | 
% 79.14/11.08  |          ~ sdtlseqdt0(v1, sz00) |  ~ aElementOf0(v0, szNzAzT0))
% 79.14/11.08  | 
% 79.14/11.08  | ALPHA: (mDefSeg) implies:
% 79.14/11.09  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ (slbdtrb0(v0) =
% 79.14/11.09  |            v1) |  ~ $i(v2) |  ~ $i(v0) |  ~ aElementOf0(v0, szNzAzT0) |  ~
% 79.14/11.09  |          aSet0(v2) |  ? [v3: $i] :  ? [v4: $i] : ($i(v3) & ( ~ aElementOf0(v3,
% 79.14/11.09  |                v2) |  ~ aElementOf0(v3, szNzAzT0) | (szszuzczcdt0(v3) = v4 &
% 79.14/11.09  |                $i(v4) &  ~ sdtlseqdt0(v4, v0))) & (aElementOf0(v3, v2) |
% 79.14/11.09  |              (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, v0) &
% 79.14/11.09  |                aElementOf0(v3, szNzAzT0)))))
% 79.14/11.09  | 
% 79.14/11.09  | ALPHA: (m__) implies:
% 79.14/11.09  |   (6)  $i(slcrc0)
% 79.14/11.09  |   (7)  $i(sz00)
% 79.14/11.09  |   (8)   ? [v0: $i] : ( ~ (v0 = slcrc0) & slbdtrb0(sz00) = v0 & $i(v0))
% 79.14/11.09  | 
% 79.14/11.09  | DELTA: instantiating (8) with fresh symbol all_45_0 gives:
% 79.14/11.09  |   (9)   ~ (all_45_0 = slcrc0) & slbdtrb0(sz00) = all_45_0 & $i(all_45_0)
% 79.14/11.09  | 
% 79.14/11.09  | ALPHA: (9) implies:
% 79.14/11.09  |   (10)   ~ (all_45_0 = slcrc0)
% 79.14/11.09  |   (11)  slbdtrb0(sz00) = all_45_0
% 79.14/11.09  | 
% 79.14/11.09  | GROUND_INST: instantiating (5) with sz00, all_45_0, slcrc0, simplifying with
% 79.14/11.09  |              (1), (3), (6), (7), (11) gives:
% 79.14/11.09  |   (12)  all_45_0 = slcrc0 |  ? [v0: $i] :  ? [v1: $i] : ($i(v0) & ( ~
% 79.14/11.09  |             aElementOf0(v0, szNzAzT0) |  ~ aElementOf0(v0, slcrc0) |
% 79.14/11.09  |             (szszuzczcdt0(v0) = v1 & $i(v1) &  ~ sdtlseqdt0(v1, sz00))) &
% 79.14/11.09  |           (aElementOf0(v0, slcrc0) | (szszuzczcdt0(v0) = v1 & $i(v1) &
% 79.14/11.09  |               sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0))))
% 79.14/11.09  | 
% 79.14/11.09  | BETA: splitting (12) gives:
% 79.14/11.09  | 
% 79.14/11.09  | Case 1:
% 79.14/11.09  | | 
% 79.14/11.09  | |   (13)  all_45_0 = slcrc0
% 79.14/11.09  | | 
% 79.14/11.09  | | REDUCE: (10), (13) imply:
% 79.14/11.09  | |   (14)  $false
% 79.14/11.10  | | 
% 79.14/11.10  | | CLOSE: (14) is inconsistent.
% 79.14/11.10  | | 
% 79.14/11.10  | Case 2:
% 79.14/11.10  | | 
% 79.14/11.10  | |   (15)   ? [v0: $i] :  ? [v1: $i] : ($i(v0) & ( ~ aElementOf0(v0, szNzAzT0)
% 79.14/11.10  | |             |  ~ aElementOf0(v0, slcrc0) | (szszuzczcdt0(v0) = v1 & $i(v1) &
% 79.14/11.10  | |                ~ sdtlseqdt0(v1, sz00))) & (aElementOf0(v0, slcrc0) |
% 79.14/11.10  | |             (szszuzczcdt0(v0) = v1 & $i(v1) & sdtlseqdt0(v1, sz00) &
% 79.14/11.10  | |               aElementOf0(v0, szNzAzT0))))
% 79.14/11.10  | | 
% 79.14/11.10  | | DELTA: instantiating (15) with fresh symbols all_70_0, all_70_1 gives:
% 79.14/11.10  | |   (16)  $i(all_70_1) & ( ~ aElementOf0(all_70_1, szNzAzT0) |  ~
% 79.14/11.10  | |           aElementOf0(all_70_1, slcrc0) | (szszuzczcdt0(all_70_1) = all_70_0
% 79.14/11.10  | |             & $i(all_70_0) &  ~ sdtlseqdt0(all_70_0, sz00))) &
% 79.14/11.10  | |         (aElementOf0(all_70_1, slcrc0) | (szszuzczcdt0(all_70_1) = all_70_0
% 79.14/11.10  | |             & $i(all_70_0) & sdtlseqdt0(all_70_0, sz00) &
% 79.14/11.10  | |             aElementOf0(all_70_1, szNzAzT0)))
% 79.14/11.10  | | 
% 79.14/11.10  | | ALPHA: (16) implies:
% 79.14/11.10  | |   (17)  $i(all_70_1)
% 79.14/11.10  | |   (18)  aElementOf0(all_70_1, slcrc0) | (szszuzczcdt0(all_70_1) = all_70_0 &
% 79.14/11.10  | |           $i(all_70_0) & sdtlseqdt0(all_70_0, sz00) & aElementOf0(all_70_1,
% 79.14/11.10  | |             szNzAzT0))
% 79.14/11.10  | | 
% 79.14/11.10  | | BETA: splitting (18) gives:
% 79.14/11.10  | | 
% 79.14/11.10  | | Case 1:
% 79.14/11.10  | | | 
% 79.14/11.10  | | |   (19)  aElementOf0(all_70_1, slcrc0)
% 79.14/11.10  | | | 
% 79.14/11.10  | | | GROUND_INST: instantiating (2) with all_70_1, simplifying with (17), (19)
% 79.14/11.10  | | |              gives:
% 79.14/11.10  | | |   (20)  $false
% 79.14/11.10  | | | 
% 79.14/11.10  | | | CLOSE: (20) is inconsistent.
% 79.14/11.10  | | | 
% 79.14/11.10  | | Case 2:
% 79.14/11.10  | | | 
% 79.14/11.10  | | |   (21)  szszuzczcdt0(all_70_1) = all_70_0 & $i(all_70_0) &
% 79.14/11.10  | | |         sdtlseqdt0(all_70_0, sz00) & aElementOf0(all_70_1, szNzAzT0)
% 79.14/11.10  | | | 
% 79.14/11.10  | | | ALPHA: (21) implies:
% 79.14/11.10  | | |   (22)  aElementOf0(all_70_1, szNzAzT0)
% 79.14/11.10  | | |   (23)  sdtlseqdt0(all_70_0, sz00)
% 79.14/11.10  | | |   (24)  szszuzczcdt0(all_70_1) = all_70_0
% 79.14/11.10  | | | 
% 79.14/11.10  | | | GROUND_INST: instantiating (4) with all_70_1, all_70_0, simplifying with
% 79.14/11.10  | | |              (17), (22), (23), (24) gives:
% 79.14/11.10  | | |   (25)  $false
% 79.14/11.10  | | | 
% 79.14/11.10  | | | CLOSE: (25) is inconsistent.
% 79.14/11.10  | | | 
% 79.14/11.10  | | End of split
% 79.14/11.10  | | 
% 79.14/11.10  | End of split
% 79.14/11.10  | 
% 79.14/11.10  End of proof
% 79.14/11.10  % SZS output end Proof for theBenchmark
% 79.14/11.10  
% 79.14/11.10  10505ms
%------------------------------------------------------------------------------