TSTP Solution File: NUM540+2 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM540+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n031.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 10:22:57 EDT 2023
% Result : Theorem 0.20s 0.66s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM540+2 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n031.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 16:53:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % File :CSE---1.6
% 0.20/0.64 % Problem :theBenchmark
% 0.20/0.64 % Transform :cnf
% 0.20/0.64 % Format :tptp:raw
% 0.20/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.64
% 0.20/0.64 % Result :Theorem 0.010000s
% 0.20/0.64 % Output :CNFRefutation 0.010000s
% 0.20/0.64 %-------------------------------------------
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 % File : NUM540+2 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.65 % Domain : Number Theory
% 0.20/0.65 % Problem : Ramsey's Infinite Theorem 08, 01 expansion
% 0.20/0.65 % Version : Especial.
% 0.20/0.65 % English :
% 0.20/0.65
% 0.20/0.65 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.20/0.65 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.20/0.65 % Source : [Pas08]
% 0.20/0.65 % Names : ramsey_08.01 [Pas08]
% 0.20/0.65
% 0.20/0.65 % Status : Theorem
% 0.20/0.65 % Rating : 0.06 v8.1.0, 0.00 v7.3.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.10 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.35 v4.0.1, 0.74 v4.0.0
% 0.20/0.65 % Syntax : Number of formulae : 52 ( 2 unt; 7 def)
% 0.20/0.65 % Number of atoms : 196 ( 30 equ)
% 0.20/0.65 % Maximal formula atoms : 8 ( 3 avg)
% 0.20/0.65 % Number of connectives : 159 ( 15 ~; 4 |; 53 &)
% 0.20/0.65 % ( 13 <=>; 74 =>; 0 <=; 0 <~>)
% 0.20/0.65 % Maximal formula depth : 12 ( 5 avg)
% 0.20/0.65 % Maximal term depth : 4 ( 1 avg)
% 0.20/0.65 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% 0.20/0.65 % Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% 0.20/0.65 % Number of variables : 91 ( 87 !; 4 ?)
% 0.20/0.65 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.65
% 0.20/0.65 % Comments : Problem generated by the SAD system [VLP07]
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 fof(mSetSort,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => $true ) ).
% 0.20/0.65
% 0.20/0.65 fof(mElmSort,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aElement0(W0)
% 0.20/0.65 => $true ) ).
% 0.20/0.65
% 0.20/0.65 fof(mEOfElem,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( aElementOf0(W1,W0)
% 0.20/0.65 => aElement0(W1) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mFinRel,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => ( isFinite0(W0)
% 0.20/0.65 => $true ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mDefEmp,definition,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( W0 = slcrc0
% 0.20/0.65 <=> ( aSet0(W0)
% 0.20/0.65 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mEmpFin,axiom,
% 0.20/0.65 isFinite0(slcrc0) ).
% 0.20/0.65
% 0.20/0.65 fof(mCntRel,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => ( isCountable0(W0)
% 0.20/0.65 => $true ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mCountNFin,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( ( aSet0(W0)
% 0.20/0.65 & isCountable0(W0) )
% 0.20/0.65 => ~ isFinite0(W0) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mCountNFin_01,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( ( aSet0(W0)
% 0.20/0.65 & isCountable0(W0) )
% 0.20/0.65 => W0 != slcrc0 ) ).
% 0.20/0.65
% 0.20/0.65 fof(mDefSub,definition,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( aSubsetOf0(W1,W0)
% 0.20/0.65 <=> ( aSet0(W1)
% 0.20/0.65 & ! [W2] :
% 0.20/0.65 ( aElementOf0(W2,W1)
% 0.20/0.65 => aElementOf0(W2,W0) ) ) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mSubFSet,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( ( aSet0(W0)
% 0.20/0.65 & isFinite0(W0) )
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( aSubsetOf0(W1,W0)
% 0.20/0.65 => isFinite0(W1) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mSubRefl,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => aSubsetOf0(W0,W0) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mSubASymm,axiom,
% 0.20/0.65 ! [W0,W1] :
% 0.20/0.65 ( ( aSet0(W0)
% 0.20/0.65 & aSet0(W1) )
% 0.20/0.65 => ( ( aSubsetOf0(W0,W1)
% 0.20/0.65 & aSubsetOf0(W1,W0) )
% 0.20/0.65 => W0 = W1 ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mSubTrans,axiom,
% 0.20/0.65 ! [W0,W1,W2] :
% 0.20/0.65 ( ( aSet0(W0)
% 0.20/0.65 & aSet0(W1)
% 0.20/0.65 & aSet0(W2) )
% 0.20/0.65 => ( ( aSubsetOf0(W0,W1)
% 0.20/0.65 & aSubsetOf0(W1,W2) )
% 0.20/0.65 => aSubsetOf0(W0,W2) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mDefCons,definition,
% 0.20/0.65 ! [W0,W1] :
% 0.20/0.65 ( ( aSet0(W0)
% 0.20/0.65 & aElement0(W1) )
% 0.20/0.65 => ! [W2] :
% 0.20/0.65 ( W2 = sdtpldt0(W0,W1)
% 0.20/0.65 <=> ( aSet0(W2)
% 0.20/0.65 & ! [W3] :
% 0.20/0.65 ( aElementOf0(W3,W2)
% 0.20/0.65 <=> ( aElement0(W3)
% 0.20/0.65 & ( aElementOf0(W3,W0)
% 0.20/0.65 | W3 = W1 ) ) ) ) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mDefDiff,definition,
% 0.20/0.65 ! [W0,W1] :
% 0.20/0.65 ( ( aSet0(W0)
% 0.20/0.65 & aElement0(W1) )
% 0.20/0.65 => ! [W2] :
% 0.20/0.65 ( W2 = sdtmndt0(W0,W1)
% 0.20/0.65 <=> ( aSet0(W2)
% 0.20/0.65 & ! [W3] :
% 0.20/0.65 ( aElementOf0(W3,W2)
% 0.20/0.65 <=> ( aElement0(W3)
% 0.20/0.65 & aElementOf0(W3,W0)
% 0.20/0.65 & W3 != W1 ) ) ) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mConsDiff,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( aElementOf0(W1,W0)
% 0.20/0.65 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mDiffCons,axiom,
% 0.20/0.65 ! [W0,W1] :
% 0.20/0.65 ( ( aElement0(W0)
% 0.20/0.65 & aSet0(W1) )
% 0.20/0.65 => ( ~ aElementOf0(W0,W1)
% 0.20/0.65 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mCConsSet,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aElement0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( ( aSet0(W1)
% 0.20/0.65 & isCountable0(W1) )
% 0.20/0.65 => isCountable0(sdtpldt0(W1,W0)) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mCDiffSet,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aElement0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( ( aSet0(W1)
% 0.20/0.65 & isCountable0(W1) )
% 0.20/0.65 => isCountable0(sdtmndt0(W1,W0)) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mFConsSet,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aElement0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( ( aSet0(W1)
% 0.20/0.65 & isFinite0(W1) )
% 0.20/0.65 => isFinite0(sdtpldt0(W1,W0)) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mFDiffSet,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aElement0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( ( aSet0(W1)
% 0.20/0.65 & isFinite0(W1) )
% 0.20/0.65 => isFinite0(sdtmndt0(W1,W0)) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mNATSet,axiom,
% 0.20/0.65 ( aSet0(szNzAzT0)
% 0.20/0.65 & isCountable0(szNzAzT0) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mZeroNum,axiom,
% 0.20/0.65 aElementOf0(sz00,szNzAzT0) ).
% 0.20/0.65
% 0.20/0.65 fof(mSuccNum,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aElementOf0(W0,szNzAzT0)
% 0.20/0.65 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
% 0.20/0.65 & szszuzczcdt0(W0) != sz00 ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mSuccEquSucc,axiom,
% 0.20/0.65 ! [W0,W1] :
% 0.20/0.65 ( ( aElementOf0(W0,szNzAzT0)
% 0.20/0.65 & aElementOf0(W1,szNzAzT0) )
% 0.20/0.65 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
% 0.20/0.65 => W0 = W1 ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mNatExtra,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 => ( W0 = sz00
% 0.20/0.66 | ? [W1] :
% 0.20/0.66 ( aElementOf0(W1,szNzAzT0)
% 0.20/0.66 & W0 = szszuzczcdt0(W1) ) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mNatNSucc,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 => W0 != szszuzczcdt0(W0) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mLessRel,axiom,
% 0.20/0.66 ! [W0,W1] :
% 0.20/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.20/0.66 => ( sdtlseqdt0(W0,W1)
% 0.20/0.66 => $true ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mZeroLess,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 => sdtlseqdt0(sz00,W0) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mNoScLessZr,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mSuccLess,axiom,
% 0.20/0.66 ! [W0,W1] :
% 0.20/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.20/0.66 => ( sdtlseqdt0(W0,W1)
% 0.20/0.66 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mLessSucc,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mLessRefl,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 => sdtlseqdt0(W0,W0) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mLessASymm,axiom,
% 0.20/0.66 ! [W0,W1] :
% 0.20/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.20/0.66 => ( ( sdtlseqdt0(W0,W1)
% 0.20/0.66 & sdtlseqdt0(W1,W0) )
% 0.20/0.66 => W0 = W1 ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mLessTrans,axiom,
% 0.20/0.66 ! [W0,W1,W2] :
% 0.20/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 & aElementOf0(W1,szNzAzT0)
% 0.20/0.66 & aElementOf0(W2,szNzAzT0) )
% 0.20/0.66 => ( ( sdtlseqdt0(W0,W1)
% 0.20/0.66 & sdtlseqdt0(W1,W2) )
% 0.20/0.66 => sdtlseqdt0(W0,W2) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mLessTotal,axiom,
% 0.20/0.66 ! [W0,W1] :
% 0.20/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.20/0.66 => ( sdtlseqdt0(W0,W1)
% 0.20/0.66 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mIHSort,axiom,
% 0.20/0.66 ! [W0,W1] :
% 0.20/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.20/0.66 => ( iLess0(W0,W1)
% 0.20/0.66 => $true ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mIH,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 => iLess0(W0,szszuzczcdt0(W0)) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mCardS,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aSet0(W0)
% 0.20/0.66 => aElement0(sbrdtbr0(W0)) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mCardNum,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aSet0(W0)
% 0.20/0.66 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
% 0.20/0.66 <=> isFinite0(W0) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mCardEmpty,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aSet0(W0)
% 0.20/0.66 => ( sbrdtbr0(W0) = sz00
% 0.20/0.66 <=> W0 = slcrc0 ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mCardCons,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( ( aSet0(W0)
% 0.20/0.66 & isFinite0(W0) )
% 0.20/0.66 => ! [W1] :
% 0.20/0.66 ( aElement0(W1)
% 0.20/0.66 => ( ~ aElementOf0(W1,W0)
% 0.20/0.66 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mCardDiff,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aSet0(W0)
% 0.20/0.66 => ! [W1] :
% 0.20/0.66 ( ( isFinite0(W0)
% 0.20/0.66 & aElementOf0(W1,W0) )
% 0.20/0.66 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mCardSub,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aSet0(W0)
% 0.20/0.66 => ! [W1] :
% 0.20/0.66 ( ( isFinite0(W0)
% 0.20/0.66 & aSubsetOf0(W1,W0) )
% 0.20/0.66 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mCardSubEx,axiom,
% 0.20/0.66 ! [W0,W1] :
% 0.20/0.66 ( ( aSet0(W0)
% 0.20/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.20/0.66 => ( ( isFinite0(W0)
% 0.20/0.66 & sdtlseqdt0(W1,sbrdtbr0(W0)) )
% 0.20/0.66 => ? [W2] :
% 0.20/0.66 ( aSubsetOf0(W2,W0)
% 0.20/0.66 & sbrdtbr0(W2) = W1 ) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mDefMin,definition,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.20/0.66 & W0 != slcrc0 )
% 0.20/0.66 => ! [W1] :
% 0.20/0.66 ( W1 = szmzizndt0(W0)
% 0.20/0.66 <=> ( aElementOf0(W1,W0)
% 0.20/0.66 & ! [W2] :
% 0.20/0.66 ( aElementOf0(W2,W0)
% 0.20/0.66 => sdtlseqdt0(W1,W2) ) ) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mDefMax,definition,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.20/0.66 & isFinite0(W0)
% 0.20/0.66 & W0 != slcrc0 )
% 0.20/0.66 => ! [W1] :
% 0.20/0.66 ( W1 = szmzazxdt0(W0)
% 0.20/0.66 <=> ( aElementOf0(W1,W0)
% 0.20/0.66 & ! [W2] :
% 0.20/0.66 ( aElementOf0(W2,W0)
% 0.20/0.66 => sdtlseqdt0(W2,W1) ) ) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mMinMin,axiom,
% 0.20/0.66 ! [W0,W1] :
% 0.20/0.66 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.20/0.66 & aSubsetOf0(W1,szNzAzT0)
% 0.20/0.66 & W0 != slcrc0
% 0.20/0.66 & W1 != slcrc0 )
% 0.20/0.66 => ( ( aElementOf0(szmzizndt0(W0),W1)
% 0.20/0.66 & aElementOf0(szmzizndt0(W1),W0) )
% 0.20/0.66 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mDefSeg,definition,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 => ! [W1] :
% 0.20/0.66 ( W1 = slbdtrb0(W0)
% 0.20/0.66 <=> ( aSet0(W1)
% 0.20/0.66 & ! [W2] :
% 0.20/0.66 ( aElementOf0(W2,W1)
% 0.20/0.66 <=> ( aElementOf0(W2,szNzAzT0)
% 0.20/0.66 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(mSegFin,axiom,
% 0.20/0.66 ! [W0] :
% 0.20/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.20/0.66 => isFinite0(slbdtrb0(W0)) ) ).
% 0.20/0.66
% 0.20/0.66 fof(m__,conjecture,
% 0.20/0.66 ( ( aSet0(slbdtrb0(sz00))
% 0.20/0.66 & ! [W0] : ~ aElementOf0(W0,slbdtrb0(sz00)) )
% 0.20/0.66 => ( ~ ? [W0] : aElementOf0(W0,slbdtrb0(sz00))
% 0.20/0.66 | slbdtrb0(sz00) = slcrc0 ) ) ).
% 0.20/0.66
% 0.20/0.66 %------------------------------------------------------------------------------
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 % Proof found
% 0.20/0.66 % SZS status Theorem for theBenchmark
% 0.20/0.66 % SZS output start Proof
% 0.20/0.66 %ClaNum:131(EqnAxiom:42)
% 0.20/0.66 %VarNum:576(SingletonVarNum:176)
% 0.20/0.66 %MaxLitNum:8
% 0.20/0.66 %MaxfuncDepth:3
% 0.20/0.66 %SharedTerms:12
% 0.20/0.66 %goalClause: 46 48 49 50
% 0.20/0.66 %singleGoalClaCount:4
% 0.20/0.66 [43]P1(a1)
% 0.20/0.66 [44]P4(a2)
% 0.20/0.66 [45]P5(a1)
% 0.20/0.66 [47]P2(a17,a1)
% 0.20/0.66 [46]P1(f3(a17))
% 0.20/0.66 [48]P2(a4,f3(a17))
% 0.20/0.66 [49]~E(f3(a17),a2)
% 0.20/0.66 [50]~P2(x501,f3(a17))
% 0.20/0.66 [51]P1(x511)+~E(x511,a2)
% 0.20/0.66 [57]~P1(x571)+P6(x571,x571)
% 0.20/0.66 [63]~P2(x631,a1)+P8(a17,x631)
% 0.20/0.66 [69]P8(x691,x691)+~P2(x691,a1)
% 0.20/0.66 [55]~P1(x551)+P3(f5(x551))
% 0.20/0.66 [59]~P2(x591,a1)+~E(f18(x591),a17)
% 0.20/0.66 [60]~P2(x601,a1)+~E(f18(x601),x601)
% 0.20/0.66 [62]~P2(x621,a1)+P4(f3(x621))
% 0.20/0.66 [70]~P2(x701,a1)+P2(f18(x701),a1)
% 0.20/0.66 [71]~P2(x711,a1)+P8(x711,f18(x711))
% 0.20/0.66 [72]~P2(x721,a1)+P7(x721,f18(x721))
% 0.20/0.66 [79]~P2(x791,a1)+~P8(f18(x791),a17)
% 0.20/0.66 [58]~P2(x582,x581)+~E(x581,a2)
% 0.20/0.66 [54]~P1(x541)+~P5(x541)+~E(x541,a2)
% 0.20/0.66 [56]~P4(x561)+~P5(x561)+~P1(x561)
% 0.20/0.66 [52]~P1(x521)+~E(x521,a2)+E(f5(x521),a17)
% 0.20/0.66 [53]~P1(x531)+E(x531,a2)+~E(f5(x531),a17)
% 0.20/0.66 [61]~P1(x611)+P2(f6(x611),x611)+E(x611,a2)
% 0.20/0.66 [66]~P1(x661)+~P4(x661)+P2(f5(x661),a1)
% 0.20/0.66 [73]~P2(x731,a1)+E(x731,a17)+P2(f7(x731),a1)
% 0.20/0.66 [74]~P1(x741)+P4(x741)+~P2(f5(x741),a1)
% 0.20/0.66 [64]~P2(x641,a1)+E(x641,a17)+E(f18(f7(x641)),x641)
% 0.20/0.66 [67]~P6(x671,x672)+P1(x671)+~P1(x672)
% 0.20/0.66 [68]~P2(x681,x682)+P3(x681)+~P1(x682)
% 0.20/0.66 [65]P1(x651)+~P2(x652,a1)+~E(x651,f3(x652))
% 0.20/0.66 [97]~P1(x971)+~P2(x972,x971)+E(f15(f16(x971,x972),x972),x971)
% 0.20/0.66 [75]~P4(x752)+~P6(x751,x752)+P4(x751)+~P1(x752)
% 0.20/0.66 [78]P2(x782,x781)+~E(x782,f19(x781))+~P6(x781,a1)+E(x781,a2)
% 0.20/0.66 [81]~P1(x811)+~P3(x812)+~P4(x811)+P4(f15(x811,x812))
% 0.20/0.66 [82]~P1(x821)+~P3(x822)+~P4(x821)+P4(f16(x821,x822))
% 0.20/0.66 [83]~P1(x831)+~P3(x832)+~P5(x831)+P5(f15(x831,x832))
% 0.20/0.66 [84]~P1(x841)+~P3(x842)+~P5(x841)+P5(f16(x841,x842))
% 0.20/0.66 [85]E(x851,x852)+~E(f18(x851),f18(x852))+~P2(x852,a1)+~P2(x851,a1)
% 0.20/0.66 [88]~P1(x882)+~P4(x882)+~P6(x881,x882)+P8(f5(x881),f5(x882))
% 0.20/0.66 [95]~P1(x951)+~P1(x952)+P6(x951,x952)+P2(f8(x952,x951),x951)
% 0.20/0.66 [101]P8(x1011,x1012)+P8(f18(x1012),x1011)+~P2(x1012,a1)+~P2(x1011,a1)
% 0.20/0.66 [108]~P8(x1081,x1082)+~P2(x1082,a1)+~P2(x1081,a1)+P8(f18(x1081),f18(x1082))
% 0.20/0.66 [110]~P1(x1101)+~P1(x1102)+P6(x1101,x1102)+~P2(f8(x1102,x1101),x1102)
% 0.20/0.66 [112]P8(x1121,x1122)+~P2(x1122,a1)+~P2(x1121,a1)+~P8(f18(x1121),f18(x1122))
% 0.20/0.66 [96]P2(x962,x961)+~P1(x961)+~P3(x962)+E(f16(f15(x961,x962),x962),x961)
% 0.20/0.66 [115]~P1(x1151)+~P4(x1151)+~P2(x1152,x1151)+E(f18(f5(f16(x1151,x1152))),f5(x1151))
% 0.20/0.66 [93]~P1(x932)+~P6(x933,x932)+P2(x931,x932)+~P2(x931,x933)
% 0.20/0.66 [76]~P1(x762)+~P3(x763)+P1(x761)+~E(x761,f15(x762,x763))
% 0.20/0.66 [77]~P1(x772)+~P3(x773)+P1(x771)+~E(x771,f16(x772,x773))
% 0.20/0.66 [89]~P2(x891,x892)+~P2(x893,a1)+P2(x891,a1)+~E(x892,f3(x893))
% 0.20/0.66 [98]~P2(x981,x983)+~P2(x982,a1)+P8(f18(x981),x982)+~E(x983,f3(x982))
% 0.20/0.66 [86]~P1(x862)+~P1(x861)+~P6(x862,x861)+~P6(x861,x862)+E(x861,x862)
% 0.20/0.66 [107]~P8(x1072,x1071)+~P8(x1071,x1072)+E(x1071,x1072)+~P2(x1072,a1)+~P2(x1071,a1)
% 0.20/0.66 [80]~P4(x801)+P2(x802,x801)+~E(x802,f20(x801))+~P6(x801,a1)+E(x801,a2)
% 0.20/0.66 [109]~P2(x1092,x1091)+P2(f11(x1091,x1092),x1091)+~P6(x1091,a1)+E(x1091,a2)+E(x1092,f19(x1091))
% 0.20/0.66 [116]~P1(x1161)+~P4(x1161)+~P2(x1162,a1)+~P8(x1162,f5(x1161))+P6(f12(x1161,x1162),x1161)
% 0.20/0.66 [117]~P1(x1171)+P2(f14(x1172,x1171),x1171)+~P2(x1172,a1)+E(x1171,f3(x1172))+P2(f14(x1172,x1171),a1)
% 0.20/0.66 [118]~P2(x1182,x1181)+~P6(x1181,a1)+~P8(x1182,f11(x1181,x1182))+E(x1181,a2)+E(x1182,f19(x1181))
% 0.20/0.66 [102]P2(x1022,x1021)+~P1(x1021)+~P3(x1022)+~P4(x1021)+E(f5(f15(x1021,x1022)),f18(f5(x1021)))
% 0.20/0.66 [114]~P1(x1141)+~P4(x1141)+~P2(x1142,a1)+~P8(x1142,f5(x1141))+E(f5(f12(x1141,x1142)),x1142)
% 0.20/0.66 [122]~P1(x1221)+P2(f14(x1222,x1221),x1221)+~P2(x1222,a1)+E(x1221,f3(x1222))+P8(f18(f14(x1222,x1221)),x1222)
% 0.20/0.66 [94]~P2(x943,x941)+P8(x942,x943)+~E(x942,f19(x941))+~P6(x941,a1)+E(x941,a2)
% 0.20/0.66 [111]P2(x1111,x1112)+~P2(x1113,a1)+~P2(x1111,a1)+~P8(f18(x1111),x1113)+~E(x1112,f3(x1113))
% 0.20/0.66 [90]~P1(x904)+~P3(x902)+~P2(x901,x903)+~E(x901,x902)+~E(x903,f16(x904,x902))
% 0.20/0.66 [91]~P1(x913)+~P3(x914)+~P2(x911,x912)+P3(x911)+~E(x912,f15(x913,x914))
% 0.20/0.66 [92]~P1(x923)+~P3(x924)+~P2(x921,x922)+P3(x921)+~E(x922,f16(x923,x924))
% 0.20/0.66 [100]~P1(x1002)+~P3(x1004)+~P2(x1001,x1003)+P2(x1001,x1002)+~E(x1003,f16(x1002,x1004))
% 0.20/0.66 [113]~P4(x1131)+~P2(x1132,x1131)+P2(f13(x1131,x1132),x1131)+~P6(x1131,a1)+E(x1131,a2)+E(x1132,f20(x1131))
% 0.20/0.66 [120]~P4(x1201)+~P2(x1202,x1201)+~P6(x1201,a1)+~P8(f13(x1201,x1202),x1202)+E(x1201,a2)+E(x1202,f20(x1201))
% 0.20/0.66 [126]~P1(x1261)+~P2(x1262,a1)+~P2(f14(x1262,x1261),x1261)+E(x1261,f3(x1262))+~P2(f14(x1262,x1261),a1)+~P8(f18(f14(x1262,x1261)),x1262)
% 0.20/0.66 [104]~P1(x1042)+~P1(x1041)+~P6(x1043,x1042)+~P6(x1041,x1043)+P6(x1041,x1042)+~P1(x1043)
% 0.20/0.66 [121]~P8(x1211,x1213)+P8(x1211,x1212)+~P8(x1213,x1212)+~P2(x1212,a1)+~P2(x1213,a1)+~P2(x1211,a1)
% 0.20/0.66 [99]~P4(x991)+~P2(x992,x991)+P8(x992,x993)+~E(x993,f20(x991))+~P6(x991,a1)+E(x991,a2)
% 0.20/0.66 [123]~P1(x1231)+~P1(x1232)+~P3(x1233)+P2(f9(x1232,x1233,x1231),x1231)+~E(f9(x1232,x1233,x1231),x1233)+E(x1231,f16(x1232,x1233))
% 0.20/0.66 [124]~P1(x1241)+~P1(x1242)+~P3(x1243)+P2(f10(x1242,x1243,x1241),x1241)+E(x1241,f15(x1242,x1243))+P3(f10(x1242,x1243,x1241))
% 0.20/0.66 [125]~P1(x1251)+~P1(x1252)+~P3(x1253)+P2(f9(x1252,x1253,x1251),x1251)+E(x1251,f16(x1252,x1253))+P3(f9(x1252,x1253,x1251))
% 0.20/0.66 [127]~P1(x1271)+~P1(x1272)+~P3(x1273)+P2(f9(x1272,x1273,x1271),x1271)+P2(f9(x1272,x1273,x1271),x1272)+E(x1271,f16(x1272,x1273))
% 0.20/0.66 [87]~P1(x874)+~P3(x873)+~P3(x871)+P2(x871,x872)+~E(x871,x873)+~E(x872,f15(x874,x873))
% 0.20/0.66 [103]~P1(x1033)+~P3(x1032)+~P2(x1031,x1034)+E(x1031,x1032)+P2(x1031,x1033)+~E(x1034,f15(x1033,x1032))
% 0.20/0.66 [105]~P1(x1053)+~P3(x1054)+~P3(x1051)+~P2(x1051,x1053)+P2(x1051,x1052)+~E(x1052,f15(x1053,x1054))
% 0.20/0.66 [119]E(f19(x1192),f19(x1191))+~P6(x1191,a1)+~P6(x1192,a1)+~P2(f19(x1191),x1192)+~P2(f19(x1192),x1191)+E(x1191,a2)+E(x1192,a2)
% 0.20/0.66 [128]~P1(x1281)+~P1(x1282)+~P3(x1283)+E(f10(x1282,x1283,x1281),x1283)+P2(f10(x1282,x1283,x1281),x1281)+P2(f10(x1282,x1283,x1281),x1282)+E(x1281,f15(x1282,x1283))
% 0.20/0.66 [129]~P1(x1291)+~P1(x1292)+~P3(x1293)+~E(f10(x1292,x1293,x1291),x1293)+~P2(f10(x1292,x1293,x1291),x1291)+E(x1291,f15(x1292,x1293))+~P3(f10(x1292,x1293,x1291))
% 0.20/0.66 [130]~P1(x1301)+~P1(x1302)+~P3(x1303)+~P2(f10(x1302,x1303,x1301),x1301)+~P2(f10(x1302,x1303,x1301),x1302)+E(x1301,f15(x1302,x1303))+~P3(f10(x1302,x1303,x1301))
% 0.20/0.66 [106]~P1(x1064)+~P3(x1062)+~P3(x1061)+~P2(x1061,x1064)+E(x1061,x1062)+P2(x1061,x1063)+~E(x1063,f16(x1064,x1062))
% 0.20/0.66 [131]~P1(x1311)+~P1(x1312)+~P3(x1313)+E(f9(x1312,x1313,x1311),x1313)+~P2(f9(x1312,x1313,x1311),x1311)+~P2(f9(x1312,x1313,x1311),x1312)+E(x1311,f16(x1312,x1313))+~P3(f9(x1312,x1313,x1311))
% 0.20/0.66 %EqnAxiom
% 0.20/0.66 [1]E(x11,x11)
% 0.20/0.66 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.66 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.20/0.66 [5]~E(x51,x52)+E(f9(x51,x53,x54),f9(x52,x53,x54))
% 0.20/0.66 [6]~E(x61,x62)+E(f9(x63,x61,x64),f9(x63,x62,x64))
% 0.20/0.66 [7]~E(x71,x72)+E(f9(x73,x74,x71),f9(x73,x74,x72))
% 0.20/0.66 [8]~E(x81,x82)+E(f10(x81,x83,x84),f10(x82,x83,x84))
% 0.20/0.66 [9]~E(x91,x92)+E(f10(x93,x91,x94),f10(x93,x92,x94))
% 0.20/0.66 [10]~E(x101,x102)+E(f10(x103,x104,x101),f10(x103,x104,x102))
% 0.20/0.66 [11]~E(x111,x112)+E(f15(x111,x113),f15(x112,x113))
% 0.20/0.66 [12]~E(x121,x122)+E(f15(x123,x121),f15(x123,x122))
% 0.20/0.66 [13]~E(x131,x132)+E(f5(x131),f5(x132))
% 0.20/0.66 [14]~E(x141,x142)+E(f19(x141),f19(x142))
% 0.20/0.66 [15]~E(x151,x152)+E(f11(x151,x153),f11(x152,x153))
% 0.20/0.66 [16]~E(x161,x162)+E(f11(x163,x161),f11(x163,x162))
% 0.20/0.66 [17]~E(x171,x172)+E(f18(x171),f18(x172))
% 0.20/0.66 [18]~E(x181,x182)+E(f8(x181,x183),f8(x182,x183))
% 0.20/0.66 [19]~E(x191,x192)+E(f8(x193,x191),f8(x193,x192))
% 0.20/0.66 [20]~E(x201,x202)+E(f6(x201),f6(x202))
% 0.20/0.66 [21]~E(x211,x212)+E(f14(x211,x213),f14(x212,x213))
% 0.20/0.66 [22]~E(x221,x222)+E(f14(x223,x221),f14(x223,x222))
% 0.20/0.66 [23]~E(x231,x232)+E(f7(x231),f7(x232))
% 0.20/0.66 [24]~E(x241,x242)+E(f16(x241,x243),f16(x242,x243))
% 0.20/0.66 [25]~E(x251,x252)+E(f16(x253,x251),f16(x253,x252))
% 0.20/0.66 [26]~E(x261,x262)+E(f13(x261,x263),f13(x262,x263))
% 0.20/0.67 [27]~E(x271,x272)+E(f13(x273,x271),f13(x273,x272))
% 0.20/0.67 [28]~E(x281,x282)+E(f20(x281),f20(x282))
% 0.20/0.67 [29]~E(x291,x292)+E(f12(x291,x293),f12(x292,x293))
% 0.20/0.67 [30]~E(x301,x302)+E(f12(x303,x301),f12(x303,x302))
% 0.20/0.67 [31]~P1(x311)+P1(x312)+~E(x311,x312)
% 0.20/0.67 [32]~P4(x321)+P4(x322)+~E(x321,x322)
% 0.20/0.67 [33]~P5(x331)+P5(x332)+~E(x331,x332)
% 0.20/0.67 [34]P2(x342,x343)+~E(x341,x342)+~P2(x341,x343)
% 0.20/0.67 [35]P2(x353,x352)+~E(x351,x352)+~P2(x353,x351)
% 0.20/0.67 [36]P6(x362,x363)+~E(x361,x362)+~P6(x361,x363)
% 0.20/0.67 [37]P6(x373,x372)+~E(x371,x372)+~P6(x373,x371)
% 0.20/0.67 [38]~P3(x381)+P3(x382)+~E(x381,x382)
% 0.20/0.67 [39]P8(x392,x393)+~E(x391,x392)+~P8(x391,x393)
% 0.20/0.67 [40]P8(x403,x402)+~E(x401,x402)+~P8(x403,x401)
% 0.20/0.67 [41]P7(x412,x413)+~E(x411,x412)+~P7(x411,x413)
% 0.20/0.67 [42]P7(x423,x422)+~E(x421,x422)+~P7(x423,x421)
% 0.20/0.67
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 cnf(132,plain,
% 0.20/0.67 ($false),
% 0.20/0.67 inference(scs_inference,[],[50,48]),
% 0.20/0.67 ['proof']).
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67 % Total time :0.010000s
%------------------------------------------------------------------------------