TSTP Solution File: NUM559+3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM559+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n010.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 10:23:06 EDT 2023
% Result : Theorem 0.21s 0.66s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM559+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 11:05:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.56 start to proof:theBenchmark
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 % File :CSE---1.6
% 0.21/0.64 % Problem :theBenchmark
% 0.21/0.64 % Transform :cnf
% 0.21/0.64 % Format :tptp:raw
% 0.21/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.64
% 0.21/0.64 % Result :Theorem 0.000000s
% 0.21/0.64 % Output :CNFRefutation 0.000000s
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 %------------------------------------------------------------------------------
% 0.21/0.64 % File : NUM559+3 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.64 % Domain : Number Theory
% 0.21/0.64 % Problem : Ramsey's Infinite Theorem 12_06, 02 expansion
% 0.21/0.64 % Version : Especial.
% 0.21/0.64 % English :
% 0.21/0.65
% 0.21/0.65 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.21/0.65 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.21/0.65 % Source : [Pas08]
% 0.21/0.65 % Names : ramsey_12_06.02 [Pas08]
% 0.21/0.65
% 0.21/0.65 % Status : ContradictoryAxioms
% 0.21/0.65 % Rating : 0.06 v7.5.0, 0.00 v7.4.0, 0.29 v7.3.0, 0.00 v6.3.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 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
% 0.21/0.65 % Syntax : Number of formulae : 70 ( 8 unt; 8 def)
% 0.21/0.65 % Number of atoms : 290 ( 46 equ)
% 0.21/0.65 % Maximal formula atoms : 43 ( 4 avg)
% 0.21/0.65 % Number of connectives : 242 ( 22 ~; 8 |; 96 &)
% 0.21/0.65 % ( 17 <=>; 99 =>; 0 <=; 0 <~>)
% 0.21/0.65 % Maximal formula depth : 17 ( 5 avg)
% 0.21/0.65 % Maximal term depth : 4 ( 1 avg)
% 0.21/0.65 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% 0.21/0.65 % Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% 0.21/0.65 % Number of variables : 118 ( 113 !; 5 ?)
% 0.21/0.65 % SPC : FOF_CAX_RFO_SEQ
% 0.21/0.65
% 0.21/0.65 % Comments : Problem generated by the SAD system [VLP07]
% 0.21/0.65 %------------------------------------------------------------------------------
% 0.21/0.65 fof(mSetSort,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aSet0(W0)
% 0.21/0.65 => $true ) ).
% 0.21/0.65
% 0.21/0.65 fof(mElmSort,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aElement0(W0)
% 0.21/0.65 => $true ) ).
% 0.21/0.65
% 0.21/0.65 fof(mEOfElem,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aSet0(W0)
% 0.21/0.65 => ! [W1] :
% 0.21/0.65 ( aElementOf0(W1,W0)
% 0.21/0.65 => aElement0(W1) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mFinRel,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aSet0(W0)
% 0.21/0.65 => ( isFinite0(W0)
% 0.21/0.65 => $true ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mDefEmp,definition,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( W0 = slcrc0
% 0.21/0.65 <=> ( aSet0(W0)
% 0.21/0.65 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mEmpFin,axiom,
% 0.21/0.65 isFinite0(slcrc0) ).
% 0.21/0.65
% 0.21/0.65 fof(mCntRel,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aSet0(W0)
% 0.21/0.65 => ( isCountable0(W0)
% 0.21/0.65 => $true ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mCountNFin,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( ( aSet0(W0)
% 0.21/0.65 & isCountable0(W0) )
% 0.21/0.65 => ~ isFinite0(W0) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mCountNFin_01,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( ( aSet0(W0)
% 0.21/0.65 & isCountable0(W0) )
% 0.21/0.65 => W0 != slcrc0 ) ).
% 0.21/0.65
% 0.21/0.65 fof(mDefSub,definition,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aSet0(W0)
% 0.21/0.65 => ! [W1] :
% 0.21/0.65 ( aSubsetOf0(W1,W0)
% 0.21/0.65 <=> ( aSet0(W1)
% 0.21/0.65 & ! [W2] :
% 0.21/0.65 ( aElementOf0(W2,W1)
% 0.21/0.65 => aElementOf0(W2,W0) ) ) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mSubFSet,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( ( aSet0(W0)
% 0.21/0.65 & isFinite0(W0) )
% 0.21/0.65 => ! [W1] :
% 0.21/0.65 ( aSubsetOf0(W1,W0)
% 0.21/0.65 => isFinite0(W1) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mSubRefl,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aSet0(W0)
% 0.21/0.65 => aSubsetOf0(W0,W0) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mSubASymm,axiom,
% 0.21/0.65 ! [W0,W1] :
% 0.21/0.65 ( ( aSet0(W0)
% 0.21/0.65 & aSet0(W1) )
% 0.21/0.65 => ( ( aSubsetOf0(W0,W1)
% 0.21/0.65 & aSubsetOf0(W1,W0) )
% 0.21/0.65 => W0 = W1 ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mSubTrans,axiom,
% 0.21/0.65 ! [W0,W1,W2] :
% 0.21/0.65 ( ( aSet0(W0)
% 0.21/0.65 & aSet0(W1)
% 0.21/0.65 & aSet0(W2) )
% 0.21/0.65 => ( ( aSubsetOf0(W0,W1)
% 0.21/0.65 & aSubsetOf0(W1,W2) )
% 0.21/0.65 => aSubsetOf0(W0,W2) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mDefCons,definition,
% 0.21/0.65 ! [W0,W1] :
% 0.21/0.65 ( ( aSet0(W0)
% 0.21/0.65 & aElement0(W1) )
% 0.21/0.65 => ! [W2] :
% 0.21/0.65 ( W2 = sdtpldt0(W0,W1)
% 0.21/0.65 <=> ( aSet0(W2)
% 0.21/0.65 & ! [W3] :
% 0.21/0.65 ( aElementOf0(W3,W2)
% 0.21/0.65 <=> ( aElement0(W3)
% 0.21/0.65 & ( aElementOf0(W3,W0)
% 0.21/0.65 | W3 = W1 ) ) ) ) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mDefDiff,definition,
% 0.21/0.65 ! [W0,W1] :
% 0.21/0.65 ( ( aSet0(W0)
% 0.21/0.65 & aElement0(W1) )
% 0.21/0.65 => ! [W2] :
% 0.21/0.65 ( W2 = sdtmndt0(W0,W1)
% 0.21/0.65 <=> ( aSet0(W2)
% 0.21/0.65 & ! [W3] :
% 0.21/0.65 ( aElementOf0(W3,W2)
% 0.21/0.65 <=> ( aElement0(W3)
% 0.21/0.65 & aElementOf0(W3,W0)
% 0.21/0.65 & W3 != W1 ) ) ) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mConsDiff,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aSet0(W0)
% 0.21/0.65 => ! [W1] :
% 0.21/0.65 ( aElementOf0(W1,W0)
% 0.21/0.65 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mDiffCons,axiom,
% 0.21/0.65 ! [W0,W1] :
% 0.21/0.65 ( ( aElement0(W0)
% 0.21/0.65 & aSet0(W1) )
% 0.21/0.65 => ( ~ aElementOf0(W0,W1)
% 0.21/0.65 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mCConsSet,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aElement0(W0)
% 0.21/0.65 => ! [W1] :
% 0.21/0.65 ( ( aSet0(W1)
% 0.21/0.65 & isCountable0(W1) )
% 0.21/0.65 => isCountable0(sdtpldt0(W1,W0)) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mCDiffSet,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aElement0(W0)
% 0.21/0.65 => ! [W1] :
% 0.21/0.65 ( ( aSet0(W1)
% 0.21/0.65 & isCountable0(W1) )
% 0.21/0.65 => isCountable0(sdtmndt0(W1,W0)) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mFConsSet,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aElement0(W0)
% 0.21/0.65 => ! [W1] :
% 0.21/0.65 ( ( aSet0(W1)
% 0.21/0.65 & isFinite0(W1) )
% 0.21/0.65 => isFinite0(sdtpldt0(W1,W0)) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mFDiffSet,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aElement0(W0)
% 0.21/0.65 => ! [W1] :
% 0.21/0.65 ( ( aSet0(W1)
% 0.21/0.65 & isFinite0(W1) )
% 0.21/0.65 => isFinite0(sdtmndt0(W1,W0)) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mNATSet,axiom,
% 0.21/0.65 ( aSet0(szNzAzT0)
% 0.21/0.65 & isCountable0(szNzAzT0) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mZeroNum,axiom,
% 0.21/0.65 aElementOf0(sz00,szNzAzT0) ).
% 0.21/0.65
% 0.21/0.65 fof(mSuccNum,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aElementOf0(W0,szNzAzT0)
% 0.21/0.65 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
% 0.21/0.65 & szszuzczcdt0(W0) != sz00 ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mSuccEquSucc,axiom,
% 0.21/0.65 ! [W0,W1] :
% 0.21/0.65 ( ( aElementOf0(W0,szNzAzT0)
% 0.21/0.65 & aElementOf0(W1,szNzAzT0) )
% 0.21/0.65 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
% 0.21/0.65 => W0 = W1 ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mNatExtra,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aElementOf0(W0,szNzAzT0)
% 0.21/0.65 => ( W0 = sz00
% 0.21/0.65 | ? [W1] :
% 0.21/0.65 ( aElementOf0(W1,szNzAzT0)
% 0.21/0.65 & W0 = szszuzczcdt0(W1) ) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mNatNSucc,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aElementOf0(W0,szNzAzT0)
% 0.21/0.65 => W0 != szszuzczcdt0(W0) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mLessRel,axiom,
% 0.21/0.65 ! [W0,W1] :
% 0.21/0.65 ( ( aElementOf0(W0,szNzAzT0)
% 0.21/0.65 & aElementOf0(W1,szNzAzT0) )
% 0.21/0.65 => ( sdtlseqdt0(W0,W1)
% 0.21/0.65 => $true ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mZeroLess,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aElementOf0(W0,szNzAzT0)
% 0.21/0.65 => sdtlseqdt0(sz00,W0) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mNoScLessZr,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aElementOf0(W0,szNzAzT0)
% 0.21/0.65 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mSuccLess,axiom,
% 0.21/0.65 ! [W0,W1] :
% 0.21/0.65 ( ( aElementOf0(W0,szNzAzT0)
% 0.21/0.65 & aElementOf0(W1,szNzAzT0) )
% 0.21/0.65 => ( sdtlseqdt0(W0,W1)
% 0.21/0.65 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(mLessSucc,axiom,
% 0.21/0.65 ! [W0] :
% 0.21/0.65 ( aElementOf0(W0,szNzAzT0)
% 0.21/0.65 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ).
% 0.21/0.65
% 0.21/0.66 fof(mLessRefl,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.21/0.66 => sdtlseqdt0(W0,W0) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mLessASymm,axiom,
% 0.21/0.66 ! [W0,W1] :
% 0.21/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.21/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.21/0.66 => ( ( sdtlseqdt0(W0,W1)
% 0.21/0.66 & sdtlseqdt0(W1,W0) )
% 0.21/0.66 => W0 = W1 ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mLessTrans,axiom,
% 0.21/0.66 ! [W0,W1,W2] :
% 0.21/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.21/0.66 & aElementOf0(W1,szNzAzT0)
% 0.21/0.66 & aElementOf0(W2,szNzAzT0) )
% 0.21/0.66 => ( ( sdtlseqdt0(W0,W1)
% 0.21/0.66 & sdtlseqdt0(W1,W2) )
% 0.21/0.66 => sdtlseqdt0(W0,W2) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mLessTotal,axiom,
% 0.21/0.66 ! [W0,W1] :
% 0.21/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.21/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.21/0.66 => ( sdtlseqdt0(W0,W1)
% 0.21/0.66 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mIHSort,axiom,
% 0.21/0.66 ! [W0,W1] :
% 0.21/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.21/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.21/0.66 => ( iLess0(W0,W1)
% 0.21/0.66 => $true ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mIH,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.21/0.66 => iLess0(W0,szszuzczcdt0(W0)) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mCardS,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( aSet0(W0)
% 0.21/0.66 => aElement0(sbrdtbr0(W0)) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mCardNum,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( aSet0(W0)
% 0.21/0.66 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
% 0.21/0.66 <=> isFinite0(W0) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mCardEmpty,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( aSet0(W0)
% 0.21/0.66 => ( sbrdtbr0(W0) = sz00
% 0.21/0.66 <=> W0 = slcrc0 ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mCardCons,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( ( aSet0(W0)
% 0.21/0.66 & isFinite0(W0) )
% 0.21/0.66 => ! [W1] :
% 0.21/0.66 ( aElement0(W1)
% 0.21/0.66 => ( ~ aElementOf0(W1,W0)
% 0.21/0.66 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mCardDiff,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( aSet0(W0)
% 0.21/0.66 => ! [W1] :
% 0.21/0.66 ( ( isFinite0(W0)
% 0.21/0.66 & aElementOf0(W1,W0) )
% 0.21/0.66 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mCardSub,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( aSet0(W0)
% 0.21/0.66 => ! [W1] :
% 0.21/0.66 ( ( isFinite0(W0)
% 0.21/0.66 & aSubsetOf0(W1,W0) )
% 0.21/0.66 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mCardSubEx,axiom,
% 0.21/0.66 ! [W0,W1] :
% 0.21/0.66 ( ( aSet0(W0)
% 0.21/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.21/0.66 => ( ( isFinite0(W0)
% 0.21/0.66 & sdtlseqdt0(W1,sbrdtbr0(W0)) )
% 0.21/0.66 => ? [W2] :
% 0.21/0.66 ( aSubsetOf0(W2,W0)
% 0.21/0.66 & sbrdtbr0(W2) = W1 ) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mDefMin,definition,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.21/0.66 & W0 != slcrc0 )
% 0.21/0.66 => ! [W1] :
% 0.21/0.66 ( W1 = szmzizndt0(W0)
% 0.21/0.66 <=> ( aElementOf0(W1,W0)
% 0.21/0.66 & ! [W2] :
% 0.21/0.66 ( aElementOf0(W2,W0)
% 0.21/0.66 => sdtlseqdt0(W1,W2) ) ) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mDefMax,definition,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.21/0.66 & isFinite0(W0)
% 0.21/0.66 & W0 != slcrc0 )
% 0.21/0.66 => ! [W1] :
% 0.21/0.66 ( W1 = szmzazxdt0(W0)
% 0.21/0.66 <=> ( aElementOf0(W1,W0)
% 0.21/0.66 & ! [W2] :
% 0.21/0.66 ( aElementOf0(W2,W0)
% 0.21/0.66 => sdtlseqdt0(W2,W1) ) ) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mMinMin,axiom,
% 0.21/0.66 ! [W0,W1] :
% 0.21/0.66 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.21/0.66 & aSubsetOf0(W1,szNzAzT0)
% 0.21/0.66 & W0 != slcrc0
% 0.21/0.66 & W1 != slcrc0 )
% 0.21/0.66 => ( ( aElementOf0(szmzizndt0(W0),W1)
% 0.21/0.66 & aElementOf0(szmzizndt0(W1),W0) )
% 0.21/0.66 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mDefSeg,definition,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.21/0.66 => ! [W1] :
% 0.21/0.66 ( W1 = slbdtrb0(W0)
% 0.21/0.66 <=> ( aSet0(W1)
% 0.21/0.66 & ! [W2] :
% 0.21/0.66 ( aElementOf0(W2,W1)
% 0.21/0.66 <=> ( aElementOf0(W2,szNzAzT0)
% 0.21/0.66 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mSegFin,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.21/0.66 => isFinite0(slbdtrb0(W0)) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mSegZero,axiom,
% 0.21/0.66 slbdtrb0(sz00) = slcrc0 ).
% 0.21/0.66
% 0.21/0.66 fof(mSegSucc,axiom,
% 0.21/0.66 ! [W0,W1] :
% 0.21/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.21/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.21/0.66 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1)))
% 0.21/0.66 <=> ( aElementOf0(W0,slbdtrb0(W1))
% 0.21/0.66 | W0 = W1 ) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mSegLess,axiom,
% 0.21/0.66 ! [W0,W1] :
% 0.21/0.66 ( ( aElementOf0(W0,szNzAzT0)
% 0.21/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.21/0.66 => ( sdtlseqdt0(W0,W1)
% 0.21/0.66 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mFinSubSeg,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.21/0.66 & isFinite0(W0) )
% 0.21/0.66 => ? [W1] :
% 0.21/0.66 ( aElementOf0(W1,szNzAzT0)
% 0.21/0.66 & aSubsetOf0(W0,slbdtrb0(W1)) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mCardSeg,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( aElementOf0(W0,szNzAzT0)
% 0.21/0.66 => sbrdtbr0(slbdtrb0(W0)) = W0 ) ).
% 0.21/0.66
% 0.21/0.66 fof(mDefSel,definition,
% 0.21/0.66 ! [W0,W1] :
% 0.21/0.66 ( ( aSet0(W0)
% 0.21/0.66 & aElementOf0(W1,szNzAzT0) )
% 0.21/0.66 => ! [W2] :
% 0.21/0.66 ( W2 = slbdtsldtrb0(W0,W1)
% 0.21/0.66 <=> ( aSet0(W2)
% 0.21/0.66 & ! [W3] :
% 0.21/0.66 ( aElementOf0(W3,W2)
% 0.21/0.66 <=> ( aSubsetOf0(W3,W0)
% 0.21/0.66 & sbrdtbr0(W3) = W1 ) ) ) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mSelFSet,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( ( aSet0(W0)
% 0.21/0.66 & isFinite0(W0) )
% 0.21/0.66 => ! [W1] :
% 0.21/0.66 ( aElementOf0(W1,szNzAzT0)
% 0.21/0.66 => isFinite0(slbdtsldtrb0(W0,W1)) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mSelNSet,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( ( aSet0(W0)
% 0.21/0.66 & ~ isFinite0(W0) )
% 0.21/0.66 => ! [W1] :
% 0.21/0.66 ( aElementOf0(W1,szNzAzT0)
% 0.21/0.66 => slbdtsldtrb0(W0,W1) != slcrc0 ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(mSelCSet,axiom,
% 0.21/0.66 ! [W0] :
% 0.21/0.66 ( ( aSet0(W0)
% 0.21/0.66 & isCountable0(W0) )
% 0.21/0.66 => ! [W1] :
% 0.21/0.66 ( ( aElementOf0(W1,szNzAzT0)
% 0.21/0.66 & W1 != sz00 )
% 0.21/0.66 => isCountable0(slbdtsldtrb0(W0,W1)) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(m__2202,hypothesis,
% 0.21/0.66 aElementOf0(xk,szNzAzT0) ).
% 0.21/0.66
% 0.21/0.66 fof(m__2202_02,hypothesis,
% 0.21/0.66 ( aSet0(xS)
% 0.21/0.66 & aSet0(xT)
% 0.21/0.66 & xk != sz00 ) ).
% 0.21/0.66
% 0.21/0.66 fof(m__2227,hypothesis,
% 0.21/0.66 ( aSet0(slbdtsldtrb0(xS,xk))
% 0.21/0.66 & ! [W0] :
% 0.21/0.66 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.21/0.66 => ( aSet0(W0)
% 0.21/0.66 & ! [W1] :
% 0.21/0.66 ( aElementOf0(W1,W0)
% 0.21/0.66 => aElementOf0(W1,xS) )
% 0.21/0.66 & aSubsetOf0(W0,xS)
% 0.21/0.66 & sbrdtbr0(W0) = xk ) )
% 0.21/0.66 & ( ( ( ( aSet0(W0)
% 0.21/0.66 & ! [W1] :
% 0.21/0.66 ( aElementOf0(W1,W0)
% 0.21/0.66 => aElementOf0(W1,xS) ) )
% 0.21/0.66 | aSubsetOf0(W0,xS) )
% 0.21/0.66 & sbrdtbr0(W0) = xk )
% 0.21/0.66 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
% 0.21/0.66 & aSet0(slbdtsldtrb0(xT,xk))
% 0.21/0.66 & ! [W0] :
% 0.21/0.66 ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
% 0.21/0.66 => ( aSet0(W0)
% 0.21/0.66 & ! [W1] :
% 0.21/0.66 ( aElementOf0(W1,W0)
% 0.21/0.66 => aElementOf0(W1,xT) )
% 0.21/0.66 & aSubsetOf0(W0,xT)
% 0.21/0.66 & sbrdtbr0(W0) = xk ) )
% 0.21/0.66 & ( ( ( ( aSet0(W0)
% 0.21/0.66 & ! [W1] :
% 0.21/0.66 ( aElementOf0(W1,W0)
% 0.21/0.66 => aElementOf0(W1,xT) ) )
% 0.21/0.66 | aSubsetOf0(W0,xT) )
% 0.21/0.66 & sbrdtbr0(W0) = xk )
% 0.21/0.66 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
% 0.21/0.66 & ! [W0] :
% 0.21/0.66 ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.21/0.66 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
% 0.21/0.66 & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
% 0.21/0.66 & ~ ( ! [W0] :
% 0.21/0.66 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.21/0.66 => ( aSet0(W0)
% 0.21/0.66 & ! [W1] :
% 0.21/0.66 ( aElementOf0(W1,W0)
% 0.21/0.66 => aElementOf0(W1,xS) )
% 0.21/0.66 & aSubsetOf0(W0,xS)
% 0.21/0.66 & sbrdtbr0(W0) = xk ) )
% 0.21/0.66 & ( ( ( ( aSet0(W0)
% 0.21/0.66 & ! [W1] :
% 0.21/0.66 ( aElementOf0(W1,W0)
% 0.21/0.66 => aElementOf0(W1,xS) ) )
% 0.21/0.66 | aSubsetOf0(W0,xS) )
% 0.21/0.66 & sbrdtbr0(W0) = xk )
% 0.21/0.66 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
% 0.21/0.66 => ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.21/0.66 | slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(m__2256,hypothesis,
% 0.21/0.66 aElementOf0(xx,xS) ).
% 0.21/0.66
% 0.21/0.66 fof(m__2270,hypothesis,
% 0.21/0.66 ( aSet0(xQ)
% 0.21/0.66 & ! [W0] :
% 0.21/0.66 ( aElementOf0(W0,xQ)
% 0.21/0.66 => aElementOf0(W0,xS) )
% 0.21/0.66 & aSubsetOf0(xQ,xS)
% 0.21/0.66 & sbrdtbr0(xQ) = xk
% 0.21/0.66 & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ) ).
% 0.21/0.66
% 0.21/0.66 fof(m__2291,hypothesis,
% 0.21/0.66 ( aSet0(xQ)
% 0.21/0.66 & isFinite0(xQ)
% 0.21/0.66 & sbrdtbr0(xQ) = xk ) ).
% 0.21/0.66
% 0.21/0.66 fof(m__2304,hypothesis,
% 0.21/0.66 ( aElement0(xy)
% 0.21/0.66 & aElementOf0(xy,xQ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(m__2323,hypothesis,
% 0.21/0.66 ~ aElementOf0(xx,xQ) ).
% 0.21/0.66
% 0.21/0.66 fof(m__2338,hypothesis,
% 0.21/0.66 ~ ~ aElementOf0(xx,xQ) ).
% 0.21/0.66
% 0.21/0.66 fof(m__,conjecture,
% 0.21/0.66 aElementOf0(xx,xT) ).
% 0.21/0.66
% 0.21/0.66 %------------------------------------------------------------------------------
% 0.21/0.66 %-------------------------------------------
% 0.21/0.66 % Proof found
% 0.21/0.66 % SZS status Theorem for theBenchmark
% 0.21/0.66 % SZS output start Proof
% 0.21/0.66 %ClaNum:200(EqnAxiom:51)
% 0.21/0.66 %VarNum:771(SingletonVarNum:238)
% 0.21/0.66 %MaxLitNum:8
% 0.21/0.66 %MaxfuncDepth:3
% 0.21/0.66 %SharedTerms:39
% 0.21/0.66 %goalClause: 77
% 0.21/0.66 %singleGoalClaCount:1
% 0.21/0.66 [55]P1(a24)
% 0.21/0.66 [56]P1(a29)
% 0.21/0.66 [57]P1(a30)
% 0.21/0.66 [59]P1(a1)
% 0.21/0.66 [60]P2(a31)
% 0.21/0.66 [61]P4(a22)
% 0.21/0.66 [62]P4(a1)
% 0.21/0.66 [63]P5(a24)
% 0.21/0.66 [64]P3(a18,a24)
% 0.21/0.66 [65]P3(a28,a24)
% 0.21/0.66 [66]P3(a32,a29)
% 0.21/0.66 [67]P3(a32,a1)
% 0.21/0.66 [68]P3(a31,a1)
% 0.21/0.66 [69]P6(a1,a29)
% 0.21/0.66 [75]~E(a18,a28)
% 0.21/0.66 [77]~P3(a32,a30)
% 0.21/0.66 [78]~P3(a32,a1)
% 0.21/0.66 [53]E(f2(a1),a28)
% 0.21/0.66 [54]E(f19(a18),a22)
% 0.21/0.66 [70]P1(f23(a29,a28))
% 0.21/0.66 [71]P1(f23(a30,a28))
% 0.21/0.66 [72]P3(a1,f23(a29,a28))
% 0.21/0.66 [73]P3(a3,f23(a29,a28))
% 0.21/0.66 [74]P6(f23(a29,a28),f23(a30,a28))
% 0.21/0.66 [76]~E(f23(a29,a28),a22)
% 0.21/0.66 [79]P1(x791)+~E(x791,a22)
% 0.21/0.66 [85]~P1(x851)+P6(x851,x851)
% 0.21/0.66 [92]~P3(x921,a1)+P3(x921,a29)
% 0.21/0.66 [93]~P3(x931,a24)+P8(a18,x931)
% 0.21/0.66 [99]P8(x991,x991)+~P3(x991,a24)
% 0.21/0.66 [83]~P1(x831)+P2(f2(x831))
% 0.21/0.66 [87]~P3(x871,a24)+~E(f25(x871),a18)
% 0.21/0.66 [88]~P3(x881,a24)+~E(f25(x881),x881)
% 0.21/0.66 [90]~P3(x901,a24)+P4(f19(x901))
% 0.21/0.66 [100]~P3(x1001,a24)+P3(f25(x1001),a24)
% 0.21/0.66 [101]~P3(x1011,a24)+P8(x1011,f25(x1011))
% 0.21/0.66 [102]~P3(x1021,a24)+P7(x1021,f25(x1021))
% 0.21/0.66 [110]~P3(x1101,a24)+~P8(f25(x1101),a18)
% 0.21/0.66 [120]~P3(x1201,f23(a29,a28))+E(f2(x1201),a28)
% 0.21/0.67 [121]~P3(x1211,f23(a30,a28))+E(f2(x1211),a28)
% 0.21/0.67 [123]P1(x1231)+~P3(x1231,f23(a29,a28))
% 0.21/0.67 [124]P1(x1241)+~P3(x1241,f23(a30,a28))
% 0.21/0.67 [139]P6(x1391,a29)+~P3(x1391,f23(a29,a28))
% 0.21/0.67 [140]P6(x1401,a30)+~P3(x1401,f23(a30,a28))
% 0.21/0.67 [163]~P3(x1631,f23(a29,a28))+P3(x1631,f23(a30,a28))
% 0.21/0.67 [91]~P3(x911,a24)+E(f2(f19(x911)),x911)
% 0.21/0.67 [86]~P3(x862,x861)+~E(x861,a22)
% 0.21/0.67 [82]~P1(x821)+~P5(x821)+~E(x821,a22)
% 0.21/0.67 [84]~P4(x841)+~P5(x841)+~P1(x841)
% 0.21/0.67 [80]~P1(x801)+~E(x801,a22)+E(f2(x801),a18)
% 0.21/0.67 [81]~P1(x811)+E(x811,a22)+~E(f2(x811),a18)
% 0.21/0.67 [89]~P1(x891)+P3(f9(x891),x891)+E(x891,a22)
% 0.21/0.67 [96]~P1(x961)+~P4(x961)+P3(f2(x961),a24)
% 0.21/0.67 [103]~P3(x1031,a24)+E(x1031,a18)+P3(f10(x1031),a24)
% 0.21/0.67 [104]~P1(x1041)+P4(x1041)+~P3(f2(x1041),a24)
% 0.21/0.67 [109]~P4(x1091)+~P6(x1091,a24)+P3(f4(x1091),a24)
% 0.21/0.67 [127]~P6(x1271,a29)+P3(x1271,f23(a29,a28))+~E(f2(x1271),a28)
% 0.21/0.67 [128]~P6(x1281,a30)+P3(x1281,f23(a30,a28))+~E(f2(x1281),a28)
% 0.21/0.67 [94]~P3(x941,a24)+E(x941,a18)+E(f25(f10(x941)),x941)
% 0.21/0.67 [125]~P4(x1251)+~P6(x1251,a24)+P6(x1251,f19(f4(x1251)))
% 0.21/0.67 [97]~P6(x971,x972)+P1(x971)+~P1(x972)
% 0.21/0.67 [98]~P3(x981,x982)+P2(x981)+~P1(x982)
% 0.21/0.67 [95]P1(x951)+~P3(x952,a24)+~E(x951,f19(x952))
% 0.21/0.67 [167]~P3(x1671,x1672)+P3(x1671,a29)+~P3(x1672,f23(a29,a28))
% 0.21/0.67 [168]~P3(x1681,x1682)+P3(x1681,a30)+~P3(x1682,f23(a30,a28))
% 0.21/0.67 [148]~P1(x1481)+~P3(x1482,x1481)+E(f20(f21(x1481,x1482),x1482),x1481)
% 0.21/0.67 [144]~P1(x1441)+P3(f5(x1441),x1441)+P3(x1441,f23(a29,a28))+~E(f2(x1441),a28)
% 0.21/0.67 [145]~P1(x1451)+P3(f7(x1451),x1451)+P3(x1451,f23(a30,a28))+~E(f2(x1451),a28)
% 0.21/0.67 [146]~P1(x1461)+P3(f8(x1461),x1461)+P3(x1461,f23(a29,a28))+~E(f2(x1461),a28)
% 0.21/0.67 [156]~P1(x1561)+P3(x1561,f23(a29,a28))+~E(f2(x1561),a28)+~P3(f5(x1561),a29)
% 0.21/0.67 [157]~P1(x1571)+P3(x1571,f23(a29,a28))+~E(f2(x1571),a28)+~P3(f8(x1571),a29)
% 0.21/0.67 [158]~P1(x1581)+P3(x1581,f23(a30,a28))+~E(f2(x1581),a28)+~P3(f7(x1581),a30)
% 0.21/0.67 [105]~P4(x1052)+~P6(x1051,x1052)+P4(x1051)+~P1(x1052)
% 0.21/0.67 [108]P3(x1082,x1081)+~E(x1082,f26(x1081))+~P6(x1081,a24)+E(x1081,a22)
% 0.21/0.67 [112]~P1(x1121)+~P2(x1122)+~P4(x1121)+P4(f20(x1121,x1122))
% 0.21/0.67 [113]~P1(x1131)+~P2(x1132)+~P4(x1131)+P4(f21(x1131,x1132))
% 0.21/0.67 [114]~P1(x1141)+~P2(x1142)+~P5(x1141)+P5(f20(x1141,x1142))
% 0.21/0.67 [115]~P1(x1151)+~P2(x1152)+~P5(x1151)+P5(f21(x1151,x1152))
% 0.21/0.67 [116]~P1(x1161)+P4(x1161)+~P3(x1162,a24)+~E(f23(x1161,x1162),a22)
% 0.21/0.67 [118]E(x1181,x1182)+~E(f25(x1181),f25(x1182))+~P3(x1182,a24)+~P3(x1181,a24)
% 0.21/0.67 [131]~P1(x1312)+~P4(x1312)+~P6(x1311,x1312)+P8(f2(x1311),f2(x1312))
% 0.21/0.67 [134]~P1(x1341)+~P4(x1341)+~P3(x1342,a24)+P4(f23(x1341,x1342))
% 0.21/0.67 [143]~P1(x1431)+~P1(x1432)+P6(x1431,x1432)+P3(f11(x1432,x1431),x1431)
% 0.21/0.67 [152]P8(x1521,x1522)+P8(f25(x1522),x1521)+~P3(x1522,a24)+~P3(x1521,a24)
% 0.21/0.67 [169]~P8(x1691,x1692)+~P3(x1692,a24)+~P3(x1691,a24)+P6(f19(x1691),f19(x1692))
% 0.21/0.67 [170]~P8(x1701,x1702)+~P3(x1702,a24)+~P3(x1701,a24)+P8(f25(x1701),f25(x1702))
% 0.21/0.67 [172]~P1(x1721)+~P1(x1722)+P6(x1721,x1722)+~P3(f11(x1722,x1721),x1722)
% 0.21/0.67 [174]P8(x1741,x1742)+~P3(x1742,a24)+~P3(x1741,a24)+~P6(f19(x1741),f19(x1742))
% 0.21/0.67 [175]P8(x1751,x1752)+~P3(x1752,a24)+~P3(x1751,a24)+~P8(f25(x1751),f25(x1752))
% 0.21/0.67 [147]P3(x1472,x1471)+~P1(x1471)+~P2(x1472)+E(f21(f20(x1471,x1472),x1472),x1471)
% 0.21/0.67 [154]~E(x1541,x1542)+~P3(x1542,a24)+~P3(x1541,a24)+P3(x1541,f19(f25(x1542)))
% 0.21/0.67 [180]~P3(x1802,a24)+~P3(x1801,a24)+~P3(x1801,f19(x1802))+P3(x1801,f19(f25(x1802)))
% 0.21/0.67 [179]~P1(x1791)+~P4(x1791)+~P3(x1792,x1791)+E(f25(f2(f21(x1791,x1792))),f2(x1791))
% 0.21/0.67 [141]~P1(x1412)+~P6(x1413,x1412)+P3(x1411,x1412)+~P3(x1411,x1413)
% 0.21/0.67 [106]~P1(x1062)+~P2(x1063)+P1(x1061)+~E(x1061,f20(x1062,x1063))
% 0.21/0.67 [107]~P1(x1072)+~P2(x1073)+P1(x1071)+~E(x1071,f21(x1072,x1073))
% 0.21/0.67 [117]~P1(x1172)+P1(x1171)+~P3(x1173,a24)+~E(x1171,f23(x1172,x1173))
% 0.21/0.67 [132]~P3(x1321,x1322)+~P3(x1323,a24)+P3(x1321,a24)+~E(x1322,f19(x1323))
% 0.21/0.67 [149]~P3(x1491,x1493)+~P3(x1492,a24)+P8(f25(x1491),x1492)+~E(x1493,f19(x1492))
% 0.21/0.67 [129]~P1(x1292)+~P1(x1291)+~P6(x1292,x1291)+~P6(x1291,x1292)+E(x1291,x1292)
% 0.21/0.67 [164]~P8(x1642,x1641)+~P8(x1641,x1642)+E(x1641,x1642)+~P3(x1642,a24)+~P3(x1641,a24)
% 0.21/0.67 [111]~P4(x1111)+P3(x1112,x1111)+~E(x1112,f27(x1111))+~P6(x1111,a24)+E(x1111,a22)
% 0.21/0.67 [137]~P1(x1372)+~P5(x1372)+~P3(x1371,a24)+E(x1371,a18)+P5(f23(x1372,x1371))
% 0.21/0.67 [171]~P3(x1712,x1711)+P3(f14(x1711,x1712),x1711)+~P6(x1711,a24)+E(x1711,a22)+E(x1712,f26(x1711))
% 0.21/0.67 [181]~P1(x1811)+~P4(x1811)+~P3(x1812,a24)+~P8(x1812,f2(x1811))+P6(f15(x1811,x1812),x1811)
% 0.21/0.67 [182]~P1(x1821)+P3(f17(x1822,x1821),x1821)+~P3(x1822,a24)+E(x1821,f19(x1822))+P3(f17(x1822,x1821),a24)
% 0.21/0.67 [183]~P3(x1832,x1831)+~P6(x1831,a24)+~P8(x1832,f14(x1831,x1832))+E(x1831,a22)+E(x1832,f26(x1831))
% 0.21/0.67 [153]P3(x1532,x1531)+~P1(x1531)+~P2(x1532)+~P4(x1531)+E(f2(f20(x1531,x1532)),f25(f2(x1531)))
% 0.21/0.67 [178]~P1(x1781)+~P4(x1781)+~P3(x1782,a24)+~P8(x1782,f2(x1781))+E(f2(f15(x1781,x1782)),x1782)
% 0.21/0.67 [184]E(x1841,x1842)+P3(x1841,f19(x1842))+~P3(x1842,a24)+~P3(x1841,a24)+~P3(x1841,f19(f25(x1842)))
% 0.21/0.67 [188]~P1(x1881)+P3(f17(x1882,x1881),x1881)+~P3(x1882,a24)+E(x1881,f19(x1882))+P8(f25(f17(x1882,x1881)),x1882)
% 0.21/0.67 [142]~P3(x1423,x1421)+P8(x1422,x1423)+~E(x1422,f26(x1421))+~P6(x1421,a24)+E(x1421,a22)
% 0.21/0.67 [173]P3(x1731,x1732)+~P3(x1733,a24)+~P3(x1731,a24)+~P8(f25(x1731),x1733)+~E(x1732,f19(x1733))
% 0.21/0.67 [133]~P1(x1334)+~P2(x1332)+~P3(x1331,x1333)+~E(x1331,x1332)+~E(x1333,f21(x1334,x1332))
% 0.21/0.67 [135]~P1(x1353)+~P2(x1354)+~P3(x1351,x1352)+P2(x1351)+~E(x1352,f20(x1353,x1354))
% 0.21/0.67 [136]~P1(x1363)+~P2(x1364)+~P3(x1361,x1362)+P2(x1361)+~E(x1362,f21(x1363,x1364))
% 0.21/0.67 [151]~P1(x1512)+~P2(x1514)+~P3(x1511,x1513)+P3(x1511,x1512)+~E(x1513,f21(x1512,x1514))
% 0.21/0.67 [159]~P1(x1594)+~P3(x1591,x1593)+~P3(x1592,a24)+E(f2(x1591),x1592)+~E(x1593,f23(x1594,x1592))
% 0.21/0.67 [165]~P1(x1652)+~P3(x1651,x1653)+P6(x1651,x1652)+~P3(x1654,a24)+~E(x1653,f23(x1652,x1654))
% 0.21/0.67 [177]~P4(x1771)+~P3(x1772,x1771)+P3(f16(x1771,x1772),x1771)+~P6(x1771,a24)+E(x1771,a22)+E(x1772,f27(x1771))
% 0.21/0.67 [186]~P4(x1861)+~P3(x1862,x1861)+~P6(x1861,a24)+~P8(f16(x1861,x1862),x1862)+E(x1861,a22)+E(x1862,f27(x1861))
% 0.21/0.67 [192]~P1(x1921)+~P3(x1922,a24)+~P3(f17(x1922,x1921),x1921)+E(x1921,f19(x1922))+~P3(f17(x1922,x1921),a24)+~P8(f25(f17(x1922,x1921)),x1922)
% 0.21/0.67 [160]~P1(x1602)+~P1(x1601)+~P6(x1603,x1602)+~P6(x1601,x1603)+P6(x1601,x1602)+~P1(x1603)
% 0.21/0.67 [187]~P8(x1871,x1873)+P8(x1871,x1872)+~P8(x1873,x1872)+~P3(x1872,a24)+~P3(x1873,a24)+~P3(x1871,a24)
% 0.21/0.67 [150]~P4(x1501)+~P3(x1502,x1501)+P8(x1502,x1503)+~E(x1503,f27(x1501))+~P6(x1501,a24)+E(x1501,a22)
% 0.21/0.67 [189]~P1(x1891)+~P1(x1892)+~P2(x1893)+P3(f12(x1892,x1893,x1891),x1891)+~E(f12(x1892,x1893,x1891),x1893)+E(x1891,f21(x1892,x1893))
% 0.21/0.67 [190]~P1(x1901)+~P1(x1902)+~P2(x1903)+P3(f13(x1902,x1903,x1901),x1901)+E(x1901,f20(x1902,x1903))+P2(f13(x1902,x1903,x1901))
% 0.21/0.67 [191]~P1(x1911)+~P1(x1912)+~P2(x1913)+P3(f12(x1912,x1913,x1911),x1911)+E(x1911,f21(x1912,x1913))+P2(f12(x1912,x1913,x1911))
% 0.21/0.67 [193]~P1(x1931)+~P1(x1932)+~P2(x1933)+P3(f12(x1932,x1933,x1931),x1931)+P3(f12(x1932,x1933,x1931),x1932)+E(x1931,f21(x1932,x1933))
% 0.21/0.67 [195]~P1(x1951)+~P1(x1952)+P3(f6(x1952,x1953,x1951),x1951)+P6(f6(x1952,x1953,x1951),x1952)+~P3(x1953,a24)+E(x1951,f23(x1952,x1953))
% 0.21/0.67 [194]~P1(x1941)+~P1(x1942)+P3(f6(x1942,x1943,x1941),x1941)+~P3(x1943,a24)+E(x1941,f23(x1942,x1943))+E(f2(f6(x1942,x1943,x1941)),x1943)
% 0.21/0.67 [130]~P1(x1304)+~P2(x1303)+~P2(x1301)+P3(x1301,x1302)+~E(x1301,x1303)+~E(x1302,f20(x1304,x1303))
% 0.21/0.67 [155]~P1(x1553)+~P2(x1552)+~P3(x1551,x1554)+E(x1551,x1552)+P3(x1551,x1553)+~E(x1554,f20(x1553,x1552))
% 0.21/0.67 [161]~P1(x1613)+~P2(x1614)+~P2(x1611)+~P3(x1611,x1613)+P3(x1611,x1612)+~E(x1612,f20(x1613,x1614))
% 0.21/0.67 [176]~P1(x1764)+~P6(x1761,x1764)+P3(x1761,x1762)+~P3(x1763,a24)+~E(x1762,f23(x1764,x1763))+~E(f2(x1761),x1763)
% 0.21/0.67 [185]E(f26(x1852),f26(x1851))+~P6(x1851,a24)+~P6(x1852,a24)+~P3(f26(x1851),x1852)+~P3(f26(x1852),x1851)+E(x1851,a22)+E(x1852,a22)
% 0.21/0.67 [196]~P1(x1961)+~P1(x1962)+~P2(x1963)+E(f13(x1962,x1963,x1961),x1963)+P3(f13(x1962,x1963,x1961),x1961)+P3(f13(x1962,x1963,x1961),x1962)+E(x1961,f20(x1962,x1963))
% 0.21/0.67 [197]~P1(x1971)+~P1(x1972)+~P2(x1973)+~E(f13(x1972,x1973,x1971),x1973)+~P3(f13(x1972,x1973,x1971),x1971)+E(x1971,f20(x1972,x1973))+~P2(f13(x1972,x1973,x1971))
% 0.21/0.67 [198]~P1(x1981)+~P1(x1982)+~P2(x1983)+~P3(f13(x1982,x1983,x1981),x1981)+~P3(f13(x1982,x1983,x1981),x1982)+E(x1981,f20(x1982,x1983))+~P2(f13(x1982,x1983,x1981))
% 0.21/0.67 [199]~P1(x1991)+~P1(x1992)+~P3(x1993,a24)+~P3(f6(x1992,x1993,x1991),x1991)+~P6(f6(x1992,x1993,x1991),x1992)+E(x1991,f23(x1992,x1993))+~E(f2(f6(x1992,x1993,x1991)),x1993)
% 0.21/0.67 [162]~P1(x1624)+~P2(x1622)+~P2(x1621)+~P3(x1621,x1624)+E(x1621,x1622)+P3(x1621,x1623)+~E(x1623,f21(x1624,x1622))
% 0.21/0.67 [200]~P1(x2001)+~P1(x2002)+~P2(x2003)+E(f12(x2002,x2003,x2001),x2003)+~P3(f12(x2002,x2003,x2001),x2001)+~P3(f12(x2002,x2003,x2001),x2002)+E(x2001,f21(x2002,x2003))+~P2(f12(x2002,x2003,x2001))
% 0.21/0.67 %EqnAxiom
% 0.21/0.67 [1]E(x11,x11)
% 0.21/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.67 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.21/0.67 [5]~E(x51,x52)+E(f12(x51,x53,x54),f12(x52,x53,x54))
% 0.21/0.67 [6]~E(x61,x62)+E(f12(x63,x61,x64),f12(x63,x62,x64))
% 0.21/0.67 [7]~E(x71,x72)+E(f12(x73,x74,x71),f12(x73,x74,x72))
% 0.21/0.67 [8]~E(x81,x82)+E(f19(x81),f19(x82))
% 0.21/0.67 [9]~E(x91,x92)+E(f23(x91,x93),f23(x92,x93))
% 0.21/0.67 [10]~E(x101,x102)+E(f23(x103,x101),f23(x103,x102))
% 0.21/0.67 [11]~E(x111,x112)+E(f26(x111),f26(x112))
% 0.21/0.67 [12]~E(x121,x122)+E(f17(x121,x123),f17(x122,x123))
% 0.21/0.67 [13]~E(x131,x132)+E(f17(x133,x131),f17(x133,x132))
% 0.21/0.67 [14]~E(x141,x142)+E(f8(x141),f8(x142))
% 0.21/0.67 [15]~E(x151,x152)+E(f14(x151,x153),f14(x152,x153))
% 0.21/0.67 [16]~E(x161,x162)+E(f14(x163,x161),f14(x163,x162))
% 0.21/0.67 [17]~E(x171,x172)+E(f21(x171,x173),f21(x172,x173))
% 0.21/0.67 [18]~E(x181,x182)+E(f21(x183,x181),f21(x183,x182))
% 0.21/0.67 [19]~E(x191,x192)+E(f15(x191,x193),f15(x192,x193))
% 0.21/0.67 [20]~E(x201,x202)+E(f15(x203,x201),f15(x203,x202))
% 0.21/0.67 [21]~E(x211,x212)+E(f25(x211),f25(x212))
% 0.21/0.67 [22]~E(x221,x222)+E(f6(x221,x223,x224),f6(x222,x223,x224))
% 0.21/0.67 [23]~E(x231,x232)+E(f6(x233,x231,x234),f6(x233,x232,x234))
% 0.21/0.67 [24]~E(x241,x242)+E(f6(x243,x244,x241),f6(x243,x244,x242))
% 0.21/0.67 [25]~E(x251,x252)+E(f13(x251,x253,x254),f13(x252,x253,x254))
% 0.21/0.67 [26]~E(x261,x262)+E(f13(x263,x261,x264),f13(x263,x262,x264))
% 0.21/0.67 [27]~E(x271,x272)+E(f13(x273,x274,x271),f13(x273,x274,x272))
% 0.21/0.67 [28]~E(x281,x282)+E(f20(x281,x283),f20(x282,x283))
% 0.21/0.67 [29]~E(x291,x292)+E(f20(x293,x291),f20(x293,x292))
% 0.21/0.67 [30]~E(x301,x302)+E(f27(x301),f27(x302))
% 0.21/0.67 [31]~E(x311,x312)+E(f9(x311),f9(x312))
% 0.21/0.67 [32]~E(x321,x322)+E(f16(x321,x323),f16(x322,x323))
% 0.21/0.67 [33]~E(x331,x332)+E(f16(x333,x331),f16(x333,x332))
% 0.21/0.67 [34]~E(x341,x342)+E(f5(x341),f5(x342))
% 0.21/0.67 [35]~E(x351,x352)+E(f11(x351,x353),f11(x352,x353))
% 0.21/0.67 [36]~E(x361,x362)+E(f11(x363,x361),f11(x363,x362))
% 0.21/0.67 [37]~E(x371,x372)+E(f10(x371),f10(x372))
% 0.21/0.67 [38]~E(x381,x382)+E(f7(x381),f7(x382))
% 0.21/0.67 [39]~E(x391,x392)+E(f4(x391),f4(x392))
% 0.21/0.67 [40]~P1(x401)+P1(x402)+~E(x401,x402)
% 0.21/0.67 [41]P3(x412,x413)+~E(x411,x412)+~P3(x411,x413)
% 0.21/0.67 [42]P3(x423,x422)+~E(x421,x422)+~P3(x423,x421)
% 0.21/0.67 [43]~P4(x431)+P4(x432)+~E(x431,x432)
% 0.21/0.67 [44]~P2(x441)+P2(x442)+~E(x441,x442)
% 0.21/0.67 [45]P8(x452,x453)+~E(x451,x452)+~P8(x451,x453)
% 0.21/0.67 [46]P8(x463,x462)+~E(x461,x462)+~P8(x463,x461)
% 0.21/0.67 [47]~P5(x471)+P5(x472)+~E(x471,x472)
% 0.21/0.67 [48]P6(x482,x483)+~E(x481,x482)+~P6(x481,x483)
% 0.21/0.67 [49]P6(x493,x492)+~E(x491,x492)+~P6(x493,x491)
% 0.21/0.67 [50]P7(x502,x503)+~E(x501,x502)+~P7(x501,x503)
% 0.21/0.67 [51]P7(x513,x512)+~E(x511,x512)+~P7(x513,x511)
% 0.21/0.67
% 0.21/0.67 %-------------------------------------------
% 0.21/0.67 cnf(201,plain,
% 0.21/0.67 ($false),
% 0.21/0.67 inference(scs_inference,[],[67,78]),
% 0.21/0.67 ['proof']).
% 0.21/0.67 % SZS output end Proof
% 0.21/0.67 % Total time :0.000000s
%------------------------------------------------------------------------------