TSTP Solution File: NUM547+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM547+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 : n009.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 10:23:00 EDT 2023
% Result : Theorem 0.57s 0.72s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM547+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 15:00:51 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 start to proof:theBenchmark
% 0.57/0.70 %-------------------------------------------
% 0.57/0.70 % File :CSE---1.6
% 0.57/0.70 % Problem :theBenchmark
% 0.57/0.70 % Transform :cnf
% 0.57/0.70 % Format :tptp:raw
% 0.57/0.70 % Command :java -jar mcs_scs.jar %d %s
% 0.57/0.70
% 0.57/0.70 % Result :Theorem 0.010000s
% 0.57/0.70 % Output :CNFRefutation 0.010000s
% 0.57/0.70 %-------------------------------------------
% 0.57/0.71 %------------------------------------------------------------------------------
% 0.57/0.71 % File : NUM547+3 : TPTP v8.1.2. Released v4.0.0.
% 0.57/0.71 % Domain : Number Theory
% 0.57/0.71 % Problem : Ramsey's Infinite Theorem 12_01, 02 expansion
% 0.57/0.71 % Version : Especial.
% 0.57/0.71 % English :
% 0.57/0.71
% 0.57/0.71 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.57/0.71 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.57/0.71 % Source : [Pas08]
% 0.57/0.71 % Names : ramsey_12_01.02 [Pas08]
% 0.57/0.71
% 0.57/0.71 % Status : Theorem
% 0.57/0.71 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.15 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.39 v4.0.1, 0.70 v4.0.0
% 0.57/0.71 % Syntax : Number of formulae : 65 ( 5 unt; 8 def)
% 0.57/0.71 % Number of atoms : 282 ( 45 equ)
% 0.57/0.71 % Maximal formula atoms : 43 ( 4 avg)
% 0.57/0.71 % Number of connectives : 236 ( 19 ~; 10 |; 91 &)
% 0.57/0.71 % ( 17 <=>; 99 =>; 0 <=; 0 <~>)
% 0.57/0.71 % Maximal formula depth : 17 ( 5 avg)
% 0.57/0.71 % Maximal term depth : 4 ( 1 avg)
% 0.57/0.71 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% 0.57/0.71 % Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% 0.57/0.71 % Number of variables : 119 ( 113 !; 6 ?)
% 0.57/0.71 % SPC : FOF_THM_RFO_SEQ
% 0.57/0.71
% 0.57/0.71 % Comments : Problem generated by the SAD system [VLP07]
% 0.57/0.71 %------------------------------------------------------------------------------
% 0.57/0.71 fof(mSetSort,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aSet0(W0)
% 0.57/0.71 => $true ) ).
% 0.57/0.71
% 0.57/0.71 fof(mElmSort,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aElement0(W0)
% 0.57/0.71 => $true ) ).
% 0.57/0.71
% 0.57/0.71 fof(mEOfElem,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aSet0(W0)
% 0.57/0.71 => ! [W1] :
% 0.57/0.71 ( aElementOf0(W1,W0)
% 0.57/0.71 => aElement0(W1) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mFinRel,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aSet0(W0)
% 0.57/0.71 => ( isFinite0(W0)
% 0.57/0.71 => $true ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mDefEmp,definition,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( W0 = slcrc0
% 0.57/0.71 <=> ( aSet0(W0)
% 0.57/0.71 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mEmpFin,axiom,
% 0.57/0.71 isFinite0(slcrc0) ).
% 0.57/0.71
% 0.57/0.71 fof(mCntRel,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aSet0(W0)
% 0.57/0.71 => ( isCountable0(W0)
% 0.57/0.71 => $true ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mCountNFin,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( ( aSet0(W0)
% 0.57/0.71 & isCountable0(W0) )
% 0.57/0.71 => ~ isFinite0(W0) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mCountNFin_01,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( ( aSet0(W0)
% 0.57/0.71 & isCountable0(W0) )
% 0.57/0.71 => W0 != slcrc0 ) ).
% 0.57/0.71
% 0.57/0.71 fof(mDefSub,definition,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aSet0(W0)
% 0.57/0.71 => ! [W1] :
% 0.57/0.71 ( aSubsetOf0(W1,W0)
% 0.57/0.71 <=> ( aSet0(W1)
% 0.57/0.71 & ! [W2] :
% 0.57/0.71 ( aElementOf0(W2,W1)
% 0.57/0.71 => aElementOf0(W2,W0) ) ) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mSubFSet,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( ( aSet0(W0)
% 0.57/0.71 & isFinite0(W0) )
% 0.57/0.71 => ! [W1] :
% 0.57/0.71 ( aSubsetOf0(W1,W0)
% 0.57/0.71 => isFinite0(W1) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mSubRefl,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aSet0(W0)
% 0.57/0.71 => aSubsetOf0(W0,W0) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mSubASymm,axiom,
% 0.57/0.71 ! [W0,W1] :
% 0.57/0.71 ( ( aSet0(W0)
% 0.57/0.71 & aSet0(W1) )
% 0.57/0.71 => ( ( aSubsetOf0(W0,W1)
% 0.57/0.71 & aSubsetOf0(W1,W0) )
% 0.57/0.71 => W0 = W1 ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mSubTrans,axiom,
% 0.57/0.71 ! [W0,W1,W2] :
% 0.57/0.71 ( ( aSet0(W0)
% 0.57/0.71 & aSet0(W1)
% 0.57/0.71 & aSet0(W2) )
% 0.57/0.71 => ( ( aSubsetOf0(W0,W1)
% 0.57/0.71 & aSubsetOf0(W1,W2) )
% 0.57/0.71 => aSubsetOf0(W0,W2) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mDefCons,definition,
% 0.57/0.71 ! [W0,W1] :
% 0.57/0.71 ( ( aSet0(W0)
% 0.57/0.71 & aElement0(W1) )
% 0.57/0.71 => ! [W2] :
% 0.57/0.71 ( W2 = sdtpldt0(W0,W1)
% 0.57/0.71 <=> ( aSet0(W2)
% 0.57/0.71 & ! [W3] :
% 0.57/0.71 ( aElementOf0(W3,W2)
% 0.57/0.71 <=> ( aElement0(W3)
% 0.57/0.71 & ( aElementOf0(W3,W0)
% 0.57/0.71 | W3 = W1 ) ) ) ) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mDefDiff,definition,
% 0.57/0.71 ! [W0,W1] :
% 0.57/0.71 ( ( aSet0(W0)
% 0.57/0.71 & aElement0(W1) )
% 0.57/0.71 => ! [W2] :
% 0.57/0.71 ( W2 = sdtmndt0(W0,W1)
% 0.57/0.71 <=> ( aSet0(W2)
% 0.57/0.71 & ! [W3] :
% 0.57/0.71 ( aElementOf0(W3,W2)
% 0.57/0.71 <=> ( aElement0(W3)
% 0.57/0.71 & aElementOf0(W3,W0)
% 0.57/0.71 & W3 != W1 ) ) ) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mConsDiff,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aSet0(W0)
% 0.57/0.71 => ! [W1] :
% 0.57/0.71 ( aElementOf0(W1,W0)
% 0.57/0.71 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mDiffCons,axiom,
% 0.57/0.71 ! [W0,W1] :
% 0.57/0.71 ( ( aElement0(W0)
% 0.57/0.71 & aSet0(W1) )
% 0.57/0.71 => ( ~ aElementOf0(W0,W1)
% 0.57/0.71 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mCConsSet,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aElement0(W0)
% 0.57/0.71 => ! [W1] :
% 0.57/0.71 ( ( aSet0(W1)
% 0.57/0.71 & isCountable0(W1) )
% 0.57/0.71 => isCountable0(sdtpldt0(W1,W0)) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mCDiffSet,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aElement0(W0)
% 0.57/0.71 => ! [W1] :
% 0.57/0.71 ( ( aSet0(W1)
% 0.57/0.71 & isCountable0(W1) )
% 0.57/0.71 => isCountable0(sdtmndt0(W1,W0)) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mFConsSet,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aElement0(W0)
% 0.57/0.71 => ! [W1] :
% 0.57/0.71 ( ( aSet0(W1)
% 0.57/0.71 & isFinite0(W1) )
% 0.57/0.71 => isFinite0(sdtpldt0(W1,W0)) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mFDiffSet,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aElement0(W0)
% 0.57/0.71 => ! [W1] :
% 0.57/0.71 ( ( aSet0(W1)
% 0.57/0.71 & isFinite0(W1) )
% 0.57/0.71 => isFinite0(sdtmndt0(W1,W0)) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mNATSet,axiom,
% 0.57/0.71 ( aSet0(szNzAzT0)
% 0.57/0.71 & isCountable0(szNzAzT0) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mZeroNum,axiom,
% 0.57/0.71 aElementOf0(sz00,szNzAzT0) ).
% 0.57/0.71
% 0.57/0.71 fof(mSuccNum,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aElementOf0(W0,szNzAzT0)
% 0.57/0.71 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
% 0.57/0.71 & szszuzczcdt0(W0) != sz00 ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mSuccEquSucc,axiom,
% 0.57/0.71 ! [W0,W1] :
% 0.57/0.71 ( ( aElementOf0(W0,szNzAzT0)
% 0.57/0.71 & aElementOf0(W1,szNzAzT0) )
% 0.57/0.71 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
% 0.57/0.71 => W0 = W1 ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mNatExtra,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aElementOf0(W0,szNzAzT0)
% 0.57/0.71 => ( W0 = sz00
% 0.57/0.71 | ? [W1] :
% 0.57/0.71 ( aElementOf0(W1,szNzAzT0)
% 0.57/0.71 & W0 = szszuzczcdt0(W1) ) ) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mNatNSucc,axiom,
% 0.57/0.71 ! [W0] :
% 0.57/0.71 ( aElementOf0(W0,szNzAzT0)
% 0.57/0.71 => W0 != szszuzczcdt0(W0) ) ).
% 0.57/0.71
% 0.57/0.71 fof(mLessRel,axiom,
% 0.57/0.71 ! [W0,W1] :
% 0.57/0.72 ( ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 & aElementOf0(W1,szNzAzT0) )
% 0.57/0.72 => ( sdtlseqdt0(W0,W1)
% 0.57/0.72 => $true ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mZeroLess,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 => sdtlseqdt0(sz00,W0) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mNoScLessZr,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mSuccLess,axiom,
% 0.57/0.72 ! [W0,W1] :
% 0.57/0.72 ( ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 & aElementOf0(W1,szNzAzT0) )
% 0.57/0.72 => ( sdtlseqdt0(W0,W1)
% 0.57/0.72 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mLessSucc,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mLessRefl,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 => sdtlseqdt0(W0,W0) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mLessASymm,axiom,
% 0.57/0.72 ! [W0,W1] :
% 0.57/0.72 ( ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 & aElementOf0(W1,szNzAzT0) )
% 0.57/0.72 => ( ( sdtlseqdt0(W0,W1)
% 0.57/0.72 & sdtlseqdt0(W1,W0) )
% 0.57/0.72 => W0 = W1 ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mLessTrans,axiom,
% 0.57/0.72 ! [W0,W1,W2] :
% 0.57/0.72 ( ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 & aElementOf0(W1,szNzAzT0)
% 0.57/0.72 & aElementOf0(W2,szNzAzT0) )
% 0.57/0.72 => ( ( sdtlseqdt0(W0,W1)
% 0.57/0.72 & sdtlseqdt0(W1,W2) )
% 0.57/0.72 => sdtlseqdt0(W0,W2) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mLessTotal,axiom,
% 0.57/0.72 ! [W0,W1] :
% 0.57/0.72 ( ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 & aElementOf0(W1,szNzAzT0) )
% 0.57/0.72 => ( sdtlseqdt0(W0,W1)
% 0.57/0.72 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mIHSort,axiom,
% 0.57/0.72 ! [W0,W1] :
% 0.57/0.72 ( ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 & aElementOf0(W1,szNzAzT0) )
% 0.57/0.72 => ( iLess0(W0,W1)
% 0.57/0.72 => $true ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mIH,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 => iLess0(W0,szszuzczcdt0(W0)) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mCardS,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aSet0(W0)
% 0.57/0.72 => aElement0(sbrdtbr0(W0)) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mCardNum,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aSet0(W0)
% 0.57/0.72 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
% 0.57/0.72 <=> isFinite0(W0) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mCardEmpty,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aSet0(W0)
% 0.57/0.72 => ( sbrdtbr0(W0) = sz00
% 0.57/0.72 <=> W0 = slcrc0 ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mCardCons,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( ( aSet0(W0)
% 0.57/0.72 & isFinite0(W0) )
% 0.57/0.72 => ! [W1] :
% 0.57/0.72 ( aElement0(W1)
% 0.57/0.72 => ( ~ aElementOf0(W1,W0)
% 0.57/0.72 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mCardDiff,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aSet0(W0)
% 0.57/0.72 => ! [W1] :
% 0.57/0.72 ( ( isFinite0(W0)
% 0.57/0.72 & aElementOf0(W1,W0) )
% 0.57/0.72 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mCardSub,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aSet0(W0)
% 0.57/0.72 => ! [W1] :
% 0.57/0.72 ( ( isFinite0(W0)
% 0.57/0.72 & aSubsetOf0(W1,W0) )
% 0.57/0.72 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mCardSubEx,axiom,
% 0.57/0.72 ! [W0,W1] :
% 0.57/0.72 ( ( aSet0(W0)
% 0.57/0.72 & aElementOf0(W1,szNzAzT0) )
% 0.57/0.72 => ( ( isFinite0(W0)
% 0.57/0.72 & sdtlseqdt0(W1,sbrdtbr0(W0)) )
% 0.57/0.72 => ? [W2] :
% 0.57/0.72 ( aSubsetOf0(W2,W0)
% 0.57/0.72 & sbrdtbr0(W2) = W1 ) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mDefMin,definition,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.57/0.72 & W0 != slcrc0 )
% 0.57/0.72 => ! [W1] :
% 0.57/0.72 ( W1 = szmzizndt0(W0)
% 0.57/0.72 <=> ( aElementOf0(W1,W0)
% 0.57/0.72 & ! [W2] :
% 0.57/0.72 ( aElementOf0(W2,W0)
% 0.57/0.72 => sdtlseqdt0(W1,W2) ) ) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mDefMax,definition,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.57/0.72 & isFinite0(W0)
% 0.57/0.72 & W0 != slcrc0 )
% 0.57/0.72 => ! [W1] :
% 0.57/0.72 ( W1 = szmzazxdt0(W0)
% 0.57/0.72 <=> ( aElementOf0(W1,W0)
% 0.57/0.72 & ! [W2] :
% 0.57/0.72 ( aElementOf0(W2,W0)
% 0.57/0.72 => sdtlseqdt0(W2,W1) ) ) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mMinMin,axiom,
% 0.57/0.72 ! [W0,W1] :
% 0.57/0.72 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.57/0.72 & aSubsetOf0(W1,szNzAzT0)
% 0.57/0.72 & W0 != slcrc0
% 0.57/0.72 & W1 != slcrc0 )
% 0.57/0.72 => ( ( aElementOf0(szmzizndt0(W0),W1)
% 0.57/0.72 & aElementOf0(szmzizndt0(W1),W0) )
% 0.57/0.72 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mDefSeg,definition,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 => ! [W1] :
% 0.57/0.72 ( W1 = slbdtrb0(W0)
% 0.57/0.72 <=> ( aSet0(W1)
% 0.57/0.72 & ! [W2] :
% 0.57/0.72 ( aElementOf0(W2,W1)
% 0.57/0.72 <=> ( aElementOf0(W2,szNzAzT0)
% 0.57/0.72 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mSegFin,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 => isFinite0(slbdtrb0(W0)) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mSegZero,axiom,
% 0.57/0.72 slbdtrb0(sz00) = slcrc0 ).
% 0.57/0.72
% 0.57/0.72 fof(mSegSucc,axiom,
% 0.57/0.72 ! [W0,W1] :
% 0.57/0.72 ( ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 & aElementOf0(W1,szNzAzT0) )
% 0.57/0.72 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1)))
% 0.57/0.72 <=> ( aElementOf0(W0,slbdtrb0(W1))
% 0.57/0.72 | W0 = W1 ) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mSegLess,axiom,
% 0.57/0.72 ! [W0,W1] :
% 0.57/0.72 ( ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 & aElementOf0(W1,szNzAzT0) )
% 0.57/0.72 => ( sdtlseqdt0(W0,W1)
% 0.57/0.72 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mFinSubSeg,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.57/0.72 & isFinite0(W0) )
% 0.57/0.72 => ? [W1] :
% 0.57/0.72 ( aElementOf0(W1,szNzAzT0)
% 0.57/0.72 & aSubsetOf0(W0,slbdtrb0(W1)) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mCardSeg,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( aElementOf0(W0,szNzAzT0)
% 0.57/0.72 => sbrdtbr0(slbdtrb0(W0)) = W0 ) ).
% 0.57/0.72
% 0.57/0.72 fof(mDefSel,definition,
% 0.57/0.72 ! [W0,W1] :
% 0.57/0.72 ( ( aSet0(W0)
% 0.57/0.72 & aElementOf0(W1,szNzAzT0) )
% 0.57/0.72 => ! [W2] :
% 0.57/0.72 ( W2 = slbdtsldtrb0(W0,W1)
% 0.57/0.72 <=> ( aSet0(W2)
% 0.57/0.72 & ! [W3] :
% 0.57/0.72 ( aElementOf0(W3,W2)
% 0.57/0.72 <=> ( aSubsetOf0(W3,W0)
% 0.57/0.72 & sbrdtbr0(W3) = W1 ) ) ) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mSelFSet,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( ( aSet0(W0)
% 0.57/0.72 & isFinite0(W0) )
% 0.57/0.72 => ! [W1] :
% 0.57/0.72 ( aElementOf0(W1,szNzAzT0)
% 0.57/0.72 => isFinite0(slbdtsldtrb0(W0,W1)) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mSelNSet,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( ( aSet0(W0)
% 0.57/0.72 & ~ isFinite0(W0) )
% 0.57/0.72 => ! [W1] :
% 0.57/0.72 ( aElementOf0(W1,szNzAzT0)
% 0.57/0.72 => slbdtsldtrb0(W0,W1) != slcrc0 ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(mSelCSet,axiom,
% 0.57/0.72 ! [W0] :
% 0.57/0.72 ( ( aSet0(W0)
% 0.57/0.72 & isCountable0(W0) )
% 0.57/0.72 => ! [W1] :
% 0.57/0.72 ( ( aElementOf0(W1,szNzAzT0)
% 0.57/0.72 & W1 != sz00 )
% 0.57/0.72 => isCountable0(slbdtsldtrb0(W0,W1)) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(m__2202,hypothesis,
% 0.57/0.72 aElementOf0(xk,szNzAzT0) ).
% 0.57/0.72
% 0.57/0.72 fof(m__2202_02,hypothesis,
% 0.57/0.72 ( aSet0(xS)
% 0.57/0.72 & aSet0(xT)
% 0.57/0.72 & xk != sz00 ) ).
% 0.57/0.72
% 0.57/0.72 fof(m__2227,hypothesis,
% 0.57/0.72 ( aSet0(slbdtsldtrb0(xS,xk))
% 0.57/0.72 & ! [W0] :
% 0.57/0.72 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.57/0.72 => ( aSet0(W0)
% 0.57/0.72 & ! [W1] :
% 0.57/0.72 ( aElementOf0(W1,W0)
% 0.57/0.72 => aElementOf0(W1,xS) )
% 0.57/0.72 & aSubsetOf0(W0,xS)
% 0.57/0.72 & sbrdtbr0(W0) = xk ) )
% 0.57/0.72 & ( ( ( ( aSet0(W0)
% 0.57/0.72 & ! [W1] :
% 0.57/0.72 ( aElementOf0(W1,W0)
% 0.57/0.72 => aElementOf0(W1,xS) ) )
% 0.57/0.72 | aSubsetOf0(W0,xS) )
% 0.57/0.72 & sbrdtbr0(W0) = xk )
% 0.57/0.72 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
% 0.57/0.72 & aSet0(slbdtsldtrb0(xT,xk))
% 0.57/0.72 & ! [W0] :
% 0.57/0.72 ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
% 0.57/0.72 => ( aSet0(W0)
% 0.57/0.72 & ! [W1] :
% 0.57/0.72 ( aElementOf0(W1,W0)
% 0.57/0.72 => aElementOf0(W1,xT) )
% 0.57/0.72 & aSubsetOf0(W0,xT)
% 0.57/0.72 & sbrdtbr0(W0) = xk ) )
% 0.57/0.72 & ( ( ( ( aSet0(W0)
% 0.57/0.72 & ! [W1] :
% 0.57/0.72 ( aElementOf0(W1,W0)
% 0.57/0.72 => aElementOf0(W1,xT) ) )
% 0.57/0.72 | aSubsetOf0(W0,xT) )
% 0.57/0.72 & sbrdtbr0(W0) = xk )
% 0.57/0.72 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
% 0.57/0.72 & ! [W0] :
% 0.57/0.72 ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.57/0.72 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
% 0.57/0.72 & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
% 0.57/0.72 & ~ ( ! [W0] :
% 0.57/0.72 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.57/0.72 => ( aSet0(W0)
% 0.57/0.72 & ! [W1] :
% 0.57/0.72 ( aElementOf0(W1,W0)
% 0.57/0.72 => aElementOf0(W1,xS) )
% 0.57/0.72 & aSubsetOf0(W0,xS)
% 0.57/0.72 & sbrdtbr0(W0) = xk ) )
% 0.57/0.72 & ( ( ( ( aSet0(W0)
% 0.57/0.72 & ! [W1] :
% 0.57/0.72 ( aElementOf0(W1,W0)
% 0.57/0.72 => aElementOf0(W1,xS) ) )
% 0.57/0.72 | aSubsetOf0(W0,xS) )
% 0.57/0.72 & sbrdtbr0(W0) = xk )
% 0.57/0.72 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
% 0.57/0.72 => ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.57/0.72 | slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ).
% 0.57/0.72
% 0.57/0.72 fof(m__2256,hypothesis,
% 0.57/0.72 aElementOf0(xx,xS) ).
% 0.57/0.72
% 0.57/0.72 fof(m__,conjecture,
% 0.57/0.72 ? [W0] :
% 0.57/0.72 ( ( ( ( aSet0(W0)
% 0.57/0.72 & ! [W1] :
% 0.57/0.72 ( aElementOf0(W1,W0)
% 0.57/0.72 => aElementOf0(W1,xS) ) )
% 0.57/0.72 | aSubsetOf0(W0,xS) )
% 0.57/0.72 & sbrdtbr0(W0) = xk )
% 0.57/0.72 | aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) ).
% 0.57/0.72
% 0.57/0.72 %------------------------------------------------------------------------------
% 0.57/0.72 %-------------------------------------------
% 0.57/0.72 % Proof found
% 0.57/0.72 % SZS status Theorem for theBenchmark
% 0.57/0.72 % SZS output start Proof
% 0.57/0.72 %ClaNum:192(EqnAxiom:52)
% 0.57/0.72 %VarNum:764(SingletonVarNum:234)
% 0.57/0.72 %MaxLitNum:8
% 0.57/0.72 %MaxfuncDepth:3
% 0.57/0.72 %SharedTerms:26
% 0.57/0.72 %goalClause: 68 78 90 99
% 0.57/0.72 %singleGoalClaCount:1
% 0.57/0.72 [54]P1(a24)
% 0.57/0.72 [55]P1(a25)
% 0.57/0.72 [56]P1(a29)
% 0.57/0.72 [57]P4(a22)
% 0.57/0.72 [58]P5(a24)
% 0.57/0.72 [59]P2(a1,a24)
% 0.57/0.72 [60]P2(a30,a24)
% 0.57/0.72 [61]P2(a31,a25)
% 0.57/0.72 [66]~E(a30,a1)
% 0.57/0.72 [53]E(f2(a1),a22)
% 0.57/0.72 [62]P1(f23(a25,a30))
% 0.57/0.72 [63]P1(f23(a29,a30))
% 0.57/0.72 [64]P2(a3,f23(a25,a30))
% 0.57/0.72 [65]P6(f23(a25,a30),f23(a29,a30))
% 0.57/0.72 [67]~E(f23(a25,a30),a22)
% 0.57/0.72 [68]~P2(x681,f23(a25,a30))
% 0.57/0.72 [69]P1(x691)+~E(x691,a22)
% 0.57/0.72 [75]~P1(x751)+P6(x751,x751)
% 0.57/0.72 [83]~P2(x831,a24)+P8(a1,x831)
% 0.57/0.72 [89]P8(x891,x891)+~P2(x891,a24)
% 0.57/0.72 [73]~P1(x731)+P3(f9(x731))
% 0.57/0.72 [77]~P2(x771,a24)+~E(f26(x771),a1)
% 0.57/0.72 [78]~P6(x781,a25)+~E(f9(x781),a30)
% 0.57/0.72 [79]~P2(x791,a24)+~E(f26(x791),x791)
% 0.57/0.72 [81]~P2(x811,a24)+P4(f2(x811))
% 0.57/0.72 [91]~P2(x911,a24)+P2(f26(x911),a24)
% 0.57/0.72 [92]~P2(x921,a24)+P8(x921,f26(x921))
% 0.57/0.72 [93]~P2(x931,a24)+P7(x931,f26(x931))
% 0.57/0.72 [102]~P2(x1021,a24)+~P8(f26(x1021),a1)
% 0.57/0.72 [113]~P2(x1131,f23(a29,a30))+E(f9(x1131),a30)
% 0.57/0.72 [116]P1(x1161)+~P2(x1161,f23(a29,a30))
% 0.57/0.72 [132]P6(x1321,a29)+~P2(x1321,f23(a29,a30))
% 0.57/0.72 [82]~P2(x821,a24)+E(f9(f2(x821)),x821)
% 0.57/0.72 [76]~P2(x762,x761)+~E(x761,a22)
% 0.57/0.72 [72]~P1(x721)+~P5(x721)+~E(x721,a22)
% 0.57/0.72 [74]~P4(x741)+~P5(x741)+~P1(x741)
% 0.57/0.72 [70]~P1(x701)+~E(x701,a22)+E(f9(x701),a1)
% 0.57/0.72 [71]~P1(x711)+E(x711,a22)+~E(f9(x711),a1)
% 0.57/0.72 [80]~P1(x801)+P2(f10(x801),x801)+E(x801,a22)
% 0.57/0.72 [86]~P1(x861)+~P4(x861)+P2(f9(x861),a24)
% 0.57/0.72 [90]~P1(x901)+P2(f11(x901),x901)+~E(f9(x901),a30)
% 0.57/0.72 [94]~P2(x941,a24)+E(x941,a1)+P2(f12(x941),a24)
% 0.57/0.73 [95]~P1(x951)+P4(x951)+~P2(f9(x951),a24)
% 0.57/0.73 [99]~P1(x991)+~P2(f11(x991),a25)+~E(f9(x991),a30)
% 0.57/0.73 [101]~P4(x1011)+~P6(x1011,a24)+P2(f4(x1011),a24)
% 0.57/0.73 [120]~P6(x1201,a29)+P2(x1201,f23(a29,a30))+~E(f9(x1201),a30)
% 0.57/0.73 [84]~P2(x841,a24)+E(x841,a1)+E(f26(f12(x841)),x841)
% 0.57/0.73 [117]~P4(x1171)+~P6(x1171,a24)+P6(x1171,f2(f4(x1171)))
% 0.57/0.73 [87]~P6(x871,x872)+P1(x871)+~P1(x872)
% 0.57/0.73 [88]~P2(x881,x882)+P3(x881)+~P1(x882)
% 0.57/0.73 [85]P1(x851)+~P2(x852,a24)+~E(x851,f2(x852))
% 0.57/0.73 [160]~P2(x1601,x1602)+P2(x1601,a29)+~P2(x1602,f23(a29,a30))
% 0.57/0.73 [140]~P1(x1401)+~P2(x1402,x1401)+E(f20(f21(x1401,x1402),x1402),x1401)
% 0.57/0.73 [136]~P1(x1361)+P2(f5(x1361),x1361)+P2(x1361,f23(a25,a30))+~E(f9(x1361),a30)
% 0.57/0.73 [137]~P1(x1371)+P2(f7(x1371),x1371)+P2(x1371,f23(a29,a30))+~E(f9(x1371),a30)
% 0.57/0.73 [138]~P1(x1381)+P2(f8(x1381),x1381)+P2(x1381,f23(a25,a30))+~E(f9(x1381),a30)
% 0.57/0.73 [148]~P1(x1481)+P2(x1481,f23(a25,a30))+~E(f9(x1481),a30)+~P2(f5(x1481),a25)
% 0.57/0.73 [149]~P1(x1491)+P2(x1491,f23(a25,a30))+~E(f9(x1491),a30)+~P2(f8(x1491),a25)
% 0.57/0.73 [150]~P1(x1501)+P2(x1501,f23(a29,a30))+~E(f9(x1501),a30)+~P2(f7(x1501),a29)
% 0.57/0.73 [96]~P4(x962)+~P6(x961,x962)+P4(x961)+~P1(x962)
% 0.57/0.73 [100]P2(x1002,x1001)+~E(x1002,f27(x1001))+~P6(x1001,a24)+E(x1001,a22)
% 0.57/0.73 [104]~P1(x1041)+~P3(x1042)+~P4(x1041)+P4(f20(x1041,x1042))
% 0.57/0.73 [105]~P1(x1051)+~P3(x1052)+~P4(x1051)+P4(f21(x1051,x1052))
% 0.57/0.73 [106]~P1(x1061)+~P3(x1062)+~P5(x1061)+P5(f20(x1061,x1062))
% 0.57/0.73 [107]~P1(x1071)+~P3(x1072)+~P5(x1071)+P5(f21(x1071,x1072))
% 0.57/0.73 [108]~P1(x1081)+P4(x1081)+~P2(x1082,a24)+~E(f23(x1081,x1082),a22)
% 0.57/0.73 [110]E(x1101,x1102)+~E(f26(x1101),f26(x1102))+~P2(x1102,a24)+~P2(x1101,a24)
% 0.57/0.73 [123]~P1(x1232)+~P4(x1232)+~P6(x1231,x1232)+P8(f9(x1231),f9(x1232))
% 0.57/0.73 [126]~P1(x1261)+~P4(x1261)+~P2(x1262,a24)+P4(f23(x1261,x1262))
% 0.57/0.73 [135]~P1(x1351)+~P1(x1352)+P6(x1351,x1352)+P2(f13(x1352,x1351),x1351)
% 0.57/0.73 [144]P8(x1441,x1442)+P8(f26(x1442),x1441)+~P2(x1442,a24)+~P2(x1441,a24)
% 0.57/0.73 [161]~P8(x1611,x1612)+~P2(x1612,a24)+~P2(x1611,a24)+P6(f2(x1611),f2(x1612))
% 0.57/0.73 [162]~P8(x1621,x1622)+~P2(x1622,a24)+~P2(x1621,a24)+P8(f26(x1621),f26(x1622))
% 0.57/0.73 [164]~P1(x1641)+~P1(x1642)+P6(x1641,x1642)+~P2(f13(x1642,x1641),x1642)
% 0.57/0.73 [166]P8(x1661,x1662)+~P2(x1662,a24)+~P2(x1661,a24)+~P6(f2(x1661),f2(x1662))
% 0.57/0.73 [167]P8(x1671,x1672)+~P2(x1672,a24)+~P2(x1671,a24)+~P8(f26(x1671),f26(x1672))
% 0.57/0.73 [139]P2(x1392,x1391)+~P1(x1391)+~P3(x1392)+E(f21(f20(x1391,x1392),x1392),x1391)
% 0.57/0.73 [146]~E(x1461,x1462)+~P2(x1462,a24)+~P2(x1461,a24)+P2(x1461,f2(f26(x1462)))
% 0.57/0.73 [172]~P2(x1722,a24)+~P2(x1721,a24)+~P2(x1721,f2(x1722))+P2(x1721,f2(f26(x1722)))
% 0.57/0.73 [171]~P1(x1711)+~P4(x1711)+~P2(x1712,x1711)+E(f26(f9(f21(x1711,x1712))),f9(x1711))
% 0.57/0.73 [133]~P1(x1332)+~P6(x1333,x1332)+P2(x1331,x1332)+~P2(x1331,x1333)
% 0.57/0.73 [97]~P1(x972)+~P3(x973)+P1(x971)+~E(x971,f20(x972,x973))
% 0.57/0.73 [98]~P1(x982)+~P3(x983)+P1(x981)+~E(x981,f21(x982,x983))
% 0.57/0.73 [109]~P1(x1092)+P1(x1091)+~P2(x1093,a24)+~E(x1091,f23(x1092,x1093))
% 0.57/0.73 [124]~P2(x1241,x1242)+~P2(x1243,a24)+P2(x1241,a24)+~E(x1242,f2(x1243))
% 0.57/0.73 [141]~P2(x1411,x1413)+~P2(x1412,a24)+P8(f26(x1411),x1412)+~E(x1413,f2(x1412))
% 0.57/0.73 [121]~P1(x1212)+~P1(x1211)+~P6(x1212,x1211)+~P6(x1211,x1212)+E(x1211,x1212)
% 0.57/0.73 [156]~P8(x1562,x1561)+~P8(x1561,x1562)+E(x1561,x1562)+~P2(x1562,a24)+~P2(x1561,a24)
% 0.57/0.73 [103]~P4(x1031)+P2(x1032,x1031)+~E(x1032,f28(x1031))+~P6(x1031,a24)+E(x1031,a22)
% 0.57/0.73 [129]~P1(x1292)+~P5(x1292)+~P2(x1291,a24)+E(x1291,a1)+P5(f23(x1292,x1291))
% 0.57/0.73 [163]~P2(x1632,x1631)+P2(f16(x1631,x1632),x1631)+~P6(x1631,a24)+E(x1631,a22)+E(x1632,f27(x1631))
% 0.57/0.73 [173]~P1(x1731)+~P4(x1731)+~P2(x1732,a24)+~P8(x1732,f9(x1731))+P6(f17(x1731,x1732),x1731)
% 0.57/0.73 [174]~P1(x1741)+P2(f19(x1742,x1741),x1741)+~P2(x1742,a24)+E(x1741,f2(x1742))+P2(f19(x1742,x1741),a24)
% 0.57/0.73 [175]~P2(x1752,x1751)+~P6(x1751,a24)+~P8(x1752,f16(x1751,x1752))+E(x1751,a22)+E(x1752,f27(x1751))
% 0.57/0.73 [145]P2(x1452,x1451)+~P1(x1451)+~P3(x1452)+~P4(x1451)+E(f9(f20(x1451,x1452)),f26(f9(x1451)))
% 0.57/0.73 [170]~P1(x1701)+~P4(x1701)+~P2(x1702,a24)+~P8(x1702,f9(x1701))+E(f9(f17(x1701,x1702)),x1702)
% 0.57/0.73 [176]E(x1761,x1762)+P2(x1761,f2(x1762))+~P2(x1762,a24)+~P2(x1761,a24)+~P2(x1761,f2(f26(x1762)))
% 0.57/0.73 [180]~P1(x1801)+P2(f19(x1802,x1801),x1801)+~P2(x1802,a24)+E(x1801,f2(x1802))+P8(f26(f19(x1802,x1801)),x1802)
% 0.57/0.73 [134]~P2(x1343,x1341)+P8(x1342,x1343)+~E(x1342,f27(x1341))+~P6(x1341,a24)+E(x1341,a22)
% 0.57/0.73 [165]P2(x1651,x1652)+~P2(x1653,a24)+~P2(x1651,a24)+~P8(f26(x1651),x1653)+~E(x1652,f2(x1653))
% 0.57/0.73 [125]~P1(x1254)+~P3(x1252)+~P2(x1251,x1253)+~E(x1251,x1252)+~E(x1253,f21(x1254,x1252))
% 0.57/0.73 [127]~P1(x1273)+~P3(x1274)+~P2(x1271,x1272)+P3(x1271)+~E(x1272,f20(x1273,x1274))
% 0.57/0.73 [128]~P1(x1283)+~P3(x1284)+~P2(x1281,x1282)+P3(x1281)+~E(x1282,f21(x1283,x1284))
% 0.57/0.73 [143]~P1(x1432)+~P3(x1434)+~P2(x1431,x1433)+P2(x1431,x1432)+~E(x1433,f21(x1432,x1434))
% 0.57/0.73 [151]~P1(x1514)+~P2(x1511,x1513)+~P2(x1512,a24)+E(f9(x1511),x1512)+~E(x1513,f23(x1514,x1512))
% 0.57/0.73 [157]~P1(x1572)+~P2(x1571,x1573)+P6(x1571,x1572)+~P2(x1574,a24)+~E(x1573,f23(x1572,x1574))
% 0.57/0.73 [169]~P4(x1691)+~P2(x1692,x1691)+P2(f18(x1691,x1692),x1691)+~P6(x1691,a24)+E(x1691,a22)+E(x1692,f28(x1691))
% 0.57/0.73 [178]~P4(x1781)+~P2(x1782,x1781)+~P6(x1781,a24)+~P8(f18(x1781,x1782),x1782)+E(x1781,a22)+E(x1782,f28(x1781))
% 0.57/0.73 [184]~P1(x1841)+~P2(x1842,a24)+~P2(f19(x1842,x1841),x1841)+E(x1841,f2(x1842))+~P2(f19(x1842,x1841),a24)+~P8(f26(f19(x1842,x1841)),x1842)
% 0.57/0.73 [152]~P1(x1522)+~P1(x1521)+~P6(x1523,x1522)+~P6(x1521,x1523)+P6(x1521,x1522)+~P1(x1523)
% 0.57/0.73 [179]~P8(x1791,x1793)+P8(x1791,x1792)+~P8(x1793,x1792)+~P2(x1792,a24)+~P2(x1793,a24)+~P2(x1791,a24)
% 0.57/0.73 [142]~P4(x1421)+~P2(x1422,x1421)+P8(x1422,x1423)+~E(x1423,f28(x1421))+~P6(x1421,a24)+E(x1421,a22)
% 0.57/0.73 [181]~P1(x1811)+~P1(x1812)+~P3(x1813)+P2(f14(x1812,x1813,x1811),x1811)+~E(f14(x1812,x1813,x1811),x1813)+E(x1811,f21(x1812,x1813))
% 0.57/0.73 [182]~P1(x1821)+~P1(x1822)+~P3(x1823)+P2(f15(x1822,x1823,x1821),x1821)+E(x1821,f20(x1822,x1823))+P3(f15(x1822,x1823,x1821))
% 0.57/0.73 [183]~P1(x1831)+~P1(x1832)+~P3(x1833)+P2(f14(x1832,x1833,x1831),x1831)+E(x1831,f21(x1832,x1833))+P3(f14(x1832,x1833,x1831))
% 0.57/0.73 [185]~P1(x1851)+~P1(x1852)+~P3(x1853)+P2(f14(x1852,x1853,x1851),x1851)+P2(f14(x1852,x1853,x1851),x1852)+E(x1851,f21(x1852,x1853))
% 0.57/0.73 [187]~P1(x1871)+~P1(x1872)+P2(f6(x1872,x1873,x1871),x1871)+P6(f6(x1872,x1873,x1871),x1872)+~P2(x1873,a24)+E(x1871,f23(x1872,x1873))
% 0.57/0.73 [186]~P1(x1861)+~P1(x1862)+P2(f6(x1862,x1863,x1861),x1861)+~P2(x1863,a24)+E(x1861,f23(x1862,x1863))+E(f9(f6(x1862,x1863,x1861)),x1863)
% 0.57/0.73 [122]~P1(x1224)+~P3(x1223)+~P3(x1221)+P2(x1221,x1222)+~E(x1221,x1223)+~E(x1222,f20(x1224,x1223))
% 0.57/0.73 [147]~P1(x1473)+~P3(x1472)+~P2(x1471,x1474)+E(x1471,x1472)+P2(x1471,x1473)+~E(x1474,f20(x1473,x1472))
% 0.57/0.73 [153]~P1(x1533)+~P3(x1534)+~P3(x1531)+~P2(x1531,x1533)+P2(x1531,x1532)+~E(x1532,f20(x1533,x1534))
% 0.57/0.73 [168]~P1(x1684)+~P6(x1681,x1684)+P2(x1681,x1682)+~P2(x1683,a24)+~E(x1682,f23(x1684,x1683))+~E(f9(x1681),x1683)
% 0.57/0.73 [177]E(f27(x1772),f27(x1771))+~P6(x1771,a24)+~P6(x1772,a24)+~P2(f27(x1771),x1772)+~P2(f27(x1772),x1771)+E(x1771,a22)+E(x1772,a22)
% 0.57/0.73 [188]~P1(x1881)+~P1(x1882)+~P3(x1883)+E(f15(x1882,x1883,x1881),x1883)+P2(f15(x1882,x1883,x1881),x1881)+P2(f15(x1882,x1883,x1881),x1882)+E(x1881,f20(x1882,x1883))
% 0.57/0.73 [189]~P1(x1891)+~P1(x1892)+~P3(x1893)+~E(f15(x1892,x1893,x1891),x1893)+~P2(f15(x1892,x1893,x1891),x1891)+E(x1891,f20(x1892,x1893))+~P3(f15(x1892,x1893,x1891))
% 0.57/0.73 [190]~P1(x1901)+~P1(x1902)+~P3(x1903)+~P2(f15(x1902,x1903,x1901),x1901)+~P2(f15(x1902,x1903,x1901),x1902)+E(x1901,f20(x1902,x1903))+~P3(f15(x1902,x1903,x1901))
% 0.57/0.73 [191]~P1(x1911)+~P1(x1912)+~P2(x1913,a24)+~P2(f6(x1912,x1913,x1911),x1911)+~P6(f6(x1912,x1913,x1911),x1912)+E(x1911,f23(x1912,x1913))+~E(f9(f6(x1912,x1913,x1911)),x1913)
% 0.57/0.73 [154]~P1(x1544)+~P3(x1542)+~P3(x1541)+~P2(x1541,x1544)+E(x1541,x1542)+P2(x1541,x1543)+~E(x1543,f21(x1544,x1542))
% 0.57/0.73 [192]~P1(x1921)+~P1(x1922)+~P3(x1923)+E(f14(x1922,x1923,x1921),x1923)+~P2(f14(x1922,x1923,x1921),x1921)+~P2(f14(x1922,x1923,x1921),x1922)+E(x1921,f21(x1922,x1923))+~P3(f14(x1922,x1923,x1921))
% 0.57/0.73 %EqnAxiom
% 0.57/0.73 [1]E(x11,x11)
% 0.57/0.73 [2]E(x22,x21)+~E(x21,x22)
% 0.57/0.73 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.57/0.73 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.57/0.73 [5]~E(x51,x52)+E(f23(x51,x53),f23(x52,x53))
% 0.57/0.73 [6]~E(x61,x62)+E(f23(x63,x61),f23(x63,x62))
% 0.57/0.73 [7]~E(x71,x72)+E(f15(x71,x73,x74),f15(x72,x73,x74))
% 0.57/0.73 [8]~E(x81,x82)+E(f15(x83,x81,x84),f15(x83,x82,x84))
% 0.57/0.73 [9]~E(x91,x92)+E(f15(x93,x94,x91),f15(x93,x94,x92))
% 0.57/0.73 [10]~E(x101,x102)+E(f16(x101,x103),f16(x102,x103))
% 0.57/0.73 [11]~E(x111,x112)+E(f16(x113,x111),f16(x113,x112))
% 0.57/0.73 [12]~E(x121,x122)+E(f20(x121,x123),f20(x122,x123))
% 0.57/0.73 [13]~E(x131,x132)+E(f20(x133,x131),f20(x133,x132))
% 0.57/0.73 [14]~E(x141,x142)+E(f6(x141,x143,x144),f6(x142,x143,x144))
% 0.57/0.73 [15]~E(x151,x152)+E(f6(x153,x151,x154),f6(x153,x152,x154))
% 0.57/0.73 [16]~E(x161,x162)+E(f6(x163,x164,x161),f6(x163,x164,x162))
% 0.57/0.73 [17]~E(x171,x172)+E(f26(x171),f26(x172))
% 0.57/0.73 [18]~E(x181,x182)+E(f17(x181,x183),f17(x182,x183))
% 0.57/0.73 [19]~E(x191,x192)+E(f17(x193,x191),f17(x193,x192))
% 0.57/0.73 [20]~E(x201,x202)+E(f9(x201),f9(x202))
% 0.57/0.73 [21]~E(x211,x212)+E(f5(x211),f5(x212))
% 0.57/0.73 [22]~E(x221,x222)+E(f19(x221,x223),f19(x222,x223))
% 0.57/0.73 [23]~E(x231,x232)+E(f19(x233,x231),f19(x233,x232))
% 0.57/0.73 [24]~E(x241,x242)+E(f27(x241),f27(x242))
% 0.57/0.73 [25]~E(x251,x252)+E(f13(x251,x253),f13(x252,x253))
% 0.57/0.73 [26]~E(x261,x262)+E(f13(x263,x261),f13(x263,x262))
% 0.57/0.73 [27]~E(x271,x272)+E(f8(x271),f8(x272))
% 0.57/0.73 [28]~E(x281,x282)+E(f10(x281),f10(x282))
% 0.57/0.73 [29]~E(x291,x292)+E(f14(x291,x293,x294),f14(x292,x293,x294))
% 0.57/0.73 [30]~E(x301,x302)+E(f14(x303,x301,x304),f14(x303,x302,x304))
% 0.57/0.73 [31]~E(x311,x312)+E(f14(x313,x314,x311),f14(x313,x314,x312))
% 0.57/0.73 [32]~E(x321,x322)+E(f21(x321,x323),f21(x322,x323))
% 0.57/0.73 [33]~E(x331,x332)+E(f21(x333,x331),f21(x333,x332))
% 0.57/0.73 [34]~E(x341,x342)+E(f28(x341),f28(x342))
% 0.57/0.73 [35]~E(x351,x352)+E(f12(x351),f12(x352))
% 0.57/0.73 [36]~E(x361,x362)+E(f18(x361,x363),f18(x362,x363))
% 0.57/0.73 [37]~E(x371,x372)+E(f18(x373,x371),f18(x373,x372))
% 0.57/0.73 [38]~E(x381,x382)+E(f7(x381),f7(x382))
% 0.57/0.73 [39]~E(x391,x392)+E(f11(x391),f11(x392))
% 0.57/0.73 [40]~E(x401,x402)+E(f4(x401),f4(x402))
% 0.57/0.73 [41]~P1(x411)+P1(x412)+~E(x411,x412)
% 0.57/0.73 [42]P2(x422,x423)+~E(x421,x422)+~P2(x421,x423)
% 0.57/0.73 [43]P2(x433,x432)+~E(x431,x432)+~P2(x433,x431)
% 0.57/0.73 [44]~P4(x441)+P4(x442)+~E(x441,x442)
% 0.57/0.73 [45]~P3(x451)+P3(x452)+~E(x451,x452)
% 0.57/0.73 [46]~P5(x461)+P5(x462)+~E(x461,x462)
% 0.57/0.73 [47]P8(x472,x473)+~E(x471,x472)+~P8(x471,x473)
% 0.57/0.73 [48]P8(x483,x482)+~E(x481,x482)+~P8(x483,x481)
% 0.57/0.73 [49]P6(x492,x493)+~E(x491,x492)+~P6(x491,x493)
% 0.57/0.73 [50]P6(x503,x502)+~E(x501,x502)+~P6(x503,x501)
% 0.57/0.73 [51]P7(x512,x513)+~E(x511,x512)+~P7(x511,x513)
% 0.57/0.73 [52]P7(x523,x522)+~E(x521,x522)+~P7(x523,x521)
% 0.57/0.73
% 0.57/0.73 %-------------------------------------------
% 0.57/0.73 cnf(193,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(scs_inference,[],[68,64]),
% 0.57/0.73 ['proof']).
% 0.57/0.73 % SZS output end Proof
% 0.57/0.73 % Total time :0.010000s
%------------------------------------------------------------------------------