TSTP Solution File: NUM552+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM552+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 : n013.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 10:23:03 EDT 2023
% Result : Theorem 0.60s 0.78s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM552+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 : n013.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 08:55:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.57 start to proof:theBenchmark
% 0.60/0.77 %-------------------------------------------
% 0.60/0.77 % File :CSE---1.6
% 0.60/0.77 % Problem :theBenchmark
% 0.60/0.77 % Transform :cnf
% 0.60/0.77 % Format :tptp:raw
% 0.60/0.77 % Command :java -jar mcs_scs.jar %d %s
% 0.60/0.77
% 0.60/0.77 % Result :Theorem 0.120000s
% 0.60/0.77 % Output :CNFRefutation 0.120000s
% 0.60/0.77 %-------------------------------------------
% 0.60/0.77 %------------------------------------------------------------------------------
% 0.60/0.77 % File : NUM552+3 : TPTP v8.1.2. Released v4.0.0.
% 0.60/0.77 % Domain : Number Theory
% 0.60/0.77 % Problem : Ramsey's Infinite Theorem 12_04, 02 expansion
% 0.60/0.77 % Version : Especial.
% 0.60/0.77 % English :
% 0.60/0.77
% 0.60/0.77 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.60/0.77 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.60/0.77 % Source : [Pas08]
% 0.60/0.77 % Names : ramsey_12_04.02 [Pas08]
% 0.60/0.77
% 0.60/0.77 % Status : Theorem
% 0.60/0.77 % Rating : 0.14 v8.1.0, 0.06 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.17 v6.0.0, 0.13 v5.5.0, 0.22 v5.4.0, 0.29 v5.3.0, 0.33 v5.2.0, 0.25 v5.1.0, 0.38 v5.0.0, 0.46 v4.1.0, 0.57 v4.0.1, 0.83 v4.0.0
% 0.60/0.77 % Syntax : Number of formulae : 68 ( 5 unt; 8 def)
% 0.60/0.77 % Number of atoms : 289 ( 46 equ)
% 0.60/0.77 % Maximal formula atoms : 43 ( 4 avg)
% 0.60/0.77 % Number of connectives : 240 ( 19 ~; 8 |; 96 &)
% 0.60/0.77 % ( 17 <=>; 100 =>; 0 <=; 0 <~>)
% 0.60/0.77 % Maximal formula depth : 17 ( 5 avg)
% 0.60/0.77 % Maximal term depth : 4 ( 1 avg)
% 0.60/0.77 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% 0.60/0.77 % Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% 0.60/0.77 % Number of variables : 118 ( 113 !; 5 ?)
% 0.60/0.77 % SPC : FOF_THM_RFO_SEQ
% 0.60/0.77
% 0.60/0.77 % Comments : Problem generated by the SAD system [VLP07]
% 0.60/0.77 %------------------------------------------------------------------------------
% 0.60/0.77 fof(mSetSort,axiom,
% 0.60/0.77 ! [W0] :
% 0.60/0.77 ( aSet0(W0)
% 0.60/0.77 => $true ) ).
% 0.60/0.77
% 0.60/0.77 fof(mElmSort,axiom,
% 0.60/0.77 ! [W0] :
% 0.60/0.77 ( aElement0(W0)
% 0.60/0.77 => $true ) ).
% 0.60/0.77
% 0.60/0.77 fof(mEOfElem,axiom,
% 0.60/0.77 ! [W0] :
% 0.60/0.77 ( aSet0(W0)
% 0.60/0.77 => ! [W1] :
% 0.60/0.77 ( aElementOf0(W1,W0)
% 0.60/0.77 => aElement0(W1) ) ) ).
% 0.60/0.77
% 0.60/0.77 fof(mFinRel,axiom,
% 0.60/0.77 ! [W0] :
% 0.60/0.77 ( aSet0(W0)
% 0.60/0.77 => ( isFinite0(W0)
% 0.60/0.78 => $true ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mDefEmp,definition,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( W0 = slcrc0
% 0.60/0.78 <=> ( aSet0(W0)
% 0.60/0.78 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mEmpFin,axiom,
% 0.60/0.78 isFinite0(slcrc0) ).
% 0.60/0.78
% 0.60/0.78 fof(mCntRel,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aSet0(W0)
% 0.60/0.78 => ( isCountable0(W0)
% 0.60/0.78 => $true ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCountNFin,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & isCountable0(W0) )
% 0.60/0.78 => ~ isFinite0(W0) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCountNFin_01,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & isCountable0(W0) )
% 0.60/0.78 => W0 != slcrc0 ) ).
% 0.60/0.78
% 0.60/0.78 fof(mDefSub,definition,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aSet0(W0)
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( aSubsetOf0(W1,W0)
% 0.60/0.78 <=> ( aSet0(W1)
% 0.60/0.78 & ! [W2] :
% 0.60/0.78 ( aElementOf0(W2,W1)
% 0.60/0.78 => aElementOf0(W2,W0) ) ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSubFSet,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & isFinite0(W0) )
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( aSubsetOf0(W1,W0)
% 0.60/0.78 => isFinite0(W1) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSubRefl,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aSet0(W0)
% 0.60/0.78 => aSubsetOf0(W0,W0) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSubASymm,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & aSet0(W1) )
% 0.60/0.78 => ( ( aSubsetOf0(W0,W1)
% 0.60/0.78 & aSubsetOf0(W1,W0) )
% 0.60/0.78 => W0 = W1 ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSubTrans,axiom,
% 0.60/0.78 ! [W0,W1,W2] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & aSet0(W1)
% 0.60/0.78 & aSet0(W2) )
% 0.60/0.78 => ( ( aSubsetOf0(W0,W1)
% 0.60/0.78 & aSubsetOf0(W1,W2) )
% 0.60/0.78 => aSubsetOf0(W0,W2) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mDefCons,definition,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & aElement0(W1) )
% 0.60/0.78 => ! [W2] :
% 0.60/0.78 ( W2 = sdtpldt0(W0,W1)
% 0.60/0.78 <=> ( aSet0(W2)
% 0.60/0.78 & ! [W3] :
% 0.60/0.78 ( aElementOf0(W3,W2)
% 0.60/0.78 <=> ( aElement0(W3)
% 0.60/0.78 & ( aElementOf0(W3,W0)
% 0.60/0.78 | W3 = W1 ) ) ) ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mDefDiff,definition,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & aElement0(W1) )
% 0.60/0.78 => ! [W2] :
% 0.60/0.78 ( W2 = sdtmndt0(W0,W1)
% 0.60/0.78 <=> ( aSet0(W2)
% 0.60/0.78 & ! [W3] :
% 0.60/0.78 ( aElementOf0(W3,W2)
% 0.60/0.78 <=> ( aElement0(W3)
% 0.60/0.78 & aElementOf0(W3,W0)
% 0.60/0.78 & W3 != W1 ) ) ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mConsDiff,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aSet0(W0)
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( aElementOf0(W1,W0)
% 0.60/0.78 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mDiffCons,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aElement0(W0)
% 0.60/0.78 & aSet0(W1) )
% 0.60/0.78 => ( ~ aElementOf0(W0,W1)
% 0.60/0.78 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCConsSet,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElement0(W0)
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( ( aSet0(W1)
% 0.60/0.78 & isCountable0(W1) )
% 0.60/0.78 => isCountable0(sdtpldt0(W1,W0)) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCDiffSet,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElement0(W0)
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( ( aSet0(W1)
% 0.60/0.78 & isCountable0(W1) )
% 0.60/0.78 => isCountable0(sdtmndt0(W1,W0)) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mFConsSet,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElement0(W0)
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( ( aSet0(W1)
% 0.60/0.78 & isFinite0(W1) )
% 0.60/0.78 => isFinite0(sdtpldt0(W1,W0)) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mFDiffSet,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElement0(W0)
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( ( aSet0(W1)
% 0.60/0.78 & isFinite0(W1) )
% 0.60/0.78 => isFinite0(sdtmndt0(W1,W0)) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mNATSet,axiom,
% 0.60/0.78 ( aSet0(szNzAzT0)
% 0.60/0.78 & isCountable0(szNzAzT0) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mZeroNum,axiom,
% 0.60/0.78 aElementOf0(sz00,szNzAzT0) ).
% 0.60/0.78
% 0.60/0.78 fof(mSuccNum,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
% 0.60/0.78 & szszuzczcdt0(W0) != sz00 ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSuccEquSucc,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 & aElementOf0(W1,szNzAzT0) )
% 0.60/0.78 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
% 0.60/0.78 => W0 = W1 ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mNatExtra,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 => ( W0 = sz00
% 0.60/0.78 | ? [W1] :
% 0.60/0.78 ( aElementOf0(W1,szNzAzT0)
% 0.60/0.78 & W0 = szszuzczcdt0(W1) ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mNatNSucc,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 => W0 != szszuzczcdt0(W0) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mLessRel,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 & aElementOf0(W1,szNzAzT0) )
% 0.60/0.78 => ( sdtlseqdt0(W0,W1)
% 0.60/0.78 => $true ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mZeroLess,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 => sdtlseqdt0(sz00,W0) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mNoScLessZr,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSuccLess,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 & aElementOf0(W1,szNzAzT0) )
% 0.60/0.78 => ( sdtlseqdt0(W0,W1)
% 0.60/0.78 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mLessSucc,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mLessRefl,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 => sdtlseqdt0(W0,W0) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mLessASymm,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 & aElementOf0(W1,szNzAzT0) )
% 0.60/0.78 => ( ( sdtlseqdt0(W0,W1)
% 0.60/0.78 & sdtlseqdt0(W1,W0) )
% 0.60/0.78 => W0 = W1 ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mLessTrans,axiom,
% 0.60/0.78 ! [W0,W1,W2] :
% 0.60/0.78 ( ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 & aElementOf0(W1,szNzAzT0)
% 0.60/0.78 & aElementOf0(W2,szNzAzT0) )
% 0.60/0.78 => ( ( sdtlseqdt0(W0,W1)
% 0.60/0.78 & sdtlseqdt0(W1,W2) )
% 0.60/0.78 => sdtlseqdt0(W0,W2) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mLessTotal,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 & aElementOf0(W1,szNzAzT0) )
% 0.60/0.78 => ( sdtlseqdt0(W0,W1)
% 0.60/0.78 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mIHSort,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 & aElementOf0(W1,szNzAzT0) )
% 0.60/0.78 => ( iLess0(W0,W1)
% 0.60/0.78 => $true ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mIH,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 => iLess0(W0,szszuzczcdt0(W0)) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCardS,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aSet0(W0)
% 0.60/0.78 => aElement0(sbrdtbr0(W0)) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCardNum,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aSet0(W0)
% 0.60/0.78 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
% 0.60/0.78 <=> isFinite0(W0) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCardEmpty,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aSet0(W0)
% 0.60/0.78 => ( sbrdtbr0(W0) = sz00
% 0.60/0.78 <=> W0 = slcrc0 ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCardCons,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & isFinite0(W0) )
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( aElement0(W1)
% 0.60/0.78 => ( ~ aElementOf0(W1,W0)
% 0.60/0.78 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCardDiff,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aSet0(W0)
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( ( isFinite0(W0)
% 0.60/0.78 & aElementOf0(W1,W0) )
% 0.60/0.78 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCardSub,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aSet0(W0)
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( ( isFinite0(W0)
% 0.60/0.78 & aSubsetOf0(W1,W0) )
% 0.60/0.78 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCardSubEx,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & aElementOf0(W1,szNzAzT0) )
% 0.60/0.78 => ( ( isFinite0(W0)
% 0.60/0.78 & sdtlseqdt0(W1,sbrdtbr0(W0)) )
% 0.60/0.78 => ? [W2] :
% 0.60/0.78 ( aSubsetOf0(W2,W0)
% 0.60/0.78 & sbrdtbr0(W2) = W1 ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mDefMin,definition,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.60/0.78 & W0 != slcrc0 )
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( W1 = szmzizndt0(W0)
% 0.60/0.78 <=> ( aElementOf0(W1,W0)
% 0.60/0.78 & ! [W2] :
% 0.60/0.78 ( aElementOf0(W2,W0)
% 0.60/0.78 => sdtlseqdt0(W1,W2) ) ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mDefMax,definition,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.60/0.78 & isFinite0(W0)
% 0.60/0.78 & W0 != slcrc0 )
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( W1 = szmzazxdt0(W0)
% 0.60/0.78 <=> ( aElementOf0(W1,W0)
% 0.60/0.78 & ! [W2] :
% 0.60/0.78 ( aElementOf0(W2,W0)
% 0.60/0.78 => sdtlseqdt0(W2,W1) ) ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mMinMin,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.60/0.78 & aSubsetOf0(W1,szNzAzT0)
% 0.60/0.78 & W0 != slcrc0
% 0.60/0.78 & W1 != slcrc0 )
% 0.60/0.78 => ( ( aElementOf0(szmzizndt0(W0),W1)
% 0.60/0.78 & aElementOf0(szmzizndt0(W1),W0) )
% 0.60/0.78 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mDefSeg,definition,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( W1 = slbdtrb0(W0)
% 0.60/0.78 <=> ( aSet0(W1)
% 0.60/0.78 & ! [W2] :
% 0.60/0.78 ( aElementOf0(W2,W1)
% 0.60/0.78 <=> ( aElementOf0(W2,szNzAzT0)
% 0.60/0.78 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSegFin,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 => isFinite0(slbdtrb0(W0)) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSegZero,axiom,
% 0.60/0.78 slbdtrb0(sz00) = slcrc0 ).
% 0.60/0.78
% 0.60/0.78 fof(mSegSucc,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 & aElementOf0(W1,szNzAzT0) )
% 0.60/0.78 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1)))
% 0.60/0.78 <=> ( aElementOf0(W0,slbdtrb0(W1))
% 0.60/0.78 | W0 = W1 ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSegLess,axiom,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 & aElementOf0(W1,szNzAzT0) )
% 0.60/0.78 => ( sdtlseqdt0(W0,W1)
% 0.60/0.78 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mFinSubSeg,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.60/0.78 & isFinite0(W0) )
% 0.60/0.78 => ? [W1] :
% 0.60/0.78 ( aElementOf0(W1,szNzAzT0)
% 0.60/0.78 & aSubsetOf0(W0,slbdtrb0(W1)) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mCardSeg,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,szNzAzT0)
% 0.60/0.78 => sbrdtbr0(slbdtrb0(W0)) = W0 ) ).
% 0.60/0.78
% 0.60/0.78 fof(mDefSel,definition,
% 0.60/0.78 ! [W0,W1] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & aElementOf0(W1,szNzAzT0) )
% 0.60/0.78 => ! [W2] :
% 0.60/0.78 ( W2 = slbdtsldtrb0(W0,W1)
% 0.60/0.78 <=> ( aSet0(W2)
% 0.60/0.78 & ! [W3] :
% 0.60/0.78 ( aElementOf0(W3,W2)
% 0.60/0.78 <=> ( aSubsetOf0(W3,W0)
% 0.60/0.78 & sbrdtbr0(W3) = W1 ) ) ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSelFSet,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & isFinite0(W0) )
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( aElementOf0(W1,szNzAzT0)
% 0.60/0.78 => isFinite0(slbdtsldtrb0(W0,W1)) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSelNSet,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & ~ isFinite0(W0) )
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( aElementOf0(W1,szNzAzT0)
% 0.60/0.78 => slbdtsldtrb0(W0,W1) != slcrc0 ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(mSelCSet,axiom,
% 0.60/0.78 ! [W0] :
% 0.60/0.78 ( ( aSet0(W0)
% 0.60/0.78 & isCountable0(W0) )
% 0.60/0.78 => ! [W1] :
% 0.60/0.78 ( ( aElementOf0(W1,szNzAzT0)
% 0.60/0.78 & W1 != sz00 )
% 0.60/0.78 => isCountable0(slbdtsldtrb0(W0,W1)) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(m__2202,hypothesis,
% 0.60/0.78 aElementOf0(xk,szNzAzT0) ).
% 0.60/0.78
% 0.60/0.78 fof(m__2202_02,hypothesis,
% 0.60/0.78 ( aSet0(xS)
% 0.60/0.78 & aSet0(xT)
% 0.60/0.78 & xk != sz00 ) ).
% 0.60/0.78
% 0.60/0.78 fof(m__2227,hypothesis,
% 0.60/0.78 ( aSet0(slbdtsldtrb0(xS,xk))
% 0.60/0.78 & ! [W0] :
% 0.60/0.78 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.60/0.78 => ( aSet0(W0)
% 0.60/0.78 & ! [W1] :
% 0.60/0.78 ( aElementOf0(W1,W0)
% 0.60/0.78 => aElementOf0(W1,xS) )
% 0.60/0.78 & aSubsetOf0(W0,xS)
% 0.60/0.78 & sbrdtbr0(W0) = xk ) )
% 0.60/0.78 & ( ( ( ( aSet0(W0)
% 0.60/0.78 & ! [W1] :
% 0.60/0.78 ( aElementOf0(W1,W0)
% 0.60/0.78 => aElementOf0(W1,xS) ) )
% 0.60/0.78 | aSubsetOf0(W0,xS) )
% 0.60/0.78 & sbrdtbr0(W0) = xk )
% 0.60/0.78 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
% 0.60/0.78 & aSet0(slbdtsldtrb0(xT,xk))
% 0.60/0.78 & ! [W0] :
% 0.60/0.78 ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
% 0.60/0.78 => ( aSet0(W0)
% 0.60/0.78 & ! [W1] :
% 0.60/0.78 ( aElementOf0(W1,W0)
% 0.60/0.78 => aElementOf0(W1,xT) )
% 0.60/0.78 & aSubsetOf0(W0,xT)
% 0.60/0.78 & sbrdtbr0(W0) = xk ) )
% 0.60/0.78 & ( ( ( ( aSet0(W0)
% 0.60/0.78 & ! [W1] :
% 0.60/0.78 ( aElementOf0(W1,W0)
% 0.60/0.78 => aElementOf0(W1,xT) ) )
% 0.60/0.78 | aSubsetOf0(W0,xT) )
% 0.60/0.78 & sbrdtbr0(W0) = xk )
% 0.60/0.78 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
% 0.60/0.78 & ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.60/0.78 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
% 0.60/0.78 & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
% 0.60/0.78 & ~ ( ! [W0] :
% 0.60/0.78 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.60/0.78 => ( aSet0(W0)
% 0.60/0.78 & ! [W1] :
% 0.60/0.78 ( aElementOf0(W1,W0)
% 0.60/0.78 => aElementOf0(W1,xS) )
% 0.60/0.78 & aSubsetOf0(W0,xS)
% 0.60/0.78 & sbrdtbr0(W0) = xk ) )
% 0.60/0.78 & ( ( ( ( aSet0(W0)
% 0.60/0.78 & ! [W1] :
% 0.60/0.78 ( aElementOf0(W1,W0)
% 0.60/0.78 => aElementOf0(W1,xS) ) )
% 0.60/0.78 | aSubsetOf0(W0,xS) )
% 0.60/0.78 & sbrdtbr0(W0) = xk )
% 0.60/0.78 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
% 0.60/0.78 => ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
% 0.60/0.78 | slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(m__2256,hypothesis,
% 0.60/0.78 aElementOf0(xx,xS) ).
% 0.60/0.78
% 0.60/0.78 fof(m__2270,hypothesis,
% 0.60/0.78 ( aSet0(xQ)
% 0.60/0.78 & ! [W0] :
% 0.60/0.78 ( aElementOf0(W0,xQ)
% 0.60/0.78 => aElementOf0(W0,xS) )
% 0.60/0.78 & aSubsetOf0(xQ,xS)
% 0.60/0.78 & sbrdtbr0(xQ) = xk
% 0.60/0.78 & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ) ).
% 0.60/0.78
% 0.60/0.78 fof(m__2291,hypothesis,
% 0.60/0.78 ( aSet0(xQ)
% 0.60/0.78 & isFinite0(xQ)
% 0.60/0.78 & sbrdtbr0(xQ) = xk ) ).
% 0.60/0.78
% 0.60/0.78 fof(m__2304,hypothesis,
% 0.60/0.78 ( aElement0(xy)
% 0.60/0.78 & aElementOf0(xy,xQ) ) ).
% 0.60/0.78
% 0.60/0.78 fof(m__,conjecture,
% 0.60/0.78 ( aElementOf0(xx,xQ)
% 0.60/0.78 => aElementOf0(xx,xT) ) ).
% 0.60/0.78
% 0.60/0.78 %------------------------------------------------------------------------------
% 0.60/0.78 %-------------------------------------------
% 0.60/0.78 % Proof found
% 0.60/0.78 % SZS status Theorem for theBenchmark
% 0.60/0.78 % SZS output start Proof
% 0.60/0.79 %ClaNum:199(EqnAxiom:51)
% 0.60/0.79 %VarNum:771(SingletonVarNum:238)
% 0.60/0.79 %MaxLitNum:8
% 0.60/0.79 %MaxfuncDepth:3
% 0.60/0.79 %SharedTerms:38
% 0.60/0.79 %goalClause: 67 77
% 0.60/0.79 %singleGoalClaCount:2
% 0.60/0.79 [55]P1(a24)
% 0.60/0.79 [56]P1(a29)
% 0.60/0.79 [57]P1(a30)
% 0.60/0.79 [59]P1(a1)
% 0.60/0.79 [60]P2(a31)
% 0.60/0.79 [61]P4(a22)
% 0.60/0.79 [62]P4(a1)
% 0.60/0.79 [63]P5(a24)
% 0.60/0.79 [64]P3(a18,a24)
% 0.60/0.79 [65]P3(a28,a24)
% 0.60/0.79 [66]P3(a32,a29)
% 0.60/0.79 [67]P3(a32,a1)
% 0.60/0.79 [68]P3(a31,a1)
% 0.60/0.79 [69]P6(a1,a29)
% 0.60/0.79 [75]~E(a18,a28)
% 0.60/0.79 [77]~P3(a32,a30)
% 0.60/0.79 [53]E(f2(a1),a28)
% 0.60/0.79 [54]E(f19(a18),a22)
% 0.60/0.79 [70]P1(f23(a29,a28))
% 0.60/0.79 [71]P1(f23(a30,a28))
% 0.60/0.79 [72]P3(a1,f23(a29,a28))
% 0.60/0.79 [73]P3(a3,f23(a29,a28))
% 0.60/0.79 [74]P6(f23(a29,a28),f23(a30,a28))
% 0.60/0.79 [76]~E(f23(a29,a28),a22)
% 0.60/0.79 [78]P1(x781)+~E(x781,a22)
% 0.60/0.79 [84]~P1(x841)+P6(x841,x841)
% 0.60/0.79 [91]~P3(x911,a1)+P3(x911,a29)
% 0.60/0.79 [92]~P3(x921,a24)+P8(a18,x921)
% 0.60/0.79 [98]P8(x981,x981)+~P3(x981,a24)
% 0.60/0.79 [82]~P1(x821)+P2(f2(x821))
% 0.60/0.79 [86]~P3(x861,a24)+~E(f25(x861),a18)
% 0.60/0.79 [87]~P3(x871,a24)+~E(f25(x871),x871)
% 0.60/0.79 [89]~P3(x891,a24)+P4(f19(x891))
% 0.60/0.79 [99]~P3(x991,a24)+P3(f25(x991),a24)
% 0.60/0.79 [100]~P3(x1001,a24)+P8(x1001,f25(x1001))
% 0.60/0.79 [101]~P3(x1011,a24)+P7(x1011,f25(x1011))
% 0.60/0.79 [109]~P3(x1091,a24)+~P8(f25(x1091),a18)
% 0.60/0.79 [119]~P3(x1191,f23(a29,a28))+E(f2(x1191),a28)
% 0.60/0.79 [120]~P3(x1201,f23(a30,a28))+E(f2(x1201),a28)
% 0.60/0.79 [122]P1(x1221)+~P3(x1221,f23(a29,a28))
% 0.60/0.79 [123]P1(x1231)+~P3(x1231,f23(a30,a28))
% 0.60/0.79 [138]P6(x1381,a29)+~P3(x1381,f23(a29,a28))
% 0.60/0.79 [139]P6(x1391,a30)+~P3(x1391,f23(a30,a28))
% 0.60/0.79 [162]~P3(x1621,f23(a29,a28))+P3(x1621,f23(a30,a28))
% 0.60/0.79 [90]~P3(x901,a24)+E(f2(f19(x901)),x901)
% 0.60/0.79 [85]~P3(x852,x851)+~E(x851,a22)
% 0.60/0.79 [81]~P1(x811)+~P5(x811)+~E(x811,a22)
% 0.60/0.79 [83]~P4(x831)+~P5(x831)+~P1(x831)
% 0.60/0.79 [79]~P1(x791)+~E(x791,a22)+E(f2(x791),a18)
% 0.60/0.79 [80]~P1(x801)+E(x801,a22)+~E(f2(x801),a18)
% 0.60/0.79 [88]~P1(x881)+P3(f9(x881),x881)+E(x881,a22)
% 0.60/0.79 [95]~P1(x951)+~P4(x951)+P3(f2(x951),a24)
% 0.60/0.79 [102]~P3(x1021,a24)+E(x1021,a18)+P3(f10(x1021),a24)
% 0.60/0.79 [103]~P1(x1031)+P4(x1031)+~P3(f2(x1031),a24)
% 0.60/0.79 [108]~P4(x1081)+~P6(x1081,a24)+P3(f4(x1081),a24)
% 0.60/0.79 [126]~P6(x1261,a29)+P3(x1261,f23(a29,a28))+~E(f2(x1261),a28)
% 0.60/0.79 [127]~P6(x1271,a30)+P3(x1271,f23(a30,a28))+~E(f2(x1271),a28)
% 0.60/0.79 [93]~P3(x931,a24)+E(x931,a18)+E(f25(f10(x931)),x931)
% 0.60/0.79 [124]~P4(x1241)+~P6(x1241,a24)+P6(x1241,f19(f4(x1241)))
% 0.60/0.79 [96]~P6(x961,x962)+P1(x961)+~P1(x962)
% 0.60/0.79 [97]~P3(x971,x972)+P2(x971)+~P1(x972)
% 0.60/0.79 [94]P1(x941)+~P3(x942,a24)+~E(x941,f19(x942))
% 0.60/0.79 [166]~P3(x1661,x1662)+P3(x1661,a29)+~P3(x1662,f23(a29,a28))
% 0.60/0.79 [167]~P3(x1671,x1672)+P3(x1671,a30)+~P3(x1672,f23(a30,a28))
% 0.60/0.79 [147]~P1(x1471)+~P3(x1472,x1471)+E(f20(f21(x1471,x1472),x1472),x1471)
% 0.60/0.79 [143]~P1(x1431)+P3(f5(x1431),x1431)+P3(x1431,f23(a29,a28))+~E(f2(x1431),a28)
% 0.60/0.79 [144]~P1(x1441)+P3(f7(x1441),x1441)+P3(x1441,f23(a30,a28))+~E(f2(x1441),a28)
% 0.60/0.79 [145]~P1(x1451)+P3(f8(x1451),x1451)+P3(x1451,f23(a29,a28))+~E(f2(x1451),a28)
% 0.60/0.79 [155]~P1(x1551)+P3(x1551,f23(a29,a28))+~E(f2(x1551),a28)+~P3(f5(x1551),a29)
% 0.60/0.79 [156]~P1(x1561)+P3(x1561,f23(a29,a28))+~E(f2(x1561),a28)+~P3(f8(x1561),a29)
% 0.60/0.79 [157]~P1(x1571)+P3(x1571,f23(a30,a28))+~E(f2(x1571),a28)+~P3(f7(x1571),a30)
% 0.60/0.79 [104]~P4(x1042)+~P6(x1041,x1042)+P4(x1041)+~P1(x1042)
% 0.60/0.79 [107]P3(x1072,x1071)+~E(x1072,f26(x1071))+~P6(x1071,a24)+E(x1071,a22)
% 0.60/0.79 [111]~P1(x1111)+~P2(x1112)+~P4(x1111)+P4(f20(x1111,x1112))
% 0.60/0.79 [112]~P1(x1121)+~P2(x1122)+~P4(x1121)+P4(f21(x1121,x1122))
% 0.60/0.79 [113]~P1(x1131)+~P2(x1132)+~P5(x1131)+P5(f20(x1131,x1132))
% 0.60/0.79 [114]~P1(x1141)+~P2(x1142)+~P5(x1141)+P5(f21(x1141,x1142))
% 0.60/0.79 [115]~P1(x1151)+P4(x1151)+~P3(x1152,a24)+~E(f23(x1151,x1152),a22)
% 0.60/0.79 [117]E(x1171,x1172)+~E(f25(x1171),f25(x1172))+~P3(x1172,a24)+~P3(x1171,a24)
% 0.60/0.79 [130]~P1(x1302)+~P4(x1302)+~P6(x1301,x1302)+P8(f2(x1301),f2(x1302))
% 0.60/0.79 [133]~P1(x1331)+~P4(x1331)+~P3(x1332,a24)+P4(f23(x1331,x1332))
% 0.60/0.79 [142]~P1(x1421)+~P1(x1422)+P6(x1421,x1422)+P3(f11(x1422,x1421),x1421)
% 0.60/0.79 [151]P8(x1511,x1512)+P8(f25(x1512),x1511)+~P3(x1512,a24)+~P3(x1511,a24)
% 0.60/0.79 [168]~P8(x1681,x1682)+~P3(x1682,a24)+~P3(x1681,a24)+P6(f19(x1681),f19(x1682))
% 0.60/0.79 [169]~P8(x1691,x1692)+~P3(x1692,a24)+~P3(x1691,a24)+P8(f25(x1691),f25(x1692))
% 0.60/0.79 [171]~P1(x1711)+~P1(x1712)+P6(x1711,x1712)+~P3(f11(x1712,x1711),x1712)
% 0.60/0.79 [173]P8(x1731,x1732)+~P3(x1732,a24)+~P3(x1731,a24)+~P6(f19(x1731),f19(x1732))
% 0.60/0.79 [174]P8(x1741,x1742)+~P3(x1742,a24)+~P3(x1741,a24)+~P8(f25(x1741),f25(x1742))
% 0.60/0.79 [146]P3(x1462,x1461)+~P1(x1461)+~P2(x1462)+E(f21(f20(x1461,x1462),x1462),x1461)
% 0.60/0.79 [153]~E(x1531,x1532)+~P3(x1532,a24)+~P3(x1531,a24)+P3(x1531,f19(f25(x1532)))
% 0.60/0.79 [179]~P3(x1792,a24)+~P3(x1791,a24)+~P3(x1791,f19(x1792))+P3(x1791,f19(f25(x1792)))
% 0.60/0.79 [178]~P1(x1781)+~P4(x1781)+~P3(x1782,x1781)+E(f25(f2(f21(x1781,x1782))),f2(x1781))
% 0.60/0.79 [140]~P1(x1402)+~P6(x1403,x1402)+P3(x1401,x1402)+~P3(x1401,x1403)
% 0.60/0.79 [105]~P1(x1052)+~P2(x1053)+P1(x1051)+~E(x1051,f20(x1052,x1053))
% 0.60/0.79 [106]~P1(x1062)+~P2(x1063)+P1(x1061)+~E(x1061,f21(x1062,x1063))
% 0.60/0.79 [116]~P1(x1162)+P1(x1161)+~P3(x1163,a24)+~E(x1161,f23(x1162,x1163))
% 0.60/0.79 [131]~P3(x1311,x1312)+~P3(x1313,a24)+P3(x1311,a24)+~E(x1312,f19(x1313))
% 0.60/0.79 [148]~P3(x1481,x1483)+~P3(x1482,a24)+P8(f25(x1481),x1482)+~E(x1483,f19(x1482))
% 0.60/0.79 [128]~P1(x1282)+~P1(x1281)+~P6(x1282,x1281)+~P6(x1281,x1282)+E(x1281,x1282)
% 0.60/0.79 [163]~P8(x1632,x1631)+~P8(x1631,x1632)+E(x1631,x1632)+~P3(x1632,a24)+~P3(x1631,a24)
% 0.60/0.79 [110]~P4(x1101)+P3(x1102,x1101)+~E(x1102,f27(x1101))+~P6(x1101,a24)+E(x1101,a22)
% 0.60/0.79 [136]~P1(x1362)+~P5(x1362)+~P3(x1361,a24)+E(x1361,a18)+P5(f23(x1362,x1361))
% 0.60/0.79 [170]~P3(x1702,x1701)+P3(f14(x1701,x1702),x1701)+~P6(x1701,a24)+E(x1701,a22)+E(x1702,f26(x1701))
% 0.60/0.79 [180]~P1(x1801)+~P4(x1801)+~P3(x1802,a24)+~P8(x1802,f2(x1801))+P6(f15(x1801,x1802),x1801)
% 0.60/0.79 [181]~P1(x1811)+P3(f17(x1812,x1811),x1811)+~P3(x1812,a24)+E(x1811,f19(x1812))+P3(f17(x1812,x1811),a24)
% 0.60/0.79 [182]~P3(x1822,x1821)+~P6(x1821,a24)+~P8(x1822,f14(x1821,x1822))+E(x1821,a22)+E(x1822,f26(x1821))
% 0.60/0.79 [152]P3(x1522,x1521)+~P1(x1521)+~P2(x1522)+~P4(x1521)+E(f2(f20(x1521,x1522)),f25(f2(x1521)))
% 0.60/0.79 [177]~P1(x1771)+~P4(x1771)+~P3(x1772,a24)+~P8(x1772,f2(x1771))+E(f2(f15(x1771,x1772)),x1772)
% 0.60/0.79 [183]E(x1831,x1832)+P3(x1831,f19(x1832))+~P3(x1832,a24)+~P3(x1831,a24)+~P3(x1831,f19(f25(x1832)))
% 0.60/0.79 [187]~P1(x1871)+P3(f17(x1872,x1871),x1871)+~P3(x1872,a24)+E(x1871,f19(x1872))+P8(f25(f17(x1872,x1871)),x1872)
% 0.60/0.79 [141]~P3(x1413,x1411)+P8(x1412,x1413)+~E(x1412,f26(x1411))+~P6(x1411,a24)+E(x1411,a22)
% 0.60/0.79 [172]P3(x1721,x1722)+~P3(x1723,a24)+~P3(x1721,a24)+~P8(f25(x1721),x1723)+~E(x1722,f19(x1723))
% 0.60/0.79 [132]~P1(x1324)+~P2(x1322)+~P3(x1321,x1323)+~E(x1321,x1322)+~E(x1323,f21(x1324,x1322))
% 0.60/0.79 [134]~P1(x1343)+~P2(x1344)+~P3(x1341,x1342)+P2(x1341)+~E(x1342,f20(x1343,x1344))
% 0.60/0.79 [135]~P1(x1353)+~P2(x1354)+~P3(x1351,x1352)+P2(x1351)+~E(x1352,f21(x1353,x1354))
% 0.60/0.79 [150]~P1(x1502)+~P2(x1504)+~P3(x1501,x1503)+P3(x1501,x1502)+~E(x1503,f21(x1502,x1504))
% 0.60/0.79 [158]~P1(x1584)+~P3(x1581,x1583)+~P3(x1582,a24)+E(f2(x1581),x1582)+~E(x1583,f23(x1584,x1582))
% 0.60/0.79 [164]~P1(x1642)+~P3(x1641,x1643)+P6(x1641,x1642)+~P3(x1644,a24)+~E(x1643,f23(x1642,x1644))
% 0.60/0.79 [176]~P4(x1761)+~P3(x1762,x1761)+P3(f16(x1761,x1762),x1761)+~P6(x1761,a24)+E(x1761,a22)+E(x1762,f27(x1761))
% 0.60/0.79 [185]~P4(x1851)+~P3(x1852,x1851)+~P6(x1851,a24)+~P8(f16(x1851,x1852),x1852)+E(x1851,a22)+E(x1852,f27(x1851))
% 0.60/0.79 [191]~P1(x1911)+~P3(x1912,a24)+~P3(f17(x1912,x1911),x1911)+E(x1911,f19(x1912))+~P3(f17(x1912,x1911),a24)+~P8(f25(f17(x1912,x1911)),x1912)
% 0.60/0.79 [159]~P1(x1592)+~P1(x1591)+~P6(x1593,x1592)+~P6(x1591,x1593)+P6(x1591,x1592)+~P1(x1593)
% 0.60/0.79 [186]~P8(x1861,x1863)+P8(x1861,x1862)+~P8(x1863,x1862)+~P3(x1862,a24)+~P3(x1863,a24)+~P3(x1861,a24)
% 0.60/0.79 [149]~P4(x1491)+~P3(x1492,x1491)+P8(x1492,x1493)+~E(x1493,f27(x1491))+~P6(x1491,a24)+E(x1491,a22)
% 0.60/0.79 [188]~P1(x1881)+~P1(x1882)+~P2(x1883)+P3(f12(x1882,x1883,x1881),x1881)+~E(f12(x1882,x1883,x1881),x1883)+E(x1881,f21(x1882,x1883))
% 0.60/0.79 [189]~P1(x1891)+~P1(x1892)+~P2(x1893)+P3(f13(x1892,x1893,x1891),x1891)+E(x1891,f20(x1892,x1893))+P2(f13(x1892,x1893,x1891))
% 0.60/0.79 [190]~P1(x1901)+~P1(x1902)+~P2(x1903)+P3(f12(x1902,x1903,x1901),x1901)+E(x1901,f21(x1902,x1903))+P2(f12(x1902,x1903,x1901))
% 0.60/0.79 [192]~P1(x1921)+~P1(x1922)+~P2(x1923)+P3(f12(x1922,x1923,x1921),x1921)+P3(f12(x1922,x1923,x1921),x1922)+E(x1921,f21(x1922,x1923))
% 0.60/0.79 [194]~P1(x1941)+~P1(x1942)+P3(f6(x1942,x1943,x1941),x1941)+P6(f6(x1942,x1943,x1941),x1942)+~P3(x1943,a24)+E(x1941,f23(x1942,x1943))
% 0.60/0.79 [193]~P1(x1931)+~P1(x1932)+P3(f6(x1932,x1933,x1931),x1931)+~P3(x1933,a24)+E(x1931,f23(x1932,x1933))+E(f2(f6(x1932,x1933,x1931)),x1933)
% 0.60/0.79 [129]~P1(x1294)+~P2(x1293)+~P2(x1291)+P3(x1291,x1292)+~E(x1291,x1293)+~E(x1292,f20(x1294,x1293))
% 0.60/0.79 [154]~P1(x1543)+~P2(x1542)+~P3(x1541,x1544)+E(x1541,x1542)+P3(x1541,x1543)+~E(x1544,f20(x1543,x1542))
% 0.60/0.79 [160]~P1(x1603)+~P2(x1604)+~P2(x1601)+~P3(x1601,x1603)+P3(x1601,x1602)+~E(x1602,f20(x1603,x1604))
% 0.60/0.79 [175]~P1(x1754)+~P6(x1751,x1754)+P3(x1751,x1752)+~P3(x1753,a24)+~E(x1752,f23(x1754,x1753))+~E(f2(x1751),x1753)
% 0.60/0.79 [184]E(f26(x1842),f26(x1841))+~P6(x1841,a24)+~P6(x1842,a24)+~P3(f26(x1841),x1842)+~P3(f26(x1842),x1841)+E(x1841,a22)+E(x1842,a22)
% 0.60/0.79 [195]~P1(x1951)+~P1(x1952)+~P2(x1953)+E(f13(x1952,x1953,x1951),x1953)+P3(f13(x1952,x1953,x1951),x1951)+P3(f13(x1952,x1953,x1951),x1952)+E(x1951,f20(x1952,x1953))
% 0.60/0.79 [196]~P1(x1961)+~P1(x1962)+~P2(x1963)+~E(f13(x1962,x1963,x1961),x1963)+~P3(f13(x1962,x1963,x1961),x1961)+E(x1961,f20(x1962,x1963))+~P2(f13(x1962,x1963,x1961))
% 0.60/0.79 [197]~P1(x1971)+~P1(x1972)+~P2(x1973)+~P3(f13(x1972,x1973,x1971),x1971)+~P3(f13(x1972,x1973,x1971),x1972)+E(x1971,f20(x1972,x1973))+~P2(f13(x1972,x1973,x1971))
% 0.60/0.79 [198]~P1(x1981)+~P1(x1982)+~P3(x1983,a24)+~P3(f6(x1982,x1983,x1981),x1981)+~P6(f6(x1982,x1983,x1981),x1982)+E(x1981,f23(x1982,x1983))+~E(f2(f6(x1982,x1983,x1981)),x1983)
% 0.60/0.79 [161]~P1(x1614)+~P2(x1612)+~P2(x1611)+~P3(x1611,x1614)+E(x1611,x1612)+P3(x1611,x1613)+~E(x1613,f21(x1614,x1612))
% 0.60/0.79 [199]~P1(x1991)+~P1(x1992)+~P2(x1993)+E(f12(x1992,x1993,x1991),x1993)+~P3(f12(x1992,x1993,x1991),x1991)+~P3(f12(x1992,x1993,x1991),x1992)+E(x1991,f21(x1992,x1993))+~P2(f12(x1992,x1993,x1991))
% 0.60/0.79 %EqnAxiom
% 0.60/0.79 [1]E(x11,x11)
% 0.60/0.79 [2]E(x22,x21)+~E(x21,x22)
% 0.60/0.79 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.60/0.79 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.60/0.79 [5]~E(x51,x52)+E(f12(x51,x53,x54),f12(x52,x53,x54))
% 0.60/0.79 [6]~E(x61,x62)+E(f12(x63,x61,x64),f12(x63,x62,x64))
% 0.60/0.79 [7]~E(x71,x72)+E(f12(x73,x74,x71),f12(x73,x74,x72))
% 0.60/0.79 [8]~E(x81,x82)+E(f19(x81),f19(x82))
% 0.60/0.79 [9]~E(x91,x92)+E(f23(x91,x93),f23(x92,x93))
% 0.60/0.79 [10]~E(x101,x102)+E(f23(x103,x101),f23(x103,x102))
% 0.60/0.79 [11]~E(x111,x112)+E(f26(x111),f26(x112))
% 0.60/0.79 [12]~E(x121,x122)+E(f17(x121,x123),f17(x122,x123))
% 0.60/0.79 [13]~E(x131,x132)+E(f17(x133,x131),f17(x133,x132))
% 0.60/0.79 [14]~E(x141,x142)+E(f8(x141),f8(x142))
% 0.60/0.79 [15]~E(x151,x152)+E(f14(x151,x153),f14(x152,x153))
% 0.60/0.79 [16]~E(x161,x162)+E(f14(x163,x161),f14(x163,x162))
% 0.60/0.79 [17]~E(x171,x172)+E(f21(x171,x173),f21(x172,x173))
% 0.60/0.79 [18]~E(x181,x182)+E(f21(x183,x181),f21(x183,x182))
% 0.60/0.79 [19]~E(x191,x192)+E(f15(x191,x193),f15(x192,x193))
% 0.60/0.79 [20]~E(x201,x202)+E(f15(x203,x201),f15(x203,x202))
% 0.60/0.79 [21]~E(x211,x212)+E(f25(x211),f25(x212))
% 0.60/0.79 [22]~E(x221,x222)+E(f6(x221,x223,x224),f6(x222,x223,x224))
% 0.60/0.79 [23]~E(x231,x232)+E(f6(x233,x231,x234),f6(x233,x232,x234))
% 0.60/0.79 [24]~E(x241,x242)+E(f6(x243,x244,x241),f6(x243,x244,x242))
% 0.60/0.79 [25]~E(x251,x252)+E(f13(x251,x253,x254),f13(x252,x253,x254))
% 0.60/0.79 [26]~E(x261,x262)+E(f13(x263,x261,x264),f13(x263,x262,x264))
% 0.60/0.79 [27]~E(x271,x272)+E(f13(x273,x274,x271),f13(x273,x274,x272))
% 0.60/0.79 [28]~E(x281,x282)+E(f20(x281,x283),f20(x282,x283))
% 0.60/0.79 [29]~E(x291,x292)+E(f20(x293,x291),f20(x293,x292))
% 0.60/0.79 [30]~E(x301,x302)+E(f27(x301),f27(x302))
% 0.60/0.79 [31]~E(x311,x312)+E(f9(x311),f9(x312))
% 0.60/0.79 [32]~E(x321,x322)+E(f16(x321,x323),f16(x322,x323))
% 0.60/0.79 [33]~E(x331,x332)+E(f16(x333,x331),f16(x333,x332))
% 0.60/0.79 [34]~E(x341,x342)+E(f5(x341),f5(x342))
% 0.60/0.79 [35]~E(x351,x352)+E(f11(x351,x353),f11(x352,x353))
% 0.60/0.79 [36]~E(x361,x362)+E(f11(x363,x361),f11(x363,x362))
% 0.60/0.79 [37]~E(x371,x372)+E(f10(x371),f10(x372))
% 0.60/0.79 [38]~E(x381,x382)+E(f7(x381),f7(x382))
% 0.60/0.79 [39]~E(x391,x392)+E(f4(x391),f4(x392))
% 0.60/0.79 [40]~P1(x401)+P1(x402)+~E(x401,x402)
% 0.60/0.79 [41]P3(x412,x413)+~E(x411,x412)+~P3(x411,x413)
% 0.60/0.79 [42]P3(x423,x422)+~E(x421,x422)+~P3(x423,x421)
% 0.60/0.79 [43]~P4(x431)+P4(x432)+~E(x431,x432)
% 0.60/0.79 [44]~P2(x441)+P2(x442)+~E(x441,x442)
% 0.60/0.79 [45]~P5(x451)+P5(x452)+~E(x451,x452)
% 0.60/0.79 [46]P6(x462,x463)+~E(x461,x462)+~P6(x461,x463)
% 0.60/0.79 [47]P6(x473,x472)+~E(x471,x472)+~P6(x473,x471)
% 0.60/0.79 [48]P8(x482,x483)+~E(x481,x482)+~P8(x481,x483)
% 0.60/0.79 [49]P8(x493,x492)+~E(x491,x492)+~P8(x493,x491)
% 0.60/0.79 [50]P7(x502,x503)+~E(x501,x502)+~P7(x501,x503)
% 0.60/0.79 [51]P7(x513,x512)+~E(x511,x512)+~P7(x513,x511)
% 0.60/0.79
% 0.60/0.79 %-------------------------------------------
% 0.60/0.79 cnf(203,plain,
% 0.60/0.79 (~P3(x2031,f19(a18))),
% 0.60/0.79 inference(scs_inference,[],[64,53,54,2,98,85])).
% 0.60/0.79 cnf(205,plain,
% 0.60/0.79 (P1(f19(a18))),
% 0.60/0.79 inference(scs_inference,[],[64,53,54,2,98,85,78])).
% 0.60/0.79 cnf(223,plain,
% 0.60/0.79 (P6(f19(a18),a24)),
% 0.60/0.79 inference(scs_inference,[],[67,77,55,63,64,65,75,73,53,54,2,98,85,78,138,122,42,41,40,3,83,81,169,168,142])).
% 0.60/0.79 cnf(225,plain,
% 0.60/0.79 (P8(a18,a28)),
% 0.60/0.79 inference(scs_inference,[],[67,77,55,63,64,65,75,73,53,54,2,98,85,78,138,122,42,41,40,3,83,81,169,168,142,92])).
% 0.60/0.79 cnf(243,plain,
% 0.60/0.79 (P4(f19(a18))),
% 0.60/0.79 inference(scs_inference,[],[67,77,55,63,64,65,68,75,73,53,54,2,98,85,78,138,122,42,41,40,3,83,81,169,168,142,92,91,84,162,109,101,100,99,90,89])).
% 0.60/0.79 cnf(291,plain,
% 0.60/0.79 (~E(a24,f19(a18))),
% 0.60/0.79 inference(scs_inference,[],[67,77,55,63,64,65,68,75,73,53,54,2,98,85,78,138,122,42,41,40,3,83,81,169,168,142,92,91,84,162,109,101,100,99,90,89,87,86,82,120,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,49,48,45])).
% 0.60/0.79 cnf(296,plain,
% 0.60/0.79 (~P3(a1,f23(a30,a28))),
% 0.60/0.79 inference(scs_inference,[],[67,77,55,60,61,63,64,65,68,75,73,53,54,2,98,85,78,138,122,42,41,40,3,83,81,169,168,142,92,91,84,162,109,101,100,99,90,89,87,86,82,120,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,49,48,45,44,43,97,167])).
% 0.60/0.79 cnf(312,plain,
% 0.60/0.79 (P3(f9(f23(a29,a28)),f23(a29,a28))),
% 0.60/0.79 inference(scs_inference,[],[67,77,55,60,61,63,64,65,68,75,76,73,53,54,70,2,98,85,78,138,122,42,41,40,3,83,81,169,168,142,92,91,84,162,109,101,100,99,90,89,87,86,82,120,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,49,48,45,44,43,97,167,94,124,108,103,102,95,93,88])).
% 0.60/0.79 cnf(391,plain,
% 0.60/0.79 (~P3(x3911,f19(a18))),
% 0.60/0.79 inference(rename_variables,[],[203])).
% 0.60/0.79 cnf(400,plain,
% 0.60/0.79 (~P3(x4001,f19(a18))),
% 0.60/0.79 inference(rename_variables,[],[203])).
% 0.60/0.79 cnf(403,plain,
% 0.60/0.79 (~P3(x4031,f19(a18))),
% 0.60/0.79 inference(rename_variables,[],[203])).
% 0.60/0.79 cnf(422,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(scs_inference,[],[66,56,69,71,74,62,72,77,75,59,63,60,65,55,64,53,312,203,391,400,403,223,291,205,243,296,225,146,157,163,128,175,194,193,126,119,83,81,167,95,80,140]),
% 0.60/0.79 ['proof']).
% 0.60/0.79 % SZS output end Proof
% 0.60/0.79 % Total time :0.120000s
%------------------------------------------------------------------------------