TSTP Solution File: NUM557+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM557+1 : 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 : n008.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 10:23:04 EDT 2023
% Result : Theorem 0.62s 0.87s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM557+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.16/0.36 % Computer : n008.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri Aug 25 13:13:02 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.22/0.59 start to proof:theBenchmark
% 0.62/0.85 %-------------------------------------------
% 0.62/0.85 % File :CSE---1.6
% 0.62/0.85 % Problem :theBenchmark
% 0.62/0.85 % Transform :cnf
% 0.62/0.85 % Format :tptp:raw
% 0.62/0.85 % Command :java -jar mcs_scs.jar %d %s
% 0.62/0.85
% 0.62/0.85 % Result :Theorem 0.170000s
% 0.62/0.85 % Output :CNFRefutation 0.170000s
% 0.62/0.85 %-------------------------------------------
% 0.62/0.85 %------------------------------------------------------------------------------
% 0.62/0.85 % File : NUM557+1 : TPTP v8.1.2. Released v4.0.0.
% 0.62/0.85 % Domain : Number Theory
% 0.62/0.85 % Problem : Ramsey's Infinite Theorem 12_05_02_03, 00 expansion
% 0.62/0.85 % Version : Especial.
% 0.62/0.85 % English :
% 0.62/0.85
% 0.62/0.86 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.62/0.86 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.62/0.86 % Source : [Pas08]
% 0.62/0.86 % Names : ramsey_12_05_02_03.00 [Pas08]
% 0.62/0.86
% 0.62/0.86 % Status : Theorem
% 0.62/0.86 % Rating : 0.31 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.17 v7.1.0, 0.26 v7.0.0, 0.30 v6.4.0, 0.35 v6.3.0, 0.38 v6.2.0, 0.44 v6.1.0, 0.50 v6.0.0, 0.39 v5.5.0, 0.44 v5.4.0, 0.50 v5.3.0, 0.56 v5.2.0, 0.35 v5.1.0, 0.43 v5.0.0, 0.54 v4.1.0, 0.57 v4.0.1, 0.74 v4.0.0
% 0.62/0.86 % Syntax : Number of formulae : 73 ( 10 unt; 8 def)
% 0.62/0.86 % Number of atoms : 249 ( 42 equ)
% 0.62/0.86 % Maximal formula atoms : 8 ( 3 avg)
% 0.62/0.86 % Number of connectives : 197 ( 21 ~; 4 |; 71 &)
% 0.62/0.86 % ( 17 <=>; 84 =>; 0 <=; 0 <~>)
% 0.62/0.86 % Maximal formula depth : 12 ( 5 avg)
% 0.62/0.86 % Maximal term depth : 4 ( 1 avg)
% 0.62/0.86 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% 0.62/0.86 % Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% 0.62/0.86 % Number of variables : 106 ( 102 !; 4 ?)
% 0.62/0.86 % SPC : FOF_THM_RFO_SEQ
% 0.62/0.86
% 0.62/0.86 % Comments : Problem generated by the SAD system [VLP07]
% 0.62/0.86 %------------------------------------------------------------------------------
% 0.62/0.86 fof(mSetSort,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aSet0(W0)
% 0.62/0.86 => $true ) ).
% 0.62/0.86
% 0.62/0.86 fof(mElmSort,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aElement0(W0)
% 0.62/0.86 => $true ) ).
% 0.62/0.86
% 0.62/0.86 fof(mEOfElem,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aSet0(W0)
% 0.62/0.86 => ! [W1] :
% 0.62/0.86 ( aElementOf0(W1,W0)
% 0.62/0.86 => aElement0(W1) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mFinRel,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aSet0(W0)
% 0.62/0.86 => ( isFinite0(W0)
% 0.62/0.86 => $true ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mDefEmp,definition,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( W0 = slcrc0
% 0.62/0.86 <=> ( aSet0(W0)
% 0.62/0.86 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mEmpFin,axiom,
% 0.62/0.86 isFinite0(slcrc0) ).
% 0.62/0.86
% 0.62/0.86 fof(mCntRel,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aSet0(W0)
% 0.62/0.86 => ( isCountable0(W0)
% 0.62/0.86 => $true ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mCountNFin,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( ( aSet0(W0)
% 0.62/0.86 & isCountable0(W0) )
% 0.62/0.86 => ~ isFinite0(W0) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mCountNFin_01,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( ( aSet0(W0)
% 0.62/0.86 & isCountable0(W0) )
% 0.62/0.86 => W0 != slcrc0 ) ).
% 0.62/0.86
% 0.62/0.86 fof(mDefSub,definition,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aSet0(W0)
% 0.62/0.86 => ! [W1] :
% 0.62/0.86 ( aSubsetOf0(W1,W0)
% 0.62/0.86 <=> ( aSet0(W1)
% 0.62/0.86 & ! [W2] :
% 0.62/0.86 ( aElementOf0(W2,W1)
% 0.62/0.86 => aElementOf0(W2,W0) ) ) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mSubFSet,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( ( aSet0(W0)
% 0.62/0.86 & isFinite0(W0) )
% 0.62/0.86 => ! [W1] :
% 0.62/0.86 ( aSubsetOf0(W1,W0)
% 0.62/0.86 => isFinite0(W1) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mSubRefl,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aSet0(W0)
% 0.62/0.86 => aSubsetOf0(W0,W0) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mSubASymm,axiom,
% 0.62/0.86 ! [W0,W1] :
% 0.62/0.86 ( ( aSet0(W0)
% 0.62/0.86 & aSet0(W1) )
% 0.62/0.86 => ( ( aSubsetOf0(W0,W1)
% 0.62/0.86 & aSubsetOf0(W1,W0) )
% 0.62/0.86 => W0 = W1 ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mSubTrans,axiom,
% 0.62/0.86 ! [W0,W1,W2] :
% 0.62/0.86 ( ( aSet0(W0)
% 0.62/0.86 & aSet0(W1)
% 0.62/0.86 & aSet0(W2) )
% 0.62/0.86 => ( ( aSubsetOf0(W0,W1)
% 0.62/0.86 & aSubsetOf0(W1,W2) )
% 0.62/0.86 => aSubsetOf0(W0,W2) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mDefCons,definition,
% 0.62/0.86 ! [W0,W1] :
% 0.62/0.86 ( ( aSet0(W0)
% 0.62/0.86 & aElement0(W1) )
% 0.62/0.86 => ! [W2] :
% 0.62/0.86 ( W2 = sdtpldt0(W0,W1)
% 0.62/0.86 <=> ( aSet0(W2)
% 0.62/0.86 & ! [W3] :
% 0.62/0.86 ( aElementOf0(W3,W2)
% 0.62/0.86 <=> ( aElement0(W3)
% 0.62/0.86 & ( aElementOf0(W3,W0)
% 0.62/0.86 | W3 = W1 ) ) ) ) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mDefDiff,definition,
% 0.62/0.86 ! [W0,W1] :
% 0.62/0.86 ( ( aSet0(W0)
% 0.62/0.86 & aElement0(W1) )
% 0.62/0.86 => ! [W2] :
% 0.62/0.86 ( W2 = sdtmndt0(W0,W1)
% 0.62/0.86 <=> ( aSet0(W2)
% 0.62/0.86 & ! [W3] :
% 0.62/0.86 ( aElementOf0(W3,W2)
% 0.62/0.86 <=> ( aElement0(W3)
% 0.62/0.86 & aElementOf0(W3,W0)
% 0.62/0.86 & W3 != W1 ) ) ) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mConsDiff,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aSet0(W0)
% 0.62/0.86 => ! [W1] :
% 0.62/0.86 ( aElementOf0(W1,W0)
% 0.62/0.86 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mDiffCons,axiom,
% 0.62/0.86 ! [W0,W1] :
% 0.62/0.86 ( ( aElement0(W0)
% 0.62/0.86 & aSet0(W1) )
% 0.62/0.86 => ( ~ aElementOf0(W0,W1)
% 0.62/0.86 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mCConsSet,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aElement0(W0)
% 0.62/0.86 => ! [W1] :
% 0.62/0.86 ( ( aSet0(W1)
% 0.62/0.86 & isCountable0(W1) )
% 0.62/0.86 => isCountable0(sdtpldt0(W1,W0)) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mCDiffSet,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aElement0(W0)
% 0.62/0.86 => ! [W1] :
% 0.62/0.86 ( ( aSet0(W1)
% 0.62/0.86 & isCountable0(W1) )
% 0.62/0.86 => isCountable0(sdtmndt0(W1,W0)) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mFConsSet,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aElement0(W0)
% 0.62/0.86 => ! [W1] :
% 0.62/0.86 ( ( aSet0(W1)
% 0.62/0.86 & isFinite0(W1) )
% 0.62/0.86 => isFinite0(sdtpldt0(W1,W0)) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mFDiffSet,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aElement0(W0)
% 0.62/0.86 => ! [W1] :
% 0.62/0.86 ( ( aSet0(W1)
% 0.62/0.86 & isFinite0(W1) )
% 0.62/0.86 => isFinite0(sdtmndt0(W1,W0)) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mNATSet,axiom,
% 0.62/0.86 ( aSet0(szNzAzT0)
% 0.62/0.86 & isCountable0(szNzAzT0) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mZeroNum,axiom,
% 0.62/0.86 aElementOf0(sz00,szNzAzT0) ).
% 0.62/0.86
% 0.62/0.86 fof(mSuccNum,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aElementOf0(W0,szNzAzT0)
% 0.62/0.86 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
% 0.62/0.86 & szszuzczcdt0(W0) != sz00 ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mSuccEquSucc,axiom,
% 0.62/0.86 ! [W0,W1] :
% 0.62/0.86 ( ( aElementOf0(W0,szNzAzT0)
% 0.62/0.86 & aElementOf0(W1,szNzAzT0) )
% 0.62/0.86 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
% 0.62/0.86 => W0 = W1 ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mNatExtra,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aElementOf0(W0,szNzAzT0)
% 0.62/0.86 => ( W0 = sz00
% 0.62/0.86 | ? [W1] :
% 0.62/0.86 ( aElementOf0(W1,szNzAzT0)
% 0.62/0.86 & W0 = szszuzczcdt0(W1) ) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mNatNSucc,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aElementOf0(W0,szNzAzT0)
% 0.62/0.86 => W0 != szszuzczcdt0(W0) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mLessRel,axiom,
% 0.62/0.86 ! [W0,W1] :
% 0.62/0.86 ( ( aElementOf0(W0,szNzAzT0)
% 0.62/0.86 & aElementOf0(W1,szNzAzT0) )
% 0.62/0.86 => ( sdtlseqdt0(W0,W1)
% 0.62/0.86 => $true ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mZeroLess,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aElementOf0(W0,szNzAzT0)
% 0.62/0.86 => sdtlseqdt0(sz00,W0) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mNoScLessZr,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aElementOf0(W0,szNzAzT0)
% 0.62/0.86 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mSuccLess,axiom,
% 0.62/0.86 ! [W0,W1] :
% 0.62/0.86 ( ( aElementOf0(W0,szNzAzT0)
% 0.62/0.86 & aElementOf0(W1,szNzAzT0) )
% 0.62/0.86 => ( sdtlseqdt0(W0,W1)
% 0.62/0.86 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ).
% 0.62/0.86
% 0.62/0.86 fof(mLessSucc,axiom,
% 0.62/0.86 ! [W0] :
% 0.62/0.86 ( aElementOf0(W0,szNzAzT0)
% 0.62/0.86 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mLessRefl,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( aElementOf0(W0,szNzAzT0)
% 0.62/0.87 => sdtlseqdt0(W0,W0) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mLessASymm,axiom,
% 0.62/0.87 ! [W0,W1] :
% 0.62/0.87 ( ( aElementOf0(W0,szNzAzT0)
% 0.62/0.87 & aElementOf0(W1,szNzAzT0) )
% 0.62/0.87 => ( ( sdtlseqdt0(W0,W1)
% 0.62/0.87 & sdtlseqdt0(W1,W0) )
% 0.62/0.87 => W0 = W1 ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mLessTrans,axiom,
% 0.62/0.87 ! [W0,W1,W2] :
% 0.62/0.87 ( ( aElementOf0(W0,szNzAzT0)
% 0.62/0.87 & aElementOf0(W1,szNzAzT0)
% 0.62/0.87 & aElementOf0(W2,szNzAzT0) )
% 0.62/0.87 => ( ( sdtlseqdt0(W0,W1)
% 0.62/0.87 & sdtlseqdt0(W1,W2) )
% 0.62/0.87 => sdtlseqdt0(W0,W2) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mLessTotal,axiom,
% 0.62/0.87 ! [W0,W1] :
% 0.62/0.87 ( ( aElementOf0(W0,szNzAzT0)
% 0.62/0.87 & aElementOf0(W1,szNzAzT0) )
% 0.62/0.87 => ( sdtlseqdt0(W0,W1)
% 0.62/0.87 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mIHSort,axiom,
% 0.62/0.87 ! [W0,W1] :
% 0.62/0.87 ( ( aElementOf0(W0,szNzAzT0)
% 0.62/0.87 & aElementOf0(W1,szNzAzT0) )
% 0.62/0.87 => ( iLess0(W0,W1)
% 0.62/0.87 => $true ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mIH,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( aElementOf0(W0,szNzAzT0)
% 0.62/0.87 => iLess0(W0,szszuzczcdt0(W0)) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mCardS,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( aSet0(W0)
% 0.62/0.87 => aElement0(sbrdtbr0(W0)) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mCardNum,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( aSet0(W0)
% 0.62/0.87 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
% 0.62/0.87 <=> isFinite0(W0) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mCardEmpty,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( aSet0(W0)
% 0.62/0.87 => ( sbrdtbr0(W0) = sz00
% 0.62/0.87 <=> W0 = slcrc0 ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mCardCons,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( ( aSet0(W0)
% 0.62/0.87 & isFinite0(W0) )
% 0.62/0.87 => ! [W1] :
% 0.62/0.87 ( aElement0(W1)
% 0.62/0.87 => ( ~ aElementOf0(W1,W0)
% 0.62/0.87 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mCardDiff,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( aSet0(W0)
% 0.62/0.87 => ! [W1] :
% 0.62/0.87 ( ( isFinite0(W0)
% 0.62/0.87 & aElementOf0(W1,W0) )
% 0.62/0.87 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mCardSub,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( aSet0(W0)
% 0.62/0.87 => ! [W1] :
% 0.62/0.87 ( ( isFinite0(W0)
% 0.62/0.87 & aSubsetOf0(W1,W0) )
% 0.62/0.87 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mCardSubEx,axiom,
% 0.62/0.87 ! [W0,W1] :
% 0.62/0.87 ( ( aSet0(W0)
% 0.62/0.87 & aElementOf0(W1,szNzAzT0) )
% 0.62/0.87 => ( ( isFinite0(W0)
% 0.62/0.87 & sdtlseqdt0(W1,sbrdtbr0(W0)) )
% 0.62/0.87 => ? [W2] :
% 0.62/0.87 ( aSubsetOf0(W2,W0)
% 0.62/0.87 & sbrdtbr0(W2) = W1 ) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mDefMin,definition,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.62/0.87 & W0 != slcrc0 )
% 0.62/0.87 => ! [W1] :
% 0.62/0.87 ( W1 = szmzizndt0(W0)
% 0.62/0.87 <=> ( aElementOf0(W1,W0)
% 0.62/0.87 & ! [W2] :
% 0.62/0.87 ( aElementOf0(W2,W0)
% 0.62/0.87 => sdtlseqdt0(W1,W2) ) ) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mDefMax,definition,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.62/0.87 & isFinite0(W0)
% 0.62/0.87 & W0 != slcrc0 )
% 0.62/0.87 => ! [W1] :
% 0.62/0.87 ( W1 = szmzazxdt0(W0)
% 0.62/0.87 <=> ( aElementOf0(W1,W0)
% 0.62/0.87 & ! [W2] :
% 0.62/0.87 ( aElementOf0(W2,W0)
% 0.62/0.87 => sdtlseqdt0(W2,W1) ) ) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mMinMin,axiom,
% 0.62/0.87 ! [W0,W1] :
% 0.62/0.87 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.62/0.87 & aSubsetOf0(W1,szNzAzT0)
% 0.62/0.87 & W0 != slcrc0
% 0.62/0.87 & W1 != slcrc0 )
% 0.62/0.87 => ( ( aElementOf0(szmzizndt0(W0),W1)
% 0.62/0.87 & aElementOf0(szmzizndt0(W1),W0) )
% 0.62/0.87 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mDefSeg,definition,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( aElementOf0(W0,szNzAzT0)
% 0.62/0.87 => ! [W1] :
% 0.62/0.87 ( W1 = slbdtrb0(W0)
% 0.62/0.87 <=> ( aSet0(W1)
% 0.62/0.87 & ! [W2] :
% 0.62/0.87 ( aElementOf0(W2,W1)
% 0.62/0.87 <=> ( aElementOf0(W2,szNzAzT0)
% 0.62/0.87 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mSegFin,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( aElementOf0(W0,szNzAzT0)
% 0.62/0.87 => isFinite0(slbdtrb0(W0)) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mSegZero,axiom,
% 0.62/0.87 slbdtrb0(sz00) = slcrc0 ).
% 0.62/0.87
% 0.62/0.87 fof(mSegSucc,axiom,
% 0.62/0.87 ! [W0,W1] :
% 0.62/0.87 ( ( aElementOf0(W0,szNzAzT0)
% 0.62/0.87 & aElementOf0(W1,szNzAzT0) )
% 0.62/0.87 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1)))
% 0.62/0.87 <=> ( aElementOf0(W0,slbdtrb0(W1))
% 0.62/0.87 | W0 = W1 ) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mSegLess,axiom,
% 0.62/0.87 ! [W0,W1] :
% 0.62/0.87 ( ( aElementOf0(W0,szNzAzT0)
% 0.62/0.87 & aElementOf0(W1,szNzAzT0) )
% 0.62/0.87 => ( sdtlseqdt0(W0,W1)
% 0.62/0.87 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mFinSubSeg,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( ( aSubsetOf0(W0,szNzAzT0)
% 0.62/0.87 & isFinite0(W0) )
% 0.62/0.87 => ? [W1] :
% 0.62/0.87 ( aElementOf0(W1,szNzAzT0)
% 0.62/0.87 & aSubsetOf0(W0,slbdtrb0(W1)) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mCardSeg,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( aElementOf0(W0,szNzAzT0)
% 0.62/0.87 => sbrdtbr0(slbdtrb0(W0)) = W0 ) ).
% 0.62/0.87
% 0.62/0.87 fof(mDefSel,definition,
% 0.62/0.87 ! [W0,W1] :
% 0.62/0.87 ( ( aSet0(W0)
% 0.62/0.87 & aElementOf0(W1,szNzAzT0) )
% 0.62/0.87 => ! [W2] :
% 0.62/0.87 ( W2 = slbdtsldtrb0(W0,W1)
% 0.62/0.87 <=> ( aSet0(W2)
% 0.62/0.87 & ! [W3] :
% 0.62/0.87 ( aElementOf0(W3,W2)
% 0.62/0.87 <=> ( aSubsetOf0(W3,W0)
% 0.62/0.87 & sbrdtbr0(W3) = W1 ) ) ) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mSelFSet,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( ( aSet0(W0)
% 0.62/0.87 & isFinite0(W0) )
% 0.62/0.87 => ! [W1] :
% 0.62/0.87 ( aElementOf0(W1,szNzAzT0)
% 0.62/0.87 => isFinite0(slbdtsldtrb0(W0,W1)) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mSelNSet,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( ( aSet0(W0)
% 0.62/0.87 & ~ isFinite0(W0) )
% 0.62/0.87 => ! [W1] :
% 0.62/0.87 ( aElementOf0(W1,szNzAzT0)
% 0.62/0.87 => slbdtsldtrb0(W0,W1) != slcrc0 ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(mSelCSet,axiom,
% 0.62/0.87 ! [W0] :
% 0.62/0.87 ( ( aSet0(W0)
% 0.62/0.87 & isCountable0(W0) )
% 0.62/0.87 => ! [W1] :
% 0.62/0.87 ( ( aElementOf0(W1,szNzAzT0)
% 0.62/0.87 & W1 != sz00 )
% 0.62/0.87 => isCountable0(slbdtsldtrb0(W0,W1)) ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2202,hypothesis,
% 0.62/0.87 aElementOf0(xk,szNzAzT0) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2202_02,hypothesis,
% 0.62/0.87 ( aSet0(xS)
% 0.62/0.87 & aSet0(xT)
% 0.62/0.87 & xk != sz00 ) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2227,hypothesis,
% 0.62/0.87 ( aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
% 0.62/0.87 & slbdtsldtrb0(xS,xk) != slcrc0 ) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2256,hypothesis,
% 0.62/0.87 aElementOf0(xx,xS) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2270,hypothesis,
% 0.62/0.87 aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2291,hypothesis,
% 0.62/0.87 ( aSet0(xQ)
% 0.62/0.87 & isFinite0(xQ)
% 0.62/0.87 & sbrdtbr0(xQ) = xk ) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2304,hypothesis,
% 0.62/0.87 ( aElement0(xy)
% 0.62/0.87 & aElementOf0(xy,xQ) ) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2323,hypothesis,
% 0.62/0.87 ~ aElementOf0(xx,xQ) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2338,hypothesis,
% 0.62/0.87 ~ aElementOf0(xx,xQ) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2357,hypothesis,
% 0.62/0.87 xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2411,hypothesis,
% 0.62/0.87 ( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
% 0.62/0.87 & szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk ) ).
% 0.62/0.87
% 0.62/0.87 fof(m__2431,hypothesis,
% 0.62/0.87 ( aSubsetOf0(xP,xS)
% 0.62/0.87 & sbrdtbr0(xP) = xk ) ).
% 0.62/0.87
% 0.62/0.87 fof(m__,conjecture,
% 0.62/0.87 aElementOf0(xP,slbdtsldtrb0(xS,xk)) ).
% 0.62/0.87
% 0.62/0.87 %------------------------------------------------------------------------------
% 0.62/0.87 %-------------------------------------------
% 0.62/0.87 % Proof found
% 0.62/0.87 % SZS status Theorem for theBenchmark
% 0.62/0.87 % SZS output start Proof
% 0.62/0.87 %ClaNum:173(EqnAxiom:48)
% 0.62/0.87 %VarNum:714(SingletonVarNum:218)
% 0.62/0.87 %MaxLitNum:8
% 0.62/0.87 %MaxfuncDepth:3
% 0.62/0.87 %SharedTerms:44
% 0.62/0.87 %goalClause: 74
% 0.62/0.87 %singleGoalClaCount:1
% 0.62/0.87 [52]P1(a21)
% 0.62/0.87 [53]P1(a26)
% 0.62/0.87 [54]P1(a27)
% 0.62/0.87 [55]P1(a1)
% 0.62/0.87 [56]P2(a28)
% 0.62/0.87 [57]P4(a19)
% 0.62/0.87 [58]P4(a1)
% 0.62/0.87 [59]P5(a21)
% 0.62/0.87 [60]P3(a15,a21)
% 0.62/0.87 [61]P3(a25,a21)
% 0.62/0.87 [62]P3(a29,a26)
% 0.62/0.87 [63]P3(a28,a1)
% 0.62/0.87 [64]P6(a14,a26)
% 0.62/0.87 [69]~E(a15,a25)
% 0.62/0.87 [72]~P3(a29,a1)
% 0.62/0.87 [49]E(f2(a1),a25)
% 0.62/0.87 [50]E(f2(a14),a25)
% 0.62/0.87 [51]E(f16(a15),a19)
% 0.62/0.87 [66]P3(a1,f20(a26,a25))
% 0.62/0.87 [68]P6(f20(a26,a25),f20(a27,a25))
% 0.62/0.87 [70]~E(f20(a26,a25),a19)
% 0.62/0.87 [73]~P3(a29,f17(a1,a28))
% 0.62/0.87 [74]~P3(a14,f20(a26,a25))
% 0.62/0.87 [65]E(f18(f17(a1,a28),a29),a14)
% 0.62/0.88 [67]E(f22(f2(f17(a1,a28))),a25)
% 0.62/0.88 [75]P1(x751)+~E(x751,a19)
% 0.62/0.88 [81]~P1(x811)+P6(x811,x811)
% 0.62/0.88 [88]~P3(x881,a21)+P8(a15,x881)
% 0.62/0.88 [94]P8(x941,x941)+~P3(x941,a21)
% 0.62/0.88 [79]~P1(x791)+P2(f2(x791))
% 0.62/0.88 [83]~P3(x831,a21)+~E(f22(x831),a15)
% 0.62/0.88 [84]~P3(x841,a21)+~E(f22(x841),x841)
% 0.62/0.88 [86]~P3(x861,a21)+P4(f16(x861))
% 0.62/0.88 [95]~P3(x951,a21)+P3(f22(x951),a21)
% 0.62/0.88 [96]~P3(x961,a21)+P8(x961,f22(x961))
% 0.62/0.88 [97]~P3(x971,a21)+P7(x971,f22(x971))
% 0.62/0.88 [105]~P3(x1051,a21)+~P8(f22(x1051),a15)
% 0.62/0.88 [87]~P3(x871,a21)+E(f2(f16(x871)),x871)
% 0.62/0.88 [82]~P3(x822,x821)+~E(x821,a19)
% 0.62/0.88 [78]~P1(x781)+~P5(x781)+~E(x781,a19)
% 0.62/0.88 [80]~P4(x801)+~P5(x801)+~P1(x801)
% 0.62/0.88 [76]~P1(x761)+~E(x761,a19)+E(f2(x761),a15)
% 0.62/0.88 [77]~P1(x771)+E(x771,a19)+~E(f2(x771),a15)
% 0.62/0.88 [85]~P1(x851)+P3(f3(x851),x851)+E(x851,a19)
% 0.62/0.88 [91]~P1(x911)+~P4(x911)+P3(f2(x911),a21)
% 0.62/0.88 [98]~P3(x981,a21)+E(x981,a15)+P3(f6(x981),a21)
% 0.62/0.88 [99]~P1(x991)+P4(x991)+~P3(f2(x991),a21)
% 0.62/0.88 [104]~P4(x1041)+~P6(x1041,a21)+P3(f4(x1041),a21)
% 0.62/0.88 [89]~P3(x891,a21)+E(x891,a15)+E(f22(f6(x891)),x891)
% 0.62/0.88 [114]~P4(x1141)+~P6(x1141,a21)+P6(x1141,f16(f4(x1141)))
% 0.62/0.88 [92]~P6(x921,x922)+P1(x921)+~P1(x922)
% 0.62/0.88 [93]~P3(x931,x932)+P2(x931)+~P1(x932)
% 0.62/0.88 [90]P1(x901)+~P3(x902,a21)+~E(x901,f16(x902))
% 0.62/0.88 [128]~P1(x1281)+~P3(x1282,x1281)+E(f18(f17(x1281,x1282),x1282),x1281)
% 0.62/0.88 [100]~P4(x1002)+~P6(x1001,x1002)+P4(x1001)+~P1(x1002)
% 0.62/0.88 [103]P3(x1032,x1031)+~E(x1032,f23(x1031))+~P6(x1031,a21)+E(x1031,a19)
% 0.62/0.88 [107]~P1(x1071)+~P2(x1072)+~P4(x1071)+P4(f18(x1071,x1072))
% 0.62/0.88 [108]~P1(x1081)+~P2(x1082)+~P4(x1081)+P4(f17(x1081,x1082))
% 0.62/0.88 [109]~P1(x1091)+~P2(x1092)+~P5(x1091)+P5(f18(x1091,x1092))
% 0.62/0.88 [110]~P1(x1101)+~P2(x1102)+~P5(x1101)+P5(f17(x1101,x1102))
% 0.62/0.88 [111]~P1(x1111)+P4(x1111)+~P3(x1112,a21)+~E(f20(x1111,x1112),a19)
% 0.62/0.88 [113]E(x1131,x1132)+~E(f22(x1131),f22(x1132))+~P3(x1132,a21)+~P3(x1131,a21)
% 0.62/0.88 [117]~P1(x1172)+~P4(x1172)+~P6(x1171,x1172)+P8(f2(x1171),f2(x1172))
% 0.62/0.88 [120]~P1(x1201)+~P4(x1201)+~P3(x1202,a21)+P4(f20(x1201,x1202))
% 0.62/0.88 [126]~P1(x1261)+~P1(x1262)+P6(x1261,x1262)+P3(f7(x1262,x1261),x1261)
% 0.62/0.88 [132]P8(x1321,x1322)+P8(f22(x1322),x1321)+~P3(x1322,a21)+~P3(x1321,a21)
% 0.62/0.88 [142]~P8(x1421,x1422)+~P3(x1422,a21)+~P3(x1421,a21)+P6(f16(x1421),f16(x1422))
% 0.62/0.88 [143]~P8(x1431,x1432)+~P3(x1432,a21)+~P3(x1431,a21)+P8(f22(x1431),f22(x1432))
% 0.62/0.88 [145]~P1(x1451)+~P1(x1452)+P6(x1451,x1452)+~P3(f7(x1452,x1451),x1452)
% 0.62/0.88 [147]P8(x1471,x1472)+~P3(x1472,a21)+~P3(x1471,a21)+~P6(f16(x1471),f16(x1472))
% 0.62/0.88 [148]P8(x1481,x1482)+~P3(x1482,a21)+~P3(x1481,a21)+~P8(f22(x1481),f22(x1482))
% 0.62/0.88 [127]P3(x1272,x1271)+~P1(x1271)+~P2(x1272)+E(f17(f18(x1271,x1272),x1272),x1271)
% 0.62/0.88 [134]~E(x1341,x1342)+~P3(x1342,a21)+~P3(x1341,a21)+P3(x1341,f16(f22(x1342)))
% 0.62/0.88 [153]~P3(x1532,a21)+~P3(x1531,a21)+~P3(x1531,f16(x1532))+P3(x1531,f16(f22(x1532)))
% 0.62/0.88 [152]~P1(x1521)+~P4(x1521)+~P3(x1522,x1521)+E(f22(f2(f17(x1521,x1522))),f2(x1521))
% 0.62/0.88 [124]~P1(x1242)+~P6(x1243,x1242)+P3(x1241,x1242)+~P3(x1241,x1243)
% 0.62/0.88 [101]~P1(x1012)+~P2(x1013)+P1(x1011)+~E(x1011,f18(x1012,x1013))
% 0.62/0.88 [102]~P1(x1022)+~P2(x1023)+P1(x1021)+~E(x1021,f17(x1022,x1023))
% 0.62/0.88 [112]~P1(x1122)+P1(x1121)+~P3(x1123,a21)+~E(x1121,f20(x1122,x1123))
% 0.62/0.88 [118]~P3(x1181,x1182)+~P3(x1183,a21)+P3(x1181,a21)+~E(x1182,f16(x1183))
% 0.62/0.88 [129]~P3(x1291,x1293)+~P3(x1292,a21)+P8(f22(x1291),x1292)+~E(x1293,f16(x1292))
% 0.62/0.88 [115]~P1(x1152)+~P1(x1151)+~P6(x1152,x1151)+~P6(x1151,x1152)+E(x1151,x1152)
% 0.62/0.88 [140]~P8(x1402,x1401)+~P8(x1401,x1402)+E(x1401,x1402)+~P3(x1402,a21)+~P3(x1401,a21)
% 0.62/0.88 [106]~P4(x1061)+P3(x1062,x1061)+~E(x1062,f24(x1061))+~P6(x1061,a21)+E(x1061,a19)
% 0.62/0.88 [123]~P1(x1232)+~P5(x1232)+~P3(x1231,a21)+E(x1231,a15)+P5(f20(x1232,x1231))
% 0.62/0.88 [144]~P3(x1442,x1441)+P3(f10(x1441,x1442),x1441)+~P6(x1441,a21)+E(x1441,a19)+E(x1442,f23(x1441))
% 0.62/0.88 [154]~P1(x1541)+~P4(x1541)+~P3(x1542,a21)+~P8(x1542,f2(x1541))+P6(f11(x1541,x1542),x1541)
% 0.62/0.88 [155]~P1(x1551)+P3(f13(x1552,x1551),x1551)+~P3(x1552,a21)+E(x1551,f16(x1552))+P3(f13(x1552,x1551),a21)
% 0.62/0.88 [156]~P3(x1562,x1561)+~P6(x1561,a21)+~P8(x1562,f10(x1561,x1562))+E(x1561,a19)+E(x1562,f23(x1561))
% 0.62/0.88 [133]P3(x1332,x1331)+~P1(x1331)+~P2(x1332)+~P4(x1331)+E(f2(f18(x1331,x1332)),f22(f2(x1331)))
% 0.62/0.88 [151]~P1(x1511)+~P4(x1511)+~P3(x1512,a21)+~P8(x1512,f2(x1511))+E(f2(f11(x1511,x1512)),x1512)
% 0.62/0.88 [157]E(x1571,x1572)+P3(x1571,f16(x1572))+~P3(x1572,a21)+~P3(x1571,a21)+~P3(x1571,f16(f22(x1572)))
% 0.62/0.88 [161]~P1(x1611)+P3(f13(x1612,x1611),x1611)+~P3(x1612,a21)+E(x1611,f16(x1612))+P8(f22(f13(x1612,x1611)),x1612)
% 0.62/0.88 [125]~P3(x1253,x1251)+P8(x1252,x1253)+~E(x1252,f23(x1251))+~P6(x1251,a21)+E(x1251,a19)
% 0.62/0.88 [146]P3(x1461,x1462)+~P3(x1463,a21)+~P3(x1461,a21)+~P8(f22(x1461),x1463)+~E(x1462,f16(x1463))
% 0.62/0.88 [119]~P1(x1194)+~P2(x1192)+~P3(x1191,x1193)+~E(x1191,x1192)+~E(x1193,f17(x1194,x1192))
% 0.62/0.88 [121]~P1(x1213)+~P2(x1214)+~P3(x1211,x1212)+P2(x1211)+~E(x1212,f18(x1213,x1214))
% 0.62/0.88 [122]~P1(x1223)+~P2(x1224)+~P3(x1221,x1222)+P2(x1221)+~E(x1222,f17(x1223,x1224))
% 0.62/0.88 [131]~P1(x1312)+~P2(x1314)+~P3(x1311,x1313)+P3(x1311,x1312)+~E(x1313,f17(x1312,x1314))
% 0.62/0.88 [136]~P1(x1364)+~P3(x1361,x1363)+~P3(x1362,a21)+E(f2(x1361),x1362)+~E(x1363,f20(x1364,x1362))
% 0.62/0.88 [141]~P1(x1412)+~P3(x1411,x1413)+P6(x1411,x1412)+~P3(x1414,a21)+~E(x1413,f20(x1412,x1414))
% 0.62/0.88 [150]~P4(x1501)+~P3(x1502,x1501)+P3(f12(x1501,x1502),x1501)+~P6(x1501,a21)+E(x1501,a19)+E(x1502,f24(x1501))
% 0.62/0.88 [159]~P4(x1591)+~P3(x1592,x1591)+~P6(x1591,a21)+~P8(f12(x1591,x1592),x1592)+E(x1591,a19)+E(x1592,f24(x1591))
% 0.62/0.88 [165]~P1(x1651)+~P3(x1652,a21)+~P3(f13(x1652,x1651),x1651)+E(x1651,f16(x1652))+~P3(f13(x1652,x1651),a21)+~P8(f22(f13(x1652,x1651)),x1652)
% 0.62/0.88 [137]~P1(x1372)+~P1(x1371)+~P6(x1373,x1372)+~P6(x1371,x1373)+P6(x1371,x1372)+~P1(x1373)
% 0.62/0.88 [160]~P8(x1601,x1603)+P8(x1601,x1602)+~P8(x1603,x1602)+~P3(x1602,a21)+~P3(x1603,a21)+~P3(x1601,a21)
% 0.62/0.88 [130]~P4(x1301)+~P3(x1302,x1301)+P8(x1302,x1303)+~E(x1303,f24(x1301))+~P6(x1301,a21)+E(x1301,a19)
% 0.62/0.88 [162]~P1(x1621)+~P1(x1622)+~P2(x1623)+P3(f8(x1622,x1623,x1621),x1621)+~E(f8(x1622,x1623,x1621),x1623)+E(x1621,f17(x1622,x1623))
% 0.62/0.88 [163]~P1(x1631)+~P1(x1632)+~P2(x1633)+P3(f9(x1632,x1633,x1631),x1631)+E(x1631,f18(x1632,x1633))+P2(f9(x1632,x1633,x1631))
% 0.62/0.88 [164]~P1(x1641)+~P1(x1642)+~P2(x1643)+P3(f8(x1642,x1643,x1641),x1641)+E(x1641,f17(x1642,x1643))+P2(f8(x1642,x1643,x1641))
% 0.62/0.88 [166]~P1(x1661)+~P1(x1662)+~P2(x1663)+P3(f8(x1662,x1663,x1661),x1661)+P3(f8(x1662,x1663,x1661),x1662)+E(x1661,f17(x1662,x1663))
% 0.62/0.88 [168]~P1(x1681)+~P1(x1682)+P3(f5(x1682,x1683,x1681),x1681)+P6(f5(x1682,x1683,x1681),x1682)+~P3(x1683,a21)+E(x1681,f20(x1682,x1683))
% 0.62/0.88 [167]~P1(x1671)+~P1(x1672)+P3(f5(x1672,x1673,x1671),x1671)+~P3(x1673,a21)+E(x1671,f20(x1672,x1673))+E(f2(f5(x1672,x1673,x1671)),x1673)
% 0.62/0.88 [116]~P1(x1164)+~P2(x1163)+~P2(x1161)+P3(x1161,x1162)+~E(x1161,x1163)+~E(x1162,f18(x1164,x1163))
% 0.62/0.88 [135]~P1(x1353)+~P2(x1352)+~P3(x1351,x1354)+E(x1351,x1352)+P3(x1351,x1353)+~E(x1354,f18(x1353,x1352))
% 0.62/0.88 [138]~P1(x1383)+~P2(x1384)+~P2(x1381)+~P3(x1381,x1383)+P3(x1381,x1382)+~E(x1382,f18(x1383,x1384))
% 0.62/0.88 [149]~P1(x1494)+~P6(x1491,x1494)+P3(x1491,x1492)+~P3(x1493,a21)+~E(x1492,f20(x1494,x1493))+~E(f2(x1491),x1493)
% 0.62/0.88 [158]E(f23(x1582),f23(x1581))+~P6(x1581,a21)+~P6(x1582,a21)+~P3(f23(x1581),x1582)+~P3(f23(x1582),x1581)+E(x1581,a19)+E(x1582,a19)
% 0.62/0.88 [169]~P1(x1691)+~P1(x1692)+~P2(x1693)+E(f9(x1692,x1693,x1691),x1693)+P3(f9(x1692,x1693,x1691),x1691)+P3(f9(x1692,x1693,x1691),x1692)+E(x1691,f18(x1692,x1693))
% 0.62/0.88 [170]~P1(x1701)+~P1(x1702)+~P2(x1703)+~E(f9(x1702,x1703,x1701),x1703)+~P3(f9(x1702,x1703,x1701),x1701)+E(x1701,f18(x1702,x1703))+~P2(f9(x1702,x1703,x1701))
% 0.62/0.88 [171]~P1(x1711)+~P1(x1712)+~P2(x1713)+~P3(f9(x1712,x1713,x1711),x1711)+~P3(f9(x1712,x1713,x1711),x1712)+E(x1711,f18(x1712,x1713))+~P2(f9(x1712,x1713,x1711))
% 0.62/0.88 [172]~P1(x1721)+~P1(x1722)+~P3(x1723,a21)+~P3(f5(x1722,x1723,x1721),x1721)+~P6(f5(x1722,x1723,x1721),x1722)+E(x1721,f20(x1722,x1723))+~E(f2(f5(x1722,x1723,x1721)),x1723)
% 0.62/0.88 [139]~P1(x1394)+~P2(x1392)+~P2(x1391)+~P3(x1391,x1394)+E(x1391,x1392)+P3(x1391,x1393)+~E(x1393,f17(x1394,x1392))
% 0.62/0.88 [173]~P1(x1731)+~P1(x1732)+~P2(x1733)+E(f8(x1732,x1733,x1731),x1733)+~P3(f8(x1732,x1733,x1731),x1731)+~P3(f8(x1732,x1733,x1731),x1732)+E(x1731,f17(x1732,x1733))+~P2(f8(x1732,x1733,x1731))
% 0.62/0.88 %EqnAxiom
% 0.62/0.88 [1]E(x11,x11)
% 0.62/0.88 [2]E(x22,x21)+~E(x21,x22)
% 0.62/0.88 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.62/0.88 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.62/0.88 [5]~E(x51,x52)+E(f8(x51,x53,x54),f8(x52,x53,x54))
% 0.62/0.88 [6]~E(x61,x62)+E(f8(x63,x61,x64),f8(x63,x62,x64))
% 0.62/0.88 [7]~E(x71,x72)+E(f8(x73,x74,x71),f8(x73,x74,x72))
% 0.62/0.88 [8]~E(x81,x82)+E(f16(x81),f16(x82))
% 0.62/0.88 [9]~E(x91,x92)+E(f17(x91,x93),f17(x92,x93))
% 0.62/0.88 [10]~E(x101,x102)+E(f17(x103,x101),f17(x103,x102))
% 0.62/0.88 [11]~E(x111,x112)+E(f18(x111,x113),f18(x112,x113))
% 0.62/0.88 [12]~E(x121,x122)+E(f18(x123,x121),f18(x123,x122))
% 0.62/0.88 [13]~E(x131,x132)+E(f20(x131,x133),f20(x132,x133))
% 0.62/0.88 [14]~E(x141,x142)+E(f20(x143,x141),f20(x143,x142))
% 0.62/0.88 [15]~E(x151,x152)+E(f13(x151,x153),f13(x152,x153))
% 0.62/0.88 [16]~E(x161,x162)+E(f13(x163,x161),f13(x163,x162))
% 0.62/0.88 [17]~E(x171,x172)+E(f11(x171,x173),f11(x172,x173))
% 0.62/0.88 [18]~E(x181,x182)+E(f11(x183,x181),f11(x183,x182))
% 0.62/0.88 [19]~E(x191,x192)+E(f22(x191),f22(x192))
% 0.62/0.88 [20]~E(x201,x202)+E(f9(x201,x203,x204),f9(x202,x203,x204))
% 0.62/0.88 [21]~E(x211,x212)+E(f9(x213,x211,x214),f9(x213,x212,x214))
% 0.62/0.88 [22]~E(x221,x222)+E(f9(x223,x224,x221),f9(x223,x224,x222))
% 0.62/0.88 [23]~E(x231,x232)+E(f23(x231),f23(x232))
% 0.62/0.88 [24]~E(x241,x242)+E(f4(x241),f4(x242))
% 0.62/0.88 [25]~E(x251,x252)+E(f12(x251,x253),f12(x252,x253))
% 0.62/0.88 [26]~E(x261,x262)+E(f12(x263,x261),f12(x263,x262))
% 0.62/0.88 [27]~E(x271,x272)+E(f24(x271),f24(x272))
% 0.62/0.88 [28]~E(x281,x282)+E(f5(x281,x283,x284),f5(x282,x283,x284))
% 0.62/0.88 [29]~E(x291,x292)+E(f5(x293,x291,x294),f5(x293,x292,x294))
% 0.62/0.88 [30]~E(x301,x302)+E(f5(x303,x304,x301),f5(x303,x304,x302))
% 0.62/0.88 [31]~E(x311,x312)+E(f10(x311,x313),f10(x312,x313))
% 0.62/0.88 [32]~E(x321,x322)+E(f10(x323,x321),f10(x323,x322))
% 0.62/0.88 [33]~E(x331,x332)+E(f6(x331),f6(x332))
% 0.62/0.88 [34]~E(x341,x342)+E(f7(x341,x343),f7(x342,x343))
% 0.62/0.88 [35]~E(x351,x352)+E(f7(x353,x351),f7(x353,x352))
% 0.62/0.88 [36]~E(x361,x362)+E(f3(x361),f3(x362))
% 0.62/0.88 [37]~P1(x371)+P1(x372)+~E(x371,x372)
% 0.62/0.88 [38]P3(x382,x383)+~E(x381,x382)+~P3(x381,x383)
% 0.62/0.88 [39]P3(x393,x392)+~E(x391,x392)+~P3(x393,x391)
% 0.62/0.88 [40]P6(x402,x403)+~E(x401,x402)+~P6(x401,x403)
% 0.62/0.88 [41]P6(x413,x412)+~E(x411,x412)+~P6(x413,x411)
% 0.62/0.88 [42]~P2(x421)+P2(x422)+~E(x421,x422)
% 0.62/0.88 [43]~P4(x431)+P4(x432)+~E(x431,x432)
% 0.62/0.88 [44]P8(x442,x443)+~E(x441,x442)+~P8(x441,x443)
% 0.62/0.88 [45]P8(x453,x452)+~E(x451,x452)+~P8(x453,x451)
% 0.62/0.88 [46]~P5(x461)+P5(x462)+~E(x461,x462)
% 0.62/0.88 [47]P7(x472,x473)+~E(x471,x472)+~P7(x471,x473)
% 0.62/0.88 [48]P7(x483,x482)+~E(x481,x482)+~P7(x483,x481)
% 0.62/0.88
% 0.62/0.88 %-------------------------------------------
% 0.62/0.88 cnf(177,plain,
% 0.62/0.88 (~P3(x1771,f16(a15))),
% 0.62/0.88 inference(scs_inference,[],[60,49,51,2,94,82])).
% 0.62/0.88 cnf(179,plain,
% 0.62/0.88 (P1(f16(a15))),
% 0.62/0.88 inference(scs_inference,[],[60,49,51,2,94,82,75])).
% 0.62/0.88 cnf(181,plain,
% 0.62/0.88 (~E(a21,f16(a15))),
% 0.62/0.88 inference(scs_inference,[],[60,49,51,2,94,82,75,39])).
% 0.62/0.88 cnf(182,plain,
% 0.62/0.88 (P3(f2(a1),a21)),
% 0.62/0.88 inference(scs_inference,[],[60,61,49,51,2,94,82,75,39,38])).
% 0.62/0.88 cnf(183,plain,
% 0.62/0.88 (P1(a19)),
% 0.62/0.88 inference(scs_inference,[],[60,61,49,51,2,94,82,75,39,38,37])).
% 0.62/0.88 cnf(185,plain,
% 0.62/0.88 (~P4(a21)),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80])).
% 0.62/0.88 cnf(187,plain,
% 0.62/0.88 (~P5(f16(a15))),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80,78])).
% 0.62/0.88 cnf(191,plain,
% 0.62/0.88 (P6(f16(a15),f16(a15))),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142])).
% 0.62/0.88 cnf(193,plain,
% 0.62/0.88 (P8(a15,a25)),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88])).
% 0.62/0.88 cnf(195,plain,
% 0.62/0.88 (P6(a21,a21)),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81])).
% 0.62/0.88 cnf(197,plain,
% 0.62/0.88 (~P8(f22(a15),a15)),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105])).
% 0.62/0.88 cnf(203,plain,
% 0.62/0.88 (P3(f22(a15),a21)),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95])).
% 0.62/0.88 cnf(207,plain,
% 0.62/0.88 (P4(f16(a15))),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86])).
% 0.62/0.88 cnf(209,plain,
% 0.62/0.88 (~E(f22(a15),a15)),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86,84])).
% 0.62/0.88 cnf(237,plain,
% 0.62/0.88 (E(f20(x2371,f2(a1)),f20(x2371,a25))),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86,84,83,79,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14])).
% 0.62/0.88 cnf(243,plain,
% 0.62/0.88 (E(f16(f2(a1)),f16(a25))),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86,84,83,79,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8])).
% 0.62/0.88 cnf(248,plain,
% 0.62/0.88 (~P8(f22(a15),f2(f16(a15)))),
% 0.62/0.88 inference(scs_inference,[],[52,59,60,61,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86,84,83,79,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,45])).
% 0.62/0.88 cnf(256,plain,
% 0.62/0.88 (P1(f16(f2(a1)))),
% 0.62/0.88 inference(scs_inference,[],[52,53,56,57,59,60,61,64,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86,84,83,79,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,45,44,43,42,93,92,90])).
% 0.62/0.88 cnf(258,plain,
% 0.62/0.88 (~P3(f2(a21),a21)),
% 0.62/0.88 inference(scs_inference,[],[52,53,56,57,59,60,61,64,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86,84,83,79,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,45,44,43,42,93,92,90,99])).
% 0.62/0.88 cnf(264,plain,
% 0.62/0.88 (E(f22(f6(f22(a15))),f22(a15))),
% 0.62/0.88 inference(scs_inference,[],[52,53,56,57,59,60,61,64,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86,84,83,79,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,45,44,43,42,93,92,90,99,98,91,89])).
% 0.62/0.88 cnf(266,plain,
% 0.62/0.88 (E(f18(f17(a21,a15),a15),a21)),
% 0.62/0.88 inference(scs_inference,[],[52,53,56,57,59,60,61,64,69,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86,84,83,79,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,45,44,43,42,93,92,90,99,98,91,89,128])).
% 0.62/0.88 cnf(288,plain,
% 0.62/0.88 (~P8(f22(f22(a15)),f22(a15))),
% 0.62/0.88 inference(scs_inference,[],[52,53,55,56,57,58,59,60,61,62,64,69,72,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86,84,83,79,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,45,44,43,42,93,92,90,99,98,91,89,128,124,100,118,112,120,111,110,109,108,107,148])).
% 0.62/0.88 cnf(290,plain,
% 0.62/0.88 (~P6(f16(f22(a15)),f16(a15))),
% 0.62/0.88 inference(scs_inference,[],[52,53,55,56,57,58,59,60,61,62,64,69,72,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86,84,83,79,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,45,44,43,42,93,92,90,99,98,91,89,128,124,100,118,112,120,111,110,109,108,107,148,147])).
% 0.62/0.88 cnf(296,plain,
% 0.62/0.88 (P8(f2(f16(a15)),f2(f16(a15)))),
% 0.62/0.88 inference(scs_inference,[],[52,53,55,56,57,58,59,60,61,62,64,69,72,49,51,2,94,82,75,39,38,37,3,80,78,143,142,88,81,105,97,96,95,87,86,84,83,79,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,45,44,43,42,93,92,90,99,98,91,89,128,124,100,118,112,120,111,110,109,108,107,148,147,145,126,117])).
% 0.62/0.88 cnf(337,plain,
% 0.62/0.88 (~P3(x3371,f16(a15))),
% 0.62/0.88 inference(rename_variables,[],[177])).
% 0.62/0.88 cnf(342,plain,
% 0.62/0.88 (E(f20(x3421,f2(a1)),f20(x3421,a25))),
% 0.62/0.88 inference(rename_variables,[],[237])).
% 0.62/0.88 cnf(352,plain,
% 0.62/0.88 (E(f20(x3521,f2(a1)),f20(x3521,a25))),
% 0.62/0.88 inference(rename_variables,[],[237])).
% 0.62/0.88 cnf(368,plain,
% 0.62/0.88 (P3(f2(f16(a15)),a21)),
% 0.62/0.88 inference(scs_inference,[],[54,63,58,62,53,69,59,51,55,57,61,56,52,60,181,237,342,177,209,288,290,179,187,191,207,203,183,185,193,129,113,127,140,141,46,93,128,100,112,111,108,123,155,82,41,40,80,91])).
% 0.62/0.88 cnf(378,plain,
% 0.62/0.88 (P8(f2(f16(a15)),a15)),
% 0.62/0.88 inference(scs_inference,[],[54,63,58,62,53,69,59,51,55,57,61,56,52,60,49,181,237,342,177,209,248,288,290,179,187,191,207,182,203,183,185,193,129,113,127,140,141,46,93,128,100,112,111,108,123,155,82,41,40,80,91,134,132,120,107,148])).
% 0.62/0.88 cnf(381,plain,
% 0.62/0.88 (~P3(x3811,f16(a15))),
% 0.62/0.88 inference(rename_variables,[],[177])).
% 0.62/0.88 cnf(389,plain,
% 0.62/0.88 (~P3(a14,f20(a26,f2(a1)))),
% 0.62/0.88 inference(scs_inference,[],[74,54,70,50,66,63,58,62,53,69,59,51,55,57,61,56,52,60,49,181,237,342,352,177,337,264,209,248,288,290,179,187,191,207,266,182,203,183,185,193,129,113,127,140,141,46,93,128,100,112,111,108,123,155,82,41,40,80,91,134,132,120,107,148,131,78,2,45,44,43,39])).
% 0.62/0.88 cnf(401,plain,
% 0.62/0.88 (~P3(x4011,f16(a15))),
% 0.62/0.88 inference(rename_variables,[],[177])).
% 0.62/0.88 cnf(412,plain,
% 0.62/0.88 (~P3(x4121,f16(a15))),
% 0.62/0.88 inference(rename_variables,[],[177])).
% 0.62/0.88 cnf(422,plain,
% 0.62/0.88 (P8(f2(f16(a15)),f2(a19))),
% 0.62/0.88 inference(scs_inference,[],[74,54,70,50,66,65,63,64,58,62,72,53,69,59,51,55,57,61,56,52,60,49,181,237,342,352,177,337,381,401,412,256,296,264,209,243,248,258,288,290,179,187,191,207,266,182,197,203,183,185,193,195,129,113,127,140,141,46,93,128,100,112,111,108,123,155,82,41,40,80,91,134,132,120,107,148,131,78,2,45,44,43,39,38,37,3,153,103,125,157,154,133,156,144,161,149,166,165,90,117])).
% 0.62/0.88 cnf(424,plain,
% 0.62/0.88 (~E(f2(a1),a15)),
% 0.62/0.88 inference(scs_inference,[],[74,54,70,50,66,65,63,64,58,62,72,53,69,59,51,55,57,61,56,52,60,49,181,237,342,352,177,337,381,401,412,256,296,264,209,243,248,258,288,290,179,187,191,207,266,182,197,203,183,185,193,195,129,113,127,140,141,46,93,128,100,112,111,108,123,155,82,41,40,80,91,134,132,120,107,148,131,78,2,45,44,43,39,38,37,3,153,103,125,157,154,133,156,144,161,149,166,165,90,117,77])).
% 0.62/0.88 cnf(462,plain,
% 0.62/0.88 ($false),
% 0.62/0.88 inference(scs_inference,[],[50,64,53,57,61,60,378,422,368,389,424,237,177,193,182,183,160,157,154,149]),
% 0.62/0.88 ['proof']).
% 0.62/0.88 % SZS output end Proof
% 0.62/0.88 % Total time :0.170000s
%------------------------------------------------------------------------------