TSTP Solution File: RNG049+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : RNG049+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 : n004.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 13:47:54 EDT 2023
% Result : Theorem 1.07s 1.15s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG049+1 : 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
% 0.13/0.34 % Computer : n004.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 : Sun Aug 27 02:23:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 1.07/1.14 %-------------------------------------------
% 1.07/1.14 % File :CSE---1.6
% 1.07/1.14 % Problem :theBenchmark
% 1.07/1.14 % Transform :cnf
% 1.07/1.14 % Format :tptp:raw
% 1.07/1.14 % Command :java -jar mcs_scs.jar %d %s
% 1.07/1.14
% 1.07/1.14 % Result :Theorem 0.510000s
% 1.07/1.14 % Output :CNFRefutation 0.510000s
% 1.07/1.14 %-------------------------------------------
% 1.07/1.14 %------------------------------------------------------------------------------
% 1.07/1.14 % File : RNG049+1 : TPTP v8.1.2. Released v4.0.0.
% 1.07/1.14 % Domain : Ring Theory
% 1.07/1.14 % Problem : Cauchy-Bouniakowsky-Schwarz inequality 04_03, 00 expansion
% 1.07/1.14 % Version : Especial.
% 1.07/1.14 % English :
% 1.07/1.14
% 1.07/1.14 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 1.07/1.14 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 1.07/1.14 % Source : [Pas08]
% 1.07/1.14 % Names : cauchy_04_03.00 [Pas08]
% 1.07/1.14
% 1.07/1.14 % Status : Theorem
% 1.07/1.14 % Rating : 0.36 v8.1.0, 0.33 v7.5.0, 0.38 v7.4.0, 0.27 v7.3.0, 0.34 v7.2.0, 0.31 v7.1.0, 0.30 v6.4.0, 0.35 v6.3.0, 0.29 v6.2.0, 0.40 v6.1.0, 0.53 v6.0.0, 0.48 v5.5.0, 0.67 v5.4.0, 0.71 v5.3.0, 0.70 v5.2.0, 0.55 v5.1.0, 0.62 v5.0.0, 0.71 v4.1.0, 0.74 v4.0.1, 0.87 v4.0.0
% 1.07/1.14 % Syntax : Number of formulae : 42 ( 6 unt; 1 def)
% 1.07/1.14 % Number of atoms : 156 ( 42 equ)
% 1.07/1.14 % Maximal formula atoms : 9 ( 3 avg)
% 1.07/1.14 % Number of connectives : 120 ( 6 ~; 1 |; 61 &)
% 1.07/1.14 % ( 1 <=>; 51 =>; 0 <=; 0 <~>)
% 1.07/1.14 % Maximal formula depth : 10 ( 5 avg)
% 1.07/1.14 % Maximal term depth : 5 ( 1 avg)
% 1.07/1.14 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% 1.07/1.14 % Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% 1.07/1.14 % Number of variables : 69 ( 68 !; 1 ?)
% 1.07/1.14 % SPC : FOF_THM_RFO_SEQ
% 1.07/1.14
% 1.07/1.14 % Comments : Problem generated by the SAD system [VLP07]
% 1.07/1.14 %------------------------------------------------------------------------------
% 1.07/1.14 fof(mNatSort,axiom,
% 1.07/1.14 ! [W0] :
% 1.07/1.14 ( aNaturalNumber0(W0)
% 1.07/1.14 => $true ) ).
% 1.07/1.14
% 1.07/1.14 fof(mZeroNat,axiom,
% 1.07/1.14 aNaturalNumber0(sz00) ).
% 1.07/1.14
% 1.07/1.14 fof(mSuccNat,axiom,
% 1.07/1.14 ! [W0] :
% 1.07/1.14 ( aNaturalNumber0(W0)
% 1.07/1.14 => ( aNaturalNumber0(szszuzczcdt0(W0))
% 1.07/1.14 & szszuzczcdt0(W0) != sz00 ) ) ).
% 1.07/1.14
% 1.07/1.14 fof(mNatExtr,axiom,
% 1.07/1.14 ! [W0] :
% 1.07/1.14 ( ( aNaturalNumber0(W0)
% 1.07/1.14 & W0 != sz00 )
% 1.07/1.14 => ? [W1] :
% 1.07/1.14 ( aNaturalNumber0(W1)
% 1.07/1.14 & W0 = szszuzczcdt0(W1) ) ) ).
% 1.07/1.14
% 1.07/1.14 fof(mSuccEqu,axiom,
% 1.07/1.14 ! [W0,W1] :
% 1.07/1.14 ( ( aNaturalNumber0(W0)
% 1.07/1.14 & aNaturalNumber0(W1) )
% 1.07/1.14 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
% 1.07/1.14 => W0 = W1 ) ) ).
% 1.07/1.14
% 1.07/1.14 fof(mIHOrd,axiom,
% 1.07/1.14 ! [W0,W1] :
% 1.07/1.14 ( ( aNaturalNumber0(W0)
% 1.07/1.14 & aNaturalNumber0(W1) )
% 1.07/1.14 => ( iLess0(W0,W1)
% 1.07/1.14 => $true ) ) ).
% 1.07/1.14
% 1.07/1.14 fof(mIH,axiom,
% 1.07/1.14 ! [W0] :
% 1.07/1.14 ( aNaturalNumber0(W0)
% 1.07/1.14 => iLess0(W0,szszuzczcdt0(W0)) ) ).
% 1.07/1.14
% 1.07/1.14 fof(mScSort,axiom,
% 1.07/1.14 ! [W0] :
% 1.07/1.14 ( aScalar0(W0)
% 1.07/1.14 => $true ) ).
% 1.07/1.14
% 1.07/1.14 fof(mSZeroSc,axiom,
% 1.07/1.14 aScalar0(sz0z00) ).
% 1.07/1.14
% 1.07/1.14 fof(mSumSc,axiom,
% 1.07/1.14 ! [W0,W1] :
% 1.07/1.14 ( ( aScalar0(W0)
% 1.07/1.14 & aScalar0(W1) )
% 1.07/1.14 => aScalar0(sdtpldt0(W0,W1)) ) ).
% 1.07/1.14
% 1.07/1.14 fof(mMulSc,axiom,
% 1.07/1.14 ! [W0,W1] :
% 1.07/1.14 ( ( aScalar0(W0)
% 1.07/1.14 & aScalar0(W1) )
% 1.07/1.14 => aScalar0(sdtasdt0(W0,W1)) ) ).
% 1.07/1.14
% 1.07/1.14 fof(mNegSc,axiom,
% 1.07/1.14 ! [W0] :
% 1.07/1.14 ( aScalar0(W0)
% 1.07/1.14 => aScalar0(smndt0(W0)) ) ).
% 1.07/1.14
% 1.07/1.14 fof(mScZero,axiom,
% 1.07/1.14 ! [W0] :
% 1.07/1.14 ( aScalar0(W0)
% 1.07/1.14 => ( sdtpldt0(W0,sz0z00) = W0
% 1.07/1.14 & sdtpldt0(sz0z00,W0) = W0
% 1.07/1.14 & sdtasdt0(W0,sz0z00) = sz0z00
% 1.07/1.14 & sdtasdt0(sz0z00,W0) = sz0z00
% 1.07/1.14 & sdtpldt0(W0,smndt0(W0)) = sz0z00
% 1.07/1.14 & sdtpldt0(smndt0(W0),W0) = sz0z00
% 1.07/1.14 & smndt0(smndt0(W0)) = W0
% 1.07/1.14 & smndt0(sz0z00) = sz0z00 ) ) ).
% 1.07/1.14
% 1.07/1.14 fof(mArith,axiom,
% 1.07/1.14 ! [W0,W1,W2] :
% 1.07/1.14 ( ( aScalar0(W0)
% 1.07/1.14 & aScalar0(W1)
% 1.07/1.14 & aScalar0(W2) )
% 1.07/1.14 => ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2))
% 1.07/1.14 & sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
% 1.07/1.14 & sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
% 1.07/1.14 & sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ).
% 1.07/1.14
% 1.07/1.14 fof(mDistr,axiom,
% 1.07/1.14 ! [W0,W1,W2] :
% 1.07/1.14 ( ( aScalar0(W0)
% 1.07/1.14 & aScalar0(W1)
% 1.07/1.14 & aScalar0(W2) )
% 1.07/1.14 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 1.07/1.14 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ).
% 1.07/1.14
% 1.07/1.14 fof(mDistr2,axiom,
% 1.07/1.14 ! [W0,W1,W2,W3] :
% 1.07/1.14 ( ( aScalar0(W0)
% 1.07/1.14 & aScalar0(W1)
% 1.07/1.15 & aScalar0(W2)
% 1.07/1.15 & aScalar0(W3) )
% 1.07/1.15 => sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mMNeg,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aScalar0(W0)
% 1.07/1.15 & aScalar0(W1) )
% 1.07/1.15 => ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1))
% 1.07/1.15 & sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mMDNeg,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aScalar0(W0)
% 1.07/1.15 & aScalar0(W1) )
% 1.07/1.15 => sdtasdt0(smndt0(W0),smndt0(W1)) = sdtasdt0(W0,W1) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mLess,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aScalar0(W0)
% 1.07/1.15 & aScalar0(W1) )
% 1.07/1.15 => ( sdtlseqdt0(W0,W1)
% 1.07/1.15 => $true ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mLERef,axiom,
% 1.07/1.15 ! [W0] :
% 1.07/1.15 ( aScalar0(W0)
% 1.07/1.15 => sdtlseqdt0(W0,W0) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mLEASm,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aScalar0(W0)
% 1.07/1.15 & aScalar0(W1) )
% 1.07/1.15 => ( ( sdtlseqdt0(W0,W1)
% 1.07/1.15 & sdtlseqdt0(W1,W0) )
% 1.07/1.15 => W0 = W1 ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mLETrn,axiom,
% 1.07/1.15 ! [W0,W1,W2] :
% 1.07/1.15 ( ( aScalar0(W0)
% 1.07/1.15 & aScalar0(W1)
% 1.07/1.15 & aScalar0(W2) )
% 1.07/1.15 => ( ( sdtlseqdt0(W0,W1)
% 1.07/1.15 & sdtlseqdt0(W1,W2) )
% 1.07/1.15 => sdtlseqdt0(W0,W2) ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mLEMon,axiom,
% 1.07/1.15 ! [W0,W1,W2,W3] :
% 1.07/1.15 ( ( aScalar0(W0)
% 1.07/1.15 & aScalar0(W1)
% 1.07/1.15 & aScalar0(W2)
% 1.07/1.15 & aScalar0(W3) )
% 1.07/1.15 => ( ( sdtlseqdt0(W0,W1)
% 1.07/1.15 & sdtlseqdt0(W2,W3) )
% 1.07/1.15 => sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mLEMonM,axiom,
% 1.07/1.15 ! [W0,W1,W2,W3] :
% 1.07/1.15 ( ( aScalar0(W0)
% 1.07/1.15 & aScalar0(W1)
% 1.07/1.15 & aScalar0(W2)
% 1.07/1.15 & aScalar0(W3) )
% 1.07/1.15 => ( ( sdtlseqdt0(W0,W1)
% 1.07/1.15 & sdtlseqdt0(sz0z00,W2)
% 1.07/1.15 & sdtlseqdt0(W2,W3) )
% 1.07/1.15 => sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mLETot,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aScalar0(W0)
% 1.07/1.15 & aScalar0(W1) )
% 1.07/1.15 => ( sdtlseqdt0(W0,W1)
% 1.07/1.15 | sdtlseqdt0(W1,W0) ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mPosMon,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aScalar0(W0)
% 1.07/1.15 & aScalar0(W1) )
% 1.07/1.15 => ( ( sdtlseqdt0(sz0z00,W0)
% 1.07/1.15 & sdtlseqdt0(sz0z00,W1) )
% 1.07/1.15 => ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
% 1.07/1.15 & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mSqPos,axiom,
% 1.07/1.15 ! [W0] :
% 1.07/1.15 ( aScalar0(W0)
% 1.07/1.15 => sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mSqrt,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aScalar0(W0)
% 1.07/1.15 & aScalar0(W1) )
% 1.07/1.15 => ( ( sdtlseqdt0(sz0z00,W0)
% 1.07/1.15 & sdtlseqdt0(sz0z00,W1)
% 1.07/1.15 & sdtasdt0(W0,W0) = sdtasdt0(W1,W1) )
% 1.07/1.15 => W0 = W1 ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mVcSort,axiom,
% 1.07/1.15 ! [W0] :
% 1.07/1.15 ( aVector0(W0)
% 1.07/1.15 => $true ) ).
% 1.07/1.15
% 1.07/1.15 fof(mDimNat,axiom,
% 1.07/1.15 ! [W0] :
% 1.07/1.15 ( aVector0(W0)
% 1.07/1.15 => aNaturalNumber0(aDimensionOf0(W0)) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mElmSc,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aVector0(W0)
% 1.07/1.15 & aNaturalNumber0(W1) )
% 1.07/1.15 => aScalar0(sdtlbdtrb0(W0,W1)) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mDefInit,definition,
% 1.07/1.15 ! [W0] :
% 1.07/1.15 ( aVector0(W0)
% 1.07/1.15 => ( aDimensionOf0(W0) != sz00
% 1.07/1.15 => ! [W1] :
% 1.07/1.15 ( W1 = sziznziztdt0(W0)
% 1.07/1.15 <=> ( aVector0(W1)
% 1.07/1.15 & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
% 1.07/1.15 & ! [W2] :
% 1.07/1.15 ( aNaturalNumber0(W2)
% 1.07/1.15 => sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mEqInit,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aVector0(W0)
% 1.07/1.15 & aVector0(W1) )
% 1.07/1.15 => ( ( aDimensionOf0(W0) = aDimensionOf0(W1)
% 1.07/1.15 & aDimensionOf0(W1) != sz00 )
% 1.07/1.15 => aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mScPr,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aVector0(W0)
% 1.07/1.15 & aVector0(W1) )
% 1.07/1.15 => ( aDimensionOf0(W0) = aDimensionOf0(W1)
% 1.07/1.15 => aScalar0(sdtasasdt0(W0,W1)) ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mDefSPZ,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aVector0(W0)
% 1.07/1.15 & aVector0(W1) )
% 1.07/1.15 => ( ( aDimensionOf0(W0) = aDimensionOf0(W1)
% 1.07/1.15 & aDimensionOf0(W1) = sz00 )
% 1.07/1.15 => sdtasasdt0(W0,W1) = sz0z00 ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(mDefSPN,axiom,
% 1.07/1.15 ! [W0,W1] :
% 1.07/1.15 ( ( aVector0(W0)
% 1.07/1.15 & aVector0(W1) )
% 1.07/1.15 => ( ( aDimensionOf0(W0) = aDimensionOf0(W1)
% 1.07/1.15 & aDimensionOf0(W1) != sz00 )
% 1.07/1.15 => sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(m__1542,hypothesis,
% 1.07/1.15 aVector0(xs) ).
% 1.07/1.15
% 1.07/1.15 fof(m__1516,hypothesis,
% 1.07/1.15 ! [W0] :
% 1.07/1.15 ( aVector0(W0)
% 1.07/1.15 => ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
% 1.07/1.15 => sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ) ).
% 1.07/1.15
% 1.07/1.15 fof(m__1542_01,hypothesis,
% 1.07/1.15 aDimensionOf0(xs) != sz00 ).
% 1.07/1.15
% 1.07/1.15 fof(m__1568,hypothesis,
% 1.07/1.15 sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ).
% 1.07/1.15
% 1.07/1.15 fof(m__1590,hypothesis,
% 1.07/1.15 ( sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
% 1.07/1.15 & sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ).
% 1.07/1.15
% 1.07/1.15 fof(m__,conjecture,
% 1.07/1.15 sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ).
% 1.07/1.15
% 1.07/1.15 %------------------------------------------------------------------------------
% 1.07/1.15 %-------------------------------------------
% 1.07/1.15 % Proof found
% 1.07/1.15 % SZS status Theorem for theBenchmark
% 1.07/1.15 % SZS output start Proof
% 1.07/1.15 %ClaNum:82(EqnAxiom:25)
% 1.07/1.15 %VarNum:297(SingletonVarNum:94)
% 1.07/1.15 %MaxLitNum:8
% 1.07/1.15 %MaxfuncDepth:4
% 1.07/1.15 %SharedTerms:20
% 1.07/1.15 %goalClause: 33
% 1.07/1.15 %singleGoalClaCount:1
% 1.07/1.15 [26]P1(a1)
% 1.07/1.15 [27]P2(a10)
% 1.07/1.15 [28]P3(a11)
% 1.07/1.15 [32]~E(f3(a11),a1)
% 1.07/1.15 [33]~P4(a10,f2(a11,a11))
% 1.07/1.15 [29]P4(a10,f2(f12(a11),f12(a11)))
% 1.07/1.15 [30]P4(a10,f7(f6(a11,f3(a11)),f6(a11,f3(a11))))
% 1.07/1.15 [31]E(f8(f2(f12(a11),f12(a11)),f7(f6(a11,f3(a11)),f6(a11,f3(a11)))),f2(a11,a11))
% 1.07/1.15 [46]~P2(x461)+P4(x461,x461)
% 1.07/1.15 [34]~P2(x341)+E(f9(a10),a10)
% 1.07/1.15 [35]~P1(x351)+~E(f13(x351),a1)
% 1.07/1.15 [36]~P1(x361)+P1(f13(x361))
% 1.07/1.15 [37]~P3(x371)+P1(f3(x371))
% 1.07/1.15 [38]~P2(x381)+P2(f9(x381))
% 1.07/1.15 [41]~P2(x411)+E(f7(x411,a10),a10)
% 1.07/1.15 [42]~P2(x421)+E(f7(a10,x421),a10)
% 1.07/1.15 [44]~P2(x441)+E(f8(x441,a10),x441)
% 1.07/1.15 [45]~P2(x451)+E(f8(a10,x451),x451)
% 1.07/1.15 [50]~P1(x501)+P5(x501,f13(x501))
% 1.07/1.15 [57]~P2(x571)+P4(a10,f7(x571,x571))
% 1.07/1.15 [39]~P2(x391)+E(f9(f9(x391)),x391)
% 1.07/1.15 [48]~P2(x481)+E(f8(x481,f9(x481)),a10)
% 1.07/1.15 [49]~P2(x491)+E(f8(f9(x491),x491),a10)
% 1.07/1.15 [40]~P1(x401)+E(x401,a1)+P1(f4(x401))
% 1.07/1.15 [70]~P3(x701)+~P5(f3(x701),f3(a11))+P4(a10,f2(x701,x701))
% 1.07/1.15 [43]~P1(x431)+E(x431,a1)+E(f13(f4(x431)),x431)
% 1.07/1.15 [54]~P2(x542)+~P2(x541)+P2(f8(x541,x542))
% 1.07/1.15 [55]~P2(x552)+~P2(x551)+P2(f7(x551,x552))
% 1.07/1.15 [56]~P1(x562)+~P3(x561)+P2(f6(x561,x562))
% 1.07/1.15 [62]~P2(x622)+~P2(x621)+E(f7(f9(x621),f9(x622)),f7(x621,x622))
% 1.07/1.15 [66]~P2(x662)+~P2(x661)+E(f9(f7(x661,x662)),f7(x661,f9(x662)))
% 1.07/1.15 [67]~P2(x672)+~P2(x671)+E(f9(f7(x671,x672)),f7(f9(x671),x672))
% 1.07/1.15 [53]P4(x532,x531)+~P2(x531)+~P2(x532)+P4(x531,x532)
% 1.07/1.15 [47]~P3(x471)+P3(x472)+~E(x472,f12(x471))+E(f3(x471),a1)
% 1.07/1.15 [51]~P1(x512)+~P1(x511)+E(x511,x512)+~E(f13(x511),f13(x512))
% 1.07/1.15 [64]~P3(x642)+~P3(x641)+~E(f3(x641),f3(x642))+P2(f2(x641,x642))
% 1.07/1.15 [52]~P3(x521)+~E(x522,f12(x521))+E(f3(x521),a1)+E(f13(f3(x522)),f3(x521))
% 1.07/1.15 [59]~P2(x592)+~P2(x591)+~P2(x593)+E(f8(x591,x592),f8(x592,x591))
% 1.07/1.15 [60]~P2(x602)+~P2(x601)+~P2(x603)+E(f7(x601,x602),f7(x602,x601))
% 1.07/1.15 [73]~P2(x733)+~P2(x732)+~P2(x731)+E(f8(f8(x731,x732),x733),f8(x731,f8(x732,x733)))
% 1.07/1.15 [74]~P2(x743)+~P2(x742)+~P2(x741)+E(f7(f7(x741,x742),x743),f7(x741,f7(x742,x743)))
% 1.07/1.15 [76]~P2(x763)+~P2(x762)+~P2(x761)+E(f8(f7(x761,x762),f7(x761,x763)),f7(x761,f8(x762,x763)))
% 1.07/1.15 [77]~P2(x772)+~P2(x773)+~P2(x771)+E(f8(f7(x771,x772),f7(x773,x772)),f7(f8(x771,x773),x772))
% 1.07/1.15 [65]~P2(x652)+~P2(x651)+~P4(x652,x651)+~P4(x651,x652)+E(x651,x652)
% 1.07/1.15 [58]~P3(x582)+~P3(x581)+~E(f3(x581),f3(x582))+~E(f3(x582),a1)+E(f2(x581,x582),a10)
% 1.07/1.15 [71]~P2(x712)+~P2(x711)+~P4(a10,x712)+~P4(a10,x711)+P4(a10,f8(x711,x712))
% 1.07/1.15 [72]~P2(x722)+~P2(x721)+~P4(a10,x722)+~P4(a10,x721)+P4(a10,f7(x721,x722))
% 1.07/1.15 [61]~P3(x611)+~P3(x612)+~E(f3(x612),f3(x611))+E(f3(x611),a1)+E(f3(f12(x612)),f3(f12(x611)))
% 1.07/1.15 [81]~P3(x811)+~P3(x812)+~E(f3(x812),f3(x811))+E(f3(x811),a1)+E(f8(f2(f12(x812),f12(x811)),f7(f6(x812,f3(x812)),f6(x811,f3(x811)))),f2(x812,x811))
% 1.07/1.15 [63]~P1(x633)+~P3(x631)+~E(x632,f12(x631))+E(f6(x632,x633),f6(x631,x633))+E(f3(x631),a1)
% 1.07/1.15 [82]~P2(x823)+~P2(x822)+~P2(x824)+~P2(x821)+E(f8(f8(f7(x821,x822),f7(x821,x823)),f8(f7(x824,x822),f7(x824,x823))),f7(f8(x821,x824),f8(x822,x823)))
% 1.07/1.15 [75]~P2(x752)+~P2(x751)+E(x751,x752)+~E(f7(x751,x751),f7(x752,x752))+~P4(a10,x752)+~P4(a10,x751)
% 1.07/1.15 [68]~P3(x681)+~P3(x682)+E(x681,f12(x682))+E(f3(x682),a1)+P1(f5(x682,x681))+~E(f13(f3(x681)),f3(x682))
% 1.07/1.15 [80]~P3(x802)+~P3(x801)+E(x801,f12(x802))+E(f3(x802),a1)+~E(f13(f3(x801)),f3(x802))+~E(f6(x801,f5(x802,x801)),f6(x802,f5(x802,x801)))
% 1.07/1.15 [69]~P2(x692)+~P2(x691)+~P4(x693,x692)+~P4(x691,x693)+P4(x691,x692)+~P2(x693)
% 1.07/1.15 [78]~P2(x784)+~P2(x782)+~P2(x783)+~P2(x781)+~P4(x782,x784)+~P4(x781,x783)+P4(f8(x781,x782),f8(x783,x784))
% 1.07/1.15 [79]~P2(x794)+~P2(x792)+~P2(x793)+~P2(x791)+~P4(x792,x794)+~P4(x791,x793)+~P4(a10,x792)+P4(f7(x791,x792),f7(x793,x794))
% 1.07/1.15 %EqnAxiom
% 1.07/1.15 [1]E(x11,x11)
% 1.07/1.15 [2]E(x22,x21)+~E(x21,x22)
% 1.07/1.15 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.07/1.15 [4]~E(x41,x42)+E(f12(x41),f12(x42))
% 1.07/1.15 [5]~E(x51,x52)+E(f7(x51,x53),f7(x52,x53))
% 1.07/1.15 [6]~E(x61,x62)+E(f7(x63,x61),f7(x63,x62))
% 1.07/1.15 [7]~E(x71,x72)+E(f2(x71,x73),f2(x72,x73))
% 1.07/1.15 [8]~E(x81,x82)+E(f2(x83,x81),f2(x83,x82))
% 1.07/1.15 [9]~E(x91,x92)+E(f3(x91),f3(x92))
% 1.07/1.15 [10]~E(x101,x102)+E(f6(x101,x103),f6(x102,x103))
% 1.07/1.15 [11]~E(x111,x112)+E(f6(x113,x111),f6(x113,x112))
% 1.07/1.15 [12]~E(x121,x122)+E(f8(x121,x123),f8(x122,x123))
% 1.07/1.15 [13]~E(x131,x132)+E(f8(x133,x131),f8(x133,x132))
% 1.07/1.15 [14]~E(x141,x142)+E(f9(x141),f9(x142))
% 1.07/1.15 [15]~E(x151,x152)+E(f13(x151),f13(x152))
% 1.07/1.15 [16]~E(x161,x162)+E(f4(x161),f4(x162))
% 1.07/1.15 [17]~E(x171,x172)+E(f5(x171,x173),f5(x172,x173))
% 1.07/1.15 [18]~E(x181,x182)+E(f5(x183,x181),f5(x183,x182))
% 1.07/1.15 [19]~P1(x191)+P1(x192)+~E(x191,x192)
% 1.07/1.15 [20]~P2(x201)+P2(x202)+~E(x201,x202)
% 1.07/1.15 [21]~P3(x211)+P3(x212)+~E(x211,x212)
% 1.07/1.15 [22]P4(x222,x223)+~E(x221,x222)+~P4(x221,x223)
% 1.07/1.15 [23]P4(x233,x232)+~E(x231,x232)+~P4(x233,x231)
% 1.07/1.15 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243)
% 1.07/1.15 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251)
% 1.07/1.15
% 1.07/1.15 %-------------------------------------------
% 1.07/1.15 cnf(83,plain,
% 1.07/1.15 (E(f2(a11,a11),f8(f2(f12(a11),f12(a11)),f7(f6(a11,f3(a11)),f6(a11,f3(a11)))))),
% 1.07/1.15 inference(scs_inference,[],[31,2])).
% 1.07/1.15 cnf(84,plain,
% 1.07/1.15 (~E(f2(f12(a11),f12(a11)),f2(a11,a11))),
% 1.07/1.15 inference(scs_inference,[],[33,29,31,2,23])).
% 1.07/1.15 cnf(85,plain,
% 1.07/1.15 (~E(f2(f12(a11),f12(a11)),f8(f2(f12(a11),f12(a11)),f7(f6(a11,f3(a11)),f6(a11,f3(a11)))))),
% 1.07/1.15 inference(scs_inference,[],[33,29,31,2,23,3])).
% 1.07/1.15 cnf(86,plain,
% 1.07/1.15 (~P5(f3(a11),f3(a11))),
% 1.07/1.15 inference(scs_inference,[],[33,28,29,31,2,23,3,70])).
% 1.07/1.15 cnf(88,plain,
% 1.07/1.15 (P4(a10,a10)),
% 1.07/1.15 inference(scs_inference,[],[33,27,28,29,31,2,23,3,70,53])).
% 1.07/1.15 cnf(90,plain,
% 1.07/1.15 (P4(f7(a10,a10),f7(a10,a10))),
% 1.07/1.15 inference(scs_inference,[],[33,27,28,29,31,2,23,3,70,53,79])).
% 1.07/1.15 cnf(91,plain,
% 1.07/1.15 (E(f9(a10),a10)),
% 1.07/1.15 inference(scs_inference,[],[33,27,28,29,31,2,23,3,70,53,79,34])).
% 1.07/1.16 cnf(95,plain,
% 1.07/1.16 (E(f8(a10,a10),a10)),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45])).
% 1.07/1.16 cnf(97,plain,
% 1.07/1.16 (E(f7(a10,a10),a10)),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42])).
% 1.07/1.16 cnf(99,plain,
% 1.07/1.16 (E(f9(f9(a10)),a10)),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39])).
% 1.07/1.16 cnf(101,plain,
% 1.07/1.16 (P2(f9(a10))),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38])).
% 1.07/1.16 cnf(103,plain,
% 1.07/1.16 (P1(f3(a11))),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38,37])).
% 1.07/1.16 cnf(105,plain,
% 1.07/1.16 (P1(f13(a1))),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38,37,36])).
% 1.07/1.16 cnf(107,plain,
% 1.07/1.16 (~E(f13(a1),a1)),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38,37,36,35])).
% 1.07/1.16 cnf(114,plain,
% 1.07/1.16 (E(f8(x1141,f9(a10)),f8(x1141,a10))),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38,37,36,35,18,17,16,15,14,13])).
% 1.07/1.16 cnf(115,plain,
% 1.07/1.16 (E(f8(f9(a10),x1151),f8(a10,x1151))),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38,37,36,35,18,17,16,15,14,13,12])).
% 1.07/1.16 cnf(118,plain,
% 1.07/1.16 (E(f3(f9(a10)),f3(a10))),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38,37,36,35,18,17,16,15,14,13,12,11,10,9])).
% 1.07/1.16 cnf(121,plain,
% 1.07/1.16 (E(f7(x1211,f9(a10)),f7(x1211,a10))),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38,37,36,35,18,17,16,15,14,13,12,11,10,9,8,7,6])).
% 1.07/1.16 cnf(122,plain,
% 1.07/1.16 (E(f7(f9(a10),x1221),f7(a10,x1221))),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38,37,36,35,18,17,16,15,14,13,12,11,10,9,8,7,6,5])).
% 1.07/1.16 cnf(123,plain,
% 1.07/1.16 (E(f12(f9(a10)),f12(a10))),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38,37,36,35,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4])).
% 1.07/1.16 cnf(124,plain,
% 1.07/1.16 (P4(a10,f7(a10,a10))),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38,37,36,35,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,57])).
% 1.07/1.16 cnf(130,plain,
% 1.07/1.16 (~P5(f3(a11),x1301)+~E(x1301,f3(a11))),
% 1.07/1.16 inference(scs_inference,[],[33,26,27,28,29,31,2,23,3,70,53,79,34,50,45,42,39,38,37,36,35,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,57,49,48,25])).
% 1.07/1.16 cnf(182,plain,
% 1.07/1.16 (P4(f9(a10),f9(a10))),
% 1.07/1.16 inference(scs_inference,[],[101,46])).
% 1.07/1.16 cnf(188,plain,
% 1.07/1.16 (P2(f8(a10,a10))),
% 1.07/1.16 inference(scs_inference,[],[27,101,46,44,41,54])).
% 1.07/1.16 cnf(190,plain,
% 1.07/1.16 (E(f13(f4(f3(a11))),f3(a11))),
% 1.07/1.16 inference(scs_inference,[],[32,27,101,103,46,44,41,54,43])).
% 1.07/1.16 cnf(192,plain,
% 1.07/1.16 (P1(f4(f3(a11)))),
% 1.07/1.16 inference(scs_inference,[],[32,27,101,103,46,44,41,54,43,40])).
% 1.07/1.16 cnf(194,plain,
% 1.07/1.16 (E(f9(f7(a10,a10)),f7(f9(a10),a10))),
% 1.07/1.16 inference(scs_inference,[],[32,27,101,103,46,44,41,54,43,40,67])).
% 1.07/1.16 cnf(196,plain,
% 1.07/1.16 (E(f7(f7(a10,a10),a10),f7(a10,f7(a10,a10)))),
% 1.07/1.16 inference(scs_inference,[],[32,27,101,103,46,44,41,54,43,40,67,74])).
% 1.07/1.16 cnf(200,plain,
% 1.07/1.16 (E(f8(f7(a10,a10),f7(a10,a10)),f7(a10,f8(a10,a10)))),
% 1.07/1.16 inference(scs_inference,[],[32,27,101,103,46,44,41,54,43,40,67,74,73,76])).
% 1.07/1.16 cnf(202,plain,
% 1.07/1.16 (P4(a10,f8(a10,a10))),
% 1.07/1.16 inference(scs_inference,[],[32,27,88,101,103,46,44,41,54,43,40,67,74,73,76,71])).
% 1.07/1.16 cnf(204,plain,
% 1.07/1.16 (E(f8(f8(f7(a10,a10),f7(a10,a10)),f8(f7(a10,a10),f7(a10,a10))),f7(f8(a10,a10),f8(a10,a10)))),
% 1.07/1.16 inference(scs_inference,[],[32,27,88,101,103,46,44,41,54,43,40,67,74,73,76,71,82])).
% 1.07/1.16 cnf(206,plain,
% 1.07/1.16 (P4(f8(a10,a10),f8(a10,a10))),
% 1.07/1.16 inference(scs_inference,[],[32,27,88,101,103,46,44,41,54,43,40,67,74,73,76,71,82,78])).
% 1.07/1.16 cnf(208,plain,
% 1.07/1.16 (~P5(f3(a11),f13(f4(f3(a11))))),
% 1.07/1.16 inference(scs_inference,[],[32,27,86,88,101,103,46,44,41,54,43,40,67,74,73,76,71,82,78,25])).
% 1.07/1.16 cnf(209,plain,
% 1.07/1.16 (~P4(f9(f9(a10)),f2(a11,a11))),
% 1.07/1.16 inference(scs_inference,[],[33,32,27,86,88,101,103,99,46,44,41,54,43,40,67,74,73,76,71,82,78,25,22])).
% 1.07/1.16 cnf(210,plain,
% 1.07/1.16 (P2(f6(a11,a1))),
% 1.07/1.16 inference(scs_inference,[],[33,28,32,26,27,86,88,101,103,99,46,44,41,54,43,40,67,74,73,76,71,82,78,25,22,56])).
% 1.07/1.16 cnf(212,plain,
% 1.07/1.16 (P2(f7(a10,a10))),
% 1.07/1.16 inference(scs_inference,[],[33,28,32,26,27,86,88,101,103,99,46,44,41,54,43,40,67,74,73,76,71,82,78,25,22,56,55])).
% 1.07/1.16 cnf(216,plain,
% 1.07/1.16 (E(f7(f9(a10),f9(a10)),f7(a10,a10))),
% 1.07/1.16 inference(scs_inference,[],[33,28,32,26,27,86,88,101,103,99,46,44,41,54,43,40,67,74,73,76,71,82,78,25,22,56,55,66,62])).
% 1.07/1.16 cnf(218,plain,
% 1.07/1.16 (E(f8(f7(a10,a10),f7(a10,a10)),f7(f8(a10,a10),a10))),
% 1.07/1.16 inference(scs_inference,[],[33,28,32,26,27,86,88,101,103,99,46,44,41,54,43,40,67,74,73,76,71,82,78,25,22,56,55,66,62,77])).
% 1.07/1.16 cnf(223,plain,
% 1.07/1.16 (~P5(f13(f4(f3(a11))),f3(a11))),
% 1.07/1.16 inference(scs_inference,[],[33,28,32,26,27,86,124,88,101,103,99,46,44,41,54,43,40,67,74,73,76,71,82,78,25,22,56,55,66,62,77,72,2,24])).
% 1.07/1.16 cnf(224,plain,
% 1.07/1.16 (~P4(a10,f8(f2(f12(a11),f12(a11)),f7(f6(a11,f3(a11)),f6(a11,f3(a11)))))),
% 1.07/1.16 inference(scs_inference,[],[33,31,28,32,26,27,86,124,88,101,103,99,46,44,41,54,43,40,67,74,73,76,71,82,78,25,22,56,55,66,62,77,72,2,24,23])).
% 1.07/1.16 cnf(235,plain,
% 1.07/1.16 (~E(a11,f9(a10))+~P4(a10,f9(a10))+E(a11,f12(a11))+~E(f13(f3(a11)),f3(a11))),
% 1.07/1.16 inference(scs_inference,[],[33,31,28,32,26,27,86,124,118,88,101,103,99,46,44,41,54,43,40,67,74,73,76,71,82,78,25,22,56,55,66,62,77,72,2,24,23,3,21,79,58,69,68,80])).
% 1.07/1.16 cnf(237,plain,
% 1.07/1.16 (~E(a11,f9(a10))+~P4(a10,f9(a10))+~P3(a10)+P3(f12(f9(a10)))+E(f3(a10),a1)),
% 1.07/1.16 inference(scs_inference,[],[33,31,28,32,26,27,86,124,118,123,88,101,103,99,46,44,41,54,43,40,67,74,73,76,71,82,78,25,22,56,55,66,62,77,72,2,24,23,3,21,79,58,69,68,80,47])).
% 1.07/1.16 cnf(244,plain,
% 1.07/1.16 (P4(f8(f7(a10,a10),f7(a10,a10)),f8(f7(a10,a10),f7(a10,a10)))),
% 1.07/1.16 inference(scs_inference,[],[212,90,124,74,71,78])).
% 1.07/1.16 cnf(248,plain,
% 1.07/1.16 (E(f8(f8(f7(a10,a10),f7(a10,a10)),f7(a10,a10)),f8(f7(a10,a10),f8(f7(a10,a10),f7(a10,a10))))),
% 1.07/1.16 inference(scs_inference,[],[27,206,212,188,90,124,88,74,71,78,79,73])).
% 1.07/1.16 cnf(250,plain,
% 1.07/1.16 (E(f8(f7(f7(a10,a10),f7(a10,a10)),f7(f7(a10,a10),f7(a10,a10))),f7(f8(f7(a10,a10),f7(a10,a10)),f7(a10,a10)))),
% 1.07/1.16 inference(scs_inference,[],[27,206,212,188,90,124,88,74,71,78,79,73,77])).
% 1.07/1.16 cnf(252,plain,
% 1.07/1.16 (E(f8(f7(f7(a10,a10),f7(a10,a10)),f7(f7(a10,a10),f7(a10,a10))),f7(f7(a10,a10),f8(f7(a10,a10),f7(a10,a10))))),
% 1.07/1.16 inference(scs_inference,[],[27,206,212,188,90,124,88,74,71,78,79,73,77,76])).
% 1.07/1.16 cnf(254,plain,
% 1.07/1.16 (P4(a10,f7(f7(a10,a10),f7(a10,a10)))),
% 1.07/1.16 inference(scs_inference,[],[27,206,212,188,90,124,88,74,71,78,79,73,77,76,72])).
% 1.07/1.16 cnf(256,plain,
% 1.07/1.16 (E(f7(f8(a10,a10),f8(a10,a10)),f8(f8(f7(a10,a10),f7(a10,a10)),f8(f7(a10,a10),f7(a10,a10))))),
% 1.07/1.16 inference(scs_inference,[],[27,206,204,212,188,90,124,88,74,71,78,79,73,77,76,72,2])).
% 1.07/1.16 cnf(258,plain,
% 1.07/1.16 (P4(a10,f9(a10))),
% 1.07/1.16 inference(scs_inference,[],[31,27,206,204,212,188,209,182,91,90,124,88,74,71,78,79,73,77,76,72,2,23,22])).
% 1.07/1.16 cnf(265,plain,
% 1.07/1.16 (~E(x2651,f12(a11))+E(f13(f3(x2651)),f3(a11))),
% 1.07/1.16 inference(scs_inference,[],[26,29,31,28,32,27,206,204,212,216,188,97,209,182,91,90,124,88,74,71,78,79,73,77,76,72,2,23,22,3,19,235,237,75,52])).
% 1.07/1.16 cnf(270,plain,
% 1.07/1.16 (E(f13(f3(f12(a11))),f3(a11))),
% 1.07/1.16 inference(equality_inference,[],[265])).
% 1.07/1.16 cnf(272,plain,
% 1.07/1.16 (~P5(f3(a11),f13(f3(f12(a11))))),
% 1.07/1.16 inference(scs_inference,[],[270,130])).
% 1.07/1.16 cnf(273,plain,
% 1.07/1.16 (P4(f7(f8(a10,a10),f8(a10,a10)),f7(f8(a10,a10),f8(a10,a10)))),
% 1.07/1.16 inference(scs_inference,[],[202,270,206,188,130,79])).
% 1.07/1.16 cnf(277,plain,
% 1.07/1.16 (~P4(f8(a10,a10),f8(f2(f12(a11),f12(a11)),f7(f6(a11,f3(a11)),f6(a11,f3(a11)))))),
% 1.07/1.16 inference(scs_inference,[],[202,95,270,224,206,188,130,79,78,22])).
% 1.07/1.16 cnf(279,plain,
% 1.07/1.16 (~E(f8(f2(f12(a11),f12(a11)),f7(f6(a11,f3(a11)),f6(a11,f3(a11)))),f2(f12(a11),f12(a11)))),
% 1.07/1.16 inference(scs_inference,[],[244,202,200,85,95,270,224,206,188,130,79,78,22,23,2])).
% 1.07/1.16 cnf(282,plain,
% 1.07/1.16 (~E(a10,x2821)+P2(x2821)),
% 1.07/1.16 inference(scs_inference,[],[27,244,202,200,85,196,95,121,270,224,206,188,130,79,78,22,23,2,3,20])).
% 1.07/1.16 cnf(291,plain,
% 1.07/1.16 (P4(f7(f9(a10),f9(a10)),f7(f9(a10),f9(a10)))),
% 1.07/1.16 inference(scs_inference,[],[258,182,210,101,46,79])).
% 1.07/1.16 cnf(293,plain,
% 1.07/1.16 (P4(f8(f8(f7(a10,a10),f7(a10,a10)),f8(f7(a10,a10),f7(a10,a10))),f7(f8(a10,a10),f8(a10,a10)))),
% 1.07/1.16 inference(scs_inference,[],[273,256,258,182,210,101,46,79,22])).
% 1.07/1.16 cnf(295,plain,
% 1.07/1.16 (~P4(f8(a10,a10),f2(a11,a11))),
% 1.15/1.16 inference(scs_inference,[],[83,248,273,256,277,258,182,210,101,46,79,22,2,23])).
% 1.15/1.16 cnf(301,plain,
% 1.15/1.16 (P1(f13(f4(f3(a11))))),
% 1.15/1.16 inference(scs_inference,[],[83,31,248,273,256,277,279,192,258,182,210,101,46,79,22,2,23,3,50,39,36])).
% 1.15/1.16 cnf(303,plain,
% 1.15/1.16 (P2(f2(a11,a11))),
% 1.15/1.16 inference(scs_inference,[],[83,31,28,248,273,256,277,279,192,258,182,210,101,46,79,22,2,23,3,50,39,36,64])).
% 1.15/1.16 cnf(305,plain,
% 1.15/1.16 (P2(f8(f2(f12(a11),f12(a11)),f7(f6(a11,f3(a11)),f6(a11,f3(a11)))))),
% 1.15/1.16 inference(scs_inference,[],[83,31,28,248,273,256,277,279,192,258,182,210,101,46,79,22,2,23,3,50,39,36,64,20])).
% 1.15/1.16 cnf(306,plain,
% 1.15/1.16 (~P4(f9(a10),f8(f2(f12(a11),f12(a11)),f7(f6(a11,f3(a11)),f6(a11,f3(a11)))))),
% 1.15/1.16 inference(scs_inference,[],[27,83,31,28,248,273,256,277,279,192,258,182,224,210,101,46,79,22,2,23,3,50,39,36,64,20,69])).
% 1.15/1.16 cnf(308,plain,
% 1.15/1.16 (P5(f4(f3(a11)),f3(a11))),
% 1.15/1.16 inference(scs_inference,[],[27,83,31,28,248,273,256,277,279,190,192,258,182,224,210,101,46,79,22,2,23,3,50,39,36,64,20,69,25])).
% 1.15/1.16 cnf(311,plain,
% 1.15/1.16 (~E(f4(f3(a11)),f3(a11))),
% 1.15/1.16 inference(scs_inference,[],[27,83,31,28,248,273,256,277,208,279,190,192,258,182,224,210,188,101,46,79,22,2,23,3,50,39,36,64,20,69,25,53,24])).
% 1.15/1.16 cnf(315,plain,
% 1.15/1.16 (P3(x3151)+~E(x3151,f12(a11))),
% 1.15/1.16 inference(scs_inference,[],[27,83,31,28,32,248,273,256,277,208,279,190,192,254,258,182,224,210,188,101,88,46,79,22,2,23,3,50,39,36,64,20,69,25,53,24,19,75,47])).
% 1.15/1.16 cnf(324,plain,
% 1.15/1.16 (P3(f12(a11))),
% 1.15/1.16 inference(equality_inference,[],[315])).
% 1.15/1.16 cnf(325,plain,
% 1.15/1.16 (P1(f3(f12(a11)))),
% 1.15/1.16 inference(scs_inference,[],[324,37])).
% 1.15/1.16 cnf(334,plain,
% 1.15/1.16 (E(f8(x3341,f8(f7(a10,a10),f7(a10,a10))),f8(x3341,f7(f8(a10,a10),a10)))),
% 1.15/1.16 inference(scs_inference,[],[218,301,303,324,37,45,42,35,14,13])).
% 1.15/1.16 cnf(335,plain,
% 1.15/1.16 (E(f8(f8(f7(a10,a10),f7(a10,a10)),x3351),f8(f7(f8(a10,a10),a10),x3351))),
% 1.15/1.16 inference(scs_inference,[],[218,301,303,324,37,45,42,35,14,13,12])).
% 1.15/1.16 cnf(336,plain,
% 1.15/1.16 (E(f6(x3361,f8(f7(a10,a10),f7(a10,a10))),f6(x3361,f7(f8(a10,a10),a10)))),
% 1.15/1.16 inference(scs_inference,[],[218,301,303,324,37,45,42,35,14,13,12,11])).
% 1.15/1.16 cnf(337,plain,
% 1.15/1.16 (E(f6(f8(f7(a10,a10),f7(a10,a10)),x3371),f6(f7(f8(a10,a10),a10),x3371))),
% 1.15/1.16 inference(scs_inference,[],[218,301,303,324,37,45,42,35,14,13,12,11,10])).
% 1.15/1.16 cnf(343,plain,
% 1.15/1.16 (P4(a10,f7(f2(a11,a11),f2(a11,a11)))),
% 1.15/1.16 inference(scs_inference,[],[218,301,303,324,37,45,42,35,14,13,12,11,10,9,7,6,5,4,57])).
% 1.15/1.16 cnf(349,plain,
% 1.15/1.16 (P2(f9(f2(a11,a11)))),
% 1.15/1.16 inference(scs_inference,[],[218,301,303,324,37,45,42,35,14,13,12,11,10,9,7,6,5,4,57,49,48,38])).
% 1.15/1.16 cnf(356,plain,
% 1.15/1.16 (P2(f7(f2(a11,a11),f2(a11,a11)))),
% 1.15/1.16 inference(scs_inference,[],[218,301,303,324,37,45,42,35,14,13,12,11,10,9,7,6,5,4,57,49,48,38,18,17,16,15,8,55])).
% 1.15/1.16 cnf(358,plain,
% 1.15/1.16 (P4(f2(a11,a11),f2(a11,a11))),
% 1.15/1.16 inference(scs_inference,[],[218,301,303,324,37,45,42,35,14,13,12,11,10,9,7,6,5,4,57,49,48,38,18,17,16,15,8,55,53])).
% 1.15/1.16 cnf(361,plain,
% 1.15/1.16 (~E(f4(f3(a11)),f13(f4(f3(a11))))),
% 1.15/1.16 inference(scs_inference,[],[218,301,303,223,308,324,190,37,45,42,35,14,13,12,11,10,9,7,6,5,4,57,49,48,38,18,17,16,15,8,55,53,25,24])).
% 1.15/1.16 cnf(365,plain,
% 1.15/1.16 (E(f8(f7(f7(a10,a10),f7(a10,a10)),f7(f7(a10,a10),f7(a10,a10))),f7(f7(a10,a10),f7(f8(a10,a10),a10)))),
% 1.15/1.16 inference(scs_inference,[],[252,291,218,301,303,122,223,308,311,324,190,37,45,42,35,14,13,12,11,10,9,7,6,5,4,57,49,48,38,18,17,16,15,8,55,53,25,24,22,2,3])).
% 1.15/1.16 cnf(373,plain,
% 1.15/1.16 (P1(f4(f13(a1)))),
% 1.15/1.16 inference(scs_inference,[],[27,83,252,291,218,301,303,122,223,308,311,105,324,107,190,118,258,101,37,45,42,35,14,13,12,11,10,9,7,6,5,4,57,49,48,38,18,17,16,15,8,55,53,25,24,22,2,3,23,65,58,68,40])).
% 1.15/1.16 cnf(377,plain,
% 1.15/1.16 (P2(f8(f2(a11,a11),f2(a11,a11)))),
% 1.15/1.16 inference(scs_inference,[],[27,83,32,28,252,291,218,301,303,122,223,308,311,105,324,107,190,118,258,101,37,45,42,35,14,13,12,11,10,9,7,6,5,4,57,49,48,38,18,17,16,15,8,55,53,25,24,22,2,3,23,65,58,68,40,80,54])).
% 1.15/1.16 cnf(385,plain,
% 1.15/1.16 (E(f13(f4(f13(a1))),f13(a1))),
% 1.15/1.16 inference(scs_inference,[],[27,83,32,28,252,291,218,301,303,122,223,308,311,105,324,107,190,118,258,101,37,45,42,35,14,13,12,11,10,9,7,6,5,4,57,49,48,38,18,17,16,15,8,55,53,25,24,22,2,3,23,65,58,68,40,80,54,44,41,67,43])).
% 1.15/1.16 cnf(397,plain,
% 1.15/1.16 (P2(f8(f8(f2(a11,a11),f2(a11,a11)),f8(f2(a11,a11),f2(a11,a11))))),
% 1.15/1.16 inference(scs_inference,[],[377,210,67,54])).
% 1.15/1.16 cnf(399,plain,
% 1.15/1.16 (P2(f6(a11,f3(f12(a11))))),
% 1.15/1.16 inference(scs_inference,[],[28,377,325,210,67,54,56])).
% 1.15/1.16 cnf(405,plain,
% 1.15/1.16 (P2(f7(f8(f2(a11,a11),f2(a11,a11)),f8(f2(a11,a11),f2(a11,a11))))),
% 1.15/1.16 inference(scs_inference,[],[28,377,325,210,67,54,56,66,62,55])).
% 1.15/1.16 cnf(410,plain,
% 1.15/1.16 (~P4(f8(a10,f9(a10)),f2(a11,a11))),
% 1.15/1.16 inference(scs_inference,[],[28,377,295,306,114,325,272,305,270,210,101,67,54,56,66,62,55,53,24,22])).
% 1.15/1.16 cnf(412,plain,
% 1.15/1.16 (E(f7(f8(f7(a10,a10),f7(a10,a10)),f7(a10,a10)),f8(f7(f7(a10,a10),f7(a10,a10)),f7(f7(a10,a10),f7(a10,a10))))),
% 1.15/1.16 inference(scs_inference,[],[28,250,377,295,306,114,325,272,305,270,210,101,67,54,56,66,62,55,53,24,22,2])).
% 1.15/1.16 cnf(413,plain,
% 1.15/1.16 (E(f8(f8(f7(a10,a10),f7(a10,a10)),f8(f7(a10,a10),f7(a10,a10))),f8(f7(f8(a10,a10),a10),f7(f8(a10,a10),a10)))),
% 1.15/1.16 inference(scs_inference,[],[28,250,377,334,335,295,306,114,325,272,305,270,210,101,67,54,56,66,62,55,53,24,22,2,3])).
% 1.15/1.16 cnf(416,plain,
% 1.15/1.16 (P4(f8(f8(f7(a10,a10),f7(a10,a10)),f8(f7(a10,a10),f7(a10,a10))),f8(f8(f7(a10,a10),f7(a10,a10)),f8(f7(a10,a10),f7(a10,a10))))),
% 1.15/1.16 inference(scs_inference,[],[28,250,377,293,334,335,295,306,114,325,272,305,256,270,210,101,67,54,56,66,62,55,53,24,22,2,3,23])).
% 1.15/1.16 cnf(417,plain,
% 1.15/1.16 (E(f4(f13(a1)),a1)),
% 1.15/1.16 inference(scs_inference,[],[28,250,377,293,334,335,295,306,114,325,373,272,385,305,256,270,210,101,26,67,54,56,66,62,55,53,24,22,2,3,23,51])).
% 1.15/1.16 cnf(442,plain,
% 1.15/1.16 (E(f7(f7(f8(a10,a10),f8(a10,a10)),f8(a10,a10)),f7(f8(a10,a10),f7(f8(a10,a10),f8(a10,a10))))),
% 1.15/1.16 inference(scs_inference,[],[188,74])).
% 1.15/1.16 cnf(450,plain,
% 1.15/1.16 (P4(f2(a11,a11),f8(a10,a10))),
% 1.15/1.16 inference(scs_inference,[],[295,188,303,74,73,77,76,53])).
% 1.15/1.16 cnf(453,plain,
% 1.15/1.16 (~E(f3(a11),f4(f13(a1)))),
% 1.15/1.16 inference(scs_inference,[],[83,32,358,417,295,188,303,74,73,77,76,53,22,3])).
% 1.15/1.16 cnf(455,plain,
% 1.15/1.16 (~P4(f8(a10,f9(a10)),f8(f2(f12(a11),f12(a11)),f7(f6(a11,f3(a11)),f6(a11,f3(a11)))))),
% 1.15/1.16 inference(scs_inference,[],[83,31,32,358,410,361,417,295,188,303,74,73,77,76,53,22,3,2,23])).
% 1.15/1.16 cnf(477,plain,
% 1.15/1.16 (P4(a10,f8(f7(f2(a11,a11),f2(a11,a11)),f7(f2(a11,a11),f2(a11,a11))))),
% 1.15/1.16 inference(scs_inference,[],[397,343,356,101,72,46,76,71])).
% 1.15/1.16 cnf(495,plain,
% 1.15/1.16 (P1(f13(f13(a1)))),
% 1.15/1.16 inference(scs_inference,[],[442,397,412,416,365,413,349,343,356,305,105,224,101,27,72,46,76,71,74,73,77,53,22,2,3,23,39,50,36])).
% 1.15/1.16 cnf(533,plain,
% 1.15/1.16 (E(f6(x5331,f9(f7(a10,a10))),f6(x5331,f7(f9(a10),a10)))),
% 1.15/1.16 inference(scs_inference,[],[32,450,405,336,337,453,194,455,115,495,399,272,95,190,103,26,55,53,24,22,3,2,23,35,41,51,13,11])).
% 1.15/1.16 cnf(543,plain,
% 1.15/1.16 (E(f8(f9(f9(f2(a11,a11))),f9(f2(a11,a11))),a10)),
% 1.15/1.16 inference(scs_inference,[],[32,450,405,336,337,453,194,455,115,495,399,272,95,349,190,103,26,55,53,24,22,3,2,23,35,41,51,13,11,7,5,4,45,42,57,49])).
% 1.15/1.16 cnf(555,plain,
% 1.15/1.16 (E(f6(f9(f7(a10,a10)),x5551),f6(f7(f9(a10),a10),x5551))),
% 1.15/1.16 inference(scs_inference,[],[32,450,405,336,337,453,194,455,115,495,399,272,95,349,190,103,26,55,53,24,22,3,2,23,35,41,51,13,11,7,5,4,45,42,57,49,48,44,38,17,16,14,12,10])).
% 1.15/1.16 cnf(566,plain,
% 1.15/1.16 (P2(f2(f12(a11),f12(a11)))),
% 1.15/1.16 inference(scs_inference,[],[31,32,450,405,336,337,453,194,455,115,495,399,272,95,202,349,190,103,324,26,188,55,53,24,22,3,2,23,35,41,51,13,11,7,5,4,45,42,57,49,48,44,38,17,16,14,12,10,9,8,6,15,18,19,72,71,64])).
% 1.15/1.16 cnf(575,plain,
% 1.15/1.16 (~P5(f13(f3(f12(a11))),f3(a11))),
% 1.15/1.16 inference(scs_inference,[],[86,566,270,46,24])).
% 1.15/1.16 cnf(601,plain,
% 1.15/1.16 (E(f9(f7(f8(a10,a10),f8(a10,a10))),f7(f9(f8(a10,a10)),f8(a10,a10)))),
% 1.15/1.16 inference(scs_inference,[],[495,324,212,188,56,66,67])).
% 1.15/1.16 cnf(605,plain,
% 1.15/1.16 (P2(f8(f7(f2(a11,a11),f2(a11,a11)),f7(f2(a11,a11),f2(a11,a11))))),
% 1.15/1.16 inference(scs_inference,[],[495,356,324,212,188,56,66,67,62,54])).
% 1.15/1.16 cnf(667,plain,
% 1.15/1.16 (~P2(f6(a11,f3(a11)))),
% 1.15/1.16 inference(scs_inference,[],[84,90,88,601,605,533,555,477,575,543,97,308,301,566,190,33,224,30,29,324,188,303,27,56,66,62,79,71,25,24,22,2,3,23,282,39,50,36,20,72,65,55])).
% 1.15/1.16 cnf(689,plain,
% 1.15/1.16 ($false),
% 1.15/1.16 inference(scs_inference,[],[667,103,28,56]),
% 1.15/1.16 ['proof']).
% 1.15/1.16 % SZS output end Proof
% 1.15/1.16 % Total time :0.510000s
%------------------------------------------------------------------------------