TSTP Solution File: RNG061+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : RNG061+2 : 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 : n012.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 13:47:58 EDT 2023
% Result : Theorem 3.41s 3.53s
% Output : CNFRefutation 3.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG061+2 : 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 : n012.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 02:30:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 3.41/3.51 %-------------------------------------------
% 3.41/3.51 % File :CSE---1.6
% 3.41/3.51 % Problem :theBenchmark
% 3.41/3.51 % Transform :cnf
% 3.41/3.51 % Format :tptp:raw
% 3.41/3.51 % Command :java -jar mcs_scs.jar %d %s
% 3.41/3.51
% 3.41/3.51 % Result :Theorem 2.870000s
% 3.41/3.51 % Output :CNFRefutation 2.870000s
% 3.41/3.51 %-------------------------------------------
% 3.41/3.51 %------------------------------------------------------------------------------
% 3.41/3.51 % File : RNG061+2 : TPTP v8.1.2. Released v4.0.0.
% 3.41/3.51 % Domain : Ring Theory
% 3.41/3.51 % Problem : Cauchy-Bouniakowsky-Schwarz inequality 05_16_02_03, 01 expansion
% 3.41/3.51 % Version : Especial.
% 3.41/3.51 % English :
% 3.41/3.51
% 3.41/3.51 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 3.41/3.51 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 3.41/3.51 % Source : [Pas08]
% 3.41/3.51 % Names : cauchy_05_16_02_03.01 [Pas08]
% 3.41/3.51
% 3.41/3.51 % Status : Theorem
% 3.41/3.51 % Rating : 0.33 v7.5.0, 0.28 v7.4.0, 0.33 v7.3.0, 0.38 v7.2.0, 0.34 v7.1.0, 0.39 v7.0.0, 0.33 v6.4.0, 0.38 v6.3.0, 0.29 v6.2.0, 0.28 v6.1.0, 0.40 v6.0.0, 0.39 v5.5.0, 0.59 v5.4.0, 0.61 v5.3.0, 0.63 v5.2.0, 0.45 v5.1.0, 0.52 v5.0.0, 0.62 v4.1.0, 0.65 v4.0.1, 0.87 v4.0.0
% 3.41/3.51 % Syntax : Number of formulae : 60 ( 8 unt; 1 def)
% 3.41/3.51 % Number of atoms : 199 ( 66 equ)
% 3.41/3.51 % Maximal formula atoms : 9 ( 3 avg)
% 3.41/3.51 % Number of connectives : 145 ( 6 ~; 1 |; 82 &)
% 3.41/3.51 % ( 1 <=>; 55 =>; 0 <=; 0 <~>)
% 3.41/3.51 % Maximal formula depth : 10 ( 4 avg)
% 3.41/3.51 % Maximal term depth : 5 ( 1 avg)
% 3.41/3.51 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% 3.41/3.51 % Number of functors : 26 ( 26 usr; 18 con; 0-2 aty)
% 3.41/3.51 % Number of variables : 73 ( 72 !; 1 ?)
% 3.41/3.51 % SPC : FOF_THM_RFO_SEQ
% 3.41/3.51
% 3.41/3.51 % Comments : Problem generated by the SAD system [VLP07]
% 3.41/3.51 %------------------------------------------------------------------------------
% 3.41/3.51 fof(mNatSort,axiom,
% 3.41/3.51 ! [W0] :
% 3.41/3.51 ( aNaturalNumber0(W0)
% 3.41/3.51 => $true ) ).
% 3.41/3.51
% 3.41/3.51 fof(mZeroNat,axiom,
% 3.41/3.51 aNaturalNumber0(sz00) ).
% 3.41/3.51
% 3.41/3.51 fof(mSuccNat,axiom,
% 3.41/3.51 ! [W0] :
% 3.41/3.51 ( aNaturalNumber0(W0)
% 3.41/3.51 => ( aNaturalNumber0(szszuzczcdt0(W0))
% 3.41/3.51 & szszuzczcdt0(W0) != sz00 ) ) ).
% 3.41/3.51
% 3.41/3.51 fof(mNatExtr,axiom,
% 3.41/3.51 ! [W0] :
% 3.41/3.51 ( ( aNaturalNumber0(W0)
% 3.41/3.52 & W0 != sz00 )
% 3.41/3.52 => ? [W1] :
% 3.41/3.52 ( aNaturalNumber0(W1)
% 3.41/3.52 & W0 = szszuzczcdt0(W1) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mSuccEqu,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aNaturalNumber0(W0)
% 3.41/3.52 & aNaturalNumber0(W1) )
% 3.41/3.52 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
% 3.41/3.52 => W0 = W1 ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mIHOrd,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aNaturalNumber0(W0)
% 3.41/3.52 & aNaturalNumber0(W1) )
% 3.41/3.52 => ( iLess0(W0,W1)
% 3.41/3.52 => $true ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mIH,axiom,
% 3.41/3.52 ! [W0] :
% 3.41/3.52 ( aNaturalNumber0(W0)
% 3.41/3.52 => iLess0(W0,szszuzczcdt0(W0)) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mScSort,axiom,
% 3.41/3.52 ! [W0] :
% 3.41/3.52 ( aScalar0(W0)
% 3.41/3.52 => $true ) ).
% 3.41/3.52
% 3.41/3.52 fof(mSZeroSc,axiom,
% 3.41/3.52 aScalar0(sz0z00) ).
% 3.41/3.52
% 3.41/3.52 fof(mSumSc,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1) )
% 3.41/3.52 => aScalar0(sdtpldt0(W0,W1)) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mMulSc,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1) )
% 3.41/3.52 => aScalar0(sdtasdt0(W0,W1)) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mNegSc,axiom,
% 3.41/3.52 ! [W0] :
% 3.41/3.52 ( aScalar0(W0)
% 3.41/3.52 => aScalar0(smndt0(W0)) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mScZero,axiom,
% 3.41/3.52 ! [W0] :
% 3.41/3.52 ( aScalar0(W0)
% 3.41/3.52 => ( sdtpldt0(W0,sz0z00) = W0
% 3.41/3.52 & sdtpldt0(sz0z00,W0) = W0
% 3.41/3.52 & sdtasdt0(W0,sz0z00) = sz0z00
% 3.41/3.52 & sdtasdt0(sz0z00,W0) = sz0z00
% 3.41/3.52 & sdtpldt0(W0,smndt0(W0)) = sz0z00
% 3.41/3.52 & sdtpldt0(smndt0(W0),W0) = sz0z00
% 3.41/3.52 & smndt0(smndt0(W0)) = W0
% 3.41/3.52 & smndt0(sz0z00) = sz0z00 ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mArith,axiom,
% 3.41/3.52 ! [W0,W1,W2] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1)
% 3.41/3.52 & aScalar0(W2) )
% 3.41/3.52 => ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2))
% 3.41/3.52 & sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
% 3.41/3.52 & sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
% 3.41/3.52 & sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mDistr,axiom,
% 3.41/3.52 ! [W0,W1,W2] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1)
% 3.41/3.52 & aScalar0(W2) )
% 3.41/3.52 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 3.41/3.52 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mDistr2,axiom,
% 3.41/3.52 ! [W0,W1,W2,W3] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1)
% 3.41/3.52 & aScalar0(W2)
% 3.41/3.52 & aScalar0(W3) )
% 3.41/3.52 => sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mMNeg,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1) )
% 3.41/3.52 => ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1))
% 3.41/3.52 & sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mMDNeg,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1) )
% 3.41/3.52 => sdtasdt0(smndt0(W0),smndt0(W1)) = sdtasdt0(W0,W1) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mLess,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1) )
% 3.41/3.52 => ( sdtlseqdt0(W0,W1)
% 3.41/3.52 => $true ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mLERef,axiom,
% 3.41/3.52 ! [W0] :
% 3.41/3.52 ( aScalar0(W0)
% 3.41/3.52 => sdtlseqdt0(W0,W0) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mLEASm,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1) )
% 3.41/3.52 => ( ( sdtlseqdt0(W0,W1)
% 3.41/3.52 & sdtlseqdt0(W1,W0) )
% 3.41/3.52 => W0 = W1 ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mLETrn,axiom,
% 3.41/3.52 ! [W0,W1,W2] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1)
% 3.41/3.52 & aScalar0(W2) )
% 3.41/3.52 => ( ( sdtlseqdt0(W0,W1)
% 3.41/3.52 & sdtlseqdt0(W1,W2) )
% 3.41/3.52 => sdtlseqdt0(W0,W2) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mLEMon,axiom,
% 3.41/3.52 ! [W0,W1,W2,W3] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1)
% 3.41/3.52 & aScalar0(W2)
% 3.41/3.52 & aScalar0(W3) )
% 3.41/3.52 => ( ( sdtlseqdt0(W0,W1)
% 3.41/3.52 & sdtlseqdt0(W2,W3) )
% 3.41/3.52 => sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mLEMonM,axiom,
% 3.41/3.52 ! [W0,W1,W2,W3] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1)
% 3.41/3.52 & aScalar0(W2)
% 3.41/3.52 & aScalar0(W3) )
% 3.41/3.52 => ( ( sdtlseqdt0(W0,W1)
% 3.41/3.52 & sdtlseqdt0(sz0z00,W2)
% 3.41/3.52 & sdtlseqdt0(W2,W3) )
% 3.41/3.52 => sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mLETot,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1) )
% 3.41/3.52 => ( sdtlseqdt0(W0,W1)
% 3.41/3.52 | sdtlseqdt0(W1,W0) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mPosMon,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1) )
% 3.41/3.52 => ( ( sdtlseqdt0(sz0z00,W0)
% 3.41/3.52 & sdtlseqdt0(sz0z00,W1) )
% 3.41/3.52 => ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
% 3.41/3.52 & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mSqPos,axiom,
% 3.41/3.52 ! [W0] :
% 3.41/3.52 ( aScalar0(W0)
% 3.41/3.52 => sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mSqrt,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aScalar0(W0)
% 3.41/3.52 & aScalar0(W1) )
% 3.41/3.52 => ( ( sdtlseqdt0(sz0z00,W0)
% 3.41/3.52 & sdtlseqdt0(sz0z00,W1)
% 3.41/3.52 & sdtasdt0(W0,W0) = sdtasdt0(W1,W1) )
% 3.41/3.52 => W0 = W1 ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mVcSort,axiom,
% 3.41/3.52 ! [W0] :
% 3.41/3.52 ( aVector0(W0)
% 3.41/3.52 => $true ) ).
% 3.41/3.52
% 3.41/3.52 fof(mDimNat,axiom,
% 3.41/3.52 ! [W0] :
% 3.41/3.52 ( aVector0(W0)
% 3.41/3.52 => aNaturalNumber0(aDimensionOf0(W0)) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mElmSc,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aVector0(W0)
% 3.41/3.52 & aNaturalNumber0(W1) )
% 3.41/3.52 => aScalar0(sdtlbdtrb0(W0,W1)) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mDefInit,definition,
% 3.41/3.52 ! [W0] :
% 3.41/3.52 ( aVector0(W0)
% 3.41/3.52 => ( aDimensionOf0(W0) != sz00
% 3.41/3.52 => ! [W1] :
% 3.41/3.52 ( W1 = sziznziztdt0(W0)
% 3.41/3.52 <=> ( aVector0(W1)
% 3.41/3.52 & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
% 3.41/3.52 & ! [W2] :
% 3.41/3.52 ( aNaturalNumber0(W2)
% 3.41/3.52 => sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mEqInit,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aVector0(W0)
% 3.41/3.52 & aVector0(W1) )
% 3.41/3.52 => ( ( aDimensionOf0(W0) = aDimensionOf0(W1)
% 3.41/3.52 & aDimensionOf0(W1) != sz00 )
% 3.41/3.52 => aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mScPr,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aVector0(W0)
% 3.41/3.52 & aVector0(W1) )
% 3.41/3.52 => ( aDimensionOf0(W0) = aDimensionOf0(W1)
% 3.41/3.52 => aScalar0(sdtasasdt0(W0,W1)) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mDefSPZ,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aVector0(W0)
% 3.41/3.52 & aVector0(W1) )
% 3.41/3.52 => ( ( aDimensionOf0(W0) = aDimensionOf0(W1)
% 3.41/3.52 & aDimensionOf0(W1) = sz00 )
% 3.41/3.52 => sdtasasdt0(W0,W1) = sz0z00 ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mDefSPN,axiom,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aVector0(W0)
% 3.41/3.52 & aVector0(W1) )
% 3.41/3.52 => ( ( aDimensionOf0(W0) = aDimensionOf0(W1)
% 3.41/3.52 & aDimensionOf0(W1) != sz00 )
% 3.41/3.52 => sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(mScSqPos,axiom,
% 3.41/3.52 ! [W0] :
% 3.41/3.52 ( aVector0(W0)
% 3.41/3.52 => sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1678,hypothesis,
% 3.41/3.52 ( aVector0(xs)
% 3.41/3.52 & aVector0(xt) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1652,hypothesis,
% 3.41/3.52 ! [W0,W1] :
% 3.41/3.52 ( ( aVector0(W0)
% 3.41/3.52 & aVector0(W1) )
% 3.41/3.52 => ( aDimensionOf0(W0) = aDimensionOf0(W1)
% 3.41/3.52 => ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
% 3.41/3.52 => sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) ) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1678_01,hypothesis,
% 3.41/3.52 aDimensionOf0(xs) = aDimensionOf0(xt) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1692,hypothesis,
% 3.41/3.52 aDimensionOf0(xs) != sz00 ).
% 3.41/3.52
% 3.41/3.52 fof(m__1709,hypothesis,
% 3.41/3.52 ( aVector0(xp)
% 3.41/3.52 & szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
% 3.41/3.52 & ! [W0] :
% 3.41/3.52 ( aNaturalNumber0(W0)
% 3.41/3.52 => sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0) )
% 3.41/3.52 & xp = sziznziztdt0(xs) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1726,hypothesis,
% 3.41/3.52 ( aVector0(xq)
% 3.41/3.52 & szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
% 3.41/3.52 & ! [W0] :
% 3.41/3.52 ( aNaturalNumber0(W0)
% 3.41/3.52 => sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0) )
% 3.41/3.52 & xq = sziznziztdt0(xt) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1746,hypothesis,
% 3.41/3.52 ( aScalar0(xA)
% 3.41/3.52 & xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1766,hypothesis,
% 3.41/3.52 ( aScalar0(xB)
% 3.41/3.52 & xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1783,hypothesis,
% 3.41/3.52 ( aScalar0(xC)
% 3.41/3.52 & xC = sdtasasdt0(xp,xp) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1800,hypothesis,
% 3.41/3.52 ( aScalar0(xD)
% 3.41/3.52 & xD = sdtasasdt0(xq,xq) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1820,hypothesis,
% 3.41/3.52 ( aScalar0(xE)
% 3.41/3.52 & xE = sdtasasdt0(xp,xq) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1837,hypothesis,
% 3.41/3.52 ( aScalar0(xF)
% 3.41/3.52 & xF = sdtasdt0(xA,xA) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1854,hypothesis,
% 3.41/3.52 ( aScalar0(xG)
% 3.41/3.52 & xG = sdtasdt0(xB,xB) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1873,hypothesis,
% 3.41/3.52 ( aScalar0(xH)
% 3.41/3.52 & xH = sdtasdt0(xA,xB) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1892,hypothesis,
% 3.41/3.52 ( aScalar0(xR)
% 3.41/3.52 & xR = sdtasdt0(xC,xG) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1911,hypothesis,
% 3.41/3.52 ( aScalar0(xP)
% 3.41/3.52 & xP = sdtasdt0(xE,xH) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1930,hypothesis,
% 3.41/3.52 ( aScalar0(xS)
% 3.41/3.52 & xS = sdtasdt0(xF,xD) ) ).
% 3.41/3.52
% 3.41/3.52 fof(m__1949,hypothesis,
% 3.41/3.53 ( aScalar0(xN)
% 3.41/3.53 & xN = sdtasdt0(xR,xS) ) ).
% 3.41/3.53
% 3.41/3.53 fof(m__1967,hypothesis,
% 3.41/3.53 sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ).
% 3.41/3.53
% 3.41/3.53 fof(m__2004,hypothesis,
% 3.41/3.53 sdtlseqdt0(sdtasdt0(xP,xP),xN) ).
% 3.41/3.53
% 3.41/3.53 fof(m__2144,hypothesis,
% 3.41/3.53 ( sdtasdt0(xR,smndt0(xS)) = smndt0(xN)
% 3.41/3.53 & sdtasdt0(smndt0(xS),xR) = smndt0(xN)
% 3.41/3.53 & sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ) ).
% 3.41/3.53
% 3.41/3.53 fof(m__2180,hypothesis,
% 3.41/3.53 sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) ).
% 3.41/3.53
% 3.41/3.53 fof(m__,conjecture,
% 3.41/3.53 sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) ).
% 3.41/3.53
% 3.41/3.53 %------------------------------------------------------------------------------
% 3.41/3.53 %-------------------------------------------
% 3.41/3.53 % Proof found
% 3.41/3.53 % SZS status Theorem for theBenchmark
% 3.41/3.53 % SZS output start Proof
% 3.41/3.53 %ClaNum:120(EqnAxiom:25)
% 3.41/3.53 %VarNum:315(SingletonVarNum:98)
% 3.41/3.53 %MaxLitNum:8
% 3.41/3.53 %MaxfuncDepth:4
% 3.41/3.53 %SharedTerms:100
% 3.41/3.53 %goalClause: 68
% 3.41/3.53 %singleGoalClaCount:1
% 3.41/3.53 [28]P1(a3)
% 3.41/3.53 [29]P2(a12)
% 3.41/3.53 [30]P2(a14)
% 3.41/3.53 [31]P2(a16)
% 3.41/3.53 [32]P2(a17)
% 3.41/3.53 [33]P2(a18)
% 3.41/3.53 [34]P2(a19)
% 3.41/3.53 [35]P2(a20)
% 3.41/3.53 [36]P2(a21)
% 3.41/3.53 [37]P2(a22)
% 3.41/3.53 [38]P2(a23)
% 3.41/3.53 [39]P2(a24)
% 3.41/3.53 [40]P2(a26)
% 3.41/3.53 [41]P2(a25)
% 3.41/3.53 [42]P3(a1)
% 3.41/3.53 [43]P3(a28)
% 3.41/3.53 [44]P3(a13)
% 3.41/3.53 [45]P3(a27)
% 3.41/3.53 [26]E(f2(a1),a13)
% 3.41/3.53 [27]E(f2(a28),a27)
% 3.41/3.53 [46]E(f4(a28),f4(a1))
% 3.41/3.53 [49]E(f5(a13,a13),a17)
% 3.41/3.53 [50]E(f5(a27,a27),a18)
% 3.41/3.53 [51]E(f5(a13,a27),a19)
% 3.41/3.53 [52]E(f8(a14,a14),a20)
% 3.41/3.53 [53]E(f8(a16,a16),a21)
% 3.41/3.53 [54]E(f8(a14,a16),a22)
% 3.41/3.53 [55]E(f8(a17,a21),a23)
% 3.41/3.53 [56]E(f8(a19,a22),a24)
% 3.41/3.53 [57]E(f8(a20,a18),a26)
% 3.41/3.53 [58]E(f8(a23,a26),a25)
% 3.41/3.53 [64]P4(f8(a24,a24),a25)
% 3.41/3.53 [65]P4(f8(a19,a19),f8(a17,a18))
% 3.41/3.53 [67]~E(f4(a1),a3)
% 3.41/3.53 [47]E(f15(f4(a13)),f4(a1))
% 3.41/3.53 [48]E(f15(f4(a27)),f4(a28))
% 3.41/3.53 [59]E(f9(a1,f4(a1)),a14)
% 3.41/3.53 [60]E(f9(a28,f4(a28)),a16)
% 3.41/3.53 [61]E(f8(a23,f10(a26)),f10(a25))
% 3.41/3.53 [62]E(f8(f10(a26),a23),f10(a25))
% 3.41/3.53 [63]E(f8(f10(a26),f10(a26)),f8(a26,a26))
% 3.41/3.53 [66]E(f11(f11(f8(a23,a23),f10(a25)),f11(f10(a25),f8(a26,a26))),f8(f11(a23,f10(a26)),f11(a23,f10(a26))))
% 3.41/3.53 [68]~E(f11(f11(f8(a23,a23),f10(a25)),f11(f8(a26,a26),f10(a25))),f8(f11(a23,f10(a26)),f11(a23,f10(a26))))
% 3.41/3.53 [81]~P2(x811)+P4(x811,x811)
% 3.41/3.53 [69]~P2(x691)+E(f10(a12),a12)
% 3.41/3.53 [70]~P1(x701)+~E(f15(x701),a3)
% 3.41/3.53 [71]~P1(x711)+P1(f15(x711))
% 3.41/3.53 [72]~P3(x721)+P1(f4(x721))
% 3.41/3.53 [73]~P2(x731)+P2(f10(x731))
% 3.41/3.53 [76]~P2(x761)+E(f8(x761,a12),a12)
% 3.41/3.53 [77]~P2(x771)+E(f8(a12,x771),a12)
% 3.41/3.53 [79]~P2(x791)+E(f11(x791,a12),x791)
% 3.41/3.53 [80]~P2(x801)+E(f11(a12,x801),x801)
% 3.41/3.53 [85]~P1(x851)+P5(x851,f15(x851))
% 3.41/3.53 [87]~P1(x871)+E(f9(a13,x871),f9(a1,x871))
% 3.41/3.53 [88]~P1(x881)+E(f9(a28,x881),f9(a27,x881))
% 3.41/3.53 [94]~P2(x941)+P4(a12,f8(x941,x941))
% 3.41/3.53 [95]~P3(x951)+P4(a12,f5(x951,x951))
% 3.41/3.53 [74]~P2(x741)+E(f10(f10(x741)),x741)
% 3.41/3.53 [83]~P2(x831)+E(f11(x831,f10(x831)),a12)
% 3.41/3.53 [84]~P2(x841)+E(f11(f10(x841),x841),a12)
% 3.41/3.53 [75]~P1(x751)+E(x751,a3)+P1(f6(x751))
% 3.41/3.53 [78]~P1(x781)+E(x781,a3)+E(f15(f6(x781)),x781)
% 3.41/3.53 [91]~P2(x912)+~P2(x911)+P2(f11(x911,x912))
% 3.41/3.53 [92]~P2(x922)+~P2(x921)+P2(f8(x921,x922))
% 3.41/3.53 [93]~P1(x932)+~P3(x931)+P2(f9(x931,x932))
% 3.41/3.53 [100]~P2(x1002)+~P2(x1001)+E(f8(f10(x1001),f10(x1002)),f8(x1001,x1002))
% 3.41/3.53 [104]~P2(x1042)+~P2(x1041)+E(f10(f8(x1041,x1042)),f8(x1041,f10(x1042)))
% 3.41/3.53 [105]~P2(x1052)+~P2(x1051)+E(f10(f8(x1051,x1052)),f8(f10(x1051),x1052))
% 3.41/3.53 [90]P4(x902,x901)+~P2(x901)+~P2(x902)+P4(x901,x902)
% 3.41/3.53 [82]~P3(x821)+P3(x822)+~E(x822,f2(x821))+E(f4(x821),a3)
% 3.41/3.53 [86]~P1(x862)+~P1(x861)+E(x861,x862)+~E(f15(x861),f15(x862))
% 3.41/3.53 [102]~P3(x1022)+~P3(x1021)+~E(f4(x1021),f4(x1022))+P2(f5(x1021,x1022))
% 3.41/3.53 [89]~P3(x891)+~E(x892,f2(x891))+E(f4(x891),a3)+E(f15(f4(x892)),f4(x891))
% 3.41/3.53 [97]~P2(x972)+~P2(x971)+~P2(x973)+E(f11(x971,x972),f11(x972,x971))
% 3.41/3.53 [98]~P2(x982)+~P2(x981)+~P2(x983)+E(f8(x981,x982),f8(x982,x981))
% 3.41/3.53 [110]~P2(x1103)+~P2(x1102)+~P2(x1101)+E(f11(f11(x1101,x1102),x1103),f11(x1101,f11(x1102,x1103)))
% 3.41/3.53 [111]~P2(x1113)+~P2(x1112)+~P2(x1111)+E(f8(f8(x1111,x1112),x1113),f8(x1111,f8(x1112,x1113)))
% 3.41/3.53 [113]~P2(x1133)+~P2(x1132)+~P2(x1131)+E(f11(f8(x1131,x1132),f8(x1131,x1133)),f8(x1131,f11(x1132,x1133)))
% 3.41/3.53 [114]~P2(x1142)+~P2(x1143)+~P2(x1141)+E(f11(f8(x1141,x1142),f8(x1143,x1142)),f8(f11(x1141,x1143),x1142))
% 3.41/3.53 [103]~P2(x1032)+~P2(x1031)+~P4(x1032,x1031)+~P4(x1031,x1032)+E(x1031,x1032)
% 3.41/3.53 [96]~P3(x962)+~P3(x961)+~E(f4(x961),f4(x962))+~E(f4(x962),a3)+E(f5(x961,x962),a12)
% 3.41/3.53 [108]~P2(x1082)+~P2(x1081)+~P4(a12,x1082)+~P4(a12,x1081)+P4(a12,f11(x1081,x1082))
% 3.41/3.53 [109]~P2(x1092)+~P2(x1091)+~P4(a12,x1092)+~P4(a12,x1091)+P4(a12,f8(x1091,x1092))
% 3.41/3.53 [99]~P3(x991)+~P3(x992)+~E(f4(x992),f4(x991))+E(f4(x991),a3)+E(f4(f2(x992)),f4(f2(x991)))
% 3.41/3.53 [119]~P3(x1192)+~P3(x1191)+~E(f4(x1191),f4(x1192))+~P5(f4(x1191),f4(a1))+P4(f8(f5(x1191,x1192),f5(x1191,x1192)),f8(f5(x1191,x1191),f5(x1192,x1192)))
% 3.41/3.53 [118]~P3(x1181)+~P3(x1182)+~E(f4(x1182),f4(x1181))+E(f4(x1181),a3)+E(f11(f5(f2(x1182),f2(x1181)),f8(f9(x1182,f4(x1182)),f9(x1181,f4(x1181)))),f5(x1182,x1181))
% 3.41/3.53 [101]~P1(x1013)+~P3(x1011)+~E(x1012,f2(x1011))+E(f9(x1012,x1013),f9(x1011,x1013))+E(f4(x1011),a3)
% 3.41/3.53 [120]~P2(x1203)+~P2(x1202)+~P2(x1204)+~P2(x1201)+E(f11(f11(f8(x1201,x1202),f8(x1201,x1203)),f11(f8(x1204,x1202),f8(x1204,x1203))),f8(f11(x1201,x1204),f11(x1202,x1203)))
% 3.41/3.53 [112]~P2(x1122)+~P2(x1121)+E(x1121,x1122)+~E(f8(x1121,x1121),f8(x1122,x1122))+~P4(a12,x1122)+~P4(a12,x1121)
% 3.41/3.53 [106]~P3(x1061)+~P3(x1062)+E(x1061,f2(x1062))+E(f4(x1062),a3)+P1(f7(x1062,x1061))+~E(f15(f4(x1061)),f4(x1062))
% 3.41/3.53 [117]~P3(x1172)+~P3(x1171)+E(x1171,f2(x1172))+E(f4(x1172),a3)+~E(f15(f4(x1171)),f4(x1172))+~E(f9(x1171,f7(x1172,x1171)),f9(x1172,f7(x1172,x1171)))
% 3.41/3.53 [107]~P2(x1072)+~P2(x1071)+~P4(x1073,x1072)+~P4(x1071,x1073)+P4(x1071,x1072)+~P2(x1073)
% 3.41/3.53 [115]~P2(x1154)+~P2(x1152)+~P2(x1153)+~P2(x1151)+~P4(x1152,x1154)+~P4(x1151,x1153)+P4(f11(x1151,x1152),f11(x1153,x1154))
% 3.41/3.53 [116]~P2(x1164)+~P2(x1162)+~P2(x1163)+~P2(x1161)+~P4(x1162,x1164)+~P4(x1161,x1163)+~P4(a12,x1162)+P4(f8(x1161,x1162),f8(x1163,x1164))
% 3.41/3.53 %EqnAxiom
% 3.41/3.53 [1]E(x11,x11)
% 3.41/3.53 [2]E(x22,x21)+~E(x21,x22)
% 3.41/3.53 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 3.41/3.53 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 3.41/3.53 [5]~E(x51,x52)+E(f8(x51,x53),f8(x52,x53))
% 3.41/3.53 [6]~E(x61,x62)+E(f8(x63,x61),f8(x63,x62))
% 3.41/3.53 [7]~E(x71,x72)+E(f4(x71),f4(x72))
% 3.41/3.53 [8]~E(x81,x82)+E(f11(x81,x83),f11(x82,x83))
% 3.41/3.53 [9]~E(x91,x92)+E(f11(x93,x91),f11(x93,x92))
% 3.41/3.53 [10]~E(x101,x102)+E(f5(x101,x103),f5(x102,x103))
% 3.41/3.53 [11]~E(x111,x112)+E(f5(x113,x111),f5(x113,x112))
% 3.41/3.53 [12]~E(x121,x122)+E(f15(x121),f15(x122))
% 3.41/3.53 [13]~E(x131,x132)+E(f9(x131,x133),f9(x132,x133))
% 3.41/3.53 [14]~E(x141,x142)+E(f9(x143,x141),f9(x143,x142))
% 3.41/3.53 [15]~E(x151,x152)+E(f10(x151),f10(x152))
% 3.41/3.53 [16]~E(x161,x162)+E(f6(x161),f6(x162))
% 3.41/3.53 [17]~E(x171,x172)+E(f7(x171,x173),f7(x172,x173))
% 3.41/3.53 [18]~E(x181,x182)+E(f7(x183,x181),f7(x183,x182))
% 3.41/3.53 [19]~P1(x191)+P1(x192)+~E(x191,x192)
% 3.41/3.53 [20]~P2(x201)+P2(x202)+~E(x201,x202)
% 3.41/3.53 [21]P4(x212,x213)+~E(x211,x212)+~P4(x211,x213)
% 3.41/3.53 [22]P4(x223,x222)+~E(x221,x222)+~P4(x223,x221)
% 3.41/3.53 [23]~P3(x231)+P3(x232)+~E(x231,x232)
% 3.41/3.53 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243)
% 3.41/3.53 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251)
% 3.41/3.53
% 3.41/3.53 %-------------------------------------------
% 3.41/3.53 cnf(121,plain,
% 3.41/3.53 (E(a13,f2(a1))),
% 3.41/3.53 inference(scs_inference,[],[26,2])).
% 3.41/3.53 cnf(122,plain,
% 3.41/3.53 (P3(f2(a1))),
% 3.41/3.53 inference(scs_inference,[],[44,26,2,23])).
% 3.41/3.53 cnf(123,plain,
% 3.41/3.53 (E(f15(f4(a27)),f4(a1))),
% 3.41/3.53 inference(scs_inference,[],[44,26,46,48,2,23,3])).
% 3.41/3.53 cnf(124,plain,
% 3.41/3.53 (P4(a12,a12)),
% 3.41/3.53 inference(scs_inference,[],[29,44,26,46,48,2,23,3,90])).
% 3.41/3.53 cnf(126,plain,
% 3.41/3.53 (E(f9(a13,a3),f9(a1,a3))),
% 3.41/3.53 inference(scs_inference,[],[28,29,42,44,26,67,46,48,2,23,3,90,101])).
% 3.41/3.53 cnf(128,plain,
% 3.41/3.53 (E(f4(f2(a28)),f4(f2(a1)))),
% 3.41/3.53 inference(scs_inference,[],[28,29,42,43,44,26,67,46,48,2,23,3,90,101,99])).
% 3.41/3.53 cnf(130,plain,
% 3.41/3.53 (P4(f8(a12,a12),f8(a12,a12))),
% 3.41/3.53 inference(scs_inference,[],[28,29,42,43,44,26,67,46,48,2,23,3,90,101,99,116])).
% 3.41/3.53 cnf(131,plain,
% 3.41/3.53 (P4(a14,a14)),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81])).
% 3.41/3.53 cnf(133,plain,
% 3.41/3.53 (E(f10(a12),a12)),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69])).
% 3.41/3.53 cnf(135,plain,
% 3.41/3.53 (P5(a3,f15(a3))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85])).
% 3.41/3.53 cnf(137,plain,
% 3.41/3.53 (E(f11(a12,a12),a12)),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80])).
% 3.41/3.53 cnf(139,plain,
% 3.41/3.53 (E(f11(a14,a12),a14)),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79])).
% 3.41/3.53 cnf(141,plain,
% 3.41/3.53 (E(f8(a12,a12),a12)),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77])).
% 3.41/3.53 cnf(143,plain,
% 3.41/3.53 (E(f8(a14,a12),a12)),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76])).
% 3.41/3.53 cnf(149,plain,
% 3.41/3.53 (P1(f4(a1))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72])).
% 3.41/3.53 cnf(151,plain,
% 3.41/3.53 (P1(f15(a3))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71])).
% 3.41/3.53 cnf(153,plain,
% 3.41/3.53 (~E(f15(a3),a3)),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70])).
% 3.41/3.53 cnf(155,plain,
% 3.41/3.53 (E(f7(x1551,f2(a1)),f7(x1551,a13))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18])).
% 3.41/3.53 cnf(160,plain,
% 3.41/3.53 (E(f9(f2(a1),x1601),f9(a13,x1601))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13])).
% 3.41/3.53 cnf(162,plain,
% 3.41/3.53 (E(f5(x1621,f2(a1)),f5(x1621,a13))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11])).
% 3.41/3.53 cnf(163,plain,
% 3.41/3.53 (E(f5(f2(a1),x1631),f5(a13,x1631))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10])).
% 3.41/3.53 cnf(165,plain,
% 3.41/3.53 (E(f11(f2(a1),x1651),f11(a13,x1651))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8])).
% 3.41/3.53 cnf(166,plain,
% 3.41/3.53 (E(f4(f2(a1)),f4(a13))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7])).
% 3.41/3.53 cnf(169,plain,
% 3.41/3.53 (E(f2(f2(a1)),f2(a13))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4])).
% 3.41/3.53 cnf(170,plain,
% 3.41/3.53 (P4(a12,f5(a1,a1))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95])).
% 3.41/3.53 cnf(172,plain,
% 3.41/3.53 (P4(a12,f8(a12,a12))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94])).
% 3.41/3.53 cnf(176,plain,
% 3.41/3.53 (E(f9(a13,f4(a1)),f9(a1,f4(a1)))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87])).
% 3.41/3.53 cnf(182,plain,
% 3.41/3.53 (~E(a12,x1821)+P2(x1821)),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87,84,83,20])).
% 3.41/3.53 cnf(183,plain,
% 3.41/3.53 (P2(f9(a1,a3))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87,84,83,20,93])).
% 3.41/3.53 cnf(185,plain,
% 3.41/3.53 (P2(f8(a12,a12))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87,84,83,20,93,92])).
% 3.41/3.53 cnf(187,plain,
% 3.41/3.53 (P2(f11(a12,a12))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87,84,83,20,93,92,91])).
% 3.41/3.53 cnf(189,plain,
% 3.41/3.53 (E(f15(f6(f4(a1))),f4(a1))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87,84,83,20,93,92,91,78])).
% 3.41/3.53 cnf(191,plain,
% 3.41/3.53 (P1(f6(f4(a1)))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87,84,83,20,93,92,91,78,75])).
% 3.41/3.53 cnf(199,plain,
% 3.41/3.53 (~E(a12,x1991)+E(f8(a12,x1991),f8(x1991,a12))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87,84,83,20,93,92,91,78,75,105,104,100,98])).
% 3.41/3.53 cnf(201,plain,
% 3.41/3.53 (~E(a12,x2011)+E(f11(a12,x2011),f11(x2011,a12))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87,84,83,20,93,92,91,78,75,105,104,100,98,97])).
% 3.41/3.53 cnf(203,plain,
% 3.41/3.53 (~E(a12,x2031)+~E(f15(f4(a1)),f15(a3))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87,84,83,20,93,92,91,78,75,105,104,100,98,97,86])).
% 3.41/3.53 cnf(209,plain,
% 3.41/3.53 (~E(a12,x2091)+E(f11(f8(a12,a12),f8(a12,a12)),f8(f11(a12,a12),a12))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87,84,83,20,93,92,91,78,75,105,104,100,98,97,86,111,110,114])).
% 3.41/3.53 cnf(211,plain,
% 3.41/3.53 (~E(a12,x2111)+E(f11(f8(a12,a12),f8(a12,a12)),f8(a12,f11(a12,a12)))),
% 3.41/3.53 inference(scs_inference,[],[28,29,30,42,43,44,26,67,46,48,2,23,3,90,101,99,116,81,69,85,80,79,77,76,74,73,72,71,70,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,95,94,88,87,84,83,20,93,92,91,78,75,105,104,100,98,97,86,111,110,114,113])).
% 3.41/3.53 cnf(239,plain,
% 3.41/3.53 (E(f11(f8(a12,a12),f8(a12,a12)),f8(f11(a12,a12),a12))),
% 3.41/3.53 inference(equality_inference,[],[209])).
% 3.41/3.53 cnf(240,plain,
% 3.41/3.53 (E(f11(f8(a12,a12),f8(a12,a12)),f8(a12,f11(a12,a12)))),
% 3.41/3.53 inference(equality_inference,[],[211])).
% 3.41/3.53 cnf(242,plain,
% 3.41/3.53 (~P2(x2421)+~P2(x2422)+E(f11(x2422,x2421),f11(x2421,x2422))),
% 3.41/3.53 inference(scs_inference,[],[31,97])).
% 3.41/3.53 cnf(250,plain,
% 3.41/3.53 (E(f15(f6(f15(a3))),f15(a3))),
% 3.41/3.53 inference(scs_inference,[],[31,45,28,151,153,93,92,91,78])).
% 3.41/3.53 cnf(252,plain,
% 3.41/3.53 (E(f8(f10(a16),f10(a16)),f8(a16,a16))),
% 3.41/3.53 inference(scs_inference,[],[31,45,28,151,153,93,92,91,78,100])).
% 3.41/3.53 cnf(258,plain,
% 3.41/3.53 (P4(f8(a12,a12),a12)),
% 3.41/3.53 inference(scs_inference,[],[31,45,28,141,130,151,153,93,92,91,78,100,111,120,22])).
% 3.41/3.53 cnf(259,plain,
% 3.41/3.53 (~E(f11(f11(f8(a23,a23),f10(a25)),f11(f8(a26,a26),f10(a25))),f11(f11(f8(a23,a23),f10(a25)),f11(f10(a25),f8(a26,a26))))),
% 3.41/3.53 inference(scs_inference,[],[68,31,45,66,28,141,130,151,153,93,92,91,78,100,111,120,22,3])).
% 3.41/3.53 cnf(260,plain,
% 3.41/3.53 (P1(f6(f15(a3)))),
% 3.41/3.53 inference(scs_inference,[],[68,31,45,66,28,141,130,151,153,93,92,91,78,100,111,120,22,3,75])).
% 3.41/3.53 cnf(274,plain,
% 3.41/3.53 (~E(f11(f8(a26,a26),f10(a25)),f11(f10(a25),f8(a26,a26)))),
% 3.41/3.53 inference(scs_inference,[],[68,31,45,66,43,46,67,28,42,141,130,151,153,93,92,91,78,100,111,120,22,3,75,105,104,110,114,113,118,9])).
% 3.41/3.53 cnf(277,plain,
% 3.41/3.53 (P4(a12,f8(f8(a12,a12),f8(a12,a12)))),
% 3.41/3.53 inference(scs_inference,[],[68,31,45,66,43,46,67,28,42,185,172,141,130,151,153,93,92,91,78,100,111,120,22,3,75,105,104,110,114,113,118,9,2,19,109])).
% 3.41/3.53 cnf(279,plain,
% 3.41/3.53 (P4(a12,f11(a12,a12))),
% 3.41/3.53 inference(scs_inference,[],[68,31,45,66,43,46,67,28,42,29,185,124,172,141,130,151,153,93,92,91,78,100,111,120,22,3,75,105,104,110,114,113,118,9,2,19,109,108])).
% 3.41/3.53 cnf(285,plain,
% 3.41/3.53 (E(f6(f15(a3)),a3)),
% 3.41/3.53 inference(scs_inference,[],[68,31,45,66,30,43,46,67,28,42,29,185,124,172,141,130,151,153,131,93,92,91,78,100,111,120,22,3,75,105,104,110,114,113,118,9,2,19,109,108,115,116,86])).
% 3.41/3.53 cnf(298,plain,
% 3.41/3.53 (E(a12,f8(a12,a12))),
% 3.41/3.53 inference(scs_inference,[],[32,29,258,172,185,111,103])).
% 3.41/3.53 cnf(310,plain,
% 3.41/3.53 (P4(f8(a12,a12),f11(a12,a12))),
% 3.41/3.53 inference(scs_inference,[],[32,29,187,279,258,172,185,124,111,103,120,115,114,109,108,21])).
% 3.41/3.53 cnf(311,plain,
% 3.41/3.53 (E(f4(f2(a28)),f4(a13))),
% 3.41/3.53 inference(scs_inference,[],[32,29,128,187,279,166,258,172,185,124,111,103,120,115,114,109,108,21,3])).
% 3.41/3.53 cnf(317,plain,
% 3.41/3.53 (E(a27,f2(a28))),
% 3.41/3.53 inference(scs_inference,[],[32,27,29,128,187,279,166,258,172,185,124,111,103,120,115,114,109,108,21,3,110,113,9,2])).
% 3.41/3.53 cnf(318,plain,
% 3.41/3.53 (~E(f15(f4(a1)),f15(a3))),
% 3.41/3.53 inference(scs_inference,[],[32,27,29,128,187,279,166,258,172,185,124,111,103,120,115,114,109,108,21,3,110,113,9,2,203])).
% 3.41/3.53 cnf(330,plain,
% 3.41/3.53 (P4(a17,a17)),
% 3.41/3.53 inference(scs_inference,[],[32,27,44,28,29,128,187,279,166,169,258,130,172,185,124,111,103,120,115,114,109,108,21,3,110,113,9,2,203,201,199,101,116,112,90])).
% 3.41/3.53 cnf(336,plain,
% 3.41/3.53 (~E(f4(a13),a3)+E(f5(a13,a13),a12)),
% 3.41/3.53 inference(scs_inference,[],[32,27,44,28,29,128,187,279,166,169,258,135,130,172,185,124,111,103,120,115,114,109,108,21,3,110,113,9,2,203,201,199,101,116,112,90,25,24,102,96])).
% 3.41/3.53 cnf(342,plain,
% 3.41/3.53 (P3(f2(a28))),
% 3.41/3.53 inference(scs_inference,[],[45,317,23])).
% 3.41/3.53 cnf(347,plain,
% 3.41/3.53 (~E(a3,f4(a1))),
% 3.41/3.53 inference(scs_inference,[],[33,49,45,67,162,317,23,120,3,2])).
% 3.41/3.53 cnf(350,plain,
% 3.41/3.53 (P2(f5(f2(a28),a13))),
% 3.41/3.53 inference(scs_inference,[],[33,49,45,44,67,162,311,317,169,23,120,3,2,89,102])).
% 3.41/3.53 cnf(356,plain,
% 3.41/3.53 (P4(a12,f11(f8(a12,a12),f8(a12,a12)))),
% 3.41/3.53 inference(scs_inference,[],[33,49,45,44,67,28,162,311,149,317,169,172,187,185,279,23,120,3,2,89,102,86,109,108])).
% 3.41/3.53 cnf(365,plain,
% 3.41/3.53 (P4(f11(f8(a12,a12),f8(a12,a12)),f11(f11(a12,a12),f11(a12,a12)))),
% 3.41/3.53 inference(scs_inference,[],[310,187,185,115])).
% 3.41/3.53 cnf(367,plain,
% 3.41/3.53 (~E(f4(a1),f6(f15(a3)))),
% 3.41/3.53 inference(scs_inference,[],[67,310,285,187,185,115,3])).
% 3.41/3.54 cnf(368,plain,
% 3.41/3.54 (E(a18,f5(a27,a27))),
% 3.41/3.54 inference(scs_inference,[],[50,67,310,285,187,185,115,3,2])).
% 3.41/3.54 cnf(371,plain,
% 3.41/3.54 (~E(f15(f6(f4(a1))),a3)),
% 3.41/3.54 inference(scs_inference,[],[50,44,67,310,285,191,169,187,185,115,3,2,82,70])).
% 3.41/3.54 cnf(383,plain,
% 3.41/3.54 (P5(f6(f4(a1)),f15(f6(f4(a1))))),
% 3.41/3.54 inference(scs_inference,[],[34,50,44,67,310,277,285,191,169,187,185,115,3,2,82,70,88,84,83,112,76,85])).
% 3.41/3.54 cnf(393,plain,
% 3.41/3.54 (P1(f4(f2(a1)))),
% 3.41/3.54 inference(scs_inference,[],[34,50,122,44,67,310,277,285,191,169,187,185,115,3,2,82,70,88,84,83,112,76,85,80,77,74,73,72])).
% 3.41/3.54 cnf(395,plain,
% 3.41/3.54 (P1(f15(f6(f4(a1))))),
% 3.41/3.54 inference(scs_inference,[],[34,50,122,44,67,310,277,285,191,169,187,185,115,3,2,82,70,88,84,83,112,76,85,80,77,74,73,72,71])).
% 3.41/3.54 cnf(402,plain,
% 3.41/3.54 (E(f2(f2(a28)),f2(a27))),
% 3.41/3.54 inference(scs_inference,[],[27,34,50,122,44,67,310,277,285,191,169,187,185,115,3,2,82,70,88,84,83,112,76,85,80,77,74,73,72,71,16,15,14,8,6,4])).
% 3.41/3.54 cnf(403,plain,
% 3.41/3.54 (P4(a12,f5(f2(a1),f2(a1)))),
% 3.41/3.54 inference(scs_inference,[],[27,34,50,122,44,67,310,277,285,191,169,187,185,115,3,2,82,70,88,84,83,112,76,85,80,77,74,73,72,71,16,15,14,8,6,4,95])).
% 3.41/3.54 cnf(420,plain,
% 3.41/3.54 (P4(a20,a20)),
% 3.41/3.54 inference(scs_inference,[],[35,81])).
% 3.41/3.54 cnf(429,plain,
% 3.41/3.54 (E(f5(f2(a28),x4291),f5(a27,x4291))),
% 3.41/3.54 inference(scs_inference,[],[27,35,393,81,79,87,18,17,11,10])).
% 3.41/3.54 cnf(430,plain,
% 3.41/3.54 (E(f4(f2(a28)),f4(a27))),
% 3.41/3.54 inference(scs_inference,[],[27,35,393,81,79,87,18,17,11,10,7])).
% 3.41/3.54 cnf(434,plain,
% 3.41/3.54 (~E(f11(f10(a25),f8(a26,a26)),f11(f8(a26,a26),f10(a25)))),
% 3.41/3.54 inference(scs_inference,[],[27,35,59,274,176,393,81,79,87,18,17,11,10,7,5,13,3,2])).
% 3.41/3.54 cnf(469,plain,
% 3.41/3.54 (P1(f6(f15(f6(f4(a1)))))),
% 3.41/3.54 inference(scs_inference,[],[28,37,43,395,371,92,91,100,93,105,104,75])).
% 3.41/3.54 cnf(475,plain,
% 3.41/3.54 (E(a19,f5(a13,a27))),
% 3.41/3.54 inference(scs_inference,[],[28,37,51,43,189,395,239,163,383,356,371,92,91,100,93,105,104,75,25,22,3,2])).
% 3.41/3.54 cnf(495,plain,
% 3.41/3.54 (~E(f15(f4(a1)),f15(f6(f15(a3))))),
% 3.41/3.54 inference(scs_inference,[],[45,367,260,430,149,342,102,86])).
% 3.41/3.54 cnf(506,plain,
% 3.41/3.54 (P4(a12,f5(f2(a1),a13))),
% 3.41/3.54 inference(scs_inference,[],[38,45,365,240,367,403,260,162,430,149,342,102,86,104,111,105,114,21,22])).
% 3.41/3.54 cnf(508,plain,
% 3.41/3.54 (~E(a3,f15(f4(a13)))),
% 3.41/3.54 inference(scs_inference,[],[38,47,45,365,347,240,367,403,260,162,430,149,342,102,86,104,111,105,114,21,22,3])).
% 3.41/3.54 cnf(510,plain,
% 3.41/3.54 (P4(a23,a23)),
% 3.41/3.54 inference(scs_inference,[],[38,47,45,365,347,240,367,403,260,162,430,149,342,102,86,104,111,105,114,21,22,3,2,90])).
% 3.41/3.54 cnf(516,plain,
% 3.41/3.54 (E(f11(x5161,f8(a14,a14)),f11(x5161,a20))),
% 3.41/3.54 inference(scs_inference,[],[38,52,47,45,365,347,240,367,403,260,162,430,149,342,102,86,104,111,105,114,21,22,3,2,90,110,113,9])).
% 3.41/3.54 cnf(545,plain,
% 3.41/3.54 (E(a22,f8(a14,a16))),
% 3.41/3.54 inference(scs_inference,[],[29,40,54,124,35,420,516,165,279,187,111,108,120,114,113,116,110,3,2])).
% 3.41/3.54 cnf(558,plain,
% 3.41/3.54 (~E(f15(f15(f6(f4(a1)))),a3)),
% 3.41/3.54 inference(scs_inference,[],[29,40,54,124,35,420,516,165,395,260,279,187,111,108,120,114,113,116,110,3,2,88,84,77,74,73,71,70])).
% 3.41/3.54 cnf(562,plain,
% 3.41/3.54 (P4(a12,f8(a26,a26))),
% 3.41/3.54 inference(scs_inference,[],[29,40,54,124,35,43,420,516,165,395,260,279,187,111,108,120,114,113,116,110,3,2,88,84,77,74,73,71,70,95,94])).
% 3.41/3.54 cnf(572,plain,
% 3.41/3.54 (P1(f4(a28))),
% 3.41/3.54 inference(scs_inference,[],[29,40,54,124,35,43,420,516,165,395,260,279,187,111,108,120,114,113,116,110,3,2,88,84,77,74,73,71,70,95,94,83,76,85,80,72])).
% 3.41/3.54 cnf(580,plain,
% 3.41/3.54 (E(f8(x5801,f8(a14,a16)),f8(x5801,a22))),
% 3.41/3.54 inference(scs_inference,[],[29,40,54,124,35,43,420,516,165,395,260,279,187,111,108,120,114,113,116,110,3,2,88,84,77,74,73,71,70,95,94,83,76,85,80,72,16,14,8,4,12,15,6])).
% 3.41/3.54 cnf(581,plain,
% 3.41/3.54 (P2(f5(f2(a1),f2(a1)))),
% 3.41/3.54 inference(scs_inference,[],[29,40,54,124,35,122,43,420,516,165,395,260,279,187,111,108,120,114,113,116,110,3,2,88,84,77,74,73,71,70,95,94,83,76,85,80,72,16,14,8,4,12,15,6,102])).
% 3.41/3.54 cnf(586,plain,
% 3.41/3.54 (P1(f4(a13))),
% 3.41/3.54 inference(scs_inference,[],[29,40,54,124,35,122,43,420,516,165,189,403,395,260,393,166,279,187,111,108,120,114,113,116,110,3,2,88,84,77,74,73,71,70,95,94,83,76,85,80,72,16,14,8,4,12,15,6,102,24,109,19])).
% 3.41/3.54 cnf(613,plain,
% 3.41/3.54 (P4(f8(a14,a12),a12)),
% 3.41/3.54 inference(scs_inference,[],[29,36,30,124,581,429,350,143,131,403,120,20,109,116,110,113,22])).
% 3.41/3.54 cnf(617,plain,
% 3.41/3.54 (P4(a21,a21)),
% 3.41/3.54 inference(scs_inference,[],[29,56,36,30,124,581,429,495,580,350,143,131,403,120,20,109,116,110,113,22,3,2,81])).
% 3.41/3.54 cnf(628,plain,
% 3.41/3.54 (E(f8(f8(a17,a21),x6281),f8(a23,x6281))),
% 3.41/3.54 inference(scs_inference,[],[29,55,56,36,30,45,124,581,429,495,580,350,572,143,402,131,403,120,20,109,116,110,113,22,3,2,81,79,87,89,18,11,10,5])).
% 3.41/3.54 cnf(644,plain,
% 3.41/3.54 (E(f7(f9(a13,a3),x6441),f7(f9(a1,a3),x6441))),
% 3.41/3.54 inference(scs_inference,[],[30,126,92,17])).
% 3.41/3.54 cnf(651,plain,
% 3.41/3.54 (~E(f15(f15(f6(f4(a1)))),f6(f15(a3)))),
% 3.41/3.54 inference(scs_inference,[],[30,126,124,558,613,285,298,581,403,29,92,17,7,120,109,22,3])).
% 3.41/3.54 cnf(652,plain,
% 3.41/3.54 (E(f9(a1,a3),f9(a13,a3))),
% 3.41/3.54 inference(scs_inference,[],[30,126,124,558,613,285,298,581,403,29,92,17,7,120,109,22,3,2])).
% 3.41/3.54 cnf(655,plain,
% 3.41/3.54 (E(f8(f10(a14),f10(a14)),f8(a14,a14))),
% 3.41/3.54 inference(scs_inference,[],[30,126,124,558,613,285,298,581,403,29,92,17,7,120,109,22,3,2,91,100])).
% 3.41/3.54 cnf(657,plain,
% 3.41/3.54 (P2(f9(f2(a1),f4(a13)))),
% 3.41/3.54 inference(scs_inference,[],[30,126,122,124,586,558,613,285,298,581,403,29,92,17,7,120,109,22,3,2,91,100,93])).
% 3.41/3.54 cnf(669,plain,
% 3.41/3.54 (P2(f8(a24,a24))),
% 3.41/3.54 inference(scs_inference,[],[39,91,92])).
% 3.41/3.54 cnf(677,plain,
% 3.41/3.54 (~E(f6(f15(a3)),f15(f15(f6(f4(a1)))))),
% 3.41/3.54 inference(scs_inference,[],[58,39,644,651,155,91,92,100,13,3,2])).
% 3.41/3.54 cnf(688,plain,
% 3.41/3.54 (~E(a14,x6881)+P2(x6881)+E(f9(f2(f2(a1)),f4(a28)),f9(a13,f4(a28)))),
% 3.41/3.54 inference(scs_inference,[],[30,58,39,64,41,44,644,469,651,155,572,131,169,91,92,100,13,3,2,115,104,101,336,105,19,20])).
% 3.41/3.54 cnf(700,plain,
% 3.41/3.54 (E(a16,f9(a28,f4(a28)))),
% 3.41/3.54 inference(scs_inference,[],[60,61,33,628,104,105,3,2])).
% 3.41/3.54 cnf(703,plain,
% 3.41/3.54 (P1(f15(f4(a13)))),
% 3.41/3.54 inference(scs_inference,[],[60,61,33,122,44,628,586,166,104,105,3,2,96,71])).
% 3.41/3.54 cnf(711,plain,
% 3.41/3.54 (P4(a12,f5(a27,a27))),
% 3.41/3.54 inference(scs_inference,[],[31,60,61,33,45,122,44,628,586,166,104,105,3,2,96,71,88,74,73,95])).
% 3.41/3.54 cnf(713,plain,
% 3.41/3.54 (P4(a12,f8(a16,a16))),
% 3.41/3.54 inference(scs_inference,[],[31,60,61,33,45,122,44,628,586,166,104,105,3,2,96,71,88,74,73,95,94])).
% 3.41/3.54 cnf(719,plain,
% 3.41/3.54 (P5(f4(a13),f15(f4(a13)))),
% 3.41/3.54 inference(scs_inference,[],[31,60,61,33,45,122,44,628,586,166,104,105,3,2,96,71,88,74,73,95,94,84,76,85])).
% 3.41/3.54 cnf(725,plain,
% 3.41/3.54 (P1(f4(a27))),
% 3.41/3.54 inference(scs_inference,[],[31,60,61,33,45,122,44,628,586,166,104,105,3,2,96,71,88,74,73,95,94,84,76,85,70,77,72])).
% 3.41/3.54 cnf(734,plain,
% 3.41/3.54 (P1(f6(f15(f4(a13))))),
% 3.41/3.54 inference(scs_inference,[],[31,60,61,33,45,122,44,628,586,166,104,105,3,2,96,71,88,74,73,95,94,84,76,85,70,77,72,83,16,14,4,80,75])).
% 3.41/3.54 cnf(737,plain,
% 3.41/3.54 (E(f15(f6(f15(f4(a13)))),f15(f4(a13)))),
% 3.41/3.54 inference(scs_inference,[],[31,60,61,33,45,122,44,628,365,239,586,166,104,105,3,2,96,71,88,74,73,95,94,84,76,85,70,77,72,83,16,14,4,80,75,21,78])).
% 3.41/3.54 cnf(743,plain,
% 3.41/3.54 (E(f6(f15(f4(a13))),f4(a13))),
% 3.41/3.54 inference(scs_inference,[],[31,60,61,33,46,45,43,122,44,42,124,628,365,239,586,166,29,104,105,3,2,96,71,88,74,73,95,94,84,76,85,70,77,72,83,16,14,4,80,75,21,78,119,112,86])).
% 3.41/3.54 cnf(747,plain,
% 3.41/3.54 (E(f8(x7471,f9(a28,f4(a28))),f8(x7471,a16))),
% 3.41/3.54 inference(scs_inference,[],[31,60,61,33,46,45,43,122,44,42,124,628,365,239,586,166,29,104,105,3,2,96,71,88,74,73,95,94,84,76,85,70,77,72,83,16,14,4,80,75,21,78,119,112,86,15,8,6])).
% 3.41/3.54 cnf(748,plain,
% 3.41/3.54 (P2(f8(a18,a18))),
% 3.41/3.54 inference(scs_inference,[],[31,60,61,33,46,45,43,122,44,42,124,628,365,239,586,166,29,104,105,3,2,96,71,88,74,73,95,94,84,76,85,70,77,72,83,16,14,4,80,75,21,78,119,112,86,15,8,6,92])).
% 3.41/3.54 cnf(776,plain,
% 3.41/3.54 (P5(f4(a13),f4(a1))),
% 3.41/3.54 inference(scs_inference,[],[47,64,41,669,719,115,92,111,114,25])).
% 3.41/3.54 cnf(778,plain,
% 3.41/3.54 (P4(a12,a21)),
% 3.41/3.54 inference(scs_inference,[],[53,47,64,41,652,183,669,719,713,115,92,111,114,25,20,22])).
% 3.41/3.54 cnf(783,plain,
% 3.41/3.54 (P4(a16,a16)),
% 3.41/3.54 inference(scs_inference,[],[31,53,47,64,41,36,124,652,183,677,669,719,713,259,285,29,115,92,111,114,25,20,22,3,2,112,81])).
% 3.41/3.54 cnf(792,plain,
% 3.41/3.54 (~E(f15(a3),f15(f15(f4(a13))))),
% 3.41/3.54 inference(scs_inference,[],[31,62,53,47,64,41,36,124,652,183,677,669,703,719,713,508,259,285,28,29,115,92,111,114,25,20,22,3,2,112,81,79,87,18,11,5,86])).
% 3.41/3.54 cnf(828,plain,
% 3.41/3.54 (P2(f5(a27,a27))),
% 3.41/3.54 inference(scs_inference,[],[39,36,33,368,778,108,111,114,110,113,20])).
% 3.41/3.54 cnf(831,plain,
% 3.41/3.54 (E(a24,f8(a19,a22))),
% 3.41/3.54 inference(scs_inference,[],[56,52,39,36,33,655,783,700,368,778,108,111,114,110,113,20,22,3,2])).
% 3.41/3.54 cnf(832,plain,
% 3.41/3.54 (P4(f11(f8(a12,a12),f8(a12,a12)),f11(f8(a12,a12),f8(a12,a12)))),
% 3.41/3.54 inference(scs_inference,[],[56,52,130,39,36,33,655,783,700,368,778,185,108,111,114,110,113,20,22,3,2,115])).
% 3.41/3.54 cnf(844,plain,
% 3.41/3.54 (P4(a24,a24)),
% 3.41/3.54 inference(scs_inference,[],[50,56,52,130,39,128,36,33,43,44,122,124,617,655,783,776,700,368,778,342,185,29,108,111,114,110,113,20,22,3,2,115,99,17,7,116,106,119,90])).
% 3.41/3.54 cnf(866,plain,
% 3.41/3.54 (~E(f15(f15(f4(a13))),f15(a3))),
% 3.41/3.54 inference(scs_inference,[],[32,49,35,36,124,330,792,163,778,29,120,108,116,110,113,3,2])).
% 3.41/3.54 cnf(873,plain,
% 3.41/3.54 (~E(f15(f15(f6(f4(a1)))),f15(a3))),
% 3.41/3.54 inference(scs_inference,[],[32,49,35,36,43,124,330,792,163,371,778,395,28,29,120,108,116,110,113,3,2,91,100,102,86])).
% 3.41/3.54 cnf(881,plain,
% 3.41/3.54 (P2(f11(a18,a18))),
% 3.41/3.54 inference(scs_inference,[],[33,91])).
% 3.41/3.54 cnf(887,plain,
% 3.41/3.54 (P4(a12,f8(a21,a21))),
% 3.41/3.54 inference(scs_inference,[],[33,34,36,778,91,100,120,109])).
% 3.41/3.54 cnf(889,plain,
% 3.41/3.54 (E(f9(f8(a20,a18),x8891),f9(a26,x8891))),
% 3.41/3.54 inference(scs_inference,[],[33,57,34,36,778,91,100,120,109,13])).
% 3.41/3.54 cnf(892,plain,
% 3.41/3.54 (P4(a12,a18)),
% 3.41/3.54 inference(scs_inference,[],[33,57,50,34,36,475,711,778,91,100,120,109,13,9,20,22])).
% 3.41/3.54 cnf(893,plain,
% 3.41/3.54 (~E(f15(f15(f4(a13))),f15(f6(f15(a3))))),
% 3.41/3.54 inference(scs_inference,[],[33,57,50,34,36,866,475,711,250,778,91,100,120,109,13,9,20,22,3])).
% 3.41/3.54 cnf(894,plain,
% 3.41/3.54 (E(a26,f8(a20,a18))),
% 3.41/3.54 inference(scs_inference,[],[33,57,50,34,36,866,475,711,250,778,91,100,120,109,13,9,20,22,3,2])).
% 3.41/3.54 cnf(903,plain,
% 3.41/3.54 (P5(f6(f15(f4(a13))),f15(f6(f15(f4(a13)))))),
% 3.41/3.54 inference(scs_inference,[],[33,57,50,34,36,734,866,475,711,250,725,778,91,100,120,109,13,9,20,22,3,2,71,88,73,76,85])).
% 3.41/3.54 cnf(909,plain,
% 3.41/3.54 (P1(f4(f2(a28)))),
% 3.41/3.54 inference(scs_inference,[],[33,57,50,34,36,734,866,475,711,250,725,778,342,91,100,120,109,13,9,20,22,3,2,71,88,73,76,85,70,74,72])).
% 3.41/3.54 cnf(911,plain,
% 3.41/3.54 (P4(a12,f8(a18,a18))),
% 3.41/3.54 inference(scs_inference,[],[33,57,50,34,36,734,866,475,711,250,725,778,342,91,100,120,109,13,9,20,22,3,2,71,88,73,76,85,70,74,72,94])).
% 3.41/3.54 cnf(917,plain,
% 3.41/3.54 (P4(a12,f5(a13,a13))),
% 3.41/3.54 inference(scs_inference,[],[33,57,50,34,36,44,734,866,475,711,250,725,778,342,91,100,120,109,13,9,20,22,3,2,71,88,73,76,85,70,74,72,94,84,83,95])).
% 3.41/3.54 cnf(921,plain,
% 3.41/3.54 (E(f9(x9211,f8(a20,a18)),f9(x9211,a26))),
% 3.41/3.54 inference(scs_inference,[],[33,57,50,34,36,44,734,866,475,711,250,725,778,342,91,100,120,109,13,9,20,22,3,2,71,88,73,76,85,70,74,72,94,84,83,95,77,14])).
% 3.41/3.54 cnf(922,plain,
% 3.41/3.54 (E(f2(f8(a20,a18)),f2(a26))),
% 3.41/3.54 inference(scs_inference,[],[33,57,50,34,36,44,734,866,475,711,250,725,778,342,91,100,120,109,13,9,20,22,3,2,71,88,73,76,85,70,74,72,94,84,83,95,77,14,4])).
% 3.41/3.54 cnf(925,plain,
% 3.41/3.54 (P2(f5(f2(a28),f2(a28)))),
% 3.41/3.54 inference(scs_inference,[],[33,57,50,34,36,44,734,866,475,711,250,725,778,342,91,100,120,109,13,9,20,22,3,2,71,88,73,76,85,70,74,72,94,84,83,95,77,14,4,80,102])).
% 3.41/3.54 cnf(941,plain,
% 3.41/3.54 (E(f8(x9411,f8(a20,a18)),f8(x9411,a26))),
% 3.41/3.54 inference(scs_inference,[],[33,57,65,50,34,36,44,828,734,866,475,711,250,725,617,778,342,29,91,100,120,109,13,9,20,22,3,2,71,88,73,76,85,70,74,72,94,84,83,95,77,14,4,80,102,12,108,116,106,112,115,16,15,8,6])).
% 3.41/3.54 cnf(944,plain,
% 3.41/3.54 (P4(a18,a18)),
% 3.41/3.54 inference(scs_inference,[],[33,57,65,50,34,36,44,828,734,866,475,711,250,725,617,778,342,29,91,100,120,109,13,9,20,22,3,2,71,88,73,76,85,70,74,72,94,84,83,95,77,14,4,80,102,12,108,116,106,112,115,16,15,8,6,104,90])).
% 3.41/3.54 cnf(961,plain,
% 3.41/3.54 (~E(f15(f6(f15(a3))),f15(f15(f4(a13))))),
% 3.41/3.54 inference(scs_inference,[],[33,59,131,37,41,124,944,893,889,921,892,368,30,29,105,104,120,109,12,116,22,3,2])).
% 3.41/3.54 cnf(964,plain,
% 3.41/3.54 (P4(a22,a22)),
% 3.41/3.54 inference(scs_inference,[],[33,59,131,37,41,124,944,893,889,921,909,892,368,30,29,105,104,120,109,12,116,22,3,2,87,81])).
% 3.41/3.54 cnf(968,plain,
% 3.41/3.54 (E(f7(x9681,f9(a1,f4(a1))),f7(x9681,a14))),
% 3.41/3.54 inference(scs_inference,[],[33,59,131,37,41,124,944,893,889,921,909,892,368,30,29,105,104,120,109,12,116,22,3,2,87,81,79,18])).
% 3.41/3.54 cnf(970,plain,
% 3.41/3.54 (P2(f8(a23,a23))),
% 3.41/3.54 inference(scs_inference,[],[33,59,131,38,37,41,124,944,893,889,921,909,892,368,30,29,105,104,120,109,12,116,22,3,2,87,81,79,18,11,92])).
% 3.41/3.54 cnf(980,plain,
% 3.41/3.54 (P5(f6(f15(f4(a13))),f15(f4(a13)))),
% 3.41/3.54 inference(scs_inference,[],[33,59,131,64,38,37,41,124,944,903,893,889,921,909,892,737,368,669,30,29,105,104,120,109,12,116,22,3,2,87,81,79,18,11,92,10,5,115,107,108,25])).
% 3.41/3.54 cnf(1004,plain,
% 3.41/3.54 (E(a12,f10(a12))),
% 3.41/3.54 inference(scs_inference,[],[34,133,53,35,961,747,420,92,115,12,3,2])).
% 3.41/3.54 cnf(1008,plain,
% 3.41/3.54 (E(f7(f10(a12),x10081),f7(a12,x10081))),
% 3.41/3.54 inference(scs_inference,[],[34,133,53,35,42,67,961,747,420,92,115,12,3,2,118,7,17])).
% 3.41/3.54 cnf(1019,plain,
% 3.41/3.54 (P4(f8(a12,f11(a12,a12)),f11(f8(a12,a12),f8(a12,a12)))),
% 3.41/3.54 inference(scs_inference,[],[34,133,53,35,42,67,124,832,961,911,748,747,420,240,29,92,115,12,3,2,118,7,17,111,114,105,109,116,21])).
% 3.41/3.54 cnf(1044,plain,
% 3.41/3.54 (P2(f5(f2(a1),a13))),
% 3.41/3.54 inference(scs_inference,[],[122,44,166,102])).
% 3.41/3.54 cnf(1053,plain,
% 3.41/3.54 (~E(f15(f15(f6(f4(a1)))),f15(f6(f15(a3))))),
% 3.41/3.54 inference(scs_inference,[],[61,47,39,35,122,44,980,873,831,250,166,102,111,114,25,12,20,3])).
% 3.41/3.54 cnf(1077,plain,
% 3.41/3.54 (~E(f15(f6(f4(a1))),f6(f15(a3)))),
% 3.41/3.54 inference(scs_inference,[],[37,36,1053,111,110,113,114,12])).
% 3.41/3.54 cnf(1086,plain,
% 3.41/3.54 (P5(f4(a27),f15(f4(a27)))),
% 3.41/3.54 inference(scs_inference,[],[35,66,37,36,1053,968,1008,725,111,110,113,114,12,3,2,73,76,85])).
% 3.41/3.54 cnf(1088,plain,
% 3.41/3.54 (P1(f15(f4(a27)))),
% 3.41/3.54 inference(scs_inference,[],[35,66,37,36,1053,968,1008,725,111,110,113,114,12,3,2,73,76,85,71])).
% 3.41/3.54 cnf(1098,plain,
% 3.41/3.54 (~E(f15(f4(a27)),a3)),
% 3.41/3.54 inference(scs_inference,[],[35,66,37,36,1053,968,1008,725,572,111,110,113,114,12,3,2,73,76,85,71,88,74,84,83,70])).
% 3.41/3.54 cnf(1104,plain,
% 3.41/3.54 (P4(a12,f5(f2(a28),f2(a28)))),
% 3.41/3.54 inference(scs_inference,[],[35,66,37,36,1053,968,1008,725,572,342,111,110,113,114,12,3,2,73,76,85,71,88,74,84,83,70,94,77,95])).
% 3.41/3.54 cnf(1106,plain,
% 3.41/3.54 (P2(f11(a23,a23))),
% 3.41/3.54 inference(scs_inference,[],[35,66,38,37,36,1053,968,1008,725,572,342,111,110,113,114,12,3,2,73,76,85,71,88,74,84,83,70,94,77,95,91])).
% 3.41/3.54 cnf(1112,plain,
% 3.41/3.54 (P1(f6(f15(f4(a27))))),
% 3.41/3.54 inference(scs_inference,[],[35,66,38,37,36,45,42,67,1053,968,1008,725,572,342,111,110,113,114,12,3,2,73,76,85,71,88,74,84,83,70,94,77,95,91,100,118,75])).
% 3.41/3.54 cnf(1119,plain,
% 3.41/3.54 (E(f11(f8(f10(a26),f10(a26)),x11191),f11(f8(a26,a26),x11191))),
% 3.41/3.54 inference(scs_inference,[],[35,66,63,38,37,36,45,42,67,1053,968,1008,725,572,342,111,110,113,114,12,3,2,73,76,85,71,88,74,84,83,70,94,77,95,91,100,118,75,14,4,80,16,8])).
% 3.41/3.54 cnf(1122,plain,
% 3.41/3.54 (E(f15(f6(f15(f4(a27)))),f15(f4(a27)))),
% 3.41/3.54 inference(scs_inference,[],[35,66,63,38,37,36,45,42,67,1053,968,1008,743,903,725,572,342,111,110,113,114,12,3,2,73,76,85,71,88,74,84,83,70,94,77,95,91,100,118,75,14,4,80,16,8,6,24,78])).
% 3.41/3.54 cnf(1128,plain,
% 3.41/3.54 (E(f6(f15(f4(a27))),f4(a27))),
% 3.41/3.54 inference(scs_inference,[],[35,66,63,38,37,36,45,42,67,1053,968,1008,922,743,903,725,572,342,111,110,113,114,12,3,2,73,76,85,71,88,74,84,83,70,94,77,95,91,100,118,75,14,4,80,16,8,6,24,78,82,89,86])).
% 3.41/3.54 cnf(1138,plain,
% 3.41/3.54 (P2(f11(a26,a26))),
% 3.41/3.54 inference(scs_inference,[],[40,91])).
% 3.41/3.54 cnf(1153,plain,
% 3.41/3.54 (E(f15(f15(f4(a27))),f15(f4(a28)))),
% 3.41/3.54 inference(scs_inference,[],[35,48,130,40,41,970,925,1104,420,172,185,91,100,115,108,9,116,110,113,12])).
% 3.41/3.54 cnf(1154,plain,
% 3.41/3.54 (E(f15(f6(f15(f4(a27)))),f4(a28))),
% 3.41/3.54 inference(scs_inference,[],[35,48,130,40,41,970,925,1122,1104,420,172,185,91,100,115,108,9,116,110,113,12,3])).
% 3.41/3.54 cnf(1155,plain,
% 3.41/3.54 (~E(f6(f15(a3)),f15(f6(f4(a1))))),
% 3.41/3.54 inference(scs_inference,[],[35,48,130,40,41,970,925,1122,1077,1104,420,172,185,91,100,115,108,9,116,110,113,12,3,2])).
% 3.41/3.54 cnf(1177,plain,
% 3.41/3.54 (P2(f5(a1,a1))),
% 3.41/3.54 inference(scs_inference,[],[35,48,130,39,40,41,43,42,970,925,1112,1122,1077,1088,1104,318,151,420,909,172,185,91,100,115,108,9,116,110,113,12,3,2,93,87,79,81,18,11,86,13,78,5,104,10,120,102])).
% 3.41/3.54 cnf(1193,plain,
% 3.41/3.54 (~E(f11(f10(a25),f8(a26,a26)),f11(f8(f10(a26),f10(a26)),f10(a25)))),
% 3.41/3.54 inference(scs_inference,[],[36,41,40,124,1177,434,1119,894,170,29,104,120,108,113,20,3])).
% 3.41/3.54 cnf(1195,plain,
% 3.41/3.54 (E(a12,f11(a12,a12))),
% 3.41/3.54 inference(scs_inference,[],[36,137,41,40,124,1177,434,1119,894,170,29,104,120,108,113,20,3,2])).
% 3.41/3.54 cnf(1206,plain,
% 3.41/3.54 (P4(a12,a17)),
% 3.41/3.54 inference(scs_inference,[],[36,137,49,41,40,44,124,1177,434,1119,1155,917,894,170,1004,311,260,395,342,29,104,120,108,113,20,3,2,201,199,99,86,105,22])).
% 3.41/3.54 cnf(1225,plain,
% 3.41/3.54 (P2(f8(a21,a21))),
% 3.41/3.54 inference(scs_inference,[],[36,56,131,617,30,73,17,115,92])).
% 3.41/3.54 cnf(1240,plain,
% 3.41/3.54 (P2(f9(a28,f15(f4(a27))))),
% 3.41/3.54 inference(scs_inference,[],[36,56,123,133,131,128,39,43,122,124,1019,1044,1193,1086,887,1195,506,1088,617,239,342,30,73,17,115,92,21,22,3,2,96,105,109,108,25,93])).
% 3.41/3.54 cnf(1246,plain,
% 3.41/3.54 (~P5(f8(a19,a22),x12461)+P5(a24,x12461)+~P4(f11(a23,a23),f11(a23,a23))),
% 3.41/3.54 inference(scs_inference,[],[36,56,123,133,131,128,39,43,122,124,1106,1019,1044,1193,1086,887,1195,506,1088,617,239,342,30,73,17,115,92,21,22,3,2,96,105,109,108,25,93,119,107,24])).
% 3.41/3.54 cnf(1258,plain,
% 3.41/3.54 (E(a14,f11(a14,a12))),
% 3.41/3.54 inference(scs_inference,[],[37,139,53,130,124,1225,964,252,887,545,172,185,29,116,109,20,3,2])).
% 3.41/3.54 cnf(1265,plain,
% 3.41/3.54 (E(f9(a28,f15(f4(a27))),f9(a27,f15(f4(a27))))),
% 3.41/3.54 inference(scs_inference,[],[37,139,53,130,124,1225,964,252,887,545,1088,172,185,29,116,109,20,3,2,688,76,74,88])).
% 3.41/3.54 cnf(1267,plain,
% 3.41/3.54 (P5(f6(f15(f4(a27))),f15(f6(f15(f4(a27)))))),
% 3.41/3.54 inference(scs_inference,[],[37,139,53,130,124,1225,964,252,887,1112,545,1088,172,185,29,116,109,20,3,2,688,76,74,88,85])).
% 3.41/3.54 cnf(1277,plain,
% 3.41/3.54 (~E(f15(f6(f15(f4(a27)))),a3)),
% 3.41/3.54 inference(scs_inference,[],[37,139,53,130,124,1225,964,252,887,1112,545,1088,172,185,29,116,109,20,3,2,688,76,74,88,85,71,77,84,83,70])).
% 3.41/3.54 cnf(1311,plain,
% 3.41/3.54 (~E(f4(a28),a3)),
% 3.41/3.54 inference(scs_inference,[],[61,1128,1138,1267,1265,1154,1240,1277,111,24,114,9,25,20,3])).
% 3.41/3.54 cnf(1420,plain,
% 3.41/3.54 (P2(f8(a26,a26))),
% 3.41/3.54 inference(scs_inference,[],[38,126,58,131,40,45,43,124,881,657,941,1258,1098,1311,160,510,1004,105,104,115,110,113,9,21,22,20,3,2,99,17,92])).
% 3.41/3.54 cnf(1422,plain,
% 3.41/3.54 (~E(f15(f15(f4(a27))),f15(a3))),
% 3.41/3.54 inference(scs_inference,[],[38,126,58,131,40,45,43,124,881,657,941,1258,1098,1311,160,510,1004,1088,28,105,104,115,110,113,9,21,22,20,3,2,99,17,92,86])).
% 3.41/3.54 cnf(1427,plain,
% 3.41/3.54 (~P2(f10(a25))),
% 3.41/3.54 inference(scs_inference,[],[38,126,58,131,40,45,43,124,881,657,941,1206,1258,1098,1311,274,330,160,510,1004,1088,32,28,29,105,104,115,110,113,9,21,22,20,3,2,99,17,92,86,116,1246,242])).
% 3.41/3.54 cnf(1453,plain,
% 3.41/3.54 (~P2(f8(f10(a26),a23))),
% 3.41/3.54 inference(scs_inference,[],[39,143,62,1420,1427,844,562,73,92,115,108,110,113,12,20])).
% 3.41/3.54 cnf(1469,plain,
% 3.41/3.54 (P1(f15(f4(a1)))),
% 3.41/3.54 inference(scs_inference,[],[39,143,62,1420,1422,1427,844,562,1153,149,73,92,115,108,110,113,12,20,3,2,182,88,76,77,74,84,85,71])).
% 3.41/3.54 cnf(1512,plain,
% 3.41/3.54 ($false),
% 3.41/3.54 inference(scs_inference,[],[121,41,42,67,1469,1453,1427,182,101,73]),
% 3.41/3.54 ['proof']).
% 3.41/3.54 % SZS output end Proof
% 3.41/3.54 % Total time :2.870000s
%------------------------------------------------------------------------------