TSTP Solution File: NUM472+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM472+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:22:19 EDT 2023
% Result : Theorem 0.20s 0.76s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM472+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 16:27:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.74 %-------------------------------------------
% 0.20/0.74 % File :CSE---1.6
% 0.20/0.74 % Problem :theBenchmark
% 0.20/0.74 % Transform :cnf
% 0.20/0.74 % Format :tptp:raw
% 0.20/0.74 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.74
% 0.20/0.74 % Result :Theorem 0.100000s
% 0.20/0.74 % Output :CNFRefutation 0.100000s
% 0.20/0.74 %-------------------------------------------
% 0.20/0.74 %------------------------------------------------------------------------------
% 0.20/0.74 % File : NUM472+2 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.74 % Domain : Number Theory
% 0.20/0.74 % Problem : Square root of a prime is irrational 10_03_01, 01 expansion
% 0.20/0.74 % Version : Especial.
% 0.20/0.74 % English :
% 0.20/0.74
% 0.20/0.74 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista
% 0.20/0.74 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.20/0.74 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.20/0.74 % Source : [Pas08]
% 0.20/0.74 % Names : primes_10_03_01.01 [Pas08]
% 0.20/0.74
% 0.20/0.74 % Status : Theorem
% 0.20/0.74 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.04 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.15 v5.1.0, 0.33 v4.1.0, 0.39 v4.0.1, 0.70 v4.0.0
% 0.20/0.74 % Syntax : Number of formulae : 39 ( 2 unt; 4 def)
% 0.20/0.74 % Number of atoms : 171 ( 55 equ)
% 0.20/0.74 % Maximal formula atoms : 10 ( 4 avg)
% 0.20/0.74 % Number of connectives : 147 ( 15 ~; 7 |; 72 &)
% 0.20/0.74 % ( 4 <=>; 49 =>; 0 <=; 0 <~>)
% 0.20/0.74 % Maximal formula depth : 11 ( 6 avg)
% 0.20/0.74 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.74 % Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% 0.20/0.74 % Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% 0.20/0.74 % Number of variables : 73 ( 68 !; 5 ?)
% 0.20/0.74 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.74
% 0.20/0.74 % Comments : Problem generated by the SAD system [VLP07]
% 0.20/0.74 %------------------------------------------------------------------------------
% 0.20/0.74 fof(mNatSort,axiom,
% 0.20/0.74 ! [W0] :
% 0.20/0.74 ( aNaturalNumber0(W0)
% 0.20/0.74 => $true ) ).
% 0.20/0.74
% 0.20/0.74 fof(mSortsC,axiom,
% 0.20/0.74 aNaturalNumber0(sz00) ).
% 0.20/0.74
% 0.20/0.74 fof(mSortsC_01,axiom,
% 0.20/0.74 ( aNaturalNumber0(sz10)
% 0.20/0.75 & sz10 != sz00 ) ).
% 0.20/0.75
% 0.20/0.75 fof(mSortsB,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mSortsB_02,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mAddComm,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mAddAsso,axiom,
% 0.20/0.75 ! [W0,W1,W2] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1)
% 0.20/0.75 & aNaturalNumber0(W2) )
% 0.20/0.75 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
% 0.20/0.75
% 0.20/0.75 fof(m_AddZero,axiom,
% 0.20/0.75 ! [W0] :
% 0.20/0.75 ( aNaturalNumber0(W0)
% 0.20/0.75 => ( sdtpldt0(W0,sz00) = W0
% 0.20/0.75 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mMulComm,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mMulAsso,axiom,
% 0.20/0.75 ! [W0,W1,W2] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1)
% 0.20/0.75 & aNaturalNumber0(W2) )
% 0.20/0.75 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
% 0.20/0.75
% 0.20/0.75 fof(m_MulUnit,axiom,
% 0.20/0.75 ! [W0] :
% 0.20/0.75 ( aNaturalNumber0(W0)
% 0.20/0.75 => ( sdtasdt0(W0,sz10) = W0
% 0.20/0.75 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(m_MulZero,axiom,
% 0.20/0.75 ! [W0] :
% 0.20/0.75 ( aNaturalNumber0(W0)
% 0.20/0.75 => ( sdtasdt0(W0,sz00) = sz00
% 0.20/0.75 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mAMDistr,axiom,
% 0.20/0.75 ! [W0,W1,W2] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1)
% 0.20/0.75 & aNaturalNumber0(W2) )
% 0.20/0.75 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.20/0.75 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mAddCanc,axiom,
% 0.20/0.75 ! [W0,W1,W2] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1)
% 0.20/0.75 & aNaturalNumber0(W2) )
% 0.20/0.75 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
% 0.20/0.75 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
% 0.20/0.75 => W1 = W2 ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mMulCanc,axiom,
% 0.20/0.75 ! [W0] :
% 0.20/0.75 ( aNaturalNumber0(W0)
% 0.20/0.75 => ( W0 != sz00
% 0.20/0.75 => ! [W1,W2] :
% 0.20/0.75 ( ( aNaturalNumber0(W1)
% 0.20/0.75 & aNaturalNumber0(W2) )
% 0.20/0.75 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2)
% 0.20/0.75 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
% 0.20/0.75 => W1 = W2 ) ) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mZeroAdd,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( sdtpldt0(W0,W1) = sz00
% 0.20/0.75 => ( W0 = sz00
% 0.20/0.75 & W1 = sz00 ) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mZeroMul,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( sdtasdt0(W0,W1) = sz00
% 0.20/0.75 => ( W0 = sz00
% 0.20/0.75 | W1 = sz00 ) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mDefLE,definition,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( sdtlseqdt0(W0,W1)
% 0.20/0.75 <=> ? [W2] :
% 0.20/0.75 ( aNaturalNumber0(W2)
% 0.20/0.75 & sdtpldt0(W0,W2) = W1 ) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mDefDiff,definition,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( sdtlseqdt0(W0,W1)
% 0.20/0.75 => ! [W2] :
% 0.20/0.75 ( W2 = sdtmndt0(W1,W0)
% 0.20/0.75 <=> ( aNaturalNumber0(W2)
% 0.20/0.75 & sdtpldt0(W0,W2) = W1 ) ) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mLERefl,axiom,
% 0.20/0.75 ! [W0] :
% 0.20/0.75 ( aNaturalNumber0(W0)
% 0.20/0.75 => sdtlseqdt0(W0,W0) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mLEAsym,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( ( sdtlseqdt0(W0,W1)
% 0.20/0.75 & sdtlseqdt0(W1,W0) )
% 0.20/0.75 => W0 = W1 ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mLETran,axiom,
% 0.20/0.75 ! [W0,W1,W2] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1)
% 0.20/0.75 & aNaturalNumber0(W2) )
% 0.20/0.75 => ( ( sdtlseqdt0(W0,W1)
% 0.20/0.75 & sdtlseqdt0(W1,W2) )
% 0.20/0.75 => sdtlseqdt0(W0,W2) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mLETotal,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( sdtlseqdt0(W0,W1)
% 0.20/0.75 | ( W1 != W0
% 0.20/0.75 & sdtlseqdt0(W1,W0) ) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mMonAdd,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( ( W0 != W1
% 0.20/0.75 & sdtlseqdt0(W0,W1) )
% 0.20/0.75 => ! [W2] :
% 0.20/0.75 ( aNaturalNumber0(W2)
% 0.20/0.75 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)
% 0.20/0.75 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
% 0.20/0.75 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
% 0.20/0.75 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mMonMul,axiom,
% 0.20/0.75 ! [W0,W1,W2] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1)
% 0.20/0.75 & aNaturalNumber0(W2) )
% 0.20/0.75 => ( ( W0 != sz00
% 0.20/0.75 & W1 != W2
% 0.20/0.75 & sdtlseqdt0(W1,W2) )
% 0.20/0.75 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2)
% 0.20/0.75 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.20/0.75 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
% 0.20/0.75 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mLENTr,axiom,
% 0.20/0.75 ! [W0] :
% 0.20/0.75 ( aNaturalNumber0(W0)
% 0.20/0.75 => ( W0 = sz00
% 0.20/0.75 | W0 = sz10
% 0.20/0.75 | ( sz10 != W0
% 0.20/0.75 & sdtlseqdt0(sz10,W0) ) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mMonMul2,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( W0 != sz00
% 0.20/0.75 => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mIH,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( iLess0(W0,W1)
% 0.20/0.75 => $true ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mIH_03,axiom,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( ( W0 != W1
% 0.20/0.75 & sdtlseqdt0(W0,W1) )
% 0.20/0.75 => iLess0(W0,W1) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mDefDiv,definition,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( doDivides0(W0,W1)
% 0.20/0.75 <=> ? [W2] :
% 0.20/0.75 ( aNaturalNumber0(W2)
% 0.20/0.75 & W1 = sdtasdt0(W0,W2) ) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mDefQuot,definition,
% 0.20/0.75 ! [W0,W1] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1) )
% 0.20/0.75 => ( ( W0 != sz00
% 0.20/0.75 & doDivides0(W0,W1) )
% 0.20/0.75 => ! [W2] :
% 0.20/0.75 ( W2 = sdtsldt0(W1,W0)
% 0.20/0.75 <=> ( aNaturalNumber0(W2)
% 0.20/0.75 & W1 = sdtasdt0(W0,W2) ) ) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mDivTrans,axiom,
% 0.20/0.75 ! [W0,W1,W2] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1)
% 0.20/0.75 & aNaturalNumber0(W2) )
% 0.20/0.75 => ( ( doDivides0(W0,W1)
% 0.20/0.75 & doDivides0(W1,W2) )
% 0.20/0.75 => doDivides0(W0,W2) ) ) ).
% 0.20/0.75
% 0.20/0.75 fof(mDivSum,axiom,
% 0.20/0.75 ! [W0,W1,W2] :
% 0.20/0.75 ( ( aNaturalNumber0(W0)
% 0.20/0.75 & aNaturalNumber0(W1)
% 0.20/0.75 & aNaturalNumber0(W2) )
% 0.20/0.76 => ( ( doDivides0(W0,W1)
% 0.20/0.76 & doDivides0(W0,W2) )
% 0.20/0.76 => doDivides0(W0,sdtpldt0(W1,W2)) ) ) ).
% 0.20/0.76
% 0.20/0.76 fof(m__1324,hypothesis,
% 0.20/0.76 ( aNaturalNumber0(xl)
% 0.20/0.76 & aNaturalNumber0(xm)
% 0.20/0.76 & aNaturalNumber0(xn) ) ).
% 0.20/0.76
% 0.20/0.76 fof(m__1324_04,hypothesis,
% 0.20/0.76 ( ? [W0] :
% 0.20/0.76 ( aNaturalNumber0(W0)
% 0.20/0.76 & xm = sdtasdt0(xl,W0) )
% 0.20/0.76 & doDivides0(xl,xm)
% 0.20/0.76 & ? [W0] :
% 0.20/0.76 ( aNaturalNumber0(W0)
% 0.20/0.76 & sdtpldt0(xm,xn) = sdtasdt0(xl,W0) )
% 0.20/0.76 & doDivides0(xl,sdtpldt0(xm,xn)) ) ).
% 0.20/0.76
% 0.20/0.76 fof(m__1347,hypothesis,
% 0.20/0.76 xl != sz00 ).
% 0.20/0.76
% 0.20/0.76 fof(m__1360,hypothesis,
% 0.20/0.76 ( aNaturalNumber0(xp)
% 0.20/0.76 & xm = sdtasdt0(xl,xp)
% 0.20/0.76 & xp = sdtsldt0(xm,xl) ) ).
% 0.20/0.76
% 0.20/0.76 fof(m__1379,hypothesis,
% 0.20/0.76 ( aNaturalNumber0(xq)
% 0.20/0.76 & sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
% 0.20/0.76 & xq = sdtsldt0(sdtpldt0(xm,xn),xl) ) ).
% 0.20/0.76
% 0.20/0.76 fof(m__,conjecture,
% 0.20/0.76 ( ? [W0] :
% 0.20/0.76 ( aNaturalNumber0(W0)
% 0.20/0.76 & sdtpldt0(xm,W0) = sdtpldt0(xm,xn) )
% 0.20/0.76 | sdtlseqdt0(xm,sdtpldt0(xm,xn)) ) ).
% 0.20/0.76
% 0.20/0.76 %------------------------------------------------------------------------------
% 0.20/0.76 %-------------------------------------------
% 0.20/0.76 % Proof found
% 0.20/0.76 % SZS status Theorem for theBenchmark
% 0.20/0.76 % SZS output start Proof
% 0.20/0.76 %ClaNum:94(EqnAxiom:22)
% 0.20/0.76 %VarNum:350(SingletonVarNum:110)
% 0.20/0.76 %MaxLitNum:7
% 0.20/0.76 %MaxfuncDepth:2
% 0.20/0.76 %SharedTerms:36
% 0.20/0.76 %goalClause: 42 58
% 0.20/0.76 %singleGoalClaCount:1
% 0.20/0.76 [23]P1(a1)
% 0.20/0.76 [24]P1(a10)
% 0.20/0.76 [25]P1(a11)
% 0.20/0.76 [26]P1(a12)
% 0.20/0.76 [27]P1(a13)
% 0.20/0.76 [28]P1(a14)
% 0.20/0.76 [29]P1(a15)
% 0.20/0.76 [30]P1(a2)
% 0.20/0.76 [31]P1(a5)
% 0.20/0.76 [35]P2(a11,a12)
% 0.20/0.76 [40]~E(a1,a10)
% 0.20/0.76 [41]~E(a1,a11)
% 0.20/0.76 [32]E(f6(a11,a14),a12)
% 0.20/0.76 [33]E(f6(a11,a2),a12)
% 0.20/0.76 [34]E(f7(a12,a11),a14)
% 0.20/0.76 [36]E(f8(a12,a13),f6(a11,a15))
% 0.20/0.76 [37]E(f8(a12,a13),f6(a11,a5))
% 0.20/0.76 [39]P2(a11,f8(a12,a13))
% 0.20/0.76 [42]~P3(a12,f8(a12,a13))
% 0.20/0.76 [38]E(f7(f8(a12,a13),a11),a15)
% 0.20/0.76 [49]~P1(x491)+P3(x491,x491)
% 0.20/0.76 [43]~P1(x431)+E(f6(a1,x431),a1)
% 0.20/0.76 [44]~P1(x441)+E(f6(x441,a1),a1)
% 0.20/0.76 [45]~P1(x451)+E(f8(a1,x451),x451)
% 0.20/0.76 [46]~P1(x461)+E(f6(a10,x461),x461)
% 0.20/0.76 [47]~P1(x471)+E(f8(x471,a1),x471)
% 0.20/0.76 [48]~P1(x481)+E(f6(x481,a10),x481)
% 0.20/0.76 [58]~P1(x581)+~E(f8(a12,x581),f8(a12,a13))
% 0.20/0.76 [55]~P1(x552)+~P1(x551)+E(f8(x551,x552),f8(x552,x551))
% 0.20/0.76 [56]~P1(x562)+~P1(x561)+E(f6(x561,x562),f6(x562,x561))
% 0.20/0.76 [59]~P1(x592)+~P1(x591)+P1(f8(x591,x592))
% 0.20/0.76 [60]~P1(x602)+~P1(x601)+P1(f6(x601,x602))
% 0.20/0.76 [50]~P1(x501)+E(x501,a10)+P3(a10,x501)+E(x501,a1)
% 0.20/0.76 [51]~E(x512,x511)+~P1(x511)+~P1(x512)+P3(x511,x512)
% 0.20/0.76 [57]P3(x572,x571)+~P1(x571)+~P1(x572)+P3(x571,x572)
% 0.20/0.76 [52]~P1(x522)+~P1(x521)+E(x521,a1)+~E(f8(x522,x521),a1)
% 0.20/0.76 [53]~P1(x532)+~P1(x531)+E(x531,a1)+~E(f8(x531,x532),a1)
% 0.20/0.76 [62]~P1(x622)+~P1(x621)+P3(x622,f6(x622,x621))+E(x621,a1)
% 0.20/0.76 [68]~P1(x682)+~P1(x681)+~P3(x681,x682)+P1(f3(x681,x682))
% 0.20/0.76 [69]~P1(x692)+~P1(x691)+~P2(x691,x692)+P1(f4(x691,x692))
% 0.20/0.76 [76]~P1(x761)+~P1(x762)+~P2(x761,x762)+E(f6(x761,f4(x761,x762)),x762)
% 0.20/0.76 [77]~P1(x772)+~P1(x771)+~P3(x771,x772)+E(f8(x771,f3(x771,x772)),x772)
% 0.20/0.76 [86]~P1(x863)+~P1(x862)+~P1(x861)+E(f8(f8(x861,x862),x863),f8(x861,f8(x862,x863)))
% 0.20/0.76 [87]~P1(x873)+~P1(x872)+~P1(x871)+E(f6(f6(x871,x872),x873),f6(x871,f6(x872,x873)))
% 0.20/0.76 [93]~P1(x933)+~P1(x932)+~P1(x931)+E(f8(f6(x931,x932),f6(x931,x933)),f6(x931,f8(x932,x933)))
% 0.20/0.76 [94]~P1(x942)+~P1(x943)+~P1(x941)+E(f8(f6(x941,x942),f6(x943,x942)),f6(f8(x941,x943),x942))
% 0.20/0.76 [61]P4(x611,x612)+~P1(x612)+~P1(x611)+~P3(x611,x612)+E(x611,x612)
% 0.20/0.76 [65]~P1(x652)+~P1(x651)+~P3(x652,x651)+~P3(x651,x652)+E(x651,x652)
% 0.20/0.76 [54]~P1(x541)+~P1(x542)+E(x541,a1)+E(x542,a1)+~E(f6(x542,x541),a1)
% 0.20/0.76 [63]~P1(x631)+~P1(x632)+~P1(x633)+P2(x631,x632)+~E(x632,f6(x631,x633))
% 0.20/0.76 [64]~P1(x642)+~P1(x641)+~P1(x643)+P3(x641,x642)+~E(f8(x641,x643),x642)
% 0.20/0.76 [66]~P1(x663)+~P1(x662)+~P3(x663,x662)+P1(x661)+~E(x661,f9(x662,x663))
% 0.20/0.76 [70]~P1(x702)+~P1(x701)+~P1(x703)+E(x701,x702)+~E(f8(x703,x701),f8(x703,x702))
% 0.20/0.76 [71]~P1(x712)+~P1(x713)+~P1(x711)+E(x711,x712)+~E(f8(x711,x713),f8(x712,x713))
% 0.20/0.76 [74]~P1(x743)+~P1(x741)+~P3(x741,x743)+~E(x742,f9(x743,x741))+E(f8(x741,x742),x743)
% 0.20/0.76 [78]~P1(x782)+~P1(x781)+~P3(x783,x782)+~P3(x781,x783)+P3(x781,x782)+~P1(x783)
% 0.20/0.76 [79]~P1(x792)+~P1(x791)+~P2(x793,x792)+~P2(x791,x793)+P2(x791,x792)+~P1(x793)
% 0.20/0.76 [67]~P1(x671)+~P1(x673)+~P2(x671,x673)+P1(x672)+E(x671,a1)+~E(x672,f7(x673,x671))
% 0.20/0.76 [72]~P1(x722)+~P1(x721)+~P1(x723)+E(x721,x722)+~E(f6(x723,x721),f6(x723,x722))+E(x723,a1)
% 0.20/0.76 [73]~P1(x732)+~P1(x733)+~P1(x731)+E(x731,x732)+~E(f6(x731,x733),f6(x732,x733))+E(x733,a1)
% 0.20/0.76 [75]~P1(x751)+~P1(x752)+~P2(x751,x752)+~E(x753,f7(x752,x751))+E(x751,a1)+E(x752,f6(x751,x753))
% 0.20/0.76 [80]~P1(x802)+~P1(x803)+~P1(x801)+~P3(x803,x802)+~E(f8(x803,x801),x802)+E(x801,f9(x802,x803))
% 0.20/0.76 [88]~P1(x883)+~P1(x882)+~P1(x881)+~P2(x881,x883)+~P2(x881,x882)+P2(x881,f8(x882,x883))
% 0.20/0.76 [89]~P1(x892)+~P1(x891)+~P1(x893)+~P3(x891,x892)+E(x891,x892)+P3(f8(x893,x891),f8(x893,x892))
% 0.20/0.76 [90]~P1(x902)+~P1(x903)+~P1(x901)+~P3(x901,x902)+E(x901,x902)+P3(f8(x901,x903),f8(x902,x903))
% 0.20/0.76 [81]~P1(x811)+~P1(x813)+~P1(x812)+~P2(x811,x813)+~E(x813,f6(x811,x812))+E(x811,a1)+E(x812,f7(x813,x811))
% 0.20/0.76 [91]~P1(x912)+~P1(x911)+~P1(x913)+~P3(x911,x912)+E(x911,x912)+P3(f6(x913,x911),f6(x913,x912))+E(x913,a1)
% 0.20/0.76 [92]~P1(x922)+~P1(x923)+~P1(x921)+~P3(x921,x922)+E(x921,x922)+P3(f6(x921,x923),f6(x922,x923))+E(x923,a1)
% 0.20/0.76 %EqnAxiom
% 0.20/0.76 [1]E(x11,x11)
% 0.20/0.76 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.76 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.76 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.20/0.76 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.20/0.76 [6]~E(x61,x62)+E(f8(x61,x63),f8(x62,x63))
% 0.20/0.76 [7]~E(x71,x72)+E(f8(x73,x71),f8(x73,x72))
% 0.20/0.76 [8]~E(x81,x82)+E(f7(x81,x83),f7(x82,x83))
% 0.20/0.76 [9]~E(x91,x92)+E(f7(x93,x91),f7(x93,x92))
% 0.20/0.76 [10]~E(x101,x102)+E(f9(x101,x103),f9(x102,x103))
% 0.20/0.76 [11]~E(x111,x112)+E(f9(x113,x111),f9(x113,x112))
% 0.20/0.76 [12]~E(x121,x122)+E(f3(x121,x123),f3(x122,x123))
% 0.20/0.76 [13]~E(x131,x132)+E(f3(x133,x131),f3(x133,x132))
% 0.20/0.76 [14]~E(x141,x142)+E(f4(x141,x143),f4(x142,x143))
% 0.20/0.76 [15]~E(x151,x152)+E(f4(x153,x151),f4(x153,x152))
% 0.20/0.76 [16]~P1(x161)+P1(x162)+~E(x161,x162)
% 0.20/0.76 [17]P3(x172,x173)+~E(x171,x172)+~P3(x171,x173)
% 0.20/0.76 [18]P3(x183,x182)+~E(x181,x182)+~P3(x183,x181)
% 0.20/0.76 [19]P4(x192,x193)+~E(x191,x192)+~P4(x191,x193)
% 0.20/0.76 [20]P4(x203,x202)+~E(x201,x202)+~P4(x203,x201)
% 0.20/0.76 [21]P2(x212,x213)+~E(x211,x212)+~P2(x211,x213)
% 0.20/0.76 [22]P2(x223,x222)+~E(x221,x222)+~P2(x223,x221)
% 0.20/0.76
% 0.20/0.76 %-------------------------------------------
% 0.20/0.76 cnf(97,plain,
% 0.20/0.76 (P1(f6(a11,a14))),
% 0.20/0.76 inference(scs_inference,[],[26,35,32,2,22,16])).
% 0.20/0.76 cnf(102,plain,
% 0.20/0.76 (~E(f8(a12,a1),f8(a12,a13))),
% 0.20/0.76 inference(scs_inference,[],[23,24,26,35,32,2,22,16,57,49,58])).
% 0.20/0.76 cnf(125,plain,
% 0.20/0.76 (E(f8(f6(a11,a14),x1251),f8(a12,x1251))),
% 0.20/0.76 inference(scs_inference,[],[23,24,25,26,35,32,2,22,16,57,49,58,48,47,46,45,44,43,15,14,13,12,11,10,9,8,7,6])).
% 0.20/0.76 cnf(129,plain,
% 0.20/0.76 (~P3(f6(a11,a14),f8(a12,a13))),
% 0.20/0.76 inference(scs_inference,[],[42,23,24,25,26,35,32,2,22,16,57,49,58,48,47,46,45,44,43,15,14,13,12,11,10,9,8,7,6,5,4,18,17])).
% 0.20/0.76 cnf(135,plain,
% 0.20/0.76 (P3(a11,a11)),
% 0.20/0.76 inference(scs_inference,[],[42,23,24,25,26,35,40,32,2,22,16,57,49,58,48,47,46,45,44,43,15,14,13,12,11,10,9,8,7,6,5,4,18,17,3,60,59,51])).
% 0.20/0.76 cnf(139,plain,
% 0.20/0.76 (P1(f3(a1,a1))),
% 0.20/0.76 inference(scs_inference,[],[42,23,24,25,26,35,40,32,2,22,16,57,49,58,48,47,46,45,44,43,15,14,13,12,11,10,9,8,7,6,5,4,18,17,3,60,59,51,69,68])).
% 0.20/0.76 cnf(145,plain,
% 0.20/0.76 (E(f8(a1,f3(a1,a1)),a1)),
% 0.20/0.76 inference(scs_inference,[],[42,23,24,25,26,35,40,32,2,22,16,57,49,58,48,47,46,45,44,43,15,14,13,12,11,10,9,8,7,6,5,4,18,17,3,60,59,51,69,68,87,86,77])).
% 0.20/0.76 cnf(197,plain,
% 0.20/0.76 (~E(a11,a1)),
% 0.20/0.76 inference(scs_inference,[],[42,27,41,33,25,23,102,135,139,145,60,59,68,77,94,93,7,17,52,87,86,2])).
% 0.20/0.76 cnf(237,plain,
% 0.20/0.76 ($false),
% 0.20/0.76 inference(scs_inference,[],[23,26,27,25,125,129,197,97,53,64,59]),
% 0.20/0.76 ['proof']).
% 0.20/0.76 % SZS output end Proof
% 0.20/0.76 % Total time :0.100000s
%------------------------------------------------------------------------------