TSTP Solution File: NUM484+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM484+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 : n024.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 10:22:24 EDT 2023
% Result : Theorem 0.16s 0.61s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : NUM484+1 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Aug 25 16:11:09 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.16/0.55 start to proof:theBenchmark
% 0.16/0.60 %-------------------------------------------
% 0.16/0.60 % File :CSE---1.6
% 0.16/0.60 % Problem :theBenchmark
% 0.16/0.60 % Transform :cnf
% 0.16/0.60 % Format :tptp:raw
% 0.16/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.16/0.60
% 0.16/0.60 % Result :Theorem 0.000000s
% 0.16/0.60 % Output :CNFRefutation 0.000000s
% 0.16/0.60 %-------------------------------------------
% 0.16/0.60 %------------------------------------------------------------------------------
% 0.16/0.60 % File : NUM484+1 : TPTP v8.1.2. Released v4.0.0.
% 0.16/0.60 % Domain : Number Theory
% 0.16/0.60 % Problem : Square root of a prime is irrational 13_03, 00 expansion
% 0.16/0.60 % Version : Especial.
% 0.16/0.60 % English :
% 0.16/0.60
% 0.16/0.60 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista
% 0.16/0.60 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.16/0.60 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.16/0.60 % Source : [Pas08]
% 0.16/0.60 % Names : primes_13_03.00 [Pas08]
% 0.16/0.60
% 0.16/0.60 % Status : ContradictoryAxioms
% 0.16/0.60 % Rating : 0.06 v7.5.0, 0.00 v7.4.0, 0.29 v7.3.0, 0.00 v6.1.0, 0.03 v6.0.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.05 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.1, 0.61 v4.0.0
% 0.16/0.60 % Syntax : Number of formulae : 43 ( 4 unt; 5 def)
% 0.16/0.60 % Number of atoms : 192 ( 58 equ)
% 0.16/0.60 % Maximal formula atoms : 10 ( 4 avg)
% 0.16/0.60 % Number of connectives : 174 ( 25 ~; 7 |; 77 &)
% 0.16/0.60 % ( 5 <=>; 60 =>; 0 <=; 0 <~>)
% 0.16/0.60 % Maximal formula depth : 11 ( 6 avg)
% 0.16/0.60 % Maximal term depth : 3 ( 1 avg)
% 0.16/0.60 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% 0.16/0.60 % Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% 0.16/0.60 % Number of variables : 83 ( 79 !; 4 ?)
% 0.16/0.60 % SPC : FOF_CAX_RFO_SEQ
% 0.16/0.61
% 0.16/0.61 % Comments : Problem generated by the SAD system [VLP07]
% 0.16/0.61 %------------------------------------------------------------------------------
% 0.16/0.61 fof(mNatSort,axiom,
% 0.16/0.61 ! [W0] :
% 0.16/0.61 ( aNaturalNumber0(W0)
% 0.16/0.61 => $true ) ).
% 0.16/0.61
% 0.16/0.61 fof(mSortsC,axiom,
% 0.16/0.61 aNaturalNumber0(sz00) ).
% 0.16/0.61
% 0.16/0.61 fof(mSortsC_01,axiom,
% 0.16/0.61 ( aNaturalNumber0(sz10)
% 0.16/0.61 & sz10 != sz00 ) ).
% 0.16/0.61
% 0.16/0.61 fof(mSortsB,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mSortsB_02,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mAddComm,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mAddAsso,axiom,
% 0.16/0.61 ! [W0,W1,W2] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1)
% 0.16/0.61 & aNaturalNumber0(W2) )
% 0.16/0.61 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
% 0.16/0.61
% 0.16/0.61 fof(m_AddZero,axiom,
% 0.16/0.61 ! [W0] :
% 0.16/0.61 ( aNaturalNumber0(W0)
% 0.16/0.61 => ( sdtpldt0(W0,sz00) = W0
% 0.16/0.61 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mMulComm,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mMulAsso,axiom,
% 0.16/0.61 ! [W0,W1,W2] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1)
% 0.16/0.61 & aNaturalNumber0(W2) )
% 0.16/0.61 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
% 0.16/0.61
% 0.16/0.61 fof(m_MulUnit,axiom,
% 0.16/0.61 ! [W0] :
% 0.16/0.61 ( aNaturalNumber0(W0)
% 0.16/0.61 => ( sdtasdt0(W0,sz10) = W0
% 0.16/0.61 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(m_MulZero,axiom,
% 0.16/0.61 ! [W0] :
% 0.16/0.61 ( aNaturalNumber0(W0)
% 0.16/0.61 => ( sdtasdt0(W0,sz00) = sz00
% 0.16/0.61 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mAMDistr,axiom,
% 0.16/0.61 ! [W0,W1,W2] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1)
% 0.16/0.61 & aNaturalNumber0(W2) )
% 0.16/0.61 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.16/0.61 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mAddCanc,axiom,
% 0.16/0.61 ! [W0,W1,W2] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1)
% 0.16/0.61 & aNaturalNumber0(W2) )
% 0.16/0.61 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
% 0.16/0.61 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
% 0.16/0.61 => W1 = W2 ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mMulCanc,axiom,
% 0.16/0.61 ! [W0] :
% 0.16/0.61 ( aNaturalNumber0(W0)
% 0.16/0.61 => ( W0 != sz00
% 0.16/0.61 => ! [W1,W2] :
% 0.16/0.61 ( ( aNaturalNumber0(W1)
% 0.16/0.61 & aNaturalNumber0(W2) )
% 0.16/0.61 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2)
% 0.16/0.61 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
% 0.16/0.61 => W1 = W2 ) ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mZeroAdd,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( sdtpldt0(W0,W1) = sz00
% 0.16/0.61 => ( W0 = sz00
% 0.16/0.61 & W1 = sz00 ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mZeroMul,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( sdtasdt0(W0,W1) = sz00
% 0.16/0.61 => ( W0 = sz00
% 0.16/0.61 | W1 = sz00 ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mDefLE,definition,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( sdtlseqdt0(W0,W1)
% 0.16/0.61 <=> ? [W2] :
% 0.16/0.61 ( aNaturalNumber0(W2)
% 0.16/0.61 & sdtpldt0(W0,W2) = W1 ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mDefDiff,definition,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( sdtlseqdt0(W0,W1)
% 0.16/0.61 => ! [W2] :
% 0.16/0.61 ( W2 = sdtmndt0(W1,W0)
% 0.16/0.61 <=> ( aNaturalNumber0(W2)
% 0.16/0.61 & sdtpldt0(W0,W2) = W1 ) ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mLERefl,axiom,
% 0.16/0.61 ! [W0] :
% 0.16/0.61 ( aNaturalNumber0(W0)
% 0.16/0.61 => sdtlseqdt0(W0,W0) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mLEAsym,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( ( sdtlseqdt0(W0,W1)
% 0.16/0.61 & sdtlseqdt0(W1,W0) )
% 0.16/0.61 => W0 = W1 ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mLETran,axiom,
% 0.16/0.61 ! [W0,W1,W2] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1)
% 0.16/0.61 & aNaturalNumber0(W2) )
% 0.16/0.61 => ( ( sdtlseqdt0(W0,W1)
% 0.16/0.61 & sdtlseqdt0(W1,W2) )
% 0.16/0.61 => sdtlseqdt0(W0,W2) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mLETotal,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( sdtlseqdt0(W0,W1)
% 0.16/0.61 | ( W1 != W0
% 0.16/0.61 & sdtlseqdt0(W1,W0) ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mMonAdd,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( ( W0 != W1
% 0.16/0.61 & sdtlseqdt0(W0,W1) )
% 0.16/0.61 => ! [W2] :
% 0.16/0.61 ( aNaturalNumber0(W2)
% 0.16/0.61 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)
% 0.16/0.61 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
% 0.16/0.61 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
% 0.16/0.61 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mMonMul,axiom,
% 0.16/0.61 ! [W0,W1,W2] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1)
% 0.16/0.61 & aNaturalNumber0(W2) )
% 0.16/0.61 => ( ( W0 != sz00
% 0.16/0.61 & W1 != W2
% 0.16/0.61 & sdtlseqdt0(W1,W2) )
% 0.16/0.61 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2)
% 0.16/0.61 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.16/0.61 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
% 0.16/0.61 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mLENTr,axiom,
% 0.16/0.61 ! [W0] :
% 0.16/0.61 ( aNaturalNumber0(W0)
% 0.16/0.61 => ( W0 = sz00
% 0.16/0.61 | W0 = sz10
% 0.16/0.61 | ( sz10 != W0
% 0.16/0.61 & sdtlseqdt0(sz10,W0) ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mMonMul2,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( W0 != sz00
% 0.16/0.61 => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mIH,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( iLess0(W0,W1)
% 0.16/0.61 => $true ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mIH_03,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( ( W0 != W1
% 0.16/0.61 & sdtlseqdt0(W0,W1) )
% 0.16/0.61 => iLess0(W0,W1) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mDefDiv,definition,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( doDivides0(W0,W1)
% 0.16/0.61 <=> ? [W2] :
% 0.16/0.61 ( aNaturalNumber0(W2)
% 0.16/0.61 & W1 = sdtasdt0(W0,W2) ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mDefQuot,definition,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( ( W0 != sz00
% 0.16/0.61 & doDivides0(W0,W1) )
% 0.16/0.61 => ! [W2] :
% 0.16/0.61 ( W2 = sdtsldt0(W1,W0)
% 0.16/0.61 <=> ( aNaturalNumber0(W2)
% 0.16/0.61 & W1 = sdtasdt0(W0,W2) ) ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mDivTrans,axiom,
% 0.16/0.61 ! [W0,W1,W2] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1)
% 0.16/0.61 & aNaturalNumber0(W2) )
% 0.16/0.61 => ( ( doDivides0(W0,W1)
% 0.16/0.61 & doDivides0(W1,W2) )
% 0.16/0.61 => doDivides0(W0,W2) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mDivSum,axiom,
% 0.16/0.61 ! [W0,W1,W2] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1)
% 0.16/0.61 & aNaturalNumber0(W2) )
% 0.16/0.61 => ( ( doDivides0(W0,W1)
% 0.16/0.61 & doDivides0(W0,W2) )
% 0.16/0.61 => doDivides0(W0,sdtpldt0(W1,W2)) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mDivMin,axiom,
% 0.16/0.61 ! [W0,W1,W2] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1)
% 0.16/0.61 & aNaturalNumber0(W2) )
% 0.16/0.61 => ( ( doDivides0(W0,W1)
% 0.16/0.61 & doDivides0(W0,sdtpldt0(W1,W2)) )
% 0.16/0.61 => doDivides0(W0,W2) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mDivLE,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( ( doDivides0(W0,W1)
% 0.16/0.61 & W1 != sz00 )
% 0.16/0.61 => sdtlseqdt0(W0,W1) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mDivAsso,axiom,
% 0.16/0.61 ! [W0,W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & aNaturalNumber0(W1) )
% 0.16/0.61 => ( ( W0 != sz00
% 0.16/0.61 & doDivides0(W0,W1) )
% 0.16/0.61 => ! [W2] :
% 0.16/0.61 ( aNaturalNumber0(W2)
% 0.16/0.61 => sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(mDefPrime,definition,
% 0.16/0.61 ! [W0] :
% 0.16/0.61 ( aNaturalNumber0(W0)
% 0.16/0.61 => ( isPrime0(W0)
% 0.16/0.61 <=> ( W0 != sz00
% 0.16/0.61 & W0 != sz10
% 0.16/0.61 & ! [W1] :
% 0.16/0.61 ( ( aNaturalNumber0(W1)
% 0.16/0.61 & doDivides0(W1,W0) )
% 0.16/0.61 => ( W1 = sz10
% 0.16/0.61 | W1 = W0 ) ) ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(m__1716,hypothesis,
% 0.16/0.61 aNaturalNumber0(xk) ).
% 0.16/0.61
% 0.16/0.61 fof(m__1700,hypothesis,
% 0.16/0.61 ! [W0] :
% 0.16/0.61 ( ( aNaturalNumber0(W0)
% 0.16/0.61 & W0 != sz00
% 0.16/0.61 & W0 != sz10 )
% 0.16/0.61 => ( iLess0(W0,xk)
% 0.16/0.61 => ? [W1] :
% 0.16/0.61 ( aNaturalNumber0(W1)
% 0.16/0.61 & doDivides0(W1,W0)
% 0.16/0.61 & isPrime0(W1) ) ) ) ).
% 0.16/0.61
% 0.16/0.61 fof(m__1716_04,hypothesis,
% 0.16/0.61 ( xk != sz00
% 0.16/0.61 & xk != sz10 ) ).
% 0.16/0.61
% 0.16/0.61 fof(m__1725,hypothesis,
% 0.16/0.61 ~ isPrime0(xk) ).
% 0.16/0.61
% 0.16/0.61 fof(m__1737,hypothesis,
% 0.16/0.61 ~ ~ isPrime0(xk) ).
% 0.16/0.61
% 0.16/0.61 fof(m__,conjecture,
% 0.16/0.61 ? [W0] :
% 0.16/0.61 ( aNaturalNumber0(W0)
% 0.16/0.61 & doDivides0(W0,xk)
% 0.16/0.61 & isPrime0(W0) ) ).
% 0.16/0.61
% 0.16/0.61 %------------------------------------------------------------------------------
% 0.16/0.61 %-------------------------------------------
% 0.16/0.61 % Proof found
% 0.16/0.61 % SZS status Theorem for theBenchmark
% 0.16/0.61 % SZS output start Proof
% 0.16/0.61 %ClaNum:98(EqnAxiom:25)
% 0.16/0.61 %VarNum:432(SingletonVarNum:129)
% 0.16/0.61 %MaxLitNum:7
% 0.16/0.61 %MaxfuncDepth:2
% 0.16/0.61 %SharedTerms:11
% 0.16/0.61 %goalClause: 48
% 0.16/0.61 [26]P1(a1)
% 0.16/0.61 [27]P1(a10)
% 0.16/0.61 [28]P1(a11)
% 0.16/0.61 [29]P2(a11)
% 0.16/0.61 [30]~E(a1,a10)
% 0.16/0.61 [31]~E(a1,a11)
% 0.16/0.61 [32]~E(a11,a10)
% 0.16/0.61 [33]~P2(a11)
% 0.16/0.61 [42]~P1(x421)+P5(x421,x421)
% 0.16/0.61 [36]~P1(x361)+E(f2(a1,x361),a1)
% 0.16/0.61 [37]~P1(x371)+E(f2(x371,a1),a1)
% 0.16/0.61 [38]~P1(x381)+E(f7(a1,x381),x381)
% 0.16/0.61 [39]~P1(x391)+E(f2(a10,x391),x391)
% 0.16/0.61 [40]~P1(x401)+E(f7(x401,a1),x401)
% 0.16/0.62 [41]~P1(x411)+E(f2(x411,a10),x411)
% 0.16/0.62 [34]~P1(x341)+~P2(x341)+~E(x341,a1)
% 0.16/0.62 [35]~P1(x351)+~P2(x351)+~E(x351,a10)
% 0.16/0.62 [48]~P2(x481)+~P1(x481)+~P3(x481,a11)
% 0.16/0.62 [55]~P1(x552)+~P1(x551)+E(f7(x551,x552),f7(x552,x551))
% 0.16/0.62 [56]~P1(x562)+~P1(x561)+E(f2(x561,x562),f2(x562,x561))
% 0.16/0.62 [58]~P1(x582)+~P1(x581)+P1(f7(x581,x582))
% 0.16/0.62 [59]~P1(x592)+~P1(x591)+P1(f2(x591,x592))
% 0.16/0.62 [44]~P1(x441)+E(x441,a10)+P5(a10,x441)+E(x441,a1)
% 0.16/0.62 [47]~E(x472,x471)+~P1(x471)+~P1(x472)+P5(x471,x472)
% 0.16/0.62 [57]P5(x572,x571)+~P1(x571)+~P1(x572)+P5(x571,x572)
% 0.16/0.62 [50]~P1(x502)+~P1(x501)+E(x501,a1)+~E(f7(x502,x501),a1)
% 0.16/0.62 [51]~P1(x512)+~P1(x511)+E(x511,a1)+~E(f7(x511,x512),a1)
% 0.16/0.62 [64]~P1(x642)+~P1(x641)+P5(x642,f2(x642,x641))+E(x641,a1)
% 0.16/0.62 [70]~P1(x702)+~P1(x701)+~P5(x701,x702)+P1(f4(x701,x702))
% 0.16/0.62 [71]~P1(x712)+~P1(x711)+~P3(x711,x712)+P1(f5(x711,x712))
% 0.16/0.62 [78]~P1(x781)+~P1(x782)+~P3(x781,x782)+E(f2(x781,f5(x781,x782)),x782)
% 0.16/0.62 [79]~P1(x792)+~P1(x791)+~P5(x791,x792)+E(f7(x791,f4(x791,x792)),x792)
% 0.16/0.62 [88]~P1(x883)+~P1(x882)+~P1(x881)+E(f7(f7(x881,x882),x883),f7(x881,f7(x882,x883)))
% 0.16/0.62 [89]~P1(x893)+~P1(x892)+~P1(x891)+E(f2(f2(x891,x892),x893),f2(x891,f2(x892,x893)))
% 0.16/0.62 [97]~P1(x973)+~P1(x972)+~P1(x971)+E(f7(f2(x971,x972),f2(x971,x973)),f2(x971,f7(x972,x973)))
% 0.16/0.62 [98]~P1(x982)+~P1(x983)+~P1(x981)+E(f7(f2(x981,x982),f2(x983,x982)),f2(f7(x981,x983),x982))
% 0.16/0.62 [43]P2(x431)+~P1(x431)+E(x431,a10)+E(x431,a1)+~E(f3(x431),a10)
% 0.16/0.62 [45]P2(x451)+~P1(x451)+E(x451,a10)+~E(f3(x451),x451)+E(x451,a1)
% 0.16/0.62 [46]P2(x461)+~P1(x461)+E(x461,a10)+E(x461,a1)+P1(f3(x461))
% 0.16/0.62 [49]P2(x491)+~P1(x491)+E(x491,a10)+P3(f3(x491),x491)+E(x491,a1)
% 0.16/0.62 [53]~P1(x531)+E(x531,a10)+~P4(x531,a11)+E(x531,a1)+P1(f6(x531))
% 0.16/0.62 [54]~P1(x541)+E(x541,a10)+~P4(x541,a11)+E(x541,a1)+P2(f6(x541))
% 0.16/0.62 [61]~P1(x611)+E(x611,a10)+P3(f6(x611),x611)+~P4(x611,a11)+E(x611,a1)
% 0.16/0.62 [62]~P1(x621)+~P1(x622)+~P3(x622,x621)+P5(x622,x621)+E(x621,a1)
% 0.16/0.62 [63]P4(x631,x632)+~P1(x632)+~P1(x631)+~P5(x631,x632)+E(x631,x632)
% 0.16/0.62 [67]~P1(x672)+~P1(x671)+~P5(x672,x671)+~P5(x671,x672)+E(x671,x672)
% 0.16/0.62 [52]~P1(x521)+~P1(x522)+E(x521,a1)+E(x522,a1)+~E(f2(x522,x521),a1)
% 0.16/0.62 [65]~P1(x651)+~P1(x652)+~P1(x653)+P3(x651,x652)+~E(x652,f2(x651,x653))
% 0.16/0.62 [66]~P1(x662)+~P1(x661)+~P1(x663)+P5(x661,x662)+~E(f7(x661,x663),x662)
% 0.16/0.62 [68]~P1(x683)+~P1(x682)+~P5(x683,x682)+P1(x681)+~E(x681,f8(x682,x683))
% 0.16/0.62 [72]~P1(x722)+~P1(x721)+~P1(x723)+E(x721,x722)+~E(f7(x723,x721),f7(x723,x722))
% 0.16/0.62 [73]~P1(x732)+~P1(x733)+~P1(x731)+E(x731,x732)+~E(f7(x731,x733),f7(x732,x733))
% 0.16/0.62 [76]~P1(x763)+~P1(x761)+~P5(x761,x763)+~E(x762,f8(x763,x761))+E(f7(x761,x762),x763)
% 0.16/0.62 [60]~P1(x602)+~P1(x601)+~P2(x602)+~P3(x601,x602)+E(x601,x602)+E(x601,a10)
% 0.16/0.62 [80]~P1(x802)+~P1(x801)+~P5(x803,x802)+~P5(x801,x803)+P5(x801,x802)+~P1(x803)
% 0.16/0.62 [81]~P1(x812)+~P1(x811)+~P3(x813,x812)+~P3(x811,x813)+P3(x811,x812)+~P1(x813)
% 0.16/0.62 [69]~P1(x691)+~P1(x693)+~P3(x691,x693)+P1(x692)+E(x691,a1)+~E(x692,f9(x693,x691))
% 0.16/0.62 [74]~P1(x742)+~P1(x741)+~P1(x743)+E(x741,x742)+~E(f2(x743,x741),f2(x743,x742))+E(x743,a1)
% 0.16/0.62 [75]~P1(x752)+~P1(x753)+~P1(x751)+E(x751,x752)+~E(f2(x751,x753),f2(x752,x753))+E(x753,a1)
% 0.16/0.62 [77]~P1(x771)+~P1(x772)+~P3(x771,x772)+~E(x773,f9(x772,x771))+E(x771,a1)+E(x772,f2(x771,x773))
% 0.16/0.62 [82]~P1(x822)+~P1(x823)+~P1(x821)+~P5(x823,x822)+~E(f7(x823,x821),x822)+E(x821,f8(x822,x823))
% 0.16/0.62 [90]~P1(x903)+~P1(x902)+~P1(x901)+~P3(x901,x903)+~P3(x901,x902)+P3(x901,f7(x902,x903))
% 0.16/0.62 [91]~P1(x912)+~P1(x911)+~P1(x913)+~P5(x911,x912)+E(x911,x912)+P5(f7(x913,x911),f7(x913,x912))
% 0.16/0.62 [92]~P1(x922)+~P1(x923)+~P1(x921)+~P5(x921,x922)+E(x921,x922)+P5(f7(x921,x923),f7(x922,x923))
% 0.16/0.62 [95]~P1(x952)+~P1(x951)+~P3(x951,x953)+P3(x951,x952)+~P1(x953)+~P3(x951,f7(x953,x952))
% 0.16/0.62 [96]~P1(x962)+~P1(x963)+~P1(x961)+~P3(x961,x963)+E(x961,a1)+E(f9(f2(x962,x963),x961),f2(x962,f9(x963,x961)))
% 0.16/0.62 [83]~P1(x831)+~P1(x833)+~P1(x832)+~P3(x831,x833)+~E(x833,f2(x831,x832))+E(x831,a1)+E(x832,f9(x833,x831))
% 0.16/0.62 [93]~P1(x932)+~P1(x931)+~P1(x933)+~P5(x931,x932)+E(x931,x932)+P5(f2(x933,x931),f2(x933,x932))+E(x933,a1)
% 0.16/0.62 [94]~P1(x942)+~P1(x943)+~P1(x941)+~P5(x941,x942)+E(x941,x942)+P5(f2(x941,x943),f2(x942,x943))+E(x943,a1)
% 0.16/0.62 %EqnAxiom
% 0.16/0.62 [1]E(x11,x11)
% 0.16/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.16/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.16/0.62 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.16/0.62 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.16/0.62 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63))
% 0.16/0.62 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72))
% 0.16/0.62 [8]~E(x81,x82)+E(f9(x81,x83),f9(x82,x83))
% 0.16/0.62 [9]~E(x91,x92)+E(f9(x93,x91),f9(x93,x92))
% 0.16/0.62 [10]~E(x101,x102)+E(f8(x101,x103),f8(x102,x103))
% 0.16/0.62 [11]~E(x111,x112)+E(f8(x113,x111),f8(x113,x112))
% 0.16/0.62 [12]~E(x121,x122)+E(f4(x121,x123),f4(x122,x123))
% 0.16/0.62 [13]~E(x131,x132)+E(f4(x133,x131),f4(x133,x132))
% 0.16/0.62 [14]~E(x141,x142)+E(f5(x141,x143),f5(x142,x143))
% 0.16/0.62 [15]~E(x151,x152)+E(f5(x153,x151),f5(x153,x152))
% 0.16/0.62 [16]~E(x161,x162)+E(f3(x161),f3(x162))
% 0.16/0.62 [17]~E(x171,x172)+E(f6(x171),f6(x172))
% 0.16/0.62 [18]~P1(x181)+P1(x182)+~E(x181,x182)
% 0.16/0.62 [19]P3(x192,x193)+~E(x191,x192)+~P3(x191,x193)
% 0.16/0.62 [20]P3(x203,x202)+~E(x201,x202)+~P3(x203,x201)
% 0.16/0.62 [21]P4(x212,x213)+~E(x211,x212)+~P4(x211,x213)
% 0.16/0.62 [22]P4(x223,x222)+~E(x221,x222)+~P4(x223,x221)
% 0.16/0.62 [23]~P2(x231)+P2(x232)+~E(x231,x232)
% 0.16/0.62 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243)
% 0.16/0.62 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251)
% 0.16/0.62
% 0.16/0.62 %-------------------------------------------
% 0.16/0.62 cnf(99,plain,
% 0.16/0.62 ($false),
% 0.16/0.62 inference(scs_inference,[],[29,33]),
% 0.16/0.62 ['proof']).
% 0.16/0.62 % SZS output end Proof
% 0.16/0.62 % Total time :0.000000s
%------------------------------------------------------------------------------