TSTP Solution File: NUM489+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM489+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 : n029.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 10:22:26 EDT 2023
% Result : Theorem 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM489+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 16:42:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.55 start to proof:theBenchmark
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % File :CSE---1.6
% 0.20/0.62 % Problem :theBenchmark
% 0.20/0.62 % Transform :cnf
% 0.20/0.62 % Format :tptp:raw
% 0.20/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.62
% 0.20/0.62 % Result :Theorem 0.000000s
% 0.20/0.62 % Output :CNFRefutation 0.000000s
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 %------------------------------------------------------------------------------
% 0.20/0.62 % File : NUM489+1 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.62 % Domain : Number Theory
% 0.20/0.62 % Problem : Square root of a prime is irrational 14_01_03_01, 00 expansion
% 0.20/0.62 % Version : Especial.
% 0.20/0.62 % English :
% 0.20/0.62
% 0.20/0.62 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista
% 0.20/0.62 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.20/0.62 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.20/0.62 % Source : [Pas08]
% 0.20/0.62 % Names : primes_14_01_03_01.00 [Pas08]
% 0.20/0.62
% 0.20/0.62 % Status : Theorem
% 0.20/0.62 % Rating : 0.19 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.2.0, 0.14 v7.1.0, 0.13 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.17 v6.2.0, 0.28 v6.1.0, 0.37 v6.0.0, 0.26 v5.5.0, 0.37 v5.4.0, 0.39 v5.3.0, 0.44 v5.2.0, 0.25 v5.1.0, 0.38 v5.0.0, 0.42 v4.1.0, 0.48 v4.0.1, 0.78 v4.0.0
% 0.20/0.62 % Syntax : Number of formulae : 45 ( 4 unt; 5 def)
% 0.20/0.62 % Number of atoms : 201 ( 59 equ)
% 0.20/0.62 % Maximal formula atoms : 10 ( 4 avg)
% 0.20/0.62 % Number of connectives : 177 ( 21 ~; 8 |; 81 &)
% 0.20/0.62 % ( 5 <=>; 62 =>; 0 <=; 0 <~>)
% 0.20/0.62 % Maximal formula depth : 11 ( 6 avg)
% 0.20/0.62 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.62 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% 0.20/0.62 % Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% 0.20/0.62 % Number of variables : 85 ( 82 !; 3 ?)
% 0.20/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.62
% 0.20/0.62 % Comments : Problem generated by the SAD system [VLP07]
% 0.20/0.62 %------------------------------------------------------------------------------
% 0.20/0.62 fof(mNatSort,axiom,
% 0.20/0.62 ! [W0] :
% 0.20/0.62 ( aNaturalNumber0(W0)
% 0.20/0.62 => $true ) ).
% 0.20/0.62
% 0.20/0.62 fof(mSortsC,axiom,
% 0.20/0.62 aNaturalNumber0(sz00) ).
% 0.20/0.62
% 0.20/0.62 fof(mSortsC_01,axiom,
% 0.20/0.62 ( aNaturalNumber0(sz10)
% 0.20/0.62 & sz10 != sz00 ) ).
% 0.20/0.62
% 0.20/0.62 fof(mSortsB,axiom,
% 0.20/0.62 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mSortsB_02,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mAddComm,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mAddAsso,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1)
% 0.20/0.63 & aNaturalNumber0(W2) )
% 0.20/0.63 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(m_AddZero,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aNaturalNumber0(W0)
% 0.20/0.63 => ( sdtpldt0(W0,sz00) = W0
% 0.20/0.63 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mMulComm,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mMulAsso,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1)
% 0.20/0.63 & aNaturalNumber0(W2) )
% 0.20/0.63 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(m_MulUnit,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aNaturalNumber0(W0)
% 0.20/0.63 => ( sdtasdt0(W0,sz10) = W0
% 0.20/0.63 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(m_MulZero,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aNaturalNumber0(W0)
% 0.20/0.63 => ( sdtasdt0(W0,sz00) = sz00
% 0.20/0.63 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mAMDistr,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1)
% 0.20/0.63 & aNaturalNumber0(W2) )
% 0.20/0.63 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.20/0.63 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mAddCanc,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1)
% 0.20/0.63 & aNaturalNumber0(W2) )
% 0.20/0.63 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
% 0.20/0.63 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
% 0.20/0.63 => W1 = W2 ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mMulCanc,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aNaturalNumber0(W0)
% 0.20/0.63 => ( W0 != sz00
% 0.20/0.63 => ! [W1,W2] :
% 0.20/0.63 ( ( aNaturalNumber0(W1)
% 0.20/0.63 & aNaturalNumber0(W2) )
% 0.20/0.63 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2)
% 0.20/0.63 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
% 0.20/0.63 => W1 = W2 ) ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mZeroAdd,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( sdtpldt0(W0,W1) = sz00
% 0.20/0.63 => ( W0 = sz00
% 0.20/0.63 & W1 = sz00 ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mZeroMul,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( sdtasdt0(W0,W1) = sz00
% 0.20/0.63 => ( W0 = sz00
% 0.20/0.63 | W1 = sz00 ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mDefLE,definition,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( sdtlseqdt0(W0,W1)
% 0.20/0.63 <=> ? [W2] :
% 0.20/0.63 ( aNaturalNumber0(W2)
% 0.20/0.63 & sdtpldt0(W0,W2) = W1 ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mDefDiff,definition,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( sdtlseqdt0(W0,W1)
% 0.20/0.63 => ! [W2] :
% 0.20/0.63 ( W2 = sdtmndt0(W1,W0)
% 0.20/0.63 <=> ( aNaturalNumber0(W2)
% 0.20/0.63 & sdtpldt0(W0,W2) = W1 ) ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mLERefl,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aNaturalNumber0(W0)
% 0.20/0.63 => sdtlseqdt0(W0,W0) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mLEAsym,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( ( sdtlseqdt0(W0,W1)
% 0.20/0.63 & sdtlseqdt0(W1,W0) )
% 0.20/0.63 => W0 = W1 ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mLETran,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1)
% 0.20/0.63 & aNaturalNumber0(W2) )
% 0.20/0.63 => ( ( sdtlseqdt0(W0,W1)
% 0.20/0.63 & sdtlseqdt0(W1,W2) )
% 0.20/0.63 => sdtlseqdt0(W0,W2) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mLETotal,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( sdtlseqdt0(W0,W1)
% 0.20/0.63 | ( W1 != W0
% 0.20/0.63 & sdtlseqdt0(W1,W0) ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mMonAdd,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( ( W0 != W1
% 0.20/0.63 & sdtlseqdt0(W0,W1) )
% 0.20/0.63 => ! [W2] :
% 0.20/0.63 ( aNaturalNumber0(W2)
% 0.20/0.63 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)
% 0.20/0.63 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
% 0.20/0.63 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
% 0.20/0.63 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mMonMul,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1)
% 0.20/0.63 & aNaturalNumber0(W2) )
% 0.20/0.63 => ( ( W0 != sz00
% 0.20/0.63 & W1 != W2
% 0.20/0.63 & sdtlseqdt0(W1,W2) )
% 0.20/0.63 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2)
% 0.20/0.63 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.20/0.63 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
% 0.20/0.63 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mLENTr,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aNaturalNumber0(W0)
% 0.20/0.63 => ( W0 = sz00
% 0.20/0.63 | W0 = sz10
% 0.20/0.63 | ( sz10 != W0
% 0.20/0.63 & sdtlseqdt0(sz10,W0) ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mMonMul2,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( W0 != sz00
% 0.20/0.63 => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mIH,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( iLess0(W0,W1)
% 0.20/0.63 => $true ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mIH_03,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( ( W0 != W1
% 0.20/0.63 & sdtlseqdt0(W0,W1) )
% 0.20/0.63 => iLess0(W0,W1) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mDefDiv,definition,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( doDivides0(W0,W1)
% 0.20/0.63 <=> ? [W2] :
% 0.20/0.63 ( aNaturalNumber0(W2)
% 0.20/0.63 & W1 = sdtasdt0(W0,W2) ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mDefQuot,definition,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1) )
% 0.20/0.63 => ( ( W0 != sz00
% 0.20/0.63 & doDivides0(W0,W1) )
% 0.20/0.63 => ! [W2] :
% 0.20/0.63 ( W2 = sdtsldt0(W1,W0)
% 0.20/0.63 <=> ( aNaturalNumber0(W2)
% 0.20/0.63 & W1 = sdtasdt0(W0,W2) ) ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mDivTrans,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1)
% 0.20/0.63 & aNaturalNumber0(W2) )
% 0.20/0.63 => ( ( doDivides0(W0,W1)
% 0.20/0.63 & doDivides0(W1,W2) )
% 0.20/0.63 => doDivides0(W0,W2) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mDivSum,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aNaturalNumber0(W0)
% 0.20/0.63 & aNaturalNumber0(W1)
% 0.20/0.63 & aNaturalNumber0(W2) )
% 0.20/0.63 => ( ( doDivides0(W0,W1)
% 0.20/0.63 & doDivides0(W0,W2) )
% 0.20/0.63 => doDivides0(W0,sdtpldt0(W1,W2)) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mDivMin,axiom,
% 0.20/0.64 ! [W0,W1,W2] :
% 0.20/0.64 ( ( aNaturalNumber0(W0)
% 0.20/0.64 & aNaturalNumber0(W1)
% 0.20/0.64 & aNaturalNumber0(W2) )
% 0.20/0.64 => ( ( doDivides0(W0,W1)
% 0.20/0.64 & doDivides0(W0,sdtpldt0(W1,W2)) )
% 0.20/0.64 => doDivides0(W0,W2) ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(mDivLE,axiom,
% 0.20/0.64 ! [W0,W1] :
% 0.20/0.64 ( ( aNaturalNumber0(W0)
% 0.20/0.64 & aNaturalNumber0(W1) )
% 0.20/0.64 => ( ( doDivides0(W0,W1)
% 0.20/0.64 & W1 != sz00 )
% 0.20/0.64 => sdtlseqdt0(W0,W1) ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(mDivAsso,axiom,
% 0.20/0.64 ! [W0,W1] :
% 0.20/0.64 ( ( aNaturalNumber0(W0)
% 0.20/0.64 & aNaturalNumber0(W1) )
% 0.20/0.64 => ( ( W0 != sz00
% 0.20/0.64 & doDivides0(W0,W1) )
% 0.20/0.64 => ! [W2] :
% 0.20/0.64 ( aNaturalNumber0(W2)
% 0.20/0.64 => sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(mDefPrime,definition,
% 0.20/0.64 ! [W0] :
% 0.20/0.64 ( aNaturalNumber0(W0)
% 0.20/0.64 => ( isPrime0(W0)
% 0.20/0.64 <=> ( W0 != sz00
% 0.20/0.64 & W0 != sz10
% 0.20/0.64 & ! [W1] :
% 0.20/0.64 ( ( aNaturalNumber0(W1)
% 0.20/0.64 & doDivides0(W1,W0) )
% 0.20/0.64 => ( W1 = sz10
% 0.20/0.64 | W1 = W0 ) ) ) ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(mPrimDiv,axiom,
% 0.20/0.64 ! [W0] :
% 0.20/0.64 ( ( aNaturalNumber0(W0)
% 0.20/0.64 & W0 != sz00
% 0.20/0.64 & W0 != sz10 )
% 0.20/0.64 => ? [W1] :
% 0.20/0.64 ( aNaturalNumber0(W1)
% 0.20/0.64 & doDivides0(W1,W0)
% 0.20/0.64 & isPrime0(W1) ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(m__1837,hypothesis,
% 0.20/0.64 ( aNaturalNumber0(xn)
% 0.20/0.64 & aNaturalNumber0(xm)
% 0.20/0.64 & aNaturalNumber0(xp) ) ).
% 0.20/0.64
% 0.20/0.64 fof(m__1799,hypothesis,
% 0.20/0.64 ! [W0,W1,W2] :
% 0.20/0.64 ( ( aNaturalNumber0(W0)
% 0.20/0.64 & aNaturalNumber0(W1)
% 0.20/0.64 & aNaturalNumber0(W2) )
% 0.20/0.64 => ( ( isPrime0(W2)
% 0.20/0.64 & doDivides0(W2,sdtasdt0(W0,W1)) )
% 0.20/0.64 => ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
% 0.20/0.64 => ( doDivides0(W2,W0)
% 0.20/0.64 | doDivides0(W2,W1) ) ) ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(m__1860,hypothesis,
% 0.20/0.64 ( isPrime0(xp)
% 0.20/0.64 & doDivides0(xp,sdtasdt0(xn,xm)) ) ).
% 0.20/0.64
% 0.20/0.64 fof(m__1870,hypothesis,
% 0.20/0.64 sdtlseqdt0(xp,xn) ).
% 0.20/0.64
% 0.20/0.64 fof(m__1883,hypothesis,
% 0.20/0.64 xr = sdtmndt0(xn,xp) ).
% 0.20/0.64
% 0.20/0.64 fof(m__1894,hypothesis,
% 0.20/0.64 ( xr != xn
% 0.20/0.64 & sdtlseqdt0(xr,xn) ) ).
% 0.20/0.64
% 0.20/0.64 fof(m__,conjecture,
% 0.20/0.64 xn = sdtpldt0(xp,xr) ).
% 0.20/0.64
% 0.20/0.64 %------------------------------------------------------------------------------
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark
% 0.20/0.64 % SZS output start Proof
% 0.20/0.64 %ClaNum:103(EqnAxiom:25)
% 0.20/0.64 %VarNum:440(SingletonVarNum:131)
% 0.20/0.64 %MaxLitNum:8
% 0.20/0.64 %MaxfuncDepth:2
% 0.20/0.64 %SharedTerms:24
% 0.20/0.64 %goalClause: 38
% 0.20/0.64 %singleGoalClaCount:1
% 0.20/0.64 [26]P1(a1)
% 0.20/0.64 [27]P1(a10)
% 0.20/0.64 [28]P1(a11)
% 0.20/0.64 [29]P1(a12)
% 0.20/0.64 [30]P1(a13)
% 0.20/0.64 [31]P2(a13)
% 0.20/0.64 [33]P5(a13,a11)
% 0.20/0.64 [34]P5(a14,a11)
% 0.20/0.64 [36]~E(a1,a10)
% 0.20/0.64 [37]~E(a14,a11)
% 0.20/0.64 [32]E(f2(a11,a13),a14)
% 0.20/0.64 [35]P3(a13,f3(a11,a12))
% 0.20/0.64 [38]~E(f8(a13,a14),a11)
% 0.20/0.64 [49]~P1(x491)+P5(x491,x491)
% 0.20/0.64 [41]~P1(x411)+E(f3(a1,x411),a1)
% 0.20/0.64 [42]~P1(x421)+E(f3(x421,a1),a1)
% 0.20/0.64 [43]~P1(x431)+E(f8(a1,x431),x431)
% 0.20/0.64 [44]~P1(x441)+E(f3(a10,x441),x441)
% 0.20/0.64 [45]~P1(x451)+E(f8(x451,a1),x451)
% 0.20/0.64 [46]~P1(x461)+E(f3(x461,a10),x461)
% 0.20/0.64 [39]~P1(x391)+~P2(x391)+~E(x391,a1)
% 0.20/0.64 [40]~P1(x401)+~P2(x401)+~E(x401,a10)
% 0.20/0.64 [60]~P1(x602)+~P1(x601)+E(f8(x601,x602),f8(x602,x601))
% 0.20/0.64 [61]~P1(x612)+~P1(x611)+E(f3(x611,x612),f3(x612,x611))
% 0.20/0.64 [63]~P1(x632)+~P1(x631)+P1(f8(x631,x632))
% 0.20/0.64 [64]~P1(x642)+~P1(x641)+P1(f3(x641,x642))
% 0.20/0.64 [51]~P1(x511)+E(x511,a10)+P5(a10,x511)+E(x511,a1)
% 0.20/0.64 [47]~P1(x471)+E(x471,a10)+E(x471,a1)+P1(f4(x471))
% 0.20/0.64 [48]~P1(x481)+E(x481,a10)+E(x481,a1)+P2(f4(x481))
% 0.20/0.64 [54]~P1(x541)+E(x541,a10)+P3(f4(x541),x541)+E(x541,a1)
% 0.20/0.64 [55]~E(x552,x551)+~P1(x551)+~P1(x552)+P5(x551,x552)
% 0.20/0.64 [62]P5(x622,x621)+~P1(x621)+~P1(x622)+P5(x621,x622)
% 0.20/0.64 [57]~P1(x572)+~P1(x571)+E(x571,a1)+~E(f8(x572,x571),a1)
% 0.20/0.64 [58]~P1(x582)+~P1(x581)+E(x581,a1)+~E(f8(x581,x582),a1)
% 0.20/0.64 [68]~P1(x682)+~P1(x681)+P5(x682,f3(x682,x681))+E(x681,a1)
% 0.20/0.64 [74]~P1(x742)+~P1(x741)+~P5(x741,x742)+P1(f6(x741,x742))
% 0.20/0.64 [75]~P1(x752)+~P1(x751)+~P3(x751,x752)+P1(f7(x751,x752))
% 0.20/0.64 [82]~P1(x821)+~P1(x822)+~P3(x821,x822)+E(f3(x821,f7(x821,x822)),x822)
% 0.20/0.64 [83]~P1(x832)+~P1(x831)+~P5(x831,x832)+E(f8(x831,f6(x831,x832)),x832)
% 0.20/0.64 [92]~P1(x923)+~P1(x922)+~P1(x921)+E(f8(f8(x921,x922),x923),f8(x921,f8(x922,x923)))
% 0.20/0.64 [93]~P1(x933)+~P1(x932)+~P1(x931)+E(f3(f3(x931,x932),x933),f3(x931,f3(x932,x933)))
% 0.20/0.64 [101]~P1(x1013)+~P1(x1012)+~P1(x1011)+E(f8(f3(x1011,x1012),f3(x1011,x1013)),f3(x1011,f8(x1012,x1013)))
% 0.20/0.64 [102]~P1(x1022)+~P1(x1023)+~P1(x1021)+E(f8(f3(x1021,x1022),f3(x1023,x1022)),f3(f8(x1021,x1023),x1022))
% 0.20/0.64 [50]P2(x501)+~P1(x501)+E(x501,a10)+E(x501,a1)+~E(f5(x501),a10)
% 0.20/0.64 [52]P2(x521)+~P1(x521)+E(x521,a10)+~E(f5(x521),x521)+E(x521,a1)
% 0.20/0.64 [53]P2(x531)+~P1(x531)+E(x531,a10)+E(x531,a1)+P1(f5(x531))
% 0.20/0.64 [56]P2(x561)+~P1(x561)+E(x561,a10)+P3(f5(x561),x561)+E(x561,a1)
% 0.20/0.64 [66]~P1(x661)+~P1(x662)+~P3(x662,x661)+P5(x662,x661)+E(x661,a1)
% 0.20/0.64 [67]P4(x671,x672)+~P1(x672)+~P1(x671)+~P5(x671,x672)+E(x671,x672)
% 0.20/0.64 [71]~P1(x712)+~P1(x711)+~P5(x712,x711)+~P5(x711,x712)+E(x711,x712)
% 0.20/0.64 [59]~P1(x591)+~P1(x592)+E(x591,a1)+E(x592,a1)+~E(f3(x592,x591),a1)
% 0.20/0.64 [69]~P1(x691)+~P1(x692)+~P1(x693)+P3(x691,x692)+~E(x692,f3(x691,x693))
% 0.20/0.64 [70]~P1(x702)+~P1(x701)+~P1(x703)+P5(x701,x702)+~E(f8(x701,x703),x702)
% 0.20/0.64 [72]~P1(x723)+~P1(x722)+~P5(x723,x722)+P1(x721)+~E(x721,f2(x722,x723))
% 0.20/0.64 [76]~P1(x762)+~P1(x761)+~P1(x763)+E(x761,x762)+~E(f8(x763,x761),f8(x763,x762))
% 0.20/0.64 [77]~P1(x772)+~P1(x773)+~P1(x771)+E(x771,x772)+~E(f8(x771,x773),f8(x772,x773))
% 0.20/0.64 [80]~P1(x803)+~P1(x801)+~P5(x801,x803)+~E(x802,f2(x803,x801))+E(f8(x801,x802),x803)
% 0.20/0.64 [65]~P1(x652)+~P1(x651)+~P2(x652)+~P3(x651,x652)+E(x651,x652)+E(x651,a10)
% 0.20/0.64 [84]~P1(x842)+~P1(x841)+~P5(x843,x842)+~P5(x841,x843)+P5(x841,x842)+~P1(x843)
% 0.20/0.64 [85]~P1(x852)+~P1(x851)+~P3(x853,x852)+~P3(x851,x853)+P3(x851,x852)+~P1(x853)
% 0.20/0.64 [73]~P1(x731)+~P1(x733)+~P3(x731,x733)+P1(x732)+E(x731,a1)+~E(x732,f9(x733,x731))
% 0.20/0.64 [78]~P1(x782)+~P1(x781)+~P1(x783)+E(x781,x782)+~E(f3(x783,x781),f3(x783,x782))+E(x783,a1)
% 0.20/0.64 [79]~P1(x792)+~P1(x793)+~P1(x791)+E(x791,x792)+~E(f3(x791,x793),f3(x792,x793))+E(x793,a1)
% 0.20/0.64 [81]~P1(x811)+~P1(x812)+~P3(x811,x812)+~E(x813,f9(x812,x811))+E(x811,a1)+E(x812,f3(x811,x813))
% 0.20/0.64 [86]~P1(x862)+~P1(x863)+~P1(x861)+~P5(x863,x862)+~E(f8(x863,x861),x862)+E(x861,f2(x862,x863))
% 0.20/0.64 [94]~P1(x943)+~P1(x942)+~P1(x941)+~P3(x941,x943)+~P3(x941,x942)+P3(x941,f8(x942,x943))
% 0.20/0.64 [95]~P1(x952)+~P1(x951)+~P1(x953)+~P5(x951,x952)+E(x951,x952)+P5(f8(x953,x951),f8(x953,x952))
% 0.20/0.64 [96]~P1(x962)+~P1(x963)+~P1(x961)+~P5(x961,x962)+E(x961,x962)+P5(f8(x961,x963),f8(x962,x963))
% 0.20/0.64 [99]~P1(x992)+~P1(x991)+~P3(x991,x993)+P3(x991,x992)+~P1(x993)+~P3(x991,f8(x993,x992))
% 0.20/0.64 [100]~P1(x1002)+~P1(x1003)+~P1(x1001)+~P3(x1001,x1003)+E(x1001,a1)+E(f9(f3(x1002,x1003),x1001),f3(x1002,f9(x1003,x1001)))
% 0.20/0.64 [87]~P1(x871)+~P1(x873)+~P1(x872)+~P3(x871,x873)+~E(x873,f3(x871,x872))+E(x871,a1)+E(x872,f9(x873,x871))
% 0.20/0.64 [97]~P1(x972)+~P1(x971)+~P1(x973)+~P5(x971,x972)+E(x971,x972)+P5(f3(x973,x971),f3(x973,x972))+E(x973,a1)
% 0.20/0.64 [98]~P1(x982)+~P1(x983)+~P1(x981)+~P5(x981,x982)+E(x981,x982)+P5(f3(x981,x983),f3(x982,x983))+E(x983,a1)
% 0.20/0.64 [103]~P1(x1031)+~P1(x1032)+~P1(x1033)+~P2(x1031)+P3(x1031,x1032)+P3(x1031,x1033)+~P3(x1031,f3(x1033,x1032))+~P4(f8(f8(x1033,x1032),x1031),f8(f8(a11,a12),a13))
% 0.20/0.64 %EqnAxiom
% 0.20/0.64 [1]E(x11,x11)
% 0.20/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.64 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.20/0.64 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.20/0.64 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.20/0.64 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.20/0.64 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83))
% 0.20/0.64 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92))
% 0.20/0.64 [10]~E(x101,x102)+E(f9(x101,x103),f9(x102,x103))
% 0.20/0.64 [11]~E(x111,x112)+E(f9(x113,x111),f9(x113,x112))
% 0.20/0.64 [12]~E(x121,x122)+E(f6(x121,x123),f6(x122,x123))
% 0.20/0.64 [13]~E(x131,x132)+E(f6(x133,x131),f6(x133,x132))
% 0.20/0.64 [14]~E(x141,x142)+E(f7(x141,x143),f7(x142,x143))
% 0.20/0.64 [15]~E(x151,x152)+E(f7(x153,x151),f7(x153,x152))
% 0.20/0.64 [16]~E(x161,x162)+E(f5(x161),f5(x162))
% 0.20/0.64 [17]~E(x171,x172)+E(f4(x171),f4(x172))
% 0.20/0.64 [18]~P1(x181)+P1(x182)+~E(x181,x182)
% 0.20/0.64 [19]P4(x192,x193)+~E(x191,x192)+~P4(x191,x193)
% 0.20/0.64 [20]P4(x203,x202)+~E(x201,x202)+~P4(x203,x201)
% 0.20/0.64 [21]P3(x212,x213)+~E(x211,x212)+~P3(x211,x213)
% 0.20/0.64 [22]P3(x223,x222)+~E(x221,x222)+~P3(x223,x221)
% 0.20/0.64 [23]~P2(x231)+P2(x232)+~E(x231,x232)
% 0.20/0.64 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243)
% 0.20/0.64 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251)
% 0.20/0.64
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 cnf(108,plain,
% 0.20/0.64 ($false),
% 0.20/0.64 inference(scs_inference,[],[38,26,28,30,33,34,32,2,24,62,72,80]),
% 0.20/0.64 ['proof']).
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time :0.000000s
%------------------------------------------------------------------------------