TSTP Solution File: NUM519+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM519+1 : 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 : n022.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 10:22:49 EDT 2023
% Result : Theorem 0.20s 0.68s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM519+1 : 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
% 0.12/0.34 % Computer : n022.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 14:57:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.60 start to proof:theBenchmark
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 % File :CSE---1.6
% 0.20/0.67 % Problem :theBenchmark
% 0.20/0.67 % Transform :cnf
% 0.20/0.67 % Format :tptp:raw
% 0.20/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.67
% 0.20/0.67 % Result :Theorem 0.000000s
% 0.20/0.67 % Output :CNFRefutation 0.000000s
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 %------------------------------------------------------------------------------
% 0.20/0.67 % File : NUM519+1 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.67 % Domain : Number Theory
% 0.20/0.67 % Problem : Square root of a prime is irrational 14_03_03_07, 00 expansion
% 0.20/0.67 % Version : Especial.
% 0.20/0.67 % English :
% 0.20/0.67
% 0.20/0.67 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista
% 0.20/0.67 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.20/0.67 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.20/0.67 % Source : [Pas08]
% 0.20/0.67 % Names : primes_14_03_03_07.00 [Pas08]
% 0.20/0.67
% 0.20/0.67 % Status : ContradictoryAxioms
% 0.20/0.67 % Rating : 0.14 v7.5.0, 0.09 v7.4.0, 0.29 v7.3.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.08 v6.1.0, 0.07 v6.0.0, 0.04 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.1.0, 0.24 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.1, 0.57 v4.0.0
% 0.20/0.67 % Syntax : Number of formulae : 54 ( 6 unt; 5 def)
% 0.20/0.67 % Number of atoms : 220 ( 64 equ)
% 0.20/0.67 % Maximal formula atoms : 10 ( 4 avg)
% 0.20/0.67 % Number of connectives : 196 ( 30 ~; 11 |; 88 &)
% 0.20/0.67 % ( 5 <=>; 62 =>; 0 <=; 0 <~>)
% 0.20/0.67 % Maximal formula depth : 11 ( 5 avg)
% 0.20/0.67 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.67 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% 0.20/0.67 % Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% 0.20/0.67 % Number of variables : 85 ( 82 !; 3 ?)
% 0.20/0.67 % SPC : FOF_CAX_RFO_SEQ
% 0.20/0.67
% 0.20/0.67 % Comments : Problem generated by the SAD system [VLP07]
% 0.20/0.67 %------------------------------------------------------------------------------
% 0.20/0.67 fof(mNatSort,axiom,
% 0.20/0.67 ! [W0] :
% 0.20/0.67 ( aNaturalNumber0(W0)
% 0.20/0.67 => $true ) ).
% 0.20/0.67
% 0.20/0.67 fof(mSortsC,axiom,
% 0.20/0.67 aNaturalNumber0(sz00) ).
% 0.20/0.67
% 0.20/0.67 fof(mSortsC_01,axiom,
% 0.20/0.67 ( aNaturalNumber0(sz10)
% 0.20/0.67 & sz10 != sz00 ) ).
% 0.20/0.67
% 0.20/0.67 fof(mSortsB,axiom,
% 0.20/0.67 ! [W0,W1] :
% 0.20/0.67 ( ( aNaturalNumber0(W0)
% 0.20/0.67 & aNaturalNumber0(W1) )
% 0.20/0.67 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ).
% 0.20/0.67
% 0.20/0.67 fof(mSortsB_02,axiom,
% 0.20/0.67 ! [W0,W1] :
% 0.20/0.67 ( ( aNaturalNumber0(W0)
% 0.20/0.67 & aNaturalNumber0(W1) )
% 0.20/0.67 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ).
% 0.20/0.67
% 0.20/0.67 fof(mAddComm,axiom,
% 0.20/0.67 ! [W0,W1] :
% 0.20/0.67 ( ( aNaturalNumber0(W0)
% 0.20/0.67 & aNaturalNumber0(W1) )
% 0.20/0.67 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.20/0.67
% 0.20/0.67 fof(mAddAsso,axiom,
% 0.20/0.67 ! [W0,W1,W2] :
% 0.20/0.67 ( ( aNaturalNumber0(W0)
% 0.20/0.67 & aNaturalNumber0(W1)
% 0.20/0.67 & aNaturalNumber0(W2) )
% 0.20/0.67 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
% 0.20/0.67
% 0.20/0.67 fof(m_AddZero,axiom,
% 0.20/0.67 ! [W0] :
% 0.20/0.67 ( aNaturalNumber0(W0)
% 0.20/0.67 => ( sdtpldt0(W0,sz00) = W0
% 0.20/0.67 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.20/0.67
% 0.20/0.67 fof(mMulComm,axiom,
% 0.20/0.67 ! [W0,W1] :
% 0.20/0.67 ( ( aNaturalNumber0(W0)
% 0.20/0.67 & aNaturalNumber0(W1) )
% 0.20/0.67 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.20/0.67
% 0.20/0.67 fof(mMulAsso,axiom,
% 0.20/0.67 ! [W0,W1,W2] :
% 0.20/0.67 ( ( aNaturalNumber0(W0)
% 0.20/0.67 & aNaturalNumber0(W1)
% 0.20/0.67 & aNaturalNumber0(W2) )
% 0.20/0.67 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
% 0.20/0.67
% 0.20/0.68 fof(m_MulUnit,axiom,
% 0.20/0.68 ! [W0] :
% 0.20/0.68 ( aNaturalNumber0(W0)
% 0.20/0.68 => ( sdtasdt0(W0,sz10) = W0
% 0.20/0.68 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(m_MulZero,axiom,
% 0.20/0.68 ! [W0] :
% 0.20/0.68 ( aNaturalNumber0(W0)
% 0.20/0.68 => ( sdtasdt0(W0,sz00) = sz00
% 0.20/0.68 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mAMDistr,axiom,
% 0.20/0.68 ! [W0,W1,W2] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1)
% 0.20/0.68 & aNaturalNumber0(W2) )
% 0.20/0.68 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.20/0.68 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mAddCanc,axiom,
% 0.20/0.68 ! [W0,W1,W2] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1)
% 0.20/0.68 & aNaturalNumber0(W2) )
% 0.20/0.68 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
% 0.20/0.68 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
% 0.20/0.68 => W1 = W2 ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mMulCanc,axiom,
% 0.20/0.68 ! [W0] :
% 0.20/0.68 ( aNaturalNumber0(W0)
% 0.20/0.68 => ( W0 != sz00
% 0.20/0.68 => ! [W1,W2] :
% 0.20/0.68 ( ( aNaturalNumber0(W1)
% 0.20/0.68 & aNaturalNumber0(W2) )
% 0.20/0.68 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2)
% 0.20/0.68 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
% 0.20/0.68 => W1 = W2 ) ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mZeroAdd,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( sdtpldt0(W0,W1) = sz00
% 0.20/0.68 => ( W0 = sz00
% 0.20/0.68 & W1 = sz00 ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mZeroMul,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( sdtasdt0(W0,W1) = sz00
% 0.20/0.68 => ( W0 = sz00
% 0.20/0.68 | W1 = sz00 ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mDefLE,definition,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( sdtlseqdt0(W0,W1)
% 0.20/0.68 <=> ? [W2] :
% 0.20/0.68 ( aNaturalNumber0(W2)
% 0.20/0.68 & sdtpldt0(W0,W2) = W1 ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mDefDiff,definition,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( sdtlseqdt0(W0,W1)
% 0.20/0.68 => ! [W2] :
% 0.20/0.68 ( W2 = sdtmndt0(W1,W0)
% 0.20/0.68 <=> ( aNaturalNumber0(W2)
% 0.20/0.68 & sdtpldt0(W0,W2) = W1 ) ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mLERefl,axiom,
% 0.20/0.68 ! [W0] :
% 0.20/0.68 ( aNaturalNumber0(W0)
% 0.20/0.68 => sdtlseqdt0(W0,W0) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mLEAsym,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( ( sdtlseqdt0(W0,W1)
% 0.20/0.68 & sdtlseqdt0(W1,W0) )
% 0.20/0.68 => W0 = W1 ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mLETran,axiom,
% 0.20/0.68 ! [W0,W1,W2] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1)
% 0.20/0.68 & aNaturalNumber0(W2) )
% 0.20/0.68 => ( ( sdtlseqdt0(W0,W1)
% 0.20/0.68 & sdtlseqdt0(W1,W2) )
% 0.20/0.68 => sdtlseqdt0(W0,W2) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mLETotal,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( sdtlseqdt0(W0,W1)
% 0.20/0.68 | ( W1 != W0
% 0.20/0.68 & sdtlseqdt0(W1,W0) ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mMonAdd,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( ( W0 != W1
% 0.20/0.68 & sdtlseqdt0(W0,W1) )
% 0.20/0.68 => ! [W2] :
% 0.20/0.68 ( aNaturalNumber0(W2)
% 0.20/0.68 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)
% 0.20/0.68 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
% 0.20/0.68 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
% 0.20/0.68 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mMonMul,axiom,
% 0.20/0.68 ! [W0,W1,W2] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1)
% 0.20/0.68 & aNaturalNumber0(W2) )
% 0.20/0.68 => ( ( W0 != sz00
% 0.20/0.68 & W1 != W2
% 0.20/0.68 & sdtlseqdt0(W1,W2) )
% 0.20/0.68 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2)
% 0.20/0.68 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.20/0.68 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
% 0.20/0.68 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mLENTr,axiom,
% 0.20/0.68 ! [W0] :
% 0.20/0.68 ( aNaturalNumber0(W0)
% 0.20/0.68 => ( W0 = sz00
% 0.20/0.68 | W0 = sz10
% 0.20/0.68 | ( sz10 != W0
% 0.20/0.68 & sdtlseqdt0(sz10,W0) ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mMonMul2,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( W0 != sz00
% 0.20/0.68 => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mIH,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( iLess0(W0,W1)
% 0.20/0.68 => $true ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mIH_03,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( ( W0 != W1
% 0.20/0.68 & sdtlseqdt0(W0,W1) )
% 0.20/0.68 => iLess0(W0,W1) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mDefDiv,definition,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( doDivides0(W0,W1)
% 0.20/0.68 <=> ? [W2] :
% 0.20/0.68 ( aNaturalNumber0(W2)
% 0.20/0.68 & W1 = sdtasdt0(W0,W2) ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mDefQuot,definition,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( ( W0 != sz00
% 0.20/0.68 & doDivides0(W0,W1) )
% 0.20/0.68 => ! [W2] :
% 0.20/0.68 ( W2 = sdtsldt0(W1,W0)
% 0.20/0.68 <=> ( aNaturalNumber0(W2)
% 0.20/0.68 & W1 = sdtasdt0(W0,W2) ) ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mDivTrans,axiom,
% 0.20/0.68 ! [W0,W1,W2] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1)
% 0.20/0.68 & aNaturalNumber0(W2) )
% 0.20/0.68 => ( ( doDivides0(W0,W1)
% 0.20/0.68 & doDivides0(W1,W2) )
% 0.20/0.68 => doDivides0(W0,W2) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mDivSum,axiom,
% 0.20/0.68 ! [W0,W1,W2] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1)
% 0.20/0.68 & aNaturalNumber0(W2) )
% 0.20/0.68 => ( ( doDivides0(W0,W1)
% 0.20/0.68 & doDivides0(W0,W2) )
% 0.20/0.68 => doDivides0(W0,sdtpldt0(W1,W2)) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mDivMin,axiom,
% 0.20/0.68 ! [W0,W1,W2] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1)
% 0.20/0.68 & aNaturalNumber0(W2) )
% 0.20/0.68 => ( ( doDivides0(W0,W1)
% 0.20/0.68 & doDivides0(W0,sdtpldt0(W1,W2)) )
% 0.20/0.68 => doDivides0(W0,W2) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mDivLE,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( ( doDivides0(W0,W1)
% 0.20/0.68 & W1 != sz00 )
% 0.20/0.68 => sdtlseqdt0(W0,W1) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mDivAsso,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1) )
% 0.20/0.68 => ( ( W0 != sz00
% 0.20/0.68 & doDivides0(W0,W1) )
% 0.20/0.68 => ! [W2] :
% 0.20/0.68 ( aNaturalNumber0(W2)
% 0.20/0.68 => sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mDefPrime,definition,
% 0.20/0.68 ! [W0] :
% 0.20/0.68 ( aNaturalNumber0(W0)
% 0.20/0.68 => ( isPrime0(W0)
% 0.20/0.68 <=> ( W0 != sz00
% 0.20/0.68 & W0 != sz10
% 0.20/0.68 & ! [W1] :
% 0.20/0.68 ( ( aNaturalNumber0(W1)
% 0.20/0.68 & doDivides0(W1,W0) )
% 0.20/0.68 => ( W1 = sz10
% 0.20/0.68 | W1 = W0 ) ) ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mPrimDiv,axiom,
% 0.20/0.68 ! [W0] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & W0 != sz00
% 0.20/0.68 & W0 != sz10 )
% 0.20/0.68 => ? [W1] :
% 0.20/0.68 ( aNaturalNumber0(W1)
% 0.20/0.68 & doDivides0(W1,W0)
% 0.20/0.68 & isPrime0(W1) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(m__1837,hypothesis,
% 0.20/0.68 ( aNaturalNumber0(xn)
% 0.20/0.68 & aNaturalNumber0(xm)
% 0.20/0.68 & aNaturalNumber0(xp) ) ).
% 0.20/0.68
% 0.20/0.68 fof(m__1799,hypothesis,
% 0.20/0.68 ! [W0,W1,W2] :
% 0.20/0.68 ( ( aNaturalNumber0(W0)
% 0.20/0.68 & aNaturalNumber0(W1)
% 0.20/0.68 & aNaturalNumber0(W2) )
% 0.20/0.68 => ( ( isPrime0(W2)
% 0.20/0.68 & doDivides0(W2,sdtasdt0(W0,W1)) )
% 0.20/0.68 => ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
% 0.20/0.68 => ( doDivides0(W2,W0)
% 0.20/0.68 | doDivides0(W2,W1) ) ) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(m__1860,hypothesis,
% 0.20/0.68 ( isPrime0(xp)
% 0.20/0.68 & doDivides0(xp,sdtasdt0(xn,xm)) ) ).
% 0.20/0.68
% 0.20/0.68 fof(m__1870,hypothesis,
% 0.20/0.68 ~ sdtlseqdt0(xp,xn) ).
% 0.20/0.68
% 0.20/0.68 fof(m__2075,hypothesis,
% 0.20/0.68 ~ sdtlseqdt0(xp,xm) ).
% 0.20/0.68
% 0.20/0.68 fof(m__2287,hypothesis,
% 0.20/0.68 ( xn != xp
% 0.20/0.68 & sdtlseqdt0(xn,xp)
% 0.20/0.68 & xm != xp
% 0.20/0.68 & sdtlseqdt0(xm,xp) ) ).
% 0.20/0.68
% 0.20/0.68 fof(m__2306,hypothesis,
% 0.20/0.68 xk = sdtsldt0(sdtasdt0(xn,xm),xp) ).
% 0.20/0.68
% 0.20/0.68 fof(m__2315,hypothesis,
% 0.20/0.68 ~ ( xk = sz00
% 0.20/0.68 | xk = sz10 ) ).
% 0.20/0.68
% 0.20/0.68 fof(m__2327,hypothesis,
% 0.20/0.68 ( xk != sz00
% 0.20/0.68 & xk != sz10 ) ).
% 0.20/0.68
% 0.20/0.68 fof(m__2342,hypothesis,
% 0.20/0.68 ( aNaturalNumber0(xr)
% 0.20/0.68 & doDivides0(xr,xk)
% 0.20/0.68 & isPrime0(xr) ) ).
% 0.20/0.68
% 0.20/0.68 fof(m__2362,hypothesis,
% 0.20/0.68 ( sdtlseqdt0(xr,xk)
% 0.20/0.68 & doDivides0(xr,sdtasdt0(xn,xm)) ) ).
% 0.20/0.68
% 0.20/0.68 fof(m__2377,hypothesis,
% 0.20/0.68 ( xk != xp
% 0.20/0.68 & sdtlseqdt0(xk,xp) ) ).
% 0.20/0.68
% 0.20/0.68 fof(m__2449,hypothesis,
% 0.20/0.68 ( doDivides0(xr,xn)
% 0.20/0.68 | doDivides0(xr,xm) ) ).
% 0.20/0.68
% 0.20/0.68 fof(m__2487,hypothesis,
% 0.20/0.68 ~ doDivides0(xr,xn) ).
% 0.20/0.68
% 0.20/0.68 fof(m__2698,hypothesis,
% 0.20/0.68 ~ doDivides0(xr,xm) ).
% 0.20/0.68
% 0.20/0.68 fof(m__,conjecture,
% 0.20/0.68 ( doDivides0(xp,xn)
% 0.20/0.68 | doDivides0(xp,xm) ) ).
% 0.20/0.68
% 0.20/0.68 %------------------------------------------------------------------------------
% 0.20/0.68 %-------------------------------------------
% 0.20/0.68 % Proof found
% 0.20/0.68 % SZS status Theorem for theBenchmark
% 0.20/0.68 % SZS output start Proof
% 0.20/0.68 %ClaNum:121(EqnAxiom:25)
% 0.20/0.68 %VarNum:440(SingletonVarNum:131)
% 0.20/0.68 %MaxLitNum:8
% 0.20/0.68 %MaxfuncDepth:2
% 0.20/0.68 %SharedTerms:41
% 0.20/0.68 %goalClause: 52 53
% 0.20/0.68 %singleGoalClaCount:2
% 0.20/0.68 [26]P1(a1)
% 0.20/0.68 [27]P1(a10)
% 0.20/0.68 [28]P1(a11)
% 0.20/0.68 [29]P1(a12)
% 0.20/0.68 [30]P1(a14)
% 0.20/0.68 [31]P1(a15)
% 0.20/0.68 [32]P2(a14)
% 0.20/0.68 [33]P2(a15)
% 0.20/0.68 [34]P5(a11,a14)
% 0.20/0.68 [35]P5(a12,a14)
% 0.20/0.68 [36]P5(a13,a14)
% 0.20/0.68 [37]P5(a15,a13)
% 0.20/0.68 [38]P3(a15,a13)
% 0.20/0.68 [42]~E(a1,a10)
% 0.20/0.68 [43]~E(a14,a11)
% 0.20/0.68 [44]~E(a14,a12)
% 0.20/0.68 [46]~E(a1,a13)
% 0.20/0.68 [48]~E(a13,a10)
% 0.20/0.68 [49]~E(a13,a14)
% 0.20/0.68 [50]~P5(a14,a11)
% 0.20/0.68 [51]~P5(a14,a12)
% 0.20/0.68 [52]~P3(a14,a11)
% 0.20/0.68 [53]~P3(a14,a12)
% 0.20/0.68 [54]~P3(a15,a11)
% 0.20/0.68 [55]~P3(a15,a12)
% 0.20/0.68 [40]P3(a14,f2(a11,a12))
% 0.20/0.68 [41]P3(a15,f2(a11,a12))
% 0.20/0.68 [39]E(f7(f2(a11,a12),a14),a13)
% 0.20/0.68 [68]P3(a15,a11)+P3(a15,a12)
% 0.20/0.68 [66]~P1(x661)+P5(x661,x661)
% 0.20/0.68 [58]~P1(x581)+E(f2(a1,x581),a1)
% 0.20/0.68 [59]~P1(x591)+E(f2(x591,a1),a1)
% 0.20/0.68 [60]~P1(x601)+E(f8(a1,x601),x601)
% 0.20/0.68 [61]~P1(x611)+E(f2(a10,x611),x611)
% 0.20/0.68 [62]~P1(x621)+E(f8(x621,a1),x621)
% 0.20/0.68 [63]~P1(x631)+E(f2(x631,a10),x631)
% 0.20/0.68 [56]~P1(x561)+~P2(x561)+~E(x561,a1)
% 0.20/0.68 [57]~P1(x571)+~P2(x571)+~E(x571,a10)
% 0.20/0.68 [78]~P1(x782)+~P1(x781)+E(f8(x781,x782),f8(x782,x781))
% 0.20/0.68 [79]~P1(x792)+~P1(x791)+E(f2(x791,x792),f2(x792,x791))
% 0.20/0.68 [81]~P1(x812)+~P1(x811)+P1(f8(x811,x812))
% 0.20/0.68 [82]~P1(x822)+~P1(x821)+P1(f2(x821,x822))
% 0.20/0.68 [69]~P1(x691)+E(x691,a10)+P5(a10,x691)+E(x691,a1)
% 0.20/0.68 [64]~P1(x641)+E(x641,a10)+E(x641,a1)+P1(f3(x641))
% 0.20/0.68 [65]~P1(x651)+E(x651,a10)+E(x651,a1)+P2(f3(x651))
% 0.20/0.68 [72]~P1(x721)+E(x721,a10)+P3(f3(x721),x721)+E(x721,a1)
% 0.20/0.68 [73]~E(x732,x731)+~P1(x731)+~P1(x732)+P5(x731,x732)
% 0.20/0.68 [80]P5(x802,x801)+~P1(x801)+~P1(x802)+P5(x801,x802)
% 0.20/0.68 [75]~P1(x752)+~P1(x751)+E(x751,a1)+~E(f8(x752,x751),a1)
% 0.20/0.69 [76]~P1(x762)+~P1(x761)+E(x761,a1)+~E(f8(x761,x762),a1)
% 0.20/0.69 [86]~P1(x862)+~P1(x861)+P5(x862,f2(x862,x861))+E(x861,a1)
% 0.20/0.69 [92]~P1(x922)+~P1(x921)+~P5(x921,x922)+P1(f5(x921,x922))
% 0.20/0.69 [93]~P1(x932)+~P1(x931)+~P3(x931,x932)+P1(f6(x931,x932))
% 0.20/0.69 [100]~P1(x1001)+~P1(x1002)+~P3(x1001,x1002)+E(f2(x1001,f6(x1001,x1002)),x1002)
% 0.20/0.69 [101]~P1(x1012)+~P1(x1011)+~P5(x1011,x1012)+E(f8(x1011,f5(x1011,x1012)),x1012)
% 0.20/0.69 [110]~P1(x1103)+~P1(x1102)+~P1(x1101)+E(f8(f8(x1101,x1102),x1103),f8(x1101,f8(x1102,x1103)))
% 0.20/0.69 [111]~P1(x1113)+~P1(x1112)+~P1(x1111)+E(f2(f2(x1111,x1112),x1113),f2(x1111,f2(x1112,x1113)))
% 0.20/0.69 [119]~P1(x1193)+~P1(x1192)+~P1(x1191)+E(f8(f2(x1191,x1192),f2(x1191,x1193)),f2(x1191,f8(x1192,x1193)))
% 0.20/0.69 [120]~P1(x1202)+~P1(x1203)+~P1(x1201)+E(f8(f2(x1201,x1202),f2(x1203,x1202)),f2(f8(x1201,x1203),x1202))
% 0.20/0.69 [67]P2(x671)+~P1(x671)+E(x671,a10)+E(x671,a1)+~E(f4(x671),a10)
% 0.20/0.69 [70]P2(x701)+~P1(x701)+E(x701,a10)+~E(f4(x701),x701)+E(x701,a1)
% 0.20/0.69 [71]P2(x711)+~P1(x711)+E(x711,a10)+E(x711,a1)+P1(f4(x711))
% 0.20/0.69 [74]P2(x741)+~P1(x741)+E(x741,a10)+P3(f4(x741),x741)+E(x741,a1)
% 0.20/0.69 [84]~P1(x841)+~P1(x842)+~P3(x842,x841)+P5(x842,x841)+E(x841,a1)
% 0.20/0.69 [85]P4(x851,x852)+~P1(x852)+~P1(x851)+~P5(x851,x852)+E(x851,x852)
% 0.20/0.69 [89]~P1(x892)+~P1(x891)+~P5(x892,x891)+~P5(x891,x892)+E(x891,x892)
% 0.20/0.69 [77]~P1(x771)+~P1(x772)+E(x771,a1)+E(x772,a1)+~E(f2(x772,x771),a1)
% 0.20/0.69 [87]~P1(x871)+~P1(x872)+~P1(x873)+P3(x871,x872)+~E(x872,f2(x871,x873))
% 0.20/0.69 [88]~P1(x882)+~P1(x881)+~P1(x883)+P5(x881,x882)+~E(f8(x881,x883),x882)
% 0.20/0.69 [90]~P1(x903)+~P1(x902)+~P5(x903,x902)+P1(x901)+~E(x901,f9(x902,x903))
% 0.20/0.69 [94]~P1(x942)+~P1(x941)+~P1(x943)+E(x941,x942)+~E(f8(x943,x941),f8(x943,x942))
% 0.20/0.69 [95]~P1(x952)+~P1(x953)+~P1(x951)+E(x951,x952)+~E(f8(x951,x953),f8(x952,x953))
% 0.20/0.69 [98]~P1(x983)+~P1(x981)+~P5(x981,x983)+~E(x982,f9(x983,x981))+E(f8(x981,x982),x983)
% 0.20/0.69 [83]~P1(x832)+~P1(x831)+~P2(x832)+~P3(x831,x832)+E(x831,x832)+E(x831,a10)
% 0.20/0.69 [102]~P1(x1022)+~P1(x1021)+~P5(x1023,x1022)+~P5(x1021,x1023)+P5(x1021,x1022)+~P1(x1023)
% 0.20/0.69 [103]~P1(x1032)+~P1(x1031)+~P3(x1033,x1032)+~P3(x1031,x1033)+P3(x1031,x1032)+~P1(x1033)
% 0.20/0.69 [91]~P1(x911)+~P1(x913)+~P3(x911,x913)+P1(x912)+E(x911,a1)+~E(x912,f7(x913,x911))
% 0.20/0.69 [96]~P1(x962)+~P1(x961)+~P1(x963)+E(x961,x962)+~E(f2(x963,x961),f2(x963,x962))+E(x963,a1)
% 0.20/0.69 [97]~P1(x972)+~P1(x973)+~P1(x971)+E(x971,x972)+~E(f2(x971,x973),f2(x972,x973))+E(x973,a1)
% 0.20/0.69 [99]~P1(x991)+~P1(x992)+~P3(x991,x992)+~E(x993,f7(x992,x991))+E(x991,a1)+E(x992,f2(x991,x993))
% 0.20/0.69 [104]~P1(x1042)+~P1(x1043)+~P1(x1041)+~P5(x1043,x1042)+~E(f8(x1043,x1041),x1042)+E(x1041,f9(x1042,x1043))
% 0.20/0.69 [112]~P1(x1123)+~P1(x1122)+~P1(x1121)+~P3(x1121,x1123)+~P3(x1121,x1122)+P3(x1121,f8(x1122,x1123))
% 0.20/0.69 [113]~P1(x1132)+~P1(x1131)+~P1(x1133)+~P5(x1131,x1132)+E(x1131,x1132)+P5(f8(x1133,x1131),f8(x1133,x1132))
% 0.20/0.69 [114]~P1(x1142)+~P1(x1143)+~P1(x1141)+~P5(x1141,x1142)+E(x1141,x1142)+P5(f8(x1141,x1143),f8(x1142,x1143))
% 0.20/0.69 [117]~P1(x1172)+~P1(x1171)+~P3(x1171,x1173)+P3(x1171,x1172)+~P1(x1173)+~P3(x1171,f8(x1173,x1172))
% 0.20/0.69 [118]~P1(x1182)+~P1(x1183)+~P1(x1181)+~P3(x1181,x1183)+E(x1181,a1)+E(f7(f2(x1182,x1183),x1181),f2(x1182,f7(x1183,x1181)))
% 0.20/0.69 [105]~P1(x1051)+~P1(x1053)+~P1(x1052)+~P3(x1051,x1053)+~E(x1053,f2(x1051,x1052))+E(x1051,a1)+E(x1052,f7(x1053,x1051))
% 0.20/0.69 [115]~P1(x1152)+~P1(x1151)+~P1(x1153)+~P5(x1151,x1152)+E(x1151,x1152)+P5(f2(x1153,x1151),f2(x1153,x1152))+E(x1153,a1)
% 0.20/0.69 [116]~P1(x1162)+~P1(x1163)+~P1(x1161)+~P5(x1161,x1162)+E(x1161,x1162)+P5(f2(x1161,x1163),f2(x1162,x1163))+E(x1163,a1)
% 0.20/0.69 [121]~P1(x1211)+~P1(x1212)+~P1(x1213)+~P2(x1211)+P3(x1211,x1212)+P3(x1211,x1213)+~P3(x1211,f2(x1213,x1212))+~P4(f8(f8(x1213,x1212),x1211),f8(f8(a11,a12),a14))
% 0.20/0.69 %EqnAxiom
% 0.20/0.69 [1]E(x11,x11)
% 0.20/0.69 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.69 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.20/0.69 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.20/0.69 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63))
% 0.20/0.69 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72))
% 0.20/0.69 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83))
% 0.20/0.69 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92))
% 0.20/0.69 [10]~E(x101,x102)+E(f9(x101,x103),f9(x102,x103))
% 0.20/0.69 [11]~E(x111,x112)+E(f9(x113,x111),f9(x113,x112))
% 0.20/0.69 [12]~E(x121,x122)+E(f5(x121,x123),f5(x122,x123))
% 0.20/0.69 [13]~E(x131,x132)+E(f5(x133,x131),f5(x133,x132))
% 0.20/0.69 [14]~E(x141,x142)+E(f6(x141,x143),f6(x142,x143))
% 0.20/0.69 [15]~E(x151,x152)+E(f6(x153,x151),f6(x153,x152))
% 0.20/0.69 [16]~E(x161,x162)+E(f4(x161),f4(x162))
% 0.20/0.69 [17]~E(x171,x172)+E(f3(x171),f3(x172))
% 0.20/0.69 [18]~P1(x181)+P1(x182)+~E(x181,x182)
% 0.20/0.69 [19]P4(x192,x193)+~E(x191,x192)+~P4(x191,x193)
% 0.20/0.69 [20]P4(x203,x202)+~E(x201,x202)+~P4(x203,x201)
% 0.20/0.69 [21]P3(x212,x213)+~E(x211,x212)+~P3(x211,x213)
% 0.20/0.69 [22]P3(x223,x222)+~E(x221,x222)+~P3(x223,x221)
% 0.20/0.69 [23]~P2(x231)+P2(x232)+~E(x231,x232)
% 0.20/0.69 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243)
% 0.20/0.69 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251)
% 0.20/0.69
% 0.20/0.69 %-------------------------------------------
% 0.20/0.69 cnf(122,plain,
% 0.20/0.69 ($false),
% 0.20/0.69 inference(scs_inference,[],[54,55,68]),
% 0.20/0.69 ['proof']).
% 0.20/0.69 % SZS output end Proof
% 0.20/0.69 % Total time :0.000000s
%------------------------------------------------------------------------------