TSTP Solution File: NUM530+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM530+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 : n028.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 10:22:53 EDT 2023
% Result : Theorem 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM530+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
% 0.13/0.34 % Computer : n028.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 : Fri Aug 25 10:19:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % File :CSE---1.6
% 0.19/0.62 % Problem :theBenchmark
% 0.19/0.62 % Transform :cnf
% 0.19/0.62 % Format :tptp:raw
% 0.19/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.62
% 0.19/0.62 % Result :Theorem 0.000000s
% 0.19/0.62 % Output :CNFRefutation 0.000000s
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 %------------------------------------------------------------------------------
% 0.19/0.62 % File : NUM530+1 : TPTP v8.1.2. Released v4.0.0.
% 0.19/0.62 % Domain : Number Theory
% 0.19/0.62 % Problem : Square root of a prime is irrational 15_06, 00 expansion
% 0.19/0.62 % Version : Especial.
% 0.19/0.62 % English :
% 0.19/0.62
% 0.19/0.62 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista
% 0.19/0.62 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.19/0.62 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.19/0.62 % Source : [Pas08]
% 0.19/0.62 % Names : primes_15_06.00 [Pas08]
% 0.19/0.62
% 0.19/0.62 % Status : ContradictoryAxioms
% 0.19/0.62 % Rating : 0.08 v7.5.0, 0.03 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 v5.4.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.10 v5.1.0, 0.14 v5.0.0, 0.17 v4.1.0, 0.26 v4.0.1, 0.61 v4.0.0
% 0.19/0.62 % Syntax : Number of formulae : 49 ( 7 unt; 5 def)
% 0.19/0.62 % Number of atoms : 215 ( 67 equ)
% 0.19/0.62 % Maximal formula atoms : 10 ( 4 avg)
% 0.19/0.62 % Number of connectives : 195 ( 29 ~; 8 |; 89 &)
% 0.19/0.62 % ( 5 <=>; 64 =>; 0 <=; 0 <~>)
% 0.19/0.62 % Maximal formula depth : 11 ( 6 avg)
% 0.19/0.62 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.62 % Number of predicates : 8 ( 5 usr; 2 prp; 0-2 aty)
% 0.19/0.62 % Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% 0.19/0.62 % Number of variables : 88 ( 85 !; 3 ?)
% 0.19/0.62 % SPC : FOF_CAX_RFO_SEQ
% 0.19/0.62
% 0.19/0.62 % Comments : Problem generated by the SAD system [VLP07]
% 0.19/0.62 %------------------------------------------------------------------------------
% 0.19/0.62 fof(mNatSort,axiom,
% 0.19/0.62 ! [W0] :
% 0.19/0.62 ( aNaturalNumber0(W0)
% 0.19/0.62 => $true ) ).
% 0.19/0.62
% 0.19/0.62 fof(mSortsC,axiom,
% 0.19/0.62 aNaturalNumber0(sz00) ).
% 0.19/0.62
% 0.19/0.62 fof(mSortsC_01,axiom,
% 0.19/0.62 ( aNaturalNumber0(sz10)
% 0.19/0.62 & sz10 != sz00 ) ).
% 0.19/0.62
% 0.19/0.62 fof(mSortsB,axiom,
% 0.19/0.62 ! [W0,W1] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1) )
% 0.19/0.62 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mSortsB_02,axiom,
% 0.19/0.62 ! [W0,W1] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1) )
% 0.19/0.62 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mAddComm,axiom,
% 0.19/0.62 ! [W0,W1] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1) )
% 0.19/0.62 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mAddAsso,axiom,
% 0.19/0.62 ! [W0,W1,W2] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1)
% 0.19/0.63 & aNaturalNumber0(W2) )
% 0.19/0.63 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
% 0.19/0.63
% 0.19/0.63 fof(m_AddZero,axiom,
% 0.19/0.63 ! [W0] :
% 0.19/0.63 ( aNaturalNumber0(W0)
% 0.19/0.63 => ( sdtpldt0(W0,sz00) = W0
% 0.19/0.63 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mMulComm,axiom,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mMulAsso,axiom,
% 0.19/0.63 ! [W0,W1,W2] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1)
% 0.19/0.63 & aNaturalNumber0(W2) )
% 0.19/0.63 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
% 0.19/0.63
% 0.19/0.63 fof(m_MulUnit,axiom,
% 0.19/0.63 ! [W0] :
% 0.19/0.63 ( aNaturalNumber0(W0)
% 0.19/0.63 => ( sdtasdt0(W0,sz10) = W0
% 0.19/0.63 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(m_MulZero,axiom,
% 0.19/0.63 ! [W0] :
% 0.19/0.63 ( aNaturalNumber0(W0)
% 0.19/0.63 => ( sdtasdt0(W0,sz00) = sz00
% 0.19/0.63 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mAMDistr,axiom,
% 0.19/0.63 ! [W0,W1,W2] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1)
% 0.19/0.63 & aNaturalNumber0(W2) )
% 0.19/0.63 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.19/0.63 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mAddCanc,axiom,
% 0.19/0.63 ! [W0,W1,W2] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1)
% 0.19/0.63 & aNaturalNumber0(W2) )
% 0.19/0.63 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
% 0.19/0.63 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
% 0.19/0.63 => W1 = W2 ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mMulCanc,axiom,
% 0.19/0.63 ! [W0] :
% 0.19/0.63 ( aNaturalNumber0(W0)
% 0.19/0.63 => ( W0 != sz00
% 0.19/0.63 => ! [W1,W2] :
% 0.19/0.63 ( ( aNaturalNumber0(W1)
% 0.19/0.63 & aNaturalNumber0(W2) )
% 0.19/0.63 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2)
% 0.19/0.63 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
% 0.19/0.63 => W1 = W2 ) ) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mZeroAdd,axiom,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( sdtpldt0(W0,W1) = sz00
% 0.19/0.63 => ( W0 = sz00
% 0.19/0.63 & W1 = sz00 ) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mZeroMul,axiom,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( sdtasdt0(W0,W1) = sz00
% 0.19/0.63 => ( W0 = sz00
% 0.19/0.63 | W1 = sz00 ) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mDefLE,definition,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( sdtlseqdt0(W0,W1)
% 0.19/0.63 <=> ? [W2] :
% 0.19/0.63 ( aNaturalNumber0(W2)
% 0.19/0.63 & sdtpldt0(W0,W2) = W1 ) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mDefDiff,definition,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( sdtlseqdt0(W0,W1)
% 0.19/0.63 => ! [W2] :
% 0.19/0.63 ( W2 = sdtmndt0(W1,W0)
% 0.19/0.63 <=> ( aNaturalNumber0(W2)
% 0.19/0.63 & sdtpldt0(W0,W2) = W1 ) ) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mLERefl,axiom,
% 0.19/0.63 ! [W0] :
% 0.19/0.63 ( aNaturalNumber0(W0)
% 0.19/0.63 => sdtlseqdt0(W0,W0) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mLEAsym,axiom,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( ( sdtlseqdt0(W0,W1)
% 0.19/0.63 & sdtlseqdt0(W1,W0) )
% 0.19/0.63 => W0 = W1 ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mLETran,axiom,
% 0.19/0.63 ! [W0,W1,W2] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1)
% 0.19/0.63 & aNaturalNumber0(W2) )
% 0.19/0.63 => ( ( sdtlseqdt0(W0,W1)
% 0.19/0.63 & sdtlseqdt0(W1,W2) )
% 0.19/0.63 => sdtlseqdt0(W0,W2) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mLETotal,axiom,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( sdtlseqdt0(W0,W1)
% 0.19/0.63 | ( W1 != W0
% 0.19/0.63 & sdtlseqdt0(W1,W0) ) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mMonAdd,axiom,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( ( W0 != W1
% 0.19/0.63 & sdtlseqdt0(W0,W1) )
% 0.19/0.63 => ! [W2] :
% 0.19/0.63 ( aNaturalNumber0(W2)
% 0.19/0.63 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)
% 0.19/0.63 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
% 0.19/0.63 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
% 0.19/0.63 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mMonMul,axiom,
% 0.19/0.63 ! [W0,W1,W2] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1)
% 0.19/0.63 & aNaturalNumber0(W2) )
% 0.19/0.63 => ( ( W0 != sz00
% 0.19/0.63 & W1 != W2
% 0.19/0.63 & sdtlseqdt0(W1,W2) )
% 0.19/0.63 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2)
% 0.19/0.63 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.19/0.63 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
% 0.19/0.63 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mLENTr,axiom,
% 0.19/0.63 ! [W0] :
% 0.19/0.63 ( aNaturalNumber0(W0)
% 0.19/0.63 => ( W0 = sz00
% 0.19/0.63 | W0 = sz10
% 0.19/0.63 | ( sz10 != W0
% 0.19/0.63 & sdtlseqdt0(sz10,W0) ) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mMonMul2,axiom,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( W0 != sz00
% 0.19/0.63 => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mIH,axiom,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( iLess0(W0,W1)
% 0.19/0.63 => $true ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mIH_03,axiom,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( ( W0 != W1
% 0.19/0.63 & sdtlseqdt0(W0,W1) )
% 0.19/0.63 => iLess0(W0,W1) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mDefDiv,definition,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( doDivides0(W0,W1)
% 0.19/0.63 <=> ? [W2] :
% 0.19/0.63 ( aNaturalNumber0(W2)
% 0.19/0.63 & W1 = sdtasdt0(W0,W2) ) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mDefQuot,definition,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1) )
% 0.19/0.63 => ( ( W0 != sz00
% 0.19/0.63 & doDivides0(W0,W1) )
% 0.19/0.63 => ! [W2] :
% 0.19/0.63 ( W2 = sdtsldt0(W1,W0)
% 0.19/0.63 <=> ( aNaturalNumber0(W2)
% 0.19/0.63 & W1 = sdtasdt0(W0,W2) ) ) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mDivTrans,axiom,
% 0.19/0.63 ! [W0,W1,W2] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1)
% 0.19/0.63 & aNaturalNumber0(W2) )
% 0.19/0.63 => ( ( doDivides0(W0,W1)
% 0.19/0.63 & doDivides0(W1,W2) )
% 0.19/0.63 => doDivides0(W0,W2) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mDivSum,axiom,
% 0.19/0.63 ! [W0,W1,W2] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1)
% 0.19/0.63 & aNaturalNumber0(W2) )
% 0.19/0.63 => ( ( doDivides0(W0,W1)
% 0.19/0.63 & doDivides0(W0,W2) )
% 0.19/0.63 => doDivides0(W0,sdtpldt0(W1,W2)) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mDivMin,axiom,
% 0.19/0.63 ! [W0,W1,W2] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.63 & aNaturalNumber0(W1)
% 0.19/0.63 & aNaturalNumber0(W2) )
% 0.19/0.63 => ( ( doDivides0(W0,W1)
% 0.19/0.63 & doDivides0(W0,sdtpldt0(W1,W2)) )
% 0.19/0.63 => doDivides0(W0,W2) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(mDivLE,axiom,
% 0.19/0.63 ! [W0,W1] :
% 0.19/0.63 ( ( aNaturalNumber0(W0)
% 0.19/0.64 & aNaturalNumber0(W1) )
% 0.19/0.64 => ( ( doDivides0(W0,W1)
% 0.19/0.64 & W1 != sz00 )
% 0.19/0.64 => sdtlseqdt0(W0,W1) ) ) ).
% 0.19/0.64
% 0.19/0.64 fof(mDivAsso,axiom,
% 0.19/0.64 ! [W0,W1] :
% 0.19/0.64 ( ( aNaturalNumber0(W0)
% 0.19/0.64 & aNaturalNumber0(W1) )
% 0.19/0.64 => ( ( W0 != sz00
% 0.19/0.64 & doDivides0(W0,W1) )
% 0.19/0.64 => ! [W2] :
% 0.19/0.64 ( aNaturalNumber0(W2)
% 0.19/0.64 => sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ).
% 0.19/0.64
% 0.19/0.64 fof(mDefPrime,definition,
% 0.19/0.64 ! [W0] :
% 0.19/0.64 ( aNaturalNumber0(W0)
% 0.19/0.64 => ( isPrime0(W0)
% 0.19/0.64 <=> ( W0 != sz00
% 0.19/0.64 & W0 != sz10
% 0.19/0.64 & ! [W1] :
% 0.19/0.64 ( ( aNaturalNumber0(W1)
% 0.19/0.64 & doDivides0(W1,W0) )
% 0.19/0.64 => ( W1 = sz10
% 0.19/0.64 | W1 = W0 ) ) ) ) ) ).
% 0.19/0.64
% 0.19/0.64 fof(mPrimDiv,axiom,
% 0.19/0.64 ! [W0] :
% 0.19/0.64 ( ( aNaturalNumber0(W0)
% 0.19/0.64 & W0 != sz00
% 0.19/0.64 & W0 != sz10 )
% 0.19/0.64 => ? [W1] :
% 0.19/0.64 ( aNaturalNumber0(W1)
% 0.19/0.64 & doDivides0(W1,W0)
% 0.19/0.64 & isPrime0(W1) ) ) ).
% 0.19/0.64
% 0.19/0.64 fof(mPDP,axiom,
% 0.19/0.64 ! [W0,W1,W2] :
% 0.19/0.64 ( ( aNaturalNumber0(W0)
% 0.19/0.64 & aNaturalNumber0(W1)
% 0.19/0.64 & aNaturalNumber0(W2) )
% 0.19/0.64 => ( ( isPrime0(W2)
% 0.19/0.64 & doDivides0(W2,sdtasdt0(W0,W1)) )
% 0.19/0.64 => ( doDivides0(W2,W0)
% 0.19/0.64 | doDivides0(W2,W1) ) ) ) ).
% 0.19/0.64
% 0.19/0.64 fof(m__2987,hypothesis,
% 0.19/0.64 ( aNaturalNumber0(xn)
% 0.19/0.64 & aNaturalNumber0(xm)
% 0.19/0.64 & aNaturalNumber0(xp)
% 0.19/0.64 & xn != sz00
% 0.19/0.64 & xm != sz00
% 0.19/0.64 & xp != sz00 ) ).
% 0.19/0.64
% 0.19/0.64 fof(m__2963,hypothesis,
% 0.19/0.64 ! [W0,W1,W2] :
% 0.19/0.64 ( ( aNaturalNumber0(W0)
% 0.19/0.64 & aNaturalNumber0(W1)
% 0.19/0.64 & aNaturalNumber0(W2)
% 0.19/0.64 & W0 != sz00
% 0.19/0.64 & W1 != sz00
% 0.19/0.64 & W2 != sz00 )
% 0.19/0.64 => ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0)
% 0.19/0.64 => ( iLess0(W0,xn)
% 0.19/0.64 => ~ isPrime0(W2) ) ) ) ).
% 0.19/0.64
% 0.19/0.64 fof(m__3014,hypothesis,
% 0.19/0.64 sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn) ).
% 0.19/0.64
% 0.19/0.64 fof(m__3025,hypothesis,
% 0.19/0.64 isPrime0(xp) ).
% 0.19/0.64
% 0.19/0.64 fof(m__3046,hypothesis,
% 0.19/0.64 ( doDivides0(xp,sdtasdt0(xn,xn))
% 0.19/0.64 & doDivides0(xp,xn) ) ).
% 0.19/0.64
% 0.19/0.64 fof(m__3059,hypothesis,
% 0.19/0.64 xq = sdtsldt0(xn,xp) ).
% 0.19/0.64
% 0.19/0.64 fof(m__3082,hypothesis,
% 0.19/0.64 sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)) ).
% 0.19/0.64
% 0.19/0.64 fof(m__3124,hypothesis,
% 0.19/0.64 ( xm != xn
% 0.19/0.64 & sdtlseqdt0(xm,xn) ) ).
% 0.19/0.64
% 0.19/0.64 fof(m__3161,hypothesis,
% 0.19/0.64 ~ isPrime0(xp) ).
% 0.19/0.64
% 0.19/0.64 fof(m__,conjecture,
% 0.19/0.64 $false ).
% 0.19/0.64
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 % Proof found
% 0.19/0.64 % SZS status Theorem for theBenchmark
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 %ClaNum:109(EqnAxiom:25)
% 0.19/0.64 %VarNum:450(SingletonVarNum:134)
% 0.19/0.64 %MaxLitNum:9
% 0.19/0.64 %MaxfuncDepth:2
% 0.19/0.64 %SharedTerms:30
% 0.19/0.64 [26]P1(a1)
% 0.19/0.64 [27]P1(a10)
% 0.19/0.64 [28]P1(a11)
% 0.19/0.64 [29]P1(a12)
% 0.19/0.64 [30]P1(a13)
% 0.19/0.64 [31]P2(a13)
% 0.19/0.64 [33]P5(a12,a11)
% 0.19/0.64 [34]P3(a13,a11)
% 0.19/0.64 [38]~E(a1,a10)
% 0.19/0.64 [39]~E(a1,a11)
% 0.19/0.64 [40]~E(a1,a12)
% 0.19/0.64 [41]~E(a12,a11)
% 0.19/0.64 [42]~E(a1,a13)
% 0.19/0.64 [43]~P2(a13)
% 0.19/0.64 [32]E(f2(a11,a13),a14)
% 0.19/0.64 [35]P3(a13,f3(a11,a11))
% 0.19/0.64 [36]E(f3(a13,f3(a14,a14)),f3(a12,a12))
% 0.19/0.64 [37]E(f3(a13,f3(a12,a12)),f3(a11,a11))
% 0.19/0.64 [54]~P1(x541)+P5(x541,x541)
% 0.19/0.64 [46]~P1(x461)+E(f3(a1,x461),a1)
% 0.19/0.64 [47]~P1(x471)+E(f3(x471,a1),a1)
% 0.19/0.64 [48]~P1(x481)+E(f8(a1,x481),x481)
% 0.19/0.64 [49]~P1(x491)+E(f3(a10,x491),x491)
% 0.19/0.64 [50]~P1(x501)+E(f8(x501,a1),x501)
% 0.19/0.64 [51]~P1(x511)+E(f3(x511,a10),x511)
% 0.19/0.64 [44]~P1(x441)+~P2(x441)+~E(x441,a1)
% 0.19/0.64 [45]~P1(x451)+~P2(x451)+~E(x451,a10)
% 0.19/0.64 [65]~P1(x652)+~P1(x651)+E(f8(x651,x652),f8(x652,x651))
% 0.19/0.64 [66]~P1(x662)+~P1(x661)+E(f3(x661,x662),f3(x662,x661))
% 0.19/0.64 [68]~P1(x682)+~P1(x681)+P1(f8(x681,x682))
% 0.19/0.64 [69]~P1(x692)+~P1(x691)+P1(f3(x691,x692))
% 0.19/0.64 [56]~P1(x561)+E(x561,a10)+P5(a10,x561)+E(x561,a1)
% 0.19/0.64 [52]~P1(x521)+E(x521,a10)+E(x521,a1)+P1(f4(x521))
% 0.19/0.64 [53]~P1(x531)+E(x531,a10)+E(x531,a1)+P2(f4(x531))
% 0.19/0.64 [59]~P1(x591)+E(x591,a10)+P3(f4(x591),x591)+E(x591,a1)
% 0.19/0.64 [60]~E(x602,x601)+~P1(x601)+~P1(x602)+P5(x601,x602)
% 0.19/0.64 [67]P5(x672,x671)+~P1(x671)+~P1(x672)+P5(x671,x672)
% 0.19/0.64 [62]~P1(x622)+~P1(x621)+E(x621,a1)+~E(f8(x622,x621),a1)
% 0.19/0.64 [63]~P1(x632)+~P1(x631)+E(x631,a1)+~E(f8(x631,x632),a1)
% 0.19/0.64 [73]~P1(x732)+~P1(x731)+P5(x732,f3(x732,x731))+E(x731,a1)
% 0.19/0.64 [79]~P1(x792)+~P1(x791)+~P5(x791,x792)+P1(f6(x791,x792))
% 0.19/0.64 [80]~P1(x802)+~P1(x801)+~P3(x801,x802)+P1(f7(x801,x802))
% 0.19/0.64 [87]~P1(x871)+~P1(x872)+~P3(x871,x872)+E(f3(x871,f7(x871,x872)),x872)
% 0.19/0.64 [88]~P1(x882)+~P1(x881)+~P5(x881,x882)+E(f8(x881,f6(x881,x882)),x882)
% 0.19/0.64 [97]~P1(x973)+~P1(x972)+~P1(x971)+E(f8(f8(x971,x972),x973),f8(x971,f8(x972,x973)))
% 0.19/0.64 [98]~P1(x983)+~P1(x982)+~P1(x981)+E(f3(f3(x981,x982),x983),f3(x981,f3(x982,x983)))
% 0.19/0.64 [107]~P1(x1073)+~P1(x1072)+~P1(x1071)+E(f8(f3(x1071,x1072),f3(x1071,x1073)),f3(x1071,f8(x1072,x1073)))
% 0.19/0.64 [108]~P1(x1082)+~P1(x1083)+~P1(x1081)+E(f8(f3(x1081,x1082),f3(x1083,x1082)),f3(f8(x1081,x1083),x1082))
% 0.19/0.64 [55]P2(x551)+~P1(x551)+E(x551,a10)+E(x551,a1)+~E(f5(x551),a10)
% 0.19/0.64 [57]P2(x571)+~P1(x571)+E(x571,a10)+~E(f5(x571),x571)+E(x571,a1)
% 0.19/0.64 [58]P2(x581)+~P1(x581)+E(x581,a10)+E(x581,a1)+P1(f5(x581))
% 0.19/0.64 [61]P2(x611)+~P1(x611)+E(x611,a10)+P3(f5(x611),x611)+E(x611,a1)
% 0.19/0.64 [71]~P1(x711)+~P1(x712)+~P3(x712,x711)+P5(x712,x711)+E(x711,a1)
% 0.19/0.64 [72]P4(x721,x722)+~P1(x722)+~P1(x721)+~P5(x721,x722)+E(x721,x722)
% 0.19/0.64 [76]~P1(x762)+~P1(x761)+~P5(x762,x761)+~P5(x761,x762)+E(x761,x762)
% 0.19/0.64 [64]~P1(x641)+~P1(x642)+E(x641,a1)+E(x642,a1)+~E(f3(x642,x641),a1)
% 0.19/0.64 [74]~P1(x741)+~P1(x742)+~P1(x743)+P3(x741,x742)+~E(x742,f3(x741,x743))
% 0.19/0.64 [75]~P1(x752)+~P1(x751)+~P1(x753)+P5(x751,x752)+~E(f8(x751,x753),x752)
% 0.19/0.64 [77]~P1(x773)+~P1(x772)+~P5(x773,x772)+P1(x771)+~E(x771,f9(x772,x773))
% 0.19/0.64 [81]~P1(x812)+~P1(x811)+~P1(x813)+E(x811,x812)+~E(f8(x813,x811),f8(x813,x812))
% 0.19/0.64 [82]~P1(x822)+~P1(x823)+~P1(x821)+E(x821,x822)+~E(f8(x821,x823),f8(x822,x823))
% 0.19/0.64 [85]~P1(x853)+~P1(x851)+~P5(x851,x853)+~E(x852,f9(x853,x851))+E(f8(x851,x852),x853)
% 0.19/0.64 [70]~P1(x702)+~P1(x701)+~P2(x702)+~P3(x701,x702)+E(x701,x702)+E(x701,a10)
% 0.19/0.64 [89]~P1(x892)+~P1(x891)+~P5(x893,x892)+~P5(x891,x893)+P5(x891,x892)+~P1(x893)
% 0.19/0.64 [90]~P1(x902)+~P1(x901)+~P3(x903,x902)+~P3(x901,x903)+P3(x901,x902)+~P1(x903)
% 0.19/0.64 [78]~P1(x781)+~P1(x783)+~P3(x781,x783)+P1(x782)+E(x781,a1)+~E(x782,f2(x783,x781))
% 0.19/0.64 [83]~P1(x832)+~P1(x831)+~P1(x833)+E(x831,x832)+~E(f3(x833,x831),f3(x833,x832))+E(x833,a1)
% 0.19/0.64 [84]~P1(x842)+~P1(x843)+~P1(x841)+E(x841,x842)+~E(f3(x841,x843),f3(x842,x843))+E(x843,a1)
% 0.19/0.64 [86]~P1(x861)+~P1(x862)+~P3(x861,x862)+~E(x863,f2(x862,x861))+E(x861,a1)+E(x862,f3(x861,x863))
% 0.19/0.64 [91]~P1(x912)+~P1(x913)+~P1(x911)+~P5(x913,x912)+~E(f8(x913,x911),x912)+E(x911,f9(x912,x913))
% 0.19/0.64 [99]~P1(x993)+~P1(x992)+~P1(x991)+~P3(x991,x993)+~P3(x991,x992)+P3(x991,f8(x992,x993))
% 0.19/0.64 [100]~P1(x1002)+~P1(x1001)+~P1(x1003)+~P5(x1001,x1002)+E(x1001,x1002)+P5(f8(x1003,x1001),f8(x1003,x1002))
% 0.19/0.64 [101]~P1(x1012)+~P1(x1013)+~P1(x1011)+~P5(x1011,x1012)+E(x1011,x1012)+P5(f8(x1011,x1013),f8(x1012,x1013))
% 0.19/0.64 [105]~P1(x1052)+~P1(x1051)+~P3(x1051,x1053)+P3(x1051,x1052)+~P1(x1053)+~P3(x1051,f8(x1053,x1052))
% 0.19/0.64 [106]~P1(x1062)+~P1(x1063)+~P1(x1061)+~P3(x1061,x1063)+E(x1061,a1)+E(f3(x1062,f2(x1063,x1061)),f2(f3(x1062,x1063),x1061))
% 0.19/0.64 [92]~P1(x921)+~P1(x923)+~P1(x922)+~P3(x921,x923)+~E(x923,f3(x921,x922))+E(x921,a1)+E(x922,f2(x923,x921))
% 0.19/0.64 [102]~P1(x1022)+~P1(x1021)+~P1(x1023)+~P5(x1021,x1022)+E(x1021,x1022)+P5(f3(x1023,x1021),f3(x1023,x1022))+E(x1023,a1)
% 0.19/0.64 [103]~P1(x1032)+~P1(x1033)+~P1(x1031)+~P5(x1031,x1032)+E(x1031,x1032)+P5(f3(x1031,x1033),f3(x1032,x1033))+E(x1033,a1)
% 0.19/0.64 [104]~P1(x1041)+~P1(x1042)+~P1(x1043)+~P2(x1041)+P3(x1041,x1042)+P3(x1041,x1043)+~P3(x1041,f3(x1043,x1042))
% 0.19/0.64 [109]~P1(x1091)+~P1(x1092)+~P1(x1093)+~P2(x1091)+~P4(x1093,a11)+E(x1091,a1)+E(x1092,a1)+E(x1093,a1)+~E(f3(x1091,f3(x1092,x1092)),f3(x1093,x1093))
% 0.19/0.64 %EqnAxiom
% 0.19/0.64 [1]E(x11,x11)
% 0.19/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.64 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.19/0.64 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.19/0.64 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.19/0.64 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.19/0.64 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83))
% 0.19/0.64 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92))
% 0.19/0.64 [10]~E(x101,x102)+E(f7(x101,x103),f7(x102,x103))
% 0.19/0.64 [11]~E(x111,x112)+E(f7(x113,x111),f7(x113,x112))
% 0.19/0.64 [12]~E(x121,x122)+E(f6(x121,x123),f6(x122,x123))
% 0.19/0.64 [13]~E(x131,x132)+E(f6(x133,x131),f6(x133,x132))
% 0.19/0.64 [14]~E(x141,x142)+E(f9(x141,x143),f9(x142,x143))
% 0.19/0.64 [15]~E(x151,x152)+E(f9(x153,x151),f9(x153,x152))
% 0.19/0.64 [16]~E(x161,x162)+E(f4(x161),f4(x162))
% 0.19/0.64 [17]~E(x171,x172)+E(f5(x171),f5(x172))
% 0.19/0.64 [18]~P1(x181)+P1(x182)+~E(x181,x182)
% 0.19/0.64 [19]P4(x192,x193)+~E(x191,x192)+~P4(x191,x193)
% 0.19/0.64 [20]P4(x203,x202)+~E(x201,x202)+~P4(x203,x201)
% 0.19/0.64 [21]~P2(x211)+P2(x212)+~E(x211,x212)
% 0.19/0.64 [22]P3(x222,x223)+~E(x221,x222)+~P3(x221,x223)
% 0.19/0.64 [23]P3(x233,x232)+~E(x231,x232)+~P3(x233,x231)
% 0.19/0.64 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243)
% 0.19/0.64 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251)
% 0.19/0.64
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 cnf(110,plain,
% 0.19/0.64 ($false),
% 0.19/0.64 inference(scs_inference,[],[31,43]),
% 0.19/0.64 ['proof']).
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64 % Total time :0.000000s
%------------------------------------------------------------------------------