TSTP Solution File: NUM483+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM483+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n013.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 : 600s
% DateTime : Mon Jul 18 09:32:56 EDT 2022
% Result : Theorem 0.28s 9.47s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 35
% Syntax : Number of formulae : 292 ( 54 unt; 0 def)
% Number of atoms : 1107 ( 319 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 1414 ( 599 ~; 675 |; 91 &)
% ( 5 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 393 ( 6 sgn 129 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mDefDiff) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mDefLE) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m_AddZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mSortsC) ).
fof(mLERefl,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mLERefl) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mDefDiv) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mMulComm) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m_MulZero) ).
fof(m__1716,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__1716) ).
fof(mDivMin,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,sdtpldt0(X2,X3)) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mDivMin) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mAddComm) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m_MulUnit) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mSortsC_01) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mLETotal) ).
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mMonAdd) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mSortsB) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mLEAsym) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mMonMul2) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mAddAsso) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mAMDistr) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mSortsB_02) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mMulAsso) ).
fof(m__1716_04,hypothesis,
( xk != sz00
& xk != sz10 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__1716_04) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mZeroAdd) ).
fof(mLENTr,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sz00
| X1 = sz10
| ( sz10 != X1
& sdtlseqdt0(sz10,X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mLENTr) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X2,X3) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mDivTrans) ).
fof(mDivSum,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,X3) )
=> doDivides0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mDivSum) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mDefQuot) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mLETran) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mDefPrime) ).
fof(m__1725,hypothesis,
~ isPrime0(xk),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__1725) ).
fof(m__,conjecture,
? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,xk)
& isPrime0(X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mDivLE) ).
fof(m__1700,hypothesis,
! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ( iLess0(X1,xk)
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__1700) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mIH_03) ).
fof(c_0_35,plain,
! [X4,X5,X6,X6] :
( ( aNaturalNumber0(X6)
| X6 != sdtmndt0(X5,X4)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtpldt0(X4,X6) = X5
| X6 != sdtmndt0(X5,X4)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| sdtpldt0(X4,X6) != X5
| X6 = sdtmndt0(X5,X4)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])])]) ).
fof(c_0_36,plain,
! [X4,X5,X7] :
( ( aNaturalNumber0(esk1_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtpldt0(X4,esk1_2(X4,X5)) = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X7)
| sdtpldt0(X4,X7) != X5
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])])])]) ).
cnf(c_0_37,plain,
( X3 = sdtmndt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_38,plain,
( sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_39,plain,
! [X2] :
( ( sdtpldt0(X2,sz00) = X2
| ~ aNaturalNumber0(X2) )
& ( X2 = sdtpldt0(sz00,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_40,plain,
( X1 = sdtmndt0(X2,X3)
| sdtpldt0(X3,X1) != X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_42,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_43,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])]) ).
fof(c_0_44,plain,
! [X4,X5,X7] :
( ( aNaturalNumber0(esk2_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( X5 = sdtasdt0(X4,esk2_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X7)
| X5 != sdtasdt0(X4,X7)
| doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])])])]) ).
fof(c_0_45,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtasdt0(X3,X4) = sdtasdt0(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_46,plain,
( aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| X3 != sdtmndt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,plain,
( sdtmndt0(X1,X1) = sz00
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])])]) ).
cnf(c_0_48,plain,
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,plain,
( doDivides0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_51,plain,
! [X2] :
( ( sdtasdt0(X2,sz00) = sz00
| ~ aNaturalNumber0(X2) )
& ( sz00 = sdtasdt0(sz00,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_52,plain,
( aNaturalNumber0(X1)
| X1 != sz00
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_53,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__1716]) ).
fof(c_0_54,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ doDivides0(X4,X5)
| ~ doDivides0(X4,sdtpldt0(X5,X6))
| doDivides0(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).
fof(c_0_55,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtpldt0(X3,X4) = sdtpldt0(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_56,plain,
( doDivides0(X1,X2)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,hypothesis,
( aNaturalNumber0(X1)
| X1 != sz00 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_59,plain,
! [X2] :
( ( sdtasdt0(X2,sz10) = X2
| ~ aNaturalNumber0(X2) )
& ( X2 = sdtasdt0(sz10,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_60,plain,
( doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X3,X2))
| ~ doDivides0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,plain,
( doDivides0(sz00,X1)
| X1 != sz00
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_42])]),c_0_58]) ).
cnf(c_0_63,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_65,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_66,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_67,plain,
( doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X2,X3))
| ~ doDivides0(X1,X3)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,hypothesis,
( doDivides0(sz00,X1)
| X1 != sz00 ),
inference(spm,[status(thm)],[c_0_62,c_0_53]) ).
cnf(c_0_69,plain,
( doDivides0(X1,sz00)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_41]),c_0_42])]) ).
cnf(c_0_70,plain,
( doDivides0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_63]),c_0_64])])]) ).
cnf(c_0_71,plain,
( X1 = sz00
| ~ doDivides0(sz00,X1)
| ~ aNaturalNumber0(esk2_2(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_42])]) ).
cnf(c_0_72,plain,
( aNaturalNumber0(esk2_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_73,hypothesis,
( doDivides0(sz00,X1)
| sdtpldt0(X1,X2) != sz00
| ~ doDivides0(sz00,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_42])]) ).
cnf(c_0_74,plain,
( doDivides0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,plain,
( X1 = sz00
| ~ doDivides0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_42])]) ).
cnf(c_0_76,hypothesis,
( doDivides0(sz00,X1)
| sdtpldt0(X1,sz00) != sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_42])]) ).
cnf(c_0_77,hypothesis,
( X1 = sz00
| sdtpldt0(X1,sz00) != sz00
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
fof(c_0_78,plain,
! [X3,X4] :
( ( X4 != X3
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) )
& ( sdtlseqdt0(X4,X3)
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_79,hypothesis,
( X1 = sz00
| sdtpldt0(sz00,X1) != sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_61]),c_0_42])]) ).
cnf(c_0_80,plain,
( sdtpldt0(X2,esk1_2(X2,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_81,plain,
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_82,hypothesis,
( esk1_2(sz00,X1) = sz00
| X1 != sz00
| ~ sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(esk1_2(sz00,X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_42])]),c_0_58]) ).
cnf(c_0_83,plain,
( aNaturalNumber0(esk1_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_84,hypothesis,
( sdtlseqdt0(xk,X1)
| sdtlseqdt0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_53]) ).
cnf(c_0_85,hypothesis,
( esk1_2(sz00,X1) = sz00
| X1 != sz00
| ~ sdtlseqdt0(sz00,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_42])]),c_0_58]) ).
fof(c_0_86,plain,
! [X4,X5,X6] :
( ( sdtpldt0(X6,X4) != sdtpldt0(X6,X5)
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtpldt0(X4,X6) != sdtpldt0(X5,X6)
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])])])]) ).
cnf(c_0_87,plain,
( sdtlseqdt0(esk1_2(X1,X2),X3)
| sdtlseqdt0(X3,esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_83]) ).
cnf(c_0_88,hypothesis,
sdtlseqdt0(xk,xk),
inference(spm,[status(thm)],[c_0_84,c_0_53]) ).
cnf(c_0_89,hypothesis,
( sdtpldt0(sz00,sz00) = X1
| X1 != sz00
| ~ sdtlseqdt0(sz00,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_85]),c_0_42])]),c_0_58]) ).
cnf(c_0_90,plain,
( X2 = X1
| sdtlseqdt0(sdtpldt0(X3,X2),sdtpldt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_91,hypothesis,
( sdtlseqdt0(X1,esk1_2(xk,xk))
| sdtlseqdt0(esk1_2(xk,xk),X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_53])]) ).
cnf(c_0_92,hypothesis,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_48]),c_0_42])]) ).
fof(c_0_93,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_94,plain,
( X1 = esk1_2(X2,X3)
| sdtlseqdt0(X3,sdtpldt0(X2,X1))
| ~ sdtlseqdt0(esk1_2(X2,X3),X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_80]),c_0_83]) ).
cnf(c_0_95,hypothesis,
( sdtlseqdt0(esk1_2(xk,xk),sz00)
| sdtlseqdt0(sz00,esk1_2(xk,xk)) ),
inference(spm,[status(thm)],[c_0_91,c_0_42]) ).
cnf(c_0_96,hypothesis,
( sdtlseqdt0(sz00,X1)
| sz00 != X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_92]),c_0_42])]),c_0_58]) ).
fof(c_0_97,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| X3 = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_98,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_99,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_100,plain,
( esk1_2(X1,X2) = X3
| sdtlseqdt0(sdtpldt0(X1,X3),X2)
| ~ sdtlseqdt0(X3,esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_80]),c_0_83]) ).
cnf(c_0_101,hypothesis,
( sdtlseqdt0(sz00,esk1_2(xk,xk))
| sdtlseqdt0(xk,sdtpldt0(xk,sz00)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_88]),c_0_53]),c_0_42])]),c_0_96]) ).
fof(c_0_102,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| X3 = sz00
| sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
cnf(c_0_103,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_104,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_105,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_98]),c_0_42])])]) ).
cnf(c_0_106,plain,
( sdtlseqdt0(sz10,X1)
| sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_64]) ).
cnf(c_0_107,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_38]),c_0_99]) ).
cnf(c_0_108,hypothesis,
( esk1_2(xk,xk) = sz00
| sdtlseqdt0(xk,sdtpldt0(xk,sz00))
| sdtlseqdt0(sdtpldt0(xk,sz00),xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_88]),c_0_53]),c_0_42])]) ).
fof(c_0_109,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_110,plain,
( sdtlseqdt0(X1,sdtasdt0(X1,X2))
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_111,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_103]),c_0_64])])]) ).
cnf(c_0_112,plain,
( X1 = sz00
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_42])]) ).
cnf(c_0_113,plain,
( sdtlseqdt0(sz00,sz10)
| sdtlseqdt0(sz10,sz00) ),
inference(spm,[status(thm)],[c_0_106,c_0_42]) ).
cnf(c_0_114,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_115,plain,
( sdtpldt0(X1,X2) = X1
| ~ sdtlseqdt0(sdtpldt0(X1,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_107]),c_0_99]) ).
cnf(c_0_116,hypothesis,
( sdtpldt0(xk,sz00) = xk
| sdtlseqdt0(sdtpldt0(xk,sz00),xk)
| sdtlseqdt0(xk,sdtpldt0(xk,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_108]),c_0_88]),c_0_53])]) ).
cnf(c_0_117,plain,
( sdtlseqdt0(X1,X2)
| sdtpldt0(X3,X1) != X2
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_61]) ).
cnf(c_0_118,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
fof(c_0_119,plain,
! [X4,X5,X6] :
( ( sdtasdt0(X4,sdtpldt0(X5,X6)) = sdtpldt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtasdt0(sdtpldt0(X5,X6),X4) = sdtpldt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_120,plain,
( esk2_2(X1,X2) = sz00
| sdtlseqdt0(X1,X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_66]),c_0_72]) ).
cnf(c_0_121,plain,
( doDivides0(sz10,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_111]),c_0_64])]) ).
cnf(c_0_122,plain,
sdtlseqdt0(sz00,sz10),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_64])]),c_0_114]) ).
cnf(c_0_123,hypothesis,
( sdtpldt0(xk,sz00) = xk
| sdtlseqdt0(xk,sdtpldt0(xk,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_53]),c_0_42])]) ).
cnf(c_0_124,plain,
( sdtlseqdt0(X1,X2)
| sdtpldt0(X3,sdtpldt0(X4,X1)) != X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_99]) ).
cnf(c_0_125,hypothesis,
( sdtpldt0(sz00,sdtpldt0(sz00,X1)) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_92]),c_0_42])]) ).
fof(c_0_126,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_127,plain,
( sdtasdt0(X3,sdtpldt0(X2,X1)) = sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_128,plain,
( sdtasdt0(X1,sz00) = X2
| sdtlseqdt0(X1,X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_120]) ).
cnf(c_0_129,hypothesis,
doDivides0(sz10,sz00),
inference(spm,[status(thm)],[c_0_121,c_0_53]) ).
cnf(c_0_130,plain,
~ sdtlseqdt0(sz10,sz00),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_122]),c_0_42]),c_0_64])]),c_0_114]) ).
cnf(c_0_131,hypothesis,
( sdtpldt0(xk,sz00) = xk
| ~ sdtlseqdt0(sdtpldt0(xk,sz00),xk)
| ~ aNaturalNumber0(sdtpldt0(xk,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_123]),c_0_53])]) ).
cnf(c_0_132,hypothesis,
( sdtlseqdt0(X1,X2)
| sdtpldt0(sz00,X1) != X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_42])]) ).
cnf(c_0_133,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_134,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_63]),c_0_64])]) ).
cnf(c_0_135,hypothesis,
sdtasdt0(sz10,sz00) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_64]),c_0_42])]),c_0_130]) ).
fof(c_0_136,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| sdtasdt0(sdtasdt0(X4,X5),X6) = sdtasdt0(X4,sdtasdt0(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_137,hypothesis,
( sdtpldt0(xk,sz00) = xk
| sdtpldt0(sz00,sdtpldt0(xk,sz00)) != xk
| ~ aNaturalNumber0(sdtpldt0(xk,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_53])]) ).
cnf(c_0_138,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_118]),c_0_42])]),c_0_99]) ).
cnf(c_0_139,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_49]),c_0_133]) ).
cnf(c_0_140,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_127]),c_0_133]),c_0_133]) ).
cnf(c_0_141,hypothesis,
sdtasdt0(sz10,sdtpldt0(sz00,sz10)) = sdtpldt0(sz00,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_64]),c_0_42])]) ).
cnf(c_0_142,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_143,hypothesis,
( sdtpldt0(xk,sz00) = xk
| sdtpldt0(sz00,xk) != xk
| ~ aNaturalNumber0(sdtpldt0(xk,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_53]),c_0_42])]) ).
cnf(c_0_144,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_139,c_0_50]) ).
cnf(c_0_145,hypothesis,
aNaturalNumber0(sdtpldt0(sz00,sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_64]),c_0_42])]) ).
cnf(c_0_146,plain,
( sdtasdt0(sdtpldt0(X2,X1),X3) = sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_147,plain,
( sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_65]),c_0_42])]) ).
cnf(c_0_148,hypothesis,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_135]),c_0_42]),c_0_64])]) ).
cnf(c_0_149,plain,
( doDivides0(sdtpldt0(X1,X2),X2)
| ~ doDivides0(sdtpldt0(X1,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_70]),c_0_99]) ).
cnf(c_0_150,hypothesis,
( sdtpldt0(xk,sz00) = xk
| sdtpldt0(sz00,xk) != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_99]),c_0_42]),c_0_53])]) ).
cnf(c_0_151,hypothesis,
( sdtlseqdt0(sz00,xk)
| sdtlseqdt0(xk,sz00) ),
inference(spm,[status(thm)],[c_0_84,c_0_42]) ).
cnf(c_0_152,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[m__1716_04]) ).
cnf(c_0_153,hypothesis,
doDivides0(sdtpldt0(sz00,sz10),sdtpldt0(sz00,sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_141]),c_0_64])]),c_0_145])]) ).
cnf(c_0_154,plain,
( sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_103]),c_0_64])]) ).
cnf(c_0_155,hypothesis,
sdtasdt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_148]),c_0_64]),c_0_42])]) ).
fof(c_0_156,plain,
! [X3,X4] :
( ( X3 = sz00
| sdtpldt0(X3,X4) != sz00
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) )
& ( X4 = sz00
| sdtpldt0(X3,X4) != sz00
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
cnf(c_0_157,hypothesis,
( doDivides0(xk,sz00)
| sdtpldt0(sz00,xk) != xk
| ~ doDivides0(xk,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_53]),c_0_42])]) ).
cnf(c_0_158,hypothesis,
sdtlseqdt0(sz00,xk),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_151]),c_0_53])]),c_0_152]) ).
fof(c_0_159,plain,
! [X2] :
( ( sz10 != X2
| X2 = sz00
| X2 = sz10
| ~ aNaturalNumber0(X2) )
& ( sdtlseqdt0(sz10,X2)
| X2 = sz00
| X2 = sz10
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLENTr])])]) ).
cnf(c_0_160,hypothesis,
( doDivides0(sdtpldt0(sz00,sz10),sz10)
| ~ doDivides0(sdtpldt0(sz00,sz10),sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_153]),c_0_42]),c_0_64]),c_0_145])]) ).
cnf(c_0_161,hypothesis,
sdtasdt0(sdtpldt0(sz00,sz10),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_92]),c_0_42])]) ).
cnf(c_0_162,plain,
( X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_163,hypothesis,
( doDivides0(xk,sz00)
| sdtpldt0(sz00,xk) != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_70]),c_0_53])]) ).
cnf(c_0_164,hypothesis,
~ sdtlseqdt0(xk,sz00),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_158]),c_0_42]),c_0_53])]),c_0_152]) ).
cnf(c_0_165,plain,
( X1 = sz10
| X1 = sz00
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_166,hypothesis,
( sdtlseqdt0(sdtpldt0(sz00,sz10),sz10)
| ~ doDivides0(sdtpldt0(sz00,sz10),sz00) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_160]),c_0_161]),c_0_145]),c_0_64])]),c_0_114]) ).
cnf(c_0_167,plain,
( doDivides0(X1,X2)
| X2 != sz00
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_65]),c_0_42])]),c_0_58]) ).
cnf(c_0_168,plain,
( sdtasdt0(X1,X2) = sz00
| sdtasdt0(X1,sdtpldt0(X3,X2)) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_127]),c_0_133]),c_0_133]) ).
cnf(c_0_169,hypothesis,
sdtasdt0(sz10,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_98]),c_0_64])]) ).
fof(c_0_170,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ doDivides0(X4,X5)
| ~ doDivides0(X5,X6)
| doDivides0(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
fof(c_0_171,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ doDivides0(X4,X5)
| ~ doDivides0(X4,X6)
| doDivides0(X4,sdtpldt0(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_172,hypothesis,
( sdtasdt0(xk,sz00) = sz00
| sdtpldt0(sz00,xk) != xk ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_163]),c_0_53]),c_0_42])]),c_0_164]) ).
cnf(c_0_173,plain,
( X1 = sz00
| X1 = sz10
| ~ sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_165]),c_0_64])]) ).
cnf(c_0_174,hypothesis,
sdtlseqdt0(sdtpldt0(sz00,sz10),sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_145])]) ).
cnf(c_0_175,hypothesis,
sdtpldt0(sz00,sz10) != sz00,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_141]),c_0_64]),c_0_42])]),c_0_169]),c_0_114]) ).
cnf(c_0_176,plain,
( doDivides0(X1,X2)
| ~ doDivides0(X3,X2)
| ~ doDivides0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_177,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ doDivides0(X1,X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_178,hypothesis,
sdtasdt0(xk,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_98]),c_0_53])]) ).
cnf(c_0_179,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_145])]),c_0_175]) ).
cnf(c_0_180,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ doDivides0(X1,X4)
| ~ doDivides0(X4,X3)
| ~ doDivides0(X4,X2)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_99]) ).
cnf(c_0_181,hypothesis,
sdtpldt0(sz00,xk) = sdtasdt0(xk,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_178]),c_0_179]),c_0_53]),c_0_42])]) ).
fof(c_0_182,plain,
! [X4,X5,X6,X6] :
( ( aNaturalNumber0(X6)
| X6 != sdtsldt0(X5,X4)
| X4 = sz00
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( X5 = sdtasdt0(X4,X6)
| X6 != sdtsldt0(X5,X4)
| X4 = sz00
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| X5 != sdtasdt0(X4,X6)
| X6 = sdtsldt0(X5,X4)
| X4 = sz00
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])])])]) ).
cnf(c_0_183,plain,
( doDivides0(sz10,sdtpldt0(X1,X2))
| ~ doDivides0(X3,X2)
| ~ doDivides0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_111]),c_0_64])]) ).
cnf(c_0_184,hypothesis,
sdtasdt0(xk,sz10) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_181]),c_0_53])]) ).
cnf(c_0_185,plain,
( X2 = sz00
| X3 = sdtsldt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_182]) ).
cnf(c_0_186,hypothesis,
( doDivides0(sz10,sdtpldt0(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_129]),c_0_64]),c_0_42])]),c_0_111]) ).
cnf(c_0_187,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_99]) ).
cnf(c_0_188,hypothesis,
sdtpldt0(sz00,xk) = xk,
inference(rw,[status(thm)],[c_0_181,c_0_184]) ).
cnf(c_0_189,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[c_0_185,c_0_49]) ).
cnf(c_0_190,hypothesis,
( doDivides0(sz10,xk)
| sdtpldt0(sz00,xk) != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_150]),c_0_53])]) ).
cnf(c_0_191,plain,
( sdtpldt0(X2,X3) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| X3 != sdtmndt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_192,hypothesis,
sdtmndt0(xk,sz00) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_53]),c_0_42])]) ).
cnf(c_0_193,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_189]),c_0_133]) ).
cnf(c_0_194,hypothesis,
sdtasdt0(sz10,xk) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_184]),c_0_64]),c_0_53])]) ).
cnf(c_0_195,hypothesis,
( doDivides0(sz10,xk)
| sdtasdt0(xk,sz10) != xk ),
inference(rw,[status(thm)],[c_0_190,c_0_181]) ).
fof(c_0_196,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ sdtlseqdt0(X4,X5)
| ~ sdtlseqdt0(X5,X6)
| sdtlseqdt0(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_197,plain,
( doDivides0(X1,esk1_2(X2,X3))
| ~ doDivides0(X1,X3)
| ~ doDivides0(X1,X2)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_80]),c_0_83]) ).
cnf(c_0_198,hypothesis,
( sdtpldt0(sz00,X1) = xk
| X1 != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_158]),c_0_42]),c_0_53])]) ).
cnf(c_0_199,hypothesis,
doDivides0(xk,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_178]),c_0_42]),c_0_53])]) ).
cnf(c_0_200,hypothesis,
( aNaturalNumber0(X1)
| X1 != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_192]),c_0_158]),c_0_42]),c_0_53])]) ).
cnf(c_0_201,plain,
( X2 = sz00
| X1 = sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_182]) ).
cnf(c_0_202,hypothesis,
sdtsldt0(xk,sz10) = xk,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_53]),c_0_64])]),c_0_114]) ).
cnf(c_0_203,hypothesis,
doDivides0(sz10,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_195,c_0_184])]) ).
cnf(c_0_204,hypothesis,
( sdtlseqdt0(sz10,xk)
| sdtlseqdt0(xk,sz10) ),
inference(spm,[status(thm)],[c_0_84,c_0_64]) ).
cnf(c_0_205,hypothesis,
xk != sz10,
inference(split_conjunct,[status(thm)],[m__1716_04]) ).
cnf(c_0_206,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_196]) ).
fof(c_0_207,plain,
! [X3,X4] :
( ( X3 != sz00
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( X3 != sz10
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| X4 = sz10
| X4 = X3
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( aNaturalNumber0(esk3_1(X3))
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( doDivides0(esk3_1(X3),X3)
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( esk3_1(X3) != sz10
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( esk3_1(X3) != X3
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])])])]) ).
cnf(c_0_208,plain,
( doDivides0(X1,esk1_2(X2,X3))
| ~ doDivides0(X1,X4)
| ~ doDivides0(X4,X3)
| ~ doDivides0(X4,X2)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_197]),c_0_83]) ).
cnf(c_0_209,hypothesis,
( doDivides0(xk,X1)
| X1 != xk ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_198]),c_0_199]),c_0_42])]),c_0_200]) ).
cnf(c_0_210,hypothesis,
( sdtasdt0(sz10,X1) = xk
| X1 != xk ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_203]),c_0_64]),c_0_53])]),c_0_114]) ).
cnf(c_0_211,plain,
( sdtpldt0(X1,X2) = X1
| X2 != sz00
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_47]),c_0_48]) ).
cnf(c_0_212,hypothesis,
( sdtlseqdt0(X1,esk1_2(sz00,xk))
| sdtlseqdt0(esk1_2(sz00,xk),X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_158]),c_0_42]),c_0_53])]) ).
cnf(c_0_213,hypothesis,
sdtlseqdt0(sz10,xk),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_204]),c_0_53])]),c_0_152]),c_0_205]) ).
cnf(c_0_214,hypothesis,
sdtsldt0(sz00,sz10) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_135]),c_0_42]),c_0_64])]),c_0_114]) ).
cnf(c_0_215,hypothesis,
sdtsldt0(sz10,sz10) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_169]),c_0_64])]),c_0_114]) ).
cnf(c_0_216,hypothesis,
doDivides0(sz10,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_169]),c_0_64])]) ).
cnf(c_0_217,plain,
( sdtlseqdt0(X1,sz10)
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_122]),c_0_42]),c_0_64])]) ).
cnf(c_0_218,plain,
( isPrime0(X1)
| X1 = sz10
| X1 = sz00
| doDivides0(esk3_1(X1),X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_207]) ).
fof(c_0_219,hypothesis,
~ isPrime0(xk),
inference(fof_simplification,[status(thm)],[m__1725]) ).
cnf(c_0_220,plain,
( sdtasdt0(X1,X2) = X1
| X2 = sz00
| ~ sdtlseqdt0(sdtasdt0(X1,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_110]),c_0_133]) ).
cnf(c_0_221,hypothesis,
( doDivides0(xk,esk1_2(X1,X2))
| X3 != xk
| ~ doDivides0(X3,X2)
| ~ doDivides0(X3,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_53])]),c_0_200]) ).
cnf(c_0_222,hypothesis,
( doDivides0(X1,xk)
| X1 != xk ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_210]),c_0_64])]),c_0_200]) ).
cnf(c_0_223,plain,
( sdtlseqdt0(X1,X2)
| X1 != sz00
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_211])]),c_0_58]) ).
cnf(c_0_224,hypothesis,
( sdtlseqdt0(esk1_2(sz00,xk),sz10)
| sdtlseqdt0(sz10,esk1_2(sz00,xk)) ),
inference(spm,[status(thm)],[c_0_212,c_0_64]) ).
cnf(c_0_225,hypothesis,
~ sdtlseqdt0(xk,sz10),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_213]),c_0_64]),c_0_53])]),c_0_205]) ).
cnf(c_0_226,hypothesis,
( sdtasdt0(sz10,X1) = sz00
| X1 != sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_214]),c_0_129]),c_0_64]),c_0_42])]),c_0_114]) ).
cnf(c_0_227,hypothesis,
( sdtasdt0(sz10,X1) = sz10
| X1 != sz10 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_215]),c_0_216]),c_0_64])]),c_0_114]) ).
fof(c_0_228,negated_conjecture,
~ ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,xk)
& isPrime0(X1) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_229,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ doDivides0(X3,X4)
| X4 = sz00
| sdtlseqdt0(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
cnf(c_0_230,plain,
( sdtlseqdt0(X1,sz10)
| ~ sdtlseqdt0(X2,sz00)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_217]),c_0_64])]) ).
cnf(c_0_231,plain,
( sdtpldt0(X1,X2) = sz00
| sdtpldt0(X1,X2) = sz10
| isPrime0(sdtpldt0(X1,X2))
| doDivides0(esk3_1(sdtpldt0(X1,X2)),X1)
| ~ doDivides0(esk3_1(sdtpldt0(X1,X2)),X2)
| ~ aNaturalNumber0(esk3_1(sdtpldt0(X1,X2)))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_218]),c_0_99]) ).
cnf(c_0_232,hypothesis,
~ isPrime0(xk),
inference(split_conjunct,[status(thm)],[c_0_219]) ).
cnf(c_0_233,plain,
( esk2_2(X1,X2) = sz00
| X2 = X1
| ~ doDivides0(X1,X2)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_66]),c_0_72]) ).
cnf(c_0_234,hypothesis,
( doDivides0(xk,esk1_2(X1,xk))
| X2 != xk
| ~ doDivides0(X2,X1)
| ~ sdtlseqdt0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_53])]) ).
cnf(c_0_235,plain,
( X1 = X2
| X2 != sz00
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_223]),c_0_58]) ).
cnf(c_0_236,hypothesis,
( esk1_2(sz00,xk) = sz10
| sdtlseqdt0(sz10,esk1_2(sz00,xk)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_224]),c_0_179]),c_0_158]),c_0_42]),c_0_64]),c_0_53])]),c_0_225]) ).
cnf(c_0_237,hypothesis,
( X1 != sz00
| X1 != sz10 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_114]) ).
fof(c_0_238,negated_conjecture,
! [X2] :
( ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,xk)
| ~ isPrime0(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_228])]) ).
fof(c_0_239,hypothesis,
! [X3] :
( ( aNaturalNumber0(esk4_1(X3))
| ~ iLess0(X3,xk)
| ~ aNaturalNumber0(X3)
| X3 = sz00
| X3 = sz10 )
& ( doDivides0(esk4_1(X3),X3)
| ~ iLess0(X3,xk)
| ~ aNaturalNumber0(X3)
| X3 = sz00
| X3 = sz10 )
& ( isPrime0(esk4_1(X3))
| ~ iLess0(X3,xk)
| ~ aNaturalNumber0(X3)
| X3 = sz00
| X3 = sz10 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1700])])])])])]) ).
cnf(c_0_240,plain,
( isPrime0(X1)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk3_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_207]) ).
cnf(c_0_241,plain,
( sdtlseqdt0(X1,X2)
| X2 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_242,plain,
( sdtlseqdt0(X1,sz10)
| X2 != sz00
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_223]),c_0_42])]),c_0_58]) ).
cnf(c_0_243,hypothesis,
( sdtlseqdt0(xk,X1)
| xk != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_188]),c_0_42]),c_0_53])]) ).
cnf(c_0_244,hypothesis,
( doDivides0(esk3_1(xk),xk)
| sdtpldt0(sz00,xk) != xk
| ~ aNaturalNumber0(esk3_1(xk)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_150]),c_0_42]),c_0_53])]),c_0_152]),c_0_205]),c_0_232]),c_0_74]) ).
cnf(c_0_245,plain,
( sdtasdt0(X1,sz00) = X2
| X2 = X1
| ~ doDivides0(X1,X2)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_233]) ).
cnf(c_0_246,hypothesis,
doDivides0(xk,esk1_2(sz00,xk)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_199]),c_0_158]),c_0_42])]) ).
cnf(c_0_247,hypothesis,
esk1_2(sz00,xk) != sz00,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_64])]),c_0_237]) ).
cnf(c_0_248,hypothesis,
( sdtmndt0(xk,xk) = sz00
| sdtpldt0(sz00,xk) != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_150]),c_0_42]),c_0_53])]) ).
cnf(c_0_249,negated_conjecture,
( ~ isPrime0(X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_250,hypothesis,
( X1 = sz10
| X1 = sz00
| isPrime0(esk4_1(X1))
| ~ aNaturalNumber0(X1)
| ~ iLess0(X1,xk) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_251,hypothesis,
( X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk4_1(X1))
| ~ aNaturalNumber0(X1)
| ~ iLess0(X1,xk) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_252,plain,
( X1 = sz10
| isPrime0(X1)
| doDivides0(X2,X1)
| ~ doDivides0(X2,esk3_1(X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_218]),c_0_240]),c_0_167]) ).
cnf(c_0_253,hypothesis,
( X1 = sz10
| X1 = sz00
| doDivides0(esk4_1(X1),X1)
| ~ aNaturalNumber0(X1)
| ~ iLess0(X1,xk) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_254,plain,
( X1 = sz10
| X1 = sz00
| isPrime0(X1)
| sdtlseqdt0(esk3_1(X1),X1)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_218]),c_0_240]) ).
cnf(c_0_255,plain,
( isPrime0(X1)
| X1 = sz10
| X1 = sz00
| ~ aNaturalNumber0(X1)
| esk3_1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_207]) ).
cnf(c_0_256,hypothesis,
( X1 != sz00
| xk != X1 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_53])]),c_0_225]),c_0_58]) ).
cnf(c_0_257,hypothesis,
( doDivides0(esk3_1(xk),xk)
| sdtasdt0(xk,sz10) != xk
| ~ aNaturalNumber0(esk3_1(xk)) ),
inference(rw,[status(thm)],[c_0_244,c_0_181]) ).
cnf(c_0_258,hypothesis,
( esk1_2(sz00,xk) = xk
| ~ sdtlseqdt0(esk1_2(sz00,xk),xk)
| ~ aNaturalNumber0(esk1_2(sz00,xk)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_246]),c_0_178]),c_0_53])]),c_0_247]) ).
cnf(c_0_259,plain,
( sdtlseqdt0(esk1_2(X1,X2),X2)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_80])]),c_0_83]) ).
cnf(c_0_260,plain,
( sdtpldt0(X1,X2) = sz00
| sdtpldt0(X1,X2) = sz10
| isPrime0(sdtpldt0(X1,X2))
| doDivides0(esk3_1(sdtpldt0(X1,X2)),X2)
| ~ doDivides0(esk3_1(sdtpldt0(X1,X2)),X1)
| ~ aNaturalNumber0(esk3_1(sdtpldt0(X1,X2)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_218]),c_0_99]) ).
cnf(c_0_261,plain,
( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_191]) ).
cnf(c_0_262,plain,
( aNaturalNumber0(sdtmndt0(X1,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_263,hypothesis,
( sdtmndt0(xk,xk) = sz00
| sdtasdt0(xk,sz10) != xk ),
inference(rw,[status(thm)],[c_0_248,c_0_181]) ).
cnf(c_0_264,negated_conjecture,
( X1 = sz00
| X1 = sz10
| ~ doDivides0(esk4_1(X1),xk)
| ~ iLess0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_250]),c_0_251]) ).
cnf(c_0_265,hypothesis,
( esk3_1(X1) = sz00
| esk3_1(X1) = sz10
| X1 = sz10
| isPrime0(X1)
| doDivides0(esk4_1(esk3_1(X1)),X1)
| ~ iLess0(esk3_1(X1),xk)
| ~ aNaturalNumber0(esk3_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_251]) ).
fof(c_0_266,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| X3 = X4
| ~ sdtlseqdt0(X3,X4)
| iLess0(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).
cnf(c_0_267,plain,
( X1 = sz00
| X1 = sz10
| isPrime0(X1)
| ~ sdtlseqdt0(X1,esk3_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_254]),c_0_240]),c_0_255]) ).
cnf(c_0_268,hypothesis,
( sdtlseqdt0(xk,X1)
| X1 != xk ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_209]),c_0_178]),c_0_53])]),c_0_200]),c_0_256]) ).
cnf(c_0_269,hypothesis,
( doDivides0(esk3_1(xk),xk)
| ~ aNaturalNumber0(esk3_1(xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_257,c_0_184])]) ).
cnf(c_0_270,hypothesis,
( esk1_2(sz00,xk) = xk
| ~ aNaturalNumber0(esk1_2(sz00,xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_259]),c_0_158]),c_0_42]),c_0_53])]) ).
cnf(c_0_271,plain,
( X1 = sz10
| X1 = sz00
| isPrime0(X1)
| doDivides0(esk3_1(X1),sdtmndt0(X1,X2))
| ~ doDivides0(esk3_1(X1),X2)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_262]),c_0_240]) ).
cnf(c_0_272,hypothesis,
sdtmndt0(xk,xk) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_263,c_0_184])]) ).
cnf(c_0_273,negated_conjecture,
( esk3_1(xk) = sz10
| esk3_1(xk) = sz00
| ~ iLess0(esk3_1(xk),xk)
| ~ aNaturalNumber0(esk3_1(xk)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_265]),c_0_53])]),c_0_205]),c_0_232]) ).
cnf(c_0_274,plain,
( iLess0(X1,X2)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_275,hypothesis,
esk3_1(xk) != xk,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_268]),c_0_53])]),c_0_152]),c_0_205]),c_0_232]) ).
cnf(c_0_276,hypothesis,
( sdtlseqdt0(esk3_1(xk),xk)
| ~ aNaturalNumber0(esk3_1(xk)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_269]),c_0_53])]),c_0_152]) ).
cnf(c_0_277,plain,
( X1 = sz10
| X1 = sz00
| isPrime0(X1)
| doDivides0(esk3_1(X1),esk1_2(X2,X1))
| ~ doDivides0(esk3_1(X1),X2)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_80]),c_0_83]),c_0_240]) ).
cnf(c_0_278,hypothesis,
esk1_2(sz00,xk) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_270,c_0_83]),c_0_158]),c_0_42]),c_0_53])]) ).
cnf(c_0_279,hypothesis,
( doDivides0(esk3_1(xk),sz00)
| ~ doDivides0(esk3_1(xk),xk) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_271,c_0_272]),c_0_88]),c_0_53])]),c_0_205]),c_0_152]),c_0_232]) ).
cnf(c_0_280,negated_conjecture,
( esk3_1(xk) = sz00
| esk3_1(xk) = sz10
| ~ aNaturalNumber0(esk3_1(xk)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_274]),c_0_53])]),c_0_275]),c_0_276]) ).
cnf(c_0_281,plain,
( doDivides0(sz00,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_65]),c_0_42])]) ).
cnf(c_0_282,hypothesis,
( doDivides0(esk3_1(xk),xk)
| ~ doDivides0(esk3_1(xk),sz00) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_278]),c_0_158]),c_0_42]),c_0_53])]),c_0_205]),c_0_152]),c_0_232]) ).
cnf(c_0_283,hypothesis,
doDivides0(esk3_1(xk),sz00),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_218]),c_0_53])]),c_0_205]),c_0_152]),c_0_232]) ).
cnf(c_0_284,plain,
( isPrime0(X1)
| X1 = sz10
| X1 = sz00
| ~ aNaturalNumber0(X1)
| esk3_1(X1) != sz10 ),
inference(split_conjunct,[status(thm)],[c_0_207]) ).
cnf(c_0_285,negated_conjecture,
( esk3_1(xk) = sz10
| esk3_1(xk) = sz00 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_280,c_0_240]),c_0_53])]),c_0_205]),c_0_152]),c_0_232]) ).
cnf(c_0_286,plain,
( esk1_2(X1,X2) = sz00
| ~ doDivides0(sz00,X2)
| ~ doDivides0(sz00,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_197]),c_0_42])]),c_0_83]) ).
cnf(c_0_287,hypothesis,
doDivides0(sz00,sz00),
inference(spm,[status(thm)],[c_0_281,c_0_53]) ).
cnf(c_0_288,hypothesis,
doDivides0(esk3_1(xk),xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_282,c_0_283])]) ).
cnf(c_0_289,negated_conjecture,
esk3_1(xk) = sz00,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_284,c_0_285]),c_0_53])]),c_0_205]),c_0_152]),c_0_232]) ).
cnf(c_0_290,hypothesis,
~ doDivides0(sz00,xk),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_278,c_0_286]),c_0_287]),c_0_158]),c_0_42]),c_0_53])]),c_0_152]) ).
cnf(c_0_291,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_288,c_0_289]),c_0_290]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM483+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n013.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 : 600
% 0.13/0.34 % DateTime : Tue Jul 5 08:03:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.28/9.47 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.28/9.47 # Preprocessing time : 0.018 s
% 0.28/9.47
% 0.28/9.47 # Proof found!
% 0.28/9.47 # SZS status Theorem
% 0.28/9.47 # SZS output start CNFRefutation
% See solution above
% 0.28/9.47 # Proof object total steps : 292
% 0.28/9.47 # Proof object clause steps : 225
% 0.28/9.47 # Proof object formula steps : 67
% 0.28/9.47 # Proof object conjectures : 9
% 0.28/9.47 # Proof object clause conjectures : 6
% 0.28/9.47 # Proof object formula conjectures : 3
% 0.28/9.47 # Proof object initial clauses used : 53
% 0.28/9.47 # Proof object initial formulas used : 35
% 0.28/9.47 # Proof object generating inferences : 161
% 0.28/9.47 # Proof object simplifying inferences : 407
% 0.28/9.47 # Training examples: 0 positive, 0 negative
% 0.28/9.47 # Parsed axioms : 42
% 0.28/9.47 # Removed by relevancy pruning/SinE : 0
% 0.28/9.47 # Initial clauses : 75
% 0.28/9.47 # Removed in clause preprocessing : 3
% 0.28/9.47 # Initial clauses in saturation : 72
% 0.28/9.47 # Processed clauses : 10576
% 0.28/9.47 # ...of these trivial : 295
% 0.28/9.47 # ...subsumed : 7759
% 0.28/9.47 # ...remaining for further processing : 2522
% 0.28/9.47 # Other redundant clauses eliminated : 1992
% 0.28/9.47 # Clauses deleted for lack of memory : 375960
% 0.28/9.47 # Backward-subsumed : 167
% 0.28/9.47 # Backward-rewritten : 379
% 0.28/9.47 # Generated clauses : 481234
% 0.28/9.47 # ...of the previous two non-trivial : 469579
% 0.28/9.47 # Contextual simplify-reflections : 5571
% 0.28/9.47 # Paramodulations : 478994
% 0.28/9.47 # Factorizations : 1
% 0.28/9.47 # Equation resolutions : 2238
% 0.28/9.47 # Current number of processed clauses : 1974
% 0.28/9.47 # Positive orientable unit clauses : 126
% 0.28/9.47 # Positive unorientable unit clauses: 0
% 0.28/9.47 # Negative unit clauses : 44
% 0.28/9.47 # Non-unit-clauses : 1804
% 0.28/9.47 # Current number of unprocessed clauses: 69592
% 0.28/9.47 # ...number of literals in the above : 449735
% 0.28/9.47 # Current number of archived formulas : 0
% 0.28/9.47 # Current number of archived clauses : 547
% 0.28/9.47 # Clause-clause subsumption calls (NU) : 1385794
% 0.28/9.47 # Rec. Clause-clause subsumption calls : 232659
% 0.28/9.47 # Non-unit clause-clause subsumptions : 9017
% 0.28/9.47 # Unit Clause-clause subsumption calls : 18091
% 0.28/9.47 # Rewrite failures with RHS unbound : 0
% 0.28/9.47 # BW rewrite match attempts : 53
% 0.28/9.47 # BW rewrite match successes : 47
% 0.28/9.47 # Condensation attempts : 0
% 0.28/9.47 # Condensation successes : 0
% 0.28/9.47 # Termbank termtop insertions : 12358832
% 0.28/9.47
% 0.28/9.47 # -------------------------------------------------
% 0.28/9.47 # User time : 8.751 s
% 0.28/9.47 # System time : 0.116 s
% 0.28/9.47 # Total time : 8.867 s
% 0.28/9.47 # Maximum resident set size: 133492 pages
% 0.28/23.41 eprover: CPU time limit exceeded, terminating
% 0.28/23.42 eprover: CPU time limit exceeded, terminating
% 0.28/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.43 eprover: No such file or directory
% 0.28/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.43 eprover: No such file or directory
% 0.28/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.28/23.43 eprover: No such file or directory
% 0.28/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.43 eprover: No such file or directory
% 0.28/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.44 eprover: No such file or directory
% 0.28/23.44 eprover: CPU time limit exceeded, terminating
% 0.28/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.28/23.44 eprover: No such file or directory
% 0.28/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.44 eprover: No such file or directory
% 0.28/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.28/23.45 eprover: No such file or directory
% 0.28/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.45 eprover: No such file or directory
% 0.28/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.45 eprover: No such file or directory
% 0.28/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.28/23.45 eprover: No such file or directory
% 0.28/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.45 eprover: No such file or directory
% 0.28/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.45 eprover: No such file or directory
% 0.28/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.28/23.46 eprover: No such file or directory
% 0.28/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.46 eprover: No such file or directory
% 0.28/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.46 eprover: No such file or directory
% 0.28/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.28/23.46 eprover: No such file or directory
% 0.28/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.46 eprover: No such file or directory
% 0.28/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.46 eprover: No such file or directory
% 0.28/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.47 eprover: No such file or directory
% 0.28/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.28/23.47 eprover: No such file or directory
% 0.28/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.47 eprover: No such file or directory
% 0.28/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.28/23.47 eprover: No such file or directory
% 0.28/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.47 eprover: No such file or directory
% 0.28/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.28/23.47 eprover: No such file or directory
% 0.28/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.48 eprover: No such file or directory
% 0.28/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.28/23.48 eprover: No such file or directory
% 0.28/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.48 eprover: No such file or directory
% 0.28/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.28/23.48 eprover: No such file or directory
% 0.28/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.49 eprover: No such file or directory
% 0.28/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.49 eprover: No such file or directory
% 0.28/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.50 eprover: No such file or directory
% 0.28/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.28/23.50 eprover: No such file or directory
%------------------------------------------------------------------------------