TSTP Solution File: NUM510+1 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : NUM510+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:56:06 EDT 2023
% Result : Theorem 0.15s 0.53s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 32
% Syntax : Number of formulae : 162 ( 45 unt; 0 def)
% Number of atoms : 590 ( 188 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 714 ( 286 ~; 310 |; 76 &)
% ( 4 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 192 ( 0 sgn; 100 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mSortsB_02) ).
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/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mDefQuot) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',m_MulUnit) ).
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/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mMonAdd) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mSortsC_01) ).
fof(m__2287,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',m__2287) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',m__1837) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',m_AddZero) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mZeroMul) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mLETran) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mSortsC) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mSortsB) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X2,X3) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mDivTrans) ).
fof(m__2487,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',m__2487) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',m__2342) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mMonMul2) ).
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/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mDivSum) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mAddComm) ).
fof(m__,conjecture,
( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',m__) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mAddCanc) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mDivLE) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mMulCanc) ).
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/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mDivMin) ).
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/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mDefPrime) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',m__1860) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',mZeroAdd) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',m__2306) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',m_MulZero) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p',m__2315) ).
fof(c_0_32,plain,
! [X71,X72,X74] :
( ( aNaturalNumber0(esk2_2(X71,X72))
| ~ doDivides0(X71,X72)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X72) )
& ( X72 = sdtasdt0(X71,esk2_2(X71,X72))
| ~ doDivides0(X71,X72)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X72) )
& ( ~ aNaturalNumber0(X74)
| X72 != sdtasdt0(X71,X74)
| doDivides0(X71,X72)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X72) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_33,plain,
! [X58,X59] :
( ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X59)
| aNaturalNumber0(sdtasdt0(X58,X59)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_34,plain,
! [X30,X31,X32] :
( ( aNaturalNumber0(X32)
| X32 != sdtsldt0(X31,X30)
| X30 = sz00
| ~ doDivides0(X30,X31)
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31) )
& ( X31 = sdtasdt0(X30,X32)
| X32 != sdtsldt0(X31,X30)
| X30 = sz00
| ~ doDivides0(X30,X31)
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31) )
& ( ~ aNaturalNumber0(X32)
| X31 != sdtasdt0(X30,X32)
| X32 = sdtsldt0(X31,X30)
| X30 = sz00
| ~ doDivides0(X30,X31)
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_35,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_37,plain,
! [X78] :
( ( sdtasdt0(X78,sz10) = X78
| ~ aNaturalNumber0(X78) )
& ( X78 = sdtasdt0(sz10,X78)
| ~ aNaturalNumber0(X78) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
fof(c_0_38,plain,
! [X16,X17,X18] :
( ( sdtpldt0(X18,X16) != sdtpldt0(X18,X17)
| ~ aNaturalNumber0(X18)
| X16 = X17
| ~ sdtlseqdt0(X16,X17)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17) )
& ( sdtlseqdt0(sdtpldt0(X18,X16),sdtpldt0(X18,X17))
| ~ aNaturalNumber0(X18)
| X16 = X17
| ~ sdtlseqdt0(X16,X17)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17) )
& ( sdtpldt0(X16,X18) != sdtpldt0(X17,X18)
| ~ aNaturalNumber0(X18)
| X16 = X17
| ~ sdtlseqdt0(X16,X17)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17) )
& ( sdtlseqdt0(sdtpldt0(X16,X18),sdtpldt0(X17,X18))
| ~ aNaturalNumber0(X18)
| X16 = X17
| ~ sdtlseqdt0(X16,X17)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
cnf(c_0_39,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_35]),c_0_36]) ).
cnf(c_0_41,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_43,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| X2 = X3
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_46,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_47,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
fof(c_0_48,plain,
! [X43] :
( ( sdtpldt0(X43,sz00) = X43
| ~ aNaturalNumber0(X43) )
& ( X43 = sdtpldt0(sz00,X43)
| ~ aNaturalNumber0(X43) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_49,plain,
! [X69,X70] :
( ~ aNaturalNumber0(X69)
| ~ aNaturalNumber0(X70)
| sdtasdt0(X69,X70) != sz00
| X69 = sz00
| X70 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_50,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_51,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_52,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_53,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_54,plain,
! [X11,X12,X13] :
( ~ aNaturalNumber0(X11)
| ~ aNaturalNumber0(X12)
| ~ aNaturalNumber0(X13)
| ~ sdtlseqdt0(X11,X12)
| ~ sdtlseqdt0(X12,X13)
| sdtlseqdt0(X11,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_55,hypothesis,
( sdtlseqdt0(sdtpldt0(X1,xn),sdtpldt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]),c_0_47]) ).
cnf(c_0_56,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_58,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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
fof(c_0_59,plain,
! [X36,X37] :
( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X37)
| aNaturalNumber0(sdtpldt0(X36,X37)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_60,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,plain,
( sdtasdt0(sz10,sdtsldt0(X1,sz10)) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_42])]),c_0_52]) ).
cnf(c_0_62,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,hypothesis,
sdtlseqdt0(sdtpldt0(sz00,xn),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_45])]) ).
cnf(c_0_65,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_66,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_67,plain,
( sdtsldt0(sz00,sz10) = sz00
| ~ aNaturalNumber0(sdtsldt0(sz00,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_42])]),c_0_52])]),c_0_57])]) ).
cnf(c_0_68,plain,
( aNaturalNumber0(sdtsldt0(X1,sz10))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_51]),c_0_42])]),c_0_52]) ).
cnf(c_0_69,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,sdtpldt0(sz00,xn))
| ~ aNaturalNumber0(sdtpldt0(sz00,xn))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_45])]) ).
cnf(c_0_70,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_65]),c_0_66]) ).
fof(c_0_71,plain,
! [X75,X76,X77] :
( ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77)
| ~ doDivides0(X75,X76)
| ~ doDivides0(X76,X77)
| doDivides0(X75,X77) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
cnf(c_0_72,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_57])]) ).
cnf(c_0_73,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_56]),c_0_46])]) ).
cnf(c_0_74,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_56]),c_0_57])]) ).
cnf(c_0_75,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_76,hypothesis,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[m__2487]) ).
cnf(c_0_77,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_78,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_79,plain,
! [X23,X24] :
( ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X24)
| X23 = sz00
| sdtlseqdt0(X24,sdtasdt0(X24,X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(c_0_80,plain,
! [X52,X53,X54] :
( ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54)
| ~ doDivides0(X52,X53)
| ~ doDivides0(X52,X54)
| doDivides0(X52,sdtpldt0(X53,X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_81,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_72]),c_0_57])]) ).
cnf(c_0_82,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_83,hypothesis,
sdtlseqdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_57]),c_0_46])]) ).
cnf(c_0_84,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_85,hypothesis,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_46]),c_0_77])]) ).
fof(c_0_86,plain,
! [X60,X61] :
( ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61)
| sdtasdt0(X60,X61) = sdtasdt0(X61,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_87,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_78]),c_0_36]),c_0_40]) ).
cnf(c_0_88,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_90,plain,
doDivides0(sz10,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_81]),c_0_42]),c_0_57])]) ).
fof(c_0_91,plain,
! [X38,X39] :
( ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39)
| sdtpldt0(X38,X39) = sdtpldt0(X39,X38) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_92,hypothesis,
sdtpldt0(sz00,esk1_2(sz00,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_45]),c_0_57])]) ).
cnf(c_0_93,hypothesis,
aNaturalNumber0(esk1_2(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_83]),c_0_45]),c_0_57])]) ).
cnf(c_0_94,hypothesis,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_51]),c_0_42]),c_0_77])]) ).
fof(c_0_95,negated_conjecture,
~ ( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_96,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_97,plain,
( sdtsldt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_41]),c_0_42])]),c_0_52]) ).
cnf(c_0_98,plain,
( sdtsldt0(X1,sz10) = sz00
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_61]),c_0_42])]),c_0_68]) ).
cnf(c_0_99,plain,
( 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_89,c_0_90]),c_0_57]),c_0_42])]),c_0_51]) ).
cnf(c_0_100,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_101,hypothesis,
esk1_2(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_92]),c_0_93])]) ).
cnf(c_0_102,hypothesis,
sdtasdt0(sz10,sdtsldt0(xn,sz10)) = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_94]),c_0_42]),c_0_46])]),c_0_52]) ).
cnf(c_0_103,hypothesis,
aNaturalNumber0(sdtsldt0(xn,sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_94]),c_0_42]),c_0_46])]),c_0_52]) ).
fof(c_0_104,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(fof_nnf,[status(thm)],[c_0_95]) ).
cnf(c_0_105,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_96]) ).
cnf(c_0_106,hypothesis,
( sdtasdt0(xr,sdtsldt0(xn,xr)) = xn
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_76]),c_0_77]),c_0_46])]) ).
cnf(c_0_107,hypothesis,
( xr = sz00
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_76]),c_0_77]),c_0_46])]) ).
fof(c_0_108,plain,
! [X47,X48,X49] :
( ( sdtpldt0(X47,X48) != sdtpldt0(X47,X49)
| X48 = X49
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48)
| ~ aNaturalNumber0(X49) )
& ( sdtpldt0(X48,X47) != sdtpldt0(X49,X47)
| X48 = X49
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48)
| ~ aNaturalNumber0(X49) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_109,plain,
( sz00 = X1
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
fof(c_0_110,plain,
! [X25,X26] :
( ~ aNaturalNumber0(X25)
| ~ aNaturalNumber0(X26)
| ~ doDivides0(X25,X26)
| X26 = sz00
| sdtlseqdt0(X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
cnf(c_0_111,plain,
( doDivides0(sz10,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_57])]) ).
cnf(c_0_112,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[c_0_92,c_0_101]) ).
fof(c_0_113,plain,
! [X66,X67,X68] :
( ( sdtasdt0(X66,X67) != sdtasdt0(X66,X68)
| X67 = X68
| ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68)
| X66 = sz00
| ~ aNaturalNumber0(X66) )
& ( sdtasdt0(X67,X66) != sdtasdt0(X68,X66)
| X67 = X68
| ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68)
| X66 = sz00
| ~ aNaturalNumber0(X66) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_114,hypothesis,
sdtsldt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_102]),c_0_103])]) ).
cnf(c_0_115,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_116,hypothesis,
( xr = sz00
| sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_77])]),c_0_107]) ).
fof(c_0_117,plain,
! [X55,X56,X57] :
( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X57)
| ~ doDivides0(X55,X56)
| ~ doDivides0(X55,sdtpldt0(X56,X57))
| doDivides0(X55,X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).
cnf(c_0_118,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_119,hypothesis,
( sdtpldt0(sz00,xn) = sz00
| sdtlseqdt0(sz10,xp)
| ~ aNaturalNumber0(sdtpldt0(sz00,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_109]),c_0_42])]) ).
cnf(c_0_120,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_121,hypothesis,
doDivides0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_45])]) ).
cnf(c_0_122,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_123,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(rw,[status(thm)],[c_0_102,c_0_114]) ).
cnf(c_0_124,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| xr = sz00 ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
fof(c_0_125,plain,
! [X79,X80] :
( ( X79 != sz00
| ~ isPrime0(X79)
| ~ aNaturalNumber0(X79) )
& ( X79 != sz10
| ~ isPrime0(X79)
| ~ aNaturalNumber0(X79) )
& ( ~ aNaturalNumber0(X80)
| ~ doDivides0(X80,X79)
| X80 = sz10
| X80 = X79
| ~ isPrime0(X79)
| ~ aNaturalNumber0(X79) )
& ( aNaturalNumber0(esk3_1(X79))
| X79 = sz00
| X79 = sz10
| isPrime0(X79)
| ~ aNaturalNumber0(X79) )
& ( doDivides0(esk3_1(X79),X79)
| X79 = sz00
| X79 = sz10
| isPrime0(X79)
| ~ aNaturalNumber0(X79) )
& ( esk3_1(X79) != sz10
| X79 = sz00
| X79 = sz10
| isPrime0(X79)
| ~ aNaturalNumber0(X79) )
& ( esk3_1(X79) != X79
| X79 = sz00
| X79 = sz10
| isPrime0(X79)
| ~ aNaturalNumber0(X79) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).
cnf(c_0_126,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_127,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_128,hypothesis,
( xp = X1
| sdtpldt0(sz00,X1) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_112]),c_0_45]),c_0_57])]) ).
cnf(c_0_129,hypothesis,
( sdtpldt0(sz00,xn) = sz00
| sdtlseqdt0(sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_66]),c_0_46]),c_0_57])]) ).
cnf(c_0_130,hypothesis,
( xp = sz00
| sdtlseqdt0(sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_45]),c_0_42])]) ).
cnf(c_0_131,hypothesis,
( xn = sz00
| sz10 = X1
| sdtasdt0(X1,xn) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_46]),c_0_42])]) ).
cnf(c_0_132,hypothesis,
( sdtasdt0(xr,xn) = xn
| xr = sz00 ),
inference(spm,[status(thm)],[c_0_106,c_0_124]) ).
cnf(c_0_133,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_134,hypothesis,
( doDivides0(xp,X1)
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xn,xm),X1))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_45])]) ).
cnf(c_0_135,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_136,plain,
! [X50,X51] :
( ( X50 = sz00
| sdtpldt0(X50,X51) != sz00
| ~ aNaturalNumber0(X50)
| ~ aNaturalNumber0(X51) )
& ( X51 = sz00
| sdtpldt0(X50,X51) != sz00
| ~ aNaturalNumber0(X50)
| ~ aNaturalNumber0(X51) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
cnf(c_0_137,hypothesis,
sdtlseqdt0(sz10,xp),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_46])]),c_0_47]),c_0_130]) ).
cnf(c_0_138,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_139,hypothesis,
( xr = sz00
| xr = sz10
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_77])]) ).
cnf(c_0_140,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_133]),c_0_42])]) ).
cnf(c_0_141,plain,
( X1 != sz00
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_142,hypothesis,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_127]),c_0_57])]) ).
cnf(c_0_143,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_144,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_145,hypothesis,
sdtpldt0(sz10,esk1_2(sz10,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_137]),c_0_45]),c_0_42])]) ).
cnf(c_0_146,hypothesis,
aNaturalNumber0(esk1_2(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_137]),c_0_45]),c_0_42])]) ).
cnf(c_0_147,hypothesis,
( xn = sz00
| xr = sz00 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140]) ).
cnf(c_0_148,plain,
~ isPrime0(sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_141]),c_0_57])]) ).
cnf(c_0_149,hypothesis,
doDivides0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_36]),c_0_143]),c_0_46])]) ).
cnf(c_0_150,hypothesis,
xp != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_146]),c_0_42])]),c_0_52]) ).
cnf(c_0_151,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_152,hypothesis,
xn = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_147]),c_0_148]) ).
fof(c_0_153,plain,
! [X65] :
( ( sdtasdt0(X65,sz00) = sz00
| ~ aNaturalNumber0(X65) )
& ( sz00 = sdtasdt0(sz00,X65)
| ~ aNaturalNumber0(X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_154,hypothesis,
sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_149]),c_0_45]),c_0_57])]),c_0_150]) ).
cnf(c_0_155,hypothesis,
aNaturalNumber0(sdtsldt0(sz00,xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_149]),c_0_45]),c_0_57])]),c_0_150]) ).
fof(c_0_156,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_157,hypothesis,
sdtsldt0(sdtasdt0(sz00,xm),xp) = xk,
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_158,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_159,hypothesis,
sdtsldt0(sz00,xp) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_154]),c_0_155]),c_0_45])]),c_0_150]) ).
cnf(c_0_160,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_161,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_159]),c_0_143])]),c_0_160]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : NUM510+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.12 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n024.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 2400
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Oct 2 13:42:12 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.RPRvg5IVgA/E---3.1_2986.p
% 0.15/0.53 # Version: 3.1pre001
% 0.15/0.53 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.53 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.15/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.15/0.53 # Starting sh5l with 300s (1) cores
% 0.15/0.53 # sh5l with pid 3082 completed with status 0
% 0.15/0.53 # Result found by sh5l
% 0.15/0.53 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.53 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.15/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.15/0.53 # Starting sh5l with 300s (1) cores
% 0.15/0.53 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/0.53 # Search class: FGHSF-FFMM21-SFFFFFNN
% 0.15/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.53 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 0.15/0.53 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with pid 3090 completed with status 0
% 0.15/0.53 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v
% 0.15/0.53 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.53 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.15/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.15/0.53 # Starting sh5l with 300s (1) cores
% 0.15/0.53 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/0.53 # Search class: FGHSF-FFMM21-SFFFFFNN
% 0.15/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.53 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 0.15/0.53 # Preprocessing time : 0.002 s
% 0.15/0.53 # Presaturation interreduction done
% 0.15/0.53
% 0.15/0.53 # Proof found!
% 0.15/0.53 # SZS status Theorem
% 0.15/0.53 # SZS output start CNFRefutation
% See solution above
% 0.15/0.53 # Parsed axioms : 53
% 0.15/0.53 # Removed by relevancy pruning/SinE : 1
% 0.15/0.53 # Initial clauses : 94
% 0.15/0.53 # Removed in clause preprocessing : 3
% 0.15/0.53 # Initial clauses in saturation : 91
% 0.15/0.53 # Processed clauses : 1085
% 0.15/0.53 # ...of these trivial : 16
% 0.15/0.53 # ...subsumed : 461
% 0.15/0.53 # ...remaining for further processing : 608
% 0.15/0.53 # Other redundant clauses eliminated : 24
% 0.15/0.53 # Clauses deleted for lack of memory : 0
% 0.15/0.53 # Backward-subsumed : 85
% 0.15/0.53 # Backward-rewritten : 160
% 0.15/0.53 # Generated clauses : 3135
% 0.15/0.53 # ...of the previous two non-redundant : 2596
% 0.15/0.53 # ...aggressively subsumed : 0
% 0.15/0.53 # Contextual simplify-reflections : 78
% 0.15/0.53 # Paramodulations : 3099
% 0.15/0.53 # Factorizations : 5
% 0.15/0.53 # NegExts : 0
% 0.15/0.53 # Equation resolutions : 29
% 0.15/0.53 # Total rewrite steps : 4346
% 0.15/0.53 # Propositional unsat checks : 0
% 0.15/0.53 # Propositional check models : 0
% 0.15/0.53 # Propositional check unsatisfiable : 0
% 0.15/0.53 # Propositional clauses : 0
% 0.15/0.53 # Propositional clauses after purity: 0
% 0.15/0.53 # Propositional unsat core size : 0
% 0.15/0.53 # Propositional preprocessing time : 0.000
% 0.15/0.53 # Propositional encoding time : 0.000
% 0.15/0.53 # Propositional solver time : 0.000
% 0.15/0.53 # Success case prop preproc time : 0.000
% 0.15/0.53 # Success case prop encoding time : 0.000
% 0.15/0.53 # Success case prop solver time : 0.000
% 0.15/0.53 # Current number of processed clauses : 270
% 0.15/0.53 # Positive orientable unit clauses : 67
% 0.15/0.53 # Positive unorientable unit clauses: 0
% 0.15/0.53 # Negative unit clauses : 12
% 0.15/0.53 # Non-unit-clauses : 191
% 0.15/0.53 # Current number of unprocessed clauses: 1509
% 0.15/0.53 # ...number of literals in the above : 6897
% 0.15/0.53 # Current number of archived formulas : 0
% 0.15/0.53 # Current number of archived clauses : 330
% 0.15/0.53 # Clause-clause subsumption calls (NU) : 11915
% 0.15/0.53 # Rec. Clause-clause subsumption calls : 4749
% 0.15/0.53 # Non-unit clause-clause subsumptions : 577
% 0.15/0.53 # Unit Clause-clause subsumption calls : 969
% 0.15/0.53 # Rewrite failures with RHS unbound : 0
% 0.15/0.53 # BW rewrite match attempts : 25
% 0.15/0.53 # BW rewrite match successes : 25
% 0.15/0.53 # Condensation attempts : 0
% 0.15/0.53 # Condensation successes : 0
% 0.15/0.53 # Termbank termtop insertions : 57828
% 0.15/0.53
% 0.15/0.53 # -------------------------------------------------
% 0.15/0.53 # User time : 0.087 s
% 0.15/0.53 # System time : 0.003 s
% 0.15/0.53 # Total time : 0.090 s
% 0.15/0.53 # Maximum resident set size: 2052 pages
% 0.15/0.53
% 0.15/0.53 # -------------------------------------------------
% 0.15/0.53 # User time : 0.088 s
% 0.15/0.53 # System time : 0.005 s
% 0.15/0.53 # Total time : 0.094 s
% 0.15/0.53 # Maximum resident set size: 1740 pages
% 0.15/0.53 % E---3.1 exiting
% 0.15/0.53 % E---3.1 exiting
%------------------------------------------------------------------------------