TSTP Solution File: NUM510+1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM510+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 01:14:23 EDT 2024
% Result : Theorem 1.11s 0.61s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 33
% Syntax : Number of formulae : 183 ( 49 unt; 0 def)
% Number of atoms : 675 ( 219 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 809 ( 317 ~; 330 |; 101 &)
% ( 6 <=>; 55 =>; 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 : 218 ( 0 sgn 119 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/benchmark/theBenchmark.p',mDefQuot) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
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/benchmark/theBenchmark.p',mMonAdd) ).
fof(m__2287,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(m__2487,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__,conjecture,
( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
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/benchmark/theBenchmark.p',mDivSum) ).
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/benchmark/theBenchmark.p',mDefPrime) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
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/benchmark/theBenchmark.p',mDivMin) ).
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/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(c_0_33,plain,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_34,plain,
! [X8,X9,X11] :
( ( aNaturalNumber0(esk1_2(X8,X9))
| ~ doDivides0(X8,X9)
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X9) )
& ( X9 = sdtasdt0(X8,esk1_2(X8,X9))
| ~ doDivides0(X8,X9)
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X9) )
& ( ~ aNaturalNumber0(X11)
| X9 != sdtasdt0(X8,X11)
| doDivides0(X8,X9)
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X9) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_35,plain,
! [X50,X51] :
( ~ aNaturalNumber0(X50)
| ~ aNaturalNumber0(X51)
| aNaturalNumber0(sdtasdt0(X50,X51)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_36,plain,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_37,plain,
! [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)) ) ) ) ),
inference(fof_simplification,[status(thm)],[mMonAdd]) ).
fof(c_0_38,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
inference(fof_simplification,[status(thm)],[m__2287]) ).
fof(c_0_39,plain,
! [X81,X82,X83] :
( ( aNaturalNumber0(X83)
| X83 != sdtsldt0(X82,X81)
| X81 = sz00
| ~ doDivides0(X81,X82)
| ~ aNaturalNumber0(X81)
| ~ aNaturalNumber0(X82) )
& ( X82 = sdtasdt0(X81,X83)
| X83 != sdtsldt0(X82,X81)
| X81 = sz00
| ~ doDivides0(X81,X82)
| ~ aNaturalNumber0(X81)
| ~ aNaturalNumber0(X82) )
& ( ~ aNaturalNumber0(X83)
| X82 != sdtasdt0(X81,X83)
| X83 = sdtsldt0(X82,X81)
| X81 = sz00
| ~ doDivides0(X81,X82)
| ~ aNaturalNumber0(X81)
| ~ aNaturalNumber0(X82) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])])]) ).
cnf(c_0_40,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_42,plain,
! [X87] :
( ( sdtasdt0(X87,sz10) = X87
| ~ aNaturalNumber0(X87) )
& ( X87 = sdtasdt0(sz10,X87)
| ~ aNaturalNumber0(X87) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_43,plain,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
inference(fof_nnf,[status(thm)],[c_0_36]) ).
fof(c_0_44,plain,
! [X47,X48,X49] :
( ( sdtpldt0(X49,X47) != sdtpldt0(X49,X48)
| ~ aNaturalNumber0(X49)
| X47 = X48
| ~ sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48) )
& ( sdtlseqdt0(sdtpldt0(X49,X47),sdtpldt0(X49,X48))
| ~ aNaturalNumber0(X49)
| X47 = X48
| ~ sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48) )
& ( sdtpldt0(X47,X49) != sdtpldt0(X48,X49)
| ~ aNaturalNumber0(X49)
| X47 = X48
| ~ sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48) )
& ( sdtlseqdt0(sdtpldt0(X47,X49),sdtpldt0(X48,X49))
| ~ aNaturalNumber0(X49)
| X47 = X48
| ~ sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])]) ).
fof(c_0_45,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
inference(fof_nnf,[status(thm)],[c_0_38]) ).
cnf(c_0_46,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_39]) ).
cnf(c_0_47,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_41]) ).
cnf(c_0_48,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,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_44]) ).
cnf(c_0_51,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_53,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_54,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_55,plain,
! [X34] :
( ( sdtpldt0(X34,sz00) = X34
| ~ aNaturalNumber0(X34) )
& ( X34 = sdtpldt0(sz00,X34)
| ~ aNaturalNumber0(X34) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
fof(c_0_56,plain,
! [X43,X44,X46] :
( ( aNaturalNumber0(esk2_2(X43,X44))
| ~ sdtlseqdt0(X43,X44)
| ~ aNaturalNumber0(X43)
| ~ aNaturalNumber0(X44) )
& ( sdtpldt0(X43,esk2_2(X43,X44)) = X44
| ~ sdtlseqdt0(X43,X44)
| ~ aNaturalNumber0(X43)
| ~ aNaturalNumber0(X44) )
& ( ~ aNaturalNumber0(X46)
| sdtpldt0(X43,X46) != X44
| sdtlseqdt0(X43,X44)
| ~ aNaturalNumber0(X43)
| ~ aNaturalNumber0(X44) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_57,plain,
! [X27,X28] :
( ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X28)
| aNaturalNumber0(sdtpldt0(X27,X28)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
fof(c_0_58,plain,
! [X12,X13,X14] :
( ~ aNaturalNumber0(X12)
| ~ aNaturalNumber0(X13)
| ~ aNaturalNumber0(X14)
| ~ doDivides0(X12,X13)
| ~ doDivides0(X13,X14)
| doDivides0(X12,X14) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])])]) ).
fof(c_0_59,plain,
! [X61,X62] :
( ~ aNaturalNumber0(X61)
| ~ aNaturalNumber0(X62)
| sdtasdt0(X61,X62) != sz00
| X61 = sz00
| X62 = sz00 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
cnf(c_0_60,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_61,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_62,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_63,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_64,plain,
! [X76,X77,X78] :
( ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77)
| ~ aNaturalNumber0(X78)
| ~ sdtlseqdt0(X76,X77)
| ~ sdtlseqdt0(X77,X78)
| sdtlseqdt0(X76,X78) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).
cnf(c_0_65,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_50,c_0_51]),c_0_52]),c_0_53])]),c_0_54]) ).
cnf(c_0_66,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_67,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_68,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_69,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_70,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_71,hypothesis,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[m__2487]) ).
cnf(c_0_72,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
fof(c_0_73,plain,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
cnf(c_0_74,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_75,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_60,c_0_61]),c_0_49])]),c_0_62]) ).
cnf(c_0_76,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_63]) ).
cnf(c_0_77,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_78,hypothesis,
sdtlseqdt0(sdtpldt0(sz00,xn),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_52])]) ).
cnf(c_0_79,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_68]),c_0_69]) ).
cnf(c_0_80,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_70,c_0_71]),c_0_53]),c_0_72])]) ).
fof(c_0_81,plain,
! [X66,X67] :
( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67)
| X66 = sz00
| sdtlseqdt0(X67,sdtasdt0(X67,X66)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])])]) ).
fof(c_0_82,plain,
! [X52,X53] :
( ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| sdtasdt0(X52,X53) = sdtasdt0(X53,X52) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_83,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_74,c_0_75]),c_0_49])]),c_0_62])]),c_0_67])]) ).
cnf(c_0_84,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_76,c_0_61]),c_0_49])]),c_0_62]) ).
cnf(c_0_85,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_77,c_0_78]),c_0_52])]) ).
cnf(c_0_86,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_66]),c_0_67])]) ).
cnf(c_0_87,hypothesis,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_61]),c_0_49]),c_0_72])]) ).
fof(c_0_88,negated_conjecture,
~ ( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_89,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_90,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_91,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_67])]) ).
cnf(c_0_92,hypothesis,
( sdtlseqdt0(sz00,xp)
| ~ aNaturalNumber0(sdtpldt0(sz00,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_67])]) ).
fof(c_0_93,plain,
! [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 ) ) ) ),
inference(fof_simplification,[status(thm)],[mMulCanc]) ).
cnf(c_0_94,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_60,c_0_87]),c_0_49]),c_0_53])]),c_0_62]) ).
cnf(c_0_95,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_76,c_0_87]),c_0_49]),c_0_53])]),c_0_62]) ).
fof(c_0_96,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])]) ).
cnf(c_0_97,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_98,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_60,c_0_71]),c_0_72]),c_0_53])]) ).
cnf(c_0_99,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_76,c_0_71]),c_0_72]),c_0_53])]) ).
cnf(c_0_100,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_39]) ).
fof(c_0_101,plain,
! [X15,X16,X17] :
( ~ aNaturalNumber0(X15)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17)
| ~ doDivides0(X15,X16)
| ~ doDivides0(X15,X17)
| doDivides0(X15,sdtpldt0(X16,X17)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])])]) ).
cnf(c_0_102,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_91]),c_0_67])]) ).
cnf(c_0_103,plain,
( sdtpldt0(X1,esk2_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_104,hypothesis,
sdtlseqdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_66]),c_0_53])]) ).
cnf(c_0_105,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
fof(c_0_106,plain,
! [X58,X59,X60] :
( ( sdtasdt0(X58,X59) != sdtasdt0(X58,X60)
| X59 = X60
| ~ aNaturalNumber0(X59)
| ~ aNaturalNumber0(X60)
| X58 = sz00
| ~ aNaturalNumber0(X58) )
& ( sdtasdt0(X59,X58) != sdtasdt0(X60,X58)
| X59 = X60
| ~ aNaturalNumber0(X59)
| ~ aNaturalNumber0(X60)
| X58 = sz00
| ~ aNaturalNumber0(X58) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])])])])]) ).
cnf(c_0_107,hypothesis,
sdtsldt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_94]),c_0_95])]) ).
cnf(c_0_108,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_109,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_97,c_0_98]),c_0_72])]),c_0_99]) ).
fof(c_0_110,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefPrime]) ).
cnf(c_0_111,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_100]),c_0_41]),c_0_47]) ).
cnf(c_0_112,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_101]) ).
cnf(c_0_113,plain,
doDivides0(sz10,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_102]),c_0_49]),c_0_67])]) ).
fof(c_0_114,plain,
! [X29,X30] :
( ~ aNaturalNumber0(X29)
| ~ aNaturalNumber0(X30)
| sdtpldt0(X29,X30) = sdtpldt0(X30,X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_115,hypothesis,
sdtpldt0(sz00,esk2_2(sz00,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_52]),c_0_67])]) ).
cnf(c_0_116,hypothesis,
aNaturalNumber0(esk2_2(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_104]),c_0_52]),c_0_67])]) ).
cnf(c_0_117,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_118,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(rw,[status(thm)],[c_0_94,c_0_107]) ).
cnf(c_0_119,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| xr = sz00 ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
fof(c_0_120,plain,
! [X68,X69] :
( ( X68 != sz00
| ~ isPrime0(X68)
| ~ aNaturalNumber0(X68) )
& ( X68 != sz10
| ~ isPrime0(X68)
| ~ aNaturalNumber0(X68) )
& ( ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X68)
| X69 = sz10
| X69 = X68
| ~ isPrime0(X68)
| ~ aNaturalNumber0(X68) )
& ( aNaturalNumber0(esk3_1(X68))
| X68 = sz00
| X68 = sz10
| isPrime0(X68)
| ~ aNaturalNumber0(X68) )
& ( doDivides0(esk3_1(X68),X68)
| X68 = sz00
| X68 = sz10
| isPrime0(X68)
| ~ aNaturalNumber0(X68) )
& ( esk3_1(X68) != sz10
| X68 = sz00
| X68 = sz10
| isPrime0(X68)
| ~ aNaturalNumber0(X68) )
& ( esk3_1(X68) != X68
| X68 = sz00
| X68 = sz10
| isPrime0(X68)
| ~ aNaturalNumber0(X68) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_110])])])])])]) ).
cnf(c_0_121,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_111,c_0_48]),c_0_49])]),c_0_62]) ).
cnf(c_0_122,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_89,c_0_75]),c_0_49])]),c_0_84]) ).
fof(c_0_123,plain,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mDivLE]) ).
cnf(c_0_124,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_112,c_0_113]),c_0_67]),c_0_49])]),c_0_61]) ).
cnf(c_0_125,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_126,hypothesis,
esk2_2(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_115]),c_0_116])]) ).
fof(c_0_127,plain,
! [X18,X19,X20] :
( ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X20)
| ~ doDivides0(X18,X19)
| ~ doDivides0(X18,sdtpldt0(X19,X20))
| doDivides0(X18,X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])])]) ).
cnf(c_0_128,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_117,c_0_118]),c_0_53]),c_0_49])]) ).
cnf(c_0_129,hypothesis,
( sdtasdt0(xr,xn) = xn
| xr = sz00 ),
inference(spm,[status(thm)],[c_0_98,c_0_119]) ).
cnf(c_0_130,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
fof(c_0_131,plain,
! [X38,X39,X40] :
( ( sdtpldt0(X38,X39) != sdtpldt0(X38,X40)
| X39 = X40
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39)
| ~ aNaturalNumber0(X40) )
& ( sdtpldt0(X39,X38) != sdtpldt0(X40,X38)
| X39 = X40
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39)
| ~ aNaturalNumber0(X40) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])])]) ).
cnf(c_0_132,plain,
( sz00 = X1
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
fof(c_0_133,plain,
! [X21,X22] :
( ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X22)
| ~ doDivides0(X21,X22)
| X22 = sz00
| sdtlseqdt0(X21,X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_123])])]) ).
cnf(c_0_134,plain,
( doDivides0(sz10,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_67])]) ).
cnf(c_0_135,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[c_0_115,c_0_126]) ).
cnf(c_0_136,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_127]) ).
cnf(c_0_137,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
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_128,c_0_129]),c_0_72])]) ).
cnf(c_0_140,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_130]),c_0_49])]) ).
cnf(c_0_141,plain,
( X1 != sz00
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_142,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_143,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_85,c_0_132]),c_0_49])]) ).
cnf(c_0_144,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_145,hypothesis,
doDivides0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_52])]) ).
cnf(c_0_146,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_136,c_0_137]),c_0_52])]) ).
cnf(c_0_147,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_148,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_149,plain,
~ isPrime0(sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_141]),c_0_67])]) ).
cnf(c_0_150,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_142,c_0_135]),c_0_52]),c_0_67])]) ).
cnf(c_0_151,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_143,c_0_69]),c_0_53]),c_0_67])]) ).
cnf(c_0_152,hypothesis,
( xp = sz00
| sdtlseqdt0(sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_52]),c_0_49])]) ).
cnf(c_0_153,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_146,c_0_147]),c_0_137]),c_0_67])]) ).
cnf(c_0_154,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_155,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_156,hypothesis,
xn = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_148]),c_0_149]) ).
fof(c_0_157,plain,
! [X57] :
( ( sdtasdt0(X57,sz00) = sz00
| ~ aNaturalNumber0(X57) )
& ( sz00 = sdtasdt0(sz00,X57)
| ~ aNaturalNumber0(X57) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
fof(c_0_158,plain,
! [X41,X42] :
( ( X41 = sz00
| sdtpldt0(X41,X42) != sz00
| ~ aNaturalNumber0(X41)
| ~ aNaturalNumber0(X42) )
& ( X42 = sz00
| sdtpldt0(X41,X42) != sz00
| ~ aNaturalNumber0(X41)
| ~ aNaturalNumber0(X42) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])])]) ).
cnf(c_0_159,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_150,c_0_151]),c_0_53])]),c_0_54]),c_0_152]) ).
cnf(c_0_160,plain,
( X1 = sdtasdt0(X2,esk1_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_161,hypothesis,
doDivides0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_41]),c_0_154]),c_0_53])]) ).
cnf(c_0_162,hypothesis,
sdtsldt0(sdtasdt0(sz00,xm),xp) = xk,
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_163,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_164,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_165,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_166,hypothesis,
sdtpldt0(sz10,esk2_2(sz10,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_159]),c_0_52]),c_0_49])]) ).
cnf(c_0_167,hypothesis,
aNaturalNumber0(esk2_2(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_159]),c_0_52]),c_0_49])]) ).
fof(c_0_168,plain,
! [X74,X75] :
( ~ aNaturalNumber0(X74)
| ~ aNaturalNumber0(X75)
| ~ sdtlseqdt0(X74,X75)
| ~ sdtlseqdt0(X75,X74)
| X74 = X75 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
cnf(c_0_169,hypothesis,
sdtasdt0(xp,esk1_2(xp,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_52]),c_0_67])]) ).
cnf(c_0_170,hypothesis,
sdtsldt0(sz00,xp) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_154])]) ).
cnf(c_0_171,hypothesis,
aNaturalNumber0(esk1_2(xp,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_161]),c_0_67]),c_0_52])]) ).
cnf(c_0_172,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_165,c_0_166]),c_0_167]),c_0_49])]),c_0_62]) ).
cnf(c_0_173,hypothesis,
( xp = sz00
| aNaturalNumber0(sdtsldt0(sz00,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_161]),c_0_52]),c_0_67])]) ).
cnf(c_0_174,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_175,hypothesis,
esk1_2(xp,sz00) = 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_111,c_0_169]),c_0_170]),c_0_52]),c_0_171])]),c_0_172]) ).
cnf(c_0_176,hypothesis,
aNaturalNumber0(sdtsldt0(sz00,xp)),
inference(sr,[status(thm)],[c_0_173,c_0_172]) ).
fof(c_0_177,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2315])]) ).
cnf(c_0_178,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_174,c_0_89]),c_0_41]) ).
cnf(c_0_179,hypothesis,
sdtasdt0(xp,xk) = sz00,
inference(rw,[status(thm)],[c_0_169,c_0_175]) ).
cnf(c_0_180,hypothesis,
aNaturalNumber0(xk),
inference(rw,[status(thm)],[c_0_176,c_0_170]) ).
cnf(c_0_181,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_177]) ).
cnf(c_0_182,hypothesis,
$false,
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_178,c_0_179]),c_0_104]),c_0_52]),c_0_180])]),c_0_172]),c_0_181]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM510+1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 04:42:08 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 1.11/0.61 # Version: 3.1.0
% 1.11/0.61 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.11/0.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.61 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.11/0.61 # Starting new_bool_3 with 300s (1) cores
% 1.11/0.61 # Starting new_bool_1 with 300s (1) cores
% 1.11/0.61 # Starting sh5l with 300s (1) cores
% 1.11/0.61 # new_bool_3 with pid 12996 completed with status 0
% 1.11/0.61 # Result found by new_bool_3
% 1.11/0.61 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.11/0.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.61 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.11/0.61 # Starting new_bool_3 with 300s (1) cores
% 1.11/0.61 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.11/0.61 # Search class: FGHSF-FFMM21-SFFFFFNN
% 1.11/0.61 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.11/0.61 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 1.11/0.61 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with pid 13001 completed with status 0
% 1.11/0.61 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v
% 1.11/0.61 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.11/0.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.61 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.11/0.61 # Starting new_bool_3 with 300s (1) cores
% 1.11/0.61 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.11/0.61 # Search class: FGHSF-FFMM21-SFFFFFNN
% 1.11/0.61 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.11/0.61 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 1.11/0.61 # Preprocessing time : 0.002 s
% 1.11/0.61 # Presaturation interreduction done
% 1.11/0.61
% 1.11/0.61 # Proof found!
% 1.11/0.61 # SZS status Theorem
% 1.11/0.61 # SZS output start CNFRefutation
% See solution above
% 1.11/0.61 # Parsed axioms : 53
% 1.11/0.61 # Removed by relevancy pruning/SinE : 1
% 1.11/0.61 # Initial clauses : 94
% 1.11/0.61 # Removed in clause preprocessing : 3
% 1.11/0.61 # Initial clauses in saturation : 91
% 1.11/0.61 # Processed clauses : 1278
% 1.11/0.61 # ...of these trivial : 14
% 1.11/0.61 # ...subsumed : 554
% 1.11/0.61 # ...remaining for further processing : 710
% 1.11/0.61 # Other redundant clauses eliminated : 24
% 1.11/0.61 # Clauses deleted for lack of memory : 0
% 1.11/0.61 # Backward-subsumed : 95
% 1.11/0.61 # Backward-rewritten : 202
% 1.11/0.61 # Generated clauses : 3808
% 1.11/0.61 # ...of the previous two non-redundant : 3114
% 1.11/0.61 # ...aggressively subsumed : 0
% 1.11/0.61 # Contextual simplify-reflections : 84
% 1.11/0.61 # Paramodulations : 3771
% 1.11/0.61 # Factorizations : 5
% 1.11/0.61 # NegExts : 0
% 1.11/0.61 # Equation resolutions : 29
% 1.11/0.61 # Disequality decompositions : 0
% 1.11/0.61 # Total rewrite steps : 5434
% 1.11/0.61 # ...of those cached : 5334
% 1.11/0.61 # Propositional unsat checks : 0
% 1.11/0.61 # Propositional check models : 0
% 1.11/0.61 # Propositional check unsatisfiable : 0
% 1.11/0.61 # Propositional clauses : 0
% 1.11/0.61 # Propositional clauses after purity: 0
% 1.11/0.61 # Propositional unsat core size : 0
% 1.11/0.61 # Propositional preprocessing time : 0.000
% 1.11/0.61 # Propositional encoding time : 0.000
% 1.11/0.61 # Propositional solver time : 0.000
% 1.11/0.61 # Success case prop preproc time : 0.000
% 1.11/0.61 # Success case prop encoding time : 0.000
% 1.11/0.61 # Success case prop solver time : 0.000
% 1.11/0.61 # Current number of processed clauses : 319
% 1.11/0.61 # Positive orientable unit clauses : 91
% 1.11/0.61 # Positive unorientable unit clauses: 0
% 1.11/0.61 # Negative unit clauses : 16
% 1.11/0.61 # Non-unit-clauses : 212
% 1.11/0.61 # Current number of unprocessed clauses: 1799
% 1.11/0.61 # ...number of literals in the above : 8068
% 1.11/0.61 # Current number of archived formulas : 0
% 1.11/0.61 # Current number of archived clauses : 383
% 1.11/0.61 # Clause-clause subsumption calls (NU) : 12310
% 1.11/0.61 # Rec. Clause-clause subsumption calls : 5033
% 1.11/0.61 # Non-unit clause-clause subsumptions : 664
% 1.11/0.61 # Unit Clause-clause subsumption calls : 1652
% 1.11/0.61 # Rewrite failures with RHS unbound : 0
% 1.11/0.61 # BW rewrite match attempts : 34
% 1.11/0.61 # BW rewrite match successes : 34
% 1.11/0.61 # Condensation attempts : 0
% 1.11/0.61 # Condensation successes : 0
% 1.11/0.61 # Termbank termtop insertions : 69728
% 1.11/0.61 # Search garbage collected termcells : 1331
% 1.11/0.61
% 1.11/0.61 # -------------------------------------------------
% 1.11/0.61 # User time : 0.110 s
% 1.11/0.61 # System time : 0.008 s
% 1.11/0.61 # Total time : 0.117 s
% 1.11/0.61 # Maximum resident set size: 2044 pages
% 1.11/0.61
% 1.11/0.61 # -------------------------------------------------
% 1.11/0.61 # User time : 0.113 s
% 1.11/0.61 # System time : 0.009 s
% 1.11/0.61 # Total time : 0.121 s
% 1.11/0.61 # Maximum resident set size: 1752 pages
% 1.11/0.61 % E---3.1 exiting
% 1.11/0.61 % E exiting
%------------------------------------------------------------------------------