%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM510+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:22 PM UTC 2026
% Result : Theorem 0.16s 0.53s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 32
% Syntax : Number of formulae : 178 ( 47 unt; 0 def)
% Number of atoms : 653 ( 215 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 781 ( 306 ~; 317 |; 99 &)
% ( 6 <=>; 53 =>; 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 : 207 ( 0 sgn 113 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X3,X1) != sdtpldt0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
fof(m__2287,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X2,X3)
& doDivides0(X1,X2) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(m__2487,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
fof(m__2342,hypothesis,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(m__,conjecture,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& sdtsldt0(xn,xr) != xn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(mDivSum,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X3)
& doDivides0(X1,X2) )
=> doDivides0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtpldt0(X2,X1) = sdtpldt0(X3,X1)
| sdtpldt0(X1,X2) = sdtpldt0(X1,X3) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X2 = sz00
& X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(m__2315,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
fof(c_0_32,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X3,X1) != sdtpldt0(X3,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[mMonAdd]) ).
fof(c_0_33,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
inference(fof_simplification,[status(thm)],[m__2287]) ).
fof(c_0_34,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_35,plain,
! [X63,X64,X66] :
( ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| doDivides0(X63,X64)
| X64 != sdtasdt0(X63,X66)
| ~ aNaturalNumber0(X66) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| X64 = sdtasdt0(X63,esk2_2(X63,X64)) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| aNaturalNumber0(esk2_2(X63,X64)) ) ),
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_36,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_37,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_38,plain,
! [X50,X51,X52] :
( ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| ~ sdtlseqdt0(X50,X51)
| X50 = X51
| ~ aNaturalNumber0(X52)
| sdtlseqdt0(sdtpldt0(X50,X52),sdtpldt0(X51,X52)) )
& ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| ~ sdtlseqdt0(X50,X51)
| X50 = X51
| ~ aNaturalNumber0(X52)
| sdtpldt0(X50,X52) != sdtpldt0(X51,X52) )
& ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| ~ sdtlseqdt0(X50,X51)
| X50 = X51
| ~ aNaturalNumber0(X52)
| sdtlseqdt0(sdtpldt0(X52,X50),sdtpldt0(X52,X51)) )
& ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| ~ sdtlseqdt0(X50,X51)
| X50 = X51
| ~ aNaturalNumber0(X52)
| sdtpldt0(X52,X50) != sdtpldt0(X52,X51) ) ),
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_32])])])])]) ).
fof(c_0_39,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
inference(fof_nnf,[status(thm)],[c_0_33]) ).
fof(c_0_40,plain,
! [X67,X68,X69] :
( ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 = sdtsldt0(X68,X67)
| X68 != sdtasdt0(X67,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| X68 = sdtasdt0(X67,X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| aNaturalNumber0(X69) ) ),
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_34])])])])]) ).
cnf(c_0_41,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_43,plain,
! [X20] :
( ( ~ aNaturalNumber0(X20)
| X20 = sdtasdt0(sz10,X20) )
& ( ~ aNaturalNumber0(X20)
| sdtasdt0(X20,sz10) = X20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_44,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| X2 = X3
| sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_49,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_50,plain,
! [X14] :
( ( ~ aNaturalNumber0(X14)
| X14 = sdtpldt0(sz00,X14) )
& ( ~ aNaturalNumber0(X14)
| sdtpldt0(X14,sz00) = X14 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
cnf(c_0_51,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2)
| X2 = sz00
| X1 = sdtasdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_52,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_42]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_54,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_55,plain,
! [X70,X71,X72] :
( doDivides0(X70,X72)
| ~ doDivides0(X71,X72)
| ~ doDivides0(X70,X71)
| ~ aNaturalNumber0(X72)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X70) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])])]) ).
fof(c_0_56,plain,
! [X45,X46,X47] :
( sdtlseqdt0(X45,X47)
| ~ sdtlseqdt0(X46,X47)
| ~ sdtlseqdt0(X45,X46)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).
cnf(c_0_57,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtpldt0(X1,xn),sdtpldt0(X1,xp)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48])]),c_0_49]) ).
cnf(c_0_58,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_60,plain,
! [X35,X36,X38] :
( ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| sdtlseqdt0(X35,X36)
| sdtpldt0(X35,X38) != X36
| ~ aNaturalNumber0(X38) )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| sdtpldt0(X35,esk1_2(X35,X36)) = X36 )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| aNaturalNumber0(esk1_2(X35,X36)) ) ),
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_61,plain,
! [X5,X6] :
( aNaturalNumber0(sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
fof(c_0_62,plain,
! [X33,X34] :
( X34 = sz00
| X33 = sz00
| sdtasdt0(X33,X34) != sz00
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
cnf(c_0_63,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_64,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]) ).
cnf(c_0_65,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_66,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_67,plain,
( ~ doDivides0(X2,X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_68,hypothesis,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[m__2487]) ).
cnf(c_0_69,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
fof(c_0_70,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
cnf(c_0_71,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_72,hypothesis,
sdtlseqdt0(sdtpldt0(sz00,xn),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_47])]) ).
cnf(c_0_73,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_74,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_75,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_76,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,sdtsldt0(X1,sz10)) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_54])]),c_0_65]) ).
cnf(c_0_77,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_66]) ).
cnf(c_0_78,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xr)
| doDivides0(X1,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_48]),c_0_69])]) ).
fof(c_0_79,negated_conjecture,
~ ( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& sdtsldt0(xn,xr) != xn ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_80,plain,
! [X57,X58] :
( sdtlseqdt0(X58,sdtasdt0(X58,X57))
| X57 = sz00
| ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X57) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])]) ).
fof(c_0_81,plain,
! [X15,X16] :
( sdtasdt0(X15,X16) = sdtasdt0(X16,X15)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_82,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(sz00,xn))
| ~ sdtlseqdt0(X1,sdtpldt0(sz00,xn))
| sdtlseqdt0(X1,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_47])]) ).
cnf(c_0_83,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_73]),c_0_74]) ).
cnf(c_0_84,plain,
( ~ aNaturalNumber0(sdtsldt0(sz00,sz10))
| sdtsldt0(sz00,sz10) = sz00 ),
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_75,c_0_76]),c_0_54])]),c_0_65])]),c_0_59])]) ).
cnf(c_0_85,plain,
( ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtsldt0(X1,sz10)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_64]),c_0_54])]),c_0_65]) ).
cnf(c_0_86,hypothesis,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_64]),c_0_54]),c_0_69])]) ).
fof(c_0_87,negated_conjecture,
~ ( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& sdtsldt0(xn,xr) != xn ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
cnf(c_0_88,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_89,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_90,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,xn)
| sdtlseqdt0(X1,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_58]),c_0_48])]) ).
cnf(c_0_91,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_58]),c_0_59])]) ).
cnf(c_0_92,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| X1 = X3
| sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_93,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mDivLE]) ).
cnf(c_0_94,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_59])]) ).
fof(c_0_95,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[mMulCanc]) ).
cnf(c_0_96,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_63,c_0_86]),c_0_54]),c_0_48])]),c_0_65]) ).
cnf(c_0_97,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_77,c_0_86]),c_0_54]),c_0_48])]),c_0_65]) ).
fof(c_0_98,negated_conjecture,
( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])]) ).
cnf(c_0_99,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_100,hypothesis,
( xr = sz00
| sdtasdt0(xr,sdtsldt0(xn,xr)) = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_68]),c_0_69]),c_0_48])]) ).
cnf(c_0_101,hypothesis,
( aNaturalNumber0(sdtsldt0(xn,xr))
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_68]),c_0_69]),c_0_48])]) ).
cnf(c_0_102,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_103,hypothesis,
sdtlseqdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_59]),c_0_48])]) ).
cnf(c_0_104,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_105,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtpldt0(xn,X1),sdtpldt0(xp,X1)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_46]),c_0_47]),c_0_48])]),c_0_49]) ).
cnf(c_0_106,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_107,plain,
! [X79,X80] :
( sdtlseqdt0(X79,X80)
| X80 = sz00
| ~ doDivides0(X79,X80)
| ~ aNaturalNumber0(X80)
| ~ aNaturalNumber0(X79) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])])]) ).
fof(c_0_108,plain,
! [X73,X74,X75] :
( doDivides0(X73,sdtpldt0(X74,X75))
| ~ doDivides0(X73,X75)
| ~ doDivides0(X73,X74)
| ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X74)
| ~ aNaturalNumber0(X73) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])])]) ).
cnf(c_0_109,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_94]),c_0_59])]) ).
fof(c_0_110,plain,
! [X28,X29,X30] :
( ( ~ aNaturalNumber0(X28)
| X28 = sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X29)
| X29 = X30
| sdtasdt0(X29,X28) != sdtasdt0(X30,X28) )
& ( ~ aNaturalNumber0(X28)
| X28 = sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X29)
| X29 = X30
| sdtasdt0(X28,X29) != sdtasdt0(X28,X30) ) ),
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_95])])])])]) ).
cnf(c_0_111,hypothesis,
sdtsldt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_96]),c_0_97])]) ).
cnf(c_0_112,negated_conjecture,
( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_113,hypothesis,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
| xr = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_69])]),c_0_101]) ).
fof(c_0_114,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
inference(fof_simplification,[status(thm)],[mDefPrime]) ).
cnf(c_0_115,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_102,c_0_103]),c_0_47]),c_0_59])]) ).
cnf(c_0_116,hypothesis,
aNaturalNumber0(esk1_2(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_103]),c_0_47]),c_0_59])]) ).
cnf(c_0_117,hypothesis,
sdtlseqdt0(sdtpldt0(xn,sz00),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_59]),c_0_47])]) ).
cnf(c_0_118,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X2)
| X2 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_119,plain,
( ~ doDivides0(X1,X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_120,plain,
doDivides0(sz10,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_109]),c_0_54]),c_0_59])]) ).
fof(c_0_121,plain,
! [X9,X10] :
( sdtpldt0(X9,X10) = sdtpldt0(X10,X9)
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_122,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| X2 = sz00
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_123,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(rw,[status(thm)],[c_0_96,c_0_111]) ).
cnf(c_0_124,negated_conjecture,
( xr = sz00
| sdtsldt0(xn,xr) = xn ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
fof(c_0_125,plain,
! [X84,X85] :
( ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != X84 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != sz10 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| doDivides0(esk3_1(X84),X84) )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| aNaturalNumber0(esk3_1(X84)) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X85 = X84
| X85 = sz10
| ~ doDivides0(X85,X84)
| ~ aNaturalNumber0(X85) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != sz10 )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != sz00 ) ),
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_114])])])])])]) ).
fof(c_0_126,plain,
! [X25,X26,X27] :
( ( ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X25)
| X26 = X27
| sdtpldt0(X26,X25) != sdtpldt0(X27,X25) )
& ( ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X25)
| X26 = X27
| sdtpldt0(X25,X26) != sdtpldt0(X25,X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])])]) ).
cnf(c_0_127,hypothesis,
esk1_2(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_115]),c_0_116])]) ).
cnf(c_0_128,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(xn,sz00))
| ~ sdtlseqdt0(X1,sdtpldt0(xn,sz00))
| sdtlseqdt0(X1,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_117]),c_0_47])]) ).
cnf(c_0_129,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtasdt0(X1,X2))
| sdtasdt0(X1,X2) = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_52]),c_0_42]) ).
cnf(c_0_130,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(sz10,sdtpldt0(X1,sz00)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_59]),c_0_54])]),c_0_64]) ).
cnf(c_0_131,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_132,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,xn) != xn
| sz10 = X1
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_48]),c_0_54])]) ).
cnf(c_0_133,hypothesis,
( xr = sz00
| sdtasdt0(xr,xn) = xn ),
inference(spm,[status(thm)],[c_0_100,c_0_124]) ).
cnf(c_0_134,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_135,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_136,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[c_0_115,c_0_127]) ).
cnf(c_0_137,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,sdtpldt0(xn,sz00))
| sdtlseqdt0(X1,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_74]),c_0_59]),c_0_48])]) ).
cnf(c_0_138,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz10,X1)
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_76]),c_0_54])]),c_0_85]) ).
cnf(c_0_139,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(sz10,sdtpldt0(sz00,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_59])]) ).
cnf(c_0_140,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_141,hypothesis,
( xn = sz00
| xr = sz10
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_69])]) ).
cnf(c_0_142,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_134]),c_0_54])]) ).
cnf(c_0_143,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_144,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sz00,X1) != xp
| xp = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_47]),c_0_59])]) ).
cnf(c_0_145,hypothesis,
( ~ aNaturalNumber0(sdtpldt0(xn,sz00))
| sdtlseqdt0(sz10,xp)
| sdtpldt0(xn,sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_54])]) ).
cnf(c_0_146,hypothesis,
doDivides0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_136]),c_0_47])]) ).
cnf(c_0_147,hypothesis,
( xr = sz00
| xn = sz00 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142]) ).
cnf(c_0_148,plain,
~ isPrime0(sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_143]),c_0_59])]) ).
cnf(c_0_149,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) != xp
| xp = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_131]),c_0_59])]) ).
cnf(c_0_150,hypothesis,
( sdtlseqdt0(sz10,xp)
| sdtpldt0(xn,sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_74]),c_0_59]),c_0_48])]) ).
cnf(c_0_151,hypothesis,
( sdtlseqdt0(sz10,xp)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_146]),c_0_47]),c_0_54])]) ).
cnf(c_0_152,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_153,hypothesis,
xn = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_147]),c_0_148]) ).
fof(c_0_154,plain,
! [X21] :
( ( ~ aNaturalNumber0(X21)
| sz00 = sdtasdt0(sz00,X21) )
& ( ~ aNaturalNumber0(X21)
| sdtasdt0(X21,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
fof(c_0_155,plain,
! [X31,X32] :
( ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X32 = sz00 )
& ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X31 = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])])]) ).
cnf(c_0_156,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_149,c_0_150]),c_0_48])]),c_0_49]),c_0_151]) ).
cnf(c_0_157,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
fof(c_0_158,plain,
! [X43,X44] :
( X43 = X44
| ~ sdtlseqdt0(X44,X43)
| ~ sdtlseqdt0(X43,X44)
| ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
cnf(c_0_159,hypothesis,
doDivides0(xp,sdtasdt0(sz00,xm)),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_160,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
cnf(c_0_161,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_162,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_155]) ).
cnf(c_0_163,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_102,c_0_156]),c_0_47]),c_0_54])]) ).
cnf(c_0_164,hypothesis,
aNaturalNumber0(esk1_2(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_156]),c_0_47]),c_0_54])]) ).
cnf(c_0_165,hypothesis,
sdtsldt0(sdtasdt0(sz00,xm),xp) = xk,
inference(spm,[status(thm)],[c_0_157,c_0_153]) ).
cnf(c_0_166,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| aNaturalNumber0(xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_152]),c_0_157]),c_0_47])]) ).
cnf(c_0_167,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_168,hypothesis,
doDivides0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_161])]) ).
cnf(c_0_169,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_162,c_0_163]),c_0_164]),c_0_54])]),c_0_65]) ).
cnf(c_0_170,hypothesis,
sdtsldt0(sz00,xp) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_160]),c_0_161])]) ).
cnf(c_0_171,hypothesis,
( aNaturalNumber0(xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_42]),c_0_161]),c_0_48])]) ).
fof(c_0_172,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2315])]) ).
cnf(c_0_173,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(sdtasdt0(X1,X2),X1)
| X2 = sz00
| sdtasdt0(X1,X2) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_88]),c_0_42]) ).
cnf(c_0_174,hypothesis,
sdtasdt0(xp,xk) = sz00,
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_168]),c_0_47]),c_0_59])]),c_0_169]),c_0_170]) ).
cnf(c_0_175,hypothesis,
aNaturalNumber0(xk),
inference(sr,[status(thm)],[c_0_171,c_0_169]) ).
cnf(c_0_176,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_177,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_173,c_0_174]),c_0_103]),c_0_47]),c_0_175])]),c_0_169]),c_0_176]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM510+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:36:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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/benchmark/theBenchmark.p
% 0.16/0.53 % Version: 3.5.1
% 0.16/0.53 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.53 % Starting sh5l with 300s (1) cores
% 0.16/0.53 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 660483 completed with status 0
% 0.16/0.53 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/0.53 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.53 % No SInE strategy applied
% 0.16/0.53 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.16/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.16/0.53 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.16/0.53 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.16/0.53 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 660488 completed with status 0
% 0.16/0.53 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/0.53 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.53 % No SInE strategy applied
% 0.16/0.53 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.16/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.53 % Preprocessing time : 0.002 s
% 0.16/0.53 % Presaturation interreduction done
% 0.16/0.53
% 0.16/0.53 % Proof found!
% 0.16/0.53 % SZS status Theorem
% 0.16/0.53 % SZS output start CNFRefutation
% See solution above
% 0.16/0.54 % Parsed axioms : 53
% 0.16/0.54 % Removed by relevancy pruning/SinE : 0
% 0.16/0.54 % Initial clauses : 97
% 0.16/0.54 % Removed in clause preprocessing : 3
% 0.16/0.54 % Initial clauses in saturation : 94
% 0.16/0.54 % Processed clauses : 1503
% 0.16/0.54 % ...of these trivial : 28
% 0.16/0.54 % ...subsumed : 630
% 0.16/0.54 % ...remaining for further processing : 845
% 0.16/0.54 % Other redundant clauses eliminated : 28
% 0.16/0.54 % Clauses deleted for lack of memory : 0
% 0.16/0.54 % Backward-subsumed : 137
% 0.16/0.54 % Backward-rewritten : 224
% 0.16/0.54 % Generated clauses : 5054
% 0.16/0.54 % ...of the previous two non-redundant : 4240
% 0.16/0.54 % ...aggressively subsumed : 0
% 0.16/0.54 % Contextual simplify-reflections : 103
% 0.16/0.54 % Paramodulations : 5008
% 0.16/0.54 % Factorizations : 5
% 0.16/0.54 % NegExts : 0
% 0.16/0.54 % Equation resolutions : 33
% 0.16/0.54 % Disequality decompositions : 0
% 0.16/0.54 % Total rewrite steps : 7011
% 0.16/0.54 % ...of those cached : 6863
% 0.16/0.54 % Propositional unsat checks : 0
% 0.16/0.54 % Propositional check models : 0
% 0.16/0.54 % Propositional check unsatisfiable : 0
% 0.16/0.54 % Propositional clauses : 0
% 0.16/0.54 % Propositional clauses after purity: 0
% 0.16/0.54 % Propositional unsat core size : 0
% 0.16/0.54 % Propositional preprocessing time : 0.000
% 0.16/0.54 % Propositional encoding time : 0.000
% 0.16/0.54 % Propositional solver time : 0.000
% 0.16/0.54 % Success case prop preproc time : 0.000
% 0.16/0.54 % Success case prop encoding time : 0.000
% 0.16/0.54 % Success case prop solver time : 0.000
% 0.16/0.54 % Current number of processed clauses : 379
% 0.16/0.54 % Positive orientable unit clauses : 135
% 0.16/0.54 % Positive unorientable unit clauses: 0
% 0.16/0.54 % Negative unit clauses : 17
% 0.16/0.54 % Non-unit-clauses : 227
% 0.16/0.54 % Current number of unprocessed clauses: 2637
% 0.16/0.54 % ...number of literals in the above : 11281
% 0.16/0.54 % Current number of archived formulas : 0
% 0.16/0.54 % Current number of archived clauses : 455
% 0.16/0.54 % Clause-clause subsumption calls (NU) : 23563
% 0.16/0.54 % Rec. Clause-clause subsumption calls : 10211
% 0.16/0.54 % Non-unit clause-clause subsumptions : 750
% 0.16/0.54 % Unit Clause-clause subsumption calls : 7299
% 0.16/0.54 % Rewrite failures with RHS unbound : 0
% 0.16/0.54 % BW rewrite match attempts : 61
% 0.16/0.54 % BW rewrite match successes : 57
% 0.16/0.54 % Condensation attempts : 0
% 0.16/0.54 % Condensation successes : 0
% 0.16/0.54 % Termbank termtop insertions : 89811
% 0.16/0.54 % Search garbage collected termcells : 1364
% 0.16/0.54
% 0.16/0.54 % -------------------------------------------------
% 0.16/0.54 % User time : 0.091 s
% 0.16/0.54 % System time : 0.008 s
% 0.16/0.54 % Total time : 0.098 s
% 0.16/0.54 % Maximum resident set size: 3944 pages
% 0.16/0.54
% 0.16/0.54 % -------------------------------------------------
% 0.16/0.54 % User time : 0.348 s
% 0.16/0.54 % System time : 0.028 s
% 0.16/0.54 % Total time : 0.377 s
% 0.16/0.54 % Maximum resident set size: 4608 pages
% 0.16/0.54 % E exiting
%------------------------------------------------------------------------------