%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM516+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 01:49:23 PM UTC 2026
% Result : Theorem 8.86s 1.69s
% Output : CNFRefutation 8.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 32
% Syntax : Number of formulae : 167 ( 32 unt; 0 def)
% Number of atoms : 636 ( 185 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 796 ( 327 ~; 322 |; 97 &)
% ( 7 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 209 ( 2 sgn 110 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(m__2504,hypothesis,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& sdtsldt0(xn,xr) != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2504) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(m__2342,hypothesis,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X2 = sz00
& X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m__2487,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(m__,conjecture,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(m__1870,hypothesis,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
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/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
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/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X2,X3)
& doDivides0(X1,X2) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__2315,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(c_0_32,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_33,plain,
! [X17,X18,X19] :
( sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19))
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_34,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_35,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_39,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_40,plain,
! [X22,X23,X24] :
( ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| sdtasdt0(sdtpldt0(X23,X24),X22) = sdtpldt0(sdtasdt0(X23,X22),sdtasdt0(X24,X22)) )
& ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| sdtasdt0(X22,sdtpldt0(X23,X24)) = sdtpldt0(sdtasdt0(X22,X23),sdtasdt0(X22,X24)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])])]) ).
cnf(c_0_41,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_44,hypothesis,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& sdtsldt0(xn,xr) != xn ),
inference(fof_simplification,[status(thm)],[m__2504]) ).
fof(c_0_45,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
fof(c_0_46,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mDivLE]) ).
cnf(c_0_47,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_48,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_49,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_50,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
fof(c_0_51,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])])]) ).
fof(c_0_52,hypothesis,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& sdtsldt0(xn,xr) != xn ),
inference(fof_nnf,[status(thm)],[c_0_44]) ).
fof(c_0_53,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_45])])]) ).
fof(c_0_54,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_55,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_46])])]) ).
fof(c_0_56,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])])])]) ).
fof(c_0_57,plain,
! [X11,X12,X13] :
( sdtpldt0(sdtpldt0(X11,X12),X13) = sdtpldt0(X11,sdtpldt0(X12,X13))
| ~ aNaturalNumber0(X13)
| ~ aNaturalNumber0(X12)
| ~ aNaturalNumber0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
fof(c_0_58,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])])]) ).
cnf(c_0_59,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz10,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz10,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_37]),c_0_38])]) ).
cnf(c_0_60,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_61,hypothesis,
sdtasdt0(sz10,sz00) = sz00,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_62,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_63,hypothesis,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_64,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_65,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_66,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_54])])])])]) ).
cnf(c_0_67,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X2)
| X2 = sz00 ),
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,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_70,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_71,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_72,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_73,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,X1) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_43])]) ).
cnf(c_0_74,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sdtlseqdt0(X1,sdtsldt0(xn,xr))
| sdtlseqdt0(X1,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).
cnf(c_0_75,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz10,X1)
| X1 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_37]),c_0_38])]) ).
cnf(c_0_76,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,hypothesis,
( sdtlseqdt0(xr,xn)
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_64]),c_0_50])]) ).
fof(c_0_78,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_79,negated_conjecture,
~ ( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_80,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,sdtpldt0(X3,X1)) != sz00
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_81,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_38])]) ).
cnf(c_0_82,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_83,hypothesis,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtlseqdt0(sz10,xn)
| sdtsldt0(xn,xr) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_38])]) ).
cnf(c_0_84,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_76]) ).
cnf(c_0_85,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,xr)
| sdtlseqdt0(X1,xn)
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_77]),c_0_64]),c_0_50])]) ).
fof(c_0_86,plain,
! [X48,X49] :
( ( ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| sdtlseqdt0(X48,X49)
| sdtlseqdt0(X49,X48) )
& ( ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| sdtlseqdt0(X48,X49)
| X49 != X48 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])])]) ).
fof(c_0_87,negated_conjecture,
~ ( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
cnf(c_0_88,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz10) != sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_38]),c_0_43])]),c_0_82]) ).
fof(c_0_89,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_90,hypothesis,
sdtsldt0(xn,xr) != xn,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_91,hypothesis,
( sdtlseqdt0(sz10,xn)
| xr = sz00
| sdtsldt0(xn,xr) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_68]),c_0_50]),c_0_64])]) ).
cnf(c_0_92,hypothesis,
( sdtlseqdt0(sz10,xn)
| xn = sz00
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_75]),c_0_38]),c_0_50])]) ).
cnf(c_0_93,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_94,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_95,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(fof_simplification,[status(thm)],[m__1870]) ).
fof(c_0_96,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])]) ).
cnf(c_0_97,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,sdtpldt0(X2,sz10)) != sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_70]),c_0_38])]),c_0_71]) ).
cnf(c_0_98,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
fof(c_0_99,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])])])])])]) ).
cnf(c_0_100,hypothesis,
( sdtlseqdt0(sz10,xn)
| xr = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]) ).
cnf(c_0_101,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(xp,X1)
| sdtlseqdt0(X1,xp) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
fof(c_0_102,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(fof_nnf,[status(thm)],[c_0_95]) ).
cnf(c_0_103,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_104,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_105,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]) ).
cnf(c_0_106,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,sdtpldt0(sz10,X2)) != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_38])]) ).
cnf(c_0_107,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_108,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,sz10)
| sdtlseqdt0(X1,xn)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_100]),c_0_64]),c_0_38])]) ).
cnf(c_0_109,hypothesis,
( sdtlseqdt0(sz10,xp)
| sdtlseqdt0(xp,sz10) ),
inference(spm,[status(thm)],[c_0_101,c_0_38]) ).
cnf(c_0_110,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_111,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_70]),c_0_94]),c_0_104]),c_0_64])]) ).
fof(c_0_112,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_105])])])])]) ).
cnf(c_0_113,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk1_2(sz10,X2))
| ~ sdtlseqdt0(sz10,X2)
| sdtpldt0(X1,X2) != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_38])]) ).
cnf(c_0_114,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_115,hypothesis,
( sdtlseqdt0(sz10,xp)
| xr = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_94])]),c_0_110]) ).
cnf(c_0_116,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz10,X1)
| sdtlseqdt0(X1,sz10) ),
inference(spm,[status(thm)],[c_0_93,c_0_38]) ).
fof(c_0_117,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]) ).
fof(c_0_118,plain,
! [X39,X40,X41] :
( ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 = sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) != X40
| ~ aNaturalNumber0(X41) )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) = X40 )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| aNaturalNumber0(X41) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])]) ).
cnf(c_0_119,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_120,negated_conjecture,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
| sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_70]),c_0_94]),c_0_104])]) ).
cnf(c_0_121,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_112]) ).
fof(c_0_122,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])])])])])]) ).
cnf(c_0_123,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(sz10,X2)
| sdtpldt0(X1,X2) != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_38])]) ).
cnf(c_0_124,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,sz10)
| sdtlseqdt0(X1,xp)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_115]),c_0_94]),c_0_38])]) ).
cnf(c_0_125,plain,
sdtlseqdt0(sz10,sz10),
inference(spm,[status(thm)],[c_0_116,c_0_38]) ).
fof(c_0_126,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_117])])])])])]) ).
cnf(c_0_127,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X3)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| X1 = sdtmndt0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_128,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_119]),c_0_71]) ).
cnf(c_0_129,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_63]),c_0_64])]),c_0_90]) ).
cnf(c_0_130,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 = sdtasdt0(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
fof(c_0_131,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])])]) ).
cnf(c_0_132,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_133,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
fof(c_0_134,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])])]) ).
cnf(c_0_135,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,xp) != sz00
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_94]),c_0_125]),c_0_38])]) ).
cnf(c_0_136,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_137,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtmndt0(sdtpldt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_127]),c_0_71]),c_0_128]) ).
cnf(c_0_138,negated_conjecture,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| sdtpldt0(sdtpldt0(xm,xp),sdtsldt0(xn,xr)) = sdtpldt0(xn,sdtpldt0(xm,xp)) ),
inference(spm,[status(thm)],[c_0_98,c_0_129]) ).
cnf(c_0_139,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk2_2(sz00,X1))
| ~ doDivides0(sz00,X1)
| X1 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_130]),c_0_43])]) ).
cnf(c_0_140,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_141,plain,
( ~ doDivides0(X2,X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_142,hypothesis,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2342]) ).
fof(c_0_143,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2315])]) ).
cnf(c_0_144,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_84,c_0_132]),c_0_133]),c_0_94])]) ).
cnf(c_0_145,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_146,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_147,hypothesis,
( xp != sz00
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_60]),c_0_43]),c_0_94])]) ).
cnf(c_0_148,plain,
~ isPrime0(sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_136]),c_0_43])]) ).
cnf(c_0_149,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtmndt0(sdtpldt0(X1,X2),X2) = X1 ),
inference(spm,[status(thm)],[c_0_137,c_0_98]) ).
cnf(c_0_150,negated_conjecture,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| sdtmndt0(sdtpldt0(xn,sdtpldt0(xm,xp)),sdtpldt0(xm,xp)) = sdtsldt0(xn,xr) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_151,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_152,plain,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(sz00,X1)
| X1 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_43])]) ).
cnf(c_0_153,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xk)
| ~ doDivides0(X1,xr)
| doDivides0(X1,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_50])]) ).
cnf(c_0_154,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_155,hypothesis,
( aNaturalNumber0(xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_104]),c_0_64])]) ).
cnf(c_0_156,hypothesis,
xp != sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]) ).
cnf(c_0_157,negated_conjecture,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtpldt0(xm,xp)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_64])]),c_0_90]) ).
cnf(c_0_158,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_151]),c_0_145]) ).
cnf(c_0_159,hypothesis,
( ~ aNaturalNumber0(xk)
| ~ doDivides0(sz00,xr) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_43])]),c_0_154]) ).
cnf(c_0_160,hypothesis,
aNaturalNumber0(xk),
inference(sr,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_161,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xm,xp))
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_84]),c_0_68]),c_0_50]),c_0_64])]) ).
cnf(c_0_162,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(sz00,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_42]),c_0_43])]) ).
cnf(c_0_163,hypothesis,
~ doDivides0(sz00,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160])]) ).
cnf(c_0_164,negated_conjecture,
xr = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_71]),c_0_94]),c_0_104])]) ).
cnf(c_0_165,hypothesis,
doDivides0(sz00,sz00),
inference(spm,[status(thm)],[c_0_162,c_0_50]) ).
cnf(c_0_166,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164]),c_0_165])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM516+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 02:37:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 8.86/1.68 % Version: 3.5.1
% 8.86/1.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.86/1.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.86/1.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.86/1.68 % Starting new_bool_3 with 300s (1) cores
% 8.86/1.68 % Starting new_bool_1 with 300s (1) cores
% 8.86/1.68 % Starting sh5l with 300s (1) cores
% 8.86/1.68 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1507245 completed with status 0
% 8.86/1.68 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 8.86/1.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.86/1.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.86/1.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.86/1.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.86/1.68 % No SInE strategy applied
% 8.86/1.68 % Search class: FGHSF-FFMM21-MFFFFFNN
% 8.86/1.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.86/1.68 % Starting SubtermCWHack with 136s (1) cores
% 8.86/1.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 8.86/1.68 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 8.86/1.69 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 8.86/1.69 % Starting new_bool_3 with 136s (1) cores
% 8.86/1.69 % SAT001_MinMin_p005000_rr_RG with pid 1507251 completed with status 0
% 8.86/1.69 % Result found by SAT001_MinMin_p005000_rr_RG
% 8.86/1.69 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.86/1.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.86/1.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.86/1.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.86/1.69 % No SInE strategy applied
% 8.86/1.69 % Search class: FGHSF-FFMM21-MFFFFFNN
% 8.86/1.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.86/1.69 % Starting SubtermCWHack with 136s (1) cores
% 8.86/1.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 8.86/1.69 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 8.86/1.69 % Preprocessing time : 0.003 s
% 8.86/1.69 % Presaturation interreduction done
% 8.86/1.69
% 8.86/1.69 % Proof found!
% 8.86/1.69 % SZS status Theorem
% 8.86/1.69 % SZS output start CNFRefutation
% See solution above
% 8.86/1.69 % Parsed axioms : 55
% 8.86/1.69 % Removed by relevancy pruning/SinE : 0
% 8.86/1.69 % Initial clauses : 100
% 8.86/1.69 % Removed in clause preprocessing : 3
% 8.86/1.69 % Initial clauses in saturation : 97
% 8.86/1.69 % Processed clauses : 5515
% 8.86/1.69 % ...of these trivial : 52
% 8.86/1.69 % ...subsumed : 3604
% 8.86/1.69 % ...remaining for further processing : 1859
% 8.86/1.69 % Other redundant clauses eliminated : 237
% 8.86/1.69 % Clauses deleted for lack of memory : 0
% 8.86/1.69 % Backward-subsumed : 406
% 8.86/1.69 % Backward-rewritten : 339
% 8.86/1.69 % Generated clauses : 44320
% 8.86/1.69 % ...of the previous two non-redundant : 41258
% 8.86/1.69 % ...aggressively subsumed : 0
% 8.86/1.69 % Contextual simplify-reflections : 304
% 8.86/1.69 % Paramodulations : 44048
% 8.86/1.69 % Factorizations : 3
% 8.86/1.69 % NegExts : 0
% 8.86/1.69 % Equation resolutions : 243
% 8.86/1.69 % Disequality decompositions : 0
% 8.86/1.69 % Total rewrite steps : 38341
% 8.86/1.69 % ...of those cached : 38208
% 8.86/1.69 % Propositional unsat checks : 0
% 8.86/1.69 % Propositional check models : 0
% 8.86/1.69 % Propositional check unsatisfiable : 0
% 8.86/1.69 % Propositional clauses : 0
% 8.86/1.69 % Propositional clauses after purity: 0
% 8.86/1.69 % Propositional unsat core size : 0
% 8.86/1.69 % Propositional preprocessing time : 0.000
% 8.86/1.69 % Propositional encoding time : 0.000
% 8.86/1.69 % Propositional solver time : 0.000
% 8.86/1.69 % Success case prop preproc time : 0.000
% 8.86/1.69 % Success case prop encoding time : 0.000
% 8.86/1.69 % Success case prop solver time : 0.000
% 8.86/1.69 % Current number of processed clauses : 988
% 8.86/1.69 % Positive orientable unit clauses : 126
% 8.86/1.69 % Positive unorientable unit clauses: 0
% 8.86/1.69 % Negative unit clauses : 40
% 8.86/1.69 % Non-unit-clauses : 822
% 8.86/1.69 % Current number of unprocessed clauses: 35635
% 8.86/1.69 % ...number of literals in the above : 233359
% 8.86/1.69 % Current number of archived formulas : 0
% 8.86/1.69 % Current number of archived clauses : 860
% 8.86/1.69 % Clause-clause subsumption calls (NU) : 213328
% 8.86/1.69 % Rec. Clause-clause subsumption calls : 74737
% 8.86/1.69 % Non-unit clause-clause subsumptions : 3586
% 8.86/1.69 % Unit Clause-clause subsumption calls : 13037
% 8.86/1.69 % Rewrite failures with RHS unbound : 0
% 8.86/1.69 % BW rewrite match attempts : 38
% 8.86/1.69 % BW rewrite match successes : 38
% 8.86/1.69 % Condensation attempts : 0
% 8.86/1.69 % Condensation successes : 0
% 8.86/1.69 % Termbank termtop insertions : 985837
% 8.86/1.69 % Search garbage collected termcells : 1370
% 8.86/1.69
% 8.86/1.69 % -------------------------------------------------
% 8.86/1.69 % User time : 1.186 s
% 8.86/1.69 % System time : 0.038 s
% 8.86/1.69 % Total time : 1.224 s
% 8.86/1.69 % Maximum resident set size: 3692 pages
% 8.86/1.69
% 8.86/1.69 % -------------------------------------------------
% 8.86/1.69 % User time : 5.608 s
% 8.86/1.69 % System time : 0.212 s
% 8.86/1.69 % Total time : 5.820 s
% 8.86/1.69 % Maximum resident set size: 4608 pages
% 8.86/1.69 % E exiting
%------------------------------------------------------------------------------