TSTP Solution File: NUM507+1 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : NUM507+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:07:27 EDT 2023
% Result : Theorem 1.94s 0.73s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 29
% Syntax : Number of formulae : 187 ( 59 unt; 0 def)
% Number of atoms : 588 ( 175 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 685 ( 284 ~; 307 |; 62 &)
% ( 3 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 197 ( 0 sgn; 84 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mMonAdd) ).
fof(m__2287,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',m__2287) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',m__1837) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mAddComm) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.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/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mDefLE) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mSortsC) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mSortsB) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mLETran) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mAddCanc) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mSortsB_02) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mDefQuot) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',m_MulUnit) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mAddAsso) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mSortsC_01) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mZeroMul) ).
fof(m__2377,hypothesis,
( xk != xp
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',m__2377) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',m__1860) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',m__2306) ).
fof(m__,conjecture,
( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',m__) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mLETotal) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mMulComm) ).
fof(m__2362,hypothesis,
( sdtlseqdt0(xr,xk)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',m__2362) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',m__2342) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mDivLE) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mLEAsym) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mMonMul2) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p',mZeroAdd) ).
fof(c_0_29,plain,
! [X16,X17,X18] :
( ( sdtpldt0(X18,X16) != sdtpldt0(X18,X17)
| ~ aNaturalNumber0(X18)
| X16 = X17
| ~ sdtlseqdt0(X16,X17)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17) )
& ( sdtlseqdt0(sdtpldt0(X18,X16),sdtpldt0(X18,X17))
| ~ aNaturalNumber0(X18)
| X16 = X17
| ~ sdtlseqdt0(X16,X17)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17) )
& ( sdtpldt0(X16,X18) != sdtpldt0(X17,X18)
| ~ aNaturalNumber0(X18)
| X16 = X17
| ~ sdtlseqdt0(X16,X17)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17) )
& ( sdtlseqdt0(sdtpldt0(X16,X18),sdtpldt0(X17,X18))
| ~ aNaturalNumber0(X18)
| X16 = X17
| ~ sdtlseqdt0(X16,X17)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
cnf(c_0_30,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_29]) ).
cnf(c_0_31,hypothesis,
sdtlseqdt0(xm,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_34,hypothesis,
xm != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
fof(c_0_35,plain,
! [X29,X30] :
( ~ aNaturalNumber0(X29)
| ~ aNaturalNumber0(X30)
| sdtpldt0(X29,X30) = sdtpldt0(X30,X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_36,hypothesis,
( sdtlseqdt0(sdtpldt0(X1,xm),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_30,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_37,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_38,plain,
! [X34] :
( ( sdtpldt0(X34,sz00) = X34
| ~ aNaturalNumber0(X34) )
& ( X34 = sdtpldt0(sz00,X34)
| ~ aNaturalNumber0(X34) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_39,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_41,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
fof(c_0_42,plain,
! [X4,X5,X7] :
( ( aNaturalNumber0(esk1_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtpldt0(X4,esk1_2(X4,X5)) = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X7)
| sdtpldt0(X4,X7) != X5
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
cnf(c_0_43,hypothesis,
( sdtlseqdt0(sdtpldt0(X1,xm),sdtpldt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_32])]) ).
cnf(c_0_44,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_46,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_30,c_0_39]),c_0_32]),c_0_40])]),c_0_41]) ).
cnf(c_0_47,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,hypothesis,
sdtlseqdt0(xm,sdtpldt0(xp,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_33])]) ).
fof(c_0_49,plain,
! [X27,X28] :
( ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X28)
| aNaturalNumber0(sdtpldt0(X27,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_50,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_51,plain,
! [X11,X12,X13] :
( ~ aNaturalNumber0(X11)
| ~ aNaturalNumber0(X12)
| ~ aNaturalNumber0(X13)
| ~ sdtlseqdt0(X11,X12)
| ~ sdtlseqdt0(X12,X13)
| sdtlseqdt0(X11,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_52,hypothesis,
( sdtlseqdt0(sdtpldt0(X1,xn),sdtpldt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_37]),c_0_32])]) ).
cnf(c_0_53,hypothesis,
( sdtpldt0(xm,esk1_2(xm,sdtpldt0(xp,sz00))) = sdtpldt0(xp,sz00)
| ~ aNaturalNumber0(sdtpldt0(xp,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_33])]) ).
cnf(c_0_54,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,hypothesis,
( aNaturalNumber0(esk1_2(xm,sdtpldt0(xp,sz00)))
| ~ aNaturalNumber0(sdtpldt0(xp,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_48]),c_0_33])]) ).
cnf(c_0_56,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,hypothesis,
sdtlseqdt0(xn,sdtpldt0(xp,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_44]),c_0_45]),c_0_40])]) ).
cnf(c_0_58,hypothesis,
sdtpldt0(xm,esk1_2(xm,sdtpldt0(xp,sz00))) = sdtpldt0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_45]),c_0_32])]) ).
cnf(c_0_59,hypothesis,
aNaturalNumber0(esk1_2(xm,sdtpldt0(xp,sz00))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_54]),c_0_45]),c_0_32])]) ).
cnf(c_0_60,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_61,hypothesis,
( sdtlseqdt0(X1,sdtpldt0(xp,sz00))
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(sdtpldt0(xp,sz00))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_40])]) ).
cnf(c_0_62,hypothesis,
aNaturalNumber0(sdtpldt0(xp,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_58]),c_0_59]),c_0_33])]) ).
cnf(c_0_63,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_60]),c_0_54]) ).
cnf(c_0_64,hypothesis,
( sdtlseqdt0(X1,sdtpldt0(xp,sz00))
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]) ).
cnf(c_0_65,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_44]),c_0_45])]) ).
cnf(c_0_66,hypothesis,
sdtlseqdt0(sz00,sdtpldt0(xp,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_45]),c_0_40])]) ).
cnf(c_0_67,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_68,hypothesis,
sdtpldt0(sz00,esk1_2(sz00,sdtpldt0(xp,sz00))) = sdtpldt0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_66]),c_0_62]),c_0_45])]) ).
cnf(c_0_69,hypothesis,
aNaturalNumber0(esk1_2(sz00,sdtpldt0(xp,sz00))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_66]),c_0_62]),c_0_45])]) ).
cnf(c_0_70,hypothesis,
sdtlseqdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_65]),c_0_45]),c_0_33])]) ).
fof(c_0_71,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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_72,hypothesis,
esk1_2(sz00,sdtpldt0(xp,sz00)) = sdtpldt0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_68]),c_0_69])]) ).
cnf(c_0_73,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_47,c_0_70]),c_0_32]),c_0_45])]) ).
cnf(c_0_74,hypothesis,
aNaturalNumber0(esk1_2(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_70]),c_0_32]),c_0_45])]) ).
cnf(c_0_75,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_76,hypothesis,
sdtpldt0(sz00,sdtpldt0(xp,sz00)) = sdtpldt0(xp,sz00),
inference(rw,[status(thm)],[c_0_68,c_0_72]) ).
cnf(c_0_77,hypothesis,
esk1_2(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_73]),c_0_74])]) ).
cnf(c_0_78,hypothesis,
( X1 = sz00
| sdtpldt0(X1,sdtpldt0(xp,sz00)) != sdtpldt0(xp,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_45]),c_0_62])]) ).
cnf(c_0_79,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[c_0_73,c_0_77]) ).
cnf(c_0_80,plain,
( sdtlseqdt0(X1,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_37]) ).
cnf(c_0_81,hypothesis,
( X1 = sz00
| sdtpldt0(X1,xp) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_37]),c_0_79]),c_0_79]),c_0_45]),c_0_32])]) ).
cnf(c_0_82,hypothesis,
sdtlseqdt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_79]),c_0_32]),c_0_45])]) ).
fof(c_0_83,plain,
! [X65,X66,X68] :
( ( aNaturalNumber0(esk2_2(X65,X66))
| ~ doDivides0(X65,X66)
| ~ aNaturalNumber0(X65)
| ~ aNaturalNumber0(X66) )
& ( X66 = sdtasdt0(X65,esk2_2(X65,X66))
| ~ doDivides0(X65,X66)
| ~ aNaturalNumber0(X65)
| ~ aNaturalNumber0(X66) )
& ( ~ aNaturalNumber0(X68)
| X66 != sdtasdt0(X65,X68)
| doDivides0(X65,X66)
| ~ aNaturalNumber0(X65)
| ~ aNaturalNumber0(X66) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_84,plain,
! [X52,X53] :
( ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| aNaturalNumber0(sdtasdt0(X52,X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_85,hypothesis,
( X1 = sz00
| sdtpldt0(xp,X1) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_37]),c_0_32])]) ).
cnf(c_0_86,hypothesis,
sdtpldt0(xp,esk1_2(xp,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_82]),c_0_32])]) ).
cnf(c_0_87,hypothesis,
aNaturalNumber0(esk1_2(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_82]),c_0_32])]) ).
fof(c_0_88,plain,
! [X78,X79,X80] :
( ( aNaturalNumber0(X80)
| X80 != sdtsldt0(X79,X78)
| X78 = sz00
| ~ doDivides0(X78,X79)
| ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X79) )
& ( X79 = sdtasdt0(X78,X80)
| X80 != sdtsldt0(X79,X78)
| X78 = sz00
| ~ doDivides0(X78,X79)
| ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X79) )
& ( ~ aNaturalNumber0(X80)
| X79 != sdtasdt0(X78,X80)
| X80 = sdtsldt0(X79,X78)
| X78 = sz00
| ~ doDivides0(X78,X79)
| ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X79) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_89,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_90,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
fof(c_0_91,plain,
! [X72] :
( ( sdtasdt0(X72,sz10) = X72
| ~ aNaturalNumber0(X72) )
& ( X72 = sdtasdt0(sz10,X72)
| ~ aNaturalNumber0(X72) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
fof(c_0_92,plain,
! [X31,X32,X33] :
( ~ aNaturalNumber0(X31)
| ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X33)
| sdtpldt0(sdtpldt0(X31,X32),X33) = sdtpldt0(X31,sdtpldt0(X32,X33)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_93,hypothesis,
esk1_2(xp,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).
cnf(c_0_94,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_88]) ).
cnf(c_0_95,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_89]),c_0_90]) ).
cnf(c_0_96,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_97,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_98,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_99,hypothesis,
sdtpldt0(xp,sz00) = xp,
inference(rw,[status(thm)],[c_0_86,c_0_93]) ).
cnf(c_0_100,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
fof(c_0_101,plain,
! [X63,X64] :
( ~ aNaturalNumber0(X63)
| ~ aNaturalNumber0(X64)
| sdtasdt0(X63,X64) != sz00
| X63 = sz00
| X64 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_102,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_94]) ).
cnf(c_0_103,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
cnf(c_0_104,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_105,hypothesis,
( sdtpldt0(xp,sdtpldt0(sz00,X1)) = sdtpldt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_45]),c_0_32])]) ).
cnf(c_0_106,hypothesis,
sdtlseqdt0(xk,xp),
inference(split_conjunct,[status(thm)],[m__2377]) ).
cnf(c_0_107,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_100]) ).
cnf(c_0_108,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_109,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
fof(c_0_110,negated_conjecture,
~ ( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_111,plain,
! [X14,X15] :
( ( X15 != X14
| sdtlseqdt0(X14,X15)
| ~ aNaturalNumber0(X14)
| ~ aNaturalNumber0(X15) )
& ( sdtlseqdt0(X15,X14)
| sdtlseqdt0(X14,X15)
| ~ aNaturalNumber0(X14)
| ~ aNaturalNumber0(X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_112,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_113,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_102,c_0_103]),c_0_97])]),c_0_104]) ).
fof(c_0_114,plain,
! [X54,X55] :
( ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X55)
| sdtasdt0(X54,X55) = sdtasdt0(X55,X54) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_115,hypothesis,
( sdtlseqdt0(xp,sdtpldt0(xp,X1))
| ~ aNaturalNumber0(sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_105]),c_0_32])]) ).
cnf(c_0_116,hypothesis,
( aNaturalNumber0(sdtpldt0(xp,X1))
| ~ aNaturalNumber0(sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_105]),c_0_32])]) ).
cnf(c_0_117,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_106]),c_0_32])]) ).
cnf(c_0_118,hypothesis,
sdtlseqdt0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2362]) ).
cnf(c_0_119,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_120,hypothesis,
( xp = sz00
| aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]),c_0_32])]) ).
fof(c_0_121,negated_conjecture,
( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(fof_nnf,[status(thm)],[c_0_110]) ).
cnf(c_0_122,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_123,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_112,c_0_113]),c_0_97])]),c_0_104])]),c_0_45])]) ).
cnf(c_0_124,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_107,c_0_103]),c_0_97])]),c_0_104]) ).
cnf(c_0_125,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_126,hypothesis,
sdtlseqdt0(xp,sdtpldt0(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_79]),c_0_32])]) ).
cnf(c_0_127,hypothesis,
aNaturalNumber0(sdtpldt0(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_79]),c_0_32])]) ).
cnf(c_0_128,hypothesis,
sdtpldt0(xm,esk1_2(xm,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_129,hypothesis,
aNaturalNumber0(esk1_2(xm,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_31]),c_0_32]),c_0_33])]) ).
fof(c_0_130,plain,
! [X25,X26] :
( ~ aNaturalNumber0(X25)
| ~ aNaturalNumber0(X26)
| ~ doDivides0(X25,X26)
| X26 = sz00
| sdtlseqdt0(X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
cnf(c_0_131,plain,
( X1 = sdtpldt0(X2,X3)
| sdtpldt0(X1,X4) != sdtpldt0(X2,sdtpldt0(X3,X4))
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_98]),c_0_54]) ).
fof(c_0_132,plain,
! [X9,X10] :
( ~ aNaturalNumber0(X9)
| ~ aNaturalNumber0(X10)
| ~ sdtlseqdt0(X9,X10)
| ~ sdtlseqdt0(X10,X9)
| X9 = X10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_133,hypothesis,
( sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119])]) ).
cnf(c_0_134,hypothesis,
( xp = sz00
| aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_90]),c_0_33]),c_0_40])]) ).
cnf(c_0_135,negated_conjecture,
( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_136,plain,
( X1 = X2
| sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_122]) ).
cnf(c_0_137,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_45])]) ).
cnf(c_0_138,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_125]) ).
cnf(c_0_139,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_88]) ).
cnf(c_0_140,hypothesis,
( sdtlseqdt0(X1,sdtpldt0(xp,xp))
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_126]),c_0_127]),c_0_32])]) ).
cnf(c_0_141,hypothesis,
sdtlseqdt0(esk1_2(xm,xp),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_128]),c_0_129]),c_0_33])]) ).
cnf(c_0_142,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_143,hypothesis,
( X1 = xp
| sdtpldt0(X1,X2) != sdtpldt0(xp,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_105]),c_0_99]),c_0_45]),c_0_32])]) ).
cnf(c_0_144,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_145,hypothesis,
( xp = sz00
| sdtlseqdt0(xr,xp) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_146,negated_conjecture,
( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| xr = xp
| sdtlseqdt0(xp,xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_32]),c_0_119])]) ).
fof(c_0_147,plain,
! [X23,X24] :
( ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X24)
| X23 = sz00
| sdtlseqdt0(X24,sdtasdt0(X24,X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
cnf(c_0_148,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_137]),c_0_45])]) ).
cnf(c_0_149,plain,
( doDivides0(sdtsldt0(X1,sz10),X1)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_113]),c_0_97])]),c_0_124]) ).
cnf(c_0_150,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_139]),c_0_90]),c_0_95]) ).
cnf(c_0_151,hypothesis,
sdtlseqdt0(esk1_2(xm,xp),sdtpldt0(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_129])]) ).
cnf(c_0_152,plain,
( sdtasdt0(X1,X2) = sz00
| sdtlseqdt0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_95]),c_0_90]) ).
cnf(c_0_153,hypothesis,
( X1 = xp
| sdtpldt0(X1,X2) != sdtpldt0(X2,xp)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_37]),c_0_32])]) ).
cnf(c_0_154,hypothesis,
( xp = sz00
| xr = xp
| ~ sdtlseqdt0(xp,xr) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_119]),c_0_32])]) ).
cnf(c_0_155,negated_conjecture,
( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| xr = xp
| sdtlseqdt0(xp,xr) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_54]),c_0_33]),c_0_40])]) ).
cnf(c_0_156,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_157,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_148]),c_0_45]),c_0_97])]) ).
cnf(c_0_158,plain,
( doDivides0(X1,sdtasdt0(sz10,X1))
| ~ aNaturalNumber0(sdtasdt0(sz10,X1))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_97])]),c_0_104]) ).
cnf(c_0_159,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_160,hypothesis,
( sdtlseqdt0(X1,sdtpldt0(xp,xp))
| ~ sdtlseqdt0(X1,esk1_2(xm,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_151]),c_0_127]),c_0_129])]) ).
cnf(c_0_161,plain,
( X1 = sz00
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_113]),c_0_97])]),c_0_124]) ).
cnf(c_0_162,hypothesis,
( X1 = xp
| sdtpldt0(X2,X1) != sdtpldt0(X2,xp)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_153,c_0_37]) ).
cnf(c_0_163,hypothesis,
( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| xr = xp
| xp = sz00 ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
fof(c_0_164,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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
cnf(c_0_165,plain,
sdtlseqdt0(sz00,sz00),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_45]),c_0_97])]),c_0_104]) ).
cnf(c_0_166,plain,
doDivides0(sz10,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_97])]) ).
cnf(c_0_167,hypothesis,
sdtpldt0(xp,esk1_2(xm,xp)) != xp,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_128]),c_0_129]),c_0_33])]),c_0_34]) ).
cnf(c_0_168,hypothesis,
( esk1_2(xm,xp) = sz00
| sdtlseqdt0(sz10,sdtpldt0(xp,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_97]),c_0_129])]) ).
cnf(c_0_169,hypothesis,
( xp = sz00
| xr = xp
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_119])]) ).
cnf(c_0_170,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_171,plain,
sdtpldt0(sz00,esk1_2(sz00,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_165]),c_0_45])]) ).
cnf(c_0_172,plain,
aNaturalNumber0(esk1_2(sz00,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_165]),c_0_45])]) ).
cnf(c_0_173,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X3,X1)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(spm,[status(thm)],[c_0_56,c_0_122]) ).
cnf(c_0_174,plain,
sdtlseqdt0(sz10,sz10),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_166]),c_0_97])]),c_0_104]) ).
cnf(c_0_175,hypothesis,
sdtlseqdt0(sz10,sdtpldt0(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_99])]) ).
cnf(c_0_176,hypothesis,
( xr = xk
| ~ sdtlseqdt0(xk,xr)
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_118]),c_0_119])]) ).
cnf(c_0_177,hypothesis,
( xr = xp
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_54]),c_0_33]),c_0_40])]) ).
cnf(c_0_178,hypothesis,
xk != xp,
inference(split_conjunct,[status(thm)],[m__2377]) ).
cnf(c_0_179,plain,
esk1_2(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_45]),c_0_172])]) ).
cnf(c_0_180,plain,
( X1 = sz00
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_65]),c_0_45])]) ).
cnf(c_0_181,plain,
( sdtlseqdt0(sz10,X1)
| sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_97])]) ).
cnf(c_0_182,hypothesis,
( sdtpldt0(xp,xp) = sz10
| ~ sdtlseqdt0(sdtpldt0(xp,xp),sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_175]),c_0_97]),c_0_127])]) ).
cnf(c_0_183,hypothesis,
xp = sz00,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_106])]),c_0_178]),c_0_134]) ).
cnf(c_0_184,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(rw,[status(thm)],[c_0_171,c_0_179]) ).
cnf(c_0_185,plain,
sdtlseqdt0(sz00,sz10),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_97]),c_0_45])]),c_0_104]) ).
cnf(c_0_186,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_183]),c_0_183]),c_0_184]),c_0_183]),c_0_183]),c_0_184]),c_0_185])]),c_0_104]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : NUM507+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.10 % Command : run_E %s %d THM
% 0.09/0.30 % Computer : n023.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 2400
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Oct 2 14:00:22 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.wP8emEwfK3/E---3.1_30543.p
% 1.94/0.73 # Version: 3.1pre001
% 1.94/0.73 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.94/0.73 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.94/0.73 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.94/0.73 # Starting new_bool_3 with 300s (1) cores
% 1.94/0.73 # Starting new_bool_1 with 300s (1) cores
% 1.94/0.73 # Starting sh5l with 300s (1) cores
% 1.94/0.73 # sh5l with pid 30623 completed with status 0
% 1.94/0.73 # Result found by sh5l
% 1.94/0.73 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.94/0.73 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.94/0.73 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.94/0.73 # Starting new_bool_3 with 300s (1) cores
% 1.94/0.73 # Starting new_bool_1 with 300s (1) cores
% 1.94/0.73 # Starting sh5l with 300s (1) cores
% 1.94/0.73 # SinE strategy is gf500_gu_R04_F100_L20000
% 1.94/0.73 # Search class: FGHSF-FFMM21-SFFFFFNN
% 1.94/0.73 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.94/0.73 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 1.94/0.73 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with pid 30625 completed with status 0
% 1.94/0.73 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v
% 1.94/0.73 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.94/0.73 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.94/0.73 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.94/0.73 # Starting new_bool_3 with 300s (1) cores
% 1.94/0.73 # Starting new_bool_1 with 300s (1) cores
% 1.94/0.73 # Starting sh5l with 300s (1) cores
% 1.94/0.73 # SinE strategy is gf500_gu_R04_F100_L20000
% 1.94/0.73 # Search class: FGHSF-FFMM21-SFFFFFNN
% 1.94/0.73 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.94/0.73 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 1.94/0.73 # Preprocessing time : 0.002 s
% 1.94/0.73 # Presaturation interreduction done
% 1.94/0.73
% 1.94/0.73 # Proof found!
% 1.94/0.73 # SZS status Theorem
% 1.94/0.73 # SZS output start CNFRefutation
% See solution above
% 1.94/0.73 # Parsed axioms : 51
% 1.94/0.73 # Removed by relevancy pruning/SinE : 1
% 1.94/0.73 # Initial clauses : 92
% 1.94/0.73 # Removed in clause preprocessing : 3
% 1.94/0.73 # Initial clauses in saturation : 89
% 1.94/0.73 # Processed clauses : 2770
% 1.94/0.73 # ...of these trivial : 84
% 1.94/0.73 # ...subsumed : 1493
% 1.94/0.73 # ...remaining for further processing : 1193
% 1.94/0.73 # Other redundant clauses eliminated : 77
% 1.94/0.73 # Clauses deleted for lack of memory : 0
% 1.94/0.73 # Backward-subsumed : 76
% 1.94/0.73 # Backward-rewritten : 559
% 1.94/0.73 # Generated clauses : 13786
% 1.94/0.73 # ...of the previous two non-redundant : 11445
% 1.94/0.73 # ...aggressively subsumed : 0
% 1.94/0.73 # Contextual simplify-reflections : 103
% 1.94/0.73 # Paramodulations : 13687
% 1.94/0.73 # Factorizations : 7
% 1.94/0.73 # NegExts : 0
% 1.94/0.73 # Equation resolutions : 92
% 1.94/0.73 # Total rewrite steps : 16455
% 1.94/0.73 # Propositional unsat checks : 0
% 1.94/0.73 # Propositional check models : 0
% 1.94/0.73 # Propositional check unsatisfiable : 0
% 1.94/0.73 # Propositional clauses : 0
% 1.94/0.73 # Propositional clauses after purity: 0
% 1.94/0.73 # Propositional unsat core size : 0
% 1.94/0.73 # Propositional preprocessing time : 0.000
% 1.94/0.73 # Propositional encoding time : 0.000
% 1.94/0.73 # Propositional solver time : 0.000
% 1.94/0.73 # Success case prop preproc time : 0.000
% 1.94/0.73 # Success case prop encoding time : 0.000
% 1.94/0.73 # Success case prop solver time : 0.000
% 1.94/0.73 # Current number of processed clauses : 468
% 1.94/0.73 # Positive orientable unit clauses : 108
% 1.94/0.73 # Positive unorientable unit clauses: 0
% 1.94/0.73 # Negative unit clauses : 8
% 1.94/0.73 # Non-unit-clauses : 352
% 1.94/0.73 # Current number of unprocessed clauses: 8578
% 1.94/0.73 # ...number of literals in the above : 38700
% 1.94/0.73 # Current number of archived formulas : 0
% 1.94/0.73 # Current number of archived clauses : 717
% 1.94/0.73 # Clause-clause subsumption calls (NU) : 50713
% 1.94/0.73 # Rec. Clause-clause subsumption calls : 30170
% 1.94/0.73 # Non-unit clause-clause subsumptions : 1571
% 1.94/0.73 # Unit Clause-clause subsumption calls : 2104
% 1.94/0.73 # Rewrite failures with RHS unbound : 0
% 1.94/0.73 # BW rewrite match attempts : 166
% 1.94/0.73 # BW rewrite match successes : 52
% 1.94/0.73 # Condensation attempts : 0
% 1.94/0.73 # Condensation successes : 0
% 1.94/0.73 # Termbank termtop insertions : 264461
% 1.94/0.73
% 1.94/0.73 # -------------------------------------------------
% 1.94/0.73 # User time : 0.297 s
% 1.94/0.73 # System time : 0.009 s
% 1.94/0.73 # Total time : 0.306 s
% 1.94/0.73 # Maximum resident set size: 2040 pages
% 1.94/0.73
% 1.94/0.73 # -------------------------------------------------
% 1.94/0.73 # User time : 0.300 s
% 1.94/0.73 # System time : 0.010 s
% 1.94/0.73 # Total time : 0.310 s
% 1.94/0.73 # Maximum resident set size: 1736 pages
% 1.94/0.73 % E---3.1 exiting
%------------------------------------------------------------------------------