TSTP Solution File: NUM503+1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : NUM503+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:56:04 EDT 2023
% Result : Theorem 4.71s 1.03s
% Output : CNFRefutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 35
% Syntax : Number of formulae : 254 ( 91 unt; 0 def)
% Number of atoms : 805 ( 268 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 938 ( 387 ~; 419 |; 89 &)
% ( 4 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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; 6 con; 0-2 aty)
% Number of variables : 263 ( 1 sgn; 116 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.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.J7nVQm4FkX/E---3.1_13044.p',mDefQuot) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',m_MulUnit) ).
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mMonAdd) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mSortsC_01) ).
fof(m__2287,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',m__2287) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',m__1837) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',m_AddZero) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mZeroMul) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mLETran) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mSortsC) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mSortsB) ).
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.J7nVQm4FkX/E---3.1_13044.p',mDefLE) ).
fof(mDivSum,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,X3) )
=> doDivides0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mDivSum) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mAddComm) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mMulComm) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mDefDiff) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mMulAsso) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',m_MulZero) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mDivLE) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mAMDistr) ).
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.J7nVQm4FkX/E---3.1_13044.p',mAddCanc) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',m__1860) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',m__2306) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mZeroAdd) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( X1 != sz00
& X2 != X3
& sdtlseqdt0(X2,X3) )
=> ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mMonMul) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mMonMul2) ).
fof(m__,conjecture,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',m__) ).
fof(m__2389,hypothesis,
sdtlseqdt0(xp,xk),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',m__2389) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X2,X3) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mDivTrans) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mLETotal) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',mLEAsym) ).
fof(m__2075,hypothesis,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',m__2075) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p',m__2315) ).
fof(c_0_35,plain,
! [X60,X61,X63] :
( ( aNaturalNumber0(esk2_2(X60,X61))
| ~ doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) )
& ( X61 = sdtasdt0(X60,esk2_2(X60,X61))
| ~ doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) )
& ( ~ aNaturalNumber0(X63)
| X61 != sdtasdt0(X60,X63)
| doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) ) ),
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_36,plain,
! [X6,X7] :
( ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X7)
| aNaturalNumber0(sdtasdt0(X6,X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_37,plain,
! [X64,X65,X66] :
( ( aNaturalNumber0(X66)
| X66 != sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) )
& ( X65 = sdtasdt0(X64,X66)
| X66 != sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) )
& ( ~ aNaturalNumber0(X66)
| X65 != sdtasdt0(X64,X66)
| X66 = sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_38,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_40,plain,
! [X19] :
( ( sdtasdt0(X19,sz10) = X19
| ~ aNaturalNumber0(X19) )
& ( X19 = sdtasdt0(sz10,X19)
| ~ aNaturalNumber0(X19) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
fof(c_0_41,plain,
! [X49,X50,X51] :
( ( sdtpldt0(X51,X49) != sdtpldt0(X51,X50)
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtlseqdt0(sdtpldt0(X51,X49),sdtpldt0(X51,X50))
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtpldt0(X49,X51) != sdtpldt0(X50,X51)
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtlseqdt0(sdtpldt0(X49,X51),sdtpldt0(X50,X51))
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
cnf(c_0_42,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_37]) ).
cnf(c_0_43,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_38]),c_0_39]) ).
cnf(c_0_44,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_46,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_41]) ).
cnf(c_0_47,hypothesis,
sdtlseqdt0(xm,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_49,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_50,hypothesis,
xm != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
fof(c_0_51,plain,
! [X13] :
( ( sdtpldt0(X13,sz00) = X13
| ~ aNaturalNumber0(X13) )
& ( X13 = sdtpldt0(sz00,X13)
| ~ aNaturalNumber0(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_52,plain,
! [X32,X33] :
( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X33)
| sdtasdt0(X32,X33) != sz00
| X32 = sz00
| X33 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_53,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_54,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_55,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_56,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_57,plain,
! [X44,X45,X46] :
( ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X45)
| ~ aNaturalNumber0(X46)
| ~ sdtlseqdt0(X44,X45)
| ~ sdtlseqdt0(X45,X46)
| sdtlseqdt0(X44,X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_58,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_46,c_0_47]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_59,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_60,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_61,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,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_53,c_0_54]),c_0_45])]),c_0_55]) ).
cnf(c_0_63,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,hypothesis,
sdtlseqdt0(sdtpldt0(sz00,xm),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_48])]) ).
fof(c_0_66,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| aNaturalNumber0(sdtpldt0(X4,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_67,plain,
! [X34,X35,X37] :
( ( aNaturalNumber0(esk1_2(X34,X35))
| ~ sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) )
& ( sdtpldt0(X34,esk1_2(X34,X35)) = X35
| ~ sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) )
& ( ~ aNaturalNumber0(X37)
| sdtpldt0(X34,X37) != X35
| sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) ) ),
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_68,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_61,c_0_62]),c_0_45])]),c_0_55])]),c_0_60])]) ).
cnf(c_0_69,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_63,c_0_54]),c_0_45])]),c_0_55]) ).
cnf(c_0_70,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,sdtpldt0(sz00,xm))
| ~ aNaturalNumber0(sdtpldt0(sz00,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_48])]) ).
cnf(c_0_71,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_72,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_73,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_60])]) ).
cnf(c_0_74,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,sdtpldt0(sz00,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_49]),c_0_60])]) ).
cnf(c_0_75,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_72]),c_0_71]) ).
fof(c_0_76,plain,
! [X70,X71,X72] :
( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X72)
| ~ doDivides0(X70,X71)
| ~ doDivides0(X70,X72)
| doDivides0(X70,sdtpldt0(X71,X72)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_77,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_73]),c_0_60])]) ).
cnf(c_0_78,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_79,hypothesis,
sdtlseqdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_60]),c_0_49])]) ).
cnf(c_0_80,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_81,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_82,plain,
doDivides0(sz10,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_77]),c_0_45]),c_0_60])]) ).
fof(c_0_83,plain,
! [X8,X9] :
( ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X9)
| sdtpldt0(X8,X9) = sdtpldt0(X9,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_84,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_78,c_0_79]),c_0_48]),c_0_60])]) ).
cnf(c_0_85,hypothesis,
aNaturalNumber0(esk1_2(sz00,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_48]),c_0_60])]) ).
cnf(c_0_86,plain,
( doDivides0(sz10,sdtpldt0(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_60]),c_0_45])]),c_0_54]) ).
cnf(c_0_87,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_88,hypothesis,
esk1_2(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_84]),c_0_85])]) ).
cnf(c_0_89,plain,
( doDivides0(sz10,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_60])]) ).
cnf(c_0_90,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[c_0_84,c_0_88]) ).
cnf(c_0_91,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_92,hypothesis,
doDivides0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_48])]) ).
cnf(c_0_93,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_94,plain,
! [X14,X15] :
( ~ aNaturalNumber0(X14)
| ~ aNaturalNumber0(X15)
| sdtasdt0(X14,X15) = sdtasdt0(X15,X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_95,hypothesis,
sdtasdt0(sz10,esk2_2(sz10,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_45]),c_0_48])]) ).
cnf(c_0_96,hypothesis,
aNaturalNumber0(esk2_2(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_92]),c_0_48]),c_0_45])]) ).
cnf(c_0_97,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_98,hypothesis,
esk2_2(sz10,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_95]),c_0_96])]) ).
cnf(c_0_99,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_97]) ).
cnf(c_0_100,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_101,plain,
! [X38,X39,X40] :
( ( aNaturalNumber0(X40)
| X40 != sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) )
& ( sdtpldt0(X38,X40) = X39
| X40 != sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) )
& ( ~ aNaturalNumber0(X40)
| sdtpldt0(X38,X40) != X39
| X40 = sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
fof(c_0_102,plain,
! [X16,X17,X18] :
( ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17)
| ~ aNaturalNumber0(X18)
| sdtasdt0(sdtasdt0(X16,X17),X18) = sdtasdt0(X16,sdtasdt0(X17,X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_103,plain,
! [X20] :
( ( sdtasdt0(X20,sz00) = sz00
| ~ aNaturalNumber0(X20) )
& ( sz00 = sdtasdt0(sz00,X20)
| ~ aNaturalNumber0(X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_104,hypothesis,
sdtasdt0(sz10,xp) = xp,
inference(rw,[status(thm)],[c_0_95,c_0_98]) ).
cnf(c_0_105,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_99,c_0_62]),c_0_45])]),c_0_69]) ).
cnf(c_0_106,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_100]),c_0_39]),c_0_43]) ).
cnf(c_0_107,plain,
( X1 = sdtmndt0(X3,X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_108,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_109,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_110,hypothesis,
doDivides0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_104]),c_0_48]),c_0_45])]) ).
fof(c_0_111,plain,
! [X76,X77] :
( ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77)
| ~ doDivides0(X76,X77)
| X77 = sz00
| sdtlseqdt0(X76,X77) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
cnf(c_0_112,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_105,c_0_106]),c_0_45])]),c_0_55]) ).
cnf(c_0_113,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_114,plain,
! [X21,X22,X23] :
( ( sdtasdt0(X21,sdtpldt0(X22,X23)) = sdtpldt0(sdtasdt0(X21,X22),sdtasdt0(X21,X23))
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X23) )
& ( sdtasdt0(sdtpldt0(X22,X23),X21) = sdtpldt0(sdtasdt0(X22,X21),sdtasdt0(X23,X21))
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X23) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_115,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_107]),c_0_71]),c_0_75]) ).
cnf(c_0_116,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_78,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_117,hypothesis,
aNaturalNumber0(esk1_2(xm,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_118,plain,
( sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_60])]) ).
cnf(c_0_119,hypothesis,
sdtasdt0(xp,esk2_2(xp,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_110]),c_0_48])]) ).
cnf(c_0_120,hypothesis,
aNaturalNumber0(esk2_2(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_110]),c_0_48])]) ).
cnf(c_0_121,plain,
( aNaturalNumber0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
fof(c_0_122,plain,
! [X24,X25,X26] :
( ( sdtpldt0(X24,X25) != sdtpldt0(X24,X26)
| X25 = X26
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25)
| ~ aNaturalNumber0(X26) )
& ( sdtpldt0(X25,X24) != sdtpldt0(X26,X24)
| X25 = X26
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25)
| ~ aNaturalNumber0(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_123,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_124,plain,
doDivides0(sz10,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_45])]) ).
cnf(c_0_125,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_126,hypothesis,
esk1_2(xm,xp) = sdtmndt0(xp,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_49]),c_0_117])]) ).
cnf(c_0_127,hypothesis,
sdtasdt0(sz00,esk2_2(xp,xp)) = sdtasdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]),c_0_48])]) ).
cnf(c_0_128,plain,
( aNaturalNumber0(sdtmndt0(X1,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_121]) ).
cnf(c_0_129,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_130,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_131,plain,
sdtlseqdt0(sz10,sz10),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_45])]),c_0_55]) ).
cnf(c_0_132,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_133,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
fof(c_0_134,plain,
! [X30,X31] :
( ( X30 = sz00
| sdtpldt0(X30,X31) != sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31) )
& ( X31 = sz00
| sdtpldt0(X30,X31) != sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
cnf(c_0_135,plain,
( sdtpldt0(sdtasdt0(sz00,X1),sz00) = sdtasdt0(sz00,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_109]),c_0_60])]) ).
cnf(c_0_136,hypothesis,
sdtpldt0(xm,sdtmndt0(xp,xm)) = xp,
inference(rw,[status(thm)],[c_0_116,c_0_126]) ).
cnf(c_0_137,hypothesis,
sdtasdt0(sz00,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_127]),c_0_120])]) ).
cnf(c_0_138,hypothesis,
aNaturalNumber0(sdtmndt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_47]),c_0_49]),c_0_48])]) ).
cnf(c_0_139,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_60])]) ).
cnf(c_0_140,plain,
sdtpldt0(sz10,esk1_2(sz10,sz10)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_131]),c_0_45])]) ).
cnf(c_0_141,plain,
aNaturalNumber0(esk1_2(sz10,sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_131]),c_0_45])]) ).
fof(c_0_142,plain,
! [X52,X53,X54] :
( ( sdtasdt0(X52,X53) != sdtasdt0(X52,X54)
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) )
& ( sdtlseqdt0(sdtasdt0(X52,X53),sdtasdt0(X52,X54))
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) )
& ( sdtasdt0(X53,X52) != sdtasdt0(X54,X52)
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) )
& ( sdtlseqdt0(sdtasdt0(X53,X52),sdtasdt0(X54,X52))
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_143,hypothesis,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_132]),c_0_133]),c_0_48])]) ).
cnf(c_0_144,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_145,plain,
! [X56,X57] :
( ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X57)
| X56 = sz00
| sdtlseqdt0(X57,sdtasdt0(X57,X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
cnf(c_0_146,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_147,hypothesis,
sdtpldt0(sdtasdt0(sz00,xm),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]),c_0_138]),c_0_49])]) ).
cnf(c_0_148,plain,
esk1_2(sz10,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141]),c_0_45])]) ).
fof(c_0_149,negated_conjecture,
~ ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_150,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_151,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_152,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_153,hypothesis,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_39]),c_0_49]),c_0_144])]) ).
cnf(c_0_154,hypothesis,
sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2389]) ).
cnf(c_0_155,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_63,c_0_132]),c_0_133]),c_0_48])]) ).
cnf(c_0_156,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_157,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_158,hypothesis,
( sdtasdt0(sz00,xm) = sz00
| ~ aNaturalNumber0(sdtasdt0(sz00,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_60])]) ).
cnf(c_0_159,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(rw,[status(thm)],[c_0_140,c_0_148]) ).
fof(c_0_160,plain,
! [X67,X68,X69] :
( ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X67,X68)
| ~ doDivides0(X68,X69)
| doDivides0(X67,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
fof(c_0_161,negated_conjecture,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(fof_nnf,[status(thm)],[c_0_149]) ).
cnf(c_0_162,hypothesis,
( X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(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_150,c_0_151]),c_0_48]),c_0_144])]),c_0_152]) ).
cnf(c_0_163,hypothesis,
( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_153]),c_0_49]),c_0_144])]) ).
cnf(c_0_164,hypothesis,
( xm = sz00
| xp != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_116]),c_0_117]),c_0_49])]) ).
cnf(c_0_165,plain,
( sdtlseqdt0(X1,sdtpldt0(X2,X3))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_75]),c_0_71]) ).
cnf(c_0_166,hypothesis,
( sdtpldt0(xp,esk1_2(xp,xk)) = xk
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_154]),c_0_48])]) ).
cnf(c_0_167,hypothesis,
( xp = sz00
| aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_39]),c_0_49]),c_0_144])]) ).
cnf(c_0_168,hypothesis,
( aNaturalNumber0(esk1_2(xp,xk))
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_154]),c_0_48])]) ).
cnf(c_0_169,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_170,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_156,c_0_97]) ).
cnf(c_0_171,hypothesis,
sdtlseqdt0(xm,sdtpldt0(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_49])]) ).
cnf(c_0_172,plain,
( sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_44]),c_0_45])]) ).
cnf(c_0_173,hypothesis,
sdtasdt0(sz00,xm) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_39]),c_0_49]),c_0_60])]) ).
cnf(c_0_174,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_159]),c_0_60]),c_0_45])]) ).
cnf(c_0_175,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_160]) ).
cnf(c_0_176,negated_conjecture,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_177,hypothesis,
( xm = sz00
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xm,xp)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_49])]),c_0_164]) ).
fof(c_0_178,plain,
! [X47,X48] :
( ( X48 != X47
| sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48) )
& ( sdtlseqdt0(X48,X47)
| sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
fof(c_0_179,plain,
! [X42,X43] :
( ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X43)
| ~ sdtlseqdt0(X42,X43)
| ~ sdtlseqdt0(X43,X42)
| X42 = X43 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_180,hypothesis,
( sdtlseqdt0(xm,sdtpldt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_181,hypothesis,
( sdtpldt0(xp,esk1_2(xp,xk)) = xk
| xp = sz00 ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_182,hypothesis,
( xp = sz00
| aNaturalNumber0(esk1_2(xp,xk)) ),
inference(spm,[status(thm)],[c_0_168,c_0_167]) ).
cnf(c_0_183,hypothesis,
( X1 = sz00
| sdtpldt0(X1,xp) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_90]),c_0_60]),c_0_48])]) ).
cnf(c_0_184,hypothesis,
sdtlseqdt0(xp,xp),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_104]),c_0_48]),c_0_45])]),c_0_55]) ).
cnf(c_0_185,hypothesis,
( aNaturalNumber0(esk1_2(xm,sdtpldt0(sz00,xp)))
| ~ aNaturalNumber0(sdtpldt0(sz00,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_171]),c_0_49])]) ).
cnf(c_0_186,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_77]),c_0_60]),c_0_45])]) ).
cnf(c_0_187,hypothesis,
sdtpldt0(sz00,xm) = sdtasdt0(sz10,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_174]),c_0_49]),c_0_60])]) ).
cnf(c_0_188,plain,
( doDivides0(X1,sdtasdt0(X2,X3))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_43]),c_0_39]) ).
cnf(c_0_189,negated_conjecture,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| xp = sz00
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(spm,[status(thm)],[c_0_176,c_0_153]) ).
cnf(c_0_190,hypothesis,
( xm = sz00
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_97]),c_0_48]),c_0_49])]) ).
cnf(c_0_191,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
cnf(c_0_192,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_179]) ).
cnf(c_0_193,hypothesis,
( xp = sz00
| sdtlseqdt0(xm,xk) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_182]) ).
cnf(c_0_194,hypothesis,
( X1 = sz00
| sdtpldt0(xp,X1) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_87]),c_0_48])]) ).
cnf(c_0_195,hypothesis,
sdtpldt0(xp,esk1_2(xp,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_184]),c_0_48])]) ).
cnf(c_0_196,hypothesis,
aNaturalNumber0(esk1_2(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_184]),c_0_48])]) ).
cnf(c_0_197,plain,
( doDivides0(sz00,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_109]),c_0_60])]) ).
cnf(c_0_198,hypothesis,
aNaturalNumber0(esk1_2(xm,sdtpldt0(sz00,xp))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_71]),c_0_48]),c_0_60])]) ).
cnf(c_0_199,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_186]),c_0_60]),c_0_45])]),c_0_55]) ).
cnf(c_0_200,hypothesis,
sdtasdt0(sz10,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_187]),c_0_49])]) ).
cnf(c_0_201,hypothesis,
( doDivides0(xp,sdtasdt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_110]),c_0_48])]) ).
cnf(c_0_202,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_203,negated_conjecture,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| xm = sz00
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_164]) ).
cnf(c_0_204,plain,
( X1 = sz00
| X2 = X3
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_150,c_0_191]) ).
cnf(c_0_205,hypothesis,
( xp = sz00
| xk = xm
| ~ sdtlseqdt0(xk,xm) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_49])]),c_0_167]) ).
cnf(c_0_206,hypothesis,
( sdtasdt0(xp,esk2_2(xp,sdtasdt0(xn,xm))) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_132]),c_0_48])]) ).
cnf(c_0_207,hypothesis,
esk1_2(xp,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_196])]) ).
cnf(c_0_208,hypothesis,
( aNaturalNumber0(esk2_2(xp,sdtasdt0(xn,xm)))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_132]),c_0_48])]) ).
cnf(c_0_209,hypothesis,
doDivides0(sz00,sz00),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_210,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_211,plain,
sdtpldt0(sz00,esk1_2(sz00,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_199]),c_0_60])]) ).
cnf(c_0_212,plain,
aNaturalNumber0(esk1_2(sz00,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_199]),c_0_60])]) ).
cnf(c_0_213,hypothesis,
sdtpldt0(sz00,xm) = xm,
inference(rw,[status(thm)],[c_0_187,c_0_200]) ).
cnf(c_0_214,hypothesis,
doDivides0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_60]),c_0_48])]) ).
cnf(c_0_215,hypothesis,
( sdtsldt0(sdtasdt0(xp,xk),xm) = xn
| xm = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_163]),c_0_49]),c_0_144])]),c_0_164]) ).
cnf(c_0_216,negated_conjecture,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| xk = xm
| xm = sz00 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_49]),c_0_48])]),c_0_167]),c_0_205]),c_0_164]) ).
cnf(c_0_217,plain,
( sdtpldt0(sdtasdt0(X1,X2),sz00) = sdtasdt0(sdtpldt0(X1,sz00),X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_109]),c_0_60])]) ).
cnf(c_0_218,hypothesis,
sdtasdt0(xp,esk2_2(xp,sdtasdt0(xn,xm))) = sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_39]),c_0_49]),c_0_144])]) ).
cnf(c_0_219,hypothesis,
sdtpldt0(xp,sz00) = xp,
inference(rw,[status(thm)],[c_0_195,c_0_207]) ).
cnf(c_0_220,hypothesis,
aNaturalNumber0(esk2_2(xp,sdtasdt0(xn,xm))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_39]),c_0_49]),c_0_144])]) ).
cnf(c_0_221,hypothesis,
sdtasdt0(sz00,esk2_2(sz00,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_209]),c_0_60])]) ).
cnf(c_0_222,hypothesis,
aNaturalNumber0(esk2_2(sz00,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_209]),c_0_60])]) ).
cnf(c_0_223,plain,
esk1_2(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_211]),c_0_60]),c_0_212])]) ).
cnf(c_0_224,hypothesis,
sdtlseqdt0(sz00,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_213]),c_0_60]),c_0_49])]) ).
cnf(c_0_225,hypothesis,
sdtasdt0(xp,esk2_2(xp,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_214]),c_0_48]),c_0_60])]) ).
cnf(c_0_226,hypothesis,
aNaturalNumber0(esk2_2(xp,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_214]),c_0_60]),c_0_48])]) ).
cnf(c_0_227,plain,
( sdtsldt0(sdtasdt0(X1,X2),X2) = X1
| X2 = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_97]) ).
cnf(c_0_228,hypothesis,
( sdtsldt0(sdtasdt0(xp,xm),xm) = xn
| xk = xm
| xm = sz00 ),
inference(spm,[status(thm)],[c_0_215,c_0_216]) ).
fof(c_0_229,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(fof_simplification,[status(thm)],[m__2075]) ).
cnf(c_0_230,plain,
( sdtpldt0(sz00,sdtasdt0(sz00,X1)) = sdtasdt0(sz00,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_109]),c_0_60])]) ).
cnf(c_0_231,hypothesis,
sdtpldt0(sdtasdt0(xn,xm),sz00) = sdtasdt0(xn,xm),
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_217,c_0_218]),c_0_219]),c_0_218]),c_0_220]),c_0_48])]) ).
cnf(c_0_232,hypothesis,
sdtasdt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_221]),c_0_221]),c_0_222]),c_0_60])]) ).
cnf(c_0_233,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(rw,[status(thm)],[c_0_211,c_0_223]) ).
cnf(c_0_234,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_218]),c_0_48])]),c_0_220])]) ).
cnf(c_0_235,hypothesis,
( sdtlseqdt0(X1,xm)
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_224]),c_0_49]),c_0_60])]) ).
cnf(c_0_236,hypothesis,
( xp = sz00
| sdtlseqdt0(esk2_2(xp,sz00),sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_225]),c_0_226]),c_0_48])]) ).
cnf(c_0_237,hypothesis,
( xk = xm
| xm = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_49]),c_0_48])]),c_0_152]) ).
cnf(c_0_238,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_239,hypothesis,
sdtasdt0(sz00,sdtasdt0(xn,xm)) = sz00,
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_230,c_0_231]),c_0_232]),c_0_233]),c_0_60]),c_0_234])]) ).
cnf(c_0_240,hypothesis,
( xp = sz00
| sdtlseqdt0(esk2_2(xp,sz00),xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_226])]) ).
cnf(c_0_241,hypothesis,
( esk2_2(xp,sz00) = sdtsldt0(sz00,xp)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_225]),c_0_48]),c_0_226])]) ).
cnf(c_0_242,hypothesis,
xm = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_237]),c_0_238]) ).
cnf(c_0_243,hypothesis,
sdtasdt0(sz00,sdtasdt0(xm,xn)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_97]),c_0_49]),c_0_144])]) ).
fof(c_0_244,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_245,hypothesis,
( xp = sz00
| sdtlseqdt0(sdtsldt0(sz00,xp),xm) ),
inference(spm,[status(thm)],[c_0_240,c_0_241]) ).
cnf(c_0_246,hypothesis,
xp != sz00,
inference(rw,[status(thm)],[c_0_50,c_0_242]) ).
cnf(c_0_247,hypothesis,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_97]),c_0_144]),c_0_49])]) ).
cnf(c_0_248,hypothesis,
sdtasdt0(sz00,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_243]),c_0_144]),c_0_49])]) ).
cnf(c_0_249,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_250,hypothesis,
sdtlseqdt0(sdtsldt0(sz00,xp),sz00),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_245,c_0_242]),c_0_246]) ).
cnf(c_0_251,hypothesis,
sdtsldt0(sz00,xp) = xk,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_242]),c_0_248]) ).
cnf(c_0_252,hypothesis,
~ sdtlseqdt0(xk,sz00),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_242]),c_0_242]),c_0_249]),c_0_246]) ).
cnf(c_0_253,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_250,c_0_251]),c_0_252]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : NUM503+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n016.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 2400
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Oct 2 14:08:06 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.J7nVQm4FkX/E---3.1_13044.p
% 4.71/1.03 # Version: 3.1pre001
% 4.71/1.03 # Preprocessing class: FSLSSMSSSSSNFFN.
% 4.71/1.03 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.71/1.03 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.71/1.03 # Starting new_bool_3 with 300s (1) cores
% 4.71/1.03 # Starting new_bool_1 with 300s (1) cores
% 4.71/1.03 # Starting sh5l with 300s (1) cores
% 4.71/1.03 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 13122 completed with status 0
% 4.71/1.03 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 4.71/1.03 # Preprocessing class: FSLSSMSSSSSNFFN.
% 4.71/1.03 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.71/1.03 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.71/1.03 # No SInE strategy applied
% 4.71/1.03 # Search class: FGHSF-FFMM21-SFFFFFNN
% 4.71/1.03 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.71/1.03 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 811s (1) cores
% 4.71/1.03 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.71/1.03 # Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 4.71/1.03 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 4.71/1.03 # Starting G----_Z1014__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 4.71/1.03 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 13128 completed with status 0
% 4.71/1.03 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 4.71/1.03 # Preprocessing class: FSLSSMSSSSSNFFN.
% 4.71/1.03 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.71/1.03 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.71/1.03 # No SInE strategy applied
% 4.71/1.03 # Search class: FGHSF-FFMM21-SFFFFFNN
% 4.71/1.03 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.71/1.03 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 811s (1) cores
% 4.71/1.03 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.71/1.03 # Preprocessing time : 0.002 s
% 4.71/1.03 # Presaturation interreduction done
% 4.71/1.03
% 4.71/1.03 # Proof found!
% 4.71/1.03 # SZS status Theorem
% 4.71/1.03 # SZS output start CNFRefutation
% See solution above
% 4.71/1.03 # Parsed axioms : 51
% 4.71/1.03 # Removed by relevancy pruning/SinE : 0
% 4.71/1.03 # Initial clauses : 94
% 4.71/1.03 # Removed in clause preprocessing : 3
% 4.71/1.03 # Initial clauses in saturation : 91
% 4.71/1.03 # Processed clauses : 3631
% 4.71/1.03 # ...of these trivial : 217
% 4.71/1.03 # ...subsumed : 1862
% 4.71/1.03 # ...remaining for further processing : 1552
% 4.71/1.03 # Other redundant clauses eliminated : 81
% 4.71/1.03 # Clauses deleted for lack of memory : 0
% 4.71/1.03 # Backward-subsumed : 160
% 4.71/1.03 # Backward-rewritten : 532
% 4.71/1.03 # Generated clauses : 28805
% 4.71/1.03 # ...of the previous two non-redundant : 25395
% 4.71/1.03 # ...aggressively subsumed : 0
% 4.71/1.03 # Contextual simplify-reflections : 319
% 4.71/1.03 # Paramodulations : 28593
% 4.71/1.03 # Factorizations : 5
% 4.71/1.03 # NegExts : 0
% 4.71/1.03 # Equation resolutions : 87
% 4.71/1.03 # Total rewrite steps : 35122
% 4.71/1.03 # Propositional unsat checks : 0
% 4.71/1.03 # Propositional check models : 0
% 4.71/1.03 # Propositional check unsatisfiable : 0
% 4.71/1.03 # Propositional clauses : 0
% 4.71/1.03 # Propositional clauses after purity: 0
% 4.71/1.03 # Propositional unsat core size : 0
% 4.71/1.03 # Propositional preprocessing time : 0.000
% 4.71/1.03 # Propositional encoding time : 0.000
% 4.71/1.03 # Propositional solver time : 0.000
% 4.71/1.03 # Success case prop preproc time : 0.000
% 4.71/1.03 # Success case prop encoding time : 0.000
% 4.71/1.03 # Success case prop solver time : 0.000
% 4.71/1.03 # Current number of processed clauses : 645
% 4.71/1.03 # Positive orientable unit clauses : 195
% 4.71/1.03 # Positive unorientable unit clauses: 0
% 4.71/1.03 # Negative unit clauses : 15
% 4.71/1.03 # Non-unit-clauses : 435
% 4.71/1.03 # Current number of unprocessed clauses: 21597
% 4.71/1.03 # ...number of literals in the above : 96293
% 4.71/1.03 # Current number of archived formulas : 0
% 4.71/1.03 # Current number of archived clauses : 896
% 4.71/1.03 # Clause-clause subsumption calls (NU) : 99085
% 4.71/1.03 # Rec. Clause-clause subsumption calls : 44772
% 4.71/1.03 # Non-unit clause-clause subsumptions : 2159
% 4.71/1.03 # Unit Clause-clause subsumption calls : 10422
% 4.71/1.03 # Rewrite failures with RHS unbound : 0
% 4.71/1.03 # BW rewrite match attempts : 141
% 4.71/1.03 # BW rewrite match successes : 102
% 4.71/1.03 # Condensation attempts : 0
% 4.71/1.03 # Condensation successes : 0
% 4.71/1.03 # Termbank termtop insertions : 534468
% 4.71/1.03
% 4.71/1.03 # -------------------------------------------------
% 4.71/1.03 # User time : 0.582 s
% 4.71/1.03 # System time : 0.016 s
% 4.71/1.03 # Total time : 0.598 s
% 4.71/1.03 # Maximum resident set size: 1996 pages
% 4.71/1.03
% 4.71/1.03 # -------------------------------------------------
% 4.71/1.03 # User time : 2.880 s
% 4.71/1.03 # System time : 0.080 s
% 4.71/1.03 # Total time : 2.959 s
% 4.71/1.03 # Maximum resident set size: 1728 pages
% 4.71/1.03 % E---3.1 exiting
% 4.71/1.03 % E---3.1 exiting
%------------------------------------------------------------------------------