TSTP Solution File: NUM526+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM526+3 : TPTP v7.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n115.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 15:21:39 EST 2018
% Result : Theorem 103.31s
% Output : CNFRefutation 103.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 81
% Number of leaves : 33
% Syntax : Number of formulae : 888 ( 95 unt; 0 def)
% Number of atoms : 3425 (1072 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 4220 (1683 ~;2334 |; 160 &)
% ( 4 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 751 ( 0 sgn 227 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtasdt0(X1,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',m_MulZero) ).
fof(2,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X2,X3) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mDivTrans) ).
fof(3,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mAddComm) ).
fof(4,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( equal(sdtasdt0(X1,X2),sz00)
=> ( equal(X1,sz00)
| equal(X2,sz00) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mZeroMul) ).
fof(5,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( ~ equal(X1,sz00)
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( equal(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| equal(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) )
=> equal(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mMulCanc) ).
fof(8,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( equal(sdtasdt0(X1,sdtpldt0(X2,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
& equal(sdtasdt0(sdtpldt0(X2,X3),X1),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mAMDistr) ).
fof(9,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(X2,sdtasdt0(X1,X3)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mDefDiv) ).
fof(11,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( ~ equal(X2,X1)
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mLETotal) ).
fof(12,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mLETran) ).
fof(14,axiom,
equal(sdtasdt0(xp,sdtasdt0(xm,xm)),sdtasdt0(xn,xn)),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',m__3014) ).
fof(15,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& ~ equal(X2,sz00) )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mDivLE) ).
fof(18,axiom,
( aNaturalNumber0(xq)
& equal(xn,sdtasdt0(xp,xq))
& equal(xq,sdtsldt0(xn,xp)) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',m__3059) ).
fof(20,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( ~ equal(X1,sz00)
& ~ equal(X2,X3)
& sdtlseqdt0(X2,X3) )
=> ( ~ equal(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& ~ equal(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mMonMul) ).
fof(21,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mDefLE) ).
fof(23,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> equal(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mLEAsym) ).
fof(24,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( ~ equal(X1,sz00)
& doDivides0(X1,X2) )
=> ! [X3] :
( equal(X3,sdtsldt0(X2,X1))
<=> ( aNaturalNumber0(X3)
& equal(X2,sdtasdt0(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mDefQuot) ).
fof(25,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(X1,sz00)
| equal(X1,sz10)
| ( ~ equal(sz10,X1)
& sdtlseqdt0(sz10,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mLENTr) ).
fof(26,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ~ equal(X1,sz00)
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mMonMul2) ).
fof(27,axiom,
( aNaturalNumber0(sz10)
& ~ equal(sz10,sz00) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mSortsC_01) ).
fof(28,conjecture,
( ~ equal(xm,xn)
& ( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(xm,X1),xn) )
| sdtlseqdt0(xm,xn) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',m__) ).
fof(29,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> equal(sdtasdt0(sdtasdt0(X1,X2),X3),sdtasdt0(X1,sdtasdt0(X2,X3))) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mMulAsso) ).
fof(32,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( equal(X3,sdtmndt0(X2,X1))
<=> ( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mDefDiff) ).
fof(33,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mSortsB_02) ).
fof(35,axiom,
equal(sdtasdt0(xm,xm),sdtasdt0(xp,sdtasdt0(xq,xq))),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',m__3082) ).
fof(36,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mSortsC) ).
fof(37,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mSortsB) ).
fof(41,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mMulComm) ).
fof(42,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( ~ equal(X1,sz00)
& doDivides0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> equal(sdtasdt0(X3,sdtsldt0(X2,X1)),sdtsldt0(sdtasdt0(X3,X2),X1)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',mDivAsso) ).
fof(43,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ~ equal(xn,sz00)
& ~ equal(xm,sz00)
& ~ equal(xp,sz00) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',m__2987) ).
fof(44,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtpldt0(X1,sz00),X1)
& equal(X1,sdtpldt0(sz00,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',m_AddZero) ).
fof(45,axiom,
( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtasdt0(xn,xn),sdtasdt0(xp,X1)) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( aNaturalNumber0(X1)
& equal(xn,sdtasdt0(xp,X1)) )
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',m__3046) ).
fof(46,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',m_MulUnit) ).
fof(47,axiom,
( ~ equal(xp,sz10)
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& equal(xp,sdtasdt0(X1,X2)) )
| doDivides0(X1,xp) ) )
=> ( equal(X1,sz10)
| equal(X1,xp) ) )
& isPrime0(xp) ),
file('/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2',m__3025) ).
fof(48,negated_conjecture,
~ ( ~ equal(xm,xn)
& ( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(xm,X1),xn) )
| sdtlseqdt0(xm,xn) ) ),
inference(assume_negation,[status(cth)],[28]) ).
fof(49,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtasdt0(X1,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X1)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(50,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtasdt0(X2,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X2)) ) ),
inference(variable_rename,[status(thm)],[49]) ).
fof(51,plain,
! [X2] :
( ( equal(sdtasdt0(X2,sz00),sz00)
| ~ aNaturalNumber0(X2) )
& ( equal(sz00,sdtasdt0(sz00,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[50]) ).
cnf(53,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[51]) ).
fof(54,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3)
| doDivides0(X1,X3) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(55,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ doDivides0(X4,X5)
| ~ doDivides0(X5,X6)
| doDivides0(X4,X6) ),
inference(variable_rename,[status(thm)],[54]) ).
cnf(56,plain,
( doDivides0(X1,X2)
| ~ doDivides0(X3,X2)
| ~ doDivides0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(57,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(58,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(sdtpldt0(X3,X4),sdtpldt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[57]) ).
cnf(59,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(60,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ equal(sdtasdt0(X1,X2),sz00)
| equal(X1,sz00)
| equal(X2,sz00) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(61,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ equal(sdtasdt0(X3,X4),sz00)
| equal(X3,sz00)
| equal(X4,sz00) ),
inference(variable_rename,[status(thm)],[60]) ).
cnf(62,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[61]) ).
fof(63,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| equal(X1,sz00)
| ! [X2,X3] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ( ~ equal(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& ~ equal(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) )
| equal(X2,X3) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(64,plain,
! [X4] :
( ~ aNaturalNumber0(X4)
| equal(X4,sz00)
| ! [X5,X6] :
( ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
& ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4)) )
| equal(X5,X6) ) ),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
& ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4)) )
| equal(X5,X6)
| equal(X4,sz00)
| ~ aNaturalNumber0(X4) ),
inference(shift_quantors,[status(thm)],[64]) ).
fof(66,plain,
! [X4,X5,X6] :
( ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
| equal(X5,X6)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| equal(X4,sz00)
| ~ aNaturalNumber0(X4) )
& ( ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
| equal(X5,X6)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| equal(X4,sz00)
| ~ aNaturalNumber0(X4) ) ),
inference(distribute,[status(thm)],[65]) ).
cnf(67,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X3,X1) != sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[66]) ).
cnf(68,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,X3) != sdtasdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[66]) ).
fof(83,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ( equal(sdtasdt0(X1,sdtpldt0(X2,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
& equal(sdtasdt0(sdtpldt0(X2,X3),X1),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(84,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ( equal(sdtasdt0(X4,sdtpldt0(X5,X6)),sdtpldt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6)))
& equal(sdtasdt0(sdtpldt0(X5,X6),X4),sdtpldt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4))) ) ),
inference(variable_rename,[status(thm)],[83]) ).
fof(85,plain,
! [X4,X5,X6] :
( ( equal(sdtasdt0(X4,sdtpldt0(X5,X6)),sdtpldt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6)))
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( equal(sdtasdt0(sdtpldt0(X5,X6),X4),sdtpldt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4)))
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[84]) ).
cnf(86,plain,
( sdtasdt0(sdtpldt0(X2,X1),X3) = sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(87,plain,
( sdtasdt0(X3,sdtpldt0(X2,X1)) = sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[85]) ).
fof(88,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ( ( ~ doDivides0(X1,X2)
| ? [X3] :
( aNaturalNumber0(X3)
& equal(X2,sdtasdt0(X1,X3)) ) )
& ( ! [X3] :
( ~ aNaturalNumber0(X3)
| ~ equal(X2,sdtasdt0(X1,X3)) )
| doDivides0(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(89,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ doDivides0(X4,X5)
| ? [X6] :
( aNaturalNumber0(X6)
& equal(X5,sdtasdt0(X4,X6)) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7)) )
| doDivides0(X4,X5) ) ) ),
inference(variable_rename,[status(thm)],[88]) ).
fof(90,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk3_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk3_2(X4,X5))) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7)) )
| doDivides0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[89]) ).
fof(91,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5) )
& ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk3_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk3_2(X4,X5))) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[90]) ).
fof(92,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk3_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(X5,sdtasdt0(X4,esk3_2(X4,X5)))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[91]) ).
cnf(93,plain,
( X1 = sdtasdt0(X2,esk3_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[92]) ).
cnf(94,plain,
( aNaturalNumber0(esk3_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[92]) ).
cnf(95,plain,
( doDivides0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[92]) ).
fof(99,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X1,X2)
| ( ~ equal(X2,X1)
& sdtlseqdt0(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(100,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtlseqdt0(X3,X4)
| ( ~ equal(X4,X3)
& sdtlseqdt0(X4,X3) ) ),
inference(variable_rename,[status(thm)],[99]) ).
fof(101,plain,
! [X3,X4] :
( ( ~ equal(X4,X3)
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) )
& ( sdtlseqdt0(X4,X3)
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) ) ),
inference(distribute,[status(thm)],[100]) ).
cnf(102,plain,
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[101]) ).
fof(104,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3)
| sdtlseqdt0(X1,X3) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(105,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ sdtlseqdt0(X4,X5)
| ~ sdtlseqdt0(X5,X6)
| sdtlseqdt0(X4,X6) ),
inference(variable_rename,[status(thm)],[104]) ).
cnf(106,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(110,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[14]) ).
fof(111,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2)
| equal(X2,sz00)
| sdtlseqdt0(X1,X2) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(112,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ doDivides0(X3,X4)
| equal(X4,sz00)
| sdtlseqdt0(X3,X4) ),
inference(variable_rename,[status(thm)],[111]) ).
cnf(113,plain,
( sdtlseqdt0(X1,X2)
| X2 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[112]) ).
cnf(125,plain,
xq = sdtsldt0(xn,xp),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(126,plain,
xn = sdtasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(127,plain,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[18]) ).
fof(131,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| equal(X1,sz00)
| equal(X2,X3)
| ~ sdtlseqdt0(X2,X3)
| ( ~ equal(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& ~ equal(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(132,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| equal(X4,sz00)
| equal(X5,X6)
| ~ sdtlseqdt0(X5,X6)
| ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
& sdtlseqdt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
& ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
& sdtlseqdt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4)) ) ),
inference(variable_rename,[status(thm)],[131]) ).
fof(133,plain,
! [X4,X5,X6] :
( ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
| equal(X4,sz00)
| equal(X5,X6)
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtlseqdt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
| equal(X4,sz00)
| equal(X5,X6)
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
| equal(X4,sz00)
| equal(X5,X6)
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtlseqdt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
| equal(X4,sz00)
| equal(X5,X6)
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[132]) ).
cnf(134,plain,
( X2 = X1
| X3 = sz00
| sdtlseqdt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[133]) ).
cnf(136,plain,
( X2 = X1
| X3 = sz00
| sdtlseqdt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[133]) ).
fof(138,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ( ( ~ sdtlseqdt0(X1,X2)
| ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) )
& ( ! [X3] :
( ~ aNaturalNumber0(X3)
| ~ equal(sdtpldt0(X1,X3),X2) )
| sdtlseqdt0(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(139,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ sdtlseqdt0(X4,X5)
| ? [X6] :
( aNaturalNumber0(X6)
& equal(sdtpldt0(X4,X6),X5) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5) )
| sdtlseqdt0(X4,X5) ) ) ),
inference(variable_rename,[status(thm)],[138]) ).
fof(140,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk4_2(X4,X5))
& equal(sdtpldt0(X4,esk4_2(X4,X5)),X5) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5) )
| sdtlseqdt0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[139]) ).
fof(141,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5) )
& ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk4_2(X4,X5))
& equal(sdtpldt0(X4,esk4_2(X4,X5)),X5) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[140]) ).
fof(142,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk4_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(sdtpldt0(X4,esk4_2(X4,X5)),X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[141]) ).
cnf(145,plain,
( sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[142]) ).
fof(149,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1)
| equal(X1,X2) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(150,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| equal(X3,X4) ),
inference(variable_rename,[status(thm)],[149]) ).
cnf(151,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[150]) ).
fof(152,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(X1,sz00)
| ~ doDivides0(X1,X2)
| ! [X3] :
( ( ~ equal(X3,sdtsldt0(X2,X1))
| ( aNaturalNumber0(X3)
& equal(X2,sdtasdt0(X1,X3)) ) )
& ( ~ aNaturalNumber0(X3)
| ~ equal(X2,sdtasdt0(X1,X3))
| equal(X3,sdtsldt0(X2,X1)) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(153,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ! [X6] :
( ( ~ equal(X6,sdtsldt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(X5,sdtasdt0(X4,X6)) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(X5,sdtasdt0(X4,X6))
| equal(X6,sdtsldt0(X5,X4)) ) ) ),
inference(variable_rename,[status(thm)],[152]) ).
fof(154,plain,
! [X4,X5,X6] :
( ( ( ~ equal(X6,sdtsldt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(X5,sdtasdt0(X4,X6)) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(X5,sdtasdt0(X4,X6))
| equal(X6,sdtsldt0(X5,X4)) ) )
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[153]) ).
fof(155,plain,
! [X4,X5,X6] :
( ( aNaturalNumber0(X6)
| ~ equal(X6,sdtsldt0(X5,X4))
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(X5,sdtasdt0(X4,X6))
| ~ equal(X6,sdtsldt0(X5,X4))
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(X5,sdtasdt0(X4,X6))
| equal(X6,sdtsldt0(X5,X4))
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[154]) ).
cnf(156,plain,
( X2 = sz00
| X3 = sdtsldt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(157,plain,
( X2 = sz00
| X1 = sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(158,plain,
( X2 = sz00
| aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[155]) ).
fof(159,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| equal(X1,sz00)
| equal(X1,sz10)
| ( ~ equal(sz10,X1)
& sdtlseqdt0(sz10,X1) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(160,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| equal(X2,sz00)
| equal(X2,sz10)
| ( ~ equal(sz10,X2)
& sdtlseqdt0(sz10,X2) ) ),
inference(variable_rename,[status(thm)],[159]) ).
fof(161,plain,
! [X2] :
( ( ~ equal(sz10,X2)
| equal(X2,sz00)
| equal(X2,sz10)
| ~ aNaturalNumber0(X2) )
& ( sdtlseqdt0(sz10,X2)
| equal(X2,sz00)
| equal(X2,sz10)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[160]) ).
cnf(162,plain,
( X1 = sz10
| X1 = sz00
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[161]) ).
fof(164,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(X1,sz00)
| sdtlseqdt0(X2,sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(165,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(X3,sz00)
| sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[164]) ).
cnf(166,plain,
( sdtlseqdt0(X1,sdtasdt0(X1,X2))
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[165]) ).
cnf(167,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[27]) ).
cnf(168,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[27]) ).
fof(169,negated_conjecture,
( equal(xm,xn)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| ~ equal(sdtpldt0(xm,X1),xn) )
& ~ sdtlseqdt0(xm,xn) ) ),
inference(fof_nnf,[status(thm)],[48]) ).
fof(170,negated_conjecture,
( equal(xm,xn)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ equal(sdtpldt0(xm,X2),xn) )
& ~ sdtlseqdt0(xm,xn) ) ),
inference(variable_rename,[status(thm)],[169]) ).
fof(171,negated_conjecture,
! [X2] :
( ( ( ~ aNaturalNumber0(X2)
| ~ equal(sdtpldt0(xm,X2),xn) )
& ~ sdtlseqdt0(xm,xn) )
| equal(xm,xn) ),
inference(shift_quantors,[status(thm)],[170]) ).
fof(172,negated_conjecture,
! [X2] :
( ( ~ aNaturalNumber0(X2)
| ~ equal(sdtpldt0(xm,X2),xn)
| equal(xm,xn) )
& ( ~ sdtlseqdt0(xm,xn)
| equal(xm,xn) ) ),
inference(distribute,[status(thm)],[171]) ).
cnf(173,negated_conjecture,
( xm = xn
| ~ sdtlseqdt0(xm,xn) ),
inference(split_conjunct,[status(thm)],[172]) ).
fof(175,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| equal(sdtasdt0(sdtasdt0(X1,X2),X3),sdtasdt0(X1,sdtasdt0(X2,X3))) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(176,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| equal(sdtasdt0(sdtasdt0(X4,X5),X6),sdtasdt0(X4,sdtasdt0(X5,X6))) ),
inference(variable_rename,[status(thm)],[175]) ).
cnf(177,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[176]) ).
fof(186,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ! [X3] :
( ( ~ equal(X3,sdtmndt0(X2,X1))
| ( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) )
& ( ~ aNaturalNumber0(X3)
| ~ equal(sdtpldt0(X1,X3),X2)
| equal(X3,sdtmndt0(X2,X1)) ) ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(187,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ sdtlseqdt0(X4,X5)
| ! [X6] :
( ( ~ equal(X6,sdtmndt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(sdtpldt0(X4,X6),X5) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4)) ) ) ),
inference(variable_rename,[status(thm)],[186]) ).
fof(188,plain,
! [X4,X5,X6] :
( ( ( ~ equal(X6,sdtmndt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(sdtpldt0(X4,X6),X5) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4)) ) )
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[187]) ).
fof(189,plain,
! [X4,X5,X6] :
( ( aNaturalNumber0(X6)
| ~ equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(sdtpldt0(X4,X6),X5)
| ~ equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[188]) ).
cnf(190,plain,
( X3 = sdtmndt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[189]) ).
cnf(192,plain,
( aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| X3 != sdtmndt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[189]) ).
fof(193,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(194,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[193]) ).
cnf(195,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[194]) ).
cnf(208,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(209,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[36]) ).
fof(210,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(211,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[210]) ).
cnf(212,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[211]) ).
fof(228,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(229,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(sdtasdt0(X3,X4),sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[228]) ).
cnf(230,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[229]) ).
fof(231,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(X1,sz00)
| ~ doDivides0(X1,X2)
| ! [X3] :
( ~ aNaturalNumber0(X3)
| equal(sdtasdt0(X3,sdtsldt0(X2,X1)),sdtsldt0(sdtasdt0(X3,X2),X1)) ) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(232,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ! [X6] :
( ~ aNaturalNumber0(X6)
| equal(sdtasdt0(X6,sdtsldt0(X5,X4)),sdtsldt0(sdtasdt0(X6,X5),X4)) ) ),
inference(variable_rename,[status(thm)],[231]) ).
fof(233,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X6)
| equal(sdtasdt0(X6,sdtsldt0(X5,X4)),sdtsldt0(sdtasdt0(X6,X5),X4))
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[232]) ).
cnf(234,plain,
( X2 = sz00
| sdtasdt0(X3,sdtsldt0(X1,X2)) = sdtsldt0(sdtasdt0(X3,X1),X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[233]) ).
cnf(235,plain,
xp != sz00,
inference(split_conjunct,[status(thm)],[43]) ).
cnf(236,plain,
xm != sz00,
inference(split_conjunct,[status(thm)],[43]) ).
cnf(237,plain,
xn != sz00,
inference(split_conjunct,[status(thm)],[43]) ).
cnf(238,plain,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(239,plain,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(240,plain,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[43]) ).
fof(241,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtpldt0(X1,sz00),X1)
& equal(X1,sdtpldt0(sz00,X1)) ) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(242,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtpldt0(X2,sz00),X2)
& equal(X2,sdtpldt0(sz00,X2)) ) ),
inference(variable_rename,[status(thm)],[241]) ).
fof(243,plain,
! [X2] :
( ( equal(sdtpldt0(X2,sz00),X2)
| ~ aNaturalNumber0(X2) )
& ( equal(X2,sdtpldt0(sz00,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[242]) ).
cnf(244,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(245,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[243]) ).
fof(246,plain,
( ? [X2] :
( aNaturalNumber0(X2)
& equal(sdtasdt0(xn,xn),sdtasdt0(xp,X2)) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X3] :
( aNaturalNumber0(X3)
& equal(xn,sdtasdt0(xp,X3)) )
& doDivides0(xp,xn) ),
inference(variable_rename,[status(thm)],[45]) ).
fof(247,plain,
( aNaturalNumber0(esk7_0)
& equal(sdtasdt0(xn,xn),sdtasdt0(xp,esk7_0))
& doDivides0(xp,sdtasdt0(xn,xn))
& aNaturalNumber0(esk8_0)
& equal(xn,sdtasdt0(xp,esk8_0))
& doDivides0(xp,xn) ),
inference(skolemize,[status(esa)],[246]) ).
cnf(248,plain,
doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[247]) ).
cnf(252,plain,
sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0),
inference(split_conjunct,[status(thm)],[247]) ).
cnf(253,plain,
aNaturalNumber0(esk7_0),
inference(split_conjunct,[status(thm)],[247]) ).
fof(254,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
inference(fof_nnf,[status(thm)],[46]) ).
fof(255,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtasdt0(X2,sz10),X2)
& equal(X2,sdtasdt0(sz10,X2)) ) ),
inference(variable_rename,[status(thm)],[254]) ).
fof(256,plain,
! [X2] :
( ( equal(sdtasdt0(X2,sz10),X2)
| ~ aNaturalNumber0(X2) )
& ( equal(X2,sdtasdt0(sz10,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[255]) ).
cnf(257,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[256]) ).
cnf(258,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[256]) ).
fof(259,plain,
( ~ equal(xp,sz10)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ equal(xp,sdtasdt0(X1,X2)) )
& ~ doDivides0(X1,xp) )
| equal(X1,sz10)
| equal(X1,xp) )
& isPrime0(xp) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(260,plain,
( ~ equal(xp,sz10)
& ! [X3] :
( ~ aNaturalNumber0(X3)
| ( ! [X4] :
( ~ aNaturalNumber0(X4)
| ~ equal(xp,sdtasdt0(X3,X4)) )
& ~ doDivides0(X3,xp) )
| equal(X3,sz10)
| equal(X3,xp) )
& isPrime0(xp) ),
inference(variable_rename,[status(thm)],[259]) ).
fof(261,plain,
! [X3,X4] :
( ( ( ( ~ aNaturalNumber0(X4)
| ~ equal(xp,sdtasdt0(X3,X4)) )
& ~ doDivides0(X3,xp) )
| ~ aNaturalNumber0(X3)
| equal(X3,sz10)
| equal(X3,xp) )
& ~ equal(xp,sz10)
& isPrime0(xp) ),
inference(shift_quantors,[status(thm)],[260]) ).
fof(262,plain,
! [X3,X4] :
( ( ~ aNaturalNumber0(X4)
| ~ equal(xp,sdtasdt0(X3,X4))
| ~ aNaturalNumber0(X3)
| equal(X3,sz10)
| equal(X3,xp) )
& ( ~ doDivides0(X3,xp)
| ~ aNaturalNumber0(X3)
| equal(X3,sz10)
| equal(X3,xp) )
& ~ equal(xp,sz10)
& isPrime0(xp) ),
inference(distribute,[status(thm)],[261]) ).
cnf(264,plain,
xp != sz10,
inference(split_conjunct,[status(thm)],[262]) ).
cnf(266,plain,
( X1 = xp
| X1 = sz10
| ~ aNaturalNumber0(X1)
| xp != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[262]) ).
cnf(289,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[195,208,theory(equality)]) ).
cnf(307,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq))
| $false ),
inference(rw,[status(thm)],[289,238,theory(equality)]) ).
cnf(308,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(cn,[status(thm)],[307,theory(equality)]) ).
cnf(320,plain,
( sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[102,240,theory(equality)]) ).
cnf(321,plain,
( sdtlseqdt0(X1,xm)
| sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[102,239,theory(equality)]) ).
cnf(325,plain,
( sdtlseqdt0(X1,xq)
| sdtlseqdt0(xq,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[102,127,theory(equality)]) ).
cnf(425,plain,
( sz00 = X1
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[166,230,theory(equality)]) ).
cnf(452,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(er,[status(thm)],[145,theory(equality)]) ).
cnf(454,plain,
( sdtlseqdt0(sz00,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[145,244,theory(equality)]) ).
cnf(460,plain,
( sdtlseqdt0(sz00,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[454,209,theory(equality)]) ).
cnf(461,plain,
( sdtlseqdt0(sz00,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[460,theory(equality)]) ).
cnf(462,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[461,theory(equality)]) ).
cnf(464,plain,
( sz00 = xn
| sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[113,248,theory(equality)]) ).
cnf(467,plain,
( sz00 = xn
| sdtlseqdt0(xp,xn)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[464,240,theory(equality)]) ).
cnf(468,plain,
( sz00 = xn
| sdtlseqdt0(xp,xn)
| $false
| $false ),
inference(rw,[status(thm)],[467,238,theory(equality)]) ).
cnf(469,plain,
( sz00 = xn
| sdtlseqdt0(xp,xn) ),
inference(cn,[status(thm)],[468,theory(equality)]) ).
cnf(470,plain,
sdtlseqdt0(xp,xn),
inference(sr,[status(thm)],[469,237,theory(equality)]) ).
cnf(575,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(er,[status(thm)],[95,theory(equality)]) ).
cnf(582,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[95,257,theory(equality)]) ).
cnf(603,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[582,168,theory(equality)]) ).
cnf(604,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[603,theory(equality)]) ).
cnf(605,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[604,theory(equality)]) ).
cnf(626,plain,
( xp = X1
| sz10 = X1
| X2 != xp
| ~ aNaturalNumber0(esk3_2(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[266,93,theory(equality)]) ).
cnf(645,plain,
( sz00 = sz10
| X1 = X2
| X1 != sdtasdt0(X2,sz10)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[67,258,theory(equality)]) ).
cnf(683,plain,
( sz00 = sz10
| X1 = X2
| X1 != sdtasdt0(X2,sz10)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[645,168,theory(equality)]) ).
cnf(684,plain,
( sz00 = sz10
| X1 = X2
| X1 != sdtasdt0(X2,sz10)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[683,theory(equality)]) ).
cnf(685,plain,
( X1 = X2
| X1 != sdtasdt0(X2,sz10)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[684,167,theory(equality)]) ).
cnf(698,plain,
( sz00 = xp
| xq = X1
| xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[68,126,theory(equality)]) ).
cnf(702,plain,
( sz00 = xp
| esk7_0 = X1
| sdtasdt0(xn,xn) != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[68,252,theory(equality)]) ).
cnf(720,plain,
( sz00 = xp
| xq = X1
| xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[698,127,theory(equality)]) ).
cnf(721,plain,
( sz00 = xp
| xq = X1
| xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[720,238,theory(equality)]) ).
cnf(722,plain,
( sz00 = xp
| xq = X1
| xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[721,theory(equality)]) ).
cnf(723,plain,
( xq = X1
| sdtasdt0(xp,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[722,235,theory(equality)]) ).
cnf(736,plain,
( sz00 = xp
| esk7_0 = X1
| sdtasdt0(xn,xn) != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[702,253,theory(equality)]) ).
cnf(737,plain,
( sz00 = xp
| esk7_0 = X1
| sdtasdt0(xn,xn) != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[736,238,theory(equality)]) ).
cnf(738,plain,
( sz00 = xp
| esk7_0 = X1
| sdtasdt0(xn,xn) != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[737,theory(equality)]) ).
cnf(739,plain,
( esk7_0 = X1
| sdtasdt0(xp,X1) != sdtasdt0(xn,xn)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[738,235,theory(equality)]) ).
cnf(796,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xq != X1
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[158,125,theory(equality)]) ).
cnf(797,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xq != X1
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[796,248,theory(equality)]) ).
cnf(798,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xq != X1
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[797,238,theory(equality)]) ).
cnf(799,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xq != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[798,240,theory(equality)]) ).
cnf(800,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xq != X1 ),
inference(cn,[status(thm)],[799,theory(equality)]) ).
cnf(801,plain,
( aNaturalNumber0(X1)
| xq != X1 ),
inference(sr,[status(thm)],[800,235,theory(equality)]) ).
cnf(804,plain,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[56,248,theory(equality)]) ).
cnf(808,plain,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xp)
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[804,238,theory(equality)]) ).
cnf(809,plain,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xp)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[808,240,theory(equality)]) ).
cnf(810,plain,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[809,theory(equality)]) ).
cnf(813,plain,
( sdtasdt0(xn,X1) = sdtasdt0(xp,sdtasdt0(xq,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[177,126,theory(equality)]) ).
cnf(820,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[177,257,theory(equality)]) ).
cnf(821,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[53,177,theory(equality)]) ).
cnf(824,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[195,177,theory(equality)]) ).
cnf(825,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[230,177,theory(equality)]) ).
cnf(841,plain,
( sdtasdt0(xn,X1) = sdtasdt0(xp,sdtasdt0(xq,X1))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[813,127,theory(equality)]) ).
cnf(842,plain,
( sdtasdt0(xn,X1) = sdtasdt0(xp,sdtasdt0(xq,X1))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[841,238,theory(equality)]) ).
cnf(843,plain,
( sdtasdt0(xn,X1) = sdtasdt0(xp,sdtasdt0(xq,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[842,theory(equality)]) ).
cnf(858,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[820,168,theory(equality)]) ).
cnf(859,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[858,theory(equality)]) ).
cnf(860,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[821,209,theory(equality)]) ).
cnf(861,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[860,theory(equality)]) ).
cnf(867,plain,
( sdtasdt0(xp,X1) = xn
| sz00 = xp
| xq != X1
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[157,125,theory(equality)]) ).
cnf(868,plain,
( sdtasdt0(xp,X1) = xn
| sz00 = xp
| xq != X1
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[867,248,theory(equality)]) ).
cnf(869,plain,
( sdtasdt0(xp,X1) = xn
| sz00 = xp
| xq != X1
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[868,238,theory(equality)]) ).
cnf(870,plain,
( sdtasdt0(xp,X1) = xn
| sz00 = xp
| xq != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[869,240,theory(equality)]) ).
cnf(871,plain,
( sdtasdt0(xp,X1) = xn
| sz00 = xp
| xq != X1 ),
inference(cn,[status(thm)],[870,theory(equality)]) ).
cnf(872,plain,
( sdtasdt0(xp,X1) = xn
| xq != X1 ),
inference(sr,[status(thm)],[871,235,theory(equality)]) ).
cnf(873,plain,
( sdtmndt0(X1,X2) = X3
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[190,145]) ).
cnf(874,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(er,[status(thm)],[873,theory(equality)]) ).
cnf(898,plain,
( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[87,258,theory(equality)]) ).
cnf(899,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[87,258,theory(equality)]) ).
cnf(902,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(sdtasdt0(X1,X3))
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(spm,[status(thm)],[212,87,theory(equality)]) ).
cnf(915,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),X3)
| sdtasdt0(X1,sdtpldt0(X2,X4)) != X3
| ~ aNaturalNumber0(sdtasdt0(X1,X4))
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X4) ),
inference(spm,[status(thm)],[145,87,theory(equality)]) ).
cnf(952,plain,
( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(X2) ),
inference(rw,[status(thm)],[898,168,theory(equality)]) ).
cnf(953,plain,
( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[952,theory(equality)]) ).
cnf(954,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| $false ),
inference(rw,[status(thm)],[899,168,theory(equality)]) ).
cnf(955,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[954,theory(equality)]) ).
cnf(1049,plain,
( sdtsldt0(X1,X2) = X3
| sz00 = X2
| sdtasdt0(X2,X3) != X1
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[156,95]) ).
cnf(1050,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| sz00 = X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(er,[status(thm)],[1049,theory(equality)]) ).
cnf(1059,plain,
( sdtsldt0(X1,X2) = X3
| sz00 = X2
| sdtasdt0(X3,X2) != X1
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[1049,230,theory(equality)]) ).
cnf(1237,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sz00 = X1
| X2 = X3
| ~ sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(sdtasdt0(X1,X3))
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[151,136,theory(equality)]) ).
cnf(1579,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[106,470,theory(equality)]) ).
cnf(1583,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xp)
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[1579,238,theory(equality)]) ).
cnf(1584,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xp)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[1583,240,theory(equality)]) ).
cnf(1585,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1584,theory(equality)]) ).
cnf(1598,plain,
( xn = sdtasdt0(xn,xn)
| xq != esk7_0 ),
inference(spm,[status(thm)],[252,872,theory(equality)]) ).
cnf(1600,plain,
( xn = sdtasdt0(xm,xm)
| xq != sdtasdt0(xq,xq) ),
inference(spm,[status(thm)],[208,872,theory(equality)]) ).
cnf(1602,plain,
( xn = sz00
| ~ aNaturalNumber0(xp)
| xq != sz00 ),
inference(spm,[status(thm)],[53,872,theory(equality)]) ).
cnf(1604,plain,
( xn = sdtasdt0(X1,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| xq != X1 ),
inference(spm,[status(thm)],[230,872,theory(equality)]) ).
cnf(1621,plain,
( sz00 = xp
| X1 = X2
| sdtlseqdt0(xn,sdtasdt0(xp,X1))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xq != X2 ),
inference(spm,[status(thm)],[136,872,theory(equality)]) ).
cnf(1638,plain,
( xn = sz00
| $false
| xq != sz00 ),
inference(rw,[status(thm)],[1602,238,theory(equality)]) ).
cnf(1639,plain,
( xn = sz00
| xq != sz00 ),
inference(cn,[status(thm)],[1638,theory(equality)]) ).
cnf(1640,plain,
xq != sz00,
inference(sr,[status(thm)],[1639,237,theory(equality)]) ).
cnf(1644,plain,
( xn = sdtasdt0(X1,xp)
| ~ aNaturalNumber0(X1)
| $false
| xq != X1 ),
inference(rw,[status(thm)],[1604,238,theory(equality)]) ).
cnf(1645,plain,
( xn = sdtasdt0(X1,xp)
| ~ aNaturalNumber0(X1)
| xq != X1 ),
inference(cn,[status(thm)],[1644,theory(equality)]) ).
cnf(1683,plain,
( sz00 = xp
| X1 = X2
| sdtlseqdt0(xn,sdtasdt0(xp,X1))
| ~ sdtlseqdt0(X2,X1)
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xq != X2 ),
inference(rw,[status(thm)],[1621,238,theory(equality)]) ).
cnf(1684,plain,
( sz00 = xp
| X1 = X2
| sdtlseqdt0(xn,sdtasdt0(xp,X1))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xq != X2 ),
inference(cn,[status(thm)],[1683,theory(equality)]) ).
cnf(1685,plain,
( X1 = X2
| sdtlseqdt0(xn,sdtasdt0(xp,X1))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xq != X2 ),
inference(sr,[status(thm)],[1684,235,theory(equality)]) ).
cnf(1731,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[106,462,theory(equality)]) ).
cnf(1734,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,sz00)
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[1731,209,theory(equality)]) ).
cnf(1735,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1734,theory(equality)]) ).
cnf(1745,plain,
( doDivides0(xn,X1)
| xn != X1
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1)
| esk7_0 != xq ),
inference(spm,[status(thm)],[95,1598,theory(equality)]) ).
cnf(1783,plain,
( doDivides0(xn,X1)
| xn != X1
| $false
| ~ aNaturalNumber0(X1)
| esk7_0 != xq ),
inference(rw,[status(thm)],[1745,240,theory(equality)]) ).
cnf(1784,plain,
( doDivides0(xn,X1)
| xn != X1
| ~ aNaturalNumber0(X1)
| esk7_0 != xq ),
inference(cn,[status(thm)],[1783,theory(equality)]) ).
cnf(1895,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xq) ),
inference(spm,[status(thm)],[308,195,theory(equality)]) ).
cnf(1899,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| $false ),
inference(rw,[status(thm)],[1895,127,theory(equality)]) ).
cnf(1900,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[1899,theory(equality)]) ).
cnf(1909,plain,
( xq = sz10
| xp != xn
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[723,258,theory(equality)]) ).
cnf(1911,plain,
( xq = X1
| sdtasdt0(X1,xp) != xn
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[723,230,theory(equality)]) ).
cnf(1919,plain,
( xq = sz10
| xp != xn
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[1909,168,theory(equality)]) ).
cnf(1920,plain,
( xq = sz10
| xp != xn
| $false
| $false ),
inference(rw,[status(thm)],[1919,238,theory(equality)]) ).
cnf(1921,plain,
( xq = sz10
| xp != xn ),
inference(cn,[status(thm)],[1920,theory(equality)]) ).
cnf(1926,plain,
( xq = X1
| sdtasdt0(X1,xp) != xn
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[1911,238,theory(equality)]) ).
cnf(1927,plain,
( xq = X1
| sdtasdt0(X1,xp) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1926,theory(equality)]) ).
cnf(1959,plain,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[320,240,theory(equality)]) ).
cnf(1960,plain,
( sdtlseqdt0(xn,xm)
| sdtlseqdt0(xm,xn) ),
inference(spm,[status(thm)],[320,239,theory(equality)]) ).
cnf(2087,plain,
( xm = xn
| sdtlseqdt0(xn,xm) ),
inference(spm,[status(thm)],[173,1960,theory(equality)]) ).
cnf(2097,plain,
( sdtlseqdt0(X1,xm)
| xm = xn
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[106,2087,theory(equality)]) ).
cnf(2101,plain,
( sdtlseqdt0(X1,xm)
| xm = xn
| ~ sdtlseqdt0(X1,xn)
| $false
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[2097,240,theory(equality)]) ).
cnf(2102,plain,
( sdtlseqdt0(X1,xm)
| xm = xn
| ~ sdtlseqdt0(X1,xn)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[2101,239,theory(equality)]) ).
cnf(2103,plain,
( sdtlseqdt0(X1,xm)
| xm = xn
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[2102,theory(equality)]) ).
cnf(2124,plain,
( sdtlseqdt0(xm,xp)
| sdtlseqdt0(xp,xm) ),
inference(spm,[status(thm)],[321,238,theory(equality)]) ).
cnf(2125,plain,
( sdtlseqdt0(xm,xq)
| sdtlseqdt0(xq,xm) ),
inference(spm,[status(thm)],[321,127,theory(equality)]) ).
cnf(2289,plain,
( sdtasdt0(X1,xp) = xn
| xq != X1 ),
inference(csr,[status(thm)],[1645,801]) ).
cnf(2295,plain,
( sz00 = xp
| sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1)
| xq != X1 ),
inference(spm,[status(thm)],[166,2289,theory(equality)]) ).
cnf(2313,plain,
( sz00 = xp
| X1 = X2
| sdtlseqdt0(xn,sdtasdt0(X1,xp))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xq != X2 ),
inference(spm,[status(thm)],[134,2289,theory(equality)]) ).
cnf(2334,plain,
( sz00 = xp
| sdtlseqdt0(X1,xn)
| $false
| ~ aNaturalNumber0(X1)
| xq != X1 ),
inference(rw,[status(thm)],[2295,238,theory(equality)]) ).
cnf(2335,plain,
( sz00 = xp
| sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| xq != X1 ),
inference(cn,[status(thm)],[2334,theory(equality)]) ).
cnf(2336,plain,
( sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| xq != X1 ),
inference(sr,[status(thm)],[2335,235,theory(equality)]) ).
cnf(2374,plain,
( sz00 = xp
| X1 = X2
| sdtlseqdt0(xn,sdtasdt0(X1,xp))
| ~ sdtlseqdt0(X2,X1)
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xq != X2 ),
inference(rw,[status(thm)],[2313,238,theory(equality)]) ).
cnf(2375,plain,
( sz00 = xp
| X1 = X2
| sdtlseqdt0(xn,sdtasdt0(X1,xp))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xq != X2 ),
inference(cn,[status(thm)],[2374,theory(equality)]) ).
cnf(2376,plain,
( X1 = X2
| sdtlseqdt0(xn,sdtasdt0(X1,xp))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xq != X2 ),
inference(sr,[status(thm)],[2375,235,theory(equality)]) ).
cnf(2498,plain,
( sdtlseqdt0(X1,xn)
| xq != X1 ),
inference(csr,[status(thm)],[2336,801]) ).
cnf(2499,plain,
( xm = xn
| xq != xm ),
inference(spm,[status(thm)],[173,2498,theory(equality)]) ).
cnf(2500,plain,
( xn = X1
| ~ sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xn)
| xq != X1 ),
inference(spm,[status(thm)],[151,2498,theory(equality)]) ).
cnf(2502,plain,
( xn = X1
| ~ sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1)
| $false
| xq != X1 ),
inference(rw,[status(thm)],[2500,240,theory(equality)]) ).
cnf(2503,plain,
( xn = X1
| ~ sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1)
| xq != X1 ),
inference(cn,[status(thm)],[2502,theory(equality)]) ).
cnf(2754,plain,
( X1 = xp
| X1 != xn
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1)
| xq != sz10 ),
inference(spm,[status(thm)],[685,872,theory(equality)]) ).
cnf(2767,plain,
( X1 = xp
| X1 != xn
| $false
| ~ aNaturalNumber0(X1)
| xq != sz10 ),
inference(rw,[status(thm)],[2754,238,theory(equality)]) ).
cnf(2768,plain,
( X1 = xp
| X1 != xn
| ~ aNaturalNumber0(X1)
| xq != sz10 ),
inference(cn,[status(thm)],[2767,theory(equality)]) ).
cnf(2791,plain,
( sz10 = xp
| xq != sz10
| sz10 != xn ),
inference(spm,[status(thm)],[2768,168,theory(equality)]) ).
cnf(2804,plain,
( xq != sz10
| xn != sz10 ),
inference(sr,[status(thm)],[2791,264,theory(equality)]) ).
cnf(2805,plain,
( xn != sz10
| xp != xn ),
inference(spm,[status(thm)],[2804,1921,theory(equality)]) ).
cnf(2811,plain,
( sdtlseqdt0(sz10,xn)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[1585,162,theory(equality)]) ).
cnf(2813,plain,
( sdtlseqdt0(xm,xn)
| sdtlseqdt0(xp,xm)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[1585,2124,theory(equality)]) ).
cnf(2822,plain,
( sdtlseqdt0(sz10,xn)
| sz10 = xp
| sz00 = xp
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[2811,168,theory(equality)]) ).
cnf(2823,plain,
( sdtlseqdt0(sz10,xn)
| sz10 = xp
| sz00 = xp
| $false
| $false ),
inference(rw,[status(thm)],[2822,238,theory(equality)]) ).
cnf(2824,plain,
( sdtlseqdt0(sz10,xn)
| sz10 = xp
| sz00 = xp ),
inference(cn,[status(thm)],[2823,theory(equality)]) ).
cnf(2825,plain,
( sdtlseqdt0(sz10,xn)
| xp = sz00 ),
inference(sr,[status(thm)],[2824,264,theory(equality)]) ).
cnf(2826,plain,
sdtlseqdt0(sz10,xn),
inference(sr,[status(thm)],[2825,235,theory(equality)]) ).
cnf(2830,plain,
( sdtlseqdt0(xm,xn)
| sdtlseqdt0(xp,xm)
| $false ),
inference(rw,[status(thm)],[2813,239,theory(equality)]) ).
cnf(2831,plain,
( sdtlseqdt0(xm,xn)
| sdtlseqdt0(xp,xm) ),
inference(cn,[status(thm)],[2830,theory(equality)]) ).
cnf(2856,plain,
( xm = xn
| sdtlseqdt0(xp,xm) ),
inference(spm,[status(thm)],[173,2831,theory(equality)]) ).
cnf(3202,plain,
( xn = X1
| xq != X1
| ~ sdtlseqdt0(xn,X1) ),
inference(csr,[status(thm)],[2503,801]) ).
cnf(3316,plain,
( esk7_0 = sdtasdt0(xm,xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(spm,[status(thm)],[739,110,theory(equality)]) ).
cnf(3328,plain,
( esk7_0 = sdtasdt0(xm,xm)
| $false ),
inference(rw,[status(thm)],[3316,1900,theory(equality)]) ).
cnf(3329,plain,
esk7_0 = sdtasdt0(xm,xm),
inference(cn,[status(thm)],[3328,theory(equality)]) ).
cnf(3349,plain,
( sz00 = xm
| sdtlseqdt0(xm,esk7_0)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[166,3329,theory(equality)]) ).
cnf(3350,plain,
( sz00 = xm
| esk7_0 != sz00
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[62,3329,theory(equality)]) ).
cnf(3352,plain,
( doDivides0(xm,X1)
| esk7_0 != X1
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[95,3329,theory(equality)]) ).
cnf(3353,plain,
( sz00 = xm
| xm = X1
| esk7_0 != sdtasdt0(X1,xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[67,3329,theory(equality)]) ).
cnf(3357,plain,
( sdtasdt0(esk7_0,X1) = sdtasdt0(xm,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[177,3329,theory(equality)]) ).
cnf(3358,plain,
( sdtpldt0(esk7_0,sdtasdt0(xm,X1)) = sdtasdt0(xm,sdtpldt0(xm,X1))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[87,3329,theory(equality)]) ).
cnf(3364,plain,
( sz00 = xm
| X1 = xm
| sdtlseqdt0(esk7_0,sdtasdt0(xm,X1))
| ~ sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[136,3329,theory(equality)]) ).
cnf(3365,plain,
( sz00 = xm
| xm = X1
| sdtlseqdt0(sdtasdt0(xm,X1),esk7_0)
| ~ sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[136,3329,theory(equality)]) ).
cnf(3368,plain,
( sdtsldt0(esk7_0,X1) = sdtasdt0(xm,sdtsldt0(xm,X1))
| sz00 = X1
| ~ doDivides0(X1,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[234,3329,theory(equality)]) ).
cnf(3378,plain,
sdtasdt0(xp,esk7_0) = sdtasdt0(xn,xn),
inference(rw,[status(thm)],[110,3329,theory(equality)]) ).
cnf(3389,plain,
( esk7_0 = xn
| sdtasdt0(xq,xq) != xq ),
inference(rw,[status(thm)],[1600,3329,theory(equality)]) ).
cnf(3400,plain,
( sz00 = xm
| sdtlseqdt0(xm,esk7_0)
| $false ),
inference(rw,[status(thm)],[3349,239,theory(equality)]) ).
cnf(3401,plain,
( sz00 = xm
| sdtlseqdt0(xm,esk7_0) ),
inference(cn,[status(thm)],[3400,theory(equality)]) ).
cnf(3402,plain,
sdtlseqdt0(xm,esk7_0),
inference(sr,[status(thm)],[3401,236,theory(equality)]) ).
cnf(3403,plain,
( sz00 = xm
| esk7_0 != sz00
| $false ),
inference(rw,[status(thm)],[3350,239,theory(equality)]) ).
cnf(3404,plain,
( sz00 = xm
| esk7_0 != sz00 ),
inference(cn,[status(thm)],[3403,theory(equality)]) ).
cnf(3405,plain,
esk7_0 != sz00,
inference(sr,[status(thm)],[3404,236,theory(equality)]) ).
cnf(3408,plain,
( doDivides0(xm,X1)
| esk7_0 != X1
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[3352,239,theory(equality)]) ).
cnf(3409,plain,
( doDivides0(xm,X1)
| esk7_0 != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[3408,theory(equality)]) ).
cnf(3410,plain,
( sz00 = xm
| xm = X1
| esk7_0 != sdtasdt0(X1,xm)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[3353,239,theory(equality)]) ).
cnf(3411,plain,
( sz00 = xm
| xm = X1
| esk7_0 != sdtasdt0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[3410,theory(equality)]) ).
cnf(3412,plain,
( xm = X1
| sdtasdt0(X1,xm) != esk7_0
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[3411,236,theory(equality)]) ).
cnf(3422,plain,
( sdtasdt0(esk7_0,X1) = sdtasdt0(xm,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[3357,239,theory(equality)]) ).
cnf(3423,plain,
( sdtasdt0(esk7_0,X1) = sdtasdt0(xm,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[3422,theory(equality)]) ).
cnf(3424,plain,
( sdtpldt0(esk7_0,sdtasdt0(xm,X1)) = sdtasdt0(xm,sdtpldt0(xm,X1))
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[3358,239,theory(equality)]) ).
cnf(3425,plain,
( sdtpldt0(esk7_0,sdtasdt0(xm,X1)) = sdtasdt0(xm,sdtpldt0(xm,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[3424,theory(equality)]) ).
cnf(3437,plain,
( sz00 = xm
| X1 = xm
| sdtlseqdt0(esk7_0,sdtasdt0(xm,X1))
| ~ sdtlseqdt0(xm,X1)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[3364,239,theory(equality)]) ).
cnf(3438,plain,
( sz00 = xm
| X1 = xm
| sdtlseqdt0(esk7_0,sdtasdt0(xm,X1))
| ~ sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[3437,theory(equality)]) ).
cnf(3439,plain,
( X1 = xm
| sdtlseqdt0(esk7_0,sdtasdt0(xm,X1))
| ~ sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[3438,236,theory(equality)]) ).
cnf(3440,plain,
( sz00 = xm
| xm = X1
| sdtlseqdt0(sdtasdt0(xm,X1),esk7_0)
| ~ sdtlseqdt0(X1,xm)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[3365,239,theory(equality)]) ).
cnf(3441,plain,
( sz00 = xm
| xm = X1
| sdtlseqdt0(sdtasdt0(xm,X1),esk7_0)
| ~ sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[3440,theory(equality)]) ).
cnf(3442,plain,
( xm = X1
| sdtlseqdt0(sdtasdt0(xm,X1),esk7_0)
| ~ sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[3441,236,theory(equality)]) ).
cnf(3449,plain,
( sdtsldt0(esk7_0,X1) = sdtasdt0(xm,sdtsldt0(xm,X1))
| sz00 = X1
| ~ doDivides0(X1,xm)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[3368,239,theory(equality)]) ).
cnf(3450,plain,
( sdtsldt0(esk7_0,X1) = sdtasdt0(xm,sdtsldt0(xm,X1))
| sz00 = X1
| ~ doDivides0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[3449,theory(equality)]) ).
cnf(3466,plain,
( esk7_0 = xm
| ~ sdtlseqdt0(esk7_0,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[151,3402,theory(equality)]) ).
cnf(3470,plain,
( esk7_0 = xm
| ~ sdtlseqdt0(esk7_0,xm)
| $false
| ~ aNaturalNumber0(esk7_0) ),
inference(rw,[status(thm)],[3466,239,theory(equality)]) ).
cnf(3471,plain,
( esk7_0 = xm
| ~ sdtlseqdt0(esk7_0,xm)
| $false
| $false ),
inference(rw,[status(thm)],[3470,253,theory(equality)]) ).
cnf(3472,plain,
( esk7_0 = xm
| ~ sdtlseqdt0(esk7_0,xm) ),
inference(cn,[status(thm)],[3471,theory(equality)]) ).
cnf(3479,plain,
( esk7_0 = xm
| xm = xn
| ~ sdtlseqdt0(esk7_0,xn)
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[3472,2103,theory(equality)]) ).
cnf(3480,plain,
( esk7_0 = xm
| xm = xn
| ~ sdtlseqdt0(esk7_0,xn)
| $false ),
inference(rw,[status(thm)],[3479,253,theory(equality)]) ).
cnf(3481,plain,
( esk7_0 = xm
| xm = xn
| ~ sdtlseqdt0(esk7_0,xn) ),
inference(cn,[status(thm)],[3480,theory(equality)]) ).
cnf(3493,plain,
( sdtpldt0(sdtasdt0(xp,X1),sdtasdt0(xn,xn)) = sdtasdt0(xp,sdtpldt0(X1,esk7_0))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[87,3378,theory(equality)]) ).
cnf(3540,plain,
( sdtpldt0(sdtasdt0(xp,X1),sdtasdt0(xn,xn)) = sdtasdt0(xp,sdtpldt0(X1,esk7_0))
| $false
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk7_0) ),
inference(rw,[status(thm)],[3493,238,theory(equality)]) ).
cnf(3541,plain,
( sdtpldt0(sdtasdt0(xp,X1),sdtasdt0(xn,xn)) = sdtasdt0(xp,sdtpldt0(X1,esk7_0))
| $false
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[3540,253,theory(equality)]) ).
cnf(3542,plain,
( sdtpldt0(sdtasdt0(xp,X1),sdtasdt0(xn,xn)) = sdtasdt0(xp,sdtpldt0(X1,esk7_0))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[3541,theory(equality)]) ).
cnf(3626,plain,
( esk7_0 = xn
| sdtasdt0(sz10,sz10) != sz10
| xp != xn ),
inference(spm,[status(thm)],[3389,1921,theory(equality)]) ).
cnf(3683,plain,
( sz00 = X1
| sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm)
| esk7_0 != X1 ),
inference(spm,[status(thm)],[113,3409,theory(equality)]) ).
cnf(3691,plain,
( sz00 = X1
| sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1)
| $false
| esk7_0 != X1 ),
inference(rw,[status(thm)],[3683,239,theory(equality)]) ).
cnf(3692,plain,
( sz00 = X1
| sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1)
| esk7_0 != X1 ),
inference(cn,[status(thm)],[3691,theory(equality)]) ).
cnf(3926,plain,
( xm = sz10
| xm != esk7_0
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[3412,257,theory(equality)]) ).
cnf(3930,plain,
( xm = sdtasdt0(X1,X2)
| sdtasdt0(X1,sdtasdt0(X2,xm)) != esk7_0
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[3412,177,theory(equality)]) ).
cnf(3932,plain,
( xm = sz10
| xm != esk7_0
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[3926,168,theory(equality)]) ).
cnf(3933,plain,
( xm = sz10
| xm != esk7_0
| $false
| $false ),
inference(rw,[status(thm)],[3932,239,theory(equality)]) ).
cnf(3934,plain,
( xm = sz10
| xm != esk7_0 ),
inference(cn,[status(thm)],[3933,theory(equality)]) ).
cnf(3943,plain,
( xm = sdtasdt0(X1,X2)
| sdtasdt0(X1,sdtasdt0(X2,xm)) != esk7_0
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[3930,239,theory(equality)]) ).
cnf(3944,plain,
( xm = sdtasdt0(X1,X2)
| sdtasdt0(X1,sdtasdt0(X2,xm)) != esk7_0
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[3943,theory(equality)]) ).
cnf(4057,plain,
( sz00 = xp
| sdtlseqdt0(xq,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq) ),
inference(spm,[status(thm)],[425,126,theory(equality)]) ).
cnf(4077,plain,
( sz00 = xp
| sdtlseqdt0(xq,xn)
| $false
| ~ aNaturalNumber0(xq) ),
inference(rw,[status(thm)],[4057,238,theory(equality)]) ).
cnf(4078,plain,
( sz00 = xp
| sdtlseqdt0(xq,xn)
| $false
| $false ),
inference(rw,[status(thm)],[4077,127,theory(equality)]) ).
cnf(4079,plain,
( sz00 = xp
| sdtlseqdt0(xq,xn) ),
inference(cn,[status(thm)],[4078,theory(equality)]) ).
cnf(4080,plain,
sdtlseqdt0(xq,xn),
inference(sr,[status(thm)],[4079,235,theory(equality)]) ).
cnf(4122,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[106,4080,theory(equality)]) ).
cnf(4130,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xq)
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[4122,127,theory(equality)]) ).
cnf(4131,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xq)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[4130,240,theory(equality)]) ).
cnf(4132,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xq)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[4131,theory(equality)]) ).
cnf(4271,plain,
( doDivides0(sz10,xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[810,605,theory(equality)]) ).
cnf(4287,plain,
( doDivides0(sz10,xn)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[4271,168,theory(equality)]) ).
cnf(4288,plain,
( doDivides0(sz10,xn)
| $false
| $false ),
inference(rw,[status(thm)],[4287,238,theory(equality)]) ).
cnf(4289,plain,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[4288,theory(equality)]) ).
cnf(4507,plain,
( esk7_0 = xn
| xp != xn
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[3626,258,theory(equality)]) ).
cnf(4511,plain,
( esk7_0 = xn
| xp != xn
| $false ),
inference(rw,[status(thm)],[4507,168,theory(equality)]) ).
cnf(4512,plain,
( esk7_0 = xn
| xp != xn ),
inference(cn,[status(thm)],[4511,theory(equality)]) ).
cnf(4534,plain,
( xm = xn
| ~ sdtlseqdt0(xn,xn)
| xp != xn ),
inference(spm,[status(thm)],[3481,4512,theory(equality)]) ).
cnf(4544,plain,
( xm = sz10
| xn != xm
| xp != xn ),
inference(spm,[status(thm)],[3934,4512,theory(equality)]) ).
cnf(4559,plain,
( xm = xn
| $false
| xp != xn ),
inference(rw,[status(thm)],[4534,1959,theory(equality)]) ).
cnf(4560,plain,
( xm = xn
| xp != xn ),
inference(cn,[status(thm)],[4559,theory(equality)]) ).
cnf(4618,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[452,212]) ).
cnf(4704,plain,
( xm = sz10
| xp != xn ),
inference(csr,[status(thm)],[4544,4560]) ).
cnf(4712,plain,
( sz10 = xn
| ~ sdtlseqdt0(sz10,xn)
| xp != xn ),
inference(spm,[status(thm)],[173,4704,theory(equality)]) ).
cnf(4742,plain,
( sz10 = xn
| $false
| xp != xn ),
inference(rw,[status(thm)],[4712,2826,theory(equality)]) ).
cnf(4743,plain,
( sz10 = xn
| xp != xn ),
inference(cn,[status(thm)],[4742,theory(equality)]) ).
cnf(4754,plain,
xp != xn,
inference(csr,[status(thm)],[4743,2805]) ).
cnf(4909,plain,
( sdtlseqdt0(xm,xn)
| sz00 = xq
| ~ aNaturalNumber0(xm)
| esk7_0 != xq
| ~ aNaturalNumber0(xq) ),
inference(spm,[status(thm)],[4132,3692,theory(equality)]) ).
cnf(4938,plain,
( sdtlseqdt0(xm,xn)
| sz00 = xq
| $false
| esk7_0 != xq
| ~ aNaturalNumber0(xq) ),
inference(rw,[status(thm)],[4909,239,theory(equality)]) ).
cnf(4939,plain,
( sdtlseqdt0(xm,xn)
| sz00 = xq
| $false
| esk7_0 != xq
| $false ),
inference(rw,[status(thm)],[4938,127,theory(equality)]) ).
cnf(4940,plain,
( sdtlseqdt0(xm,xn)
| sz00 = xq
| esk7_0 != xq ),
inference(cn,[status(thm)],[4939,theory(equality)]) ).
cnf(4941,plain,
( sdtlseqdt0(xm,xn)
| esk7_0 != xq ),
inference(sr,[status(thm)],[4940,1640,theory(equality)]) ).
cnf(4943,plain,
( xm = xn
| esk7_0 != xq ),
inference(spm,[status(thm)],[173,4941,theory(equality)]) ).
cnf(6140,plain,
( sdtasdt0(xm,xm) = sdtasdt0(esk7_0,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[3423,258,theory(equality)]) ).
cnf(6141,plain,
( sdtasdt0(xm,sz00) = sdtasdt0(esk7_0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[3423,53,theory(equality)]) ).
cnf(6164,plain,
( sz00 = sdtasdt0(xm,X1)
| xm = X2
| sdtlseqdt0(sdtasdt0(X2,sdtasdt0(xm,X1)),sdtasdt0(esk7_0,X1))
| ~ sdtlseqdt0(X2,xm)
| ~ aNaturalNumber0(sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[134,3423,theory(equality)]) ).
cnf(6171,plain,
( sdtasdt0(xm,xn) = sdtasdt0(esk7_0,xp)
| ~ aNaturalNumber0(xp)
| xq != xm ),
inference(spm,[status(thm)],[3423,2289,theory(equality)]) ).
cnf(6183,plain,
( esk7_0 = sdtasdt0(esk7_0,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[6140,3329,theory(equality)]) ).
cnf(6184,plain,
( esk7_0 = sdtasdt0(esk7_0,sz10)
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[6183,168,theory(equality)]) ).
cnf(6185,plain,
( esk7_0 = sdtasdt0(esk7_0,sz10)
| $false
| $false ),
inference(rw,[status(thm)],[6184,239,theory(equality)]) ).
cnf(6186,plain,
esk7_0 = sdtasdt0(esk7_0,sz10),
inference(cn,[status(thm)],[6185,theory(equality)]) ).
cnf(6187,plain,
( sdtasdt0(xm,sz00) = sdtasdt0(esk7_0,sz00)
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[6141,209,theory(equality)]) ).
cnf(6188,plain,
( sdtasdt0(xm,sz00) = sdtasdt0(esk7_0,sz00)
| $false
| $false ),
inference(rw,[status(thm)],[6187,239,theory(equality)]) ).
cnf(6189,plain,
sdtasdt0(xm,sz00) = sdtasdt0(esk7_0,sz00),
inference(cn,[status(thm)],[6188,theory(equality)]) ).
cnf(6240,plain,
( sz00 = sdtasdt0(xm,X1)
| xm = X2
| sdtlseqdt0(sdtasdt0(X2,sdtasdt0(xm,X1)),sdtasdt0(esk7_0,X1))
| ~ sdtlseqdt0(X2,xm)
| ~ aNaturalNumber0(sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[6164,239,theory(equality)]) ).
cnf(6241,plain,
( sz00 = sdtasdt0(xm,X1)
| xm = X2
| sdtlseqdt0(sdtasdt0(X2,sdtasdt0(xm,X1)),sdtasdt0(esk7_0,X1))
| ~ sdtlseqdt0(X2,xm)
| ~ aNaturalNumber0(sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[6240,theory(equality)]) ).
cnf(6259,plain,
( sdtasdt0(xm,xn) = sdtasdt0(esk7_0,xp)
| $false
| xq != xm ),
inference(rw,[status(thm)],[6171,238,theory(equality)]) ).
cnf(6260,plain,
( sdtasdt0(xm,xn) = sdtasdt0(esk7_0,xp)
| xq != xm ),
inference(cn,[status(thm)],[6259,theory(equality)]) ).
cnf(6279,plain,
( sz00 = esk7_0
| sz10 = X1
| esk7_0 != sdtasdt0(esk7_0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[68,6186,theory(equality)]) ).
cnf(6328,plain,
( sz00 = esk7_0
| sz10 = X1
| esk7_0 != sdtasdt0(esk7_0,X1)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(esk7_0) ),
inference(rw,[status(thm)],[6279,168,theory(equality)]) ).
cnf(6329,plain,
( sz00 = esk7_0
| sz10 = X1
| esk7_0 != sdtasdt0(esk7_0,X1)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[6328,253,theory(equality)]) ).
cnf(6330,plain,
( sz00 = esk7_0
| sz10 = X1
| esk7_0 != sdtasdt0(esk7_0,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[6329,theory(equality)]) ).
cnf(6331,plain,
( sz10 = X1
| sdtasdt0(esk7_0,X1) != esk7_0
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[6330,3405,theory(equality)]) ).
cnf(6727,plain,
( sdtasdt0(xm,sz00) = sz00
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[53,6189,theory(equality)]) ).
cnf(6748,plain,
( sdtasdt0(xm,sz00) = sz00
| $false ),
inference(rw,[status(thm)],[6727,253,theory(equality)]) ).
cnf(6749,plain,
sdtasdt0(xm,sz00) = sz00,
inference(cn,[status(thm)],[6748,theory(equality)]) ).
cnf(7404,plain,
( sz10 = xp
| xn != esk7_0
| ~ aNaturalNumber0(xp)
| xq != esk7_0 ),
inference(spm,[status(thm)],[6331,2289,theory(equality)]) ).
cnf(7421,plain,
( sz10 = xp
| xn != esk7_0
| $false
| xq != esk7_0 ),
inference(rw,[status(thm)],[7404,238,theory(equality)]) ).
cnf(7422,plain,
( sz10 = xp
| xn != esk7_0
| xq != esk7_0 ),
inference(cn,[status(thm)],[7421,theory(equality)]) ).
cnf(7423,plain,
( esk7_0 != xn
| esk7_0 != xq ),
inference(sr,[status(thm)],[7422,264,theory(equality)]) ).
cnf(7627,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[575,195]) ).
cnf(7629,plain,
( doDivides0(xm,esk7_0)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[7627,3329,theory(equality)]) ).
cnf(7631,plain,
( doDivides0(esk7_0,esk7_0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[7627,6186,theory(equality)]) ).
cnf(7634,plain,
( doDivides0(xm,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[7627,6749,theory(equality)]) ).
cnf(7642,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[7627,230,theory(equality)]) ).
cnf(7662,plain,
( doDivides0(xm,esk7_0)
| $false ),
inference(rw,[status(thm)],[7629,239,theory(equality)]) ).
cnf(7663,plain,
doDivides0(xm,esk7_0),
inference(cn,[status(thm)],[7662,theory(equality)]) ).
cnf(7668,plain,
( doDivides0(esk7_0,esk7_0)
| $false
| ~ aNaturalNumber0(esk7_0) ),
inference(rw,[status(thm)],[7631,168,theory(equality)]) ).
cnf(7669,plain,
( doDivides0(esk7_0,esk7_0)
| $false
| $false ),
inference(rw,[status(thm)],[7668,253,theory(equality)]) ).
cnf(7670,plain,
doDivides0(esk7_0,esk7_0),
inference(cn,[status(thm)],[7669,theory(equality)]) ).
cnf(7677,plain,
( doDivides0(xm,sz00)
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[7634,209,theory(equality)]) ).
cnf(7678,plain,
( doDivides0(xm,sz00)
| $false
| $false ),
inference(rw,[status(thm)],[7677,239,theory(equality)]) ).
cnf(7679,plain,
doDivides0(xm,sz00),
inference(cn,[status(thm)],[7678,theory(equality)]) ).
cnf(7716,plain,
( doDivides0(X1,esk7_0)
| ~ doDivides0(X1,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[56,7663,theory(equality)]) ).
cnf(7728,plain,
( doDivides0(X1,esk7_0)
| ~ doDivides0(X1,xm)
| $false
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[7716,239,theory(equality)]) ).
cnf(7729,plain,
( doDivides0(X1,esk7_0)
| ~ doDivides0(X1,xm)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[7728,253,theory(equality)]) ).
cnf(7730,plain,
( doDivides0(X1,esk7_0)
| ~ doDivides0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[7729,theory(equality)]) ).
cnf(8122,plain,
( sz00 = esk7_0
| sdtlseqdt0(X1,esk7_0)
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xm) ),
inference(spm,[status(thm)],[113,7730,theory(equality)]) ).
cnf(8127,plain,
( sz00 = esk7_0
| sdtlseqdt0(X1,esk7_0)
| $false
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xm) ),
inference(rw,[status(thm)],[8122,253,theory(equality)]) ).
cnf(8128,plain,
( sz00 = esk7_0
| sdtlseqdt0(X1,esk7_0)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xm) ),
inference(cn,[status(thm)],[8127,theory(equality)]) ).
cnf(8129,plain,
( sdtlseqdt0(X1,esk7_0)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xm) ),
inference(sr,[status(thm)],[8128,3405,theory(equality)]) ).
cnf(8179,plain,
( sdtlseqdt0(xn,esk7_0)
| ~ aNaturalNumber0(xn)
| esk7_0 != xq
| xn != xm
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[8129,1784,theory(equality)]) ).
cnf(8204,plain,
( sdtlseqdt0(xn,esk7_0)
| $false
| esk7_0 != xq
| xn != xm
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[8179,240,theory(equality)]) ).
cnf(8205,plain,
( sdtlseqdt0(xn,esk7_0)
| $false
| esk7_0 != xq
| xn != xm
| $false ),
inference(rw,[status(thm)],[8204,239,theory(equality)]) ).
cnf(8206,plain,
( sdtlseqdt0(xn,esk7_0)
| esk7_0 != xq
| xn != xm ),
inference(cn,[status(thm)],[8205,theory(equality)]) ).
cnf(8243,plain,
( sdtlseqdt0(xn,esk7_0)
| esk7_0 != xq ),
inference(csr,[status(thm)],[8206,4943]) ).
cnf(8247,plain,
( xn = esk7_0
| xq != esk7_0 ),
inference(spm,[status(thm)],[3202,8243,theory(equality)]) ).
cnf(8266,plain,
esk7_0 != xq,
inference(csr,[status(thm)],[8247,7423]) ).
cnf(8372,plain,
( xp = X1
| sz10 = X1
| X2 != xp
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[626,94]) ).
cnf(9831,plain,
( sz10 = xp
| sdtasdt0(xm,xn) != esk7_0
| ~ aNaturalNumber0(xp)
| xq != xm ),
inference(spm,[status(thm)],[6331,6260,theory(equality)]) ).
cnf(9937,plain,
( sz10 = xp
| sdtasdt0(xm,xn) != esk7_0
| $false
| xq != xm ),
inference(rw,[status(thm)],[9831,238,theory(equality)]) ).
cnf(9938,plain,
( sz10 = xp
| sdtasdt0(xm,xn) != esk7_0
| xq != xm ),
inference(cn,[status(thm)],[9937,theory(equality)]) ).
cnf(9939,plain,
( sdtasdt0(xm,xn) != esk7_0
| xq != xm ),
inference(sr,[status(thm)],[9938,264,theory(equality)]) ).
cnf(12651,plain,
( sdtasdt0(xp,xq) = sdtasdt0(xn,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xq) ),
inference(spm,[status(thm)],[843,258,theory(equality)]) ).
cnf(12652,plain,
( sdtasdt0(xp,sz00) = sdtasdt0(xn,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xq) ),
inference(spm,[status(thm)],[843,53,theory(equality)]) ).
cnf(12696,plain,
( xn = sdtasdt0(xn,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xq) ),
inference(rw,[status(thm)],[12651,126,theory(equality)]) ).
cnf(12697,plain,
( xn = sdtasdt0(xn,sz10)
| $false
| ~ aNaturalNumber0(xq) ),
inference(rw,[status(thm)],[12696,168,theory(equality)]) ).
cnf(12698,plain,
( xn = sdtasdt0(xn,sz10)
| $false
| $false ),
inference(rw,[status(thm)],[12697,127,theory(equality)]) ).
cnf(12699,plain,
xn = sdtasdt0(xn,sz10),
inference(cn,[status(thm)],[12698,theory(equality)]) ).
cnf(12700,plain,
( sdtasdt0(xp,sz00) = sdtasdt0(xn,sz00)
| $false
| ~ aNaturalNumber0(xq) ),
inference(rw,[status(thm)],[12652,209,theory(equality)]) ).
cnf(12701,plain,
( sdtasdt0(xp,sz00) = sdtasdt0(xn,sz00)
| $false
| $false ),
inference(rw,[status(thm)],[12700,127,theory(equality)]) ).
cnf(12702,plain,
sdtasdt0(xp,sz00) = sdtasdt0(xn,sz00),
inference(cn,[status(thm)],[12701,theory(equality)]) ).
cnf(12988,plain,
( xn = sdtasdt0(sz10,xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[230,12699,theory(equality)]) ).
cnf(12993,plain,
( doDivides0(xn,X1)
| xn != X1
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[95,12699,theory(equality)]) ).
cnf(12998,plain,
( sdtasdt0(xn,X1) = sdtasdt0(xn,sdtasdt0(sz10,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[177,12699,theory(equality)]) ).
cnf(13015,plain,
( doDivides0(xn,xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[7627,12699,theory(equality)]) ).
cnf(13027,plain,
( xn = sdtasdt0(sz10,xn)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[12988,168,theory(equality)]) ).
cnf(13028,plain,
( xn = sdtasdt0(sz10,xn)
| $false
| $false ),
inference(rw,[status(thm)],[13027,240,theory(equality)]) ).
cnf(13029,plain,
xn = sdtasdt0(sz10,xn),
inference(cn,[status(thm)],[13028,theory(equality)]) ).
cnf(13043,plain,
( doDivides0(xn,X1)
| xn != X1
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[12993,168,theory(equality)]) ).
cnf(13044,plain,
( doDivides0(xn,X1)
| xn != X1
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[13043,240,theory(equality)]) ).
cnf(13045,plain,
( doDivides0(xn,X1)
| xn != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[13044,theory(equality)]) ).
cnf(13062,plain,
( sdtasdt0(xn,X1) = sdtasdt0(xn,sdtasdt0(sz10,X1))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[12998,168,theory(equality)]) ).
cnf(13063,plain,
( sdtasdt0(xn,X1) = sdtasdt0(xn,sdtasdt0(sz10,X1))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[13062,240,theory(equality)]) ).
cnf(13064,plain,
( sdtasdt0(xn,X1) = sdtasdt0(xn,sdtasdt0(sz10,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[13063,theory(equality)]) ).
cnf(13116,plain,
( doDivides0(xn,xn)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[13015,168,theory(equality)]) ).
cnf(13117,plain,
( doDivides0(xn,xn)
| $false
| $false ),
inference(rw,[status(thm)],[13116,240,theory(equality)]) ).
cnf(13118,plain,
doDivides0(xn,xn),
inference(cn,[status(thm)],[13117,theory(equality)]) ).
cnf(13165,plain,
( sdtsldt0(X1,sz10) = xn
| sz00 = sz10
| xn != X1
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[1049,13029,theory(equality)]) ).
cnf(13234,plain,
( sdtsldt0(X1,sz10) = xn
| sz00 = sz10
| xn != X1
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[13165,240,theory(equality)]) ).
cnf(13235,plain,
( sdtsldt0(X1,sz10) = xn
| sz00 = sz10
| xn != X1
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[13234,168,theory(equality)]) ).
cnf(13236,plain,
( sdtsldt0(X1,sz10) = xn
| sz00 = sz10
| xn != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[13235,theory(equality)]) ).
cnf(13237,plain,
( sdtsldt0(X1,sz10) = xn
| xn != X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[13236,167,theory(equality)]) ).
cnf(13758,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[859,6749,theory(equality)]) ).
cnf(13842,plain,
( sdtasdt0(sz10,sz00) = sz00
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[13758,209,theory(equality)]) ).
cnf(13843,plain,
( sdtasdt0(sz10,sz00) = sz00
| $false
| $false ),
inference(rw,[status(thm)],[13842,239,theory(equality)]) ).
cnf(13844,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[13843,theory(equality)]) ).
cnf(13987,plain,
( sdtsldt0(X1,sz10) = sz00
| sz00 = sz10
| sz00 != X1
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[1049,13844,theory(equality)]) ).
cnf(14038,plain,
( sdtsldt0(X1,sz10) = sz00
| sz00 = sz10
| sz00 != X1
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[13987,209,theory(equality)]) ).
cnf(14039,plain,
( sdtsldt0(X1,sz10) = sz00
| sz00 = sz10
| sz00 != X1
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[14038,168,theory(equality)]) ).
cnf(14040,plain,
( sdtsldt0(X1,sz10) = sz00
| sz00 = sz10
| sz00 != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[14039,theory(equality)]) ).
cnf(14041,plain,
( sdtsldt0(X1,sz10) = sz00
| sz00 != X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[14040,167,theory(equality)]) ).
cnf(14127,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[861,195]) ).
cnf(14198,plain,
( sz00 = sdtasdt0(xn,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[843,14127,theory(equality)]) ).
cnf(14257,plain,
( sz00 = sdtasdt0(xn,sz00)
| $false
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[14198,209,theory(equality)]) ).
cnf(14258,plain,
( sz00 = sdtasdt0(xn,sz00)
| $false
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[14257,127,theory(equality)]) ).
cnf(14259,plain,
( sz00 = sdtasdt0(xn,sz00)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[14258,238,theory(equality)]) ).
cnf(14260,plain,
sz00 = sdtasdt0(xn,sz00),
inference(cn,[status(thm)],[14259,theory(equality)]) ).
cnf(14775,plain,
sdtasdt0(xp,sz00) = sz00,
inference(rw,[status(thm)],[12702,14260,theory(equality)]) ).
cnf(14777,plain,
( sz00 = sdtasdt0(sz00,xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[230,14775,theory(equality)]) ).
cnf(14808,plain,
( sz00 = sdtasdt0(sz00,xp)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[14777,209,theory(equality)]) ).
cnf(14809,plain,
( sz00 = sdtasdt0(sz00,xp)
| $false
| $false ),
inference(rw,[status(thm)],[14808,238,theory(equality)]) ).
cnf(14810,plain,
sz00 = sdtasdt0(sz00,xp),
inference(cn,[status(thm)],[14809,theory(equality)]) ).
cnf(15184,plain,
( sdtpldt0(sz00,sdtasdt0(X1,xp)) = sdtasdt0(sdtpldt0(sz00,X1),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[86,14810,theory(equality)]) ).
cnf(15231,plain,
( sdtpldt0(sz00,sdtasdt0(X1,xp)) = sdtasdt0(sdtpldt0(sz00,X1),xp)
| $false
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[15184,238,theory(equality)]) ).
cnf(15232,plain,
( sdtpldt0(sz00,sdtasdt0(X1,xp)) = sdtasdt0(sdtpldt0(sz00,X1),xp)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[15231,209,theory(equality)]) ).
cnf(15233,plain,
( sdtpldt0(sz00,sdtasdt0(X1,xp)) = sdtasdt0(sdtpldt0(sz00,X1),xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[15232,theory(equality)]) ).
cnf(15396,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[824,195]) ).
cnf(15676,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[825,195]) ).
cnf(15677,plain,
( sdtasdt0(X1,xn) = sdtasdt0(xq,sdtasdt0(X1,xp))
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[15676,126,theory(equality)]) ).
cnf(15700,plain,
( sdtasdt0(xn,sdtasdt0(sz10,X1)) = sdtasdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[15676,12699,theory(equality)]) ).
cnf(15850,plain,
( sdtasdt0(X1,sdtasdt0(xm,xm)) = sdtasdt0(esk7_0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[3423,15676,theory(equality)]) ).
cnf(15936,plain,
( sdtasdt0(X1,xn) = sdtasdt0(xq,sdtasdt0(X1,xp))
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[15677,127,theory(equality)]) ).
cnf(15937,plain,
( sdtasdt0(X1,xn) = sdtasdt0(xq,sdtasdt0(X1,xp))
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[15936,238,theory(equality)]) ).
cnf(15938,plain,
( sdtasdt0(X1,xn) = sdtasdt0(xq,sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[15937,theory(equality)]) ).
cnf(16003,plain,
( sdtasdt0(xn,sdtasdt0(sz10,X1)) = sdtasdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[15700,168,theory(equality)]) ).
cnf(16004,plain,
( sdtasdt0(xn,sdtasdt0(sz10,X1)) = sdtasdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[16003,240,theory(equality)]) ).
cnf(16005,plain,
( sdtasdt0(xn,sdtasdt0(sz10,X1)) = sdtasdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[16004,theory(equality)]) ).
cnf(16132,plain,
( sdtasdt0(X1,esk7_0) = sdtasdt0(esk7_0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[15850,3329,theory(equality)]) ).
cnf(16133,plain,
( sdtasdt0(X1,esk7_0) = sdtasdt0(esk7_0,X1)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[16132,239,theory(equality)]) ).
cnf(16134,plain,
( sdtasdt0(X1,esk7_0) = sdtasdt0(esk7_0,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[16133,theory(equality)]) ).
cnf(18824,plain,
( sz10 = xn
| xp = xn
| X1 != xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1)
| xn != X1 ),
inference(spm,[status(thm)],[8372,13045,theory(equality)]) ).
cnf(18855,plain,
( sz10 = xn
| xp = xn
| X1 != xp
| $false
| ~ aNaturalNumber0(X1)
| xn != X1 ),
inference(rw,[status(thm)],[18824,240,theory(equality)]) ).
cnf(18856,plain,
( sz10 = xn
| xp = xn
| X1 != xp
| ~ aNaturalNumber0(X1)
| xn != X1 ),
inference(cn,[status(thm)],[18855,theory(equality)]) ).
cnf(18857,plain,
( xn = sz10
| X1 != xp
| ~ aNaturalNumber0(X1)
| xn != X1 ),
inference(sr,[status(thm)],[18856,4754,theory(equality)]) ).
cnf(20510,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[874,212]) ).
cnf(20781,plain,
( sz00 = xn
| xn != X1
| ~ aNaturalNumber0(X1)
| sz00 != X1 ),
inference(spm,[status(thm)],[13237,14041,theory(equality)]) ).
cnf(20798,plain,
( xn != X1
| ~ aNaturalNumber0(X1)
| sz00 != X1 ),
inference(sr,[status(thm)],[20781,237,theory(equality)]) ).
cnf(21289,plain,
( sdtpldt0(xm,esk7_0) = sdtasdt0(xm,sdtpldt0(sz10,xm))
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[953,3329,theory(equality)]) ).
cnf(21294,plain,
( sdtpldt0(xm,sz00) = sdtasdt0(xm,sdtpldt0(sz10,sz00))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[953,6749,theory(equality)]) ).
cnf(21397,plain,
( sdtpldt0(xm,esk7_0) = sdtasdt0(xm,sdtpldt0(sz10,xm))
| $false ),
inference(rw,[status(thm)],[21289,239,theory(equality)]) ).
cnf(21398,plain,
sdtpldt0(xm,esk7_0) = sdtasdt0(xm,sdtpldt0(sz10,xm)),
inference(cn,[status(thm)],[21397,theory(equality)]) ).
cnf(21411,plain,
( sdtpldt0(xm,sz00) = sdtasdt0(xm,sdtpldt0(sz10,sz00))
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[21294,239,theory(equality)]) ).
cnf(21412,plain,
( sdtpldt0(xm,sz00) = sdtasdt0(xm,sdtpldt0(sz10,sz00))
| $false
| $false ),
inference(rw,[status(thm)],[21411,209,theory(equality)]) ).
cnf(21413,plain,
sdtpldt0(xm,sz00) = sdtasdt0(xm,sdtpldt0(sz10,sz00)),
inference(cn,[status(thm)],[21412,theory(equality)]) ).
cnf(21625,plain,
( sdtpldt0(esk7_0,xm) = sdtasdt0(xm,sdtpldt0(xm,sz10))
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[955,3329,theory(equality)]) ).
cnf(21743,plain,
( sdtpldt0(esk7_0,xm) = sdtasdt0(xm,sdtpldt0(xm,sz10))
| $false ),
inference(rw,[status(thm)],[21625,239,theory(equality)]) ).
cnf(21744,plain,
sdtpldt0(esk7_0,xm) = sdtasdt0(xm,sdtpldt0(xm,sz10)),
inference(cn,[status(thm)],[21743,theory(equality)]) ).
cnf(22383,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[902,195]) ).
cnf(22384,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[22383,195]) ).
cnf(25719,plain,
( xq = esk7_0
| sdtasdt0(xp,esk7_0) != xn
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[1927,16134,theory(equality)]) ).
cnf(25976,plain,
( xq = esk7_0
| sdtasdt0(xn,xn) != xn
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[25719,3378,theory(equality)]) ).
cnf(25977,plain,
( xq = esk7_0
| sdtasdt0(xn,xn) != xn
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[25976,253,theory(equality)]) ).
cnf(25978,plain,
( xq = esk7_0
| sdtasdt0(xn,xn) != xn
| $false
| $false ),
inference(rw,[status(thm)],[25977,238,theory(equality)]) ).
cnf(25979,plain,
( xq = esk7_0
| sdtasdt0(xn,xn) != xn ),
inference(cn,[status(thm)],[25978,theory(equality)]) ).
cnf(25980,plain,
sdtasdt0(xn,xn) != xn,
inference(sr,[status(thm)],[25979,8266,theory(equality)]) ).
cnf(26688,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),X3)
| sdtasdt0(X1,sdtpldt0(X2,X4)) != X3
| ~ aNaturalNumber0(sdtasdt0(X1,X4))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X4) ),
inference(csr,[status(thm)],[915,195]) ).
cnf(26689,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),X3)
| sdtasdt0(X1,sdtpldt0(X2,X4)) != X3
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X4) ),
inference(csr,[status(thm)],[26688,195]) ).
cnf(30416,plain,
( aNaturalNumber0(sdtpldt0(xm,esk7_0))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[22384,21398,theory(equality)]) ).
cnf(30544,plain,
( aNaturalNumber0(sdtpldt0(xm,esk7_0))
| $false
| ~ aNaturalNumber0(sz10) ),
inference(rw,[status(thm)],[30416,239,theory(equality)]) ).
cnf(30545,plain,
( aNaturalNumber0(sdtpldt0(xm,esk7_0))
| $false
| $false ),
inference(rw,[status(thm)],[30544,168,theory(equality)]) ).
cnf(30546,plain,
aNaturalNumber0(sdtpldt0(xm,esk7_0)),
inference(cn,[status(thm)],[30545,theory(equality)]) ).
cnf(32099,plain,
( sdtasdt0(xm,sdtpldt0(sz10,xm)) = sdtpldt0(esk7_0,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[21744,59,theory(equality)]) ).
cnf(32179,plain,
( sdtpldt0(xm,esk7_0) = sdtpldt0(esk7_0,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[32099,21398,theory(equality)]) ).
cnf(32180,plain,
( sdtpldt0(xm,esk7_0) = sdtpldt0(esk7_0,xm)
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[32179,168,theory(equality)]) ).
cnf(32181,plain,
( sdtpldt0(xm,esk7_0) = sdtpldt0(esk7_0,xm)
| $false
| $false ),
inference(rw,[status(thm)],[32180,239,theory(equality)]) ).
cnf(32182,plain,
sdtpldt0(xm,esk7_0) = sdtpldt0(esk7_0,xm),
inference(cn,[status(thm)],[32181,theory(equality)]) ).
cnf(32842,plain,
( sdtlseqdt0(esk7_0,sdtpldt0(xm,esk7_0))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[4618,32182,theory(equality)]) ).
cnf(32862,plain,
( sdtmndt0(sdtpldt0(xm,esk7_0),esk7_0) = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[20510,32182,theory(equality)]) ).
cnf(32928,plain,
( sdtlseqdt0(esk7_0,sdtpldt0(xm,esk7_0))
| $false
| ~ aNaturalNumber0(esk7_0) ),
inference(rw,[status(thm)],[32842,239,theory(equality)]) ).
cnf(32929,plain,
( sdtlseqdt0(esk7_0,sdtpldt0(xm,esk7_0))
| $false
| $false ),
inference(rw,[status(thm)],[32928,253,theory(equality)]) ).
cnf(32930,plain,
sdtlseqdt0(esk7_0,sdtpldt0(xm,esk7_0)),
inference(cn,[status(thm)],[32929,theory(equality)]) ).
cnf(32988,plain,
( sdtmndt0(sdtpldt0(xm,esk7_0),esk7_0) = xm
| $false
| ~ aNaturalNumber0(esk7_0) ),
inference(rw,[status(thm)],[32862,239,theory(equality)]) ).
cnf(32989,plain,
( sdtmndt0(sdtpldt0(xm,esk7_0),esk7_0) = xm
| $false
| $false ),
inference(rw,[status(thm)],[32988,253,theory(equality)]) ).
cnf(32990,plain,
sdtmndt0(sdtpldt0(xm,esk7_0),esk7_0) = xm,
inference(cn,[status(thm)],[32989,theory(equality)]) ).
cnf(34132,plain,
( aNaturalNumber0(X1)
| xm != X1
| ~ sdtlseqdt0(esk7_0,sdtpldt0(xm,esk7_0))
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(sdtpldt0(xm,esk7_0)) ),
inference(spm,[status(thm)],[192,32990,theory(equality)]) ).
cnf(34139,plain,
( aNaturalNumber0(X1)
| xm != X1
| $false
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(sdtpldt0(xm,esk7_0)) ),
inference(rw,[status(thm)],[34132,32930,theory(equality)]) ).
cnf(34140,plain,
( aNaturalNumber0(X1)
| xm != X1
| $false
| $false
| ~ aNaturalNumber0(sdtpldt0(xm,esk7_0)) ),
inference(rw,[status(thm)],[34139,253,theory(equality)]) ).
cnf(34141,plain,
( aNaturalNumber0(X1)
| xm != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[34140,30546,theory(equality)]) ).
cnf(34142,plain,
( aNaturalNumber0(X1)
| xm != X1 ),
inference(cn,[status(thm)],[34141,theory(equality)]) ).
cnf(42488,plain,
( sdtasdt0(xm,sz10) = sdtpldt0(xm,sz00)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[21413,245,theory(equality)]) ).
cnf(42545,plain,
( aNaturalNumber0(sdtpldt0(xm,sz00))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[22384,21413,theory(equality)]) ).
cnf(42584,plain,
( sdtasdt0(xm,sz10) = sdtpldt0(xm,sz00)
| $false ),
inference(rw,[status(thm)],[42488,168,theory(equality)]) ).
cnf(42585,plain,
sdtasdt0(xm,sz10) = sdtpldt0(xm,sz00),
inference(cn,[status(thm)],[42584,theory(equality)]) ).
cnf(42699,plain,
( aNaturalNumber0(sdtpldt0(xm,sz00))
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[42545,239,theory(equality)]) ).
cnf(42700,plain,
( aNaturalNumber0(sdtpldt0(xm,sz00))
| $false
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[42699,168,theory(equality)]) ).
cnf(42701,plain,
( aNaturalNumber0(sdtpldt0(xm,sz00))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[42700,209,theory(equality)]) ).
cnf(42702,plain,
aNaturalNumber0(sdtpldt0(xm,sz00)),
inference(cn,[status(thm)],[42701,theory(equality)]) ).
cnf(42791,plain,
( aNaturalNumber0(sdtpldt0(sz00,xm))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[42702,59,theory(equality)]) ).
cnf(42814,plain,
( aNaturalNumber0(sdtpldt0(sz00,xm))
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[42791,209,theory(equality)]) ).
cnf(42815,plain,
( aNaturalNumber0(sdtpldt0(sz00,xm))
| $false
| $false ),
inference(rw,[status(thm)],[42814,239,theory(equality)]) ).
cnf(42816,plain,
aNaturalNumber0(sdtpldt0(sz00,xm)),
inference(cn,[status(thm)],[42815,theory(equality)]) ).
cnf(42826,plain,
( sdtlseqdt0(xq,sdtpldt0(sz00,xm))
| sdtlseqdt0(sdtpldt0(sz00,xm),xq) ),
inference(spm,[status(thm)],[325,42816,theory(equality)]) ).
cnf(43013,plain,
( sdtasdt0(xm,sz10) = xm
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[245,42585,theory(equality)]) ).
cnf(43068,plain,
sdtasdt0(xm,sdtpldt0(sz10,sz00)) = sdtasdt0(xm,sz10),
inference(rw,[status(thm)],[21413,42585,theory(equality)]) ).
cnf(43071,plain,
( sdtasdt0(xm,sz10) = xm
| $false ),
inference(rw,[status(thm)],[43013,239,theory(equality)]) ).
cnf(43072,plain,
sdtasdt0(xm,sz10) = xm,
inference(cn,[status(thm)],[43071,theory(equality)]) ).
cnf(43226,plain,
( xm = sdtasdt0(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[230,43072,theory(equality)]) ).
cnf(43256,plain,
( doDivides0(xm,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[7627,43072,theory(equality)]) ).
cnf(43262,plain,
( doDivides0(sz10,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[7642,43072,theory(equality)]) ).
cnf(43265,plain,
( aNaturalNumber0(sdtasdt0(X1,xm))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[15396,43072,theory(equality)]) ).
cnf(43324,plain,
( xm = sdtasdt0(sz10,xm)
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[43226,168,theory(equality)]) ).
cnf(43325,plain,
( xm = sdtasdt0(sz10,xm)
| $false
| $false ),
inference(rw,[status(thm)],[43324,239,theory(equality)]) ).
cnf(43326,plain,
xm = sdtasdt0(sz10,xm),
inference(cn,[status(thm)],[43325,theory(equality)]) ).
cnf(43418,plain,
( doDivides0(xm,xm)
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[43256,168,theory(equality)]) ).
cnf(43419,plain,
( doDivides0(xm,xm)
| $false
| $false ),
inference(rw,[status(thm)],[43418,239,theory(equality)]) ).
cnf(43420,plain,
doDivides0(xm,xm),
inference(cn,[status(thm)],[43419,theory(equality)]) ).
cnf(43438,plain,
( doDivides0(sz10,xm)
| $false
| ~ aNaturalNumber0(sz10) ),
inference(rw,[status(thm)],[43262,239,theory(equality)]) ).
cnf(43439,plain,
( doDivides0(sz10,xm)
| $false
| $false ),
inference(rw,[status(thm)],[43438,168,theory(equality)]) ).
cnf(43440,plain,
doDivides0(sz10,xm),
inference(cn,[status(thm)],[43439,theory(equality)]) ).
cnf(43449,plain,
( aNaturalNumber0(sdtasdt0(X1,xm))
| $false
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[43265,168,theory(equality)]) ).
cnf(43450,plain,
( aNaturalNumber0(sdtasdt0(X1,xm))
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[43449,239,theory(equality)]) ).
cnf(43451,plain,
( aNaturalNumber0(sdtasdt0(X1,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[43450,theory(equality)]) ).
cnf(44045,plain,
sdtasdt0(xm,sdtpldt0(sz10,sz00)) = xm,
inference(rw,[status(thm)],[43068,43072,theory(equality)]) ).
cnf(44113,plain,
( sdtlseqdt0(sdtasdt0(xm,sz10),X1)
| xm != X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[26689,44045,theory(equality)]) ).
cnf(44293,plain,
( sdtlseqdt0(xm,X1)
| xm != X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[44113,43072,theory(equality)]) ).
cnf(44294,plain,
( sdtlseqdt0(xm,X1)
| xm != X1
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[44293,239,theory(equality)]) ).
cnf(44295,plain,
( sdtlseqdt0(xm,X1)
| xm != X1
| ~ aNaturalNumber0(X1)
| $false
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[44294,168,theory(equality)]) ).
cnf(44296,plain,
( sdtlseqdt0(xm,X1)
| xm != X1
| ~ aNaturalNumber0(X1)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[44295,209,theory(equality)]) ).
cnf(44297,plain,
( sdtlseqdt0(xm,X1)
| xm != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[44296,theory(equality)]) ).
cnf(44938,plain,
( aNaturalNumber0(sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[43451,230,theory(equality)]) ).
cnf(44985,plain,
( aNaturalNumber0(sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[44938,239,theory(equality)]) ).
cnf(44986,plain,
( aNaturalNumber0(sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[44985,theory(equality)]) ).
cnf(45007,plain,
( sdtlseqdt0(xm,X1)
| xm != X1 ),
inference(csr,[status(thm)],[44297,34142]) ).
cnf(45012,plain,
( sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xm)
| xm != xp ),
inference(spm,[status(thm)],[1585,45007,theory(equality)]) ).
cnf(45036,plain,
( sdtlseqdt0(xm,xn)
| $false
| xm != xp ),
inference(rw,[status(thm)],[45012,239,theory(equality)]) ).
cnf(45037,plain,
( sdtlseqdt0(xm,xn)
| xm != xp ),
inference(cn,[status(thm)],[45036,theory(equality)]) ).
cnf(45061,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| sz00 = X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[1050,195]) ).
cnf(45063,plain,
( sdtsldt0(esk7_0,xm) = xm
| sz00 = xm
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[45061,3329,theory(equality)]) ).
cnf(45064,plain,
( sdtsldt0(sdtasdt0(xn,xn),xp) = esk7_0
| sz00 = xp
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[45061,3378,theory(equality)]) ).
cnf(45065,plain,
( sdtsldt0(esk7_0,esk7_0) = sz10
| sz00 = esk7_0
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[45061,6186,theory(equality)]) ).
cnf(45068,plain,
( sdtsldt0(sz00,xm) = sz00
| sz00 = xm
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[45061,6749,theory(equality)]) ).
cnf(45071,plain,
( sdtsldt0(xn,xn) = sz10
| sz00 = xn
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[45061,12699,theory(equality)]) ).
cnf(45072,plain,
( sdtsldt0(xn,sz10) = xn
| sz00 = sz10
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[45061,13029,theory(equality)]) ).
cnf(45083,plain,
( sdtsldt0(xm,xm) = sz10
| sz00 = xm
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[45061,43072,theory(equality)]) ).
cnf(45084,plain,
( sdtsldt0(xm,sz10) = xm
| sz00 = sz10
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[45061,43326,theory(equality)]) ).
cnf(45146,plain,
( sdtsldt0(esk7_0,xm) = xm
| sz00 = xm
| $false ),
inference(rw,[status(thm)],[45063,239,theory(equality)]) ).
cnf(45147,plain,
( sdtsldt0(esk7_0,xm) = xm
| sz00 = xm ),
inference(cn,[status(thm)],[45146,theory(equality)]) ).
cnf(45148,plain,
sdtsldt0(esk7_0,xm) = xm,
inference(sr,[status(thm)],[45147,236,theory(equality)]) ).
cnf(45149,plain,
( sdtsldt0(sdtasdt0(xn,xn),xp) = esk7_0
| sz00 = xp
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[45064,253,theory(equality)]) ).
cnf(45150,plain,
( sdtsldt0(sdtasdt0(xn,xn),xp) = esk7_0
| sz00 = xp
| $false
| $false ),
inference(rw,[status(thm)],[45149,238,theory(equality)]) ).
cnf(45151,plain,
( sdtsldt0(sdtasdt0(xn,xn),xp) = esk7_0
| sz00 = xp ),
inference(cn,[status(thm)],[45150,theory(equality)]) ).
cnf(45152,plain,
sdtsldt0(sdtasdt0(xn,xn),xp) = esk7_0,
inference(sr,[status(thm)],[45151,235,theory(equality)]) ).
cnf(45153,plain,
( sdtsldt0(esk7_0,esk7_0) = sz10
| sz00 = esk7_0
| $false
| ~ aNaturalNumber0(esk7_0) ),
inference(rw,[status(thm)],[45065,168,theory(equality)]) ).
cnf(45154,plain,
( sdtsldt0(esk7_0,esk7_0) = sz10
| sz00 = esk7_0
| $false
| $false ),
inference(rw,[status(thm)],[45153,253,theory(equality)]) ).
cnf(45155,plain,
( sdtsldt0(esk7_0,esk7_0) = sz10
| sz00 = esk7_0 ),
inference(cn,[status(thm)],[45154,theory(equality)]) ).
cnf(45156,plain,
sdtsldt0(esk7_0,esk7_0) = sz10,
inference(sr,[status(thm)],[45155,3405,theory(equality)]) ).
cnf(45165,plain,
( sdtsldt0(sz00,xm) = sz00
| sz00 = xm
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[45068,209,theory(equality)]) ).
cnf(45166,plain,
( sdtsldt0(sz00,xm) = sz00
| sz00 = xm
| $false
| $false ),
inference(rw,[status(thm)],[45165,239,theory(equality)]) ).
cnf(45167,plain,
( sdtsldt0(sz00,xm) = sz00
| sz00 = xm ),
inference(cn,[status(thm)],[45166,theory(equality)]) ).
cnf(45168,plain,
sdtsldt0(sz00,xm) = sz00,
inference(sr,[status(thm)],[45167,236,theory(equality)]) ).
cnf(45177,plain,
( sdtsldt0(xn,xn) = sz10
| sz00 = xn
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[45071,168,theory(equality)]) ).
cnf(45178,plain,
( sdtsldt0(xn,xn) = sz10
| sz00 = xn
| $false
| $false ),
inference(rw,[status(thm)],[45177,240,theory(equality)]) ).
cnf(45179,plain,
( sdtsldt0(xn,xn) = sz10
| sz00 = xn ),
inference(cn,[status(thm)],[45178,theory(equality)]) ).
cnf(45180,plain,
sdtsldt0(xn,xn) = sz10,
inference(sr,[status(thm)],[45179,237,theory(equality)]) ).
cnf(45181,plain,
( sdtsldt0(xn,sz10) = xn
| sz00 = sz10
| $false
| ~ aNaturalNumber0(sz10) ),
inference(rw,[status(thm)],[45072,240,theory(equality)]) ).
cnf(45182,plain,
( sdtsldt0(xn,sz10) = xn
| sz00 = sz10
| $false
| $false ),
inference(rw,[status(thm)],[45181,168,theory(equality)]) ).
cnf(45183,plain,
( sdtsldt0(xn,sz10) = xn
| sz00 = sz10 ),
inference(cn,[status(thm)],[45182,theory(equality)]) ).
cnf(45184,plain,
sdtsldt0(xn,sz10) = xn,
inference(sr,[status(thm)],[45183,167,theory(equality)]) ).
cnf(45222,plain,
( sdtsldt0(xm,xm) = sz10
| sz00 = xm
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[45083,168,theory(equality)]) ).
cnf(45223,plain,
( sdtsldt0(xm,xm) = sz10
| sz00 = xm
| $false
| $false ),
inference(rw,[status(thm)],[45222,239,theory(equality)]) ).
cnf(45224,plain,
( sdtsldt0(xm,xm) = sz10
| sz00 = xm ),
inference(cn,[status(thm)],[45223,theory(equality)]) ).
cnf(45225,plain,
sdtsldt0(xm,xm) = sz10,
inference(sr,[status(thm)],[45224,236,theory(equality)]) ).
cnf(45226,plain,
( sdtsldt0(xm,sz10) = xm
| sz00 = sz10
| $false
| ~ aNaturalNumber0(sz10) ),
inference(rw,[status(thm)],[45084,239,theory(equality)]) ).
cnf(45227,plain,
( sdtsldt0(xm,sz10) = xm
| sz00 = sz10
| $false
| $false ),
inference(rw,[status(thm)],[45226,168,theory(equality)]) ).
cnf(45228,plain,
( sdtsldt0(xm,sz10) = xm
| sz00 = sz10 ),
inference(cn,[status(thm)],[45227,theory(equality)]) ).
cnf(45229,plain,
sdtsldt0(xm,sz10) = xm,
inference(sr,[status(thm)],[45228,167,theory(equality)]) ).
cnf(45331,plain,
( sdtasdt0(xm,X1) = esk7_0
| sz00 = xm
| xm != X1
| ~ doDivides0(xm,esk7_0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[157,45148,theory(equality)]) ).
cnf(45343,plain,
( sdtasdt0(xm,X1) = esk7_0
| sz00 = xm
| xm != X1
| $false
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(esk7_0) ),
inference(rw,[status(thm)],[45331,7663,theory(equality)]) ).
cnf(45344,plain,
( sdtasdt0(xm,X1) = esk7_0
| sz00 = xm
| xm != X1
| $false
| $false
| ~ aNaturalNumber0(esk7_0) ),
inference(rw,[status(thm)],[45343,239,theory(equality)]) ).
cnf(45345,plain,
( sdtasdt0(xm,X1) = esk7_0
| sz00 = xm
| xm != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[45344,253,theory(equality)]) ).
cnf(45346,plain,
( sdtasdt0(xm,X1) = esk7_0
| sz00 = xm
| xm != X1 ),
inference(cn,[status(thm)],[45345,theory(equality)]) ).
cnf(45347,plain,
( sdtasdt0(xm,X1) = esk7_0
| xm != X1 ),
inference(sr,[status(thm)],[45346,236,theory(equality)]) ).
cnf(45361,plain,
( xm = xn
| xm != xp ),
inference(spm,[status(thm)],[173,45037,theory(equality)]) ).
cnf(45441,plain,
( sz00 = esk7_0
| aNaturalNumber0(X1)
| sz10 != X1
| ~ doDivides0(esk7_0,esk7_0)
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[158,45156,theory(equality)]) ).
cnf(45448,plain,
( sz00 = esk7_0
| aNaturalNumber0(X1)
| sz10 != X1
| $false
| ~ aNaturalNumber0(esk7_0) ),
inference(rw,[status(thm)],[45441,7670,theory(equality)]) ).
cnf(45449,plain,
( sz00 = esk7_0
| aNaturalNumber0(X1)
| sz10 != X1
| $false
| $false ),
inference(rw,[status(thm)],[45448,253,theory(equality)]) ).
cnf(45450,plain,
( sz00 = esk7_0
| aNaturalNumber0(X1)
| sz10 != X1 ),
inference(cn,[status(thm)],[45449,theory(equality)]) ).
cnf(45451,plain,
( aNaturalNumber0(X1)
| sz10 != X1 ),
inference(sr,[status(thm)],[45450,3405,theory(equality)]) ).
cnf(45516,plain,
( sdtsldt0(X1,xn) = sz10
| sz00 = xn
| xn != X1
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[1059,13029,theory(equality)]) ).
cnf(45614,plain,
( sdtsldt0(X1,xn) = sz10
| sz00 = xn
| xn != X1
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[45516,168,theory(equality)]) ).
cnf(45615,plain,
( sdtsldt0(X1,xn) = sz10
| sz00 = xn
| xn != X1
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[45614,240,theory(equality)]) ).
cnf(45616,plain,
( sdtsldt0(X1,xn) = sz10
| sz00 = xn
| xn != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[45615,theory(equality)]) ).
cnf(45617,plain,
( sdtsldt0(X1,xn) = sz10
| xn != X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[45616,237,theory(equality)]) ).
cnf(45736,plain,
( sz00 = xm
| aNaturalNumber0(X1)
| sz00 != X1
| ~ doDivides0(xm,sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[158,45168,theory(equality)]) ).
cnf(45737,plain,
( sdtasdt0(xm,X1) = sz00
| sz00 = xm
| sz00 != X1
| ~ doDivides0(xm,sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[157,45168,theory(equality)]) ).
cnf(45743,plain,
( sz00 = xm
| aNaturalNumber0(X1)
| sz00 != X1
| $false
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[45736,7679,theory(equality)]) ).
cnf(45744,plain,
( sz00 = xm
| aNaturalNumber0(X1)
| sz00 != X1
| $false
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[45743,239,theory(equality)]) ).
cnf(45745,plain,
( sz00 = xm
| aNaturalNumber0(X1)
| sz00 != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[45744,209,theory(equality)]) ).
cnf(45746,plain,
( sz00 = xm
| aNaturalNumber0(X1)
| sz00 != X1 ),
inference(cn,[status(thm)],[45745,theory(equality)]) ).
cnf(45747,plain,
( aNaturalNumber0(X1)
| sz00 != X1 ),
inference(sr,[status(thm)],[45746,236,theory(equality)]) ).
cnf(45748,plain,
( sdtasdt0(xm,X1) = sz00
| sz00 = xm
| sz00 != X1
| $false
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[45737,7679,theory(equality)]) ).
cnf(45749,plain,
( sdtasdt0(xm,X1) = sz00
| sz00 = xm
| sz00 != X1
| $false
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[45748,239,theory(equality)]) ).
cnf(45750,plain,
( sdtasdt0(xm,X1) = sz00
| sz00 = xm
| sz00 != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[45749,209,theory(equality)]) ).
cnf(45751,plain,
( sdtasdt0(xm,X1) = sz00
| sz00 = xm
| sz00 != X1 ),
inference(cn,[status(thm)],[45750,theory(equality)]) ).
cnf(45752,plain,
( sdtasdt0(xm,X1) = sz00
| sz00 != X1 ),
inference(sr,[status(thm)],[45751,236,theory(equality)]) ).
cnf(45861,plain,
( xn != X1
| sz00 != X1 ),
inference(spm,[status(thm)],[20798,45747,theory(equality)]) ).
cnf(45863,plain,
( sdtasdt0(xn,X1) = xn
| sz00 = xn
| sz10 != X1
| ~ doDivides0(xn,xn)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[157,45180,theory(equality)]) ).
cnf(45873,plain,
( sdtasdt0(xn,X1) = xn
| sz00 = xn
| sz10 != X1
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[45863,13118,theory(equality)]) ).
cnf(45874,plain,
( sdtasdt0(xn,X1) = xn
| sz00 = xn
| sz10 != X1
| $false
| $false ),
inference(rw,[status(thm)],[45873,240,theory(equality)]) ).
cnf(45875,plain,
( sdtasdt0(xn,X1) = xn
| sz00 = xn
| sz10 != X1 ),
inference(cn,[status(thm)],[45874,theory(equality)]) ).
cnf(45876,plain,
( sdtasdt0(xn,X1) = xn
| sz10 != X1 ),
inference(sr,[status(thm)],[45875,237,theory(equality)]) ).
cnf(45896,plain,
( sdtasdt0(xm,X1) = xm
| sz00 = xm
| sz10 != X1
| ~ doDivides0(xm,xm)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[157,45225,theory(equality)]) ).
cnf(45908,plain,
( sdtasdt0(xm,X1) = xm
| sz00 = xm
| sz10 != X1
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[45896,43420,theory(equality)]) ).
cnf(45909,plain,
( sdtasdt0(xm,X1) = xm
| sz00 = xm
| sz10 != X1
| $false
| $false ),
inference(rw,[status(thm)],[45908,239,theory(equality)]) ).
cnf(45910,plain,
( sdtasdt0(xm,X1) = xm
| sz00 = xm
| sz10 != X1 ),
inference(cn,[status(thm)],[45909,theory(equality)]) ).
cnf(45911,plain,
( sdtasdt0(xm,X1) = xm
| sz10 != X1 ),
inference(sr,[status(thm)],[45910,236,theory(equality)]) ).
cnf(46248,plain,
( sz00 = sz10
| aNaturalNumber0(X1)
| xn != X1
| ~ doDivides0(sz10,xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[158,45184,theory(equality)]) ).
cnf(46255,plain,
( sz00 = sz10
| aNaturalNumber0(X1)
| xn != X1
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[46248,4289,theory(equality)]) ).
cnf(46256,plain,
( sz00 = sz10
| aNaturalNumber0(X1)
| xn != X1
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[46255,168,theory(equality)]) ).
cnf(46257,plain,
( sz00 = sz10
| aNaturalNumber0(X1)
| xn != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[46256,240,theory(equality)]) ).
cnf(46258,plain,
( sz00 = sz10
| aNaturalNumber0(X1)
| xn != X1 ),
inference(cn,[status(thm)],[46257,theory(equality)]) ).
cnf(46259,plain,
( aNaturalNumber0(X1)
| xn != X1 ),
inference(sr,[status(thm)],[46258,167,theory(equality)]) ).
cnf(46300,plain,
( xn = sz10
| X1 != xp
| xn != X1 ),
inference(spm,[status(thm)],[18857,46259,theory(equality)]) ).
cnf(46302,plain,
( sdtasdt0(sz10,X1) = xm
| sz00 = sz10
| xm != X1
| ~ doDivides0(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[157,45229,theory(equality)]) ).
cnf(46316,plain,
( sdtasdt0(sz10,X1) = xm
| sz00 = sz10
| xm != X1
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[46302,43440,theory(equality)]) ).
cnf(46317,plain,
( sdtasdt0(sz10,X1) = xm
| sz00 = sz10
| xm != X1
| $false
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[46316,168,theory(equality)]) ).
cnf(46318,plain,
( sdtasdt0(sz10,X1) = xm
| sz00 = sz10
| xm != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[46317,239,theory(equality)]) ).
cnf(46319,plain,
( sdtasdt0(sz10,X1) = xm
| sz00 = sz10
| xm != X1 ),
inference(cn,[status(thm)],[46318,theory(equality)]) ).
cnf(46320,plain,
( sdtasdt0(sz10,X1) = xm
| xm != X1 ),
inference(sr,[status(thm)],[46319,167,theory(equality)]) ).
cnf(46586,plain,
( xq != xm
| xm != xn ),
inference(spm,[status(thm)],[9939,45347,theory(equality)]) ).
cnf(47453,plain,
xq != xm,
inference(csr,[status(thm)],[46586,2499]) ).
cnf(49965,plain,
( sz00 = xm
| sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1)
| sz00 != X1 ),
inference(spm,[status(thm)],[425,45752,theory(equality)]) ).
cnf(50229,plain,
( sz00 = xm
| sdtlseqdt0(X1,sz00)
| $false
| ~ aNaturalNumber0(X1)
| sz00 != X1 ),
inference(rw,[status(thm)],[49965,239,theory(equality)]) ).
cnf(50230,plain,
( sz00 = xm
| sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X1)
| sz00 != X1 ),
inference(cn,[status(thm)],[50229,theory(equality)]) ).
cnf(50231,plain,
( sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X1)
| sz00 != X1 ),
inference(sr,[status(thm)],[50230,236,theory(equality)]) ).
cnf(53739,plain,
sz10 != xn,
inference(spm,[status(thm)],[25980,45876,theory(equality)]) ).
cnf(55195,plain,
( xm = sdtasdt0(X1,xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm)
| sz10 != X1 ),
inference(spm,[status(thm)],[230,45911,theory(equality)]) ).
cnf(55419,plain,
( xm = sdtasdt0(X1,xm)
| ~ aNaturalNumber0(X1)
| $false
| sz10 != X1 ),
inference(rw,[status(thm)],[55195,239,theory(equality)]) ).
cnf(55420,plain,
( xm = sdtasdt0(X1,xm)
| ~ aNaturalNumber0(X1)
| sz10 != X1 ),
inference(cn,[status(thm)],[55419,theory(equality)]) ).
cnf(59334,plain,
( X1 != xp
| xn != X1 ),
inference(sr,[status(thm)],[46300,53739,theory(equality)]) ).
cnf(59423,plain,
( xm = xn
| xq != sz10
| xm != xp ),
inference(spm,[status(thm)],[2289,46320,theory(equality)]) ).
cnf(59428,plain,
( sz00 = sz10
| sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| xm != X1 ),
inference(spm,[status(thm)],[425,46320,theory(equality)]) ).
cnf(59444,plain,
( doDivides0(X1,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| xm != X1 ),
inference(spm,[status(thm)],[7642,46320,theory(equality)]) ).
cnf(59662,plain,
( sz00 = sz10
| sdtlseqdt0(X1,xm)
| $false
| ~ aNaturalNumber0(X1)
| xm != X1 ),
inference(rw,[status(thm)],[59428,168,theory(equality)]) ).
cnf(59663,plain,
( sz00 = sz10
| sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(X1)
| xm != X1 ),
inference(cn,[status(thm)],[59662,theory(equality)]) ).
cnf(59664,plain,
( sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(X1)
| xm != X1 ),
inference(sr,[status(thm)],[59663,167,theory(equality)]) ).
cnf(59702,plain,
( doDivides0(X1,xm)
| $false
| ~ aNaturalNumber0(X1)
| xm != X1 ),
inference(rw,[status(thm)],[59444,168,theory(equality)]) ).
cnf(59703,plain,
( doDivides0(X1,xm)
| ~ aNaturalNumber0(X1)
| xm != X1 ),
inference(cn,[status(thm)],[59702,theory(equality)]) ).
cnf(60004,plain,
( xm = xn
| xm != xp ),
inference(csr,[status(thm)],[59423,45361]) ).
cnf(60005,plain,
xm != xp,
inference(csr,[status(thm)],[60004,59334]) ).
cnf(60009,plain,
( sdtlseqdt0(X1,xm)
| xm != X1 ),
inference(csr,[status(thm)],[59664,34142]) ).
cnf(63366,plain,
( sdtlseqdt0(sdtpldt0(sz00,xm),xn)
| sdtlseqdt0(xq,sdtpldt0(sz00,xm))
| ~ aNaturalNumber0(sdtpldt0(sz00,xm)) ),
inference(spm,[status(thm)],[4132,42826,theory(equality)]) ).
cnf(63382,plain,
( sdtlseqdt0(sdtpldt0(sz00,xm),xn)
| sdtlseqdt0(xq,sdtpldt0(sz00,xm))
| $false ),
inference(rw,[status(thm)],[63366,42816,theory(equality)]) ).
cnf(63383,plain,
( sdtlseqdt0(sdtpldt0(sz00,xm),xn)
| sdtlseqdt0(xq,sdtpldt0(sz00,xm)) ),
inference(cn,[status(thm)],[63382,theory(equality)]) ).
cnf(63387,plain,
( sdtlseqdt0(xq,xm)
| sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[63383,244,theory(equality)]) ).
cnf(63395,plain,
( sdtlseqdt0(xq,xm)
| sdtlseqdt0(xm,xn)
| $false ),
inference(rw,[status(thm)],[63387,239,theory(equality)]) ).
cnf(63396,plain,
( sdtlseqdt0(xq,xm)
| sdtlseqdt0(xm,xn) ),
inference(cn,[status(thm)],[63395,theory(equality)]) ).
cnf(64483,plain,
( sdtlseqdt0(X1,sz00)
| sz00 != X1 ),
inference(csr,[status(thm)],[50231,45747]) ).
cnf(67257,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sz00 = X1
| X2 = X3
| ~ sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[1237,195]) ).
cnf(67258,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sz00 = X1
| X2 = X3
| ~ sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[67257,195]) ).
cnf(67259,plain,
( sz00 = X1
| X2 = X3
| ~ sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[67258,68]) ).
cnf(71718,plain,
( doDivides0(X1,xm)
| xm != X1 ),
inference(csr,[status(thm)],[59703,34142]) ).
cnf(74163,plain,
( esk7_0 = sdtasdt0(xn,sdtsldt0(xn,xp))
| sz00 = xp
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[234,45152,theory(equality)]) ).
cnf(74188,plain,
( esk7_0 = sdtasdt0(xn,xq)
| sz00 = xp
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[74163,125,theory(equality)]) ).
cnf(74189,plain,
( esk7_0 = sdtasdt0(xn,xq)
| sz00 = xp
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[74188,248,theory(equality)]) ).
cnf(74190,plain,
( esk7_0 = sdtasdt0(xn,xq)
| sz00 = xp
| $false
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[74189,240,theory(equality)]) ).
cnf(74191,plain,
( esk7_0 = sdtasdt0(xn,xq)
| sz00 = xp
| $false
| $false
| $false ),
inference(rw,[status(thm)],[74190,238,theory(equality)]) ).
cnf(74192,plain,
( esk7_0 = sdtasdt0(xn,xq)
| sz00 = xp ),
inference(cn,[status(thm)],[74191,theory(equality)]) ).
cnf(74193,plain,
sdtasdt0(xn,xq) = esk7_0,
inference(sr,[status(thm)],[74192,235,theory(equality)]) ).
cnf(74313,plain,
( sdtsldt0(esk7_0,xn) = xq
| sz00 = xn
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[45061,74193,theory(equality)]) ).
cnf(74660,plain,
( sdtsldt0(esk7_0,xn) = xq
| sz00 = xn
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[74313,127,theory(equality)]) ).
cnf(74661,plain,
( sdtsldt0(esk7_0,xn) = xq
| sz00 = xn
| $false
| $false ),
inference(rw,[status(thm)],[74660,240,theory(equality)]) ).
cnf(74662,plain,
( sdtsldt0(esk7_0,xn) = xq
| sz00 = xn ),
inference(cn,[status(thm)],[74661,theory(equality)]) ).
cnf(74663,plain,
sdtsldt0(esk7_0,xn) = xq,
inference(sr,[status(thm)],[74662,237,theory(equality)]) ).
cnf(104794,plain,
( sdtsldt0(X1,xn) = sz10
| xn != X1 ),
inference(csr,[status(thm)],[45617,46259]) ).
cnf(111071,plain,
( X1 = X2
| sdtlseqdt0(xn,sdtasdt0(xp,X1))
| xq != X2
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[1685,801]) ).
cnf(111128,plain,
( xm = xp
| sdtlseqdt0(xn,sdtasdt0(xp,xm))
| xm = xn
| xq != xp
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[111071,2856,theory(equality)]) ).
cnf(111458,plain,
( xm = xp
| sdtlseqdt0(xn,sdtasdt0(xp,xm))
| xm = xn
| xq != xp
| $false ),
inference(rw,[status(thm)],[111128,239,theory(equality)]) ).
cnf(111459,plain,
( xm = xp
| sdtlseqdt0(xn,sdtasdt0(xp,xm))
| xm = xn
| xq != xp ),
inference(cn,[status(thm)],[111458,theory(equality)]) ).
cnf(111460,plain,
( sdtlseqdt0(xn,sdtasdt0(xp,xm))
| xm = xn
| xq != xp ),
inference(sr,[status(thm)],[111459,60005,theory(equality)]) ).
cnf(115280,plain,
( sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 != X1 ),
inference(spm,[status(thm)],[1735,64483,theory(equality)]) ).
cnf(115349,plain,
( sdtlseqdt0(X1,X2)
| sz00 != X1
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[115280,45747]) ).
cnf(115390,plain,
( sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| sz00 != X1
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[1585,115349,theory(equality)]) ).
cnf(115542,plain,
( sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| sz00 != X1
| $false ),
inference(rw,[status(thm)],[115390,238,theory(equality)]) ).
cnf(115543,plain,
( sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| sz00 != X1 ),
inference(cn,[status(thm)],[115542,theory(equality)]) ).
cnf(115680,plain,
( sdtlseqdt0(X1,xn)
| sz00 != X1 ),
inference(csr,[status(thm)],[115543,45747]) ).
cnf(115686,plain,
( xn = X1
| ~ sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xn)
| sz00 != X1 ),
inference(spm,[status(thm)],[151,115680,theory(equality)]) ).
cnf(115704,plain,
( xn = X1
| ~ sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1)
| $false
| sz00 != X1 ),
inference(rw,[status(thm)],[115686,240,theory(equality)]) ).
cnf(115705,plain,
( xn = X1
| ~ sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1)
| sz00 != X1 ),
inference(cn,[status(thm)],[115704,theory(equality)]) ).
cnf(115734,plain,
( xn = X1
| sz00 != X1
| ~ sdtlseqdt0(xn,X1) ),
inference(csr,[status(thm)],[115705,45747]) ).
cnf(115735,plain,
( sz00 != X1
| ~ sdtlseqdt0(xn,X1) ),
inference(csr,[status(thm)],[115734,45861]) ).
cnf(116078,plain,
( sdtasdt0(X1,xm) = xm
| sz10 != X1 ),
inference(csr,[status(thm)],[55420,45451]) ).
cnf(116380,plain,
( xm = xn
| sdtlseqdt0(xn,xm)
| xq != xp
| sz10 != xp ),
inference(spm,[status(thm)],[111460,116078,theory(equality)]) ).
cnf(117566,plain,
( xm = xn
| sdtlseqdt0(xn,xm)
| xq != xp ),
inference(csr,[status(thm)],[116380,2087]) ).
cnf(117567,plain,
( xm = xn
| sdtlseqdt0(xn,xm) ),
inference(csr,[status(thm)],[117566,2087]) ).
cnf(117568,plain,
sdtlseqdt0(xn,xm),
inference(csr,[status(thm)],[117567,60009]) ).
cnf(117570,plain,
( sdtlseqdt0(X1,xm)
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[106,117568,theory(equality)]) ).
cnf(117606,plain,
( sdtlseqdt0(X1,xm)
| ~ sdtlseqdt0(X1,xn)
| $false
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[117570,240,theory(equality)]) ).
cnf(117607,plain,
( sdtlseqdt0(X1,xm)
| ~ sdtlseqdt0(X1,xn)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[117606,239,theory(equality)]) ).
cnf(117608,plain,
( sdtlseqdt0(X1,xm)
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[117607,theory(equality)]) ).
cnf(118157,plain,
( xm = X1
| ~ sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(X1,xn) ),
inference(spm,[status(thm)],[151,117608,theory(equality)]) ).
cnf(118184,plain,
( xm = X1
| ~ sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1)
| $false
| ~ sdtlseqdt0(X1,xn) ),
inference(rw,[status(thm)],[118157,239,theory(equality)]) ).
cnf(118185,plain,
( xm = X1
| ~ sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,xn) ),
inference(cn,[status(thm)],[118184,theory(equality)]) ).
cnf(128186,plain,
( X1 = X2
| sdtlseqdt0(xn,sdtasdt0(X1,xp))
| xq != X2
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[2376,801]) ).
cnf(128248,plain,
( xm = xq
| sdtlseqdt0(xn,sdtasdt0(xm,xp))
| sdtlseqdt0(xm,xq)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[128186,2125,theory(equality)]) ).
cnf(128594,plain,
( xm = xq
| sdtlseqdt0(xn,sdtasdt0(xm,xp))
| sdtlseqdt0(xm,xq)
| $false ),
inference(rw,[status(thm)],[128248,239,theory(equality)]) ).
cnf(128595,plain,
( xm = xq
| sdtlseqdt0(xn,sdtasdt0(xm,xp))
| sdtlseqdt0(xm,xq) ),
inference(cn,[status(thm)],[128594,theory(equality)]) ).
cnf(128596,plain,
( sdtlseqdt0(xn,sdtasdt0(xm,xp))
| sdtlseqdt0(xm,xq) ),
inference(sr,[status(thm)],[128595,47453,theory(equality)]) ).
cnf(129836,plain,
( sdtlseqdt0(xm,xq)
| sz00 != sdtasdt0(xm,xp) ),
inference(spm,[status(thm)],[115735,128596,theory(equality)]) ).
cnf(130616,plain,
( xm = xq
| ~ sdtlseqdt0(xq,xn)
| ~ aNaturalNumber0(xq)
| sdtasdt0(xm,xp) != sz00 ),
inference(spm,[status(thm)],[118185,129836,theory(equality)]) ).
cnf(130650,plain,
( xm = xq
| $false
| ~ aNaturalNumber0(xq)
| sdtasdt0(xm,xp) != sz00 ),
inference(rw,[status(thm)],[130616,4080,theory(equality)]) ).
cnf(130651,plain,
( xm = xq
| $false
| $false
| sdtasdt0(xm,xp) != sz00 ),
inference(rw,[status(thm)],[130650,127,theory(equality)]) ).
cnf(130652,plain,
( xm = xq
| sdtasdt0(xm,xp) != sz00 ),
inference(cn,[status(thm)],[130651,theory(equality)]) ).
cnf(130653,plain,
sdtasdt0(xm,xp) != sz00,
inference(sr,[status(thm)],[130652,47453,theory(equality)]) ).
cnf(156705,plain,
( sdtpldt0(esk7_0,sz00) = sdtasdt0(xm,sdtpldt0(xm,sz00))
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[3425,6749,theory(equality)]) ).
cnf(156864,plain,
( sdtpldt0(esk7_0,sz00) = esk7_0
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[156705,42585,theory(equality)]),43072,theory(equality)]),3329,theory(equality)]) ).
cnf(156865,plain,
( sdtpldt0(esk7_0,sz00) = esk7_0
| $false ),
inference(rw,[status(thm)],[156864,209,theory(equality)]) ).
cnf(156866,plain,
sdtpldt0(esk7_0,sz00) = esk7_0,
inference(cn,[status(thm)],[156865,theory(equality)]) ).
cnf(157175,plain,
( esk7_0 = sdtpldt0(sz00,esk7_0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(esk7_0) ),
inference(spm,[status(thm)],[59,156866,theory(equality)]) ).
cnf(157278,plain,
( esk7_0 = sdtpldt0(sz00,esk7_0)
| $false
| ~ aNaturalNumber0(esk7_0) ),
inference(rw,[status(thm)],[157175,209,theory(equality)]) ).
cnf(157279,plain,
( esk7_0 = sdtpldt0(sz00,esk7_0)
| $false
| $false ),
inference(rw,[status(thm)],[157278,253,theory(equality)]) ).
cnf(157280,plain,
esk7_0 = sdtpldt0(sz00,esk7_0),
inference(cn,[status(thm)],[157279,theory(equality)]) ).
cnf(161851,plain,
( sdtasdt0(xm,sz10) = sdtsldt0(esk7_0,xn)
| sz00 = xn
| ~ doDivides0(xn,xm)
| ~ aNaturalNumber0(xn)
| xn != xm ),
inference(spm,[status(thm)],[3450,104794,theory(equality)]) ).
cnf(162271,plain,
( xm = sdtsldt0(esk7_0,xn)
| sz00 = xn
| ~ doDivides0(xn,xm)
| ~ aNaturalNumber0(xn)
| xn != xm ),
inference(rw,[status(thm)],[161851,43072,theory(equality)]) ).
cnf(162272,plain,
( xm = xq
| sz00 = xn
| ~ doDivides0(xn,xm)
| ~ aNaturalNumber0(xn)
| xn != xm ),
inference(rw,[status(thm)],[162271,74663,theory(equality)]) ).
cnf(162273,plain,
( xm = xq
| sz00 = xn
| ~ doDivides0(xn,xm)
| $false
| xn != xm ),
inference(rw,[status(thm)],[162272,240,theory(equality)]) ).
cnf(162274,plain,
( xm = xq
| sz00 = xn
| ~ doDivides0(xn,xm)
| xn != xm ),
inference(cn,[status(thm)],[162273,theory(equality)]) ).
cnf(162275,plain,
( xn = sz00
| ~ doDivides0(xn,xm)
| xm != xn ),
inference(sr,[status(thm)],[162274,47453,theory(equality)]) ).
cnf(162276,plain,
( ~ doDivides0(xn,xm)
| xm != xn ),
inference(sr,[status(thm)],[162275,237,theory(equality)]) ).
cnf(167714,plain,
( sdtpldt0(sz00,sdtasdt0(xn,xn)) = sdtasdt0(xp,sdtpldt0(sz00,esk7_0))
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[3542,14775,theory(equality)]) ).
cnf(167903,plain,
( sdtpldt0(sz00,sdtasdt0(xn,xn)) = sdtasdt0(xn,xn)
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[167714,157280,theory(equality)]),3378,theory(equality)]) ).
cnf(167904,plain,
( sdtpldt0(sz00,sdtasdt0(xn,xn)) = sdtasdt0(xn,xn)
| $false ),
inference(rw,[status(thm)],[167903,209,theory(equality)]) ).
cnf(167905,plain,
sdtpldt0(sz00,sdtasdt0(xn,xn)) = sdtasdt0(xn,xn),
inference(cn,[status(thm)],[167904,theory(equality)]) ).
cnf(175135,plain,
( sdtasdt0(X1,X2) = xm
| sdtasdt0(X1,sdtasdt0(X2,xm)) != esk7_0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[3944,195]) ).
cnf(253042,plain,
xm != xn,
inference(csr,[status(thm)],[162276,71718]) ).
cnf(253542,plain,
( sdtasdt0(xm,X1) = sz00
| xm = X2
| sdtlseqdt0(sdtasdt0(X2,sdtasdt0(xm,X1)),sdtasdt0(esk7_0,X1))
| ~ sdtlseqdt0(X2,xm)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[6241,44986]) ).
cnf(1170946,plain,
( sdtasdt0(xn,sz10) = xm
| sdtasdt0(xn,xm) != esk7_0
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[175135,13064,theory(equality)]) ).
cnf(1171855,plain,
( xn = xm
| sdtasdt0(xn,xm) != esk7_0
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[1170946,12699,theory(equality)]) ).
cnf(1171856,plain,
( xn = xm
| sdtasdt0(xn,xm) != esk7_0
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[1171855,168,theory(equality)]) ).
cnf(1171857,plain,
( xn = xm
| sdtasdt0(xn,xm) != esk7_0
| $false
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[1171856,240,theory(equality)]) ).
cnf(1171858,plain,
( xn = xm
| sdtasdt0(xn,xm) != esk7_0
| $false
| $false
| $false ),
inference(rw,[status(thm)],[1171857,239,theory(equality)]) ).
cnf(1171859,plain,
( xn = xm
| sdtasdt0(xn,xm) != esk7_0 ),
inference(cn,[status(thm)],[1171858,theory(equality)]) ).
cnf(1171860,plain,
sdtasdt0(xn,xm) != esk7_0,
inference(sr,[status(thm)],[1171859,253042,theory(equality)]) ).
cnf(1540406,plain,
( sdtpldt0(sz00,sdtasdt0(xp,esk7_0)) = sdtasdt0(sdtpldt0(sz00,esk7_0),xp)
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[15233,16134,theory(equality)]) ).
cnf(1541258,plain,
( sdtasdt0(xn,xn) = sdtasdt0(sdtpldt0(sz00,esk7_0),xp)
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1540406,3378,theory(equality)]),167905,theory(equality)]) ).
cnf(1541259,plain,
( sdtasdt0(xn,xn) = sdtasdt0(esk7_0,xp)
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[1541258,157280,theory(equality)]) ).
cnf(1541260,plain,
( sdtasdt0(xn,xn) = sdtasdt0(esk7_0,xp)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[1541259,253,theory(equality)]) ).
cnf(1541261,plain,
( sdtasdt0(xn,xn) = sdtasdt0(esk7_0,xp)
| $false
| $false ),
inference(rw,[status(thm)],[1541260,238,theory(equality)]) ).
cnf(1541262,plain,
sdtasdt0(xn,xn) = sdtasdt0(esk7_0,xp),
inference(cn,[status(thm)],[1541261,theory(equality)]) ).
cnf(1586058,plain,
( sdtasdt0(xm,xp) = sz00
| xm = xq
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(esk7_0,xp))
| ~ sdtlseqdt0(xq,xm)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[253542,15938,theory(equality)]) ).
cnf(1586974,plain,
( sdtasdt0(xm,xp) = sz00
| xm = xq
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xq,xm)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[1586058,1541262,theory(equality)]) ).
cnf(1586975,plain,
( sdtasdt0(xm,xp) = sz00
| xm = xq
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xq,xm)
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[1586974,127,theory(equality)]) ).
cnf(1586976,plain,
( sdtasdt0(xm,xp) = sz00
| xm = xq
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xq,xm)
| $false
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[1586975,238,theory(equality)]) ).
cnf(1586977,plain,
( sdtasdt0(xm,xp) = sz00
| xm = xq
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xq,xm)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[1586976,239,theory(equality)]) ).
cnf(1586978,plain,
( sdtasdt0(xm,xp) = sz00
| xm = xq
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xq,xm) ),
inference(cn,[status(thm)],[1586977,theory(equality)]) ).
cnf(1586979,plain,
( xq = xm
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xq,xm) ),
inference(sr,[status(thm)],[1586978,130653,theory(equality)]) ).
cnf(1586980,plain,
( sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xq,xm) ),
inference(sr,[status(thm)],[1586979,47453,theory(equality)]) ).
cnf(1646695,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xm,xn)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[16005,43326,theory(equality)]) ).
cnf(1647271,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xm,xn)
| $false ),
inference(rw,[status(thm)],[1646695,239,theory(equality)]) ).
cnf(1647272,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(cn,[status(thm)],[1647271,theory(equality)]) ).
cnf(1648785,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[195,1647272,theory(equality)]) ).
cnf(1648957,plain,
( xn = xm
| sdtlseqdt0(esk7_0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[3439,1647272,theory(equality)]) ).
cnf(1648958,plain,
( xm = xn
| sdtlseqdt0(sdtasdt0(xn,xm),esk7_0)
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[3442,1647272,theory(equality)]) ).
cnf(1649199,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[1648785,240,theory(equality)]) ).
cnf(1649200,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| $false
| $false ),
inference(rw,[status(thm)],[1649199,239,theory(equality)]) ).
cnf(1649201,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(cn,[status(thm)],[1649200,theory(equality)]) ).
cnf(1649779,plain,
( xn = xm
| sdtlseqdt0(esk7_0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xm,xn)
| $false ),
inference(rw,[status(thm)],[1648957,240,theory(equality)]) ).
cnf(1649780,plain,
( xn = xm
| sdtlseqdt0(esk7_0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xm,xn) ),
inference(cn,[status(thm)],[1649779,theory(equality)]) ).
cnf(1649781,plain,
( sdtlseqdt0(esk7_0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xm,xn) ),
inference(sr,[status(thm)],[1649780,253042,theory(equality)]) ).
cnf(1649782,plain,
( xm = xn
| sdtlseqdt0(sdtasdt0(xn,xm),esk7_0)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[1648958,117568,theory(equality)]) ).
cnf(1649783,plain,
( xm = xn
| sdtlseqdt0(sdtasdt0(xn,xm),esk7_0)
| $false
| $false ),
inference(rw,[status(thm)],[1649782,240,theory(equality)]) ).
cnf(1649784,plain,
( xm = xn
| sdtlseqdt0(sdtasdt0(xn,xm),esk7_0) ),
inference(cn,[status(thm)],[1649783,theory(equality)]) ).
cnf(1649785,plain,
sdtlseqdt0(sdtasdt0(xn,xm),esk7_0),
inference(sr,[status(thm)],[1649784,253042,theory(equality)]) ).
cnf(1651393,plain,
( sdtasdt0(xn,xm) = esk7_0
| ~ sdtlseqdt0(sdtasdt0(xn,xm),esk7_0)
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xm,xn) ),
inference(spm,[status(thm)],[151,1649781,theory(equality)]) ).
cnf(1651442,plain,
( sdtasdt0(xn,xm) = esk7_0
| $false
| ~ aNaturalNumber0(esk7_0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xm,xn) ),
inference(rw,[status(thm)],[1651393,1649785,theory(equality)]) ).
cnf(1651443,plain,
( sdtasdt0(xn,xm) = esk7_0
| $false
| $false
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xm,xn) ),
inference(rw,[status(thm)],[1651442,253,theory(equality)]) ).
cnf(1651444,plain,
( sdtasdt0(xn,xm) = esk7_0
| $false
| $false
| $false
| ~ sdtlseqdt0(xm,xn) ),
inference(rw,[status(thm)],[1651443,1649201,theory(equality)]) ).
cnf(1651445,plain,
( sdtasdt0(xn,xm) = esk7_0
| ~ sdtlseqdt0(xm,xn) ),
inference(cn,[status(thm)],[1651444,theory(equality)]) ).
cnf(1651446,plain,
~ sdtlseqdt0(xm,xn),
inference(sr,[status(thm)],[1651445,1171860,theory(equality)]) ).
cnf(1658791,plain,
sdtlseqdt0(xq,xm),
inference(sr,[status(thm)],[63396,1651446,theory(equality)]) ).
cnf(3277783,plain,
( sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xq,xm) ),
inference(rw,[status(thm)],[1586980,1647272,theory(equality)]) ).
cnf(3277784,plain,
( sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xn,xn))
| $false ),
inference(rw,[status(thm)],[3277783,1658791,theory(equality)]) ).
cnf(3277785,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[3277784,theory(equality)]) ).
cnf(3277801,plain,
( sz00 = xn
| xm = xn
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[67259,3277785,theory(equality)]) ).
cnf(3277869,plain,
( sz00 = xn
| xm = xn
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[3277801,117568,theory(equality)]) ).
cnf(3277870,plain,
( sz00 = xn
| xm = xn
| $false
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[3277869,240,theory(equality)]) ).
cnf(3277871,plain,
( sz00 = xn
| xm = xn
| $false
| $false
| $false ),
inference(rw,[status(thm)],[3277870,239,theory(equality)]) ).
cnf(3277872,plain,
( sz00 = xn
| xm = xn ),
inference(cn,[status(thm)],[3277871,theory(equality)]) ).
cnf(3277873,plain,
xm = xn,
inference(sr,[status(thm)],[3277872,237,theory(equality)]) ).
cnf(3277874,plain,
$false,
inference(sr,[status(thm)],[3277873,253042,theory(equality)]) ).
cnf(3277875,plain,
$false,
3277874,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM526+3 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04 % Command : Source/sine.py -e eprover -t %d %s
% 0.02/0.23 % Computer : n115.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Jan 5 07:15:29 CST 2018
% 0.02/0.23 % CPUTime :
% 0.06/0.28 % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.28 --creating new selector for []
% 29.11/29.38 eprover: CPU time limit exceeded, terminating
% 103.31/106.91 -running prover on /export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_1 with time limit 29
% 103.31/106.91 -running prover with command ['/export/starexec/sandbox2/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_1']
% 103.31/106.91 -prover status ResourceOut
% 103.31/106.91 -running prover on /export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2 with time limit 80
% 103.31/106.91 -running prover with command ['/export/starexec/sandbox2/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=80', '/export/starexec/sandbox2/tmp/tmpFIHmip/sel_theBenchmark.p_2']
% 103.31/106.91 -prover status Theorem
% 103.31/106.91 Problem theBenchmark.p solved in phase 1.
% 103.31/106.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 103.31/106.91 % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 103.31/106.91 Solved 1 out of 1.
% 103.31/106.91 # Problem is unsatisfiable (or provable), constructing proof object
% 103.31/106.91 # SZS status Theorem
% 103.31/106.91 # SZS output start CNFRefutation.
% See solution above
% 103.31/106.92 # SZS output end CNFRefutation
%------------------------------------------------------------------------------