TSTP Solution File: NUM503+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM503+3 : TPTP v7.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n100.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 15:21:34 EST 2018
% Result : Theorem 93.93s
% Output : CNFRefutation 93.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 31
% Syntax : Number of formulae : 523 ( 83 unt; 0 def)
% Number of atoms : 2055 ( 440 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 2416 ( 884 ~;1235 |; 261 &)
% ( 3 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 12 con; 0-2 aty)
% Number of variables : 438 ( 0 sgn 207 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
~ ( equal(xk,sz00)
| equal(xk,sz10) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',m__2315) ).
fof(2,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtasdt0(X1,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',m_MulZero) ).
fof(3,axiom,
( ~ equal(xp,sz00)
& ~ 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)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtasdt0(xn,xm),sdtasdt0(xp,X1)) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',m__1860) ).
fof(4,axiom,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(xk,sdtasdt0(xr,X1)) )
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& equal(xr,sdtasdt0(X1,X2)) )
| doDivides0(X1,xr) ) )
=> ( equal(X1,sz10)
| equal(X1,xr) ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',m__2342) ).
fof(6,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mAddComm) ).
fof(8,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/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mMulCanc) ).
fof(11,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/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mAMDistr) ).
fof(12,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(X2,sdtasdt0(X1,X3)) ) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mDefDiv) ).
fof(14,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( ~ equal(X2,X1)
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mLETotal) ).
fof(15,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mLETran) ).
fof(18,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& ~ equal(X2,sz00) )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mDivLE) ).
fof(19,axiom,
( ~ equal(xn,xp)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(xn,X1),xp) )
& sdtlseqdt0(xn,xp)
& ~ equal(xm,xp)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(xm,X1),xp) )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',m__2287) ).
fof(20,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',m__1837) ).
fof(24,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/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mMonMul) ).
fof(25,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mDefLE) ).
fof(27,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> equal(X1,X2) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mLEAsym) ).
fof(30,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ~ equal(X1,sz00)
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mMonMul2) ).
fof(31,axiom,
( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(xp,X1),xk) )
& sdtlseqdt0(xp,xk) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',m__2389) ).
fof(32,axiom,
( aNaturalNumber0(sz10)
& ~ equal(sz10,sz00) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mSortsC_01) ).
fof(34,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> equal(sdtasdt0(sdtasdt0(X1,X2),X3),sdtasdt0(X1,sdtasdt0(X2,X3))) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mMulAsso) ).
fof(38,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mSortsB_02) ).
fof(39,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ~ equal(X1,sz00)
& ~ equal(X1,sz10)
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( equal(X2,sz10)
| equal(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mDefPrime) ).
fof(40,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mSortsC) ).
fof(41,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mSortsB) ).
fof(42,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& ~ equal(X1,sz00)
& ~ equal(X1,sz10) )
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mPrimDiv) ).
fof(43,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( equal(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| equal(sdtpldt0(X2,X1),sdtpldt0(X3,X1)) )
=> equal(X2,X3) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mAddCanc) ).
fof(45,axiom,
( aNaturalNumber0(xk)
& equal(sdtasdt0(xn,xm),sdtasdt0(xp,xk))
& equal(xk,sdtsldt0(sdtasdt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',m__2306) ).
fof(46,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',mMulComm) ).
fof(47,axiom,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(xp,X1),xm) )
| sdtlseqdt0(xp,xm) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',m__2075) ).
fof(49,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtpldt0(X1,sz00),X1)
& equal(X1,sdtpldt0(sz00,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',m_AddZero) ).
fof(51,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2',m_MulUnit) ).
fof(53,plain,
( ~ equal(xk,sz00)
& ~ equal(xk,sz10) ),
inference(fof_nnf,[status(thm)],[1]) ).
cnf(55,plain,
xk != sz00,
inference(split_conjunct,[status(thm)],[53]) ).
fof(56,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtasdt0(X1,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X1)) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(57,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtasdt0(X2,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X2)) ) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,plain,
! [X2] :
( ( equal(sdtasdt0(X2,sz00),sz00)
| ~ aNaturalNumber0(X2) )
& ( equal(sz00,sdtasdt0(sz00,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[57]) ).
cnf(59,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(60,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(61,plain,
( ~ equal(xp,sz00)
& ~ 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)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtasdt0(xn,xm),sdtasdt0(xp,X1)) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(62,plain,
( ~ equal(xp,sz00)
& ~ 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)
& ? [X5] :
( aNaturalNumber0(X5)
& equal(sdtasdt0(xn,xm),sdtasdt0(xp,X5)) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(variable_rename,[status(thm)],[61]) ).
fof(63,plain,
( ~ equal(xp,sz00)
& ~ 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)
& aNaturalNumber0(esk1_0)
& equal(sdtasdt0(xn,xm),sdtasdt0(xp,esk1_0))
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa)],[62]) ).
fof(64,plain,
! [X3,X4] :
( ( ( ( ~ aNaturalNumber0(X4)
| ~ equal(xp,sdtasdt0(X3,X4)) )
& ~ doDivides0(X3,xp) )
| ~ aNaturalNumber0(X3)
| equal(X3,sz10)
| equal(X3,xp) )
& ~ equal(xp,sz00)
& ~ equal(xp,sz10)
& isPrime0(xp)
& aNaturalNumber0(esk1_0)
& equal(sdtasdt0(xn,xm),sdtasdt0(xp,esk1_0))
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(shift_quantors,[status(thm)],[63]) ).
fof(65,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,sz00)
& ~ equal(xp,sz10)
& isPrime0(xp)
& aNaturalNumber0(esk1_0)
& equal(sdtasdt0(xn,xm),sdtasdt0(xp,esk1_0))
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(distribute,[status(thm)],[64]) ).
cnf(67,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,esk1_0),
inference(split_conjunct,[status(thm)],[65]) ).
cnf(68,plain,
aNaturalNumber0(esk1_0),
inference(split_conjunct,[status(thm)],[65]) ).
cnf(70,plain,
xp != sz10,
inference(split_conjunct,[status(thm)],[65]) ).
cnf(71,plain,
xp != sz00,
inference(split_conjunct,[status(thm)],[65]) ).
cnf(72,plain,
( X1 = xp
| X1 = sz10
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xp) ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(74,plain,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(xk,sdtasdt0(xr,X1)) )
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ equal(xr,sdtasdt0(X1,X2)) )
& ~ doDivides0(X1,xr) )
| equal(X1,sz10)
| equal(X1,xr) )
& isPrime0(xr) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(75,plain,
( aNaturalNumber0(xr)
& ? [X3] :
( aNaturalNumber0(X3)
& equal(xk,sdtasdt0(xr,X3)) )
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& ! [X4] :
( ~ aNaturalNumber0(X4)
| ( ! [X5] :
( ~ aNaturalNumber0(X5)
| ~ equal(xr,sdtasdt0(X4,X5)) )
& ~ doDivides0(X4,xr) )
| equal(X4,sz10)
| equal(X4,xr) )
& isPrime0(xr) ),
inference(variable_rename,[status(thm)],[74]) ).
fof(76,plain,
( aNaturalNumber0(xr)
& aNaturalNumber0(esk2_0)
& equal(xk,sdtasdt0(xr,esk2_0))
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& ! [X4] :
( ~ aNaturalNumber0(X4)
| ( ! [X5] :
( ~ aNaturalNumber0(X5)
| ~ equal(xr,sdtasdt0(X4,X5)) )
& ~ doDivides0(X4,xr) )
| equal(X4,sz10)
| equal(X4,xr) )
& isPrime0(xr) ),
inference(skolemize,[status(esa)],[75]) ).
fof(77,plain,
! [X4,X5] :
( ( ( ( ~ aNaturalNumber0(X5)
| ~ equal(xr,sdtasdt0(X4,X5)) )
& ~ doDivides0(X4,xr) )
| ~ aNaturalNumber0(X4)
| equal(X4,sz10)
| equal(X4,xr) )
& aNaturalNumber0(xr)
& aNaturalNumber0(esk2_0)
& equal(xk,sdtasdt0(xr,esk2_0))
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& isPrime0(xr) ),
inference(shift_quantors,[status(thm)],[76]) ).
fof(78,plain,
! [X4,X5] :
( ( ~ aNaturalNumber0(X5)
| ~ equal(xr,sdtasdt0(X4,X5))
| ~ aNaturalNumber0(X4)
| equal(X4,sz10)
| equal(X4,xr) )
& ( ~ doDivides0(X4,xr)
| ~ aNaturalNumber0(X4)
| equal(X4,sz10)
| equal(X4,xr) )
& aNaturalNumber0(xr)
& aNaturalNumber0(esk2_0)
& equal(xk,sdtasdt0(xr,esk2_0))
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& isPrime0(xr) ),
inference(distribute,[status(thm)],[77]) ).
cnf(80,plain,
xr != sz10,
inference(split_conjunct,[status(thm)],[78]) ).
cnf(81,plain,
xr != sz00,
inference(split_conjunct,[status(thm)],[78]) ).
cnf(82,plain,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[78]) ).
cnf(83,plain,
xk = sdtasdt0(xr,esk2_0),
inference(split_conjunct,[status(thm)],[78]) ).
cnf(84,plain,
aNaturalNumber0(esk2_0),
inference(split_conjunct,[status(thm)],[78]) ).
cnf(85,plain,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[78]) ).
cnf(86,plain,
( X1 = xr
| X1 = sz10
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xr) ),
inference(split_conjunct,[status(thm)],[78]) ).
fof(91,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(92,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(sdtpldt0(X3,X4),sdtpldt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[91]) ).
cnf(93,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[92]) ).
fof(97,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)],[8]) ).
fof(98,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)],[97]) ).
fof(99,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)],[98]) ).
fof(100,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)],[99]) ).
cnf(101,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X3,X1) != sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[100]) ).
cnf(102,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,X3) != sdtasdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[100]) ).
fof(236,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)],[11]) ).
fof(237,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)],[236]) ).
fof(238,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)],[237]) ).
cnf(239,plain,
( sdtasdt0(sdtpldt0(X2,X1),X3) = sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[238]) ).
cnf(240,plain,
( sdtasdt0(X3,sdtpldt0(X2,X1)) = sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[238]) ).
fof(241,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)],[12]) ).
fof(242,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)],[241]) ).
fof(243,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk7_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk7_2(X4,X5))) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7)) )
| doDivides0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[242]) ).
fof(244,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5) )
& ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk7_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk7_2(X4,X5))) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[243]) ).
fof(245,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk7_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(X5,sdtasdt0(X4,esk7_2(X4,X5)))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[244]) ).
cnf(246,plain,
( X1 = sdtasdt0(X2,esk7_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[245]) ).
cnf(247,plain,
( aNaturalNumber0(esk7_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[245]) ).
fof(252,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X1,X2)
| ( ~ equal(X2,X1)
& sdtlseqdt0(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(253,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtlseqdt0(X3,X4)
| ( ~ equal(X4,X3)
& sdtlseqdt0(X4,X3) ) ),
inference(variable_rename,[status(thm)],[252]) ).
fof(254,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)],[253]) ).
cnf(255,plain,
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[254]) ).
fof(257,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3)
| sdtlseqdt0(X1,X3) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(258,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ sdtlseqdt0(X4,X5)
| ~ sdtlseqdt0(X5,X6)
| sdtlseqdt0(X4,X6) ),
inference(variable_rename,[status(thm)],[257]) ).
cnf(259,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[258]) ).
fof(268,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2)
| equal(X2,sz00)
| sdtlseqdt0(X1,X2) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(269,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ doDivides0(X3,X4)
| equal(X4,sz00)
| sdtlseqdt0(X3,X4) ),
inference(variable_rename,[status(thm)],[268]) ).
cnf(270,plain,
( sdtlseqdt0(X1,X2)
| X2 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[269]) ).
fof(271,plain,
( ~ equal(xn,xp)
& ? [X2] :
( aNaturalNumber0(X2)
& equal(sdtpldt0(xn,X2),xp) )
& sdtlseqdt0(xn,xp)
& ~ equal(xm,xp)
& ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtpldt0(xm,X3),xp) )
& sdtlseqdt0(xm,xp) ),
inference(variable_rename,[status(thm)],[19]) ).
fof(272,plain,
( ~ equal(xn,xp)
& aNaturalNumber0(esk8_0)
& equal(sdtpldt0(xn,esk8_0),xp)
& sdtlseqdt0(xn,xp)
& ~ equal(xm,xp)
& aNaturalNumber0(esk9_0)
& equal(sdtpldt0(xm,esk9_0),xp)
& sdtlseqdt0(xm,xp) ),
inference(skolemize,[status(esa)],[271]) ).
cnf(273,plain,
sdtlseqdt0(xm,xp),
inference(split_conjunct,[status(thm)],[272]) ).
cnf(277,plain,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[272]) ).
cnf(278,plain,
sdtpldt0(xn,esk8_0) = xp,
inference(split_conjunct,[status(thm)],[272]) ).
cnf(279,plain,
aNaturalNumber0(esk8_0),
inference(split_conjunct,[status(thm)],[272]) ).
cnf(280,plain,
xn != xp,
inference(split_conjunct,[status(thm)],[272]) ).
cnf(281,plain,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(282,plain,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(283,plain,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[20]) ).
fof(298,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)],[24]) ).
fof(299,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)],[298]) ).
fof(300,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)],[299]) ).
cnf(303,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)],[300]) ).
fof(305,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)],[25]) ).
fof(306,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)],[305]) ).
fof(307,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk10_2(X4,X5))
& equal(sdtpldt0(X4,esk10_2(X4,X5)),X5) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5) )
| sdtlseqdt0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[306]) ).
fof(308,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5) )
& ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk10_2(X4,X5))
& equal(sdtpldt0(X4,esk10_2(X4,X5)),X5) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[307]) ).
fof(309,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk10_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(sdtpldt0(X4,esk10_2(X4,X5)),X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[308]) ).
cnf(310,plain,
( sdtpldt0(X2,esk10_2(X2,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[309]) ).
cnf(311,plain,
( aNaturalNumber0(esk10_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[309]) ).
cnf(312,plain,
( sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[309]) ).
fof(316,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1)
| equal(X1,X2) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(317,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| equal(X3,X4) ),
inference(variable_rename,[status(thm)],[316]) ).
cnf(318,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[317]) ).
fof(331,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(X1,sz00)
| sdtlseqdt0(X2,sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(332,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(X3,sz00)
| sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[331]) ).
cnf(333,plain,
( sdtlseqdt0(X1,sdtasdt0(X1,X2))
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[332]) ).
fof(334,plain,
( ? [X2] :
( aNaturalNumber0(X2)
& equal(sdtpldt0(xp,X2),xk) )
& sdtlseqdt0(xp,xk) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(335,plain,
( aNaturalNumber0(esk11_0)
& equal(sdtpldt0(xp,esk11_0),xk)
& sdtlseqdt0(xp,xk) ),
inference(skolemize,[status(esa)],[334]) ).
cnf(336,plain,
sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[335]) ).
cnf(337,plain,
sdtpldt0(xp,esk11_0) = xk,
inference(split_conjunct,[status(thm)],[335]) ).
cnf(338,plain,
aNaturalNumber0(esk11_0),
inference(split_conjunct,[status(thm)],[335]) ).
cnf(340,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[32]) ).
fof(349,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)],[34]) ).
fof(350,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)],[349]) ).
cnf(351,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[350]) ).
fof(367,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[38]) ).
fof(368,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[367]) ).
cnf(369,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[368]) ).
fof(370,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( ( ~ isPrime0(X1)
| ( ~ equal(X1,sz00)
& ~ equal(X1,sz10)
& ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| equal(X2,sz10)
| equal(X2,X1) ) ) )
& ( equal(X1,sz00)
| equal(X1,sz10)
| ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& ~ equal(X2,sz10)
& ~ equal(X2,X1) )
| isPrime0(X1) ) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(371,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| ( ( ~ isPrime0(X3)
| ( ~ equal(X3,sz00)
& ~ equal(X3,sz10)
& ! [X4] :
( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| equal(X4,sz10)
| equal(X4,X3) ) ) )
& ( equal(X3,sz00)
| equal(X3,sz10)
| ? [X5] :
( aNaturalNumber0(X5)
& doDivides0(X5,X3)
& ~ equal(X5,sz10)
& ~ equal(X5,X3) )
| isPrime0(X3) ) ) ),
inference(variable_rename,[status(thm)],[370]) ).
fof(372,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| ( ( ~ isPrime0(X3)
| ( ~ equal(X3,sz00)
& ~ equal(X3,sz10)
& ! [X4] :
( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| equal(X4,sz10)
| equal(X4,X3) ) ) )
& ( equal(X3,sz00)
| equal(X3,sz10)
| ( aNaturalNumber0(esk12_1(X3))
& doDivides0(esk12_1(X3),X3)
& ~ equal(esk12_1(X3),sz10)
& ~ equal(esk12_1(X3),X3) )
| isPrime0(X3) ) ) ),
inference(skolemize,[status(esa)],[371]) ).
fof(373,plain,
! [X3,X4] :
( ( ( ( ( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| equal(X4,sz10)
| equal(X4,X3) )
& ~ equal(X3,sz00)
& ~ equal(X3,sz10) )
| ~ isPrime0(X3) )
& ( equal(X3,sz00)
| equal(X3,sz10)
| ( aNaturalNumber0(esk12_1(X3))
& doDivides0(esk12_1(X3),X3)
& ~ equal(esk12_1(X3),sz10)
& ~ equal(esk12_1(X3),X3) )
| isPrime0(X3) ) )
| ~ aNaturalNumber0(X3) ),
inference(shift_quantors,[status(thm)],[372]) ).
fof(374,plain,
! [X3,X4] :
( ( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| equal(X4,sz10)
| equal(X4,X3)
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(X3,sz00)
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(X3,sz10)
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( aNaturalNumber0(esk12_1(X3))
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( doDivides0(esk12_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk12_1(X3),sz10)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk12_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) ) ),
inference(distribute,[status(thm)],[373]) ).
cnf(379,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[374]) ).
cnf(382,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[40]) ).
fof(383,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(384,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[383]) ).
cnf(385,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[384]) ).
fof(386,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| equal(X1,sz00)
| equal(X1,sz10)
| ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(387,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10)
| ? [X4] :
( aNaturalNumber0(X4)
& doDivides0(X4,X3)
& isPrime0(X4) ) ),
inference(variable_rename,[status(thm)],[386]) ).
fof(388,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10)
| ( aNaturalNumber0(esk13_1(X3))
& doDivides0(esk13_1(X3),X3)
& isPrime0(esk13_1(X3)) ) ),
inference(skolemize,[status(esa)],[387]) ).
fof(389,plain,
! [X3] :
( ( aNaturalNumber0(esk13_1(X3))
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) )
& ( doDivides0(esk13_1(X3),X3)
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) )
& ( isPrime0(esk13_1(X3))
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) ) ),
inference(distribute,[status(thm)],[388]) ).
cnf(390,plain,
( X1 = sz10
| X1 = sz00
| isPrime0(esk13_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[389]) ).
cnf(391,plain,
( X1 = sz10
| X1 = sz00
| doDivides0(esk13_1(X1),X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[389]) ).
cnf(392,plain,
( X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk13_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[389]) ).
fof(393,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ( ~ equal(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
& ~ equal(sdtpldt0(X2,X1),sdtpldt0(X3,X1)) )
| equal(X2,X3) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(394,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ( ~ equal(sdtpldt0(X4,X5),sdtpldt0(X4,X6))
& ~ equal(sdtpldt0(X5,X4),sdtpldt0(X6,X4)) )
| equal(X5,X6) ),
inference(variable_rename,[status(thm)],[393]) ).
fof(395,plain,
! [X4,X5,X6] :
( ( ~ equal(sdtpldt0(X4,X5),sdtpldt0(X4,X6))
| equal(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( ~ equal(sdtpldt0(X5,X4),sdtpldt0(X6,X4))
| equal(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[394]) ).
cnf(396,plain,
( X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X2,X3) != sdtpldt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[395]) ).
cnf(397,plain,
( X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X3,X2) != sdtpldt0(X3,X1) ),
inference(split_conjunct,[status(thm)],[395]) ).
cnf(402,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(403,plain,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[45]) ).
fof(404,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[46]) ).
fof(405,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(sdtasdt0(X3,X4),sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[404]) ).
cnf(406,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[405]) ).
fof(407,plain,
( ! [X1] :
( ~ aNaturalNumber0(X1)
| ~ equal(sdtpldt0(xp,X1),xm) )
& ~ sdtlseqdt0(xp,xm) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(408,plain,
( ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ equal(sdtpldt0(xp,X2),xm) )
& ~ sdtlseqdt0(xp,xm) ),
inference(variable_rename,[status(thm)],[407]) ).
fof(409,plain,
! [X2] :
( ( ~ aNaturalNumber0(X2)
| ~ equal(sdtpldt0(xp,X2),xm) )
& ~ sdtlseqdt0(xp,xm) ),
inference(shift_quantors,[status(thm)],[408]) ).
cnf(411,plain,
( sdtpldt0(xp,X1) != xm
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[409]) ).
fof(416,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtpldt0(X1,sz00),X1)
& equal(X1,sdtpldt0(sz00,X1)) ) ),
inference(fof_nnf,[status(thm)],[49]) ).
fof(417,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtpldt0(X2,sz00),X2)
& equal(X2,sdtpldt0(sz00,X2)) ) ),
inference(variable_rename,[status(thm)],[416]) ).
fof(418,plain,
! [X2] :
( ( equal(sdtpldt0(X2,sz00),X2)
| ~ aNaturalNumber0(X2) )
& ( equal(X2,sdtpldt0(sz00,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[417]) ).
cnf(420,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[418]) ).
fof(428,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
inference(fof_nnf,[status(thm)],[51]) ).
fof(429,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtasdt0(X2,sz10),X2)
& equal(X2,sdtasdt0(sz10,X2)) ) ),
inference(variable_rename,[status(thm)],[428]) ).
fof(430,plain,
! [X2] :
( ( equal(sdtasdt0(X2,sz10),X2)
| ~ aNaturalNumber0(X2) )
& ( equal(X2,sdtasdt0(sz10,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[429]) ).
cnf(431,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[430]) ).
cnf(432,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[430]) ).
cnf(433,plain,
sdtasdt0(xp,xk) = sdtasdt0(xp,esk1_0),
inference(rw,[status(thm)],[67,402,theory(equality)]) ).
cnf(443,plain,
( xk != xm
| ~ aNaturalNumber0(esk11_0) ),
inference(spm,[status(thm)],[411,337,theory(equality)]) ).
cnf(444,plain,
( xk != xm
| $false ),
inference(rw,[status(thm)],[443,338,theory(equality)]) ).
cnf(445,plain,
xk != xm,
inference(cn,[status(thm)],[444,theory(equality)]) ).
cnf(447,plain,
( aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[369,402,theory(equality)]) ).
cnf(454,plain,
( aNaturalNumber0(sdtasdt0(xp,xk))
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[447,282,theory(equality)]) ).
cnf(455,plain,
( aNaturalNumber0(sdtasdt0(xp,xk))
| $false
| $false ),
inference(rw,[status(thm)],[454,283,theory(equality)]) ).
cnf(456,plain,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(cn,[status(thm)],[455,theory(equality)]) ).
cnf(492,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(er,[status(thm)],[379,theory(equality)]) ).
cnf(493,plain,
( ~ isPrime0(sz10)
| $false ),
inference(rw,[status(thm)],[492,340,theory(equality)]) ).
cnf(494,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[493,theory(equality)]) ).
cnf(518,plain,
( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[402,406,theory(equality)]) ).
cnf(530,plain,
( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[518,282,theory(equality)]) ).
cnf(531,plain,
( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
| $false
| $false ),
inference(rw,[status(thm)],[530,283,theory(equality)]) ).
cnf(532,plain,
sdtasdt0(xm,xn) = sdtasdt0(xp,xk),
inference(cn,[status(thm)],[531,theory(equality)]) ).
cnf(622,plain,
( sz00 = X1
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[333,406,theory(equality)]) ).
cnf(689,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(er,[status(thm)],[312,theory(equality)]) ).
cnf(746,plain,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[259,336,theory(equality)]) ).
cnf(754,plain,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xp)
| $false
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[746,281,theory(equality)]) ).
cnf(755,plain,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xp)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[754,403,theory(equality)]) ).
cnf(756,plain,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[755,theory(equality)]) ).
cnf(838,plain,
( xp = esk13_1(xp)
| sz10 = esk13_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk13_1(xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[72,391,theory(equality)]) ).
cnf(839,plain,
( xr = esk13_1(xr)
| sz10 = esk13_1(xr)
| sz10 = xr
| sz00 = xr
| ~ aNaturalNumber0(esk13_1(xr))
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[86,391,theory(equality)]) ).
cnf(841,plain,
( xp = esk13_1(xp)
| sz10 = esk13_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk13_1(xp))
| $false ),
inference(rw,[status(thm)],[838,281,theory(equality)]) ).
cnf(842,plain,
( xp = esk13_1(xp)
| sz10 = esk13_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk13_1(xp)) ),
inference(cn,[status(thm)],[841,theory(equality)]) ).
cnf(843,plain,
( esk13_1(xp) = xp
| esk13_1(xp) = sz10
| sz00 = xp
| ~ aNaturalNumber0(esk13_1(xp)) ),
inference(sr,[status(thm)],[842,70,theory(equality)]) ).
cnf(844,plain,
( esk13_1(xp) = xp
| esk13_1(xp) = sz10
| ~ aNaturalNumber0(esk13_1(xp)) ),
inference(sr,[status(thm)],[843,71,theory(equality)]) ).
cnf(845,plain,
( xr = esk13_1(xr)
| sz10 = esk13_1(xr)
| sz10 = xr
| sz00 = xr
| ~ aNaturalNumber0(esk13_1(xr))
| $false ),
inference(rw,[status(thm)],[839,85,theory(equality)]) ).
cnf(846,plain,
( xr = esk13_1(xr)
| sz10 = esk13_1(xr)
| sz10 = xr
| sz00 = xr
| ~ aNaturalNumber0(esk13_1(xr)) ),
inference(cn,[status(thm)],[845,theory(equality)]) ).
cnf(847,plain,
( esk13_1(xr) = xr
| esk13_1(xr) = sz10
| xr = sz00
| ~ aNaturalNumber0(esk13_1(xr)) ),
inference(sr,[status(thm)],[846,80,theory(equality)]) ).
cnf(848,plain,
( esk13_1(xr) = xr
| esk13_1(xr) = sz10
| ~ aNaturalNumber0(esk13_1(xr)) ),
inference(sr,[status(thm)],[847,81,theory(equality)]) ).
cnf(859,plain,
( sz00 = X1
| X2 != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[397,420,theory(equality)]) ).
cnf(891,plain,
( sz00 = X1
| X2 != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[859,382,theory(equality)]) ).
cnf(892,plain,
( sz00 = X1
| X2 != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[891,theory(equality)]) ).
cnf(902,plain,
( xn = X1
| xp != sdtpldt0(X1,esk8_0)
| ~ aNaturalNumber0(esk8_0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[396,278,theory(equality)]) ).
cnf(922,plain,
( xn = X1
| xp != sdtpldt0(X1,esk8_0)
| $false
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[902,279,theory(equality)]) ).
cnf(923,plain,
( xn = X1
| xp != sdtpldt0(X1,esk8_0)
| $false
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[922,283,theory(equality)]) ).
cnf(924,plain,
( xn = X1
| xp != sdtpldt0(X1,esk8_0)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[923,theory(equality)]) ).
cnf(967,plain,
( sz00 = xk
| sdtlseqdt0(xr,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[270,82,theory(equality)]) ).
cnf(971,plain,
( sz00 = xk
| sdtlseqdt0(xr,xk)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[967,403,theory(equality)]) ).
cnf(972,plain,
( sz00 = xk
| sdtlseqdt0(xr,xk)
| $false
| $false ),
inference(rw,[status(thm)],[971,85,theory(equality)]) ).
cnf(973,plain,
( sz00 = xk
| sdtlseqdt0(xr,xk) ),
inference(cn,[status(thm)],[972,theory(equality)]) ).
cnf(974,plain,
sdtlseqdt0(xr,xk),
inference(sr,[status(thm)],[973,55,theory(equality)]) ).
cnf(1050,plain,
( sdtasdt0(xk,X1) = sdtasdt0(xr,sdtasdt0(esk2_0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk2_0)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[351,83,theory(equality)]) ).
cnf(1051,plain,
( sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xn,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[351,402,theory(equality)]) ).
cnf(1054,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[369,351,theory(equality)]) ).
cnf(1055,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[60,351,theory(equality)]) ).
cnf(1057,plain,
( sdtasdt0(sz00,X2) = sdtasdt0(sz00,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[351,59,theory(equality)]) ).
cnf(1060,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[351,431,theory(equality)]) ).
cnf(1061,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)],[406,351,theory(equality)]) ).
cnf(1063,plain,
( sdtasdt0(sdtasdt0(X2,X1),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[351,406,theory(equality)]) ).
cnf(1065,plain,
( sz00 = X1
| sdtlseqdt0(sdtasdt0(X2,X3),sdtasdt0(X2,sdtasdt0(X3,X1)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[333,351,theory(equality)]) ).
cnf(1072,plain,
( sdtasdt0(xk,X1) = sdtasdt0(xr,sdtasdt0(esk2_0,X1))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[1050,84,theory(equality)]) ).
cnf(1073,plain,
( sdtasdt0(xk,X1) = sdtasdt0(xr,sdtasdt0(esk2_0,X1))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[1072,85,theory(equality)]) ).
cnf(1074,plain,
( sdtasdt0(xk,X1) = sdtasdt0(xr,sdtasdt0(esk2_0,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1073,theory(equality)]) ).
cnf(1075,plain,
( sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xn,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[1051,282,theory(equality)]) ).
cnf(1076,plain,
( sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xn,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[1075,283,theory(equality)]) ).
cnf(1077,plain,
( sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xn,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1076,theory(equality)]) ).
cnf(1084,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[1055,382,theory(equality)]) ).
cnf(1085,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1084,theory(equality)]) ).
cnf(1088,plain,
( sdtasdt0(sz00,X2) = sdtasdt0(sz00,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[1057,382,theory(equality)]) ).
cnf(1089,plain,
( sdtasdt0(sz00,X2) = sdtasdt0(sz00,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1088,theory(equality)]) ).
cnf(1094,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[1060,340,theory(equality)]) ).
cnf(1095,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1094,theory(equality)]) ).
cnf(1143,plain,
( sz00 = esk1_0
| xp = X1
| sdtasdt0(xp,xk) != sdtasdt0(X1,esk1_0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(esk1_0) ),
inference(spm,[status(thm)],[101,433,theory(equality)]) ).
cnf(1171,plain,
( sz00 = esk1_0
| xp = X1
| sdtasdt0(xp,xk) != sdtasdt0(X1,esk1_0)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(esk1_0) ),
inference(rw,[status(thm)],[1143,281,theory(equality)]) ).
cnf(1172,plain,
( sz00 = esk1_0
| xp = X1
| sdtasdt0(xp,xk) != sdtasdt0(X1,esk1_0)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[1171,68,theory(equality)]) ).
cnf(1173,plain,
( sz00 = esk1_0
| xp = X1
| sdtasdt0(xp,xk) != sdtasdt0(X1,esk1_0)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1172,theory(equality)]) ).
cnf(1202,plain,
( sz00 = xp
| esk1_0 = X1
| sdtasdt0(xp,xk) != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk1_0)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[102,433,theory(equality)]) ).
cnf(1232,plain,
( sz00 = xp
| esk1_0 = X1
| sdtasdt0(xp,xk) != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[1202,68,theory(equality)]) ).
cnf(1233,plain,
( sz00 = xp
| esk1_0 = X1
| sdtasdt0(xp,xk) != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[1232,281,theory(equality)]) ).
cnf(1234,plain,
( sz00 = xp
| esk1_0 = X1
| sdtasdt0(xp,xk) != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1233,theory(equality)]) ).
cnf(1235,plain,
( esk1_0 = X1
| sdtasdt0(xp,xk) != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[1234,71,theory(equality)]) ).
cnf(1338,plain,
( sdtpldt0(sdtasdt0(sz10,X1),X2) = sdtasdt0(sz10,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[240,431,theory(equality)]) ).
cnf(1393,plain,
( sdtpldt0(sdtasdt0(sz10,X1),X2) = sdtasdt0(sz10,sdtpldt0(X1,X2))
| $false
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(rw,[status(thm)],[1338,340,theory(equality)]) ).
cnf(1394,plain,
( sdtpldt0(sdtasdt0(sz10,X1),X2) = sdtasdt0(sz10,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[1393,theory(equality)]) ).
cnf(1409,plain,
( sdtpldt0(sdtasdt0(X1,sz10),X2) = sdtasdt0(sdtpldt0(X1,X2),sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[239,432,theory(equality)]) ).
cnf(1463,plain,
( sdtpldt0(sdtasdt0(X1,sz10),X2) = sdtasdt0(sdtpldt0(X1,X2),sz10)
| $false
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(rw,[status(thm)],[1409,340,theory(equality)]) ).
cnf(1464,plain,
( sdtpldt0(sdtasdt0(X1,sz10),X2) = sdtasdt0(sdtpldt0(X1,X2),sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[1463,theory(equality)]) ).
cnf(1521,plain,
( sz00 = X1
| xp = xn
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[303,277,theory(equality)]) ).
cnf(1530,plain,
( sz00 = X1
| xp = xn
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[1521,283,theory(equality)]) ).
cnf(1531,plain,
( sz00 = X1
| xp = xn
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[1530,281,theory(equality)]) ).
cnf(1532,plain,
( sz00 = X1
| xp = xn
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1531,theory(equality)]) ).
cnf(1533,plain,
( sz00 = X1
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[1532,280,theory(equality)]) ).
cnf(7707,plain,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[259,974,theory(equality)]) ).
cnf(7722,plain,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xr)
| $false
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[7707,85,theory(equality)]) ).
cnf(7723,plain,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xr)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[7722,403,theory(equality)]) ).
cnf(7724,plain,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[7723,theory(equality)]) ).
cnf(7784,plain,
( sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xm,sdtasdt0(xn,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[351,532,theory(equality)]) ).
cnf(7785,plain,
( sz00 = xn
| xm = X1
| sdtasdt0(xp,xk) != sdtasdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[101,532,theory(equality)]) ).
cnf(7985,plain,
( sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xm,sdtasdt0(xn,X1))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[7784,283,theory(equality)]) ).
cnf(7986,plain,
( sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xm,sdtasdt0(xn,X1))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[7985,282,theory(equality)]) ).
cnf(7987,plain,
( sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xm,sdtasdt0(xn,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[7986,theory(equality)]) ).
cnf(7988,plain,
( sz00 = xn
| xm = X1
| sdtasdt0(xp,xk) != sdtasdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[7785,282,theory(equality)]) ).
cnf(7989,plain,
( sz00 = xn
| xm = X1
| sdtasdt0(xp,xk) != sdtasdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[7988,283,theory(equality)]) ).
cnf(7990,plain,
( sz00 = xn
| xm = X1
| sdtasdt0(xp,xk) != sdtasdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[7989,theory(equality)]) ).
cnf(8557,plain,
( sdtlseqdt0(X1,xk)
| sdtlseqdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[7724,255,theory(equality)]) ).
cnf(8564,plain,
( sdtlseqdt0(X1,xk)
| sdtlseqdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[8557,85,theory(equality)]) ).
cnf(8565,plain,
( sdtlseqdt0(X1,xk)
| sdtlseqdt0(xr,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[8564,theory(equality)]) ).
cnf(9296,plain,
( sdtlseqdt0(X1,xk)
| sdtlseqdt0(xr,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[259,8565,theory(equality)]) ).
cnf(9324,plain,
( sdtlseqdt0(X1,xk)
| sdtlseqdt0(xr,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[9296,403,theory(equality)]) ).
cnf(9325,plain,
( sdtlseqdt0(X1,xk)
| sdtlseqdt0(xr,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[9324,theory(equality)]) ).
cnf(9428,plain,
( sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[756,273,theory(equality)]) ).
cnf(9438,plain,
( sdtlseqdt0(xm,xk)
| $false ),
inference(rw,[status(thm)],[9428,282,theory(equality)]) ).
cnf(9439,plain,
sdtlseqdt0(xm,xk),
inference(cn,[status(thm)],[9438,theory(equality)]) ).
cnf(9516,plain,
( sz00 = X1
| xk = xm
| sdtlseqdt0(sdtasdt0(X1,xm),sdtasdt0(X1,xk))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk) ),
inference(spm,[status(thm)],[303,9439,theory(equality)]) ).
cnf(9543,plain,
( sz00 = X1
| xk = xm
| sdtlseqdt0(sdtasdt0(X1,xm),sdtasdt0(X1,xk))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[9516,282,theory(equality)]) ).
cnf(9544,plain,
( sz00 = X1
| xk = xm
| sdtlseqdt0(sdtasdt0(X1,xm),sdtasdt0(X1,xk))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[9543,403,theory(equality)]) ).
cnf(9545,plain,
( sz00 = X1
| xk = xm
| sdtlseqdt0(sdtasdt0(X1,xm),sdtasdt0(X1,xk))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[9544,theory(equality)]) ).
cnf(9546,plain,
( sz00 = X1
| sdtlseqdt0(sdtasdt0(X1,xm),sdtasdt0(X1,xk))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[9545,445,theory(equality)]) ).
cnf(12370,plain,
( sz00 = xp
| sdtlseqdt0(esk1_0,sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(esk1_0) ),
inference(spm,[status(thm)],[622,433,theory(equality)]) ).
cnf(12398,plain,
( sz00 = xp
| sdtlseqdt0(esk1_0,sdtasdt0(xp,xk))
| $false
| ~ aNaturalNumber0(esk1_0) ),
inference(rw,[status(thm)],[12370,281,theory(equality)]) ).
cnf(12399,plain,
( sz00 = xp
| sdtlseqdt0(esk1_0,sdtasdt0(xp,xk))
| $false
| $false ),
inference(rw,[status(thm)],[12398,68,theory(equality)]) ).
cnf(12400,plain,
( sz00 = xp
| sdtlseqdt0(esk1_0,sdtasdt0(xp,xk)) ),
inference(cn,[status(thm)],[12399,theory(equality)]) ).
cnf(12401,plain,
sdtlseqdt0(esk1_0,sdtasdt0(xp,xk)),
inference(sr,[status(thm)],[12400,71,theory(equality)]) ).
cnf(13803,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[689,385]) ).
cnf(17098,plain,
( esk13_1(xp) = sz10
| esk13_1(xp) = xp
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[844,392,theory(equality)]) ).
cnf(17099,plain,
( esk13_1(xp) = sz10
| esk13_1(xp) = xp
| sz10 = xp
| sz00 = xp
| $false ),
inference(rw,[status(thm)],[17098,281,theory(equality)]) ).
cnf(17100,plain,
( esk13_1(xp) = sz10
| esk13_1(xp) = xp
| sz10 = xp
| sz00 = xp ),
inference(cn,[status(thm)],[17099,theory(equality)]) ).
cnf(17101,plain,
( esk13_1(xp) = sz10
| esk13_1(xp) = xp
| sz00 = xp ),
inference(sr,[status(thm)],[17100,70,theory(equality)]) ).
cnf(17102,plain,
( esk13_1(xp) = sz10
| esk13_1(xp) = xp ),
inference(sr,[status(thm)],[17101,71,theory(equality)]) ).
cnf(17105,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| esk13_1(xp) = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[390,17102,theory(equality)]) ).
cnf(17110,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| esk13_1(xp) = xp
| $false ),
inference(rw,[status(thm)],[17105,281,theory(equality)]) ).
cnf(17111,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| esk13_1(xp) = xp ),
inference(cn,[status(thm)],[17110,theory(equality)]) ).
cnf(17112,plain,
( sz00 = xp
| isPrime0(sz10)
| esk13_1(xp) = xp ),
inference(sr,[status(thm)],[17111,70,theory(equality)]) ).
cnf(17113,plain,
( isPrime0(sz10)
| esk13_1(xp) = xp ),
inference(sr,[status(thm)],[17112,71,theory(equality)]) ).
cnf(17114,plain,
esk13_1(xp) = xp,
inference(sr,[status(thm)],[17113,494,theory(equality)]) ).
cnf(17121,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[391,17114,theory(equality)]) ).
cnf(17130,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp)
| $false ),
inference(rw,[status(thm)],[17121,281,theory(equality)]) ).
cnf(17131,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp) ),
inference(cn,[status(thm)],[17130,theory(equality)]) ).
cnf(17132,plain,
( sz00 = xp
| doDivides0(xp,xp) ),
inference(sr,[status(thm)],[17131,70,theory(equality)]) ).
cnf(17133,plain,
doDivides0(xp,xp),
inference(sr,[status(thm)],[17132,71,theory(equality)]) ).
cnf(17134,plain,
( aNaturalNumber0(esk7_2(xp,xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[247,17133,theory(equality)]) ).
cnf(17136,plain,
( sdtasdt0(xp,esk7_2(xp,xp)) = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[246,17133,theory(equality)]) ).
cnf(17140,plain,
( aNaturalNumber0(esk7_2(xp,xp))
| $false ),
inference(rw,[status(thm)],[17134,281,theory(equality)]) ).
cnf(17141,plain,
aNaturalNumber0(esk7_2(xp,xp)),
inference(cn,[status(thm)],[17140,theory(equality)]) ).
cnf(17145,plain,
( sdtasdt0(xp,esk7_2(xp,xp)) = xp
| $false ),
inference(rw,[status(thm)],[17136,281,theory(equality)]) ).
cnf(17146,plain,
sdtasdt0(xp,esk7_2(xp,xp)) = xp,
inference(cn,[status(thm)],[17145,theory(equality)]) ).
cnf(18131,plain,
( esk13_1(xr) = sz10
| esk13_1(xr) = xr
| sz10 = xr
| sz00 = xr
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[848,392,theory(equality)]) ).
cnf(18132,plain,
( esk13_1(xr) = sz10
| esk13_1(xr) = xr
| sz10 = xr
| sz00 = xr
| $false ),
inference(rw,[status(thm)],[18131,85,theory(equality)]) ).
cnf(18133,plain,
( esk13_1(xr) = sz10
| esk13_1(xr) = xr
| sz10 = xr
| sz00 = xr ),
inference(cn,[status(thm)],[18132,theory(equality)]) ).
cnf(18134,plain,
( esk13_1(xr) = sz10
| esk13_1(xr) = xr
| xr = sz00 ),
inference(sr,[status(thm)],[18133,80,theory(equality)]) ).
cnf(18135,plain,
( esk13_1(xr) = sz10
| esk13_1(xr) = xr ),
inference(sr,[status(thm)],[18134,81,theory(equality)]) ).
cnf(18763,plain,
( sz10 = xr
| sz00 = xr
| doDivides0(xr,xr)
| esk13_1(xr) = sz10
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[391,18135,theory(equality)]) ).
cnf(18771,plain,
( sz10 = xr
| sz00 = xr
| doDivides0(xr,xr)
| esk13_1(xr) = sz10
| $false ),
inference(rw,[status(thm)],[18763,85,theory(equality)]) ).
cnf(18772,plain,
( sz10 = xr
| sz00 = xr
| doDivides0(xr,xr)
| esk13_1(xr) = sz10 ),
inference(cn,[status(thm)],[18771,theory(equality)]) ).
cnf(18773,plain,
( xr = sz00
| doDivides0(xr,xr)
| esk13_1(xr) = sz10 ),
inference(sr,[status(thm)],[18772,80,theory(equality)]) ).
cnf(18774,plain,
( doDivides0(xr,xr)
| esk13_1(xr) = sz10 ),
inference(sr,[status(thm)],[18773,81,theory(equality)]) ).
cnf(20557,plain,
( sz10 = xr
| sz00 = xr
| isPrime0(sz10)
| doDivides0(xr,xr)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[390,18774,theory(equality)]) ).
cnf(20563,plain,
( sz10 = xr
| sz00 = xr
| isPrime0(sz10)
| doDivides0(xr,xr)
| $false ),
inference(rw,[status(thm)],[20557,85,theory(equality)]) ).
cnf(20564,plain,
( sz10 = xr
| sz00 = xr
| isPrime0(sz10)
| doDivides0(xr,xr) ),
inference(cn,[status(thm)],[20563,theory(equality)]) ).
cnf(20565,plain,
( xr = sz00
| isPrime0(sz10)
| doDivides0(xr,xr) ),
inference(sr,[status(thm)],[20564,80,theory(equality)]) ).
cnf(20566,plain,
( isPrime0(sz10)
| doDivides0(xr,xr) ),
inference(sr,[status(thm)],[20565,81,theory(equality)]) ).
cnf(20567,plain,
doDivides0(xr,xr),
inference(sr,[status(thm)],[20566,494,theory(equality)]) ).
cnf(20590,plain,
( sz00 = xr
| sdtlseqdt0(xr,xr)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[270,20567,theory(equality)]) ).
cnf(20598,plain,
( sz00 = xr
| sdtlseqdt0(xr,xr)
| $false ),
inference(rw,[status(thm)],[20590,85,theory(equality)]) ).
cnf(20599,plain,
( sz00 = xr
| sdtlseqdt0(xr,xr) ),
inference(cn,[status(thm)],[20598,theory(equality)]) ).
cnf(20600,plain,
sdtlseqdt0(xr,xr),
inference(sr,[status(thm)],[20599,81,theory(equality)]) ).
cnf(20610,plain,
( aNaturalNumber0(esk10_2(xr,xr))
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[311,20600,theory(equality)]) ).
cnf(20612,plain,
( sdtpldt0(xr,esk10_2(xr,xr)) = xr
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[310,20600,theory(equality)]) ).
cnf(20617,plain,
( aNaturalNumber0(esk10_2(xr,xr))
| $false ),
inference(rw,[status(thm)],[20610,85,theory(equality)]) ).
cnf(20618,plain,
aNaturalNumber0(esk10_2(xr,xr)),
inference(cn,[status(thm)],[20617,theory(equality)]) ).
cnf(20621,plain,
( sdtpldt0(xr,esk10_2(xr,xr)) = xr
| $false ),
inference(rw,[status(thm)],[20612,85,theory(equality)]) ).
cnf(20622,plain,
sdtpldt0(xr,esk10_2(xr,xr)) = xr,
inference(cn,[status(thm)],[20621,theory(equality)]) ).
cnf(21598,plain,
( sz00 = esk10_2(xr,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(esk10_2(xr,xr)) ),
inference(spm,[status(thm)],[892,20622,theory(equality)]) ).
cnf(21643,plain,
( sz00 = esk10_2(xr,xr)
| $false
| ~ aNaturalNumber0(esk10_2(xr,xr)) ),
inference(rw,[status(thm)],[21598,85,theory(equality)]) ).
cnf(21644,plain,
( sz00 = esk10_2(xr,xr)
| $false
| $false ),
inference(rw,[status(thm)],[21643,20618,theory(equality)]) ).
cnf(21645,plain,
sz00 = esk10_2(xr,xr),
inference(cn,[status(thm)],[21644,theory(equality)]) ).
cnf(21651,plain,
sdtpldt0(xr,sz00) = xr,
inference(rw,[status(thm)],[20622,21645,theory(equality)]) ).
cnf(21662,plain,
( xr = sdtpldt0(sz00,xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[93,21651,theory(equality)]) ).
cnf(21683,plain,
( xr = sdtpldt0(sz00,xr)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[21662,382,theory(equality)]) ).
cnf(21684,plain,
( xr = sdtpldt0(sz00,xr)
| $false
| $false ),
inference(rw,[status(thm)],[21683,85,theory(equality)]) ).
cnf(21685,plain,
xr = sdtpldt0(sz00,xr),
inference(cn,[status(thm)],[21684,theory(equality)]) ).
cnf(21744,plain,
( sdtlseqdt0(sz00,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[13803,21685,theory(equality)]) ).
cnf(21782,plain,
( sdtlseqdt0(sz00,xr)
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[21744,85,theory(equality)]) ).
cnf(21783,plain,
( sdtlseqdt0(sz00,xr)
| $false
| $false ),
inference(rw,[status(thm)],[21782,382,theory(equality)]) ).
cnf(21784,plain,
sdtlseqdt0(sz00,xr),
inference(cn,[status(thm)],[21783,theory(equality)]) ).
cnf(21796,plain,
( xr = sz00
| ~ sdtlseqdt0(xr,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[318,21784,theory(equality)]) ).
cnf(21809,plain,
( xr = sz00
| ~ sdtlseqdt0(xr,sz00)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[21796,382,theory(equality)]) ).
cnf(21810,plain,
( xr = sz00
| ~ sdtlseqdt0(xr,sz00)
| $false
| $false ),
inference(rw,[status(thm)],[21809,85,theory(equality)]) ).
cnf(21811,plain,
( xr = sz00
| ~ sdtlseqdt0(xr,sz00) ),
inference(cn,[status(thm)],[21810,theory(equality)]) ).
cnf(21812,plain,
~ sdtlseqdt0(xr,sz00),
inference(sr,[status(thm)],[21811,81,theory(equality)]) ).
cnf(34603,plain,
( sdtasdt0(xr,esk2_0) = sdtasdt0(xk,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(esk2_0) ),
inference(spm,[status(thm)],[1074,432,theory(equality)]) ).
cnf(34805,plain,
( xk = sdtasdt0(xk,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(esk2_0) ),
inference(rw,[status(thm)],[34603,83,theory(equality)]) ).
cnf(34806,plain,
( xk = sdtasdt0(xk,sz10)
| $false
| ~ aNaturalNumber0(esk2_0) ),
inference(rw,[status(thm)],[34805,340,theory(equality)]) ).
cnf(34807,plain,
( xk = sdtasdt0(xk,sz10)
| $false
| $false ),
inference(rw,[status(thm)],[34806,84,theory(equality)]) ).
cnf(34808,plain,
xk = sdtasdt0(xk,sz10),
inference(cn,[status(thm)],[34807,theory(equality)]) ).
cnf(36350,plain,
( sdtasdt0(xn,sdtasdt0(xm,sz00)) = sz00
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[60,1077,theory(equality)]) ).
cnf(36555,plain,
( sdtasdt0(xn,sdtasdt0(xm,sz00)) = sz00
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[36350,456,theory(equality)]) ).
cnf(36556,plain,
( sdtasdt0(xn,sdtasdt0(xm,sz00)) = sz00
| $false
| $false ),
inference(rw,[status(thm)],[36555,382,theory(equality)]) ).
cnf(36557,plain,
sdtasdt0(xn,sdtasdt0(xm,sz00)) = sz00,
inference(cn,[status(thm)],[36556,theory(equality)]) ).
cnf(38858,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[1054,369]) ).
cnf(38865,plain,
( aNaturalNumber0(sdtasdt0(X1,xp))
| ~ aNaturalNumber0(esk7_2(xp,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[38858,17146,theory(equality)]) ).
cnf(38915,plain,
( aNaturalNumber0(sdtasdt0(X1,xp))
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[38865,17141,theory(equality)]) ).
cnf(38916,plain,
( aNaturalNumber0(sdtasdt0(X1,xp))
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[38915,281,theory(equality)]) ).
cnf(38917,plain,
( aNaturalNumber0(sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[38916,theory(equality)]) ).
cnf(38978,plain,
( aNaturalNumber0(sdtasdt0(xn,sdtasdt0(xm,xp)))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[38917,1077,theory(equality)]) ).
cnf(38995,plain,
( aNaturalNumber0(sdtasdt0(xn,sdtasdt0(xm,xp)))
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[38978,456,theory(equality)]) ).
cnf(38996,plain,
( aNaturalNumber0(sdtasdt0(xn,sdtasdt0(xm,xp)))
| $false
| $false ),
inference(rw,[status(thm)],[38995,281,theory(equality)]) ).
cnf(38997,plain,
aNaturalNumber0(sdtasdt0(xn,sdtasdt0(xm,xp))),
inference(cn,[status(thm)],[38996,theory(equality)]) ).
cnf(39049,plain,
( aNaturalNumber0(sdtasdt0(xn,sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[38997,406,theory(equality)]) ).
cnf(39051,plain,
( aNaturalNumber0(sdtasdt0(xn,sdtasdt0(xp,xm)))
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[39049,281,theory(equality)]) ).
cnf(39052,plain,
( aNaturalNumber0(sdtasdt0(xn,sdtasdt0(xp,xm)))
| $false
| $false ),
inference(rw,[status(thm)],[39051,282,theory(equality)]) ).
cnf(39053,plain,
aNaturalNumber0(sdtasdt0(xn,sdtasdt0(xp,xm))),
inference(cn,[status(thm)],[39052,theory(equality)]) ).
cnf(39093,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[1085,369]) ).
cnf(39304,plain,
( sz00 = sdtasdt0(xk,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(esk2_0)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[1074,39093,theory(equality)]) ).
cnf(39337,plain,
( sz00 = sdtasdt0(xk,sz00)
| $false
| ~ aNaturalNumber0(esk2_0)
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[39304,382,theory(equality)]) ).
cnf(39338,plain,
( sz00 = sdtasdt0(xk,sz00)
| $false
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[39337,84,theory(equality)]) ).
cnf(39339,plain,
( sz00 = sdtasdt0(xk,sz00)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[39338,85,theory(equality)]) ).
cnf(39340,plain,
sz00 = sdtasdt0(xk,sz00),
inference(cn,[status(thm)],[39339,theory(equality)]) ).
cnf(39429,plain,
( sz00 = sdtasdt0(sz00,xk)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xk) ),
inference(spm,[status(thm)],[406,39340,theory(equality)]) ).
cnf(39626,plain,
( sz00 = sdtasdt0(sz00,xk)
| $false
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[39429,382,theory(equality)]) ).
cnf(39627,plain,
( sz00 = sdtasdt0(sz00,xk)
| $false
| $false ),
inference(rw,[status(thm)],[39626,403,theory(equality)]) ).
cnf(39628,plain,
sz00 = sdtasdt0(sz00,xk),
inference(cn,[status(thm)],[39627,theory(equality)]) ).
cnf(41431,plain,
( sdtasdt0(sz00,xk) = sdtasdt0(sz00,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk) ),
inference(spm,[status(thm)],[1089,34808,theory(equality)]) ).
cnf(41631,plain,
( sz00 = sdtasdt0(sz00,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[41431,39628,theory(equality)]) ).
cnf(41632,plain,
( sz00 = sdtasdt0(sz00,sz10)
| $false
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[41631,340,theory(equality)]) ).
cnf(41633,plain,
( sz00 = sdtasdt0(sz00,sz10)
| $false
| $false ),
inference(rw,[status(thm)],[41632,403,theory(equality)]) ).
cnf(41634,plain,
sz00 = sdtasdt0(sz00,sz10),
inference(cn,[status(thm)],[41633,theory(equality)]) ).
cnf(44148,plain,
( sdtasdt0(sz10,xp) = xp
| ~ aNaturalNumber0(esk7_2(xp,xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[1095,17146,theory(equality)]) ).
cnf(44347,plain,
( sdtasdt0(sz10,xp) = xp
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[44148,17141,theory(equality)]) ).
cnf(44348,plain,
( sdtasdt0(sz10,xp) = xp
| $false
| $false ),
inference(rw,[status(thm)],[44347,281,theory(equality)]) ).
cnf(44349,plain,
sdtasdt0(sz10,xp) = xp,
inference(cn,[status(thm)],[44348,theory(equality)]) ).
cnf(44706,plain,
( xp = sdtasdt0(xp,sz10)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[406,44349,theory(equality)]) ).
cnf(44854,plain,
( xp = sdtasdt0(xp,sz10)
| $false
| ~ aNaturalNumber0(sz10) ),
inference(rw,[status(thm)],[44706,281,theory(equality)]) ).
cnf(44855,plain,
( xp = sdtasdt0(xp,sz10)
| $false
| $false ),
inference(rw,[status(thm)],[44854,340,theory(equality)]) ).
cnf(44856,plain,
xp = sdtasdt0(xp,sz10),
inference(cn,[status(thm)],[44855,theory(equality)]) ).
cnf(45576,plain,
( sdtasdt0(sz00,xp) = sdtasdt0(sz00,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[1089,44856,theory(equality)]) ).
cnf(46287,plain,
( sdtasdt0(sz00,xp) = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[45576,41634,theory(equality)]) ).
cnf(46288,plain,
( sdtasdt0(sz00,xp) = sz00
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[46287,340,theory(equality)]) ).
cnf(46289,plain,
( sdtasdt0(sz00,xp) = sz00
| $false
| $false ),
inference(rw,[status(thm)],[46288,281,theory(equality)]) ).
cnf(46290,plain,
sdtasdt0(sz00,xp) = sz00,
inference(cn,[status(thm)],[46289,theory(equality)]) ).
cnf(46304,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[1061,369]) ).
cnf(46337,plain,
( aNaturalNumber0(sdtasdt0(xm,sdtasdt0(xn,xp)))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[39053,46304,theory(equality)]) ).
cnf(46781,plain,
( sdtasdt0(X1,sdtasdt0(xr,esk2_0)) = sdtasdt0(xk,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk2_0)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[1074,46304,theory(equality)]) ).
cnf(46950,plain,
( aNaturalNumber0(sdtasdt0(xm,sdtasdt0(xn,xp)))
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[46337,282,theory(equality)]) ).
cnf(46951,plain,
( aNaturalNumber0(sdtasdt0(xm,sdtasdt0(xn,xp)))
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[46950,281,theory(equality)]) ).
cnf(46952,plain,
( aNaturalNumber0(sdtasdt0(xm,sdtasdt0(xn,xp)))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[46951,283,theory(equality)]) ).
cnf(46953,plain,
aNaturalNumber0(sdtasdt0(xm,sdtasdt0(xn,xp))),
inference(cn,[status(thm)],[46952,theory(equality)]) ).
cnf(47041,plain,
( sdtasdt0(X1,xk) = sdtasdt0(xk,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk2_0)
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[46781,83,theory(equality)]) ).
cnf(47042,plain,
( sdtasdt0(X1,xk) = sdtasdt0(xk,X1)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[47041,84,theory(equality)]) ).
cnf(47043,plain,
( sdtasdt0(X1,xk) = sdtasdt0(xk,X1)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[47042,85,theory(equality)]) ).
cnf(47044,plain,
( sdtasdt0(X1,xk) = sdtasdt0(xk,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[47043,theory(equality)]) ).
cnf(50275,plain,
( sz00 = X1
| sdtlseqdt0(sdtasdt0(X2,X3),sdtasdt0(X2,sdtasdt0(X3,X1)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[1065,369]) ).
cnf(50315,plain,
( sz00 = xp
| sdtlseqdt0(sdtasdt0(X1,sz10),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[50275,44349,theory(equality)]) ).
cnf(50514,plain,
( sz00 = xp
| sdtlseqdt0(sdtasdt0(X1,sz10),sdtasdt0(X1,xp))
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[50315,281,theory(equality)]) ).
cnf(50515,plain,
( sz00 = xp
| sdtlseqdt0(sdtasdt0(X1,sz10),sdtasdt0(X1,xp))
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[50514,340,theory(equality)]) ).
cnf(50516,plain,
( sz00 = xp
| sdtlseqdt0(sdtasdt0(X1,sz10),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[50515,theory(equality)]) ).
cnf(50517,plain,
( sdtlseqdt0(sdtasdt0(X1,sz10),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[50516,71,theory(equality)]) ).
cnf(60695,plain,
( sdtasdt0(xn,sz00) = sz00
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[36557,60,theory(equality)]) ).
cnf(60898,plain,
( sdtasdt0(xm,sdtasdt0(sz00,xn)) = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[46304,36557,theory(equality)]) ).
cnf(60917,plain,
( sdtasdt0(xn,sz00) = sz00
| $false ),
inference(rw,[status(thm)],[60695,282,theory(equality)]) ).
cnf(60918,plain,
sdtasdt0(xn,sz00) = sz00,
inference(cn,[status(thm)],[60917,theory(equality)]) ).
cnf(61532,plain,
( sdtasdt0(xm,sdtasdt0(sz00,xn)) = sz00
| $false
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[60898,283,theory(equality)]) ).
cnf(61533,plain,
( sdtasdt0(xm,sdtasdt0(sz00,xn)) = sz00
| $false
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[61532,382,theory(equality)]) ).
cnf(61534,plain,
( sdtasdt0(xm,sdtasdt0(sz00,xn)) = sz00
| $false
| $false
| $false ),
inference(rw,[status(thm)],[61533,282,theory(equality)]) ).
cnf(61535,plain,
sdtasdt0(xm,sdtasdt0(sz00,xn)) = sz00,
inference(cn,[status(thm)],[61534,theory(equality)]) ).
cnf(62413,plain,
( sz00 = sdtasdt0(sz00,xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[406,60918,theory(equality)]) ).
cnf(62620,plain,
( sz00 = sdtasdt0(sz00,xn)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[62413,382,theory(equality)]) ).
cnf(62621,plain,
( sz00 = sdtasdt0(sz00,xn)
| $false
| $false ),
inference(rw,[status(thm)],[62620,283,theory(equality)]) ).
cnf(62622,plain,
sz00 = sdtasdt0(sz00,xn),
inference(cn,[status(thm)],[62621,theory(equality)]) ).
cnf(63839,plain,
( esk1_0 = sz00
| xp = sz10
| sdtasdt0(xp,xk) != esk1_0
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(esk1_0) ),
inference(spm,[status(thm)],[1173,431,theory(equality)]) ).
cnf(63852,plain,
( esk1_0 = sz00
| xp = sz10
| sdtasdt0(xp,xk) != esk1_0
| $false
| ~ aNaturalNumber0(esk1_0) ),
inference(rw,[status(thm)],[63839,340,theory(equality)]) ).
cnf(63853,plain,
( esk1_0 = sz00
| xp = sz10
| sdtasdt0(xp,xk) != esk1_0
| $false
| $false ),
inference(rw,[status(thm)],[63852,68,theory(equality)]) ).
cnf(63854,plain,
( esk1_0 = sz00
| xp = sz10
| sdtasdt0(xp,xk) != esk1_0 ),
inference(cn,[status(thm)],[63853,theory(equality)]) ).
cnf(63855,plain,
( esk1_0 = sz00
| sdtasdt0(xp,xk) != esk1_0 ),
inference(sr,[status(thm)],[63854,70,theory(equality)]) ).
cnf(69637,plain,
sdtasdt0(xm,sz00) = sz00,
inference(rw,[status(thm)],[61535,62622,theory(equality)]) ).
cnf(73900,plain,
( esk1_0 = xk
| ~ aNaturalNumber0(xk) ),
inference(er,[status(thm)],[1235,theory(equality)]) ).
cnf(73911,plain,
( esk1_0 = xk
| $false ),
inference(rw,[status(thm)],[73900,403,theory(equality)]) ).
cnf(73912,plain,
esk1_0 = xk,
inference(cn,[status(thm)],[73911,theory(equality)]) ).
cnf(73948,plain,
sdtlseqdt0(xk,sdtasdt0(xp,xk)),
inference(rw,[status(thm)],[12401,73912,theory(equality)]) ).
cnf(73953,plain,
( xk = sz00
| sdtasdt0(xp,xk) != esk1_0 ),
inference(rw,[status(thm)],[63855,73912,theory(equality)]) ).
cnf(73954,plain,
( xk = sz00
| sdtasdt0(xp,xk) != xk ),
inference(rw,[status(thm)],[73953,73912,theory(equality)]) ).
cnf(73955,plain,
sdtasdt0(xp,xk) != xk,
inference(sr,[status(thm)],[73954,55,theory(equality)]) ).
cnf(74009,plain,
( sdtasdt0(xp,xk) = xk
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(spm,[status(thm)],[318,73948,theory(equality)]) ).
cnf(74010,plain,
( aNaturalNumber0(esk10_2(xk,sdtasdt0(xp,xk)))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(spm,[status(thm)],[311,73948,theory(equality)]) ).
cnf(74013,plain,
( sdtpldt0(xk,esk10_2(xk,sdtasdt0(xp,xk))) = sdtasdt0(xp,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(spm,[status(thm)],[310,73948,theory(equality)]) ).
cnf(74030,plain,
( sdtasdt0(xp,xk) = xk
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xk)
| $false
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(rw,[status(thm)],[74009,403,theory(equality)]) ).
cnf(74031,plain,
( sdtasdt0(xp,xk) = xk
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xk)
| $false
| $false ),
inference(rw,[status(thm)],[74030,456,theory(equality)]) ).
cnf(74032,plain,
( sdtasdt0(xp,xk) = xk
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xk) ),
inference(cn,[status(thm)],[74031,theory(equality)]) ).
cnf(74033,plain,
~ sdtlseqdt0(sdtasdt0(xp,xk),xk),
inference(sr,[status(thm)],[74032,73955,theory(equality)]) ).
cnf(74034,plain,
( aNaturalNumber0(esk10_2(xk,sdtasdt0(xp,xk)))
| $false
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(rw,[status(thm)],[74010,403,theory(equality)]) ).
cnf(74035,plain,
( aNaturalNumber0(esk10_2(xk,sdtasdt0(xp,xk)))
| $false
| $false ),
inference(rw,[status(thm)],[74034,456,theory(equality)]) ).
cnf(74036,plain,
aNaturalNumber0(esk10_2(xk,sdtasdt0(xp,xk))),
inference(cn,[status(thm)],[74035,theory(equality)]) ).
cnf(74044,plain,
( sdtpldt0(xk,esk10_2(xk,sdtasdt0(xp,xk))) = sdtasdt0(xp,xk)
| $false
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(rw,[status(thm)],[74013,403,theory(equality)]) ).
cnf(74045,plain,
( sdtpldt0(xk,esk10_2(xk,sdtasdt0(xp,xk))) = sdtasdt0(xp,xk)
| $false
| $false ),
inference(rw,[status(thm)],[74044,456,theory(equality)]) ).
cnf(74046,plain,
sdtpldt0(xk,esk10_2(xk,sdtasdt0(xp,xk))) = sdtasdt0(xp,xk),
inference(cn,[status(thm)],[74045,theory(equality)]) ).
cnf(94871,plain,
( sdtasdt0(sz10,xp) = sdtpldt0(sdtasdt0(sz10,xn),esk8_0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(esk8_0) ),
inference(spm,[status(thm)],[1394,278,theory(equality)]) ).
cnf(95116,plain,
( xp = sdtpldt0(sdtasdt0(sz10,xn),esk8_0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(esk8_0) ),
inference(rw,[status(thm)],[94871,44349,theory(equality)]) ).
cnf(95117,plain,
( xp = sdtpldt0(sdtasdt0(sz10,xn),esk8_0)
| $false
| ~ aNaturalNumber0(esk8_0) ),
inference(rw,[status(thm)],[95116,283,theory(equality)]) ).
cnf(95118,plain,
( xp = sdtpldt0(sdtasdt0(sz10,xn),esk8_0)
| $false
| $false ),
inference(rw,[status(thm)],[95117,279,theory(equality)]) ).
cnf(95119,plain,
xp = sdtpldt0(sdtasdt0(sz10,xn),esk8_0),
inference(cn,[status(thm)],[95118,theory(equality)]) ).
cnf(95678,plain,
( xn = sdtasdt0(sz10,xn)
| ~ aNaturalNumber0(sdtasdt0(sz10,xn)) ),
inference(spm,[status(thm)],[924,95119,theory(equality)]) ).
cnf(95801,plain,
( sdtasdt0(sz10,xn) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[95678,369,theory(equality)]) ).
cnf(95802,plain,
( sdtasdt0(sz10,xn) = xn
| $false
| ~ aNaturalNumber0(sz10) ),
inference(rw,[status(thm)],[95801,283,theory(equality)]) ).
cnf(95803,plain,
( sdtasdt0(sz10,xn) = xn
| $false
| $false ),
inference(rw,[status(thm)],[95802,340,theory(equality)]) ).
cnf(95804,plain,
sdtasdt0(sz10,xn) = xn,
inference(cn,[status(thm)],[95803,theory(equality)]) ).
cnf(95946,plain,
( aNaturalNumber0(sdtasdt0(X1,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[38858,95804,theory(equality)]) ).
cnf(96399,plain,
( aNaturalNumber0(sdtasdt0(X1,xn))
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[95946,283,theory(equality)]) ).
cnf(96400,plain,
( aNaturalNumber0(sdtasdt0(X1,xn))
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[96399,340,theory(equality)]) ).
cnf(96401,plain,
( aNaturalNumber0(sdtasdt0(X1,xn))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[96400,theory(equality)]) ).
cnf(121800,plain,
( sdtasdt0(sdtasdt0(xp,xk),sz10) = sdtpldt0(sdtasdt0(xk,sz10),esk10_2(xk,sdtasdt0(xp,xk)))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(esk10_2(xk,sdtasdt0(xp,xk))) ),
inference(spm,[status(thm)],[1464,74046,theory(equality)]) ).
cnf(122250,plain,
( sdtasdt0(sdtasdt0(xp,xk),sz10) = sdtasdt0(xp,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(esk10_2(xk,sdtasdt0(xp,xk))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[121800,34808,theory(equality)]),74046,theory(equality)]) ).
cnf(122251,plain,
( sdtasdt0(sdtasdt0(xp,xk),sz10) = sdtasdt0(xp,xk)
| $false
| ~ aNaturalNumber0(esk10_2(xk,sdtasdt0(xp,xk))) ),
inference(rw,[status(thm)],[122250,403,theory(equality)]) ).
cnf(122252,plain,
( sdtasdt0(sdtasdt0(xp,xk),sz10) = sdtasdt0(xp,xk)
| $false
| $false ),
inference(rw,[status(thm)],[122251,74036,theory(equality)]) ).
cnf(122253,plain,
sdtasdt0(sdtasdt0(xp,xk),sz10) = sdtasdt0(xp,xk),
inference(cn,[status(thm)],[122252,theory(equality)]) ).
cnf(131407,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xk,sdtasdt0(xp,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(spm,[status(thm)],[1063,122253,theory(equality)]) ).
cnf(132133,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xk,xp)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[131407,44856,theory(equality)]) ).
cnf(132134,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xk,xp)
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[132133,340,theory(equality)]) ).
cnf(132135,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xk,xp)
| $false
| $false
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[132134,281,theory(equality)]) ).
cnf(132136,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xk,xp)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[132135,403,theory(equality)]) ).
cnf(132137,plain,
sdtasdt0(xp,xk) = sdtasdt0(xk,xp),
inference(cn,[status(thm)],[132136,theory(equality)]) ).
cnf(154117,plain,
( sz00 = xk
| sdtlseqdt0(sdtasdt0(xk,xn),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xk) ),
inference(spm,[status(thm)],[1533,132137,theory(equality)]) ).
cnf(154167,plain,
( sz00 = xk
| sdtlseqdt0(sdtasdt0(xk,xn),sdtasdt0(xp,xk))
| $false ),
inference(rw,[status(thm)],[154117,403,theory(equality)]) ).
cnf(154168,plain,
( sz00 = xk
| sdtlseqdt0(sdtasdt0(xk,xn),sdtasdt0(xp,xk)) ),
inference(cn,[status(thm)],[154167,theory(equality)]) ).
cnf(154169,plain,
sdtlseqdt0(sdtasdt0(xk,xn),sdtasdt0(xp,xk)),
inference(sr,[status(thm)],[154168,55,theory(equality)]) ).
cnf(155876,plain,
( sdtlseqdt0(sdtasdt0(xn,xk),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xk) ),
inference(spm,[status(thm)],[154169,406,theory(equality)]) ).
cnf(155891,plain,
( sdtlseqdt0(sdtasdt0(xn,xk),sdtasdt0(xp,xk))
| $false
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[155876,283,theory(equality)]) ).
cnf(155892,plain,
( sdtlseqdt0(sdtasdt0(xn,xk),sdtasdt0(xp,xk))
| $false
| $false ),
inference(rw,[status(thm)],[155891,403,theory(equality)]) ).
cnf(155893,plain,
sdtlseqdt0(sdtasdt0(xn,xk),sdtasdt0(xp,xk)),
inference(cn,[status(thm)],[155892,theory(equality)]) ).
cnf(1181810,plain,
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(sdtasdt0(xp,xk),xp))
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(spm,[status(thm)],[50517,122253,theory(equality)]) ).
cnf(1181895,plain,
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(sdtasdt0(xp,xk),xp))
| $false ),
inference(rw,[status(thm)],[1181810,456,theory(equality)]) ).
cnf(1181896,plain,
sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(sdtasdt0(xp,xk),xp)),
inference(cn,[status(thm)],[1181895,theory(equality)]) ).
cnf(1220955,plain,
( aNaturalNumber0(sdtasdt0(xn,xk))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[96401,47044,theory(equality)]) ).
cnf(1224722,plain,
( aNaturalNumber0(sdtasdt0(xn,xk))
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[1220955,403,theory(equality)]) ).
cnf(1224723,plain,
( aNaturalNumber0(sdtasdt0(xn,xk))
| $false
| $false ),
inference(rw,[status(thm)],[1224722,283,theory(equality)]) ).
cnf(1224724,plain,
aNaturalNumber0(sdtasdt0(xn,xk)),
inference(cn,[status(thm)],[1224723,theory(equality)]) ).
cnf(1651558,plain,
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xm,sdtasdt0(xn,xp)))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[1181896,7987,theory(equality)]) ).
cnf(1653367,plain,
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xm,sdtasdt0(xn,xp)))
| $false ),
inference(rw,[status(thm)],[1651558,281,theory(equality)]) ).
cnf(1653368,plain,
sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xm,sdtasdt0(xn,xp))),
inference(cn,[status(thm)],[1653367,theory(equality)]) ).
cnf(1657821,plain,
( xn = sz00
| xm = xk
| sdtasdt0(xp,xk) != sdtasdt0(xn,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[7990,47044,theory(equality)]) ).
cnf(1657867,plain,
( xn = sz00
| xm = xk
| sdtasdt0(xp,xk) != sdtasdt0(xn,xk)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[1657821,403,theory(equality)]) ).
cnf(1657868,plain,
( xn = sz00
| xm = xk
| sdtasdt0(xp,xk) != sdtasdt0(xn,xk)
| $false
| $false ),
inference(rw,[status(thm)],[1657867,283,theory(equality)]) ).
cnf(1657869,plain,
( xn = sz00
| xm = xk
| sdtasdt0(xp,xk) != sdtasdt0(xn,xk) ),
inference(cn,[status(thm)],[1657868,theory(equality)]) ).
cnf(1657870,plain,
( xn = sz00
| sdtasdt0(xn,xk) != sdtasdt0(xp,xk) ),
inference(sr,[status(thm)],[1657869,445,theory(equality)]) ).
cnf(1979072,plain,
( sdtlseqdt0(xr,sdtasdt0(xm,sdtasdt0(xn,xp)))
| sdtlseqdt0(sdtasdt0(xp,xk),xk)
| ~ aNaturalNumber0(sdtasdt0(xm,sdtasdt0(xn,xp)))
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(spm,[status(thm)],[9325,1653368,theory(equality)]) ).
cnf(1983247,plain,
( sdtlseqdt0(xr,sdtasdt0(xm,sdtasdt0(xn,xp)))
| sdtlseqdt0(sdtasdt0(xp,xk),xk)
| $false
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(rw,[status(thm)],[1979072,46953,theory(equality)]) ).
cnf(1983248,plain,
( sdtlseqdt0(xr,sdtasdt0(xm,sdtasdt0(xn,xp)))
| sdtlseqdt0(sdtasdt0(xp,xk),xk)
| $false
| $false ),
inference(rw,[status(thm)],[1983247,456,theory(equality)]) ).
cnf(1983249,plain,
( sdtlseqdt0(xr,sdtasdt0(xm,sdtasdt0(xn,xp)))
| sdtlseqdt0(sdtasdt0(xp,xk),xk) ),
inference(cn,[status(thm)],[1983248,theory(equality)]) ).
cnf(1983250,plain,
sdtlseqdt0(xr,sdtasdt0(xm,sdtasdt0(xn,xp))),
inference(sr,[status(thm)],[1983249,74033,theory(equality)]) ).
cnf(2030039,plain,
( sz00 = xn
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xn,xk))
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[9546,402,theory(equality)]) ).
cnf(2030100,plain,
( sz00 = xn
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xn,xk))
| $false ),
inference(rw,[status(thm)],[2030039,283,theory(equality)]) ).
cnf(2030101,plain,
( sz00 = xn
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xn,xk)) ),
inference(cn,[status(thm)],[2030100,theory(equality)]) ).
cnf(2154194,plain,
( sdtasdt0(xn,xk) = sdtasdt0(xp,xk)
| xn = sz00
| ~ sdtlseqdt0(sdtasdt0(xn,xk),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xn,xk)) ),
inference(spm,[status(thm)],[318,2030101,theory(equality)]) ).
cnf(2154211,plain,
( sdtasdt0(xn,xk) = sdtasdt0(xp,xk)
| xn = sz00
| $false
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xn,xk)) ),
inference(rw,[status(thm)],[2154194,155893,theory(equality)]) ).
cnf(2154212,plain,
( sdtasdt0(xn,xk) = sdtasdt0(xp,xk)
| xn = sz00
| $false
| $false
| ~ aNaturalNumber0(sdtasdt0(xn,xk)) ),
inference(rw,[status(thm)],[2154211,456,theory(equality)]) ).
cnf(2154213,plain,
( sdtasdt0(xn,xk) = sdtasdt0(xp,xk)
| xn = sz00
| $false
| $false
| $false ),
inference(rw,[status(thm)],[2154212,1224724,theory(equality)]) ).
cnf(2154214,plain,
( sdtasdt0(xn,xk) = sdtasdt0(xp,xk)
| xn = sz00 ),
inference(cn,[status(thm)],[2154213,theory(equality)]) ).
cnf(2154262,plain,
xn = sz00,
inference(csr,[status(thm)],[2154214,1657870]) ).
cnf(2154413,plain,
sdtlseqdt0(xr,sz00),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1983250,2154262,theory(equality)]),46290,theory(equality)]),69637,theory(equality)]) ).
cnf(2154414,plain,
$false,
inference(sr,[status(thm)],[2154413,21812,theory(equality)]) ).
cnf(2154415,plain,
$false,
2154414,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM503+3 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04 % Command : Source/sine.py -e eprover -t %d %s
% 0.03/0.22 % Computer : n100.star.cs.uiowa.edu
% 0.03/0.22 % Model : x86_64 x86_64
% 0.03/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.22 % Memory : 32218.625MB
% 0.03/0.22 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.22 % CPULimit : 300
% 0.03/0.22 % DateTime : Fri Jan 5 06:09:00 CST 2018
% 0.03/0.22 % CPUTime :
% 0.03/0.27 % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.27 --creating new selector for []
% 29.07/29.40 eprover: CPU time limit exceeded, terminating
% 93.93/95.22 -running prover on /export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_1 with time limit 29
% 93.93/95.22 -running prover with command ['/export/starexec/sandbox/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_1']
% 93.93/95.22 -prover status ResourceOut
% 93.93/95.22 -running prover on /export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2 with time limit 81
% 93.93/95.22 -running prover with command ['/export/starexec/sandbox/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=81', '/export/starexec/sandbox/tmp/tmph2sHVp/sel_theBenchmark.p_2']
% 93.93/95.22 -prover status Theorem
% 93.93/95.22 Problem theBenchmark.p solved in phase 1.
% 93.93/95.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 93.93/95.22 % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 93.93/95.22 Solved 1 out of 1.
% 93.93/95.22 # Problem is unsatisfiable (or provable), constructing proof object
% 93.93/95.22 # SZS status Theorem
% 93.93/95.22 # SZS output start CNFRefutation.
% See solution above
% 93.93/95.25 # SZS output end CNFRefutation
%------------------------------------------------------------------------------