TSTP Solution File: NUM494+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM494+3 : TPTP v7.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n098.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 15:21:32 EST 2018
% Result : Theorem 25.15s
% Output : CNFRefutation 25.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 121
% Number of leaves : 30
% Syntax : Number of formulae : 476 ( 66 unt; 0 def)
% Number of atoms : 1887 ( 338 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 2312 ( 901 ~;1160 |; 211 &)
% ( 4 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 485 ( 0 sgn 216 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,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/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',m__1860) ).
fof(3,axiom,
( aNaturalNumber0(xr)
& equal(sdtpldt0(xp,xr),xn)
& equal(xr,sdtmndt0(xn,xp)) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',m__1883) ).
fof(5,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mAddComm) ).
fof(6,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( equal(sdtasdt0(X1,X2),sz00)
=> ( equal(X1,sz00)
| equal(X2,sz00) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mZeroMul) ).
fof(7,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( ~ equal(X1,sz00)
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( equal(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| equal(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) )
=> equal(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mMulCanc) ).
fof(9,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( equal(sdtasdt0(X1,sdtpldt0(X2,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
& equal(sdtasdt0(sdtpldt0(X2,X3),X1),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mAMDistr) ).
fof(10,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(X2,sdtasdt0(X1,X3)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mDefDiv) ).
fof(13,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mLETran) ).
fof(14,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,sdtpldt0(X2,X3)) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mDivMin) ).
fof(15,axiom,
( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(xp,X1),xn) )
& sdtlseqdt0(xp,xn) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',m__1870) ).
fof(16,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& ~ equal(X2,sz00) )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mDivLE) ).
fof(17,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',m__1837) ).
fof(19,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( ~ equal(X1,X2)
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( ~ equal(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& ~ equal(sdtpldt0(X1,X3),sdtpldt0(X2,X3))
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mMonAdd) ).
fof(23,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mDefLE) ).
fof(24,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> equal(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(X1,sdtpldt0(X2,X3))) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mAddAsso) ).
fof(27,axiom,
( ~ equal(xr,xn)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(xr,X1),xn) )
& sdtlseqdt0(xr,xn) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',m__1894) ).
fof(28,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(X1,sz00)
| equal(X1,sz10)
| ( ~ equal(sz10,X1)
& sdtlseqdt0(sz10,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mLENTr) ).
fof(29,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ~ equal(X1,sz00)
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mMonMul2) ).
fof(30,axiom,
( aNaturalNumber0(sz10)
& ~ equal(sz10,sz00) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mSortsC_01) ).
fof(31,conjecture,
( ~ equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X1),sdtpldt0(sdtpldt0(xn,xm),xp)) )
| sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',m__) ).
fof(35,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( equal(X3,sdtmndt0(X2,X1))
<=> ( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mDefDiff) ).
fof(36,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mSortsB_02) ).
fof(37,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/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mDefPrime) ).
fof(38,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mSortsC) ).
fof(39,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mSortsB) ).
fof(40,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& ~ equal(X1,sz00)
& ~ equal(X1,sz10) )
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mPrimDiv) ).
fof(41,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/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mAddCanc) ).
fof(43,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',mMulComm) ).
fof(45,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtpldt0(X1,sz00),X1)
& equal(X1,sdtpldt0(sz00,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',m_AddZero) ).
fof(46,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1',m_MulUnit) ).
fof(47,negated_conjecture,
~ ( ~ equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X1),sdtpldt0(sdtpldt0(xn,xm),xp)) )
| sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(assume_negation,[status(cth)],[31]) ).
fof(53,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)],[2]) ).
fof(54,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)],[53]) ).
fof(55,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)],[54]) ).
fof(56,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)],[55]) ).
fof(57,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)],[56]) ).
cnf(62,plain,
xp != sz10,
inference(split_conjunct,[status(thm)],[57]) ).
cnf(63,plain,
xp != sz00,
inference(split_conjunct,[status(thm)],[57]) ).
cnf(64,plain,
( X1 = xp
| X1 = sz10
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xp) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(67,plain,
sdtpldt0(xp,xr) = xn,
inference(split_conjunct,[status(thm)],[3]) ).
cnf(68,plain,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[3]) ).
fof(72,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(73,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(sdtpldt0(X3,X4),sdtpldt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[72]) ).
cnf(74,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[73]) ).
fof(75,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ equal(sdtasdt0(X1,X2),sz00)
| equal(X1,sz00)
| equal(X2,sz00) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(76,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ equal(sdtasdt0(X3,X4),sz00)
| equal(X3,sz00)
| equal(X4,sz00) ),
inference(variable_rename,[status(thm)],[75]) ).
cnf(77,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[76]) ).
fof(78,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)],[7]) ).
fof(79,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)],[78]) ).
fof(80,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)],[79]) ).
fof(81,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)],[80]) ).
cnf(83,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,X3) != sdtasdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[81]) ).
fof(215,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)],[9]) ).
fof(216,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)],[215]) ).
fof(217,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)],[216]) ).
cnf(219,plain,
( sdtasdt0(X3,sdtpldt0(X2,X1)) = sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[217]) ).
fof(220,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)],[10]) ).
fof(221,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)],[220]) ).
fof(222,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk6_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk6_2(X4,X5))) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7)) )
| doDivides0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[221]) ).
fof(223,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5) )
& ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk6_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk6_2(X4,X5))) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[222]) ).
fof(224,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk6_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(X5,sdtasdt0(X4,esk6_2(X4,X5)))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[223]) ).
cnf(225,plain,
( X1 = sdtasdt0(X2,esk6_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[224]) ).
cnf(226,plain,
( aNaturalNumber0(esk6_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[224]) ).
cnf(227,plain,
( doDivides0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[224]) ).
fof(236,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3)
| sdtlseqdt0(X1,X3) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(237,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ sdtlseqdt0(X4,X5)
| ~ sdtlseqdt0(X5,X6)
| sdtlseqdt0(X4,X6) ),
inference(variable_rename,[status(thm)],[236]) ).
cnf(238,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[237]) ).
fof(239,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X2,X3))
| doDivides0(X1,X3) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(240,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ doDivides0(X4,X5)
| ~ doDivides0(X4,sdtpldt0(X5,X6))
| doDivides0(X4,X6) ),
inference(variable_rename,[status(thm)],[239]) ).
cnf(241,plain,
( doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X3,X2))
| ~ doDivides0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[240]) ).
fof(242,plain,
( ? [X2] :
( aNaturalNumber0(X2)
& equal(sdtpldt0(xp,X2),xn) )
& sdtlseqdt0(xp,xn) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(243,plain,
( aNaturalNumber0(esk7_0)
& equal(sdtpldt0(xp,esk7_0),xn)
& sdtlseqdt0(xp,xn) ),
inference(skolemize,[status(esa)],[242]) ).
cnf(244,plain,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[243]) ).
fof(247,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2)
| equal(X2,sz00)
| sdtlseqdt0(X1,X2) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(248,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ doDivides0(X3,X4)
| equal(X4,sz00)
| sdtlseqdt0(X3,X4) ),
inference(variable_rename,[status(thm)],[247]) ).
cnf(249,plain,
( sdtlseqdt0(X1,X2)
| X2 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[248]) ).
cnf(250,plain,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(251,plain,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(252,plain,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[17]) ).
fof(258,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(X1,X2)
| ~ sdtlseqdt0(X1,X2)
| ! [X3] :
( ~ aNaturalNumber0(X3)
| ( ~ equal(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& ~ equal(sdtpldt0(X1,X3),sdtpldt0(X2,X3))
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(259,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ! [X6] :
( ~ aNaturalNumber0(X6)
| ( ~ equal(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
& sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
& ~ equal(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
& sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6)) ) ) ),
inference(variable_rename,[status(thm)],[258]) ).
fof(260,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X6)
| ( ~ equal(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
& sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
& ~ equal(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
& sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6)) )
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[259]) ).
fof(261,plain,
! [X4,X5,X6] :
( ( ~ equal(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
| ~ aNaturalNumber0(X6)
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
| ~ aNaturalNumber0(X6)
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ equal(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[260]) ).
cnf(262,plain,
( X2 = X1
| sdtlseqdt0(sdtpldt0(X2,X3),sdtpldt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[261]) ).
fof(279,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)],[23]) ).
fof(280,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)],[279]) ).
fof(281,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk9_2(X4,X5))
& equal(sdtpldt0(X4,esk9_2(X4,X5)),X5) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5) )
| sdtlseqdt0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[280]) ).
fof(282,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5) )
& ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk9_2(X4,X5))
& equal(sdtpldt0(X4,esk9_2(X4,X5)),X5) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[281]) ).
fof(283,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk9_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(sdtpldt0(X4,esk9_2(X4,X5)),X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[282]) ).
cnf(284,plain,
( sdtpldt0(X2,esk9_2(X2,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[283]) ).
cnf(285,plain,
( aNaturalNumber0(esk9_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[283]) ).
cnf(286,plain,
( sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[283]) ).
fof(287,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| equal(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(X1,sdtpldt0(X2,X3))) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(288,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| equal(sdtpldt0(sdtpldt0(X4,X5),X6),sdtpldt0(X4,sdtpldt0(X5,X6))) ),
inference(variable_rename,[status(thm)],[287]) ).
cnf(289,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[288]) ).
fof(300,plain,
( ~ equal(xr,xn)
& ? [X2] :
( aNaturalNumber0(X2)
& equal(sdtpldt0(xr,X2),xn) )
& sdtlseqdt0(xr,xn) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(301,plain,
( ~ equal(xr,xn)
& aNaturalNumber0(esk10_0)
& equal(sdtpldt0(xr,esk10_0),xn)
& sdtlseqdt0(xr,xn) ),
inference(skolemize,[status(esa)],[300]) ).
cnf(302,plain,
sdtlseqdt0(xr,xn),
inference(split_conjunct,[status(thm)],[301]) ).
cnf(303,plain,
sdtpldt0(xr,esk10_0) = xn,
inference(split_conjunct,[status(thm)],[301]) ).
cnf(304,plain,
aNaturalNumber0(esk10_0),
inference(split_conjunct,[status(thm)],[301]) ).
cnf(305,plain,
xr != xn,
inference(split_conjunct,[status(thm)],[301]) ).
fof(306,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| equal(X1,sz00)
| equal(X1,sz10)
| ( ~ equal(sz10,X1)
& sdtlseqdt0(sz10,X1) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(307,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| equal(X2,sz00)
| equal(X2,sz10)
| ( ~ equal(sz10,X2)
& sdtlseqdt0(sz10,X2) ) ),
inference(variable_rename,[status(thm)],[306]) ).
fof(308,plain,
! [X2] :
( ( ~ equal(sz10,X2)
| equal(X2,sz00)
| equal(X2,sz10)
| ~ aNaturalNumber0(X2) )
& ( sdtlseqdt0(sz10,X2)
| equal(X2,sz00)
| equal(X2,sz10)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[307]) ).
cnf(309,plain,
( X1 = sz10
| X1 = sz00
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[308]) ).
fof(311,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(X1,sz00)
| sdtlseqdt0(X2,sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(312,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(X3,sz00)
| sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[311]) ).
cnf(313,plain,
( sdtlseqdt0(X1,sdtasdt0(X1,X2))
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[312]) ).
cnf(314,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[30]) ).
cnf(315,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[30]) ).
fof(316,negated_conjecture,
( equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| ~ equal(sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X1),sdtpldt0(sdtpldt0(xn,xm),xp)) )
& ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(317,negated_conjecture,
( equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ equal(sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X2),sdtpldt0(sdtpldt0(xn,xm),xp)) )
& ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(variable_rename,[status(thm)],[316]) ).
fof(318,negated_conjecture,
! [X2] :
( ( ( ~ aNaturalNumber0(X2)
| ~ equal(sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X2),sdtpldt0(sdtpldt0(xn,xm),xp)) )
& ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) )
| equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(shift_quantors,[status(thm)],[317]) ).
fof(319,negated_conjecture,
! [X2] :
( ( ~ aNaturalNumber0(X2)
| ~ equal(sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) )
& ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(distribute,[status(thm)],[318]) ).
cnf(320,negated_conjecture,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(split_conjunct,[status(thm)],[319]) ).
fof(333,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ! [X3] :
( ( ~ equal(X3,sdtmndt0(X2,X1))
| ( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) )
& ( ~ aNaturalNumber0(X3)
| ~ equal(sdtpldt0(X1,X3),X2)
| equal(X3,sdtmndt0(X2,X1)) ) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(334,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ sdtlseqdt0(X4,X5)
| ! [X6] :
( ( ~ equal(X6,sdtmndt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(sdtpldt0(X4,X6),X5) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4)) ) ) ),
inference(variable_rename,[status(thm)],[333]) ).
fof(335,plain,
! [X4,X5,X6] :
( ( ( ~ equal(X6,sdtmndt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(sdtpldt0(X4,X6),X5) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4)) ) )
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[334]) ).
fof(336,plain,
! [X4,X5,X6] :
( ( aNaturalNumber0(X6)
| ~ equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(sdtpldt0(X4,X6),X5)
| ~ equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[335]) ).
cnf(337,plain,
( X3 = sdtmndt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[336]) ).
cnf(339,plain,
( aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| X3 != sdtmndt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[336]) ).
fof(340,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(341,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[340]) ).
cnf(342,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[341]) ).
fof(343,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)],[37]) ).
fof(344,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)],[343]) ).
fof(345,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(esk11_1(X3))
& doDivides0(esk11_1(X3),X3)
& ~ equal(esk11_1(X3),sz10)
& ~ equal(esk11_1(X3),X3) )
| isPrime0(X3) ) ) ),
inference(skolemize,[status(esa)],[344]) ).
fof(346,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(esk11_1(X3))
& doDivides0(esk11_1(X3),X3)
& ~ equal(esk11_1(X3),sz10)
& ~ equal(esk11_1(X3),X3) )
| isPrime0(X3) ) )
| ~ aNaturalNumber0(X3) ),
inference(shift_quantors,[status(thm)],[345]) ).
fof(347,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(esk11_1(X3))
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( doDivides0(esk11_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk11_1(X3),sz10)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk11_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) ) ),
inference(distribute,[status(thm)],[346]) ).
cnf(352,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[347]) ).
cnf(355,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[38]) ).
fof(356,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(357,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[356]) ).
cnf(358,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[357]) ).
fof(359,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| equal(X1,sz00)
| equal(X1,sz10)
| ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
inference(fof_nnf,[status(thm)],[40]) ).
fof(360,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10)
| ? [X4] :
( aNaturalNumber0(X4)
& doDivides0(X4,X3)
& isPrime0(X4) ) ),
inference(variable_rename,[status(thm)],[359]) ).
fof(361,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10)
| ( aNaturalNumber0(esk12_1(X3))
& doDivides0(esk12_1(X3),X3)
& isPrime0(esk12_1(X3)) ) ),
inference(skolemize,[status(esa)],[360]) ).
fof(362,plain,
! [X3] :
( ( aNaturalNumber0(esk12_1(X3))
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) )
& ( doDivides0(esk12_1(X3),X3)
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) )
& ( isPrime0(esk12_1(X3))
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) ) ),
inference(distribute,[status(thm)],[361]) ).
cnf(363,plain,
( X1 = sz10
| X1 = sz00
| isPrime0(esk12_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[362]) ).
cnf(364,plain,
( X1 = sz10
| X1 = sz00
| doDivides0(esk12_1(X1),X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[362]) ).
cnf(365,plain,
( X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk12_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[362]) ).
fof(366,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)],[41]) ).
fof(367,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)],[366]) ).
fof(368,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)],[367]) ).
cnf(369,plain,
( X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X2,X3) != sdtpldt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[368]) ).
cnf(370,plain,
( X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X3,X2) != sdtpldt0(X3,X1) ),
inference(split_conjunct,[status(thm)],[368]) ).
fof(374,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(375,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(sdtasdt0(X3,X4),sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[374]) ).
cnf(376,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[375]) ).
fof(381,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtpldt0(X1,sz00),X1)
& equal(X1,sdtpldt0(sz00,X1)) ) ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(382,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtpldt0(X2,sz00),X2)
& equal(X2,sdtpldt0(sz00,X2)) ) ),
inference(variable_rename,[status(thm)],[381]) ).
fof(383,plain,
! [X2] :
( ( equal(sdtpldt0(X2,sz00),X2)
| ~ aNaturalNumber0(X2) )
& ( equal(X2,sdtpldt0(sz00,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[382]) ).
cnf(384,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[383]) ).
cnf(385,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[383]) ).
fof(386,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
inference(fof_nnf,[status(thm)],[46]) ).
fof(387,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtasdt0(X2,sz10),X2)
& equal(X2,sdtasdt0(sz10,X2)) ) ),
inference(variable_rename,[status(thm)],[386]) ).
fof(388,plain,
! [X2] :
( ( equal(sdtasdt0(X2,sz10),X2)
| ~ aNaturalNumber0(X2) )
& ( equal(X2,sdtasdt0(sz10,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[387]) ).
cnf(389,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[388]) ).
cnf(390,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[388]) ).
cnf(430,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(er,[status(thm)],[352,theory(equality)]) ).
cnf(431,plain,
( ~ isPrime0(sz10)
| $false ),
inference(rw,[status(thm)],[430,315,theory(equality)]) ).
cnf(432,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[431,theory(equality)]) ).
cnf(528,plain,
( sdtlseqdt0(sz00,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[286,384,theory(equality)]) ).
cnf(543,plain,
( sdtlseqdt0(sz00,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[528,355,theory(equality)]) ).
cnf(544,plain,
( sdtlseqdt0(sz00,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[543,theory(equality)]) ).
cnf(545,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[544,theory(equality)]) ).
cnf(566,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[238,244,theory(equality)]) ).
cnf(573,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xp)
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[566,250,theory(equality)]) ).
cnf(574,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xp)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[573,252,theory(equality)]) ).
cnf(575,plain,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[574,theory(equality)]) ).
cnf(615,plain,
( sz00 = X1
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[313,376,theory(equality)]) ).
cnf(667,plain,
( sz00 = X1
| X2 != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[370,385,theory(equality)]) ).
cnf(693,plain,
( sz00 = X1
| X2 != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[667,355,theory(equality)]) ).
cnf(694,plain,
( sz00 = X1
| X2 != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[693,theory(equality)]) ).
cnf(721,plain,
( xp = X1
| xn != sdtpldt0(X1,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[369,67,theory(equality)]) ).
cnf(729,plain,
( sz00 = X1
| X2 != sdtpldt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[369,384,theory(equality)]) ).
cnf(735,plain,
( xp = X1
| xn != sdtpldt0(X1,xr)
| $false
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[721,68,theory(equality)]) ).
cnf(736,plain,
( xp = X1
| xn != sdtpldt0(X1,xr)
| $false
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[735,250,theory(equality)]) ).
cnf(737,plain,
( xp = X1
| xn != sdtpldt0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[736,theory(equality)]) ).
cnf(757,plain,
( sz00 = X1
| X2 != sdtpldt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[729,355,theory(equality)]) ).
cnf(758,plain,
( sz00 = X1
| X2 != sdtpldt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[757,theory(equality)]) ).
cnf(761,plain,
( sz10 = esk12_1(xp)
| xp = esk12_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk12_1(xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[64,364,theory(equality)]) ).
cnf(764,plain,
( sz10 = esk12_1(xp)
| xp = esk12_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk12_1(xp))
| $false ),
inference(rw,[status(thm)],[761,250,theory(equality)]) ).
cnf(765,plain,
( sz10 = esk12_1(xp)
| xp = esk12_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk12_1(xp)) ),
inference(cn,[status(thm)],[764,theory(equality)]) ).
cnf(766,plain,
( esk12_1(xp) = sz10
| esk12_1(xp) = xp
| sz00 = xp
| ~ aNaturalNumber0(esk12_1(xp)) ),
inference(sr,[status(thm)],[765,62,theory(equality)]) ).
cnf(767,plain,
( esk12_1(xp) = sz10
| esk12_1(xp) = xp
| ~ aNaturalNumber0(esk12_1(xp)) ),
inference(sr,[status(thm)],[766,63,theory(equality)]) ).
cnf(789,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[227,389,theory(equality)]) ).
cnf(790,plain,
( doDivides0(X1,X2)
| sdtasdt0(X3,X1) != X2
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[227,376,theory(equality)]) ).
cnf(805,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[789,315,theory(equality)]) ).
cnf(806,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[805,theory(equality)]) ).
cnf(807,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[806,theory(equality)]) ).
cnf(814,plain,
( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[289,67,theory(equality)]) ).
cnf(820,plain,
( aNaturalNumber0(sdtpldt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[358,289,theory(equality)]) ).
cnf(821,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[74,289,theory(equality)]) ).
cnf(823,plain,
( sdtpldt0(sdtpldt0(X2,X1),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[289,74,theory(equality)]) ).
cnf(836,plain,
( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[814,68,theory(equality)]) ).
cnf(837,plain,
( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[836,250,theory(equality)]) ).
cnf(838,plain,
( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[837,theory(equality)]) ).
cnf(885,plain,
( sdtasdt0(esk12_1(X1),esk6_2(esk12_1(X1),X1)) = X1
| sz10 = X1
| sz00 = X1
| ~ aNaturalNumber0(esk12_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[225,364,theory(equality)]) ).
cnf(903,plain,
( xn = xr
| sdtlseqdt0(sdtpldt0(xr,X1),sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[262,302,theory(equality)]) ).
cnf(911,plain,
( xn = xr
| sdtlseqdt0(sdtpldt0(xr,X1),sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[903,68,theory(equality)]) ).
cnf(912,plain,
( xn = xr
| sdtlseqdt0(sdtpldt0(xr,X1),sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[911,252,theory(equality)]) ).
cnf(913,plain,
( xn = xr
| sdtlseqdt0(sdtpldt0(xr,X1),sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[912,theory(equality)]) ).
cnf(914,plain,
( sdtlseqdt0(sdtpldt0(xr,X1),sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[913,305,theory(equality)]) ).
cnf(917,plain,
( sdtmndt0(X1,X2) = X3
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[337,286]) ).
cnf(1018,plain,
( sz00 = X1
| sz10 = X2
| X1 != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[83,390,theory(equality)]) ).
cnf(1040,plain,
( sz00 = X1
| sz10 = X2
| X1 != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[1018,315,theory(equality)]) ).
cnf(1041,plain,
( sz00 = X1
| sz10 = X2
| X1 != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1040,theory(equality)]) ).
cnf(1097,plain,
( doDivides0(X1,xr)
| ~ doDivides0(X1,xn)
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[241,67,theory(equality)]) ).
cnf(1107,plain,
( doDivides0(X1,xr)
| ~ doDivides0(X1,xn)
| ~ doDivides0(X1,xp)
| $false
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[1097,250,theory(equality)]) ).
cnf(1108,plain,
( doDivides0(X1,xr)
| ~ doDivides0(X1,xn)
| ~ doDivides0(X1,xp)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[1107,68,theory(equality)]) ).
cnf(1109,plain,
( doDivides0(X1,xr)
| ~ doDivides0(X1,xn)
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1108,theory(equality)]) ).
cnf(1124,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(sdtasdt0(X1,X3))
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(spm,[status(thm)],[358,219,theory(equality)]) ).
cnf(1132,plain,
( sdtpldt0(sdtasdt0(sz10,X1),X2) = sdtasdt0(sz10,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[219,389,theory(equality)]) ).
cnf(1177,plain,
( sdtpldt0(sdtasdt0(sz10,X1),X2) = sdtasdt0(sz10,sdtpldt0(X1,X2))
| $false
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(rw,[status(thm)],[1132,315,theory(equality)]) ).
cnf(1178,plain,
( sdtpldt0(sdtasdt0(sz10,X1),X2) = sdtasdt0(sz10,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[1177,theory(equality)]) ).
cnf(5791,plain,
( sdtpldt0(xn,X1) = sdtpldt0(xr,X1)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xr,X1),X2),sdtpldt0(sdtpldt0(xn,X1),X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(xr,X1))
| ~ aNaturalNumber0(sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[262,914,theory(equality)]) ).
cnf(6303,plain,
( sdtlseqdt0(sz10,xn)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[575,309,theory(equality)]) ).
cnf(6312,plain,
( sdtlseqdt0(sz10,xn)
| sz10 = xp
| sz00 = xp
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[6303,315,theory(equality)]) ).
cnf(6313,plain,
( sdtlseqdt0(sz10,xn)
| sz10 = xp
| sz00 = xp
| $false
| $false ),
inference(rw,[status(thm)],[6312,250,theory(equality)]) ).
cnf(6314,plain,
( sdtlseqdt0(sz10,xn)
| sz10 = xp
| sz00 = xp ),
inference(cn,[status(thm)],[6313,theory(equality)]) ).
cnf(6315,plain,
( sdtlseqdt0(sz10,xn)
| sz00 = xp ),
inference(sr,[status(thm)],[6314,62,theory(equality)]) ).
cnf(6316,plain,
sdtlseqdt0(sz10,xn),
inference(sr,[status(thm)],[6315,63,theory(equality)]) ).
cnf(6321,plain,
( aNaturalNumber0(esk9_2(sz10,xn))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[285,6316,theory(equality)]) ).
cnf(6324,plain,
( sdtpldt0(sz10,esk9_2(sz10,xn)) = xn
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[284,6316,theory(equality)]) ).
cnf(6332,plain,
( aNaturalNumber0(esk9_2(sz10,xn))
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[6321,315,theory(equality)]) ).
cnf(6333,plain,
( aNaturalNumber0(esk9_2(sz10,xn))
| $false
| $false ),
inference(rw,[status(thm)],[6332,252,theory(equality)]) ).
cnf(6334,plain,
aNaturalNumber0(esk9_2(sz10,xn)),
inference(cn,[status(thm)],[6333,theory(equality)]) ).
cnf(6341,plain,
( sdtpldt0(sz10,esk9_2(sz10,xn)) = xn
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[6324,315,theory(equality)]) ).
cnf(6342,plain,
( sdtpldt0(sz10,esk9_2(sz10,xn)) = xn
| $false
| $false ),
inference(rw,[status(thm)],[6341,252,theory(equality)]) ).
cnf(6343,plain,
sdtpldt0(sz10,esk9_2(sz10,xn)) = xn,
inference(cn,[status(thm)],[6342,theory(equality)]) ).
cnf(7341,plain,
( xp = X1
| sdtpldt0(xr,X1) != xn
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[737,74,theory(equality)]) ).
cnf(7348,plain,
( xp = X1
| sdtpldt0(xr,X1) != xn
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[7341,68,theory(equality)]) ).
cnf(7349,plain,
( xp = X1
| sdtpldt0(xr,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[7348,theory(equality)]) ).
cnf(7453,plain,
( xp = esk10_0
| ~ aNaturalNumber0(esk10_0) ),
inference(spm,[status(thm)],[7349,303,theory(equality)]) ).
cnf(7458,plain,
( xp = esk10_0
| $false ),
inference(rw,[status(thm)],[7453,304,theory(equality)]) ).
cnf(7459,plain,
xp = esk10_0,
inference(cn,[status(thm)],[7458,theory(equality)]) ).
cnf(7474,plain,
sdtpldt0(xr,xp) = xn,
inference(rw,[status(thm)],[303,7459,theory(equality)]) ).
cnf(10436,plain,
( esk12_1(xp) = xp
| esk12_1(xp) = sz10
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[767,365,theory(equality)]) ).
cnf(10437,plain,
( esk12_1(xp) = xp
| esk12_1(xp) = sz10
| sz10 = xp
| sz00 = xp
| $false ),
inference(rw,[status(thm)],[10436,250,theory(equality)]) ).
cnf(10438,plain,
( esk12_1(xp) = xp
| esk12_1(xp) = sz10
| sz10 = xp
| sz00 = xp ),
inference(cn,[status(thm)],[10437,theory(equality)]) ).
cnf(10439,plain,
( esk12_1(xp) = xp
| esk12_1(xp) = sz10
| sz00 = xp ),
inference(sr,[status(thm)],[10438,62,theory(equality)]) ).
cnf(10440,plain,
( esk12_1(xp) = xp
| esk12_1(xp) = sz10 ),
inference(sr,[status(thm)],[10439,63,theory(equality)]) ).
cnf(10443,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| esk12_1(xp) = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[363,10440,theory(equality)]) ).
cnf(10448,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| esk12_1(xp) = xp
| $false ),
inference(rw,[status(thm)],[10443,250,theory(equality)]) ).
cnf(10449,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| esk12_1(xp) = xp ),
inference(cn,[status(thm)],[10448,theory(equality)]) ).
cnf(10450,plain,
( sz00 = xp
| isPrime0(sz10)
| esk12_1(xp) = xp ),
inference(sr,[status(thm)],[10449,62,theory(equality)]) ).
cnf(10451,plain,
( isPrime0(sz10)
| esk12_1(xp) = xp ),
inference(sr,[status(thm)],[10450,63,theory(equality)]) ).
cnf(10452,plain,
esk12_1(xp) = xp,
inference(sr,[status(thm)],[10451,432,theory(equality)]) ).
cnf(10459,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[364,10452,theory(equality)]) ).
cnf(10468,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp)
| $false ),
inference(rw,[status(thm)],[10459,250,theory(equality)]) ).
cnf(10469,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp) ),
inference(cn,[status(thm)],[10468,theory(equality)]) ).
cnf(10470,plain,
( sz00 = xp
| doDivides0(xp,xp) ),
inference(sr,[status(thm)],[10469,62,theory(equality)]) ).
cnf(10471,plain,
doDivides0(xp,xp),
inference(sr,[status(thm)],[10470,63,theory(equality)]) ).
cnf(10472,plain,
( aNaturalNumber0(esk6_2(xp,xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[226,10471,theory(equality)]) ).
cnf(10473,plain,
( sz00 = xp
| sdtlseqdt0(xp,xp)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[249,10471,theory(equality)]) ).
cnf(10474,plain,
( sdtasdt0(xp,esk6_2(xp,xp)) = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[225,10471,theory(equality)]) ).
cnf(10478,plain,
( aNaturalNumber0(esk6_2(xp,xp))
| $false ),
inference(rw,[status(thm)],[10472,250,theory(equality)]) ).
cnf(10479,plain,
aNaturalNumber0(esk6_2(xp,xp)),
inference(cn,[status(thm)],[10478,theory(equality)]) ).
cnf(10480,plain,
( sz00 = xp
| sdtlseqdt0(xp,xp)
| $false ),
inference(rw,[status(thm)],[10473,250,theory(equality)]) ).
cnf(10481,plain,
( sz00 = xp
| sdtlseqdt0(xp,xp) ),
inference(cn,[status(thm)],[10480,theory(equality)]) ).
cnf(10482,plain,
sdtlseqdt0(xp,xp),
inference(sr,[status(thm)],[10481,63,theory(equality)]) ).
cnf(10483,plain,
( sdtasdt0(xp,esk6_2(xp,xp)) = xp
| $false ),
inference(rw,[status(thm)],[10474,250,theory(equality)]) ).
cnf(10484,plain,
sdtasdt0(xp,esk6_2(xp,xp)) = xp,
inference(cn,[status(thm)],[10483,theory(equality)]) ).
cnf(10492,plain,
( aNaturalNumber0(esk9_2(xp,xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[285,10482,theory(equality)]) ).
cnf(10494,plain,
( sdtpldt0(xp,esk9_2(xp,xp)) = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[284,10482,theory(equality)]) ).
cnf(10498,plain,
( aNaturalNumber0(esk9_2(xp,xp))
| $false ),
inference(rw,[status(thm)],[10492,250,theory(equality)]) ).
cnf(10499,plain,
aNaturalNumber0(esk9_2(xp,xp)),
inference(cn,[status(thm)],[10498,theory(equality)]) ).
cnf(10502,plain,
( sdtpldt0(xp,esk9_2(xp,xp)) = xp
| $false ),
inference(rw,[status(thm)],[10494,250,theory(equality)]) ).
cnf(10503,plain,
sdtpldt0(xp,esk9_2(xp,xp)) = xp,
inference(cn,[status(thm)],[10502,theory(equality)]) ).
cnf(11711,plain,
( sz00 = xp
| sdtlseqdt0(esk6_2(xp,xp),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(esk6_2(xp,xp)) ),
inference(spm,[status(thm)],[615,10484,theory(equality)]) ).
cnf(11742,plain,
( sz00 = xp
| sdtlseqdt0(esk6_2(xp,xp),xp)
| $false
| ~ aNaturalNumber0(esk6_2(xp,xp)) ),
inference(rw,[status(thm)],[11711,250,theory(equality)]) ).
cnf(11743,plain,
( sz00 = xp
| sdtlseqdt0(esk6_2(xp,xp),xp)
| $false
| $false ),
inference(rw,[status(thm)],[11742,10479,theory(equality)]) ).
cnf(11744,plain,
( sz00 = xp
| sdtlseqdt0(esk6_2(xp,xp),xp) ),
inference(cn,[status(thm)],[11743,theory(equality)]) ).
cnf(11745,plain,
sdtlseqdt0(esk6_2(xp,xp),xp),
inference(sr,[status(thm)],[11744,63,theory(equality)]) ).
cnf(11761,plain,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,esk6_2(xp,xp))
| ~ aNaturalNumber0(esk6_2(xp,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[238,11745,theory(equality)]) ).
cnf(11777,plain,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,esk6_2(xp,xp))
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[11761,10479,theory(equality)]) ).
cnf(11778,plain,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,esk6_2(xp,xp))
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[11777,250,theory(equality)]) ).
cnf(11779,plain,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,esk6_2(xp,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[11778,theory(equality)]) ).
cnf(12658,plain,
( sz00 = esk9_2(xp,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(esk9_2(xp,xp)) ),
inference(spm,[status(thm)],[694,10503,theory(equality)]) ).
cnf(12684,plain,
( sz00 = esk9_2(xp,xp)
| $false
| ~ aNaturalNumber0(esk9_2(xp,xp)) ),
inference(rw,[status(thm)],[12658,250,theory(equality)]) ).
cnf(12685,plain,
( sz00 = esk9_2(xp,xp)
| $false
| $false ),
inference(rw,[status(thm)],[12684,10499,theory(equality)]) ).
cnf(12686,plain,
sz00 = esk9_2(xp,xp),
inference(cn,[status(thm)],[12685,theory(equality)]) ).
cnf(12693,plain,
sdtpldt0(xp,sz00) = xp,
inference(rw,[status(thm)],[10503,12686,theory(equality)]) ).
cnf(12720,plain,
( sdtpldt0(xp,X1) = sdtpldt0(xp,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[289,12693,theory(equality)]) ).
cnf(12722,plain,
( doDivides0(X1,sz00)
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[241,12693,theory(equality)]) ).
cnf(12750,plain,
( sdtpldt0(xp,X1) = sdtpldt0(xp,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[12720,355,theory(equality)]) ).
cnf(12751,plain,
( sdtpldt0(xp,X1) = sdtpldt0(xp,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[12750,250,theory(equality)]) ).
cnf(12752,plain,
( sdtpldt0(xp,X1) = sdtpldt0(xp,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[12751,theory(equality)]) ).
cnf(12756,plain,
( doDivides0(X1,sz00)
| ~ doDivides0(X1,xp)
| $false
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[12722,250,theory(equality)]) ).
cnf(12757,plain,
( doDivides0(X1,sz00)
| ~ doDivides0(X1,xp)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[12756,355,theory(equality)]) ).
cnf(12758,plain,
( doDivides0(X1,sz00)
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[12757,theory(equality)]) ).
cnf(13259,plain,
( sdtlseqdt0(sz00,xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(esk6_2(xp,xp)) ),
inference(spm,[status(thm)],[11779,545,theory(equality)]) ).
cnf(13272,plain,
( sdtlseqdt0(sz00,xp)
| $false
| ~ aNaturalNumber0(esk6_2(xp,xp)) ),
inference(rw,[status(thm)],[13259,355,theory(equality)]) ).
cnf(13273,plain,
( sdtlseqdt0(sz00,xp)
| $false
| $false ),
inference(rw,[status(thm)],[13272,10479,theory(equality)]) ).
cnf(13274,plain,
sdtlseqdt0(sz00,xp),
inference(cn,[status(thm)],[13273,theory(equality)]) ).
cnf(13288,plain,
( aNaturalNumber0(esk9_2(sz00,xp))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[285,13274,theory(equality)]) ).
cnf(13291,plain,
( sdtpldt0(sz00,esk9_2(sz00,xp)) = xp
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[284,13274,theory(equality)]) ).
cnf(13308,plain,
( aNaturalNumber0(esk9_2(sz00,xp))
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[13288,355,theory(equality)]) ).
cnf(13309,plain,
( aNaturalNumber0(esk9_2(sz00,xp))
| $false
| $false ),
inference(rw,[status(thm)],[13308,250,theory(equality)]) ).
cnf(13310,plain,
aNaturalNumber0(esk9_2(sz00,xp)),
inference(cn,[status(thm)],[13309,theory(equality)]) ).
cnf(13318,plain,
( sdtpldt0(sz00,esk9_2(sz00,xp)) = xp
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[13291,355,theory(equality)]) ).
cnf(13319,plain,
( sdtpldt0(sz00,esk9_2(sz00,xp)) = xp
| $false
| $false ),
inference(rw,[status(thm)],[13318,250,theory(equality)]) ).
cnf(13320,plain,
sdtpldt0(sz00,esk9_2(sz00,xp)) = xp,
inference(cn,[status(thm)],[13319,theory(equality)]) ).
cnf(13389,plain,
( xp = esk9_2(sz00,xp)
| ~ aNaturalNumber0(esk9_2(sz00,xp)) ),
inference(spm,[status(thm)],[384,13320,theory(equality)]) ).
cnf(13408,plain,
( xp = esk9_2(sz00,xp)
| $false ),
inference(rw,[status(thm)],[13389,13310,theory(equality)]) ).
cnf(13409,plain,
xp = esk9_2(sz00,xp),
inference(cn,[status(thm)],[13408,theory(equality)]) ).
cnf(13465,plain,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[13320,13409,theory(equality)]) ).
cnf(13488,plain,
( sdtmndt0(X1,sz00) = xp
| xp != X1
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[917,13465,theory(equality)]) ).
cnf(13532,plain,
( sdtmndt0(X1,sz00) = xp
| xp != X1
| $false
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[13488,250,theory(equality)]) ).
cnf(13533,plain,
( sdtmndt0(X1,sz00) = xp
| xp != X1
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[13532,355,theory(equality)]) ).
cnf(13534,plain,
( sdtmndt0(X1,sz00) = xp
| xp != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[13533,theory(equality)]) ).
cnf(14428,plain,
( doDivides0(sz10,sz00)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[12758,807,theory(equality)]) ).
cnf(14442,plain,
( doDivides0(sz10,sz00)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[14428,315,theory(equality)]) ).
cnf(14443,plain,
( doDivides0(sz10,sz00)
| $false
| $false ),
inference(rw,[status(thm)],[14442,250,theory(equality)]) ).
cnf(14444,plain,
doDivides0(sz10,sz00),
inference(cn,[status(thm)],[14443,theory(equality)]) ).
cnf(14509,plain,
( aNaturalNumber0(esk6_2(sz10,sz00))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[226,14444,theory(equality)]) ).
cnf(14510,plain,
( sdtasdt0(sz10,esk6_2(sz10,sz00)) = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[225,14444,theory(equality)]) ).
cnf(14514,plain,
( aNaturalNumber0(esk6_2(sz10,sz00))
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[14509,315,theory(equality)]) ).
cnf(14515,plain,
( aNaturalNumber0(esk6_2(sz10,sz00))
| $false
| $false ),
inference(rw,[status(thm)],[14514,355,theory(equality)]) ).
cnf(14516,plain,
aNaturalNumber0(esk6_2(sz10,sz00)),
inference(cn,[status(thm)],[14515,theory(equality)]) ).
cnf(14517,plain,
( sdtasdt0(sz10,esk6_2(sz10,sz00)) = sz00
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[14510,315,theory(equality)]) ).
cnf(14518,plain,
( sdtasdt0(sz10,esk6_2(sz10,sz00)) = sz00
| $false
| $false ),
inference(rw,[status(thm)],[14517,355,theory(equality)]) ).
cnf(14519,plain,
sdtasdt0(sz10,esk6_2(sz10,sz00)) = sz00,
inference(cn,[status(thm)],[14518,theory(equality)]) ).
cnf(16386,plain,
( sz00 = esk6_2(sz10,sz00)
| sz00 = sz10
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(esk6_2(sz10,sz00)) ),
inference(spm,[status(thm)],[77,14519,theory(equality)]) ).
cnf(16531,plain,
( sz00 = esk6_2(sz10,sz00)
| sz00 = sz10
| $false
| ~ aNaturalNumber0(esk6_2(sz10,sz00)) ),
inference(rw,[status(thm)],[16386,315,theory(equality)]) ).
cnf(16532,plain,
( sz00 = esk6_2(sz10,sz00)
| sz00 = sz10
| $false
| $false ),
inference(rw,[status(thm)],[16531,14516,theory(equality)]) ).
cnf(16533,plain,
( sz00 = esk6_2(sz10,sz00)
| sz00 = sz10 ),
inference(cn,[status(thm)],[16532,theory(equality)]) ).
cnf(16534,plain,
esk6_2(sz10,sz00) = sz00,
inference(sr,[status(thm)],[16533,314,theory(equality)]) ).
cnf(16938,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(rw,[status(thm)],[14519,16534,theory(equality)]) ).
cnf(20719,plain,
( sdtmndt0(xp,sz00) = xp
| ~ aNaturalNumber0(xp) ),
inference(er,[status(thm)],[13534,theory(equality)]) ).
cnf(20720,plain,
( sdtmndt0(xp,sz00) = xp
| $false ),
inference(rw,[status(thm)],[20719,250,theory(equality)]) ).
cnf(20721,plain,
sdtmndt0(xp,sz00) = xp,
inference(cn,[status(thm)],[20720,theory(equality)]) ).
cnf(20722,plain,
( aNaturalNumber0(X1)
| xp != X1
| ~ sdtlseqdt0(sz00,xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[339,20721,theory(equality)]) ).
cnf(20729,plain,
( aNaturalNumber0(X1)
| xp != X1
| $false
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[20722,13274,theory(equality)]) ).
cnf(20730,plain,
( aNaturalNumber0(X1)
| xp != X1
| $false
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[20729,355,theory(equality)]) ).
cnf(20731,plain,
( aNaturalNumber0(X1)
| xp != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[20730,250,theory(equality)]) ).
cnf(20732,plain,
( aNaturalNumber0(X1)
| xp != X1 ),
inference(cn,[status(thm)],[20731,theory(equality)]) ).
cnf(23968,plain,
( sz00 = xp
| sdtpldt0(xn,X1) != sdtpldt0(xr,X1)
| ~ aNaturalNumber0(sdtpldt0(xr,X1))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[758,838,theory(equality)]) ).
cnf(24017,plain,
( sz00 = xp
| sdtpldt0(xn,X1) != sdtpldt0(xr,X1)
| ~ aNaturalNumber0(sdtpldt0(xr,X1))
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[23968,250,theory(equality)]) ).
cnf(24018,plain,
( sz00 = xp
| sdtpldt0(xn,X1) != sdtpldt0(xr,X1)
| ~ aNaturalNumber0(sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[24017,theory(equality)]) ).
cnf(24019,plain,
( sdtpldt0(xr,X1) != sdtpldt0(xn,X1)
| ~ aNaturalNumber0(sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[24018,63,theory(equality)]) ).
cnf(25118,plain,
( aNaturalNumber0(sdtpldt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[820,358]) ).
cnf(25120,plain,
( aNaturalNumber0(sdtpldt0(X1,xn))
| ~ aNaturalNumber0(esk9_2(sz10,xn))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[25118,6343,theory(equality)]) ).
cnf(25157,plain,
( aNaturalNumber0(sdtpldt0(X1,xn))
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[25120,6334,theory(equality)]) ).
cnf(25158,plain,
( aNaturalNumber0(sdtpldt0(X1,xn))
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[25157,315,theory(equality)]) ).
cnf(25159,plain,
( aNaturalNumber0(sdtpldt0(X1,xn))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[25158,theory(equality)]) ).
cnf(25211,plain,
( aNaturalNumber0(sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[25159,74,theory(equality)]) ).
cnf(25221,plain,
( aNaturalNumber0(sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[25211,252,theory(equality)]) ).
cnf(25222,plain,
( aNaturalNumber0(sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[25221,theory(equality)]) ).
cnf(25254,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[821,358]) ).
cnf(29351,plain,
( sdtasdt0(esk12_1(X1),esk6_2(esk12_1(X1),X1)) = X1
| sz10 = X1
| sz00 = X1
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[885,365]) ).
cnf(29352,plain,
( sdtasdt0(xp,esk6_2(xp,xp)) = xp
| sz00 = xp
| sz10 = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[29351,10452,theory(equality)]) ).
cnf(29549,plain,
( sdtasdt0(xp,esk6_2(xp,xp)) = xp
| sz00 = xp
| sz10 = xp
| $false ),
inference(rw,[status(thm)],[29352,250,theory(equality)]) ).
cnf(29550,plain,
( sdtasdt0(xp,esk6_2(xp,xp)) = xp
| sz00 = xp
| sz10 = xp ),
inference(cn,[status(thm)],[29549,theory(equality)]) ).
cnf(29551,plain,
( sdtasdt0(xp,esk6_2(xp,xp)) = xp
| sz10 = xp ),
inference(sr,[status(thm)],[29550,63,theory(equality)]) ).
cnf(29552,plain,
sdtasdt0(xp,esk6_2(xp,xp)) = xp,
inference(sr,[status(thm)],[29551,62,theory(equality)]) ).
cnf(29797,plain,
( sdtpldt0(xr,X1) != sdtpldt0(xn,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[24019,358,theory(equality)]) ).
cnf(29820,plain,
( sdtpldt0(xr,X1) != sdtpldt0(xn,X1)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[29797,68,theory(equality)]) ).
cnf(29821,plain,
( sdtpldt0(xr,X1) != sdtpldt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[29820,theory(equality)]) ).
cnf(35648,plain,
( sz10 = esk6_2(xp,xp)
| sz00 = xp
| ~ aNaturalNumber0(esk6_2(xp,xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[1041,29552,theory(equality)]) ).
cnf(35677,plain,
( sz10 = esk6_2(xp,xp)
| sz00 = xp
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[35648,10479,theory(equality)]) ).
cnf(35678,plain,
( sz10 = esk6_2(xp,xp)
| sz00 = xp
| $false
| $false ),
inference(rw,[status(thm)],[35677,250,theory(equality)]) ).
cnf(35679,plain,
( sz10 = esk6_2(xp,xp)
| sz00 = xp ),
inference(cn,[status(thm)],[35678,theory(equality)]) ).
cnf(35680,plain,
esk6_2(xp,xp) = sz10,
inference(sr,[status(thm)],[35679,63,theory(equality)]) ).
cnf(35690,plain,
sdtasdt0(xp,sz10) = xp,
inference(rw,[status(thm)],[29552,35680,theory(equality)]) ).
cnf(35913,plain,
( doDivides0(sz10,X1)
| xp != X1
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[790,35690,theory(equality)]) ).
cnf(36615,plain,
( doDivides0(sz10,X1)
| xp != X1
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[35913,250,theory(equality)]) ).
cnf(36616,plain,
( doDivides0(sz10,X1)
| xp != X1
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[36615,315,theory(equality)]) ).
cnf(36617,plain,
( doDivides0(sz10,X1)
| xp != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[36616,theory(equality)]) ).
cnf(36863,plain,
( doDivides0(sz10,X1)
| xp != X1 ),
inference(csr,[status(thm)],[36617,20732]) ).
cnf(36864,plain,
doDivides0(sz10,xp),
inference(er,[status(thm)],[36863,theory(equality)]) ).
cnf(50667,plain,
( doDivides0(sz10,xr)
| ~ doDivides0(sz10,xp)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[1109,807,theory(equality)]) ).
cnf(50676,plain,
( doDivides0(sz10,xr)
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[50667,36864,theory(equality)]) ).
cnf(50677,plain,
( doDivides0(sz10,xr)
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[50676,315,theory(equality)]) ).
cnf(50678,plain,
( doDivides0(sz10,xr)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[50677,252,theory(equality)]) ).
cnf(50679,plain,
doDivides0(sz10,xr),
inference(cn,[status(thm)],[50678,theory(equality)]) ).
cnf(50680,plain,
( aNaturalNumber0(esk6_2(sz10,xr))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[226,50679,theory(equality)]) ).
cnf(50682,plain,
( sdtasdt0(sz10,esk6_2(sz10,xr)) = xr
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[225,50679,theory(equality)]) ).
cnf(50687,plain,
( aNaturalNumber0(esk6_2(sz10,xr))
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[50680,315,theory(equality)]) ).
cnf(50688,plain,
( aNaturalNumber0(esk6_2(sz10,xr))
| $false
| $false ),
inference(rw,[status(thm)],[50687,68,theory(equality)]) ).
cnf(50689,plain,
aNaturalNumber0(esk6_2(sz10,xr)),
inference(cn,[status(thm)],[50688,theory(equality)]) ).
cnf(50693,plain,
( sdtasdt0(sz10,esk6_2(sz10,xr)) = xr
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[50682,315,theory(equality)]) ).
cnf(50694,plain,
( sdtasdt0(sz10,esk6_2(sz10,xr)) = xr
| $false
| $false ),
inference(rw,[status(thm)],[50693,68,theory(equality)]) ).
cnf(50695,plain,
sdtasdt0(sz10,esk6_2(sz10,xr)) = xr,
inference(cn,[status(thm)],[50694,theory(equality)]) ).
cnf(52397,plain,
( xr = esk6_2(sz10,xr)
| ~ aNaturalNumber0(esk6_2(sz10,xr)) ),
inference(spm,[status(thm)],[389,50695,theory(equality)]) ).
cnf(52562,plain,
( xr = esk6_2(sz10,xr)
| $false ),
inference(rw,[status(thm)],[52397,50689,theory(equality)]) ).
cnf(52563,plain,
xr = esk6_2(sz10,xr),
inference(cn,[status(thm)],[52562,theory(equality)]) ).
cnf(53095,plain,
sdtasdt0(sz10,xr) = xr,
inference(rw,[status(thm)],[50695,52563,theory(equality)]) ).
cnf(53236,plain,
( sz00 = sz10
| sdtlseqdt0(xr,xr)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[615,53095,theory(equality)]) ).
cnf(53665,plain,
( sz00 = sz10
| sdtlseqdt0(xr,xr)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[53236,315,theory(equality)]) ).
cnf(53666,plain,
( sz00 = sz10
| sdtlseqdt0(xr,xr)
| $false
| $false ),
inference(rw,[status(thm)],[53665,68,theory(equality)]) ).
cnf(53667,plain,
( sz00 = sz10
| sdtlseqdt0(xr,xr) ),
inference(cn,[status(thm)],[53666,theory(equality)]) ).
cnf(53668,plain,
sdtlseqdt0(xr,xr),
inference(sr,[status(thm)],[53667,314,theory(equality)]) ).
cnf(53745,plain,
( aNaturalNumber0(esk9_2(xr,xr))
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[285,53668,theory(equality)]) ).
cnf(53747,plain,
( sdtpldt0(xr,esk9_2(xr,xr)) = xr
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[284,53668,theory(equality)]) ).
cnf(53753,plain,
( aNaturalNumber0(esk9_2(xr,xr))
| $false ),
inference(rw,[status(thm)],[53745,68,theory(equality)]) ).
cnf(53754,plain,
aNaturalNumber0(esk9_2(xr,xr)),
inference(cn,[status(thm)],[53753,theory(equality)]) ).
cnf(53757,plain,
( sdtpldt0(xr,esk9_2(xr,xr)) = xr
| $false ),
inference(rw,[status(thm)],[53747,68,theory(equality)]) ).
cnf(53758,plain,
sdtpldt0(xr,esk9_2(xr,xr)) = xr,
inference(cn,[status(thm)],[53757,theory(equality)]) ).
cnf(53900,plain,
( sz00 = esk9_2(xr,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(esk9_2(xr,xr)) ),
inference(spm,[status(thm)],[694,53758,theory(equality)]) ).
cnf(53977,plain,
( sz00 = esk9_2(xr,xr)
| $false
| ~ aNaturalNumber0(esk9_2(xr,xr)) ),
inference(rw,[status(thm)],[53900,68,theory(equality)]) ).
cnf(53978,plain,
( sz00 = esk9_2(xr,xr)
| $false
| $false ),
inference(rw,[status(thm)],[53977,53754,theory(equality)]) ).
cnf(53979,plain,
sz00 = esk9_2(xr,xr),
inference(cn,[status(thm)],[53978,theory(equality)]) ).
cnf(54071,plain,
sdtpldt0(xr,sz00) = xr,
inference(rw,[status(thm)],[53758,53979,theory(equality)]) ).
cnf(54272,plain,
( xr = sdtpldt0(sz00,xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[74,54071,theory(equality)]) ).
cnf(54300,plain,
( aNaturalNumber0(sdtpldt0(X1,xr))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[25118,54071,theory(equality)]) ).
cnf(54333,plain,
( xr = sdtpldt0(sz00,xr)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[54272,355,theory(equality)]) ).
cnf(54334,plain,
( xr = sdtpldt0(sz00,xr)
| $false
| $false ),
inference(rw,[status(thm)],[54333,68,theory(equality)]) ).
cnf(54335,plain,
xr = sdtpldt0(sz00,xr),
inference(cn,[status(thm)],[54334,theory(equality)]) ).
cnf(54415,plain,
( aNaturalNumber0(sdtpldt0(X1,xr))
| $false
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[54300,355,theory(equality)]) ).
cnf(54416,plain,
( aNaturalNumber0(sdtpldt0(X1,xr))
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[54415,68,theory(equality)]) ).
cnf(54417,plain,
( aNaturalNumber0(sdtpldt0(X1,xr))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[54416,theory(equality)]) ).
cnf(54715,plain,
( sdtpldt0(sz00,sdtpldt0(xr,X1)) = sdtpldt0(X1,xr)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[25254,54335,theory(equality)]) ).
cnf(54823,plain,
( sdtpldt0(sz00,sdtpldt0(xr,X1)) = sdtpldt0(X1,xr)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[54715,68,theory(equality)]) ).
cnf(54824,plain,
( sdtpldt0(sz00,sdtpldt0(xr,X1)) = sdtpldt0(X1,xr)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[54823,355,theory(equality)]) ).
cnf(54825,plain,
( sdtpldt0(sz00,sdtpldt0(xr,X1)) = sdtpldt0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[54824,theory(equality)]) ).
cnf(55202,plain,
( aNaturalNumber0(sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[54417,74,theory(equality)]) ).
cnf(55217,plain,
( aNaturalNumber0(sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[55202,68,theory(equality)]) ).
cnf(55218,plain,
( aNaturalNumber0(sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[55217,theory(equality)]) ).
cnf(56249,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[1124,342]) ).
cnf(56250,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[56249,342]) ).
cnf(62911,plain,
( sdtasdt0(sz10,X1) = sdtpldt0(sdtasdt0(sz10,sz00),X1)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[1178,384,theory(equality)]) ).
cnf(63179,plain,
( sdtasdt0(sz10,X1) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[62911,16938,theory(equality)]) ).
cnf(63180,plain,
( sdtasdt0(sz10,X1) = sdtpldt0(sz00,X1)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[63179,355,theory(equality)]) ).
cnf(63181,plain,
( sdtasdt0(sz10,X1) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[63180,theory(equality)]) ).
cnf(263286,plain,
( sdtpldt0(xp,X1) = sdtpldt0(X1,sdtpldt0(xp,sz00))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[25254,12752,theory(equality)]) ).
cnf(263440,plain,
( sdtpldt0(xp,X1) = sdtpldt0(X1,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[263286,12693,theory(equality)]) ).
cnf(263441,plain,
( sdtpldt0(xp,X1) = sdtpldt0(X1,xp)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[263440,355,theory(equality)]) ).
cnf(263442,plain,
( sdtpldt0(xp,X1) = sdtpldt0(X1,xp)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[263441,250,theory(equality)]) ).
cnf(263443,plain,
( sdtpldt0(xp,X1) = sdtpldt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[263442,theory(equality)]) ).
cnf(263852,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtpldt0(X2,xp)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[56250,263443,theory(equality)]) ).
cnf(264630,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtpldt0(X2,xp)))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(X2) ),
inference(rw,[status(thm)],[263852,250,theory(equality)]) ).
cnf(264631,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtpldt0(X2,xp)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[264630,theory(equality)]) ).
cnf(293873,plain,
( aNaturalNumber0(sdtpldt0(sdtasdt0(sz10,X1),xp))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[264631,1178,theory(equality)]) ).
cnf(293929,plain,
( aNaturalNumber0(sdtpldt0(sdtasdt0(sz10,X1),xp))
| $false
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[293873,315,theory(equality)]) ).
cnf(293930,plain,
( aNaturalNumber0(sdtpldt0(sdtasdt0(sz10,X1),xp))
| $false
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[293929,250,theory(equality)]) ).
cnf(293931,plain,
( aNaturalNumber0(sdtpldt0(sdtasdt0(sz10,X1),xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[293930,theory(equality)]) ).
cnf(308529,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(sz00,X1),xp))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[293931,63181,theory(equality)]) ).
cnf(677782,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(X1,xr),xp))
| ~ aNaturalNumber0(sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[308529,54825,theory(equality)]) ).
cnf(680606,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(X1,xr),xp))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[677782,55218]) ).
cnf(680620,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xr,X1),xp))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[680606,74,theory(equality)]) ).
cnf(680670,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xr,X1),xp))
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[680620,68,theory(equality)]) ).
cnf(680671,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xr,X1),xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[680670,theory(equality)]) ).
cnf(868680,plain,
( sdtpldt0(xr,X1) = sdtpldt0(xn,X1)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xr,X1),X2),sdtpldt0(sdtpldt0(xn,X1),X2))
| ~ aNaturalNumber0(sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[5791,25222]) ).
cnf(868681,plain,
( sdtpldt0(xr,X1) = sdtpldt0(xn,X1)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xr,X1),X2),sdtpldt0(sdtpldt0(xn,X1),X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[868680,55218]) ).
cnf(868682,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,X1),X2),sdtpldt0(sdtpldt0(xn,X1),X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[868681,29821]) ).
cnf(868751,plain,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[320,868682,theory(equality)]) ).
cnf(869004,plain,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[868751,250,theory(equality)]) ).
cnf(869005,plain,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| $false
| $false ),
inference(rw,[status(thm)],[869004,251,theory(equality)]) ).
cnf(869006,plain,
sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp),
inference(cn,[status(thm)],[869005,theory(equality)]) ).
cnf(869142,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,sdtpldt0(xr,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[823,869006,theory(equality)]) ).
cnf(869261,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[680671,869006,theory(equality)]) ).
cnf(869348,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[869142,7474,theory(equality)]) ).
cnf(869349,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,xn)
| $false
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[869348,250,theory(equality)]) ).
cnf(869350,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,xn)
| $false
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[869349,68,theory(equality)]) ).
cnf(869351,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,xn)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[869350,251,theory(equality)]) ).
cnf(869352,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,xn),
inference(cn,[status(thm)],[869351,theory(equality)]) ).
cnf(869508,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| $false ),
inference(rw,[status(thm)],[869261,251,theory(equality)]) ).
cnf(869509,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cn,[status(thm)],[869508,theory(equality)]) ).
cnf(869675,plain,
( sz00 = xp
| sdtpldt0(xm,xn) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[694,869352,theory(equality)]) ).
cnf(869788,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(rw,[status(thm)],[869509,869352,theory(equality)]) ).
cnf(871148,plain,
( sz00 = xp
| sdtpldt0(xm,xn) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| $false ),
inference(rw,[status(thm)],[869675,250,theory(equality)]) ).
cnf(871149,plain,
( sz00 = xp
| sdtpldt0(xm,xn) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[871148,theory(equality)]) ).
cnf(871150,plain,
( sdtpldt0(xm,xn) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(sr,[status(thm)],[871149,63,theory(equality)]) ).
cnf(871292,plain,
( aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[869788,74,theory(equality)]) ).
cnf(871295,plain,
( aNaturalNumber0(sdtpldt0(xn,xm))
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[871292,252,theory(equality)]) ).
cnf(871296,plain,
( aNaturalNumber0(sdtpldt0(xn,xm))
| $false
| $false ),
inference(rw,[status(thm)],[871295,251,theory(equality)]) ).
cnf(871297,plain,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(cn,[status(thm)],[871296,theory(equality)]) ).
cnf(878934,plain,
( sdtpldt0(xm,xn) != sdtpldt0(xn,xm)
| $false ),
inference(rw,[status(thm)],[871150,871297,theory(equality)]) ).
cnf(878935,plain,
sdtpldt0(xm,xn) != sdtpldt0(xn,xm),
inference(cn,[status(thm)],[878934,theory(equality)]) ).
cnf(878936,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[878935,74,theory(equality)]) ).
cnf(878939,plain,
( $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[878936,252,theory(equality)]) ).
cnf(878940,plain,
( $false
| $false ),
inference(rw,[status(thm)],[878939,251,theory(equality)]) ).
cnf(878941,plain,
$false,
inference(cn,[status(thm)],[878940,theory(equality)]) ).
cnf(878942,plain,
$false,
878941,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM494+3 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04 % Command : Source/sine.py -e eprover -t %d %s
% 0.02/0.23 % Computer : n098.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Jan 5 06:46:30 CST 2018
% 0.02/0.23 % CPUTime :
% 0.07/0.27 % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.27 --creating new selector for []
% 25.15/25.45 -running prover on /export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1 with time limit 29
% 25.15/25.45 -running prover with command ['/export/starexec/sandbox2/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox2/tmp/tmp4gDBsu/sel_theBenchmark.p_1']
% 25.15/25.45 -prover status Theorem
% 25.15/25.45 Problem theBenchmark.p solved in phase 0.
% 25.15/25.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.15/25.45 % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.15/25.45 Solved 1 out of 1.
% 25.15/25.45 # Problem is unsatisfiable (or provable), constructing proof object
% 25.15/25.45 # SZS status Theorem
% 25.15/25.45 # SZS output start CNFRefutation.
% See solution above
% 25.15/25.46 # SZS output end CNFRefutation
%------------------------------------------------------------------------------