TSTP Solution File: NUM510+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM510+1 : TPTP v7.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n134.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 15:21:36 EST 2018
% Result : Theorem 6.10s
% Output : CNFRefutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 24
% Syntax : Number of formulae : 280 ( 35 unt; 0 def)
% Number of atoms : 1185 ( 294 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 1522 ( 617 ~; 773 |; 104 &)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 327 ( 1 sgn 137 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
~ ( equal(xk,sz00)
| equal(xk,sz10) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',m__2315) ).
fof(2,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtasdt0(X1,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',m_MulZero) ).
fof(3,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',m__1860) ).
fof(5,axiom,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',m__2342) ).
fof(9,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/tmpxWIlbr/sel_theBenchmark.p_1',mMulCanc) ).
fof(10,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',m__2487) ).
fof(14,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(X2,sdtasdt0(X1,X3)) ) ) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',mDefDiv) ).
fof(19,axiom,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',m__1870) ).
fof(20,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& ~ equal(X2,sz00) )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',mDivLE) ).
fof(22,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',m__1837) ).
fof(28,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',mDefLE) ).
fof(31,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( ~ equal(X1,sz00)
& doDivides0(X1,X2) )
=> ! [X3] :
( equal(X3,sdtsldt0(X2,X1))
<=> ( aNaturalNumber0(X3)
& equal(X2,sdtasdt0(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',mDefQuot) ).
fof(33,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ~ equal(X1,sz00)
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',mMonMul2) ).
fof(34,axiom,
( aNaturalNumber0(sz10)
& ~ equal(sz10,sz00) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',mSortsC_01) ).
fof(35,conjecture,
( ~ equal(sdtsldt0(xn,xr),xn)
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',m__) ).
fof(36,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/tmpxWIlbr/sel_theBenchmark.p_1',mMulAsso) ).
fof(37,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( equal(sdtpldt0(X1,X2),sz00)
=> ( equal(X1,sz00)
& equal(X2,sz00) ) ) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',mZeroAdd) ).
fof(40,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',mSortsB_02) ).
fof(41,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/tmpxWIlbr/sel_theBenchmark.p_1',mDefPrime) ).
fof(42,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',mSortsC) ).
fof(47,axiom,
equal(xk,sdtsldt0(sdtasdt0(xn,xm),xp)),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',m__2306) ).
fof(48,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',mMulComm) ).
fof(50,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( ~ equal(X1,sz00)
& doDivides0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> equal(sdtasdt0(X3,sdtsldt0(X2,X1)),sdtsldt0(sdtasdt0(X3,X2),X1)) ) ) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',mDivAsso) ).
fof(53,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1',m_MulUnit) ).
fof(54,negated_conjecture,
~ ( ~ equal(sdtsldt0(xn,xr),xn)
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(assume_negation,[status(cth)],[35]) ).
fof(55,plain,
~ sdtlseqdt0(xp,xn),
inference(fof_simplification,[status(thm)],[19,theory(equality)]) ).
fof(57,plain,
( ~ equal(xk,sz00)
& ~ equal(xk,sz10) ),
inference(fof_nnf,[status(thm)],[1]) ).
cnf(59,plain,
xk != sz00,
inference(split_conjunct,[status(thm)],[57]) ).
fof(60,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtasdt0(X1,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X1)) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(61,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtasdt0(X2,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X2)) ) ),
inference(variable_rename,[status(thm)],[60]) ).
fof(62,plain,
! [X2] :
( ( equal(sdtasdt0(X2,sz00),sz00)
| ~ aNaturalNumber0(X2) )
& ( equal(sz00,sdtasdt0(sz00,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[61]) ).
cnf(63,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(64,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(65,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[3]) ).
cnf(66,plain,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[3]) ).
cnf(68,plain,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[5]) ).
cnf(70,plain,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[5]) ).
fof(80,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)],[9]) ).
fof(81,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)],[80]) ).
fof(82,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)],[81]) ).
fof(83,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)],[82]) ).
cnf(84,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X3,X1) != sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[83]) ).
cnf(86,plain,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[10]) ).
fof(97,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)],[14]) ).
fof(98,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)],[97]) ).
fof(99,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk1_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk1_2(X4,X5))) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7)) )
| doDivides0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[98]) ).
fof(100,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5) )
& ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk1_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk1_2(X4,X5))) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[99]) ).
fof(101,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk1_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(X5,sdtasdt0(X4,esk1_2(X4,X5)))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[100]) ).
cnf(102,plain,
( X1 = sdtasdt0(X2,esk1_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[101]) ).
cnf(103,plain,
( aNaturalNumber0(esk1_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[101]) ).
cnf(104,plain,
( doDivides0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[101]) ).
cnf(119,plain,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[55]) ).
fof(120,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2)
| equal(X2,sz00)
| sdtlseqdt0(X1,X2) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(121,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ doDivides0(X3,X4)
| equal(X4,sz00)
| sdtlseqdt0(X3,X4) ),
inference(variable_rename,[status(thm)],[120]) ).
cnf(122,plain,
( sdtlseqdt0(X1,X2)
| X2 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[121]) ).
cnf(127,plain,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(128,plain,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(129,plain,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[22]) ).
fof(153,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)],[28]) ).
fof(154,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)],[153]) ).
fof(155,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk2_2(X4,X5))
& equal(sdtpldt0(X4,esk2_2(X4,X5)),X5) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5) )
| sdtlseqdt0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[154]) ).
fof(156,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5) )
& ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk2_2(X4,X5))
& equal(sdtpldt0(X4,esk2_2(X4,X5)),X5) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[155]) ).
fof(157,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk2_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(sdtpldt0(X4,esk2_2(X4,X5)),X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[156]) ).
cnf(158,plain,
( sdtpldt0(X2,esk2_2(X2,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(159,plain,
( aNaturalNumber0(esk2_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[157]) ).
fof(167,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(X1,sz00)
| ~ doDivides0(X1,X2)
| ! [X3] :
( ( ~ equal(X3,sdtsldt0(X2,X1))
| ( aNaturalNumber0(X3)
& equal(X2,sdtasdt0(X1,X3)) ) )
& ( ~ aNaturalNumber0(X3)
| ~ equal(X2,sdtasdt0(X1,X3))
| equal(X3,sdtsldt0(X2,X1)) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(168,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ! [X6] :
( ( ~ equal(X6,sdtsldt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(X5,sdtasdt0(X4,X6)) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(X5,sdtasdt0(X4,X6))
| equal(X6,sdtsldt0(X5,X4)) ) ) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,plain,
! [X4,X5,X6] :
( ( ( ~ equal(X6,sdtsldt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(X5,sdtasdt0(X4,X6)) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(X5,sdtasdt0(X4,X6))
| equal(X6,sdtsldt0(X5,X4)) ) )
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[168]) ).
fof(170,plain,
! [X4,X5,X6] :
( ( aNaturalNumber0(X6)
| ~ equal(X6,sdtsldt0(X5,X4))
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(X5,sdtasdt0(X4,X6))
| ~ equal(X6,sdtsldt0(X5,X4))
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(X5,sdtasdt0(X4,X6))
| equal(X6,sdtsldt0(X5,X4))
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[169]) ).
cnf(171,plain,
( X2 = sz00
| X3 = sdtsldt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(172,plain,
( X2 = sz00
| X1 = sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(173,plain,
( X2 = sz00
| aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[170]) ).
fof(179,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(X1,sz00)
| sdtlseqdt0(X2,sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(180,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(X3,sz00)
| sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[179]) ).
cnf(181,plain,
( sdtlseqdt0(X1,sdtasdt0(X1,X2))
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[180]) ).
cnf(182,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[34]) ).
cnf(183,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[34]) ).
fof(184,negated_conjecture,
( equal(sdtsldt0(xn,xr),xn)
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(fof_nnf,[status(thm)],[54]) ).
cnf(185,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(split_conjunct,[status(thm)],[184]) ).
fof(186,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)],[36]) ).
fof(187,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)],[186]) ).
cnf(188,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[187]) ).
fof(189,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ equal(sdtpldt0(X1,X2),sz00)
| ( equal(X1,sz00)
& equal(X2,sz00) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(190,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ equal(sdtpldt0(X3,X4),sz00)
| ( equal(X3,sz00)
& equal(X4,sz00) ) ),
inference(variable_rename,[status(thm)],[189]) ).
fof(191,plain,
! [X3,X4] :
( ( equal(X3,sz00)
| ~ equal(sdtpldt0(X3,X4),sz00)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) )
& ( equal(X4,sz00)
| ~ equal(sdtpldt0(X3,X4),sz00)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) ) ),
inference(distribute,[status(thm)],[190]) ).
cnf(193,plain,
( X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != sz00 ),
inference(split_conjunct,[status(thm)],[191]) ).
fof(204,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[40]) ).
fof(205,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[204]) ).
cnf(206,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[205]) ).
fof(207,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)],[41]) ).
fof(208,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)],[207]) ).
fof(209,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(esk3_1(X3))
& doDivides0(esk3_1(X3),X3)
& ~ equal(esk3_1(X3),sz10)
& ~ equal(esk3_1(X3),X3) )
| isPrime0(X3) ) ) ),
inference(skolemize,[status(esa)],[208]) ).
fof(210,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(esk3_1(X3))
& doDivides0(esk3_1(X3),X3)
& ~ equal(esk3_1(X3),sz10)
& ~ equal(esk3_1(X3),X3) )
| isPrime0(X3) ) )
| ~ aNaturalNumber0(X3) ),
inference(shift_quantors,[status(thm)],[209]) ).
fof(211,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(esk3_1(X3))
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( doDivides0(esk3_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk3_1(X3),sz10)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk3_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) ) ),
inference(distribute,[status(thm)],[210]) ).
cnf(216,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[211]) ).
cnf(217,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[211]) ).
cnf(219,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(238,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[47]) ).
fof(239,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[48]) ).
fof(240,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(sdtasdt0(X3,X4),sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[239]) ).
cnf(241,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[240]) ).
fof(243,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(X1,sz00)
| ~ doDivides0(X1,X2)
| ! [X3] :
( ~ aNaturalNumber0(X3)
| equal(sdtasdt0(X3,sdtsldt0(X2,X1)),sdtsldt0(sdtasdt0(X3,X2),X1)) ) ),
inference(fof_nnf,[status(thm)],[50]) ).
fof(244,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ! [X6] :
( ~ aNaturalNumber0(X6)
| equal(sdtasdt0(X6,sdtsldt0(X5,X4)),sdtsldt0(sdtasdt0(X6,X5),X4)) ) ),
inference(variable_rename,[status(thm)],[243]) ).
fof(245,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X6)
| equal(sdtasdt0(X6,sdtsldt0(X5,X4)),sdtsldt0(sdtasdt0(X6,X5),X4))
| equal(X4,sz00)
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[244]) ).
cnf(246,plain,
( X2 = sz00
| sdtasdt0(X3,sdtsldt0(X1,X2)) = sdtsldt0(sdtasdt0(X3,X1),X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[245]) ).
fof(254,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
inference(fof_nnf,[status(thm)],[53]) ).
fof(255,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtasdt0(X2,sz10),X2)
& equal(X2,sdtasdt0(sz10,X2)) ) ),
inference(variable_rename,[status(thm)],[254]) ).
fof(256,plain,
! [X2] :
( ( equal(sdtasdt0(X2,sz10),X2)
| ~ aNaturalNumber0(X2) )
& ( equal(X2,sdtasdt0(sz10,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[255]) ).
cnf(257,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[256]) ).
cnf(258,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[256]) ).
cnf(259,plain,
( sz00 != xr
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[217,68,theory(equality)]) ).
cnf(260,plain,
( sz00 != xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[217,66,theory(equality)]) ).
cnf(261,plain,
( sz00 != xr
| $false ),
inference(rw,[status(thm)],[259,70,theory(equality)]) ).
cnf(262,plain,
sz00 != xr,
inference(cn,[status(thm)],[261,theory(equality)]) ).
cnf(263,plain,
( sz00 != xp
| $false ),
inference(rw,[status(thm)],[260,127,theory(equality)]) ).
cnf(264,plain,
sz00 != xp,
inference(cn,[status(thm)],[263,theory(equality)]) ).
cnf(266,plain,
( sz10 != xr
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[216,68,theory(equality)]) ).
cnf(268,plain,
( sz10 != xr
| $false ),
inference(rw,[status(thm)],[266,70,theory(equality)]) ).
cnf(269,plain,
sz10 != xr,
inference(cn,[status(thm)],[268,theory(equality)]) ).
cnf(379,plain,
( sz00 = X1
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[181,241,theory(equality)]) ).
cnf(392,plain,
( sz00 = sdtasdt0(xn,xm)
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[122,65,theory(equality)]) ).
cnf(402,plain,
( sz00 = sdtasdt0(xn,xm)
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| $false ),
inference(rw,[status(thm)],[392,127,theory(equality)]) ).
cnf(403,plain,
( sz00 = sdtasdt0(xn,xm)
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[402,theory(equality)]) ).
cnf(450,plain,
( sz00 = X1
| X2 != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk2_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[193,158,theory(equality)]) ).
cnf(469,plain,
( X1 = sz00
| ~ aNaturalNumber0(esk1_2(sz00,X1))
| ~ doDivides0(sz00,X1)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[63,102,theory(equality)]) ).
cnf(471,plain,
( sz00 = esk1_2(X1,X2)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(esk1_2(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[181,102,theory(equality)]) ).
cnf(475,plain,
( X1 = sz00
| ~ aNaturalNumber0(esk1_2(sz00,X1))
| ~ doDivides0(sz00,X1)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[469,219,theory(equality)]) ).
cnf(476,plain,
( X1 = sz00
| ~ aNaturalNumber0(esk1_2(sz00,X1))
| ~ doDivides0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[475,theory(equality)]) ).
cnf(477,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(er,[status(thm)],[104,theory(equality)]) ).
cnf(479,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[104,257,theory(equality)]) ).
cnf(488,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[479,183,theory(equality)]) ).
cnf(489,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[488,theory(equality)]) ).
cnf(490,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[489,theory(equality)]) ).
cnf(497,plain,
( sz00 = X1
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[173,theory(equality)]) ).
cnf(498,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xk != X1
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spm,[status(thm)],[173,238,theory(equality)]) ).
cnf(499,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xk != X1
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(rw,[status(thm)],[498,65,theory(equality)]) ).
cnf(500,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xk != X1
| $false
| $false
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(rw,[status(thm)],[499,127,theory(equality)]) ).
cnf(501,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xk != X1
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[500,theory(equality)]) ).
cnf(571,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| sz00 = X1
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[172,theory(equality)]) ).
cnf(572,plain,
( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
| sz00 = xp
| xk != X1
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spm,[status(thm)],[172,238,theory(equality)]) ).
cnf(573,plain,
( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
| sz00 = xp
| xk != X1
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(rw,[status(thm)],[572,65,theory(equality)]) ).
cnf(574,plain,
( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
| sz00 = xp
| xk != X1
| $false
| $false
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(rw,[status(thm)],[573,127,theory(equality)]) ).
cnf(575,plain,
( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
| sz00 = xp
| xk != X1
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[574,theory(equality)]) ).
cnf(579,plain,
( sz00 = X1
| sz10 = X2
| X1 != sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[84,257,theory(equality)]) ).
cnf(595,plain,
( sz00 = X1
| sz10 = X2
| X1 != sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[579,183,theory(equality)]) ).
cnf(596,plain,
( sz00 = X1
| sz10 = X2
| X1 != sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[595,theory(equality)]) ).
cnf(634,plain,
( sdtasdt0(sz00,X2) = sdtasdt0(X1,sdtasdt0(sz00,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[188,64,theory(equality)]) ).
cnf(660,plain,
( sdtasdt0(sz00,X2) = sdtasdt0(X1,sdtasdt0(sz00,X2))
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[634,219,theory(equality)]) ).
cnf(661,plain,
( sdtasdt0(sz00,X2) = sdtasdt0(X1,sdtasdt0(sz00,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[660,theory(equality)]) ).
cnf(664,plain,
( sdtsldt0(X1,X2) = X3
| sz00 = X2
| sdtasdt0(X2,X3) != X1
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[171,104]) ).
cnf(665,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| sz00 = X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(er,[status(thm)],[664,theory(equality)]) ).
cnf(666,plain,
( sdtsldt0(X1,X2) = sz10
| sz00 = X2
| X2 != X1
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[664,258,theory(equality)]) ).
cnf(667,plain,
( sdtsldt0(X1,sz10) = X2
| sz00 = sz10
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[664,257,theory(equality)]) ).
cnf(668,plain,
( sdtsldt0(X1,X2) = sz00
| sz00 = X2
| sz00 != X1
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[664,64,theory(equality)]) ).
cnf(673,plain,
( sdtsldt0(X1,X2) = sz10
| sz00 = X2
| X2 != X1
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[666,183,theory(equality)]) ).
cnf(674,plain,
( sdtsldt0(X1,X2) = sz10
| sz00 = X2
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[673,theory(equality)]) ).
cnf(675,plain,
( sdtsldt0(X1,X1) = sz10
| sz00 = X1
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[674,theory(equality)]) ).
cnf(676,plain,
( sdtsldt0(X1,sz10) = X2
| sz00 = sz10
| X2 != X1
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[667,183,theory(equality)]) ).
cnf(677,plain,
( sdtsldt0(X1,sz10) = X2
| sz00 = sz10
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[676,theory(equality)]) ).
cnf(678,plain,
( sdtsldt0(X1,sz10) = X2
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[677,182,theory(equality)]) ).
cnf(679,plain,
( sdtsldt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[678,theory(equality)]) ).
cnf(680,plain,
( sdtsldt0(X1,X2) = sz00
| sz00 = X2
| sz00 != X1
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[668,219,theory(equality)]) ).
cnf(681,plain,
( sdtsldt0(X1,X2) = sz00
| sz00 = X2
| sz00 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[680,theory(equality)]) ).
cnf(1019,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X1,sdtsldt0(X2,sz10))
| sz00 = sz10
| ~ doDivides0(sz10,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(spm,[status(thm)],[246,679,theory(equality)]) ).
cnf(1028,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X1,sdtsldt0(X2,sz10))
| sz00 = sz10
| ~ doDivides0(sz10,X2)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(rw,[status(thm)],[1019,183,theory(equality)]) ).
cnf(1029,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X1,sdtsldt0(X2,sz10))
| sz00 = sz10
| ~ doDivides0(sz10,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(cn,[status(thm)],[1028,theory(equality)]) ).
cnf(1030,plain,
( sdtasdt0(X1,sdtsldt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ doDivides0(sz10,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(sr,[status(thm)],[1029,182,theory(equality)]) ).
cnf(1374,plain,
( sdtasdt0(X1,sdtsldt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ doDivides0(sz10,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[1030,206]) ).
cnf(1375,plain,
( sdtasdt0(X1,sdtsldt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[1374,490]) ).
cnf(1379,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sdtsldt0(X2,sz10),X1)
| ~ aNaturalNumber0(sdtsldt0(X2,sz10))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[241,1375,theory(equality)]) ).
cnf(3427,plain,
( sz00 = X1
| X2 != sz00
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[450,159]) ).
cnf(4000,plain,
( X1 = sz00
| ~ doDivides0(sz00,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[476,103,theory(equality)]) ).
cnf(4001,plain,
( X1 = sz00
| ~ doDivides0(sz00,X1)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[4000,219,theory(equality)]) ).
cnf(4002,plain,
( X1 = sz00
| ~ doDivides0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[4001,theory(equality)]) ).
cnf(4116,plain,
( esk1_2(X1,X2) = sz00
| sdtlseqdt0(X1,X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[471,103]) ).
cnf(4118,plain,
( sdtasdt0(X1,sz00) = X2
| sdtlseqdt0(X1,X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[102,4116,theory(equality)]) ).
cnf(4237,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[477,206]) ).
cnf(4242,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[4237,241,theory(equality)]) ).
cnf(4924,plain,
( aNaturalNumber0(X1)
| xk != X1
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(sr,[status(thm)],[501,264,theory(equality)]) ).
cnf(4925,plain,
( aNaturalNumber0(X1)
| xk != X1
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[4924,206,theory(equality)]) ).
cnf(4926,plain,
( aNaturalNumber0(X1)
| xk != X1
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[4925,128,theory(equality)]) ).
cnf(4927,plain,
( aNaturalNumber0(X1)
| xk != X1
| $false
| $false ),
inference(rw,[status(thm)],[4926,129,theory(equality)]) ).
cnf(4928,plain,
( aNaturalNumber0(X1)
| xk != X1 ),
inference(cn,[status(thm)],[4927,theory(equality)]) ).
cnf(6199,plain,
( sdtasdt0(sz10,X1) = sdtasdt0(X1,sz10)
| sz00 = sz10
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[1379,675,theory(equality)]) ).
cnf(6204,plain,
( sdtasdt0(sz10,X1) = sdtasdt0(X1,sz10)
| sz00 = sz10
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[6199,183,theory(equality)]) ).
cnf(6205,plain,
( sdtasdt0(sz10,X1) = sdtasdt0(X1,sz10)
| sz00 = sz10
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[6204,theory(equality)]) ).
cnf(6206,plain,
( sdtasdt0(sz10,X1) = sdtasdt0(X1,sz10)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[6205,182,theory(equality)]) ).
cnf(6479,plain,
( sdtasdt0(sz00,sz10) = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[64,6206,theory(equality)]) ).
cnf(6539,plain,
( doDivides0(X1,sdtasdt0(sz10,X1))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[4237,6206,theory(equality)]) ).
cnf(6556,plain,
( sdtasdt0(sz00,sz10) = sz00
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[6479,183,theory(equality)]) ).
cnf(6557,plain,
( sdtasdt0(sz00,sz10) = sz00
| $false
| $false ),
inference(rw,[status(thm)],[6556,219,theory(equality)]) ).
cnf(6558,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[6557,theory(equality)]) ).
cnf(6686,plain,
( doDivides0(X1,sdtasdt0(sz10,X1))
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[6539,183,theory(equality)]) ).
cnf(6687,plain,
( doDivides0(X1,sdtasdt0(sz10,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[6686,theory(equality)]) ).
cnf(6759,plain,
( doDivides0(sz10,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[4242,6558,theory(equality)]) ).
cnf(6821,plain,
( doDivides0(sz10,sz00)
| $false
| ~ aNaturalNumber0(sz10) ),
inference(rw,[status(thm)],[6759,219,theory(equality)]) ).
cnf(6822,plain,
( doDivides0(sz10,sz00)
| $false
| $false ),
inference(rw,[status(thm)],[6821,183,theory(equality)]) ).
cnf(6823,plain,
doDivides0(sz10,sz00),
inference(cn,[status(thm)],[6822,theory(equality)]) ).
cnf(7165,plain,
( sz00 = X1
| sdtlseqdt0(sdtsldt0(X2,X1),X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[379,571,theory(equality)]) ).
cnf(7256,plain,
( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
| xk != X1
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(sr,[status(thm)],[575,264,theory(equality)]) ).
cnf(7257,plain,
( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
| xk != X1
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[7256,206,theory(equality)]) ).
cnf(7259,plain,
( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
| xk != X1
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[7257,128,theory(equality)]) ).
cnf(7260,plain,
( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
| xk != X1
| $false
| $false ),
inference(rw,[status(thm)],[7259,129,theory(equality)]) ).
cnf(7261,plain,
( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
| xk != X1 ),
inference(cn,[status(thm)],[7260,theory(equality)]) ).
cnf(7310,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aNaturalNumber0(sdtasdt0(sz10,sz00))
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[4002,6687,theory(equality)]) ).
cnf(7332,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aNaturalNumber0(sdtasdt0(sz10,sz00))
| $false ),
inference(rw,[status(thm)],[7310,219,theory(equality)]) ).
cnf(7333,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aNaturalNumber0(sdtasdt0(sz10,sz00)) ),
inference(cn,[status(thm)],[7332,theory(equality)]) ).
cnf(8067,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| xk != X1 ),
inference(spm,[status(thm)],[206,7261,theory(equality)]) ).
cnf(8114,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X1)
| $false
| xk != X1 ),
inference(rw,[status(thm)],[8067,127,theory(equality)]) ).
cnf(8115,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X1)
| xk != X1 ),
inference(cn,[status(thm)],[8114,theory(equality)]) ).
cnf(8875,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[7333,206,theory(equality)]) ).
cnf(8882,plain,
( sdtasdt0(sz10,sz00) = sz00
| $false
| ~ aNaturalNumber0(sz10) ),
inference(rw,[status(thm)],[8875,219,theory(equality)]) ).
cnf(8883,plain,
( sdtasdt0(sz10,sz00) = sz00
| $false
| $false ),
inference(rw,[status(thm)],[8882,183,theory(equality)]) ).
cnf(8884,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[8883,theory(equality)]) ).
cnf(9066,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| xk != X1 ),
inference(csr,[status(thm)],[8115,4928]) ).
cnf(9067,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(er,[status(thm)],[9066,theory(equality)]) ).
cnf(9183,plain,
( sdtasdt0(xn,xm) = sz00
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| $false ),
inference(rw,[status(thm)],[403,9067,theory(equality)]) ).
cnf(9184,plain,
( sdtasdt0(xn,xm) = sz00
| sdtlseqdt0(xp,sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[9183,theory(equality)]) ).
cnf(13066,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| sz00 = X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[665,206]) ).
cnf(13068,plain,
( sdtsldt0(sz00,sz10) = sz00
| sz00 = sz10
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[13066,8884,theory(equality)]) ).
cnf(13108,plain,
( sdtsldt0(sz00,sz10) = sz00
| sz00 = sz10
| $false
| ~ aNaturalNumber0(sz10) ),
inference(rw,[status(thm)],[13068,219,theory(equality)]) ).
cnf(13109,plain,
( sdtsldt0(sz00,sz10) = sz00
| sz00 = sz10
| $false
| $false ),
inference(rw,[status(thm)],[13108,183,theory(equality)]) ).
cnf(13110,plain,
( sdtsldt0(sz00,sz10) = sz00
| sz00 = sz10 ),
inference(cn,[status(thm)],[13109,theory(equality)]) ).
cnf(13111,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(sr,[status(thm)],[13110,182,theory(equality)]) ).
cnf(13210,plain,
( sz00 = sz10
| aNaturalNumber0(X1)
| sz00 != X1
| ~ doDivides0(sz10,sz00)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[173,13111,theory(equality)]) ).
cnf(13217,plain,
( sz00 = sz10
| aNaturalNumber0(X1)
| sz00 != X1
| $false
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[13210,6823,theory(equality)]) ).
cnf(13218,plain,
( sz00 = sz10
| aNaturalNumber0(X1)
| sz00 != X1
| $false
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[13217,183,theory(equality)]) ).
cnf(13219,plain,
( sz00 = sz10
| aNaturalNumber0(X1)
| sz00 != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[13218,219,theory(equality)]) ).
cnf(13220,plain,
( sz00 = sz10
| aNaturalNumber0(X1)
| sz00 != X1 ),
inference(cn,[status(thm)],[13219,theory(equality)]) ).
cnf(13221,plain,
( aNaturalNumber0(X1)
| sz00 != X1 ),
inference(sr,[status(thm)],[13220,182,theory(equality)]) ).
cnf(13265,plain,
( sdtsldt0(X1,X2) = sz00
| sz00 = X2
| sz00 != X1
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[681,13221]) ).
cnf(13266,plain,
( sz00 = xk
| sz00 = xp
| sz00 != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[238,13265,theory(equality)]) ).
cnf(13281,plain,
( sz00 = xk
| sz00 = xp
| sz00 != sdtasdt0(xn,xm)
| $false ),
inference(rw,[status(thm)],[13266,127,theory(equality)]) ).
cnf(13282,plain,
( sz00 = xk
| sz00 = xp
| sz00 != sdtasdt0(xn,xm) ),
inference(cn,[status(thm)],[13281,theory(equality)]) ).
cnf(13283,plain,
( xp = sz00
| sdtasdt0(xn,xm) != sz00 ),
inference(sr,[status(thm)],[13282,59,theory(equality)]) ).
cnf(13284,plain,
sdtasdt0(xn,xm) != sz00,
inference(sr,[status(thm)],[13283,264,theory(equality)]) ).
cnf(13306,plain,
sdtlseqdt0(xp,sdtasdt0(xn,xm)),
inference(sr,[status(thm)],[9184,13284,theory(equality)]) ).
cnf(182259,plain,
( sdtasdt0(xr,sz00) = xn
| sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[4118,86,theory(equality)]) ).
cnf(182313,plain,
( sdtasdt0(xr,sz00) = xn
| sdtlseqdt0(xr,xn)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[182259,70,theory(equality)]) ).
cnf(182314,plain,
( sdtasdt0(xr,sz00) = xn
| sdtlseqdt0(xr,xn)
| $false
| $false ),
inference(rw,[status(thm)],[182313,129,theory(equality)]) ).
cnf(182315,plain,
( sdtasdt0(xr,sz00) = xn
| sdtlseqdt0(xr,xn) ),
inference(cn,[status(thm)],[182314,theory(equality)]) ).
cnf(182451,plain,
( sz00 = xr
| sdtasdt0(xr,sz00) = xn
| xn != sz00
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[3427,182315,theory(equality)]) ).
cnf(182510,plain,
( sz00 = xr
| sdtasdt0(xr,sz00) = xn
| xn != sz00
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[182451,70,theory(equality)]) ).
cnf(182511,plain,
( sz00 = xr
| sdtasdt0(xr,sz00) = xn
| xn != sz00
| $false
| $false ),
inference(rw,[status(thm)],[182510,129,theory(equality)]) ).
cnf(182512,plain,
( sz00 = xr
| sdtasdt0(xr,sz00) = xn
| xn != sz00 ),
inference(cn,[status(thm)],[182511,theory(equality)]) ).
cnf(182513,plain,
( sdtasdt0(xr,sz00) = xn
| xn != sz00 ),
inference(sr,[status(thm)],[182512,262,theory(equality)]) ).
cnf(183020,plain,
( xn = sdtasdt0(sz00,xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr)
| xn != sz00 ),
inference(spm,[status(thm)],[241,182513,theory(equality)]) ).
cnf(183159,plain,
( xn = sdtasdt0(sz00,xr)
| $false
| ~ aNaturalNumber0(xr)
| xn != sz00 ),
inference(rw,[status(thm)],[183020,219,theory(equality)]) ).
cnf(183160,plain,
( xn = sdtasdt0(sz00,xr)
| $false
| $false
| xn != sz00 ),
inference(rw,[status(thm)],[183159,70,theory(equality)]) ).
cnf(183161,plain,
( xn = sdtasdt0(sz00,xr)
| xn != sz00 ),
inference(cn,[status(thm)],[183160,theory(equality)]) ).
cnf(185569,plain,
( sdtasdt0(X1,xn) = xn
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X1)
| xn != sz00 ),
inference(spm,[status(thm)],[661,183161,theory(equality)]) ).
cnf(185770,plain,
( sdtasdt0(X1,xn) = xn
| $false
| ~ aNaturalNumber0(X1)
| xn != sz00 ),
inference(rw,[status(thm)],[185569,70,theory(equality)]) ).
cnf(185771,plain,
( sdtasdt0(X1,xn) = xn
| ~ aNaturalNumber0(X1)
| xn != sz00 ),
inference(cn,[status(thm)],[185770,theory(equality)]) ).
cnf(196134,plain,
( xn = sdtasdt0(xn,X1)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1)
| xn != sz00 ),
inference(spm,[status(thm)],[241,185771,theory(equality)]) ).
cnf(196417,plain,
( xn = sdtasdt0(xn,X1)
| $false
| ~ aNaturalNumber0(X1)
| xn != sz00 ),
inference(rw,[status(thm)],[196134,129,theory(equality)]) ).
cnf(196418,plain,
( xn = sdtasdt0(xn,X1)
| ~ aNaturalNumber0(X1)
| xn != sz00 ),
inference(cn,[status(thm)],[196417,theory(equality)]) ).
cnf(198008,plain,
( sdtlseqdt0(xp,xn)
| xn != sz00
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[13306,196418,theory(equality)]) ).
cnf(198366,plain,
( sdtlseqdt0(xp,xn)
| xn != sz00
| $false ),
inference(rw,[status(thm)],[198008,128,theory(equality)]) ).
cnf(198367,plain,
( sdtlseqdt0(xp,xn)
| xn != sz00 ),
inference(cn,[status(thm)],[198366,theory(equality)]) ).
cnf(198368,plain,
xn != sz00,
inference(sr,[status(thm)],[198367,119,theory(equality)]) ).
cnf(307303,plain,
( sz00 = X1
| sdtlseqdt0(sdtsldt0(X2,X1),X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[7165,497]) ).
cnf(307314,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| sz00 = xr
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[185,307303,theory(equality)]) ).
cnf(307506,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| sz00 = xr
| $false
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[307314,86,theory(equality)]) ).
cnf(307507,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| sz00 = xr
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[307506,70,theory(equality)]) ).
cnf(307508,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| sz00 = xr
| $false
| $false
| $false ),
inference(rw,[status(thm)],[307507,129,theory(equality)]) ).
cnf(307509,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| sz00 = xr ),
inference(cn,[status(thm)],[307508,theory(equality)]) ).
cnf(307510,negated_conjecture,
sdtsldt0(xn,xr) = xn,
inference(sr,[status(thm)],[307509,262,theory(equality)]) ).
cnf(307686,negated_conjecture,
( sdtasdt0(xr,xn) = xn
| sz00 = xr
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[571,307510,theory(equality)]) ).
cnf(307790,negated_conjecture,
( sdtasdt0(xr,xn) = xn
| sz00 = xr
| $false
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[307686,86,theory(equality)]) ).
cnf(307791,negated_conjecture,
( sdtasdt0(xr,xn) = xn
| sz00 = xr
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[307790,70,theory(equality)]) ).
cnf(307792,negated_conjecture,
( sdtasdt0(xr,xn) = xn
| sz00 = xr
| $false
| $false
| $false ),
inference(rw,[status(thm)],[307791,129,theory(equality)]) ).
cnf(307793,negated_conjecture,
( sdtasdt0(xr,xn) = xn
| sz00 = xr ),
inference(cn,[status(thm)],[307792,theory(equality)]) ).
cnf(307794,negated_conjecture,
sdtasdt0(xr,xn) = xn,
inference(sr,[status(thm)],[307793,262,theory(equality)]) ).
cnf(307970,negated_conjecture,
( sz10 = xr
| sz00 = xn
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[596,307794,theory(equality)]) ).
cnf(308242,negated_conjecture,
( sz10 = xr
| sz00 = xn
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[307970,70,theory(equality)]) ).
cnf(308243,negated_conjecture,
( sz10 = xr
| sz00 = xn
| $false
| $false ),
inference(rw,[status(thm)],[308242,129,theory(equality)]) ).
cnf(308244,negated_conjecture,
( sz10 = xr
| sz00 = xn ),
inference(cn,[status(thm)],[308243,theory(equality)]) ).
cnf(308245,negated_conjecture,
xn = sz00,
inference(sr,[status(thm)],[308244,269,theory(equality)]) ).
cnf(308246,negated_conjecture,
$false,
inference(sr,[status(thm)],[308245,198368,theory(equality)]) ).
cnf(308247,negated_conjecture,
$false,
308246,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM510+1 : 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 : n134.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 06:24:01 CST 2018
% 0.02/0.24 % CPUTime :
% 0.02/0.28 % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.28 --creating new selector for []
% 6.10/6.34 -running prover on /export/starexec/sandbox/tmp/tmpxWIlbr/sel_theBenchmark.p_1 with time limit 29
% 6.10/6.34 -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/tmpxWIlbr/sel_theBenchmark.p_1']
% 6.10/6.34 -prover status Theorem
% 6.10/6.34 Problem theBenchmark.p solved in phase 0.
% 6.10/6.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.10/6.34 % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.10/6.34 Solved 1 out of 1.
% 6.10/6.34 # Problem is unsatisfiable (or provable), constructing proof object
% 6.10/6.34 # SZS status Theorem
% 6.10/6.34 # SZS output start CNFRefutation.
% See solution above
% 6.10/6.34 # SZS output end CNFRefutation
%------------------------------------------------------------------------------