%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM511+3 : TPTP v7.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n071.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 4.32s
% Output : CNFRefutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 24
% Syntax : Number of formulae : 335 ( 61 unt; 0 def)
% Number of atoms : 1426 ( 278 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 1707 ( 616 ~; 798 |; 261 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 13 con; 0-2 aty)
% Number of variables : 325 ( 0 sgn 170 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
~ ( equal(xk,sz00)
| equal(xk,sz10) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',m__2315) ).
fof(3,axiom,
( ~ equal(xp,sz00)
& ~ equal(xp,sz10)
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& equal(xp,sdtasdt0(X1,X2)) )
| doDivides0(X1,xp) ) )
=> ( equal(X1,sz10)
| equal(X1,xp) ) )
& isPrime0(xp)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtasdt0(xn,xm),sdtasdt0(xp,X1)) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',m__1860) ).
fof(5,axiom,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(xk,sdtasdt0(xr,X1)) )
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& equal(xr,sdtasdt0(X1,X2)) )
| doDivides0(X1,xr) ) )
=> ( equal(X1,sz10)
| equal(X1,xr) ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',m__2342) ).
fof(6,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X2,X3) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',mDivTrans) ).
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/tmppGpgcC/sel_theBenchmark.p_1',mMulCanc) ).
fof(10,axiom,
( ? [X1] :
( aNaturalNumber0(X1)
& equal(xn,sdtasdt0(xr,X1)) )
& doDivides0(xr,xn) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',m__2487) ).
fof(13,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( equal(sdtasdt0(X1,sdtpldt0(X2,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
& equal(sdtasdt0(sdtpldt0(X2,X3),X1),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))) ) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',mAMDistr) ).
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/tmppGpgcC/sel_theBenchmark.p_1',mDefDiv) ).
fof(22,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',m__1837) ).
fof(26,axiom,
( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr))) )
=> equal(sdtsldt0(xn,xr),xn) )
& aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr)))
& ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(sdtsldt0(xn,xr),X1),xn) )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',m__2504) ).
fof(29,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',mDefLE) ).
fof(32,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/tmppGpgcC/sel_theBenchmark.p_1',mDefQuot) ).
fof(34,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ~ equal(X1,sz00)
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',mMonMul2) ).
fof(35,axiom,
( aNaturalNumber0(sz10)
& ~ equal(sz10,sz00) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',mSortsC_01) ).
fof(36,conjecture,
( ( aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr))) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,X1)) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',m__) ).
fof(37,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/tmppGpgcC/sel_theBenchmark.p_1',mMulAsso) ).
fof(41,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',mSortsB_02) ).
fof(42,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/tmppGpgcC/sel_theBenchmark.p_1',mDefPrime) ).
fof(45,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& ~ equal(X1,sz00)
& ~ equal(X1,sz10) )
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',mPrimDiv) ).
fof(48,axiom,
( aNaturalNumber0(xk)
& equal(sdtasdt0(xn,xm),sdtasdt0(xp,xk))
& equal(xk,sdtsldt0(sdtasdt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',m__2306) ).
fof(49,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',mMulComm) ).
fof(51,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/tmppGpgcC/sel_theBenchmark.p_1',mDivAsso) ).
fof(53,axiom,
( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(xr,X1),xk) )
& ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtasdt0(xn,xm),sdtasdt0(xr,X1)) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',m__2362) ).
fof(54,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1',m_MulUnit) ).
fof(55,negated_conjecture,
~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr))) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,X1)) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(assume_negation,[status(cth)],[36]) ).
fof(56,plain,
( ~ equal(xk,sz00)
& ~ equal(xk,sz10) ),
inference(fof_nnf,[status(thm)],[1]) ).
cnf(58,plain,
xk != sz00,
inference(split_conjunct,[status(thm)],[56]) ).
fof(64,plain,
( ~ equal(xp,sz00)
& ~ equal(xp,sz10)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ equal(xp,sdtasdt0(X1,X2)) )
& ~ doDivides0(X1,xp) )
| equal(X1,sz10)
| equal(X1,xp) )
& isPrime0(xp)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtasdt0(xn,xm),sdtasdt0(xp,X1)) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(65,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)],[64]) ).
fof(66,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)],[65]) ).
fof(67,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)],[66]) ).
fof(68,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)],[67]) ).
cnf(69,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[68]) ).
cnf(73,plain,
xp != sz10,
inference(split_conjunct,[status(thm)],[68]) ).
cnf(74,plain,
xp != sz00,
inference(split_conjunct,[status(thm)],[68]) ).
cnf(75,plain,
( X1 = xp
| X1 = sz10
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xp) ),
inference(split_conjunct,[status(thm)],[68]) ).
fof(89,plain,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(xk,sdtasdt0(xr,X1)) )
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ equal(xr,sdtasdt0(X1,X2)) )
& ~ doDivides0(X1,xr) )
| equal(X1,sz10)
| equal(X1,xr) )
& isPrime0(xr) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(90,plain,
( aNaturalNumber0(xr)
& ? [X3] :
( aNaturalNumber0(X3)
& equal(xk,sdtasdt0(xr,X3)) )
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& ! [X4] :
( ~ aNaturalNumber0(X4)
| ( ! [X5] :
( ~ aNaturalNumber0(X5)
| ~ equal(xr,sdtasdt0(X4,X5)) )
& ~ doDivides0(X4,xr) )
| equal(X4,sz10)
| equal(X4,xr) )
& isPrime0(xr) ),
inference(variable_rename,[status(thm)],[89]) ).
fof(91,plain,
( aNaturalNumber0(xr)
& aNaturalNumber0(esk4_0)
& equal(xk,sdtasdt0(xr,esk4_0))
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& ! [X4] :
( ~ aNaturalNumber0(X4)
| ( ! [X5] :
( ~ aNaturalNumber0(X5)
| ~ equal(xr,sdtasdt0(X4,X5)) )
& ~ doDivides0(X4,xr) )
| equal(X4,sz10)
| equal(X4,xr) )
& isPrime0(xr) ),
inference(skolemize,[status(esa)],[90]) ).
fof(92,plain,
! [X4,X5] :
( ( ( ( ~ aNaturalNumber0(X5)
| ~ equal(xr,sdtasdt0(X4,X5)) )
& ~ doDivides0(X4,xr) )
| ~ aNaturalNumber0(X4)
| equal(X4,sz10)
| equal(X4,xr) )
& aNaturalNumber0(xr)
& aNaturalNumber0(esk4_0)
& equal(xk,sdtasdt0(xr,esk4_0))
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& isPrime0(xr) ),
inference(shift_quantors,[status(thm)],[91]) ).
fof(93,plain,
! [X4,X5] :
( ( ~ aNaturalNumber0(X5)
| ~ equal(xr,sdtasdt0(X4,X5))
| ~ aNaturalNumber0(X4)
| equal(X4,sz10)
| equal(X4,xr) )
& ( ~ doDivides0(X4,xr)
| ~ aNaturalNumber0(X4)
| equal(X4,sz10)
| equal(X4,xr) )
& aNaturalNumber0(xr)
& aNaturalNumber0(esk4_0)
& equal(xk,sdtasdt0(xr,esk4_0))
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& isPrime0(xr) ),
inference(distribute,[status(thm)],[92]) ).
cnf(96,plain,
xr != sz00,
inference(split_conjunct,[status(thm)],[93]) ).
cnf(97,plain,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[93]) ).
cnf(98,plain,
xk = sdtasdt0(xr,esk4_0),
inference(split_conjunct,[status(thm)],[93]) ).
cnf(99,plain,
aNaturalNumber0(esk4_0),
inference(split_conjunct,[status(thm)],[93]) ).
cnf(100,plain,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[93]) ).
fof(103,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3)
| doDivides0(X1,X3) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(104,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ doDivides0(X4,X5)
| ~ doDivides0(X5,X6)
| doDivides0(X4,X6) ),
inference(variable_rename,[status(thm)],[103]) ).
cnf(105,plain,
( doDivides0(X1,X2)
| ~ doDivides0(X3,X2)
| ~ doDivides0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[104]) ).
fof(112,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(113,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)],[112]) ).
fof(114,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)],[113]) ).
fof(115,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)],[114]) ).
cnf(117,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,X3) != sdtasdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(118,plain,
( ? [X2] :
( aNaturalNumber0(X2)
& equal(xn,sdtasdt0(xr,X2)) )
& doDivides0(xr,xn) ),
inference(variable_rename,[status(thm)],[10]) ).
fof(119,plain,
( aNaturalNumber0(esk5_0)
& equal(xn,sdtasdt0(xr,esk5_0))
& doDivides0(xr,xn) ),
inference(skolemize,[status(esa)],[118]) ).
cnf(120,plain,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[119]) ).
cnf(121,plain,
xn = sdtasdt0(xr,esk5_0),
inference(split_conjunct,[status(thm)],[119]) ).
cnf(122,plain,
aNaturalNumber0(esk5_0),
inference(split_conjunct,[status(thm)],[119]) ).
fof(256,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)],[13]) ).
fof(257,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)],[256]) ).
fof(258,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)],[257]) ).
cnf(259,plain,
( sdtasdt0(sdtpldt0(X2,X1),X3) = sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[258]) ).
fof(261,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(262,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)],[261]) ).
fof(263,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk10_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk10_2(X4,X5))) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7)) )
| doDivides0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[262]) ).
fof(264,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5) )
& ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk10_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk10_2(X4,X5))) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[263]) ).
fof(265,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk10_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(X5,sdtasdt0(X4,esk10_2(X4,X5)))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[264]) ).
cnf(266,plain,
( X1 = sdtasdt0(X2,esk10_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[265]) ).
cnf(267,plain,
( aNaturalNumber0(esk10_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[265]) ).
cnf(268,plain,
( doDivides0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[265]) ).
cnf(301,plain,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(302,plain,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(303,plain,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[22]) ).
fof(321,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr)))
& ~ equal(sdtsldt0(xn,xr),xn)
& aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr)))
& ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(sdtsldt0(xn,xr),X1),xn) )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(322,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr)))
& ~ equal(sdtsldt0(xn,xr),xn)
& aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr)))
& ? [X2] :
( aNaturalNumber0(X2)
& equal(sdtpldt0(sdtsldt0(xn,xr),X2),xn) )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(variable_rename,[status(thm)],[321]) ).
fof(323,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr)))
& ~ equal(sdtsldt0(xn,xr),xn)
& aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr)))
& aNaturalNumber0(esk14_0)
& equal(sdtpldt0(sdtsldt0(xn,xr),esk14_0),xn)
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(skolemize,[status(esa)],[322]) ).
cnf(327,plain,
xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[323]) ).
cnf(328,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[323]) ).
fof(342,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)],[29]) ).
fof(343,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)],[342]) ).
fof(344,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk15_2(X4,X5))
& equal(sdtpldt0(X4,esk15_2(X4,X5)),X5) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5) )
| sdtlseqdt0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[343]) ).
fof(345,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5) )
& ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk15_2(X4,X5))
& equal(sdtpldt0(X4,esk15_2(X4,X5)),X5) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[344]) ).
fof(346,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk15_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(sdtpldt0(X4,esk15_2(X4,X5)),X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[345]) ).
cnf(347,plain,
( sdtpldt0(X2,esk15_2(X2,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[346]) ).
cnf(348,plain,
( aNaturalNumber0(esk15_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[346]) ).
fof(356,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)],[32]) ).
fof(357,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)],[356]) ).
fof(358,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)],[357]) ).
fof(359,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)],[358]) ).
cnf(360,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)],[359]) ).
cnf(361,plain,
( X2 = sz00
| X1 = sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[359]) ).
cnf(362,plain,
( X2 = sz00
| aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[359]) ).
fof(368,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(X1,sz00)
| sdtlseqdt0(X2,sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(369,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(X3,sz00)
| sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[368]) ).
cnf(370,plain,
( sdtlseqdt0(X1,sdtasdt0(X1,X2))
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[369]) ).
cnf(372,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[35]) ).
fof(373,negated_conjecture,
( aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr)))
& ! [X1] :
( ~ aNaturalNumber0(X1)
| ~ equal(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,X1)) )
& ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(fof_nnf,[status(thm)],[55]) ).
fof(374,negated_conjecture,
( aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr)))
& ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ equal(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,X2)) )
& ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(variable_rename,[status(thm)],[373]) ).
fof(375,negated_conjecture,
! [X2] :
( ( ~ aNaturalNumber0(X2)
| ~ equal(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,X2)) )
& ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& aNaturalNumber0(sdtsldt0(xn,xr))
& equal(xn,sdtasdt0(xr,sdtsldt0(xn,xr))) ),
inference(shift_quantors,[status(thm)],[374]) ).
cnf(378,negated_conjecture,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(split_conjunct,[status(thm)],[375]) ).
fof(380,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)],[37]) ).
fof(381,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)],[380]) ).
cnf(382,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[381]) ).
fof(398,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(399,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[398]) ).
cnf(400,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[399]) ).
fof(401,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)],[42]) ).
fof(402,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)],[401]) ).
fof(403,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(esk16_1(X3))
& doDivides0(esk16_1(X3),X3)
& ~ equal(esk16_1(X3),sz10)
& ~ equal(esk16_1(X3),X3) )
| isPrime0(X3) ) ) ),
inference(skolemize,[status(esa)],[402]) ).
fof(404,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(esk16_1(X3))
& doDivides0(esk16_1(X3),X3)
& ~ equal(esk16_1(X3),sz10)
& ~ equal(esk16_1(X3),X3) )
| isPrime0(X3) ) )
| ~ aNaturalNumber0(X3) ),
inference(shift_quantors,[status(thm)],[403]) ).
fof(405,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(esk16_1(X3))
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( doDivides0(esk16_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk16_1(X3),sz10)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk16_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) ) ),
inference(distribute,[status(thm)],[404]) ).
cnf(410,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[405]) ).
fof(417,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| equal(X1,sz00)
| equal(X1,sz10)
| ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(418,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10)
| ? [X4] :
( aNaturalNumber0(X4)
& doDivides0(X4,X3)
& isPrime0(X4) ) ),
inference(variable_rename,[status(thm)],[417]) ).
fof(419,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10)
| ( aNaturalNumber0(esk17_1(X3))
& doDivides0(esk17_1(X3),X3)
& isPrime0(esk17_1(X3)) ) ),
inference(skolemize,[status(esa)],[418]) ).
fof(420,plain,
! [X3] :
( ( aNaturalNumber0(esk17_1(X3))
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) )
& ( doDivides0(esk17_1(X3),X3)
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) )
& ( isPrime0(esk17_1(X3))
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) ) ),
inference(distribute,[status(thm)],[419]) ).
cnf(421,plain,
( X1 = sz10
| X1 = sz00
| isPrime0(esk17_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[420]) ).
cnf(422,plain,
( X1 = sz10
| X1 = sz00
| doDivides0(esk17_1(X1),X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[420]) ).
cnf(423,plain,
( X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk17_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[420]) ).
cnf(432,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(433,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(434,plain,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[48]) ).
fof(435,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[49]) ).
fof(436,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(sdtasdt0(X3,X4),sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[435]) ).
cnf(437,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[436]) ).
fof(443,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)],[51]) ).
fof(444,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)],[443]) ).
fof(445,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)],[444]) ).
cnf(446,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)],[445]) ).
fof(452,plain,
( ? [X2] :
( aNaturalNumber0(X2)
& equal(sdtpldt0(xr,X2),xk) )
& ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtasdt0(xn,xm),sdtasdt0(xr,X3)) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(variable_rename,[status(thm)],[53]) ).
fof(453,plain,
( aNaturalNumber0(esk18_0)
& equal(sdtpldt0(xr,esk18_0),xk)
& aNaturalNumber0(esk19_0)
& equal(sdtasdt0(xn,xm),sdtasdt0(xr,esk19_0))
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa)],[452]) ).
cnf(454,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[453]) ).
cnf(455,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,esk19_0),
inference(split_conjunct,[status(thm)],[453]) ).
cnf(456,plain,
aNaturalNumber0(esk19_0),
inference(split_conjunct,[status(thm)],[453]) ).
fof(459,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
inference(fof_nnf,[status(thm)],[54]) ).
fof(460,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtasdt0(X2,sz10),X2)
& equal(X2,sdtasdt0(sz10,X2)) ) ),
inference(variable_rename,[status(thm)],[459]) ).
fof(461,plain,
! [X2] :
( ( equal(sdtasdt0(X2,sz10),X2)
| ~ aNaturalNumber0(X2) )
& ( equal(X2,sdtasdt0(sz10,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[460]) ).
cnf(462,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[461]) ).
cnf(463,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[461]) ).
cnf(485,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[400,433,theory(equality)]) ).
cnf(486,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[485,434,theory(equality)]) ).
cnf(487,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| $false
| $false ),
inference(rw,[status(thm)],[486,301,theory(equality)]) ).
cnf(488,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(cn,[status(thm)],[487,theory(equality)]) ).
cnf(514,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(er,[status(thm)],[410,theory(equality)]) ).
cnf(515,plain,
( ~ isPrime0(sz10)
| $false ),
inference(rw,[status(thm)],[514,372,theory(equality)]) ).
cnf(516,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[515,theory(equality)]) ).
cnf(569,negated_conjecture,
( ~ doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr)))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(spm,[status(thm)],[378,437,theory(equality)]) ).
cnf(581,negated_conjecture,
( ~ doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr)))
| $false
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(rw,[status(thm)],[569,302,theory(equality)]) ).
cnf(582,negated_conjecture,
( ~ doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr)))
| $false
| $false ),
inference(rw,[status(thm)],[581,328,theory(equality)]) ).
cnf(583,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr))),
inference(cn,[status(thm)],[582,theory(equality)]) ).
cnf(605,plain,
( aNaturalNumber0(esk10_2(xr,xk))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(spm,[status(thm)],[267,97,theory(equality)]) ).
cnf(613,plain,
( aNaturalNumber0(esk10_2(xr,xk))
| $false
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[605,100,theory(equality)]) ).
cnf(614,plain,
( aNaturalNumber0(esk10_2(xr,xk))
| $false
| $false ),
inference(rw,[status(thm)],[613,434,theory(equality)]) ).
cnf(615,plain,
aNaturalNumber0(esk10_2(xr,xk)),
inference(cn,[status(thm)],[614,theory(equality)]) ).
cnf(695,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(er,[status(thm)],[268,theory(equality)]) ).
cnf(704,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[268,462,theory(equality)]) ).
cnf(734,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[704,372,theory(equality)]) ).
cnf(735,plain,
( doDivides0(sz10,X1)
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[734,theory(equality)]) ).
cnf(736,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[735,theory(equality)]) ).
cnf(822,plain,
( xp = esk17_1(xp)
| sz10 = esk17_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk17_1(xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[75,422,theory(equality)]) ).
cnf(825,plain,
( xp = esk17_1(xp)
| sz10 = esk17_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk17_1(xp))
| $false ),
inference(rw,[status(thm)],[822,301,theory(equality)]) ).
cnf(826,plain,
( xp = esk17_1(xp)
| sz10 = esk17_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk17_1(xp)) ),
inference(cn,[status(thm)],[825,theory(equality)]) ).
cnf(827,plain,
( esk17_1(xp) = xp
| esk17_1(xp) = sz10
| sz00 = xp
| ~ aNaturalNumber0(esk17_1(xp)) ),
inference(sr,[status(thm)],[826,73,theory(equality)]) ).
cnf(828,plain,
( esk17_1(xp) = xp
| esk17_1(xp) = sz10
| ~ aNaturalNumber0(esk17_1(xp)) ),
inference(sr,[status(thm)],[827,74,theory(equality)]) ).
cnf(860,plain,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[105,120,theory(equality)]) ).
cnf(867,plain,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xr)
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[860,100,theory(equality)]) ).
cnf(868,plain,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xr)
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[867,303,theory(equality)]) ).
cnf(869,plain,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[868,theory(equality)]) ).
cnf(911,plain,
( sz00 = xk
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[370,433,theory(equality)]) ).
cnf(932,plain,
( sz00 = xk
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[911,434,theory(equality)]) ).
cnf(933,plain,
( sz00 = xk
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| $false
| $false ),
inference(rw,[status(thm)],[932,301,theory(equality)]) ).
cnf(934,plain,
( sz00 = xk
| sdtlseqdt0(xp,sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[933,theory(equality)]) ).
cnf(935,plain,
sdtlseqdt0(xp,sdtasdt0(xn,xm)),
inference(sr,[status(thm)],[934,58,theory(equality)]) ).
cnf(956,plain,
( sdtasdt0(xr,esk10_2(xr,xk)) = xk
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(spm,[status(thm)],[266,97,theory(equality)]) ).
cnf(965,plain,
( sdtasdt0(xr,esk10_2(xr,xk)) = xk
| $false
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[956,100,theory(equality)]) ).
cnf(966,plain,
( sdtasdt0(xr,esk10_2(xr,xk)) = xk
| $false
| $false ),
inference(rw,[status(thm)],[965,434,theory(equality)]) ).
cnf(967,plain,
sdtasdt0(xr,esk10_2(xr,xk)) = xk,
inference(cn,[status(thm)],[966,theory(equality)]) ).
cnf(1053,plain,
( sz00 = X1
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[362,theory(equality)]) ).
cnf(1054,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xk != X1
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spm,[status(thm)],[362,432,theory(equality)]) ).
cnf(1055,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xk != X1
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(rw,[status(thm)],[1054,69,theory(equality)]) ).
cnf(1056,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xk != X1
| $false
| $false
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(rw,[status(thm)],[1055,301,theory(equality)]) ).
cnf(1057,plain,
( sz00 = xp
| aNaturalNumber0(X1)
| xk != X1
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[1056,theory(equality)]) ).
cnf(1058,plain,
( aNaturalNumber0(X1)
| xk != X1
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(sr,[status(thm)],[1057,74,theory(equality)]) ).
cnf(1181,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[382,462,theory(equality)]) ).
cnf(1189,plain,
( sdtasdt0(sdtasdt0(X2,X1),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[382,437,theory(equality)]) ).
cnf(1222,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[1181,372,theory(equality)]) ).
cnf(1223,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1222,theory(equality)]) ).
cnf(1535,plain,
( sz00 = xr
| esk4_0 = X1
| xk != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk4_0)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[117,98,theory(equality)]) ).
cnf(1537,plain,
( sz00 = xr
| esk5_0 = X1
| xn != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk5_0)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[117,121,theory(equality)]) ).
cnf(1545,plain,
( sz00 = xr
| esk19_0 = X1
| sdtasdt0(xn,xm) != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk19_0)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[117,455,theory(equality)]) ).
cnf(1565,plain,
( sz00 = xr
| esk4_0 = X1
| xk != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[1535,99,theory(equality)]) ).
cnf(1566,plain,
( sz00 = xr
| esk4_0 = X1
| xk != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[1565,100,theory(equality)]) ).
cnf(1567,plain,
( sz00 = xr
| esk4_0 = X1
| xk != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1566,theory(equality)]) ).
cnf(1568,plain,
( esk4_0 = X1
| sdtasdt0(xr,X1) != xk
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[1567,96,theory(equality)]) ).
cnf(1573,plain,
( sz00 = xr
| esk5_0 = X1
| xn != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[1537,122,theory(equality)]) ).
cnf(1574,plain,
( sz00 = xr
| esk5_0 = X1
| xn != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[1573,100,theory(equality)]) ).
cnf(1575,plain,
( sz00 = xr
| esk5_0 = X1
| xn != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1574,theory(equality)]) ).
cnf(1576,plain,
( esk5_0 = X1
| sdtasdt0(xr,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[1575,96,theory(equality)]) ).
cnf(1605,plain,
( sz00 = xr
| esk19_0 = X1
| sdtasdt0(xn,xm) != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[1545,456,theory(equality)]) ).
cnf(1606,plain,
( sz00 = xr
| esk19_0 = X1
| sdtasdt0(xn,xm) != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[1605,100,theory(equality)]) ).
cnf(1607,plain,
( sz00 = xr
| esk19_0 = X1
| sdtasdt0(xn,xm) != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[1606,theory(equality)]) ).
cnf(1608,plain,
( esk19_0 = X1
| sdtasdt0(xr,X1) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[1607,96,theory(equality)]) ).
cnf(1645,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| sz00 = X1
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[361,theory(equality)]) ).
cnf(1651,plain,
( sdtsldt0(X1,X2) = X3
| sz00 = X2
| sdtasdt0(X2,X3) != X1
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[360,268]) ).
cnf(1901,plain,
( sdtpldt0(sdtasdt0(X1,sz10),X2) = sdtasdt0(sdtpldt0(X1,X2),sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[259,463,theory(equality)]) ).
cnf(1973,plain,
( sdtpldt0(sdtasdt0(X1,sz10),X2) = sdtasdt0(sdtpldt0(X1,X2),sz10)
| $false
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(rw,[status(thm)],[1901,372,theory(equality)]) ).
cnf(1974,plain,
( sdtpldt0(sdtasdt0(X1,sz10),X2) = sdtasdt0(sdtpldt0(X1,X2),sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[1973,theory(equality)]) ).
cnf(2030,plain,
( sdtsldt0(sdtasdt0(X1,xn),xr) = sdtasdt0(X1,sdtsldt0(xn,xr))
| sz00 = xr
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[446,120,theory(equality)]) ).
cnf(2031,plain,
( sdtsldt0(sdtasdt0(X1,xk),xr) = sdtasdt0(X1,sdtsldt0(xk,xr))
| sz00 = xr
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(spm,[status(thm)],[446,97,theory(equality)]) ).
cnf(2038,plain,
( sdtsldt0(sdtasdt0(X1,xn),xr) = sdtasdt0(X1,sdtsldt0(xn,xr))
| sz00 = xr
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[2030,100,theory(equality)]) ).
cnf(2039,plain,
( sdtsldt0(sdtasdt0(X1,xn),xr) = sdtasdt0(X1,sdtsldt0(xn,xr))
| sz00 = xr
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[2038,303,theory(equality)]) ).
cnf(2040,plain,
( sdtsldt0(sdtasdt0(X1,xn),xr) = sdtasdt0(X1,sdtsldt0(xn,xr))
| sz00 = xr
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[2039,theory(equality)]) ).
cnf(2041,plain,
( sdtsldt0(sdtasdt0(X1,xn),xr) = sdtasdt0(X1,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[2040,96,theory(equality)]) ).
cnf(2042,plain,
( sdtsldt0(sdtasdt0(X1,xk),xr) = sdtasdt0(X1,sdtsldt0(xk,xr))
| sz00 = xr
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[2031,100,theory(equality)]) ).
cnf(2043,plain,
( sdtsldt0(sdtasdt0(X1,xk),xr) = sdtasdt0(X1,sdtsldt0(xk,xr))
| sz00 = xr
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[2042,434,theory(equality)]) ).
cnf(2044,plain,
( sdtsldt0(sdtasdt0(X1,xk),xr) = sdtasdt0(X1,sdtsldt0(xk,xr))
| sz00 = xr
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[2043,theory(equality)]) ).
cnf(2045,plain,
( sdtsldt0(sdtasdt0(X1,xk),xr) = sdtasdt0(X1,sdtsldt0(xk,xr))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[2044,96,theory(equality)]) ).
cnf(12039,plain,
( aNaturalNumber0(esk15_2(xp,sdtasdt0(xn,xm)))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spm,[status(thm)],[348,935,theory(equality)]) ).
cnf(12042,plain,
( sdtpldt0(xp,esk15_2(xp,sdtasdt0(xn,xm))) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spm,[status(thm)],[347,935,theory(equality)]) ).
cnf(12048,plain,
( aNaturalNumber0(esk15_2(xp,sdtasdt0(xn,xm)))
| $false
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(rw,[status(thm)],[12039,301,theory(equality)]) ).
cnf(12049,plain,
( aNaturalNumber0(esk15_2(xp,sdtasdt0(xn,xm)))
| $false
| $false ),
inference(rw,[status(thm)],[12048,488,theory(equality)]) ).
cnf(12050,plain,
aNaturalNumber0(esk15_2(xp,sdtasdt0(xn,xm))),
inference(cn,[status(thm)],[12049,theory(equality)]) ).
cnf(12057,plain,
( sdtpldt0(xp,esk15_2(xp,sdtasdt0(xn,xm))) = sdtasdt0(xn,xm)
| $false
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(rw,[status(thm)],[12042,301,theory(equality)]) ).
cnf(12058,plain,
( sdtpldt0(xp,esk15_2(xp,sdtasdt0(xn,xm))) = sdtasdt0(xn,xm)
| $false
| $false ),
inference(rw,[status(thm)],[12057,488,theory(equality)]) ).
cnf(12059,plain,
sdtpldt0(xp,esk15_2(xp,sdtasdt0(xn,xm))) = sdtasdt0(xn,xm),
inference(cn,[status(thm)],[12058,theory(equality)]) ).
cnf(13029,plain,
( esk5_0 = sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(spm,[status(thm)],[1576,327,theory(equality)]) ).
cnf(13041,plain,
( esk5_0 = sdtsldt0(xn,xr)
| $false ),
inference(rw,[status(thm)],[13029,328,theory(equality)]) ).
cnf(13042,plain,
esk5_0 = sdtsldt0(xn,xr),
inference(cn,[status(thm)],[13041,theory(equality)]) ).
cnf(13067,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xm,esk5_0)),
inference(rw,[status(thm)],[583,13042,theory(equality)]) ).
cnf(14048,plain,
( doDivides0(sz10,xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[869,736,theory(equality)]) ).
cnf(14059,plain,
( doDivides0(sz10,xn)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[14048,372,theory(equality)]) ).
cnf(14060,plain,
( doDivides0(sz10,xn)
| $false
| $false ),
inference(rw,[status(thm)],[14059,100,theory(equality)]) ).
cnf(14061,plain,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[14060,theory(equality)]) ).
cnf(14070,plain,
( aNaturalNumber0(esk10_2(sz10,xn))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[267,14061,theory(equality)]) ).
cnf(14072,plain,
( sdtasdt0(sz10,esk10_2(sz10,xn)) = xn
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[266,14061,theory(equality)]) ).
cnf(14076,plain,
( aNaturalNumber0(esk10_2(sz10,xn))
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[14070,372,theory(equality)]) ).
cnf(14077,plain,
( aNaturalNumber0(esk10_2(sz10,xn))
| $false
| $false ),
inference(rw,[status(thm)],[14076,303,theory(equality)]) ).
cnf(14078,plain,
aNaturalNumber0(esk10_2(sz10,xn)),
inference(cn,[status(thm)],[14077,theory(equality)]) ).
cnf(14082,plain,
( sdtasdt0(sz10,esk10_2(sz10,xn)) = xn
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[14072,372,theory(equality)]) ).
cnf(14083,plain,
( sdtasdt0(sz10,esk10_2(sz10,xn)) = xn
| $false
| $false ),
inference(rw,[status(thm)],[14082,303,theory(equality)]) ).
cnf(14084,plain,
sdtasdt0(sz10,esk10_2(sz10,xn)) = xn,
inference(cn,[status(thm)],[14083,theory(equality)]) ).
cnf(15219,plain,
( xn = esk10_2(sz10,xn)
| ~ aNaturalNumber0(esk10_2(sz10,xn)) ),
inference(spm,[status(thm)],[462,14084,theory(equality)]) ).
cnf(15354,plain,
( xn = esk10_2(sz10,xn)
| $false ),
inference(rw,[status(thm)],[15219,14078,theory(equality)]) ).
cnf(15355,plain,
xn = esk10_2(sz10,xn),
inference(cn,[status(thm)],[15354,theory(equality)]) ).
cnf(15750,plain,
sdtasdt0(sz10,xn) = xn,
inference(rw,[status(thm)],[14084,15355,theory(equality)]) ).
cnf(15754,plain,
( xn = sdtasdt0(xn,sz10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[437,15750,theory(equality)]) ).
cnf(15890,plain,
( xn = sdtasdt0(xn,sz10)
| $false
| ~ aNaturalNumber0(sz10) ),
inference(rw,[status(thm)],[15754,303,theory(equality)]) ).
cnf(15891,plain,
( xn = sdtasdt0(xn,sz10)
| $false
| $false ),
inference(rw,[status(thm)],[15890,372,theory(equality)]) ).
cnf(15892,plain,
xn = sdtasdt0(xn,sz10),
inference(cn,[status(thm)],[15891,theory(equality)]) ).
cnf(16289,plain,
( aNaturalNumber0(X1)
| xk != X1
| $false ),
inference(rw,[status(thm)],[1058,488,theory(equality)]) ).
cnf(16290,plain,
( aNaturalNumber0(X1)
| xk != X1 ),
inference(cn,[status(thm)],[16289,theory(equality)]) ).
cnf(18784,plain,
( esk4_0 = esk10_2(xr,xk)
| ~ aNaturalNumber0(esk10_2(xr,xk)) ),
inference(spm,[status(thm)],[1568,967,theory(equality)]) ).
cnf(18797,plain,
( esk4_0 = esk10_2(xr,xk)
| $false ),
inference(rw,[status(thm)],[18784,615,theory(equality)]) ).
cnf(18798,plain,
esk4_0 = esk10_2(xr,xk),
inference(cn,[status(thm)],[18797,theory(equality)]) ).
cnf(18809,plain,
sdtasdt0(xr,esk4_0) = xk,
inference(rw,[status(thm)],[967,18798,theory(equality)]) ).
cnf(18822,plain,
( sdtsldt0(X1,xr) = esk4_0
| sz00 = xr
| xk != X1
| ~ aNaturalNumber0(esk4_0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[1651,18809,theory(equality)]) ).
cnf(19037,plain,
( sdtsldt0(X1,xr) = esk4_0
| sz00 = xr
| xk != X1
| $false
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[18822,99,theory(equality)]) ).
cnf(19038,plain,
( sdtsldt0(X1,xr) = esk4_0
| sz00 = xr
| xk != X1
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[19037,100,theory(equality)]) ).
cnf(19039,plain,
( sdtsldt0(X1,xr) = esk4_0
| sz00 = xr
| xk != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[19038,theory(equality)]) ).
cnf(19040,plain,
( sdtsldt0(X1,xr) = esk4_0
| xk != X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[19039,96,theory(equality)]) ).
cnf(19688,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[695,400]) ).
cnf(20442,plain,
( sdtsldt0(X1,xr) = esk4_0
| xk != X1 ),
inference(csr,[status(thm)],[19040,16290]) ).
cnf(20443,plain,
sdtsldt0(xk,xr) = esk4_0,
inference(er,[status(thm)],[20442,theory(equality)]) ).
cnf(28849,plain,
( esk17_1(xp) = sz10
| esk17_1(xp) = xp
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[828,423,theory(equality)]) ).
cnf(28850,plain,
( esk17_1(xp) = sz10
| esk17_1(xp) = xp
| sz10 = xp
| sz00 = xp
| $false ),
inference(rw,[status(thm)],[28849,301,theory(equality)]) ).
cnf(28851,plain,
( esk17_1(xp) = sz10
| esk17_1(xp) = xp
| sz10 = xp
| sz00 = xp ),
inference(cn,[status(thm)],[28850,theory(equality)]) ).
cnf(28852,plain,
( esk17_1(xp) = sz10
| esk17_1(xp) = xp
| sz00 = xp ),
inference(sr,[status(thm)],[28851,73,theory(equality)]) ).
cnf(28853,plain,
( esk17_1(xp) = sz10
| esk17_1(xp) = xp ),
inference(sr,[status(thm)],[28852,74,theory(equality)]) ).
cnf(28856,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| esk17_1(xp) = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[421,28853,theory(equality)]) ).
cnf(28861,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| esk17_1(xp) = xp
| $false ),
inference(rw,[status(thm)],[28856,301,theory(equality)]) ).
cnf(28862,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| esk17_1(xp) = xp ),
inference(cn,[status(thm)],[28861,theory(equality)]) ).
cnf(28863,plain,
( sz00 = xp
| isPrime0(sz10)
| esk17_1(xp) = xp ),
inference(sr,[status(thm)],[28862,73,theory(equality)]) ).
cnf(28864,plain,
( isPrime0(sz10)
| esk17_1(xp) = xp ),
inference(sr,[status(thm)],[28863,74,theory(equality)]) ).
cnf(28865,plain,
esk17_1(xp) = xp,
inference(sr,[status(thm)],[28864,516,theory(equality)]) ).
cnf(28872,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[422,28865,theory(equality)]) ).
cnf(28881,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp)
| $false ),
inference(rw,[status(thm)],[28872,301,theory(equality)]) ).
cnf(28882,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp) ),
inference(cn,[status(thm)],[28881,theory(equality)]) ).
cnf(28883,plain,
( sz00 = xp
| doDivides0(xp,xp) ),
inference(sr,[status(thm)],[28882,73,theory(equality)]) ).
cnf(28884,plain,
doDivides0(xp,xp),
inference(sr,[status(thm)],[28883,74,theory(equality)]) ).
cnf(28885,plain,
( aNaturalNumber0(esk10_2(xp,xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[267,28884,theory(equality)]) ).
cnf(28887,plain,
( sdtasdt0(xp,esk10_2(xp,xp)) = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[266,28884,theory(equality)]) ).
cnf(28891,plain,
( aNaturalNumber0(esk10_2(xp,xp))
| $false ),
inference(rw,[status(thm)],[28885,301,theory(equality)]) ).
cnf(28892,plain,
aNaturalNumber0(esk10_2(xp,xp)),
inference(cn,[status(thm)],[28891,theory(equality)]) ).
cnf(28895,plain,
( sdtasdt0(xp,esk10_2(xp,xp)) = xp
| $false ),
inference(rw,[status(thm)],[28887,301,theory(equality)]) ).
cnf(28896,plain,
sdtasdt0(xp,esk10_2(xp,xp)) = xp,
inference(cn,[status(thm)],[28895,theory(equality)]) ).
cnf(40075,plain,
( sz00 = xr
| aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xr))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spm,[status(thm)],[1053,454,theory(equality)]) ).
cnf(40141,plain,
( sz00 = xr
| aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xr))
| $false
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(rw,[status(thm)],[40075,100,theory(equality)]) ).
cnf(40142,plain,
( sz00 = xr
| aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xr))
| $false
| $false ),
inference(rw,[status(thm)],[40141,488,theory(equality)]) ).
cnf(40143,plain,
( sz00 = xr
| aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xr)) ),
inference(cn,[status(thm)],[40142,theory(equality)]) ).
cnf(40144,plain,
aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xr)),
inference(sr,[status(thm)],[40143,96,theory(equality)]) ).
cnf(47692,plain,
( sdtasdt0(sz10,xp) = xp
| ~ aNaturalNumber0(esk10_2(xp,xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[1223,28896,theory(equality)]) ).
cnf(47924,plain,
( sdtasdt0(sz10,xp) = xp
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[47692,28892,theory(equality)]) ).
cnf(47925,plain,
( sdtasdt0(sz10,xp) = xp
| $false
| $false ),
inference(rw,[status(thm)],[47924,301,theory(equality)]) ).
cnf(47926,plain,
sdtasdt0(sz10,xp) = xp,
inference(cn,[status(thm)],[47925,theory(equality)]) ).
cnf(48272,plain,
( xp = sdtasdt0(xp,sz10)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[437,47926,theory(equality)]) ).
cnf(48420,plain,
( xp = sdtasdt0(xp,sz10)
| $false
| ~ aNaturalNumber0(sz10) ),
inference(rw,[status(thm)],[48272,301,theory(equality)]) ).
cnf(48421,plain,
( xp = sdtasdt0(xp,sz10)
| $false
| $false ),
inference(rw,[status(thm)],[48420,372,theory(equality)]) ).
cnf(48422,plain,
xp = sdtasdt0(xp,sz10),
inference(cn,[status(thm)],[48421,theory(equality)]) ).
cnf(101948,plain,
( sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm)
| sz00 = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spm,[status(thm)],[1645,454,theory(equality)]) ).
cnf(102052,plain,
( sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm)
| sz00 = xr
| $false
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(rw,[status(thm)],[101948,100,theory(equality)]) ).
cnf(102053,plain,
( sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm)
| sz00 = xr
| $false
| $false ),
inference(rw,[status(thm)],[102052,488,theory(equality)]) ).
cnf(102054,plain,
( sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm)
| sz00 = xr ),
inference(cn,[status(thm)],[102053,theory(equality)]) ).
cnf(102055,plain,
sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm),
inference(sr,[status(thm)],[102054,96,theory(equality)]) ).
cnf(105039,plain,
( esk19_0 = sdtsldt0(sdtasdt0(xn,xm),xr)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xr)) ),
inference(spm,[status(thm)],[1608,102055,theory(equality)]) ).
cnf(105821,plain,
( esk19_0 = sdtsldt0(sdtasdt0(xn,xm),xr)
| $false ),
inference(rw,[status(thm)],[105039,40144,theory(equality)]) ).
cnf(105822,plain,
esk19_0 = sdtsldt0(sdtasdt0(xn,xm),xr),
inference(cn,[status(thm)],[105821,theory(equality)]) ).
cnf(169270,plain,
( sdtasdt0(sdtasdt0(xn,xm),sz10) = sdtpldt0(sdtasdt0(xp,sz10),esk15_2(xp,sdtasdt0(xn,xm)))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(esk15_2(xp,sdtasdt0(xn,xm))) ),
inference(spm,[status(thm)],[1974,12059,theory(equality)]) ).
cnf(169617,plain,
( sdtasdt0(sdtasdt0(xn,xm),sz10) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(esk15_2(xp,sdtasdt0(xn,xm))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[169270,48422,theory(equality)]),12059,theory(equality)]) ).
cnf(169618,plain,
( sdtasdt0(sdtasdt0(xn,xm),sz10) = sdtasdt0(xn,xm)
| $false
| ~ aNaturalNumber0(esk15_2(xp,sdtasdt0(xn,xm))) ),
inference(rw,[status(thm)],[169617,301,theory(equality)]) ).
cnf(169619,plain,
( sdtasdt0(sdtasdt0(xn,xm),sz10) = sdtasdt0(xn,xm)
| $false
| $false ),
inference(rw,[status(thm)],[169618,12050,theory(equality)]) ).
cnf(169620,plain,
sdtasdt0(sdtasdt0(xn,xm),sz10) = sdtasdt0(xn,xm),
inference(cn,[status(thm)],[169619,theory(equality)]) ).
cnf(172218,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xm,sdtasdt0(xn,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[1189,169620,theory(equality)]) ).
cnf(172937,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xm,xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[172218,15892,theory(equality)]) ).
cnf(172938,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xm,xn)
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[172937,372,theory(equality)]) ).
cnf(172939,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xm,xn)
| $false
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[172938,303,theory(equality)]) ).
cnf(172940,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xm,xn)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[172939,302,theory(equality)]) ).
cnf(172941,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(cn,[status(thm)],[172940,theory(equality)]) ).
cnf(208406,plain,
( sdtsldt0(sdtasdt0(X1,xn),xr) = sdtasdt0(X1,esk5_0)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[2041,13042,theory(equality)]) ).
cnf(208409,plain,
( sdtsldt0(sdtasdt0(xn,xm),xr) = sdtasdt0(xm,esk5_0)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[208406,172941,theory(equality)]) ).
cnf(208434,plain,
( esk19_0 = sdtasdt0(xm,esk5_0)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[208409,105822,theory(equality)]) ).
cnf(208435,plain,
( esk19_0 = sdtasdt0(xm,esk5_0)
| $false ),
inference(rw,[status(thm)],[208434,302,theory(equality)]) ).
cnf(208436,plain,
esk19_0 = sdtasdt0(xm,esk5_0),
inference(cn,[status(thm)],[208435,theory(equality)]) ).
cnf(208734,negated_conjecture,
~ doDivides0(xp,esk19_0),
inference(rw,[status(thm)],[13067,208436,theory(equality)]) ).
cnf(210479,plain,
( sdtsldt0(sdtasdt0(X1,xk),xr) = sdtasdt0(X1,esk4_0)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[2045,20443,theory(equality)]) ).
cnf(210480,plain,
( sdtsldt0(sdtasdt0(xn,xm),xr) = sdtasdt0(xp,esk4_0)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[210479,433,theory(equality)]) ).
cnf(210500,plain,
( esk19_0 = sdtasdt0(xp,esk4_0)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[210480,105822,theory(equality)]) ).
cnf(210501,plain,
( esk19_0 = sdtasdt0(xp,esk4_0)
| $false ),
inference(rw,[status(thm)],[210500,301,theory(equality)]) ).
cnf(210502,plain,
esk19_0 = sdtasdt0(xp,esk4_0),
inference(cn,[status(thm)],[210501,theory(equality)]) ).
cnf(210750,plain,
( doDivides0(xp,esk19_0)
| ~ aNaturalNumber0(esk4_0)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[19688,210502,theory(equality)]) ).
cnf(211499,plain,
( doDivides0(xp,esk19_0)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[210750,99,theory(equality)]) ).
cnf(211500,plain,
( doDivides0(xp,esk19_0)
| $false
| $false ),
inference(rw,[status(thm)],[211499,301,theory(equality)]) ).
cnf(211501,plain,
doDivides0(xp,esk19_0),
inference(cn,[status(thm)],[211500,theory(equality)]) ).
cnf(211502,plain,
$false,
inference(sr,[status(thm)],[211501,208734,theory(equality)]) ).
cnf(211503,plain,
$false,
211502,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM511+3 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04 % Command : Source/sine.py -e eprover -t %d %s
% 0.03/0.23 % Computer : n071.star.cs.uiowa.edu
% 0.03/0.23 % Model : x86_64 x86_64
% 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23 % Memory : 32218.625MB
% 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Fri Jan 5 06:27:45 CST 2018
% 0.03/0.23 % CPUTime :
% 0.07/0.28 % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.28 --creating new selector for []
% 4.32/4.58 -running prover on /export/starexec/sandbox/tmp/tmppGpgcC/sel_theBenchmark.p_1 with time limit 29
% 4.32/4.58 -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/tmppGpgcC/sel_theBenchmark.p_1']
% 4.32/4.58 -prover status Theorem
% 4.32/4.58 Problem theBenchmark.p solved in phase 0.
% 4.32/4.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.32/4.58 % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.32/4.58 Solved 1 out of 1.
% 4.32/4.58 # Problem is unsatisfiable (or provable), constructing proof object
% 4.32/4.58 # SZS status Theorem
% 4.32/4.58 # SZS output start CNFRefutation.
% See solution above
% 4.32/4.58 # SZS output end CNFRefutation
%------------------------------------------------------------------------------