TSTP Solution File: NUM501+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM501+3 : TPTP v7.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n065.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 15:21:34 EST 2018
% Result : Theorem 3.78s
% Output : CNFRefutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 12
% Syntax : Number of formulae : 123 ( 19 unt; 0 def)
% Number of atoms : 622 ( 77 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 761 ( 262 ~; 325 |; 163 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn 80 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
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/tmpS3IEAB/sel_theBenchmark.p_1',m__1860) ).
fof(4,axiom,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(xk,sdtasdt0(xr,X1)) )
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& equal(xr,sdtasdt0(X1,X2)) )
| doDivides0(X1,xr) ) )
=> ( equal(X1,sz10)
| equal(X1,xr) ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox/tmp/tmpS3IEAB/sel_theBenchmark.p_1',m__2342) ).
fof(12,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(X2,sdtasdt0(X1,X3)) ) ) ),
file('/export/starexec/sandbox/tmp/tmpS3IEAB/sel_theBenchmark.p_1',mDefDiv) ).
fof(20,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/tmp/tmpS3IEAB/sel_theBenchmark.p_1',m__1837) ).
fof(31,axiom,
( aNaturalNumber0(sz10)
& ~ equal(sz10,sz00) ),
file('/export/starexec/sandbox/tmp/tmpS3IEAB/sel_theBenchmark.p_1',mSortsC_01) ).
fof(32,conjecture,
( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtasdt0(xn,xm),sdtasdt0(xr,X1)) )
| doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmpS3IEAB/sel_theBenchmark.p_1',m__) ).
fof(33,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/tmpS3IEAB/sel_theBenchmark.p_1',mMulAsso) ).
fof(37,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmpS3IEAB/sel_theBenchmark.p_1',mSortsB_02) ).
fof(38,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/tmpS3IEAB/sel_theBenchmark.p_1',mDefPrime) ).
fof(41,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& ~ equal(X1,sz00)
& ~ equal(X1,sz10) )
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
file('/export/starexec/sandbox/tmp/tmpS3IEAB/sel_theBenchmark.p_1',mPrimDiv) ).
fof(44,axiom,
( aNaturalNumber0(xk)
& equal(sdtasdt0(xn,xm),sdtasdt0(xp,xk))
& equal(xk,sdtsldt0(sdtasdt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/tmp/tmpS3IEAB/sel_theBenchmark.p_1',m__2306) ).
fof(45,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmpS3IEAB/sel_theBenchmark.p_1',mMulComm) ).
fof(50,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtasdt0(xn,xm),sdtasdt0(xr,X1)) )
| doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(assume_negation,[status(cth)],[32]) ).
fof(59,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(60,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)],[59]) ).
fof(61,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)],[60]) ).
fof(62,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)],[61]) ).
fof(63,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)],[62]) ).
cnf(68,plain,
xp != sz10,
inference(split_conjunct,[status(thm)],[63]) ).
cnf(69,plain,
xp != sz00,
inference(split_conjunct,[status(thm)],[63]) ).
cnf(70,plain,
( X1 = xp
| X1 = sz10
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xp) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(72,plain,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& equal(xk,sdtasdt0(xr,X1)) )
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ equal(xr,sdtasdt0(X1,X2)) )
& ~ doDivides0(X1,xr) )
| equal(X1,sz10)
| equal(X1,xr) )
& isPrime0(xr) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(73,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)],[72]) ).
fof(74,plain,
( aNaturalNumber0(xr)
& aNaturalNumber0(esk2_0)
& equal(xk,sdtasdt0(xr,esk2_0))
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& ! [X4] :
( ~ aNaturalNumber0(X4)
| ( ! [X5] :
( ~ aNaturalNumber0(X5)
| ~ equal(xr,sdtasdt0(X4,X5)) )
& ~ doDivides0(X4,xr) )
| equal(X4,sz10)
| equal(X4,xr) )
& isPrime0(xr) ),
inference(skolemize,[status(esa)],[73]) ).
fof(75,plain,
! [X4,X5] :
( ( ( ( ~ aNaturalNumber0(X5)
| ~ equal(xr,sdtasdt0(X4,X5)) )
& ~ doDivides0(X4,xr) )
| ~ aNaturalNumber0(X4)
| equal(X4,sz10)
| equal(X4,xr) )
& aNaturalNumber0(xr)
& aNaturalNumber0(esk2_0)
& equal(xk,sdtasdt0(xr,esk2_0))
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& isPrime0(xr) ),
inference(shift_quantors,[status(thm)],[74]) ).
fof(76,plain,
! [X4,X5] :
( ( ~ aNaturalNumber0(X5)
| ~ equal(xr,sdtasdt0(X4,X5))
| ~ aNaturalNumber0(X4)
| equal(X4,sz10)
| equal(X4,xr) )
& ( ~ doDivides0(X4,xr)
| ~ aNaturalNumber0(X4)
| equal(X4,sz10)
| equal(X4,xr) )
& aNaturalNumber0(xr)
& aNaturalNumber0(esk2_0)
& equal(xk,sdtasdt0(xr,esk2_0))
& doDivides0(xr,xk)
& ~ equal(xr,sz00)
& ~ equal(xr,sz10)
& isPrime0(xr) ),
inference(distribute,[status(thm)],[75]) ).
cnf(81,plain,
xk = sdtasdt0(xr,esk2_0),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(82,plain,
aNaturalNumber0(esk2_0),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(83,plain,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[76]) ).
fof(239,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ( ( ~ doDivides0(X1,X2)
| ? [X3] :
( aNaturalNumber0(X3)
& equal(X2,sdtasdt0(X1,X3)) ) )
& ( ! [X3] :
( ~ aNaturalNumber0(X3)
| ~ equal(X2,sdtasdt0(X1,X3)) )
| doDivides0(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(240,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)],[239]) ).
fof(241,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk7_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk7_2(X4,X5))) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7)) )
| doDivides0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[240]) ).
fof(242,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5) )
& ( ~ doDivides0(X4,X5)
| ( aNaturalNumber0(esk7_2(X4,X5))
& equal(X5,sdtasdt0(X4,esk7_2(X4,X5))) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[241]) ).
fof(243,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(X5,sdtasdt0(X4,X7))
| doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk7_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(X5,sdtasdt0(X4,esk7_2(X4,X5)))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[242]) ).
cnf(244,plain,
( X1 = sdtasdt0(X2,esk7_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(245,plain,
( aNaturalNumber0(esk7_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(246,plain,
( doDivides0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(279,plain,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(333,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[31]) ).
fof(334,negated_conjecture,
( ! [X1] :
( ~ aNaturalNumber0(X1)
| ~ equal(sdtasdt0(xn,xm),sdtasdt0(xr,X1)) )
& ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(fof_nnf,[status(thm)],[50]) ).
fof(335,negated_conjecture,
( ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ equal(sdtasdt0(xn,xm),sdtasdt0(xr,X2)) )
& ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(variable_rename,[status(thm)],[334]) ).
fof(336,negated_conjecture,
! [X2] :
( ( ~ aNaturalNumber0(X2)
| ~ equal(sdtasdt0(xn,xm),sdtasdt0(xr,X2)) )
& ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(shift_quantors,[status(thm)],[335]) ).
cnf(337,negated_conjecture,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[336]) ).
fof(339,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)],[33]) ).
fof(340,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)],[339]) ).
cnf(341,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[340]) ).
fof(357,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(358,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[357]) ).
cnf(359,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[358]) ).
fof(360,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)],[38]) ).
fof(361,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)],[360]) ).
fof(362,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| ( ( ~ isPrime0(X3)
| ( ~ equal(X3,sz00)
& ~ equal(X3,sz10)
& ! [X4] :
( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| equal(X4,sz10)
| equal(X4,X3) ) ) )
& ( equal(X3,sz00)
| equal(X3,sz10)
| ( aNaturalNumber0(esk11_1(X3))
& doDivides0(esk11_1(X3),X3)
& ~ equal(esk11_1(X3),sz10)
& ~ equal(esk11_1(X3),X3) )
| isPrime0(X3) ) ) ),
inference(skolemize,[status(esa)],[361]) ).
fof(363,plain,
! [X3,X4] :
( ( ( ( ( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| equal(X4,sz10)
| equal(X4,X3) )
& ~ equal(X3,sz00)
& ~ equal(X3,sz10) )
| ~ isPrime0(X3) )
& ( equal(X3,sz00)
| equal(X3,sz10)
| ( aNaturalNumber0(esk11_1(X3))
& doDivides0(esk11_1(X3),X3)
& ~ equal(esk11_1(X3),sz10)
& ~ equal(esk11_1(X3),X3) )
| isPrime0(X3) ) )
| ~ aNaturalNumber0(X3) ),
inference(shift_quantors,[status(thm)],[362]) ).
fof(364,plain,
! [X3,X4] :
( ( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| equal(X4,sz10)
| equal(X4,X3)
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(X3,sz00)
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(X3,sz10)
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( aNaturalNumber0(esk11_1(X3))
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( doDivides0(esk11_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk11_1(X3),sz10)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk11_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) ) ),
inference(distribute,[status(thm)],[363]) ).
cnf(369,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[364]) ).
fof(376,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| equal(X1,sz00)
| equal(X1,sz10)
| ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(377,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10)
| ? [X4] :
( aNaturalNumber0(X4)
& doDivides0(X4,X3)
& isPrime0(X4) ) ),
inference(variable_rename,[status(thm)],[376]) ).
fof(378,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10)
| ( aNaturalNumber0(esk12_1(X3))
& doDivides0(esk12_1(X3),X3)
& isPrime0(esk12_1(X3)) ) ),
inference(skolemize,[status(esa)],[377]) ).
fof(379,plain,
! [X3] :
( ( aNaturalNumber0(esk12_1(X3))
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) )
& ( doDivides0(esk12_1(X3),X3)
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) )
& ( isPrime0(esk12_1(X3))
| ~ aNaturalNumber0(X3)
| equal(X3,sz00)
| equal(X3,sz10) ) ),
inference(distribute,[status(thm)],[378]) ).
cnf(380,plain,
( X1 = sz10
| X1 = sz00
| isPrime0(esk12_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[379]) ).
cnf(381,plain,
( X1 = sz10
| X1 = sz00
| doDivides0(esk12_1(X1),X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[379]) ).
cnf(382,plain,
( X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk12_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[379]) ).
cnf(392,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(393,plain,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[44]) ).
fof(394,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(395,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(sdtasdt0(X3,X4),sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[394]) ).
cnf(396,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[395]) ).
cnf(417,negated_conjecture,
~ doDivides0(xr,sdtasdt0(xp,xk)),
inference(rw,[status(thm)],[337,392,theory(equality)]) ).
cnf(450,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(er,[status(thm)],[369,theory(equality)]) ).
cnf(451,plain,
( ~ isPrime0(sz10)
| $false ),
inference(rw,[status(thm)],[450,333,theory(equality)]) ).
cnf(452,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[451,theory(equality)]) ).
cnf(526,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(er,[status(thm)],[246,theory(equality)]) ).
cnf(576,plain,
( xp = esk12_1(xp)
| sz10 = esk12_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk12_1(xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[70,381,theory(equality)]) ).
cnf(582,plain,
( xp = esk12_1(xp)
| sz10 = esk12_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk12_1(xp))
| $false ),
inference(rw,[status(thm)],[576,279,theory(equality)]) ).
cnf(583,plain,
( xp = esk12_1(xp)
| sz10 = esk12_1(xp)
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(esk12_1(xp)) ),
inference(cn,[status(thm)],[582,theory(equality)]) ).
cnf(584,plain,
( esk12_1(xp) = xp
| esk12_1(xp) = sz10
| xp = sz00
| ~ aNaturalNumber0(esk12_1(xp)) ),
inference(sr,[status(thm)],[583,68,theory(equality)]) ).
cnf(585,plain,
( esk12_1(xp) = xp
| esk12_1(xp) = sz10
| ~ aNaturalNumber0(esk12_1(xp)) ),
inference(sr,[status(thm)],[584,69,theory(equality)]) ).
cnf(770,plain,
( sdtasdt0(xk,X1) = sdtasdt0(xr,sdtasdt0(esk2_0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk2_0)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[341,81,theory(equality)]) ).
cnf(773,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[359,341,theory(equality)]) ).
cnf(791,plain,
( sdtasdt0(xk,X1) = sdtasdt0(xr,sdtasdt0(esk2_0,X1))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[770,82,theory(equality)]) ).
cnf(792,plain,
( sdtasdt0(xk,X1) = sdtasdt0(xr,sdtasdt0(esk2_0,X1))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[791,83,theory(equality)]) ).
cnf(793,plain,
( sdtasdt0(xk,X1) = sdtasdt0(xr,sdtasdt0(esk2_0,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[792,theory(equality)]) ).
cnf(7658,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[526,359]) ).
cnf(11985,plain,
( esk12_1(xp) = sz10
| esk12_1(xp) = xp
| sz10 = xp
| sz00 = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[585,382,theory(equality)]) ).
cnf(11986,plain,
( esk12_1(xp) = sz10
| esk12_1(xp) = xp
| sz10 = xp
| sz00 = xp
| $false ),
inference(rw,[status(thm)],[11985,279,theory(equality)]) ).
cnf(11987,plain,
( esk12_1(xp) = sz10
| esk12_1(xp) = xp
| sz10 = xp
| sz00 = xp ),
inference(cn,[status(thm)],[11986,theory(equality)]) ).
cnf(11988,plain,
( esk12_1(xp) = sz10
| esk12_1(xp) = xp
| xp = sz00 ),
inference(sr,[status(thm)],[11987,68,theory(equality)]) ).
cnf(11989,plain,
( esk12_1(xp) = sz10
| esk12_1(xp) = xp ),
inference(sr,[status(thm)],[11988,69,theory(equality)]) ).
cnf(13829,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp)
| esk12_1(xp) = sz10
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[381,11989,theory(equality)]) ).
cnf(13835,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp)
| esk12_1(xp) = sz10
| $false ),
inference(rw,[status(thm)],[13829,279,theory(equality)]) ).
cnf(13836,plain,
( sz10 = xp
| sz00 = xp
| doDivides0(xp,xp)
| esk12_1(xp) = sz10 ),
inference(cn,[status(thm)],[13835,theory(equality)]) ).
cnf(13837,plain,
( xp = sz00
| doDivides0(xp,xp)
| esk12_1(xp) = sz10 ),
inference(sr,[status(thm)],[13836,68,theory(equality)]) ).
cnf(13838,plain,
( doDivides0(xp,xp)
| esk12_1(xp) = sz10 ),
inference(sr,[status(thm)],[13837,69,theory(equality)]) ).
cnf(14813,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| doDivides0(xp,xp)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[380,13838,theory(equality)]) ).
cnf(14822,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| doDivides0(xp,xp)
| $false ),
inference(rw,[status(thm)],[14813,279,theory(equality)]) ).
cnf(14823,plain,
( sz10 = xp
| sz00 = xp
| isPrime0(sz10)
| doDivides0(xp,xp) ),
inference(cn,[status(thm)],[14822,theory(equality)]) ).
cnf(14824,plain,
( xp = sz00
| isPrime0(sz10)
| doDivides0(xp,xp) ),
inference(sr,[status(thm)],[14823,68,theory(equality)]) ).
cnf(14825,plain,
( isPrime0(sz10)
| doDivides0(xp,xp) ),
inference(sr,[status(thm)],[14824,69,theory(equality)]) ).
cnf(14826,plain,
doDivides0(xp,xp),
inference(sr,[status(thm)],[14825,452,theory(equality)]) ).
cnf(14831,plain,
( aNaturalNumber0(esk7_2(xp,xp))
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[245,14826,theory(equality)]) ).
cnf(14833,plain,
( sdtasdt0(xp,esk7_2(xp,xp)) = xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[244,14826,theory(equality)]) ).
cnf(14838,plain,
( aNaturalNumber0(esk7_2(xp,xp))
| $false ),
inference(rw,[status(thm)],[14831,279,theory(equality)]) ).
cnf(14839,plain,
aNaturalNumber0(esk7_2(xp,xp)),
inference(cn,[status(thm)],[14838,theory(equality)]) ).
cnf(14842,plain,
( sdtasdt0(xp,esk7_2(xp,xp)) = xp
| $false ),
inference(rw,[status(thm)],[14833,279,theory(equality)]) ).
cnf(14843,plain,
sdtasdt0(xp,esk7_2(xp,xp)) = xp,
inference(cn,[status(thm)],[14842,theory(equality)]) ).
cnf(24546,plain,
( doDivides0(xr,sdtasdt0(xk,X1))
| ~ aNaturalNumber0(sdtasdt0(esk2_0,X1))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[7658,793,theory(equality)]) ).
cnf(25065,plain,
( doDivides0(xr,sdtasdt0(xk,X1))
| ~ aNaturalNumber0(sdtasdt0(esk2_0,X1))
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[24546,83,theory(equality)]) ).
cnf(25066,plain,
( doDivides0(xr,sdtasdt0(xk,X1))
| ~ aNaturalNumber0(sdtasdt0(esk2_0,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[25065,theory(equality)]) ).
cnf(29324,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[773,359]) ).
cnf(29332,plain,
( aNaturalNumber0(sdtasdt0(X1,xp))
| ~ aNaturalNumber0(esk7_2(xp,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[29324,14843,theory(equality)]) ).
cnf(29383,plain,
( aNaturalNumber0(sdtasdt0(X1,xp))
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[29332,14839,theory(equality)]) ).
cnf(29384,plain,
( aNaturalNumber0(sdtasdt0(X1,xp))
| $false
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[29383,279,theory(equality)]) ).
cnf(29385,plain,
( aNaturalNumber0(sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[29384,theory(equality)]) ).
cnf(195693,plain,
( doDivides0(xr,sdtasdt0(xk,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(esk2_0) ),
inference(spm,[status(thm)],[25066,29385,theory(equality)]) ).
cnf(195752,plain,
( doDivides0(xr,sdtasdt0(xk,xp))
| $false
| ~ aNaturalNumber0(esk2_0) ),
inference(rw,[status(thm)],[195693,279,theory(equality)]) ).
cnf(195753,plain,
( doDivides0(xr,sdtasdt0(xk,xp))
| $false
| $false ),
inference(rw,[status(thm)],[195752,82,theory(equality)]) ).
cnf(195754,plain,
doDivides0(xr,sdtasdt0(xk,xp)),
inference(cn,[status(thm)],[195753,theory(equality)]) ).
cnf(197182,plain,
( doDivides0(xr,sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(spm,[status(thm)],[195754,396,theory(equality)]) ).
cnf(197244,plain,
( doDivides0(xr,sdtasdt0(xp,xk))
| $false
| ~ aNaturalNumber0(xk) ),
inference(rw,[status(thm)],[197182,279,theory(equality)]) ).
cnf(197245,plain,
( doDivides0(xr,sdtasdt0(xp,xk))
| $false
| $false ),
inference(rw,[status(thm)],[197244,393,theory(equality)]) ).
cnf(197246,plain,
doDivides0(xr,sdtasdt0(xp,xk)),
inference(cn,[status(thm)],[197245,theory(equality)]) ).
cnf(197247,plain,
$false,
inference(sr,[status(thm)],[197246,417,theory(equality)]) ).
cnf(197248,plain,
$false,
197247,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM501+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 : n065.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 06:03:00 CST 2018
% 0.03/0.23 % CPUTime :
% 0.03/0.27 % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.27 --creating new selector for []
% 3.78/4.06 -running prover on /export/starexec/sandbox/tmp/tmpS3IEAB/sel_theBenchmark.p_1 with time limit 29
% 3.78/4.06 -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/tmpS3IEAB/sel_theBenchmark.p_1']
% 3.78/4.06 -prover status Theorem
% 3.78/4.06 Problem theBenchmark.p solved in phase 0.
% 3.78/4.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.78/4.06 % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.78/4.06 Solved 1 out of 1.
% 3.78/4.06 # Problem is unsatisfiable (or provable), constructing proof object
% 3.78/4.06 # SZS status Theorem
% 3.78/4.06 # SZS output start CNFRefutation.
% See solution above
% 3.78/4.07 # SZS output end CNFRefutation
%------------------------------------------------------------------------------