TSTP Solution File: NUM494+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM494+1 : TPTP v7.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n138.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 15:21:32 EST 2018
% Result : Theorem 7.28s
% Output : CNFRefutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 17
% Syntax : Number of formulae : 208 ( 29 unt; 0 def)
% Number of atoms : 904 ( 175 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 1178 ( 482 ~; 582 |; 96 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 237 ( 3 sgn 104 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__1860) ).
fof(3,axiom,
equal(xr,sdtmndt0(xn,xp)),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__1883) ).
fof(5,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mAddComm) ).
fof(12,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( ~ equal(X2,X1)
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mLETotal) ).
fof(15,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__1870) ).
fof(17,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__1837) ).
fof(19,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( ~ equal(X1,X2)
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( ~ equal(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& ~ equal(sdtpldt0(X1,X3),sdtpldt0(X2,X3))
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mMonAdd) ).
fof(23,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mDefLE) ).
fof(24,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> equal(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(X1,sdtpldt0(X2,X3))) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mAddAsso) ).
fof(27,axiom,
( ~ equal(xr,xn)
& sdtlseqdt0(xr,xn) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__1894) ).
fof(31,conjecture,
( ~ equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__) ).
fof(35,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( equal(X3,sdtmndt0(X2,X1))
<=> ( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mDefDiff) ).
fof(37,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ~ equal(X1,sz00)
& ~ equal(X1,sz10)
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( equal(X2,sz10)
| equal(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mDefPrime) ).
fof(38,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mSortsC) ).
fof(39,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mSortsB) ).
fof(41,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( equal(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| equal(sdtpldt0(X2,X1),sdtpldt0(X3,X1)) )
=> equal(X2,X3) ) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mAddCanc) ).
fof(45,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtpldt0(X1,sz00),X1)
& equal(X1,sdtpldt0(sz00,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m_AddZero) ).
fof(47,negated_conjecture,
~ ( ~ equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(assume_negation,[status(cth)],[31]) ).
cnf(54,plain,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[2]) ).
cnf(55,plain,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[3]) ).
fof(59,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(60,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(sdtpldt0(X3,X4),sdtpldt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[59]) ).
cnf(61,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(90,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X1,X2)
| ( ~ equal(X2,X1)
& sdtlseqdt0(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(91,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtlseqdt0(X3,X4)
| ( ~ equal(X4,X3)
& sdtlseqdt0(X4,X3) ) ),
inference(variable_rename,[status(thm)],[90]) ).
fof(92,plain,
! [X3,X4] :
( ( ~ equal(X4,X3)
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) )
& ( sdtlseqdt0(X4,X3)
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) ) ),
inference(distribute,[status(thm)],[91]) ).
cnf(93,plain,
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[92]) ).
cnf(101,plain,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(105,plain,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(106,plain,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(107,plain,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[17]) ).
fof(109,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(X1,X2)
| ~ sdtlseqdt0(X1,X2)
| ! [X3] :
( ~ aNaturalNumber0(X3)
| ( ~ equal(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& ~ equal(sdtpldt0(X1,X3),sdtpldt0(X2,X3))
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(110,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ! [X6] :
( ~ aNaturalNumber0(X6)
| ( ~ equal(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
& sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
& ~ equal(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
& sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6)) ) ) ),
inference(variable_rename,[status(thm)],[109]) ).
fof(111,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X6)
| ( ~ equal(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
& sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
& ~ equal(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
& sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6)) )
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[110]) ).
fof(112,plain,
! [X4,X5,X6] :
( ( ~ equal(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
| ~ aNaturalNumber0(X6)
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
| ~ aNaturalNumber0(X6)
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ equal(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| equal(X4,X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[111]) ).
cnf(115,plain,
( X2 = X1
| sdtlseqdt0(sdtpldt0(X3,X2),sdtpldt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[112]) ).
fof(130,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ( ( ~ sdtlseqdt0(X1,X2)
| ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) )
& ( ! [X3] :
( ~ aNaturalNumber0(X3)
| ~ equal(sdtpldt0(X1,X3),X2) )
| sdtlseqdt0(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(131,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)],[130]) ).
fof(132,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk2_2(X4,X5))
& equal(sdtpldt0(X4,esk2_2(X4,X5)),X5) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5) )
| sdtlseqdt0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[131]) ).
fof(133,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5) )
& ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk2_2(X4,X5))
& equal(sdtpldt0(X4,esk2_2(X4,X5)),X5) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[132]) ).
fof(134,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk2_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(sdtpldt0(X4,esk2_2(X4,X5)),X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[133]) ).
cnf(137,plain,
( sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[134]) ).
fof(138,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| equal(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(X1,sdtpldt0(X2,X3))) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(139,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| equal(sdtpldt0(sdtpldt0(X4,X5),X6),sdtpldt0(X4,sdtpldt0(X5,X6))) ),
inference(variable_rename,[status(thm)],[138]) ).
cnf(140,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[139]) ).
cnf(151,plain,
sdtlseqdt0(xr,xn),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(152,plain,
xr != xn,
inference(split_conjunct,[status(thm)],[27]) ).
fof(163,negated_conjecture,
( equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(fof_nnf,[status(thm)],[47]) ).
cnf(164,negated_conjecture,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(split_conjunct,[status(thm)],[163]) ).
fof(176,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ! [X3] :
( ( ~ equal(X3,sdtmndt0(X2,X1))
| ( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) )
& ( ~ aNaturalNumber0(X3)
| ~ equal(sdtpldt0(X1,X3),X2)
| equal(X3,sdtmndt0(X2,X1)) ) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(177,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ sdtlseqdt0(X4,X5)
| ! [X6] :
( ( ~ equal(X6,sdtmndt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(sdtpldt0(X4,X6),X5) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4)) ) ) ),
inference(variable_rename,[status(thm)],[176]) ).
fof(178,plain,
! [X4,X5,X6] :
( ( ( ~ equal(X6,sdtmndt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(sdtpldt0(X4,X6),X5) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4)) ) )
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[177]) ).
fof(179,plain,
! [X4,X5,X6] :
( ( aNaturalNumber0(X6)
| ~ equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(sdtpldt0(X4,X6),X5)
| ~ equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[178]) ).
cnf(180,plain,
( X3 = sdtmndt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[179]) ).
cnf(181,plain,
( sdtpldt0(X2,X3) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| X3 != sdtmndt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[179]) ).
cnf(182,plain,
( aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| X3 != sdtmndt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[179]) ).
fof(186,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( ( ~ isPrime0(X1)
| ( ~ equal(X1,sz00)
& ~ equal(X1,sz10)
& ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| equal(X2,sz10)
| equal(X2,X1) ) ) )
& ( equal(X1,sz00)
| equal(X1,sz10)
| ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& ~ equal(X2,sz10)
& ~ equal(X2,X1) )
| isPrime0(X1) ) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(187,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)],[186]) ).
fof(188,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| ( ( ~ isPrime0(X3)
| ( ~ equal(X3,sz00)
& ~ equal(X3,sz10)
& ! [X4] :
( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| equal(X4,sz10)
| equal(X4,X3) ) ) )
& ( equal(X3,sz00)
| equal(X3,sz10)
| ( aNaturalNumber0(esk3_1(X3))
& doDivides0(esk3_1(X3),X3)
& ~ equal(esk3_1(X3),sz10)
& ~ equal(esk3_1(X3),X3) )
| isPrime0(X3) ) ) ),
inference(skolemize,[status(esa)],[187]) ).
fof(189,plain,
! [X3,X4] :
( ( ( ( ( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| equal(X4,sz10)
| equal(X4,X3) )
& ~ equal(X3,sz00)
& ~ equal(X3,sz10) )
| ~ isPrime0(X3) )
& ( equal(X3,sz00)
| equal(X3,sz10)
| ( aNaturalNumber0(esk3_1(X3))
& doDivides0(esk3_1(X3),X3)
& ~ equal(esk3_1(X3),sz10)
& ~ equal(esk3_1(X3),X3) )
| isPrime0(X3) ) )
| ~ aNaturalNumber0(X3) ),
inference(shift_quantors,[status(thm)],[188]) ).
fof(190,plain,
! [X3,X4] :
( ( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| equal(X4,sz10)
| equal(X4,X3)
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(X3,sz00)
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(X3,sz10)
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( aNaturalNumber0(esk3_1(X3))
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( doDivides0(esk3_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk3_1(X3),sz10)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ equal(esk3_1(X3),X3)
| equal(X3,sz00)
| equal(X3,sz10)
| isPrime0(X3)
| ~ aNaturalNumber0(X3) ) ),
inference(distribute,[status(thm)],[189]) ).
cnf(196,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[190]) ).
cnf(198,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[38]) ).
fof(199,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(200,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[199]) ).
cnf(201,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[200]) ).
fof(209,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ( ~ equal(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
& ~ equal(sdtpldt0(X2,X1),sdtpldt0(X3,X1)) )
| equal(X2,X3) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(210,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ( ~ equal(sdtpldt0(X4,X5),sdtpldt0(X4,X6))
& ~ equal(sdtpldt0(X5,X4),sdtpldt0(X6,X4)) )
| equal(X5,X6) ),
inference(variable_rename,[status(thm)],[209]) ).
fof(211,plain,
! [X4,X5,X6] :
( ( ~ equal(sdtpldt0(X4,X5),sdtpldt0(X4,X6))
| equal(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( ~ equal(sdtpldt0(X5,X4),sdtpldt0(X6,X4))
| equal(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[210]) ).
cnf(213,plain,
( X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X3,X2) != sdtpldt0(X3,X1) ),
inference(split_conjunct,[status(thm)],[211]) ).
fof(224,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtpldt0(X1,sz00),X1)
& equal(X1,sdtpldt0(sz00,X1)) ) ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(225,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtpldt0(X2,sz00),X2)
& equal(X2,sdtpldt0(sz00,X2)) ) ),
inference(variable_rename,[status(thm)],[224]) ).
fof(226,plain,
! [X2] :
( ( equal(sdtpldt0(X2,sz00),X2)
| ~ aNaturalNumber0(X2) )
& ( equal(X2,sdtpldt0(sz00,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[225]) ).
cnf(227,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[226]) ).
cnf(228,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[226]) ).
cnf(234,plain,
( sz00 != xp
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[196,54,theory(equality)]) ).
cnf(235,plain,
( sz00 != xp
| $false ),
inference(rw,[status(thm)],[234,105,theory(equality)]) ).
cnf(236,plain,
sz00 != xp,
inference(cn,[status(thm)],[235,theory(equality)]) ).
cnf(256,plain,
( sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[93,107,theory(equality)]) ).
cnf(410,plain,
( aNaturalNumber0(sdtmndt0(X1,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[182,theory(equality)]) ).
cnf(411,plain,
( aNaturalNumber0(X1)
| xr != X1
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[182,55,theory(equality)]) ).
cnf(412,plain,
( aNaturalNumber0(X1)
| xr != X1
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[411,101,theory(equality)]) ).
cnf(413,plain,
( aNaturalNumber0(X1)
| xr != X1
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[412,105,theory(equality)]) ).
cnf(414,plain,
( aNaturalNumber0(X1)
| xr != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[413,107,theory(equality)]) ).
cnf(415,plain,
( aNaturalNumber0(X1)
| xr != X1 ),
inference(cn,[status(thm)],[414,theory(equality)]) ).
cnf(417,plain,
( sz00 = X1
| X2 != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[213,228,theory(equality)]) ).
cnf(427,plain,
( sz00 = X1
| X2 != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[417,198,theory(equality)]) ).
cnf(428,plain,
( sz00 = X1
| X2 != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[427,theory(equality)]) ).
cnf(488,plain,
( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[181,theory(equality)]) ).
cnf(489,plain,
( sdtpldt0(xp,X1) = xn
| xr != X1
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[181,55,theory(equality)]) ).
cnf(490,plain,
( sdtpldt0(xp,X1) = xn
| xr != X1
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[489,101,theory(equality)]) ).
cnf(491,plain,
( sdtpldt0(xp,X1) = xn
| xr != X1
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[490,105,theory(equality)]) ).
cnf(492,plain,
( sdtpldt0(xp,X1) = xn
| xr != X1
| $false
| $false
| $false ),
inference(rw,[status(thm)],[491,107,theory(equality)]) ).
cnf(493,plain,
( sdtpldt0(xp,X1) = xn
| xr != X1 ),
inference(cn,[status(thm)],[492,theory(equality)]) ).
cnf(505,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[228,140,theory(equality)]) ).
cnf(507,plain,
( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[140,227,theory(equality)]) ).
cnf(509,negated_conjecture,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[164,140,theory(equality)]) ).
cnf(511,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[61,140,theory(equality)]) ).
cnf(513,plain,
( sdtpldt0(sdtpldt0(X2,X1),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[140,61,theory(equality)]) ).
cnf(526,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[505,198,theory(equality)]) ).
cnf(527,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[526,theory(equality)]) ).
cnf(530,plain,
( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[507,198,theory(equality)]) ).
cnf(531,plain,
( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[530,theory(equality)]) ).
cnf(535,negated_conjecture,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
| $false
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[509,105,theory(equality)]) ).
cnf(536,negated_conjecture,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[535,106,theory(equality)]) ).
cnf(537,negated_conjecture,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[536,107,theory(equality)]) ).
cnf(538,negated_conjecture,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(cn,[status(thm)],[537,theory(equality)]) ).
cnf(597,plain,
( sdtmndt0(X1,X2) = X3
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[180,137]) ).
cnf(598,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(er,[status(thm)],[597,theory(equality)]) ).
cnf(975,plain,
( xn = sdtpldt0(X1,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| xr != X1 ),
inference(spm,[status(thm)],[61,493,theory(equality)]) ).
cnf(985,plain,
( sdtpldt0(xn,X2) = sdtpldt0(xp,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| xr != X1 ),
inference(spm,[status(thm)],[140,493,theory(equality)]) ).
cnf(986,plain,
( X1 = X2
| sdtlseqdt0(xn,sdtpldt0(xp,X1))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xr != X2 ),
inference(spm,[status(thm)],[115,493,theory(equality)]) ).
cnf(999,plain,
( xn = sdtpldt0(X1,xp)
| ~ aNaturalNumber0(X1)
| $false
| xr != X1 ),
inference(rw,[status(thm)],[975,105,theory(equality)]) ).
cnf(1000,plain,
( xn = sdtpldt0(X1,xp)
| ~ aNaturalNumber0(X1)
| xr != X1 ),
inference(cn,[status(thm)],[999,theory(equality)]) ).
cnf(1020,plain,
( sdtpldt0(xn,X2) = sdtpldt0(xp,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false
| xr != X1 ),
inference(rw,[status(thm)],[985,105,theory(equality)]) ).
cnf(1021,plain,
( sdtpldt0(xn,X2) = sdtpldt0(xp,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xr != X1 ),
inference(cn,[status(thm)],[1020,theory(equality)]) ).
cnf(1022,plain,
( X1 = X2
| sdtlseqdt0(xn,sdtpldt0(xp,X1))
| ~ sdtlseqdt0(X2,X1)
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xr != X2 ),
inference(rw,[status(thm)],[986,105,theory(equality)]) ).
cnf(1023,plain,
( X1 = X2
| sdtlseqdt0(xn,sdtpldt0(xp,X1))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| xr != X2 ),
inference(cn,[status(thm)],[1022,theory(equality)]) ).
cnf(1081,plain,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[256,107,theory(equality)]) ).
cnf(1401,plain,
( sdtpldt0(X1,xp) = xn
| xr != X1 ),
inference(csr,[status(thm)],[1000,415]) ).
cnf(3594,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[410,55,theory(equality)]) ).
cnf(3606,plain,
( aNaturalNumber0(xr)
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[3594,101,theory(equality)]) ).
cnf(3607,plain,
( aNaturalNumber0(xr)
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[3606,105,theory(equality)]) ).
cnf(3608,plain,
( aNaturalNumber0(xr)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[3607,107,theory(equality)]) ).
cnf(3609,plain,
aNaturalNumber0(xr),
inference(cn,[status(thm)],[3608,theory(equality)]) ).
cnf(5510,plain,
( sdtpldt0(xp,xr) = xn
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[488,55,theory(equality)]) ).
cnf(5542,plain,
( sdtpldt0(xp,xr) = xn
| $false
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[5510,101,theory(equality)]) ).
cnf(5543,plain,
( sdtpldt0(xp,xr) = xn
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[5542,105,theory(equality)]) ).
cnf(5544,plain,
( sdtpldt0(xp,xr) = xn
| $false
| $false
| $false ),
inference(rw,[status(thm)],[5543,107,theory(equality)]) ).
cnf(5545,plain,
sdtpldt0(xp,xr) = xn,
inference(cn,[status(thm)],[5544,theory(equality)]) ).
cnf(5579,plain,
( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[140,5545,theory(equality)]) ).
cnf(5620,plain,
( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[5579,3609,theory(equality)]) ).
cnf(5621,plain,
( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[5620,105,theory(equality)]) ).
cnf(5622,plain,
( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[5621,theory(equality)]) ).
cnf(6350,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[527,201]) ).
cnf(6556,plain,
( sdtpldt0(sz00,xn) = xn
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[531,5545,theory(equality)]) ).
cnf(6592,plain,
( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[6350,531,theory(equality)]) ).
cnf(6597,plain,
( sdtpldt0(sz00,xn) = xn
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[6556,3609,theory(equality)]) ).
cnf(6598,plain,
( sdtpldt0(sz00,xn) = xn
| $false
| $false ),
inference(rw,[status(thm)],[6597,105,theory(equality)]) ).
cnf(6599,plain,
sdtpldt0(sz00,xn) = xn,
inference(cn,[status(thm)],[6598,theory(equality)]) ).
cnf(6656,plain,
( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[6592,198,theory(equality)]) ).
cnf(6657,plain,
( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[6656,theory(equality)]) ).
cnf(6975,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[511,201]) ).
cnf(7019,plain,
( sdtpldt0(X1,X2) = X3
| sdtlseqdt0(sdtpldt0(X4,X3),sdtpldt0(X2,sdtpldt0(X4,X1)))
| ~ sdtlseqdt0(X3,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[115,6975,theory(equality)]) ).
cnf(7319,plain,
( sz00 = X1
| sdtpldt0(X3,sdtpldt0(X2,X1)) != sdtpldt0(X2,X3)
| ~ aNaturalNumber0(sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(spm,[status(thm)],[428,513,theory(equality)]) ).
cnf(7338,negated_conjecture,
( sdtpldt0(xm,sdtpldt0(xr,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[538,513,theory(equality)]) ).
cnf(7412,negated_conjecture,
( sdtpldt0(xm,sdtpldt0(xr,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
| $false
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[7338,105,theory(equality)]) ).
cnf(7413,negated_conjecture,
( sdtpldt0(xm,sdtpldt0(xr,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
| $false
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[7412,3609,theory(equality)]) ).
cnf(7414,negated_conjecture,
( sdtpldt0(xm,sdtpldt0(xr,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[7413,106,theory(equality)]) ).
cnf(7415,negated_conjecture,
( sdtpldt0(xm,sdtpldt0(xr,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(cn,[status(thm)],[7414,theory(equality)]) ).
cnf(13381,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[598,201]) ).
cnf(13410,plain,
( sdtmndt0(sdtpldt0(sz00,X1),X1) = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[13381,6657,theory(equality)]) ).
cnf(13443,plain,
( sdtmndt0(sdtpldt0(sz00,X1),X1) = sz00
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[13410,198,theory(equality)]) ).
cnf(13444,plain,
( sdtmndt0(sdtpldt0(sz00,X1),X1) = sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[13443,theory(equality)]) ).
cnf(15246,plain,
( sdtmndt0(xn,xn) = sz00
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[13444,6599,theory(equality)]) ).
cnf(15272,plain,
( sdtmndt0(xn,xn) = sz00
| $false ),
inference(rw,[status(thm)],[15246,107,theory(equality)]) ).
cnf(15273,plain,
sdtmndt0(xn,xn) = sz00,
inference(cn,[status(thm)],[15272,theory(equality)]) ).
cnf(15321,plain,
( sdtpldt0(xn,sz00) = xn
| ~ sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[488,15273,theory(equality)]) ).
cnf(15332,plain,
( sdtpldt0(xn,sz00) = xn
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[15321,1081,theory(equality)]) ).
cnf(15333,plain,
( sdtpldt0(xn,sz00) = xn
| $false
| $false ),
inference(rw,[status(thm)],[15332,107,theory(equality)]) ).
cnf(15334,plain,
sdtpldt0(xn,sz00) = xn,
inference(cn,[status(thm)],[15333,theory(equality)]) ).
cnf(56014,plain,
( sdtpldt0(xp,sdtpldt0(X1,X2)) = sdtpldt0(xn,X2)
| xr != X1
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[1021,415]) ).
cnf(56049,plain,
( sdtpldt0(xp,xn) = sdtpldt0(xn,xp)
| xr != X1
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[56014,1401,theory(equality)]) ).
cnf(56268,plain,
( sdtpldt0(xp,xn) = sdtpldt0(xn,xp)
| xr != X1
| $false ),
inference(rw,[status(thm)],[56049,105,theory(equality)]) ).
cnf(56269,plain,
( sdtpldt0(xp,xn) = sdtpldt0(xn,xp)
| xr != X1 ),
inference(cn,[status(thm)],[56268,theory(equality)]) ).
cnf(57056,plain,
( X1 = X2
| sdtlseqdt0(xn,sdtpldt0(xp,X1))
| xr != X2
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[1023,415]) ).
cnf(57058,plain,
( xn = xr
| sdtlseqdt0(xn,sdtpldt0(xp,xn))
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[57056,151,theory(equality)]) ).
cnf(57175,plain,
( xn = xr
| sdtlseqdt0(xn,sdtpldt0(xp,xn))
| $false ),
inference(rw,[status(thm)],[57058,107,theory(equality)]) ).
cnf(57176,plain,
( xn = xr
| sdtlseqdt0(xn,sdtpldt0(xp,xn)) ),
inference(cn,[status(thm)],[57175,theory(equality)]) ).
cnf(57177,plain,
sdtlseqdt0(xn,sdtpldt0(xp,xn)),
inference(sr,[status(thm)],[57176,152,theory(equality)]) ).
cnf(72313,plain,
sdtpldt0(xn,xp) = sdtpldt0(xp,xn),
inference(er,[status(thm)],[56269,theory(equality)]) ).
cnf(72335,plain,
( sz00 = xp
| sdtpldt0(xp,xn) != xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[428,72313,theory(equality)]) ).
cnf(72506,plain,
( sz00 = xp
| sdtpldt0(xp,xn) != xn
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[72335,107,theory(equality)]) ).
cnf(72507,plain,
( sz00 = xp
| sdtpldt0(xp,xn) != xn
| $false
| $false ),
inference(rw,[status(thm)],[72506,105,theory(equality)]) ).
cnf(72508,plain,
( sz00 = xp
| sdtpldt0(xp,xn) != xn ),
inference(cn,[status(thm)],[72507,theory(equality)]) ).
cnf(72509,plain,
sdtpldt0(xp,xn) != xn,
inference(sr,[status(thm)],[72508,236,theory(equality)]) ).
cnf(174671,plain,
( sdtpldt0(xp,sdtpldt0(sz00,xr)) = sdtpldt0(xn,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[5622,6657,theory(equality)]) ).
cnf(174988,plain,
( sdtpldt0(xp,sdtpldt0(sz00,xr)) = xn
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[174671,15334,theory(equality)]) ).
cnf(174989,plain,
( sdtpldt0(xp,sdtpldt0(sz00,xr)) = xn
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[174988,198,theory(equality)]) ).
cnf(174990,plain,
( sdtpldt0(xp,sdtpldt0(sz00,xr)) = xn
| $false
| $false ),
inference(rw,[status(thm)],[174989,3609,theory(equality)]) ).
cnf(174991,plain,
sdtpldt0(xp,sdtpldt0(sz00,xr)) = xn,
inference(cn,[status(thm)],[174990,theory(equality)]) ).
cnf(175678,plain,
( sdtpldt0(sz00,sdtpldt0(xr,xp)) = xn
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[6975,174991,theory(equality)]) ).
cnf(175918,plain,
( sdtpldt0(sz00,sdtpldt0(xr,xp)) = xn
| $false
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[175678,105,theory(equality)]) ).
cnf(175919,plain,
( sdtpldt0(sz00,sdtpldt0(xr,xp)) = xn
| $false
| $false
| ~ aNaturalNumber0(sz00) ),
inference(rw,[status(thm)],[175918,3609,theory(equality)]) ).
cnf(175920,plain,
( sdtpldt0(sz00,sdtpldt0(xr,xp)) = xn
| $false
| $false
| $false ),
inference(rw,[status(thm)],[175919,198,theory(equality)]) ).
cnf(175921,plain,
sdtpldt0(sz00,sdtpldt0(xr,xp)) = xn,
inference(cn,[status(thm)],[175920,theory(equality)]) ).
cnf(177662,plain,
( xn = sdtpldt0(xr,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(spm,[status(thm)],[531,175921,theory(equality)]) ).
cnf(177891,plain,
( xn = sdtpldt0(xr,xp)
| $false
| ~ aNaturalNumber0(xr) ),
inference(rw,[status(thm)],[177662,105,theory(equality)]) ).
cnf(177892,plain,
( xn = sdtpldt0(xr,xp)
| $false
| $false ),
inference(rw,[status(thm)],[177891,3609,theory(equality)]) ).
cnf(177893,plain,
xn = sdtpldt0(xr,xp),
inference(cn,[status(thm)],[177892,theory(equality)]) ).
cnf(260496,plain,
( sdtpldt0(X1,X2) = X3
| sdtlseqdt0(sdtpldt0(X4,X3),sdtpldt0(X2,sdtpldt0(X4,X1)))
| ~ sdtlseqdt0(X3,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[7019,201]) ).
cnf(338987,plain,
( sz00 = X1
| sdtpldt0(X3,sdtpldt0(X2,X1)) != sdtpldt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[7319,201]) ).
cnf(355077,negated_conjecture,
( sdtpldt0(xm,xn) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(rw,[status(thm)],[7415,177893,theory(equality)]) ).
cnf(355078,negated_conjecture,
( sdtpldt0(xm,xn) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(rw,[status(thm)],[355077,177893,theory(equality)]) ).
cnf(355104,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
| sdtpldt0(xp,xn) = xn
| ~ sdtlseqdt0(xn,sdtpldt0(xp,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(spm,[status(thm)],[355078,260496,theory(equality)]) ).
cnf(355154,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
| sdtpldt0(xp,xn) = xn
| $false
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[355104,57177,theory(equality)]) ).
cnf(355155,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
| sdtpldt0(xp,xn) = xn
| $false
| $false
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[355154,106,theory(equality)]) ).
cnf(355156,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
| sdtpldt0(xp,xn) = xn
| $false
| $false
| $false
| ~ aNaturalNumber0(xp) ),
inference(rw,[status(thm)],[355155,107,theory(equality)]) ).
cnf(355157,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
| sdtpldt0(xp,xn) = xn
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[355156,105,theory(equality)]) ).
cnf(355158,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
| sdtpldt0(xp,xn) = xn ),
inference(cn,[status(thm)],[355157,theory(equality)]) ).
cnf(355159,negated_conjecture,
sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn),
inference(sr,[status(thm)],[355158,72509,theory(equality)]) ).
cnf(355590,negated_conjecture,
( sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[338987,355159,theory(equality)]) ).
cnf(356619,negated_conjecture,
( sz00 = xp
| $false
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[355590,105,theory(equality)]) ).
cnf(356620,negated_conjecture,
( sz00 = xp
| $false
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[356619,106,theory(equality)]) ).
cnf(356621,negated_conjecture,
( sz00 = xp
| $false
| $false
| $false ),
inference(rw,[status(thm)],[356620,107,theory(equality)]) ).
cnf(356622,negated_conjecture,
sz00 = xp,
inference(cn,[status(thm)],[356621,theory(equality)]) ).
cnf(356623,negated_conjecture,
$false,
inference(sr,[status(thm)],[356622,236,theory(equality)]) ).
cnf(356624,negated_conjecture,
$false,
356623,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM494+1 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04 % Command : Source/sine.py -e eprover -t %d %s
% 0.02/0.23 % Computer : n138.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Jan 5 05:44:00 CST 2018
% 0.02/0.23 % CPUTime :
% 0.02/0.27 % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.27 --creating new selector for []
% 7.28/7.52 -running prover on /export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1 with time limit 29
% 7.28/7.52 -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/tmpm2TVOq/sel_theBenchmark.p_1']
% 7.28/7.52 -prover status Theorem
% 7.28/7.52 Problem theBenchmark.p solved in phase 0.
% 7.28/7.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.28/7.52 % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.28/7.52 Solved 1 out of 1.
% 7.28/7.52 # Problem is unsatisfiable (or provable), constructing proof object
% 7.28/7.52 # SZS status Theorem
% 7.28/7.52 # SZS output start CNFRefutation.
% See solution above
% 7.28/7.52 # SZS output end CNFRefutation
%------------------------------------------------------------------------------