TSTP Solution File: SEU165+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU165+3 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 04:59:44 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 94 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 102 ( 41 ~; 41 |; 17 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 7 sgn 28 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/tmp/tmpIGIK02/sel_SEU165+3.p_1',l55_zfmisc_1) ).
fof(2,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpIGIK02/sel_SEU165+3.p_1',d5_tarski) ).
fof(8,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/tmp/tmpIGIK02/sel_SEU165+3.p_1',t106_zfmisc_1) ).
fof(9,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
inference(assume_negation,[status(cth)],[8]) ).
fof(13,plain,
! [X1,X2,X3,X4] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ( in(X1,X3)
& in(X2,X4) ) )
& ( ~ in(X1,X3)
| ~ in(X2,X4)
| in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(14,plain,
! [X5,X6,X7,X8] :
( ( ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8))
| ( in(X5,X7)
& in(X6,X8) ) )
& ( ~ in(X5,X7)
| ~ in(X6,X8)
| in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,plain,
! [X5,X6,X7,X8] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( ~ in(X5,X7)
| ~ in(X6,X8)
| in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
inference(distribute,[status(thm)],[14]) ).
cnf(16,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(17,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(18,plain,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[15]) ).
fof(19,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(20,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[19]) ).
fof(34,negated_conjecture,
? [X1,X2,X3,X4] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X1,X3)
| ~ in(X2,X4) )
& ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ( in(X1,X3)
& in(X2,X4) ) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(35,negated_conjecture,
? [X5,X6,X7,X8] :
( ( ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8))
| ~ in(X5,X7)
| ~ in(X6,X8) )
& ( in(ordered_pair(X5,X6),cartesian_product2(X7,X8))
| ( in(X5,X7)
& in(X6,X8) ) ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,negated_conjecture,
( ( ~ in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk6_0) )
& ( in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| ( in(esk3_0,esk5_0)
& in(esk4_0,esk6_0) ) ) ),
inference(skolemize,[status(esa)],[35]) ).
fof(37,negated_conjecture,
( ( ~ in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk6_0) )
& ( in(esk3_0,esk5_0)
| in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) )
& ( in(esk4_0,esk6_0)
| in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ) ),
inference(distribute,[status(thm)],[36]) ).
cnf(38,negated_conjecture,
( in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| in(esk4_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(39,negated_conjecture,
( in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| in(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(40,negated_conjecture,
( ~ in(esk4_0,esk6_0)
| ~ in(esk3_0,esk5_0)
| ~ in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(41,negated_conjecture,
( in(esk3_0,esk5_0)
| in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[39,20,theory(equality)]),
[unfolding] ).
cnf(42,negated_conjecture,
( in(esk4_0,esk6_0)
| in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[38,20,theory(equality)]),
[unfolding] ).
cnf(43,plain,
( in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[17,20,theory(equality)]),
[unfolding] ).
cnf(44,plain,
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[18,20,theory(equality)]),
[unfolding] ).
cnf(45,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[16,20,theory(equality)]),
[unfolding] ).
cnf(47,negated_conjecture,
( ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk6_0)
| ~ in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[40,20,theory(equality)]),
[unfolding] ).
cnf(55,negated_conjecture,
in(esk4_0,esk6_0),
inference(spm,[status(thm)],[43,42,theory(equality)]) ).
cnf(66,negated_conjecture,
( ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk6_0) ),
inference(csr,[status(thm)],[47,45]) ).
cnf(71,negated_conjecture,
in(esk3_0,esk5_0),
inference(spm,[status(thm)],[44,41,theory(equality)]) ).
cnf(83,negated_conjecture,
( ~ in(esk3_0,esk5_0)
| $false ),
inference(rw,[status(thm)],[66,55,theory(equality)]) ).
cnf(84,negated_conjecture,
~ in(esk3_0,esk5_0),
inference(cn,[status(thm)],[83,theory(equality)]) ).
cnf(93,negated_conjecture,
$false,
inference(rw,[status(thm)],[84,71,theory(equality)]) ).
cnf(94,negated_conjecture,
$false,
inference(cn,[status(thm)],[93,theory(equality)]) ).
cnf(95,negated_conjecture,
$false,
94,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU165+3.p
% --creating new selector for []
% -running prover on /tmp/tmpIGIK02/sel_SEU165+3.p_1 with time limit 29
% -prover status Theorem
% Problem SEU165+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU165+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU165+3.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------