TSTP Solution File: SET962+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET962+1 : TPTP v5.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 03:55:01 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 15 unt; 0 def)
% Number of atoms : 114 ( 32 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 109 ( 40 ~; 50 |; 14 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 94 ( 5 sgn 39 !; 6 ?)
% 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/tmpiXqM3O/sel_SET962+1.p_1',l55_zfmisc_1) ).
fof(2,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpiXqM3O/sel_SET962+1.p_1',d5_tarski) ).
fof(3,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/tmp/tmpiXqM3O/sel_SET962+1.p_1',t2_tarski) ).
fof(5,conjecture,
! [X1,X2] :
( cartesian_product2(X1,X1) = cartesian_product2(X2,X2)
=> X1 = X2 ),
file('/tmp/tmpiXqM3O/sel_SET962+1.p_1',t115_zfmisc_1) ).
fof(7,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpiXqM3O/sel_SET962+1.p_1',commutativity_k2_tarski) ).
fof(10,negated_conjecture,
~ ! [X1,X2] :
( cartesian_product2(X1,X1) = cartesian_product2(X2,X2)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[5]) ).
fof(14,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(15,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)],[14]) ).
fof(16,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)],[15]) ).
cnf(17,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(18,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(20,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(21,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X2) ) )
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(23,plain,
! [X4,X5] :
( ? [X6] :
( ( ~ in(X6,X4)
| ~ in(X6,X5) )
& ( in(X6,X4)
| in(X6,X5) ) )
| X4 = X5 ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X4,X5] :
( ( ( ~ in(esk1_2(X4,X5),X4)
| ~ in(esk1_2(X4,X5),X5) )
& ( in(esk1_2(X4,X5),X4)
| in(esk1_2(X4,X5),X5) ) )
| X4 = X5 ),
inference(skolemize,[status(esa)],[23]) ).
fof(25,plain,
! [X4,X5] :
( ( ~ in(esk1_2(X4,X5),X4)
| ~ in(esk1_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk1_2(X4,X5),X4)
| in(esk1_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[24]) ).
cnf(26,plain,
( X1 = X2
| in(esk1_2(X1,X2),X2)
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(27,plain,
( X1 = X2
| ~ in(esk1_2(X1,X2),X2)
| ~ in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(31,negated_conjecture,
? [X1,X2] :
( cartesian_product2(X1,X1) = cartesian_product2(X2,X2)
& X1 != X2 ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(32,negated_conjecture,
? [X3,X4] :
( cartesian_product2(X3,X3) = cartesian_product2(X4,X4)
& X3 != X4 ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,negated_conjecture,
( cartesian_product2(esk3_0,esk3_0) = cartesian_product2(esk4_0,esk4_0)
& esk3_0 != esk4_0 ),
inference(skolemize,[status(esa)],[32]) ).
cnf(34,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,negated_conjecture,
cartesian_product2(esk3_0,esk3_0) = cartesian_product2(esk4_0,esk4_0),
inference(split_conjunct,[status(thm)],[33]) ).
fof(38,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(39,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(46,plain,
( in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[18,21,theory(equality)]),
[unfolding] ).
cnf(48,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[17,21,theory(equality)]),
[unfolding] ).
cnf(55,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[48,39,theory(equality)]) ).
cnf(56,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_2(X2,X3))),cartesian_product2(X4,X2))
| X2 = X3
| in(esk1_2(X2,X3),X3)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[55,26,theory(equality)]) ).
cnf(58,plain,
( in(X2,X4)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[46,39,theory(equality)]) ).
cnf(60,plain,
( in(X1,X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X1,X3)),cartesian_product2(X4,X2)) ),
inference(spm,[status(thm)],[58,39,theory(equality)]) ).
cnf(67,negated_conjecture,
( in(X1,esk3_0)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X1,X2)),cartesian_product2(esk4_0,esk4_0)) ),
inference(spm,[status(thm)],[60,35,theory(equality)]) ).
cnf(77,plain,
( X1 = X2
| in(unordered_pair(singleton(esk1_2(X3,X4)),unordered_pair(esk1_2(X3,X4),esk1_2(X1,X2))),cartesian_product2(X3,X1))
| in(esk1_2(X1,X2),X2)
| X3 = X4
| in(esk1_2(X3,X4),X4) ),
inference(spm,[status(thm)],[56,26,theory(equality)]) ).
cnf(127,negated_conjecture,
( in(esk1_2(esk4_0,X1),esk3_0)
| esk4_0 = X1
| in(esk1_2(esk4_0,X1),X1) ),
inference(spm,[status(thm)],[67,77,theory(equality)]) ).
cnf(133,negated_conjecture,
( esk4_0 = esk3_0
| in(esk1_2(esk4_0,esk3_0),esk3_0) ),
inference(ef,[status(thm)],[127,theory(equality)]) ).
cnf(144,negated_conjecture,
in(esk1_2(esk4_0,esk3_0),esk3_0),
inference(sr,[status(thm)],[133,34,theory(equality)]) ).
cnf(147,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_2(esk4_0,esk3_0))),cartesian_product2(X2,esk3_0))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[55,144,theory(equality)]) ).
cnf(148,negated_conjecture,
( esk4_0 = esk3_0
| ~ in(esk1_2(esk4_0,esk3_0),esk4_0) ),
inference(spm,[status(thm)],[27,144,theory(equality)]) ).
cnf(151,negated_conjecture,
~ in(esk1_2(esk4_0,esk3_0),esk4_0),
inference(sr,[status(thm)],[148,34,theory(equality)]) ).
cnf(173,negated_conjecture,
in(unordered_pair(singleton(esk1_2(esk4_0,esk3_0)),unordered_pair(esk1_2(esk4_0,esk3_0),esk1_2(esk4_0,esk3_0))),cartesian_product2(esk3_0,esk3_0)),
inference(spm,[status(thm)],[147,144,theory(equality)]) ).
cnf(184,negated_conjecture,
in(unordered_pair(singleton(esk1_2(esk4_0,esk3_0)),unordered_pair(esk1_2(esk4_0,esk3_0),esk1_2(esk4_0,esk3_0))),cartesian_product2(esk4_0,esk4_0)),
inference(rw,[status(thm)],[173,35,theory(equality)]) ).
cnf(193,negated_conjecture,
in(esk1_2(esk4_0,esk3_0),esk4_0),
inference(spm,[status(thm)],[58,184,theory(equality)]) ).
cnf(206,negated_conjecture,
$false,
inference(sr,[status(thm)],[193,151,theory(equality)]) ).
cnf(207,negated_conjecture,
$false,
206,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET962+1.p
% --creating new selector for []
% -running prover on /tmp/tmpiXqM3O/sel_SET962+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET962+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET962+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET962+1.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
%
%------------------------------------------------------------------------------