TSTP Solution File: SET979+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET979+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:58:00 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 29 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 6 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2,X3] :
( cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& cartesian_product2(X3,set_union2(X1,X2)) = set_union2(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ),
file('/tmp/tmpRz0GxI/sel_SET979+1.p_1',t120_zfmisc_1) ).
fof(6,axiom,
! [X1,X2] : unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
file('/tmp/tmpRz0GxI/sel_SET979+1.p_1',t41_enumset1) ).
fof(10,conjecture,
! [X1,X2,X3] :
( cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3))
& cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2))) ),
file('/tmp/tmpRz0GxI/sel_SET979+1.p_1',t132_zfmisc_1) ).
fof(11,negated_conjecture,
~ ! [X1,X2,X3] :
( cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3))
& cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2))) ),
inference(assume_negation,[status(cth)],[10]) ).
fof(17,plain,
! [X4,X5,X6] :
( cartesian_product2(set_union2(X4,X5),X6) = set_union2(cartesian_product2(X4,X6),cartesian_product2(X5,X6))
& cartesian_product2(X6,set_union2(X4,X5)) = set_union2(cartesian_product2(X6,X4),cartesian_product2(X6,X5)) ),
inference(variable_rename,[status(thm)],[2]) ).
cnf(18,plain,
cartesian_product2(X1,set_union2(X2,X3)) = set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,plain,
cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)),
inference(split_conjunct,[status(thm)],[17]) ).
fof(28,plain,
! [X3,X4] : unordered_pair(X3,X4) = set_union2(singleton(X3),singleton(X4)),
inference(variable_rename,[status(thm)],[6]) ).
cnf(29,plain,
unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
inference(split_conjunct,[status(thm)],[28]) ).
fof(38,negated_conjecture,
? [X1,X2,X3] :
( cartesian_product2(unordered_pair(X1,X2),X3) != set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3))
| cartesian_product2(X3,unordered_pair(X1,X2)) != set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2))) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(39,negated_conjecture,
? [X4,X5,X6] :
( cartesian_product2(unordered_pair(X4,X5),X6) != set_union2(cartesian_product2(singleton(X4),X6),cartesian_product2(singleton(X5),X6))
| cartesian_product2(X6,unordered_pair(X4,X5)) != set_union2(cartesian_product2(X6,singleton(X4)),cartesian_product2(X6,singleton(X5))) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,negated_conjecture,
( cartesian_product2(unordered_pair(esk3_0,esk4_0),esk5_0) != set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0))
| cartesian_product2(esk5_0,unordered_pair(esk3_0,esk4_0)) != set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0))) ),
inference(skolemize,[status(esa)],[39]) ).
cnf(41,negated_conjecture,
( cartesian_product2(esk5_0,unordered_pair(esk3_0,esk4_0)) != set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0)))
| cartesian_product2(unordered_pair(esk3_0,esk4_0),esk5_0) != set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0)) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(43,negated_conjecture,
( set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0))) != cartesian_product2(esk5_0,set_union2(singleton(esk3_0),singleton(esk4_0)))
| set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0)) != cartesian_product2(set_union2(singleton(esk3_0),singleton(esk4_0)),esk5_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[41,29,theory(equality)]),29,theory(equality)]),
[unfolding] ).
cnf(59,negated_conjecture,
( $false
| set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0)) != cartesian_product2(set_union2(singleton(esk3_0),singleton(esk4_0)),esk5_0) ),
inference(rw,[status(thm)],[43,18,theory(equality)]) ).
cnf(60,negated_conjecture,
set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0)) != cartesian_product2(set_union2(singleton(esk3_0),singleton(esk4_0)),esk5_0),
inference(cn,[status(thm)],[59,theory(equality)]) ).
cnf(95,negated_conjecture,
$false,
inference(rw,[status(thm)],[60,19,theory(equality)]) ).
cnf(96,negated_conjecture,
$false,
inference(cn,[status(thm)],[95,theory(equality)]) ).
cnf(97,negated_conjecture,
$false,
96,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET979+1.p
% --creating new selector for []
% -running prover on /tmp/tmpRz0GxI/sel_SET979+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET979+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET979+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET979+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
%
%------------------------------------------------------------------------------