%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET977+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 03:57:11 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 8 unt; 0 def)
% Number of atoms : 115 ( 55 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 135 ( 59 ~; 47 |; 23 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 7 sgn 52 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
<=> ( in(X1,X3)
& X2 = X4 ) ),
file('/tmp/tmp5kcM8t/sel_SET977+1.p_1',t129_zfmisc_1) ).
fof(2,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmp5kcM8t/sel_SET977+1.p_1',d5_tarski) ).
fof(4,conjecture,
! [X1,X2] :
( X1 != empty_set
=> ( cartesian_product2(singleton(X2),X1) != empty_set
& cartesian_product2(X1,singleton(X2)) != empty_set ) ),
file('/tmp/tmp5kcM8t/sel_SET977+1.p_1',t130_zfmisc_1) ).
fof(9,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmp5kcM8t/sel_SET977+1.p_1',d1_xboole_0) ).
fof(11,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
<=> ( X1 = X3
& in(X2,X4) ) ),
file('/tmp/tmp5kcM8t/sel_SET977+1.p_1',t128_zfmisc_1) ).
fof(12,negated_conjecture,
~ ! [X1,X2] :
( X1 != empty_set
=> ( cartesian_product2(singleton(X2),X1) != empty_set
& cartesian_product2(X1,singleton(X2)) != empty_set ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(16,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(17,plain,
! [X1,X2,X3,X4] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
| ( in(X1,X3)
& X2 = X4 ) )
& ( ~ in(X1,X3)
| X2 != X4
| in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4))) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(18,plain,
! [X5,X6,X7,X8] :
( ( ~ in(ordered_pair(X5,X6),cartesian_product2(X7,singleton(X8)))
| ( in(X5,X7)
& X6 = X8 ) )
& ( ~ in(X5,X7)
| X6 != X8
| in(ordered_pair(X5,X6),cartesian_product2(X7,singleton(X8))) ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,plain,
! [X5,X6,X7,X8] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,singleton(X8))) )
& ( X6 = X8
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,singleton(X8))) )
& ( ~ in(X5,X7)
| X6 != X8
| in(ordered_pair(X5,X6),cartesian_product2(X7,singleton(X8))) ) ),
inference(distribute,[status(thm)],[18]) ).
cnf(20,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
| X2 != X4
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(23,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(24,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[23]) ).
fof(28,negated_conjecture,
? [X1,X2] :
( X1 != empty_set
& ( cartesian_product2(singleton(X2),X1) = empty_set
| cartesian_product2(X1,singleton(X2)) = empty_set ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(29,negated_conjecture,
? [X3,X4] :
( X3 != empty_set
& ( cartesian_product2(singleton(X4),X3) = empty_set
| cartesian_product2(X3,singleton(X4)) = empty_set ) ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,negated_conjecture,
( esk2_0 != empty_set
& ( cartesian_product2(singleton(esk3_0),esk2_0) = empty_set
| cartesian_product2(esk2_0,singleton(esk3_0)) = empty_set ) ),
inference(skolemize,[status(esa)],[29]) ).
cnf(31,negated_conjecture,
( cartesian_product2(esk2_0,singleton(esk3_0)) = empty_set
| cartesian_product2(singleton(esk3_0),esk2_0) = empty_set ),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(32,negated_conjecture,
esk2_0 != empty_set,
inference(split_conjunct,[status(thm)],[30]) ).
fof(43,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(44,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[43]) ).
fof(45,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk5_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[44]) ).
fof(46,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk5_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[45]) ).
cnf(47,plain,
( X1 = empty_set
| in(esk5_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(48,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(50,plain,
! [X1,X2,X3,X4] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
| ( X1 = X3
& in(X2,X4) ) )
& ( X1 != X3
| ~ in(X2,X4)
| in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4)) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(51,plain,
! [X5,X6,X7,X8] :
( ( ~ in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),X8))
| ( X5 = X7
& in(X6,X8) ) )
& ( X5 != X7
| ~ in(X6,X8)
| in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),X8)) ) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,plain,
! [X5,X6,X7,X8] :
( ( X5 = X7
| ~ in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),X8)) )
& ( X5 != X7
| ~ in(X6,X8)
| in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),X8)) ) ),
inference(distribute,[status(thm)],[51]) ).
cnf(53,plain,
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
| ~ in(X2,X4)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(60,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,singleton(X4)))
| X2 != X4
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[20,24,theory(equality)]),
[unfolding] ).
cnf(61,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(singleton(X3),X4))
| X1 != X3
| ~ in(X2,X4) ),
inference(rw,[status(thm)],[53,24,theory(equality)]),
[unfolding] ).
cnf(87,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,singleton(X2)))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[60,theory(equality)]) ).
cnf(88,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(singleton(X1),X3))
| ~ in(X2,X3) ),
inference(er,[status(thm)],[61,theory(equality)]) ).
cnf(182,plain,
( empty_set != cartesian_product2(X1,singleton(X2))
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[48,87,theory(equality)]) ).
cnf(212,plain,
( empty_set != cartesian_product2(singleton(X1),X2)
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[48,88,theory(equality)]) ).
cnf(220,negated_conjecture,
( cartesian_product2(esk2_0,singleton(esk3_0)) = empty_set
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[212,31,theory(equality)]) ).
cnf(221,negated_conjecture,
~ in(X1,esk2_0),
inference(csr,[status(thm)],[220,182]) ).
cnf(222,negated_conjecture,
empty_set = esk2_0,
inference(spm,[status(thm)],[221,47,theory(equality)]) ).
cnf(223,negated_conjecture,
$false,
inference(sr,[status(thm)],[222,32,theory(equality)]) ).
cnf(224,negated_conjecture,
$false,
223,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET977+1.p
% --creating new selector for []
% -running prover on /tmp/tmp5kcM8t/sel_SET977+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET977+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET977+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET977+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
%
%------------------------------------------------------------------------------