%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET976+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 03:57:02 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 8 unt; 0 def)
% Number of atoms : 174 ( 66 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 207 ( 81 ~; 89 |; 32 &)
% ( 5 <=>; 0 =>; 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 7 sgn 46 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
<=> ( in(X1,X3)
& X2 = X4 ) ),
file('/tmp/tmpeqMJbi/sel_SET976+1.p_1',t129_zfmisc_1) ).
fof(2,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/tmp/tmpeqMJbi/sel_SET976+1.p_1',l55_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpeqMJbi/sel_SET976+1.p_1',d5_tarski) ).
fof(7,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpeqMJbi/sel_SET976+1.p_1',d1_tarski) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
<=> ( in(X1,X3)
& X2 = X4 ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(14,negated_conjecture,
? [X1,X2,X3,X4] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
| ~ in(X1,X3)
| X2 != X4 )
& ( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
| ( in(X1,X3)
& X2 = X4 ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(15,negated_conjecture,
? [X5,X6,X7,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)))
| ( in(X5,X7)
& X6 = X8 ) ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,negated_conjecture,
( ( ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0)))
| ~ in(esk1_0,esk3_0)
| esk2_0 != esk4_0 )
& ( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0)))
| ( in(esk1_0,esk3_0)
& esk2_0 = esk4_0 ) ) ),
inference(skolemize,[status(esa)],[15]) ).
fof(17,negated_conjecture,
( ( ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0)))
| ~ in(esk1_0,esk3_0)
| esk2_0 != esk4_0 )
& ( in(esk1_0,esk3_0)
| in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0))) )
& ( esk2_0 = esk4_0
| in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0))) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,negated_conjecture,
( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0)))
| esk2_0 = esk4_0 ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,negated_conjecture,
( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0)))
| in(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(20,negated_conjecture,
( esk2_0 != esk4_0
| ~ in(esk1_0,esk3_0)
| ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0))) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,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)],[2]) ).
fof(22,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)],[21]) ).
fof(23,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)],[22]) ).
cnf(24,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(26,plain,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(27,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(28,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[27]) ).
fof(36,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(37,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) != X4 )
& ( in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[37]) ).
fof(39,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) != X4 )
& ( in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[38]) ).
fof(40,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[39]) ).
cnf(43,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(44,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(51,negated_conjecture,
( esk4_0 = esk2_0
| in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)),cartesian_product2(esk3_0,singleton(esk4_0))) ),
inference(rw,[status(thm)],[18,28,theory(equality)]),
[unfolding] ).
cnf(52,negated_conjecture,
( in(esk1_0,esk3_0)
| in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)),cartesian_product2(esk3_0,singleton(esk4_0))) ),
inference(rw,[status(thm)],[19,28,theory(equality)]),
[unfolding] ).
cnf(53,plain,
( in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[25,28,theory(equality)]),
[unfolding] ).
cnf(54,plain,
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[26,28,theory(equality)]),
[unfolding] ).
cnf(55,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[24,28,theory(equality)]),
[unfolding] ).
cnf(57,negated_conjecture,
( esk4_0 != esk2_0
| ~ in(esk1_0,esk3_0)
| ~ in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)),cartesian_product2(esk3_0,singleton(esk4_0))) ),
inference(rw,[status(thm)],[20,28,theory(equality)]),
[unfolding] ).
cnf(59,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[43,theory(equality)]) ).
cnf(75,negated_conjecture,
( in(esk2_0,singleton(esk4_0))
| esk2_0 = esk4_0 ),
inference(spm,[status(thm)],[53,51,theory(equality)]) ).
cnf(82,negated_conjecture,
in(esk1_0,esk3_0),
inference(spm,[status(thm)],[54,52,theory(equality)]) ).
cnf(95,negated_conjecture,
( esk2_0 != esk4_0
| ~ in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)),cartesian_product2(esk3_0,singleton(esk4_0)))
| $false ),
inference(rw,[status(thm)],[57,82,theory(equality)]) ).
cnf(96,negated_conjecture,
( esk2_0 != esk4_0
| ~ in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)),cartesian_product2(esk3_0,singleton(esk4_0))) ),
inference(cn,[status(thm)],[95,theory(equality)]) ).
cnf(99,negated_conjecture,
( esk2_0 != esk4_0
| ~ in(esk2_0,singleton(esk4_0))
| ~ in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[96,55,theory(equality)]) ).
cnf(100,negated_conjecture,
( esk2_0 != esk4_0
| ~ in(esk2_0,singleton(esk4_0))
| $false ),
inference(rw,[status(thm)],[99,82,theory(equality)]) ).
cnf(101,negated_conjecture,
( esk2_0 != esk4_0
| ~ in(esk2_0,singleton(esk4_0)) ),
inference(cn,[status(thm)],[100,theory(equality)]) ).
cnf(112,negated_conjecture,
( X1 = esk2_0
| esk2_0 = esk4_0
| singleton(X1) != singleton(esk4_0) ),
inference(spm,[status(thm)],[44,75,theory(equality)]) ).
cnf(114,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[59,theory(equality)]) ).
cnf(117,negated_conjecture,
esk2_0 = esk4_0,
inference(er,[status(thm)],[112,theory(equality)]) ).
cnf(126,negated_conjecture,
( $false
| ~ in(esk2_0,singleton(esk4_0)) ),
inference(rw,[status(thm)],[101,117,theory(equality)]) ).
cnf(127,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[126,117,theory(equality)]),114,theory(equality)]) ).
cnf(128,negated_conjecture,
$false,
inference(cn,[status(thm)],[127,theory(equality)]) ).
cnf(129,negated_conjecture,
$false,
128,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET976+1.p
% --creating new selector for []
% -running prover on /tmp/tmpeqMJbi/sel_SET976+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET976+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET976+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET976+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
%
%------------------------------------------------------------------------------