%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET956+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 03:54:20 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 125 ( 14 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 140 ( 54 ~; 48 |; 32 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 114 ( 2 sgn 68 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpvQZwJO/sel_SET956+1.p_1',d5_tarski) ).
fof(4,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpvQZwJO/sel_SET956+1.p_1',commutativity_k2_tarski) ).
fof(5,axiom,
! [X1,X2,X3,X4] :
~ ( subset(X1,cartesian_product2(X2,X3))
& in(X4,X1)
& ! [X5,X6] :
~ ( in(X5,X2)
& in(X6,X3)
& X4 = ordered_pair(X5,X6) ) ),
file('/tmp/tmpvQZwJO/sel_SET956+1.p_1',t103_zfmisc_1) ).
fof(8,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpvQZwJO/sel_SET956+1.p_1',d3_tarski) ).
fof(9,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,cartesian_product2(X2,X3))
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X1)
=> in(ordered_pair(X5,X6),X4) ) )
=> subset(X1,X4) ),
file('/tmp/tmpvQZwJO/sel_SET956+1.p_1',t109_zfmisc_1) ).
fof(11,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,cartesian_product2(X2,X3))
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X1)
=> in(ordered_pair(X5,X6),X4) ) )
=> subset(X1,X4) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(15,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(16,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[15]) ).
fof(22,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(23,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X1,X2,X3,X4] :
( ~ subset(X1,cartesian_product2(X2,X3))
| ~ in(X4,X1)
| ? [X5,X6] :
( in(X5,X2)
& in(X6,X3)
& X4 = ordered_pair(X5,X6) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(25,plain,
! [X7,X8,X9,X10] :
( ~ subset(X7,cartesian_product2(X8,X9))
| ~ in(X10,X7)
| ? [X11,X12] :
( in(X11,X8)
& in(X12,X9)
& X10 = ordered_pair(X11,X12) ) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,plain,
! [X7,X8,X9,X10] :
( ~ subset(X7,cartesian_product2(X8,X9))
| ~ in(X10,X7)
| ( in(esk2_4(X7,X8,X9,X10),X8)
& in(esk3_4(X7,X8,X9,X10),X9)
& X10 = ordered_pair(esk2_4(X7,X8,X9,X10),esk3_4(X7,X8,X9,X10)) ) ),
inference(skolemize,[status(esa)],[25]) ).
fof(27,plain,
! [X7,X8,X9,X10] :
( ( in(esk2_4(X7,X8,X9,X10),X8)
| ~ subset(X7,cartesian_product2(X8,X9))
| ~ in(X10,X7) )
& ( in(esk3_4(X7,X8,X9,X10),X9)
| ~ subset(X7,cartesian_product2(X8,X9))
| ~ in(X10,X7) )
& ( X10 = ordered_pair(esk2_4(X7,X8,X9,X10),esk3_4(X7,X8,X9,X10))
| ~ subset(X7,cartesian_product2(X8,X9))
| ~ in(X10,X7) ) ),
inference(distribute,[status(thm)],[26]) ).
cnf(28,plain,
( X1 = ordered_pair(esk2_4(X2,X3,X4,X1),esk3_4(X2,X3,X4,X1))
| ~ in(X1,X2)
| ~ subset(X2,cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(37,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(38,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[37]) ).
fof(39,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk5_2(X4,X5),X4)
& ~ in(esk5_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[38]) ).
fof(40,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk5_2(X4,X5),X4)
& ~ in(esk5_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[39]) ).
fof(41,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk5_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk5_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[40]) ).
cnf(42,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(43,plain,
( subset(X1,X2)
| in(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(45,negated_conjecture,
? [X1,X2,X3,X4] :
( subset(X1,cartesian_product2(X2,X3))
& ! [X5,X6] :
( ~ in(ordered_pair(X5,X6),X1)
| in(ordered_pair(X5,X6),X4) )
& ~ subset(X1,X4) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(46,negated_conjecture,
? [X7,X8,X9,X10] :
( subset(X7,cartesian_product2(X8,X9))
& ! [X11,X12] :
( ~ in(ordered_pair(X11,X12),X7)
| in(ordered_pair(X11,X12),X10) )
& ~ subset(X7,X10) ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,negated_conjecture,
( subset(esk6_0,cartesian_product2(esk7_0,esk8_0))
& ! [X11,X12] :
( ~ in(ordered_pair(X11,X12),esk6_0)
| in(ordered_pair(X11,X12),esk9_0) )
& ~ subset(esk6_0,esk9_0) ),
inference(skolemize,[status(esa)],[46]) ).
fof(48,negated_conjecture,
! [X11,X12] :
( ( ~ in(ordered_pair(X11,X12),esk6_0)
| in(ordered_pair(X11,X12),esk9_0) )
& subset(esk6_0,cartesian_product2(esk7_0,esk8_0))
& ~ subset(esk6_0,esk9_0) ),
inference(shift_quantors,[status(thm)],[47]) ).
cnf(49,negated_conjecture,
~ subset(esk6_0,esk9_0),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(50,negated_conjecture,
subset(esk6_0,cartesian_product2(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(51,negated_conjecture,
( in(ordered_pair(X1,X2),esk9_0)
| ~ in(ordered_pair(X1,X2),esk6_0) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(54,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk9_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk6_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[51,16,theory(equality)]),16,theory(equality)]),
[unfolding] ).
cnf(55,plain,
( unordered_pair(unordered_pair(esk2_4(X2,X3,X4,X1),esk3_4(X2,X3,X4,X1)),singleton(esk2_4(X2,X3,X4,X1))) = X1
| ~ in(X1,X2)
| ~ subset(X2,cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[28,16,theory(equality)]),
[unfolding] ).
cnf(69,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk9_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk6_0) ),
inference(spm,[status(thm)],[54,23,theory(equality)]) ).
cnf(73,plain,
( unordered_pair(singleton(esk2_4(X2,X3,X4,X1)),unordered_pair(esk2_4(X2,X3,X4,X1),esk3_4(X2,X3,X4,X1))) = X1
| ~ in(X1,X2)
| ~ subset(X2,cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[55,23,theory(equality)]) ).
cnf(105,negated_conjecture,
( in(X4,esk9_0)
| ~ in(X4,esk6_0)
| ~ in(X4,X1)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[69,73,theory(equality)]) ).
cnf(115,negated_conjecture,
( in(X1,esk9_0)
| ~ in(X1,esk6_0) ),
inference(spm,[status(thm)],[105,50,theory(equality)]) ).
cnf(117,negated_conjecture,
( subset(X1,esk9_0)
| ~ in(esk5_2(X1,esk9_0),esk6_0) ),
inference(spm,[status(thm)],[42,115,theory(equality)]) ).
cnf(119,negated_conjecture,
subset(esk6_0,esk9_0),
inference(spm,[status(thm)],[117,43,theory(equality)]) ).
cnf(120,negated_conjecture,
$false,
inference(sr,[status(thm)],[119,49,theory(equality)]) ).
cnf(121,negated_conjecture,
$false,
120,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET956+1.p
% --creating new selector for []
% -running prover on /tmp/tmpvQZwJO/sel_SET956+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET956+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET956+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET956+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
%
%------------------------------------------------------------------------------