TSTP Solution File: SET637+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET637+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 03:06:21 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 13 unt; 0 def)
% Number of atoms : 220 ( 26 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 251 ( 97 ~; 103 |; 42 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 124 ( 4 sgn 72 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,conjecture,
! [X1,X2] :
( intersect(X1,X2)
<=> not_equal(intersection(X1,X2),empty_set) ),
file('/tmp/tmpkZ2VrE/sel_SET637+3.p_1',prove_th119) ).
fof(3,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/tmp/tmpkZ2VrE/sel_SET637+3.p_1',empty_defn) ).
fof(4,axiom,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
file('/tmp/tmpkZ2VrE/sel_SET637+3.p_1',not_equal_defn) ).
fof(5,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpkZ2VrE/sel_SET637+3.p_1',intersect_defn) ).
fof(7,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/tmp/tmpkZ2VrE/sel_SET637+3.p_1',equal_member_defn) ).
fof(8,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpkZ2VrE/sel_SET637+3.p_1',intersection_defn) ).
fof(9,axiom,
! [X1] : ~ member(X1,empty_set),
file('/tmp/tmpkZ2VrE/sel_SET637+3.p_1',empty_set_defn) ).
fof(10,negated_conjecture,
~ ! [X1,X2] :
( intersect(X1,X2)
<=> not_equal(intersection(X1,X2),empty_set) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(11,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[3,theory(equality)]) ).
fof(12,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(15,negated_conjecture,
? [X1,X2] :
( ( ~ intersect(X1,X2)
| ~ not_equal(intersection(X1,X2),empty_set) )
& ( intersect(X1,X2)
| not_equal(intersection(X1,X2),empty_set) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(16,negated_conjecture,
? [X3,X4] :
( ( ~ intersect(X3,X4)
| ~ not_equal(intersection(X3,X4),empty_set) )
& ( intersect(X3,X4)
| not_equal(intersection(X3,X4),empty_set) ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,negated_conjecture,
( ( ~ intersect(esk1_0,esk2_0)
| ~ not_equal(intersection(esk1_0,esk2_0),empty_set) )
& ( intersect(esk1_0,esk2_0)
| not_equal(intersection(esk1_0,esk2_0),empty_set) ) ),
inference(skolemize,[status(esa)],[16]) ).
cnf(18,negated_conjecture,
( not_equal(intersection(esk1_0,esk2_0),empty_set)
| intersect(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,negated_conjecture,
( ~ not_equal(intersection(esk1_0,esk2_0),empty_set)
| ~ intersect(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(20,plain,
! [X1] :
( ( ~ empty(X1)
| ! [X2] : ~ member(X2,X1) )
& ( ? [X2] : member(X2,X1)
| empty(X1) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(21,plain,
! [X3] :
( ( ~ empty(X3)
| ! [X4] : ~ member(X4,X3) )
& ( ? [X5] : member(X5,X3)
| empty(X3) ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,plain,
! [X3] :
( ( ~ empty(X3)
| ! [X4] : ~ member(X4,X3) )
& ( member(esk3_1(X3),X3)
| empty(X3) ) ),
inference(skolemize,[status(esa)],[21]) ).
fof(23,plain,
! [X3,X4] :
( ( ~ member(X4,X3)
| ~ empty(X3) )
& ( member(esk3_1(X3),X3)
| empty(X3) ) ),
inference(shift_quantors,[status(thm)],[22]) ).
cnf(24,plain,
( empty(X1)
| member(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(26,plain,
! [X1,X2] :
( ( ~ not_equal(X1,X2)
| X1 != X2 )
& ( X1 = X2
| not_equal(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(27,plain,
! [X3,X4] :
( ( ~ not_equal(X3,X4)
| X3 != X4 )
& ( X3 = X4
| not_equal(X3,X4) ) ),
inference(variable_rename,[status(thm)],[26]) ).
cnf(28,plain,
( not_equal(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(29,plain,
( X1 != X2
| ~ not_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(30,plain,
! [X1,X2] :
( ( ~ intersect(X1,X2)
| ? [X3] :
( member(X3,X1)
& member(X3,X2) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| ~ member(X3,X2) )
| intersect(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(31,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ? [X6] :
( member(X6,X4)
& member(X6,X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ( member(esk4_2(X4,X5),X4)
& member(esk4_2(X4,X5),X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(skolemize,[status(esa)],[31]) ).
fof(33,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( ~ intersect(X4,X5)
| ( member(esk4_2(X4,X5),X4)
& member(esk4_2(X4,X5),X5) ) ) ),
inference(shift_quantors,[status(thm)],[32]) ).
fof(34,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( member(esk4_2(X4,X5),X4)
| ~ intersect(X4,X5) )
& ( member(esk4_2(X4,X5),X5)
| ~ intersect(X4,X5) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(35,plain,
( member(esk4_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( member(esk4_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(37,plain,
( intersect(X1,X2)
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(41,plain,
! [X1,X2] :
( ( X1 != X2
| ! [X3] :
( ( ~ member(X3,X1)
| member(X3,X2) )
& ( ~ member(X3,X2)
| member(X3,X1) ) ) )
& ( ? [X3] :
( ( ~ member(X3,X1)
| ~ member(X3,X2) )
& ( member(X3,X1)
| member(X3,X2) ) )
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(42,plain,
! [X4,X5] :
( ( X4 != X5
| ! [X6] :
( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) )
& ( ? [X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5) )
& ( member(X7,X4)
| member(X7,X5) ) )
| X4 = X5 ) ),
inference(variable_rename,[status(thm)],[41]) ).
fof(43,plain,
! [X4,X5] :
( ( X4 != X5
| ! [X6] :
( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) )
& ( ( ( ~ member(esk5_2(X4,X5),X4)
| ~ member(esk5_2(X4,X5),X5) )
& ( member(esk5_2(X4,X5),X4)
| member(esk5_2(X4,X5),X5) ) )
| X4 = X5 ) ),
inference(skolemize,[status(esa)],[42]) ).
fof(44,plain,
! [X4,X5,X6] :
( ( ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) )
| X4 != X5 )
& ( ( ( ~ member(esk5_2(X4,X5),X4)
| ~ member(esk5_2(X4,X5),X5) )
& ( member(esk5_2(X4,X5),X4)
| member(esk5_2(X4,X5),X5) ) )
| X4 = X5 ) ),
inference(shift_quantors,[status(thm)],[43]) ).
fof(45,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| X4 != X5 )
& ( ~ member(X6,X5)
| member(X6,X4)
| X4 != X5 )
& ( ~ member(esk5_2(X4,X5),X4)
| ~ member(esk5_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk5_2(X4,X5),X4)
| member(esk5_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[44]) ).
cnf(46,plain,
( X1 = X2
| member(esk5_2(X1,X2),X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(50,plain,
! [X1,X2,X3] :
( ( ~ member(X3,intersection(X1,X2))
| ( member(X3,X1)
& member(X3,X2) ) )
& ( ~ member(X3,X1)
| ~ member(X3,X2)
| member(X3,intersection(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(51,plain,
! [X4,X5,X6] :
( ( ~ member(X6,intersection(X4,X5))
| ( member(X6,X4)
& member(X6,X5) ) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5)) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5)) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(distribute,[status(thm)],[51]) ).
cnf(53,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(54,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(55,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(56,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[12]) ).
cnf(57,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(58,plain,
~ not_equal(X1,X1),
inference(er,[status(thm)],[29,theory(equality)]) ).
cnf(63,plain,
( member(esk3_1(intersection(X1,X2)),X2)
| empty(intersection(X1,X2)) ),
inference(spm,[status(thm)],[54,24,theory(equality)]) ).
cnf(66,plain,
( member(esk3_1(intersection(X1,X2)),X1)
| empty(intersection(X1,X2)) ),
inference(spm,[status(thm)],[55,24,theory(equality)]) ).
cnf(71,plain,
( empty_set = X1
| member(esk5_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[57,46,theory(equality)]) ).
cnf(86,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[25,71,theory(equality)]) ).
cnf(104,plain,
( intersect(X1,X2)
| empty(intersection(X3,X2))
| ~ member(esk3_1(intersection(X3,X2)),X1) ),
inference(spm,[status(thm)],[37,63,theory(equality)]) ).
cnf(346,plain,
( empty(intersection(X1,X2))
| intersect(X1,X2) ),
inference(spm,[status(thm)],[104,66,theory(equality)]) ).
cnf(407,plain,
( empty_set = intersection(X1,X2)
| intersect(X1,X2) ),
inference(spm,[status(thm)],[86,346,theory(equality)]) ).
cnf(415,negated_conjecture,
( intersection(esk1_0,esk2_0) = empty_set
| ~ not_equal(intersection(esk1_0,esk2_0),empty_set) ),
inference(spm,[status(thm)],[19,407,theory(equality)]) ).
cnf(550,negated_conjecture,
intersection(esk1_0,esk2_0) = empty_set,
inference(csr,[status(thm)],[415,28]) ).
cnf(566,negated_conjecture,
( not_equal(empty_set,empty_set)
| intersect(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[18,550,theory(equality)]) ).
cnf(567,negated_conjecture,
intersect(esk1_0,esk2_0),
inference(sr,[status(thm)],[566,58,theory(equality)]) ).
cnf(582,negated_conjecture,
member(esk4_2(esk1_0,esk2_0),esk2_0),
inference(spm,[status(thm)],[35,567,theory(equality)]) ).
cnf(583,negated_conjecture,
member(esk4_2(esk1_0,esk2_0),esk1_0),
inference(spm,[status(thm)],[36,567,theory(equality)]) ).
cnf(593,negated_conjecture,
( member(esk4_2(esk1_0,esk2_0),intersection(X1,esk2_0))
| ~ member(esk4_2(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[53,582,theory(equality)]) ).
cnf(1457,negated_conjecture,
member(esk4_2(esk1_0,esk2_0),intersection(esk1_0,esk2_0)),
inference(spm,[status(thm)],[593,583,theory(equality)]) ).
cnf(1464,negated_conjecture,
member(esk4_2(esk1_0,esk2_0),empty_set),
inference(rw,[status(thm)],[1457,550,theory(equality)]) ).
cnf(1465,negated_conjecture,
$false,
inference(sr,[status(thm)],[1464,57,theory(equality)]) ).
cnf(1466,negated_conjecture,
$false,
1465,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET637+3.p
% --creating new selector for []
% -running prover on /tmp/tmpkZ2VrE/sel_SET637+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET637+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET637+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET637+3.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
%
%------------------------------------------------------------------------------