TSTP Solution File: SET008+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET008+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 02:36:12 EST 2010
% Result : Theorem 0.32s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 18 unt; 0 def)
% Number of atoms : 137 ( 29 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 159 ( 63 ~; 61 |; 30 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 5 sgn 56 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmpzALZYP/sel_SET008+3.p_1',commutativity_of_intersection) ).
fof(6,conjecture,
! [X1,X2] : intersection(difference(X1,X2),X2) = empty_set,
file('/tmp/tmpzALZYP/sel_SET008+3.p_1',prove_intersection_difference_empty_set) ).
fof(7,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/tmp/tmpzALZYP/sel_SET008+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/tmpzALZYP/sel_SET008+3.p_1',intersection_defn) ).
fof(9,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/tmp/tmpzALZYP/sel_SET008+3.p_1',difference_defn) ).
fof(10,axiom,
! [X1] : ~ member(X1,empty_set),
file('/tmp/tmpzALZYP/sel_SET008+3.p_1',empty_set_defn) ).
fof(11,negated_conjecture,
~ ! [X1,X2] : intersection(difference(X1,X2),X2) = empty_set,
inference(assume_negation,[status(cth)],[6]) ).
fof(13,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(14,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(15,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(16,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[15]) ).
fof(39,negated_conjecture,
? [X1,X2] : intersection(difference(X1,X2),X2) != empty_set,
inference(fof_nnf,[status(thm)],[11]) ).
fof(40,negated_conjecture,
? [X3,X4] : intersection(difference(X3,X4),X4) != empty_set,
inference(variable_rename,[status(thm)],[39]) ).
fof(41,negated_conjecture,
intersection(difference(esk3_0,esk4_0),esk4_0) != empty_set,
inference(skolemize,[status(esa)],[40]) ).
cnf(42,negated_conjecture,
intersection(difference(esk3_0,esk4_0),esk4_0) != empty_set,
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,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(44,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)],[43]) ).
fof(45,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)],[44]) ).
fof(46,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)],[45]) ).
fof(47,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)],[46]) ).
cnf(48,plain,
( X1 = X2
| member(esk5_2(X1,X2),X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(52,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(53,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)],[52]) ).
fof(54,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)],[53]) ).
cnf(56,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(57,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(58,plain,
! [X1,X2,X3] :
( ( ~ member(X3,difference(X1,X2))
| ( member(X3,X1)
& ~ member(X3,X2) ) )
& ( ~ member(X3,X1)
| member(X3,X2)
| member(X3,difference(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(59,plain,
! [X4,X5,X6] :
( ( ~ member(X6,difference(X4,X5))
| ( member(X6,X4)
& ~ member(X6,X5) ) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[58]) ).
fof(60,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X5)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(distribute,[status(thm)],[59]) ).
cnf(62,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(64,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[14]) ).
cnf(65,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(66,negated_conjecture,
intersection(esk4_0,difference(esk3_0,esk4_0)) != empty_set,
inference(rw,[status(thm)],[42,16,theory(equality)]) ).
cnf(96,plain,
( empty_set = X1
| member(esk5_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[65,48,theory(equality)]) ).
cnf(121,plain,
( member(esk5_2(empty_set,intersection(X1,X2)),X2)
| empty_set = intersection(X1,X2) ),
inference(spm,[status(thm)],[56,96,theory(equality)]) ).
cnf(122,plain,
( member(esk5_2(empty_set,intersection(X1,X2)),X1)
| empty_set = intersection(X1,X2) ),
inference(spm,[status(thm)],[57,96,theory(equality)]) ).
cnf(135,plain,
( intersection(X1,difference(X2,X3)) = empty_set
| ~ member(esk5_2(empty_set,intersection(X1,difference(X2,X3))),X3) ),
inference(spm,[status(thm)],[62,121,theory(equality)]) ).
cnf(2759,plain,
intersection(X1,difference(X2,X1)) = empty_set,
inference(spm,[status(thm)],[135,122,theory(equality)]) ).
cnf(2858,negated_conjecture,
$false,
inference(rw,[status(thm)],[66,2759,theory(equality)]) ).
cnf(2859,negated_conjecture,
$false,
inference(cn,[status(thm)],[2858,theory(equality)]) ).
cnf(2860,negated_conjecture,
$false,
2859,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET008+3.p
% --creating new selector for []
% -running prover on /tmp/tmpzALZYP/sel_SET008+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET008+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET008+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET008+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
%
%------------------------------------------------------------------------------