%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET594+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 02:59:29 EST 2010
% Result : Theorem 2.16s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 5 unt; 0 def)
% Number of atoms : 124 ( 6 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 138 ( 51 ~; 55 |; 26 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 3 sgn 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmp7qPaaa/sel_SET594+3.p_1',subset_defn) ).
fof(3,conjecture,
! [X1,X2,X3] :
( union(intersection(X1,X2),intersection(X1,X3)) = X1
=> subset(X1,union(X2,X3)) ),
file('/tmp/tmp7qPaaa/sel_SET594+3.p_1',prove_th53) ).
fof(5,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmp7qPaaa/sel_SET594+3.p_1',union_defn) ).
fof(8,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmp7qPaaa/sel_SET594+3.p_1',intersection_defn) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
( union(intersection(X1,X2),intersection(X1,X3)) = X1
=> subset(X1,union(X2,X3)) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(13,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(14,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[14]) ).
fof(16,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[15]) ).
fof(17,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,negated_conjecture,
? [X1,X2,X3] :
( union(intersection(X1,X2),intersection(X1,X3)) = X1
& ~ subset(X1,union(X2,X3)) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(22,negated_conjecture,
? [X4,X5,X6] :
( union(intersection(X4,X5),intersection(X4,X6)) = X4
& ~ subset(X4,union(X5,X6)) ),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,negated_conjecture,
( union(intersection(esk2_0,esk3_0),intersection(esk2_0,esk4_0)) = esk2_0
& ~ subset(esk2_0,union(esk3_0,esk4_0)) ),
inference(skolemize,[status(esa)],[22]) ).
cnf(24,negated_conjecture,
~ subset(esk2_0,union(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,negated_conjecture,
union(intersection(esk2_0,esk3_0),intersection(esk2_0,esk4_0)) = esk2_0,
inference(split_conjunct,[status(thm)],[23]) ).
fof(32,plain,
! [X1,X2,X3] :
( ( ~ member(X3,union(X1,X2))
| member(X3,X1)
| member(X3,X2) )
& ( ( ~ member(X3,X1)
& ~ member(X3,X2) )
| member(X3,union(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(33,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ( ~ member(X6,X4)
& ~ member(X6,X5) )
| member(X6,union(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(35,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(37,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(49,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(50,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)],[49]) ).
fof(51,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)],[50]) ).
cnf(53,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(74,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[18,35,theory(equality)]) ).
cnf(75,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[18,36,theory(equality)]) ).
cnf(83,negated_conjecture,
( member(X1,intersection(esk2_0,esk4_0))
| member(X1,intersection(esk2_0,esk3_0))
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[37,25,theory(equality)]) ).
cnf(129,negated_conjecture,
( member(X1,esk4_0)
| member(X1,intersection(esk2_0,esk3_0))
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[53,83,theory(equality)]) ).
cnf(383,negated_conjecture,
( member(X1,esk3_0)
| member(X1,esk4_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[53,129,theory(equality)]) ).
cnf(395,negated_conjecture,
( subset(X1,union(X2,esk4_0))
| member(esk1_2(X1,union(X2,esk4_0)),esk3_0)
| ~ member(esk1_2(X1,union(X2,esk4_0)),esk2_0) ),
inference(spm,[status(thm)],[74,383,theory(equality)]) ).
cnf(20289,negated_conjecture,
( subset(X1,union(esk3_0,esk4_0))
| ~ member(esk1_2(X1,union(esk3_0,esk4_0)),esk2_0) ),
inference(spm,[status(thm)],[75,395,theory(equality)]) ).
cnf(62966,negated_conjecture,
subset(esk2_0,union(esk3_0,esk4_0)),
inference(spm,[status(thm)],[20289,19,theory(equality)]) ).
cnf(62999,negated_conjecture,
$false,
inference(sr,[status(thm)],[62966,24,theory(equality)]) ).
cnf(63000,negated_conjecture,
$false,
62999,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET594+3.p
% --creating new selector for []
% -running prover on /tmp/tmp7qPaaa/sel_SET594+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET594+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET594+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET594+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
%
%------------------------------------------------------------------------------