%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET201+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 02:54:58 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 12 unt; 0 def)
% Number of atoms : 122 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 123 ( 46 ~; 47 |; 25 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 95 ( 6 sgn 42 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmpvasbwP/sel_SET201+3.p_1',commutativity_of_intersection) ).
fof(2,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpvasbwP/sel_SET201+3.p_1',subset_defn) ).
fof(5,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(intersection(X1,X3),intersection(X2,X4)) ),
file('/tmp/tmpvasbwP/sel_SET201+3.p_1',prove_th41) ).
fof(6,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpvasbwP/sel_SET201+3.p_1',intersection_defn) ).
fof(7,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(intersection(X1,X3),intersection(X2,X4)) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(8,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(9,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[8]) ).
fof(10,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(11,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)],[10]) ).
fof(12,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)],[11]) ).
fof(13,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)],[12]) ).
fof(14,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)],[13]) ).
cnf(15,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(17,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[14]) ).
fof(29,negated_conjecture,
? [X1,X2,X3,X4] :
( subset(X1,X2)
& subset(X3,X4)
& ~ subset(intersection(X1,X3),intersection(X2,X4)) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(30,negated_conjecture,
? [X5,X6,X7,X8] :
( subset(X5,X6)
& subset(X7,X8)
& ~ subset(intersection(X5,X7),intersection(X6,X8)) ),
inference(variable_rename,[status(thm)],[29]) ).
fof(31,negated_conjecture,
( subset(esk3_0,esk4_0)
& subset(esk5_0,esk6_0)
& ~ subset(intersection(esk3_0,esk5_0),intersection(esk4_0,esk6_0)) ),
inference(skolemize,[status(esa)],[30]) ).
cnf(32,negated_conjecture,
~ subset(intersection(esk3_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(33,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(34,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[31]) ).
fof(35,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)],[6]) ).
fof(36,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)],[35]) ).
fof(37,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)],[36]) ).
cnf(38,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(39,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(40,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(43,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[39,16,theory(equality)]) ).
cnf(46,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[40,16,theory(equality)]) ).
cnf(47,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[17,34,theory(equality)]) ).
cnf(48,negated_conjecture,
( member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[17,33,theory(equality)]) ).
cnf(56,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[15,38,theory(equality)]) ).
cnf(65,negated_conjecture,
( subset(X1,esk4_0)
| ~ member(esk1_2(X1,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[15,47,theory(equality)]) ).
cnf(67,negated_conjecture,
( subset(X1,esk6_0)
| ~ member(esk1_2(X1,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[15,48,theory(equality)]) ).
cnf(78,negated_conjecture,
subset(intersection(X1,esk3_0),esk4_0),
inference(spm,[status(thm)],[65,43,theory(equality)]) ).
cnf(82,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,intersection(X2,esk3_0)) ),
inference(spm,[status(thm)],[17,78,theory(equality)]) ).
cnf(100,negated_conjecture,
subset(intersection(esk5_0,X1),esk6_0),
inference(spm,[status(thm)],[67,46,theory(equality)]) ).
cnf(104,negated_conjecture,
( member(X1,esk6_0)
| ~ member(X1,intersection(esk5_0,X2)) ),
inference(spm,[status(thm)],[17,100,theory(equality)]) ).
cnf(119,negated_conjecture,
( member(esk1_2(intersection(X1,esk3_0),X2),esk4_0)
| subset(intersection(X1,esk3_0),X2) ),
inference(spm,[status(thm)],[82,16,theory(equality)]) ).
cnf(143,negated_conjecture,
( member(esk1_2(intersection(esk5_0,X1),X2),esk6_0)
| subset(intersection(esk5_0,X1),X2) ),
inference(spm,[status(thm)],[104,16,theory(equality)]) ).
cnf(169,negated_conjecture,
( subset(intersection(X1,esk3_0),intersection(X2,esk4_0))
| ~ member(esk1_2(intersection(X1,esk3_0),intersection(X2,esk4_0)),X2) ),
inference(spm,[status(thm)],[56,119,theory(equality)]) ).
cnf(1430,negated_conjecture,
subset(intersection(esk5_0,esk3_0),intersection(esk6_0,esk4_0)),
inference(spm,[status(thm)],[169,143,theory(equality)]) ).
cnf(1445,negated_conjecture,
subset(intersection(esk3_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1430,9,theory(equality)]),9,theory(equality)]) ).
cnf(1446,negated_conjecture,
$false,
inference(sr,[status(thm)],[1445,32,theory(equality)]) ).
cnf(1447,negated_conjecture,
$false,
1446,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET201+3.p
% --creating new selector for []
% -running prover on /tmp/tmpvasbwP/sel_SET201+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET201+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET201+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET201+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
%
%------------------------------------------------------------------------------