TSTP Solution File: SET929+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET929+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 03:48:11 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 6 unt; 0 def)
% Number of atoms : 104 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 115 ( 46 ~; 46 |; 19 &)
% ( 4 <=>; 0 =>; 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 : 43 ( 2 sgn 24 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = empty_set
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/tmp/tmpQcgVyK/sel_SET929+1.p_1',t73_zfmisc_1) ).
fof(3,axiom,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/tmp/tmpQcgVyK/sel_SET929+1.p_1',t38_zfmisc_1) ).
fof(5,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpQcgVyK/sel_SET929+1.p_1',t37_xboole_1) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = empty_set
<=> ( in(X1,X3)
& in(X2,X3) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(13,negated_conjecture,
? [X1,X2,X3] :
( ( set_difference(unordered_pair(X1,X2),X3) != empty_set
| ~ in(X1,X3)
| ~ in(X2,X3) )
& ( set_difference(unordered_pair(X1,X2),X3) = empty_set
| ( in(X1,X3)
& in(X2,X3) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(14,negated_conjecture,
? [X4,X5,X6] :
( ( set_difference(unordered_pair(X4,X5),X6) != empty_set
| ~ in(X4,X6)
| ~ in(X5,X6) )
& ( set_difference(unordered_pair(X4,X5),X6) = empty_set
| ( in(X4,X6)
& in(X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,negated_conjecture,
( ( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != empty_set
| ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk3_0) )
& ( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) = empty_set
| ( in(esk1_0,esk3_0)
& in(esk2_0,esk3_0) ) ) ),
inference(skolemize,[status(esa)],[14]) ).
fof(16,negated_conjecture,
( ( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != empty_set
| ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk3_0) )
& ( in(esk1_0,esk3_0)
| set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) = empty_set )
& ( in(esk2_0,esk3_0)
| set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) = empty_set ) ),
inference(distribute,[status(thm)],[15]) ).
cnf(17,negated_conjecture,
( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) = empty_set
| in(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(18,negated_conjecture,
( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) = empty_set
| in(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(19,negated_conjecture,
( ~ in(esk2_0,esk3_0)
| ~ in(esk1_0,esk3_0)
| set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != empty_set ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(23,plain,
! [X1,X2,X3] :
( ( ~ subset(unordered_pair(X1,X2),X3)
| ( in(X1,X3)
& in(X2,X3) ) )
& ( ~ in(X1,X3)
| ~ in(X2,X3)
| subset(unordered_pair(X1,X2),X3) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(24,plain,
! [X4,X5,X6] :
( ( ~ subset(unordered_pair(X4,X5),X6)
| ( in(X4,X6)
& in(X5,X6) ) )
& ( ~ in(X4,X6)
| ~ in(X5,X6)
| subset(unordered_pair(X4,X5),X6) ) ),
inference(variable_rename,[status(thm)],[23]) ).
fof(25,plain,
! [X4,X5,X6] :
( ( in(X4,X6)
| ~ subset(unordered_pair(X4,X5),X6) )
& ( in(X5,X6)
| ~ subset(unordered_pair(X4,X5),X6) )
& ( ~ in(X4,X6)
| ~ in(X5,X6)
| subset(unordered_pair(X4,X5),X6) ) ),
inference(distribute,[status(thm)],[24]) ).
cnf(26,plain,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(27,plain,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(28,plain,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(31,plain,
! [X1,X2] :
( ( set_difference(X1,X2) != empty_set
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(32,plain,
! [X3,X4] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| set_difference(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[31]) ).
cnf(33,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(34,plain,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(44,negated_conjecture,
( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[34,18,theory(equality)]) ).
cnf(45,negated_conjecture,
( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| in(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[34,17,theory(equality)]) ).
cnf(69,negated_conjecture,
in(esk1_0,esk3_0),
inference(csr,[status(thm)],[44,28]) ).
cnf(71,negated_conjecture,
( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != empty_set
| $false
| ~ in(esk2_0,esk3_0) ),
inference(rw,[status(thm)],[19,69,theory(equality)]) ).
cnf(72,negated_conjecture,
( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != empty_set
| ~ in(esk2_0,esk3_0) ),
inference(cn,[status(thm)],[71,theory(equality)]) ).
cnf(78,negated_conjecture,
in(esk2_0,esk3_0),
inference(csr,[status(thm)],[45,27]) ).
cnf(82,negated_conjecture,
( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != empty_set
| $false ),
inference(rw,[status(thm)],[72,78,theory(equality)]) ).
cnf(83,negated_conjecture,
set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != empty_set,
inference(cn,[status(thm)],[82,theory(equality)]) ).
cnf(84,negated_conjecture,
~ subset(unordered_pair(esk1_0,esk2_0),esk3_0),
inference(spm,[status(thm)],[83,33,theory(equality)]) ).
cnf(85,negated_conjecture,
( ~ in(esk2_0,esk3_0)
| ~ in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[84,26,theory(equality)]) ).
cnf(86,negated_conjecture,
( $false
| ~ in(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[85,78,theory(equality)]) ).
cnf(87,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[86,69,theory(equality)]) ).
cnf(88,negated_conjecture,
$false,
inference(cn,[status(thm)],[87,theory(equality)]) ).
cnf(89,negated_conjecture,
$false,
88,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET929+1.p
% --creating new selector for []
% -running prover on /tmp/tmpQcgVyK/sel_SET929+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET929+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET929+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET929+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
%
%------------------------------------------------------------------------------