TSTP Solution File: SET923+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET923+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 03:47:44 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 61 ( 43 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 69 ( 30 ~; 19 |; 18 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/tmp/tmpbWCE7q/sel_SET923+1.p_1',l4_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpbWCE7q/sel_SET923+1.p_1',t37_xboole_1) ).
fof(5,conjecture,
! [X1,X2] :
~ ( set_difference(X1,singleton(X2)) = empty_set
& X1 != empty_set
& X1 != singleton(X2) ),
file('/tmp/tmpbWCE7q/sel_SET923+1.p_1',t66_zfmisc_1) ).
fof(8,negated_conjecture,
~ ! [X1,X2] :
~ ( set_difference(X1,singleton(X2)) = empty_set
& X1 != empty_set
& X1 != singleton(X2) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(10,plain,
! [X1,X2] :
( ( ~ subset(X1,singleton(X2))
| X1 = empty_set
| X1 = singleton(X2) )
& ( ( X1 != empty_set
& X1 != singleton(X2) )
| subset(X1,singleton(X2)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(11,plain,
! [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( ( X3 != empty_set
& X3 != singleton(X4) )
| subset(X3,singleton(X4)) ) ),
inference(variable_rename,[status(thm)],[10]) ).
fof(12,plain,
! [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X3 != empty_set
| subset(X3,singleton(X4)) )
& ( X3 != singleton(X4)
| subset(X3,singleton(X4)) ) ),
inference(distribute,[status(thm)],[11]) ).
cnf(15,plain,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[12]) ).
fof(19,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)],[3]) ).
fof(20,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)],[19]) ).
cnf(22,plain,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(26,negated_conjecture,
? [X1,X2] :
( set_difference(X1,singleton(X2)) = empty_set
& X1 != empty_set
& X1 != singleton(X2) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(27,negated_conjecture,
? [X3,X4] :
( set_difference(X3,singleton(X4)) = empty_set
& X3 != empty_set
& X3 != singleton(X4) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,negated_conjecture,
( set_difference(esk3_0,singleton(esk4_0)) = empty_set
& esk3_0 != empty_set
& esk3_0 != singleton(esk4_0) ),
inference(skolemize,[status(esa)],[27]) ).
cnf(29,negated_conjecture,
esk3_0 != singleton(esk4_0),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(30,negated_conjecture,
esk3_0 != empty_set,
inference(split_conjunct,[status(thm)],[28]) ).
cnf(31,negated_conjecture,
set_difference(esk3_0,singleton(esk4_0)) = empty_set,
inference(split_conjunct,[status(thm)],[28]) ).
cnf(35,negated_conjecture,
subset(esk3_0,singleton(esk4_0)),
inference(spm,[status(thm)],[22,31,theory(equality)]) ).
cnf(39,negated_conjecture,
( singleton(esk4_0) = esk3_0
| empty_set = esk3_0 ),
inference(spm,[status(thm)],[15,35,theory(equality)]) ).
cnf(40,negated_conjecture,
esk3_0 = empty_set,
inference(sr,[status(thm)],[39,29,theory(equality)]) ).
cnf(41,negated_conjecture,
$false,
inference(sr,[status(thm)],[40,30,theory(equality)]) ).
cnf(42,negated_conjecture,
$false,
41,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET923+1.p
% --creating new selector for []
% -running prover on /tmp/tmpbWCE7q/sel_SET923+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET923+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET923+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET923+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
%
%------------------------------------------------------------------------------