%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET691+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 03:16:09 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 110 ( 45 ~; 40 |; 20 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 2 sgn 31 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpvP3_fd/sel_SET691+4.p_1',subset) ).
fof(2,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpvP3_fd/sel_SET691+4.p_1',equal_set) ).
fof(3,axiom,
! [X3] : ~ member(X3,empty_set),
file('/tmp/tmpvP3_fd/sel_SET691+4.p_1',empty_set) ).
fof(4,conjecture,
! [X1] :
( subset(X1,empty_set)
<=> equal_set(X1,empty_set) ),
file('/tmp/tmpvP3_fd/sel_SET691+4.p_1',thI16) ).
fof(5,negated_conjecture,
~ ! [X1] :
( subset(X1,empty_set)
<=> equal_set(X1,empty_set) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(6,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[3,theory(equality)]) ).
fof(7,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)],[1]) ).
fof(8,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)],[7]) ).
fof(9,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)],[8]) ).
fof(10,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)],[9]) ).
fof(11,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)],[10]) ).
cnf(13,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[11]) ).
fof(15,plain,
! [X1,X2] :
( ( ~ equal_set(X1,X2)
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| equal_set(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(16,plain,
! [X3,X4] :
( ( ~ equal_set(X3,X4)
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(20,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,plain,
! [X4] : ~ member(X4,empty_set),
inference(variable_rename,[status(thm)],[6]) ).
cnf(22,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,negated_conjecture,
? [X1] :
( ( ~ subset(X1,empty_set)
| ~ equal_set(X1,empty_set) )
& ( subset(X1,empty_set)
| equal_set(X1,empty_set) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(24,negated_conjecture,
? [X2] :
( ( ~ subset(X2,empty_set)
| ~ equal_set(X2,empty_set) )
& ( subset(X2,empty_set)
| equal_set(X2,empty_set) ) ),
inference(variable_rename,[status(thm)],[23]) ).
fof(25,negated_conjecture,
( ( ~ subset(esk2_0,empty_set)
| ~ equal_set(esk2_0,empty_set) )
& ( subset(esk2_0,empty_set)
| equal_set(esk2_0,empty_set) ) ),
inference(skolemize,[status(esa)],[24]) ).
cnf(26,negated_conjecture,
( equal_set(esk2_0,empty_set)
| subset(esk2_0,empty_set) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(27,negated_conjecture,
( ~ equal_set(esk2_0,empty_set)
| ~ subset(esk2_0,empty_set) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(31,negated_conjecture,
( ~ subset(esk2_0,empty_set)
| ~ subset(empty_set,esk2_0) ),
inference(spm,[status(thm)],[27,18,theory(equality)]) ).
cnf(34,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[22,13,theory(equality)]) ).
cnf(37,negated_conjecture,
( ~ subset(esk2_0,empty_set)
| $false ),
inference(rw,[status(thm)],[31,34,theory(equality)]) ).
cnf(38,negated_conjecture,
~ subset(esk2_0,empty_set),
inference(cn,[status(thm)],[37,theory(equality)]) ).
cnf(39,negated_conjecture,
equal_set(esk2_0,empty_set),
inference(sr,[status(thm)],[26,38,theory(equality)]) ).
cnf(41,negated_conjecture,
subset(esk2_0,empty_set),
inference(spm,[status(thm)],[20,39,theory(equality)]) ).
cnf(45,negated_conjecture,
$false,
inference(sr,[status(thm)],[41,38,theory(equality)]) ).
cnf(46,negated_conjecture,
$false,
45,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET691+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpvP3_fd/sel_SET691+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET691+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET691+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET691+4.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
%
%------------------------------------------------------------------------------