TSTP Solution File: SET366+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET366+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 02:56:18 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 67 ( 30 ~; 22 |; 12 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 2 sgn 29 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpy7Pqe3/sel_SET366+4.p_1',subset) ).
fof(2,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/tmp/tmpy7Pqe3/sel_SET366+4.p_1',power_set) ).
fof(3,axiom,
! [X3] : ~ member(X3,empty_set),
file('/tmp/tmpy7Pqe3/sel_SET366+4.p_1',empty_set) ).
fof(4,conjecture,
! [X1] : member(empty_set,power_set(X1)),
file('/tmp/tmpy7Pqe3/sel_SET366+4.p_1',thI47) ).
fof(5,negated_conjecture,
~ ! [X1] : member(empty_set,power_set(X1)),
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,
! [X3,X1] :
( ( ~ member(X3,power_set(X1))
| subset(X3,X1) )
& ( ~ subset(X3,X1)
| member(X3,power_set(X1)) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(16,plain,
! [X4,X5] :
( ( ~ member(X4,power_set(X5))
| subset(X4,X5) )
& ( ~ subset(X4,X5)
| member(X4,power_set(X5)) ) ),
inference(variable_rename,[status(thm)],[15]) ).
cnf(17,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(19,plain,
! [X4] : ~ member(X4,empty_set),
inference(variable_rename,[status(thm)],[6]) ).
cnf(20,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,negated_conjecture,
? [X1] : ~ member(empty_set,power_set(X1)),
inference(fof_nnf,[status(thm)],[5]) ).
fof(22,negated_conjecture,
? [X2] : ~ member(empty_set,power_set(X2)),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,negated_conjecture,
~ member(empty_set,power_set(esk2_0)),
inference(skolemize,[status(esa)],[22]) ).
cnf(24,negated_conjecture,
~ member(empty_set,power_set(esk2_0)),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,negated_conjecture,
~ subset(empty_set,esk2_0),
inference(spm,[status(thm)],[24,17,theory(equality)]) ).
cnf(27,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[20,13,theory(equality)]) ).
cnf(32,negated_conjecture,
$false,
inference(rw,[status(thm)],[25,27,theory(equality)]) ).
cnf(33,negated_conjecture,
$false,
inference(cn,[status(thm)],[32,theory(equality)]) ).
cnf(34,negated_conjecture,
$false,
33,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET366+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpy7Pqe3/sel_SET366+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET366+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET366+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET366+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
%
%------------------------------------------------------------------------------