TSTP Solution File: SET886+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET886+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 03:43:33 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 39 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 5 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 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 : 39 ( 3 sgn 21 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> unordered_pair(X1,X2) = singleton(X3) ),
file('/tmp/tmpCplwJb/sel_SET886+1.p_1',t27_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpCplwJb/sel_SET886+1.p_1',commutativity_k2_tarski) ).
fof(4,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpCplwJb/sel_SET886+1.p_1',t69_enumset1) ).
fof(7,axiom,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> X1 = X3 ),
file('/tmp/tmpCplwJb/sel_SET886+1.p_1',t26_zfmisc_1) ).
fof(8,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> unordered_pair(X1,X2) = singleton(X3) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(10,negated_conjecture,
? [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
& unordered_pair(X1,X2) != singleton(X3) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(11,negated_conjecture,
? [X4,X5,X6] :
( subset(unordered_pair(X4,X5),singleton(X6))
& unordered_pair(X4,X5) != singleton(X6) ),
inference(variable_rename,[status(thm)],[10]) ).
fof(12,negated_conjecture,
( subset(unordered_pair(esk1_0,esk2_0),singleton(esk3_0))
& unordered_pair(esk1_0,esk2_0) != singleton(esk3_0) ),
inference(skolemize,[status(esa)],[11]) ).
cnf(13,negated_conjecture,
unordered_pair(esk1_0,esk2_0) != singleton(esk3_0),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(14,negated_conjecture,
subset(unordered_pair(esk1_0,esk2_0),singleton(esk3_0)),
inference(split_conjunct,[status(thm)],[12]) ).
fof(18,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[3]) ).
cnf(19,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[4]) ).
cnf(21,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[20]) ).
fof(27,plain,
! [X1,X2,X3] :
( ~ subset(unordered_pair(X1,X2),singleton(X3))
| X1 = X3 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(28,plain,
! [X4,X5,X6] :
( ~ subset(unordered_pair(X4,X5),singleton(X6))
| X4 = X6 ),
inference(variable_rename,[status(thm)],[27]) ).
cnf(29,plain,
( X1 = X2
| ~ subset(unordered_pair(X1,X3),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(30,negated_conjecture,
subset(unordered_pair(esk1_0,esk2_0),unordered_pair(esk3_0,esk3_0)),
inference(rw,[status(thm)],[14,21,theory(equality)]),
[unfolding] ).
cnf(31,plain,
( X1 = X2
| ~ subset(unordered_pair(X1,X3),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[29,21,theory(equality)]),
[unfolding] ).
cnf(32,negated_conjecture,
unordered_pair(esk1_0,esk2_0) != unordered_pair(esk3_0,esk3_0),
inference(rw,[status(thm)],[13,21,theory(equality)]),
[unfolding] ).
cnf(37,negated_conjecture,
esk1_0 = esk3_0,
inference(spm,[status(thm)],[31,30,theory(equality)]) ).
cnf(38,plain,
( X1 = X2
| ~ subset(unordered_pair(X3,X1),unordered_pair(X2,X2)) ),
inference(spm,[status(thm)],[31,19,theory(equality)]) ).
cnf(42,negated_conjecture,
subset(unordered_pair(esk3_0,esk2_0),unordered_pair(esk3_0,esk3_0)),
inference(rw,[status(thm)],[30,37,theory(equality)]) ).
cnf(43,negated_conjecture,
unordered_pair(esk3_0,esk2_0) != unordered_pair(esk3_0,esk3_0),
inference(rw,[status(thm)],[32,37,theory(equality)]) ).
cnf(48,negated_conjecture,
esk2_0 = esk3_0,
inference(spm,[status(thm)],[38,42,theory(equality)]) ).
cnf(54,negated_conjecture,
$false,
inference(rw,[status(thm)],[43,48,theory(equality)]) ).
cnf(55,negated_conjecture,
$false,
inference(cn,[status(thm)],[54,theory(equality)]) ).
cnf(56,negated_conjecture,
$false,
55,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET886+1.p
% --creating new selector for []
% -running prover on /tmp/tmpCplwJb/sel_SET886+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET886+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET886+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET886+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
%
%------------------------------------------------------------------------------