TSTP Solution File: SET903+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET903+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 03:45:32 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 100 ( 98 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 117 ( 41 ~; 42 |; 34 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& ~ ( X2 = singleton(X1)
& X3 = singleton(X1) )
& ~ ( X2 = empty_set
& X3 = singleton(X1) )
& ~ ( X2 = singleton(X1)
& X3 = empty_set ) ),
file('/tmp/tmpMRcwOv/sel_SET903+1.p_1',t43_zfmisc_1) ).
fof(3,conjecture,
! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& X2 != X3
& X2 != empty_set
& X3 != empty_set ),
file('/tmp/tmpMRcwOv/sel_SET903+1.p_1',t44_zfmisc_1) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& X2 != X3
& X2 != empty_set
& X3 != empty_set ),
inference(assume_negation,[status(cth)],[3]) ).
fof(14,plain,
! [X1,X2,X3] :
( singleton(X1) != set_union2(X2,X3)
| ( X2 = singleton(X1)
& X3 = singleton(X1) )
| ( X2 = empty_set
& X3 = singleton(X1) )
| ( X2 = singleton(X1)
& X3 = empty_set ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(15,plain,
! [X4,X5,X6] :
( singleton(X4) != set_union2(X5,X6)
| ( X5 = singleton(X4)
& X6 = singleton(X4) )
| ( X5 = empty_set
& X6 = singleton(X4) )
| ( X5 = singleton(X4)
& X6 = empty_set ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,plain,
! [X4,X5,X6] :
( ( X5 = singleton(X4)
| X5 = empty_set
| X5 = singleton(X4)
| singleton(X4) != set_union2(X5,X6) )
& ( X6 = empty_set
| X5 = empty_set
| X5 = singleton(X4)
| singleton(X4) != set_union2(X5,X6) )
& ( X5 = singleton(X4)
| X6 = singleton(X4)
| X5 = singleton(X4)
| singleton(X4) != set_union2(X5,X6) )
& ( X6 = empty_set
| X6 = singleton(X4)
| X5 = singleton(X4)
| singleton(X4) != set_union2(X5,X6) )
& ( X5 = singleton(X4)
| X5 = empty_set
| X6 = singleton(X4)
| singleton(X4) != set_union2(X5,X6) )
& ( X6 = empty_set
| X5 = empty_set
| X6 = singleton(X4)
| singleton(X4) != set_union2(X5,X6) )
& ( X5 = singleton(X4)
| X6 = singleton(X4)
| X6 = singleton(X4)
| singleton(X4) != set_union2(X5,X6) )
& ( X6 = empty_set
| X6 = singleton(X4)
| X6 = singleton(X4)
| singleton(X4) != set_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[15]) ).
cnf(17,plain,
( X3 = singleton(X1)
| X3 = singleton(X1)
| X3 = empty_set
| singleton(X1) != set_union2(X2,X3) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(24,plain,
( X2 = singleton(X1)
| X2 = empty_set
| X2 = singleton(X1)
| singleton(X1) != set_union2(X2,X3) ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(28,negated_conjecture,
? [X1,X2,X3] :
( singleton(X1) = set_union2(X2,X3)
& X2 != X3
& X2 != empty_set
& X3 != empty_set ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(29,negated_conjecture,
? [X4,X5,X6] :
( singleton(X4) = set_union2(X5,X6)
& X5 != X6
& X5 != empty_set
& X6 != empty_set ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,negated_conjecture,
( singleton(esk2_0) = set_union2(esk3_0,esk4_0)
& esk3_0 != esk4_0
& esk3_0 != empty_set
& esk4_0 != empty_set ),
inference(skolemize,[status(esa)],[29]) ).
cnf(31,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[30]) ).
cnf(32,negated_conjecture,
esk3_0 != empty_set,
inference(split_conjunct,[status(thm)],[30]) ).
cnf(33,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[30]) ).
cnf(34,negated_conjecture,
singleton(esk2_0) = set_union2(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(53,negated_conjecture,
( singleton(X1) = esk4_0
| empty_set = esk4_0
| singleton(esk2_0) != singleton(X1) ),
inference(spm,[status(thm)],[17,34,theory(equality)]) ).
cnf(57,negated_conjecture,
( singleton(X1) = esk4_0
| singleton(esk2_0) != singleton(X1) ),
inference(sr,[status(thm)],[53,31,theory(equality)]) ).
cnf(79,negated_conjecture,
singleton(esk2_0) = esk4_0,
inference(er,[status(thm)],[57,theory(equality)]) ).
cnf(80,negated_conjecture,
set_union2(esk3_0,esk4_0) = esk4_0,
inference(rw,[status(thm)],[34,79,theory(equality)]) ).
cnf(83,negated_conjecture,
( singleton(X1) = esk3_0
| empty_set = esk3_0
| esk4_0 != singleton(X1) ),
inference(spm,[status(thm)],[24,80,theory(equality)]) ).
cnf(87,negated_conjecture,
( singleton(X1) = esk3_0
| singleton(X1) != esk4_0 ),
inference(sr,[status(thm)],[83,32,theory(equality)]) ).
cnf(88,negated_conjecture,
esk4_0 = esk3_0,
inference(spm,[status(thm)],[87,79,theory(equality)]) ).
cnf(89,negated_conjecture,
$false,
inference(sr,[status(thm)],[88,33,theory(equality)]) ).
cnf(90,negated_conjecture,
$false,
89,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET903+1.p
% --creating new selector for []
% -running prover on /tmp/tmpMRcwOv/sel_SET903+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET903+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET903+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET903+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
%
%------------------------------------------------------------------------------