TSTP Solution File: SET185+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET185+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 02:54:10 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 16 unt; 0 def)
% Number of atoms : 146 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 146 ( 54 ~; 60 |; 26 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 94 ( 5 sgn 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpBc2kk0/sel_SET185+3.p_1',subset_defn) ).
fof(2,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> union(X1,X2) = X2 ),
file('/tmp/tmpBc2kk0/sel_SET185+3.p_1',prove_subset_union) ).
fof(3,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpBc2kk0/sel_SET185+3.p_1',equal_defn) ).
fof(4,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmpBc2kk0/sel_SET185+3.p_1',union_defn) ).
fof(5,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpBc2kk0/sel_SET185+3.p_1',commutativity_of_union) ).
fof(8,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> union(X1,X2) = X2 ),
inference(assume_negation,[status(cth)],[2]) ).
fof(9,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(10,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)],[9]) ).
fof(11,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)],[10]) ).
fof(12,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)],[11]) ).
fof(13,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)],[12]) ).
cnf(14,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(15,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(16,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(17,negated_conjecture,
? [X1,X2] :
( subset(X1,X2)
& union(X1,X2) != X2 ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(18,negated_conjecture,
? [X3,X4] :
( subset(X3,X4)
& union(X3,X4) != X4 ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,negated_conjecture,
( subset(esk2_0,esk3_0)
& union(esk2_0,esk3_0) != esk3_0 ),
inference(skolemize,[status(esa)],[18]) ).
cnf(20,negated_conjecture,
union(esk2_0,esk3_0) != esk3_0,
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[19]) ).
fof(22,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(23,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[23]) ).
cnf(25,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(28,plain,
! [X1,X2,X3] :
( ( ~ member(X3,union(X1,X2))
| member(X3,X1)
| member(X3,X2) )
& ( ( ~ member(X3,X1)
& ~ member(X3,X2) )
| member(X3,union(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(29,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ( ~ member(X6,X4)
& ~ member(X6,X5) )
| member(X6,union(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[29]) ).
cnf(31,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(33,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(34,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(35,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(51,negated_conjecture,
union(esk3_0,esk2_0) != esk3_0,
inference(rw,[status(thm)],[20,35,theory(equality)]) ).
cnf(53,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[16,21,theory(equality)]) ).
cnf(60,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[14,31,theory(equality)]) ).
cnf(65,plain,
( member(esk1_2(union(X1,X2),X3),X2)
| member(esk1_2(union(X1,X2),X3),X1)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[33,15,theory(equality)]) ).
cnf(75,negated_conjecture,
( member(esk1_2(esk2_0,X1),esk3_0)
| subset(esk2_0,X1) ),
inference(spm,[status(thm)],[53,15,theory(equality)]) ).
cnf(88,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[60,15,theory(equality)]) ).
cnf(91,negated_conjecture,
subset(esk2_0,union(X1,esk3_0)),
inference(spm,[status(thm)],[60,75,theory(equality)]) ).
cnf(95,negated_conjecture,
( member(X1,union(X2,esk3_0))
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[16,91,theory(equality)]) ).
cnf(96,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[88,35,theory(equality)]) ).
cnf(117,negated_conjecture,
( subset(X1,union(X2,esk3_0))
| ~ member(esk1_2(X1,union(X2,esk3_0)),esk2_0) ),
inference(spm,[status(thm)],[14,95,theory(equality)]) ).
cnf(148,plain,
( member(esk1_2(union(X4,X4),X5),X4)
| subset(union(X4,X4),X5) ),
inference(ef,[status(thm)],[65,theory(equality)]) ).
cnf(195,plain,
subset(union(X1,X1),X1),
inference(spm,[status(thm)],[14,148,theory(equality)]) ).
cnf(204,plain,
( X1 = union(X1,X1)
| ~ subset(X1,union(X1,X1)) ),
inference(spm,[status(thm)],[25,195,theory(equality)]) ).
cnf(210,plain,
( X1 = union(X1,X1)
| $false ),
inference(rw,[status(thm)],[204,96,theory(equality)]) ).
cnf(211,plain,
X1 = union(X1,X1),
inference(cn,[status(thm)],[210,theory(equality)]) ).
cnf(227,negated_conjecture,
( subset(X1,esk3_0)
| ~ member(esk1_2(X1,esk3_0),esk2_0) ),
inference(spm,[status(thm)],[117,211,theory(equality)]) ).
cnf(262,negated_conjecture,
( subset(union(esk2_0,X1),esk3_0)
| member(esk1_2(union(esk2_0,X1),esk3_0),X1) ),
inference(spm,[status(thm)],[227,65,theory(equality)]) ).
cnf(277,negated_conjecture,
subset(union(esk2_0,esk3_0),esk3_0),
inference(spm,[status(thm)],[14,262,theory(equality)]) ).
cnf(282,negated_conjecture,
subset(union(esk3_0,esk2_0),esk3_0),
inference(rw,[status(thm)],[277,35,theory(equality)]) ).
cnf(286,negated_conjecture,
( esk3_0 = union(esk3_0,esk2_0)
| ~ subset(esk3_0,union(esk3_0,esk2_0)) ),
inference(spm,[status(thm)],[25,282,theory(equality)]) ).
cnf(289,negated_conjecture,
( esk3_0 = union(esk3_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[286,96,theory(equality)]) ).
cnf(290,negated_conjecture,
esk3_0 = union(esk3_0,esk2_0),
inference(cn,[status(thm)],[289,theory(equality)]) ).
cnf(291,negated_conjecture,
$false,
inference(sr,[status(thm)],[290,51,theory(equality)]) ).
cnf(292,negated_conjecture,
$false,
291,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET185+3.p
% --creating new selector for []
% -running prover on /tmp/tmpBc2kk0/sel_SET185+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET185+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET185+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET185+3.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
%
%------------------------------------------------------------------------------