TSTP Solution File: SET584+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET584+3 : 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 03:02:46 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 103 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 105 ( 39 ~; 42 |; 19 &)
% ( 2 <=>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 2 sgn 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpnK2HkG/sel_SET584+3.p_1',subset_defn) ).
fof(2,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmpnK2HkG/sel_SET584+3.p_1',union_defn) ).
fof(3,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(union(X1,X3),union(X2,X3)) ),
file('/tmp/tmpnK2HkG/sel_SET584+3.p_1',prove_th33) ).
fof(4,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpnK2HkG/sel_SET584+3.p_1',commutativity_of_union) ).
fof(7,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(union(X1,X3),union(X2,X3)) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(8,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(9,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)],[8]) ).
fof(10,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)],[9]) ).
fof(11,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)],[10]) ).
fof(12,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)],[11]) ).
cnf(13,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(14,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(15,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[12]) ).
fof(16,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)],[2]) ).
fof(17,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)],[16]) ).
fof(18,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)],[17]) ).
cnf(19,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(20,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(21,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(22,negated_conjecture,
? [X1,X2,X3] :
( subset(X1,X2)
& ~ subset(union(X1,X3),union(X2,X3)) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(23,negated_conjecture,
? [X4,X5,X6] :
( subset(X4,X5)
& ~ subset(union(X4,X6),union(X5,X6)) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,negated_conjecture,
( subset(esk2_0,esk3_0)
& ~ subset(union(esk2_0,esk4_0),union(esk3_0,esk4_0)) ),
inference(skolemize,[status(esa)],[23]) ).
cnf(25,negated_conjecture,
~ subset(union(esk2_0,esk4_0),union(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(26,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[24]) ).
fof(27,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(28,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(45,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[13,19,theory(equality)]) ).
cnf(46,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[13,20,theory(equality)]) ).
cnf(48,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[15,26,theory(equality)]) ).
cnf(52,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)],[21,14,theory(equality)]) ).
cnf(86,negated_conjecture,
( subset(X1,union(esk3_0,X2))
| ~ member(esk1_2(X1,union(esk3_0,X2)),esk2_0) ),
inference(spm,[status(thm)],[46,48,theory(equality)]) ).
cnf(124,plain,
( subset(union(X1,X2),union(X3,X1))
| member(esk1_2(union(X1,X2),union(X3,X1)),X2) ),
inference(spm,[status(thm)],[45,52,theory(equality)]) ).
cnf(1650,negated_conjecture,
subset(union(X1,esk2_0),union(esk3_0,X1)),
inference(spm,[status(thm)],[86,124,theory(equality)]) ).
cnf(1663,negated_conjecture,
subset(union(esk2_0,X1),union(esk3_0,X1)),
inference(spm,[status(thm)],[1650,28,theory(equality)]) ).
cnf(1698,negated_conjecture,
$false,
inference(rw,[status(thm)],[25,1663,theory(equality)]) ).
cnf(1699,negated_conjecture,
$false,
inference(cn,[status(thm)],[1698,theory(equality)]) ).
cnf(1700,negated_conjecture,
$false,
1699,
[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/SET584+3.p
% --creating new selector for []
% -running prover on /tmp/tmpnK2HkG/sel_SET584+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET584+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET584+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET584+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
%
%------------------------------------------------------------------------------