TSTP Solution File: SET580+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET580+3 : 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 02:57:43 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 11 unt; 0 def)
% Number of atoms : 180 ( 3 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 199 ( 74 ~; 92 |; 26 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 4 sgn 37 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/tmp/tmp5hobFy/sel_SET580+3.p_1',symmetric_difference_defn) ).
fof(4,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmp5hobFy/sel_SET580+3.p_1',union_defn) ).
fof(6,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/tmp/tmp5hobFy/sel_SET580+3.p_1',difference_defn) ).
fof(7,conjecture,
! [X1,X2,X3] :
( member(X1,symmetric_difference(X2,X3))
<=> ~ ( member(X1,X2)
<=> member(X1,X3) ) ),
file('/tmp/tmp5hobFy/sel_SET580+3.p_1',prove_th23) ).
fof(8,negated_conjecture,
~ ! [X1,X2,X3] :
( member(X1,symmetric_difference(X2,X3))
<=> ~ ( member(X1,X2)
<=> member(X1,X3) ) ),
inference(assume_negation,[status(cth)],[7]) ).
fof(9,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(14,plain,
! [X3,X4] : symmetric_difference(X3,X4) = union(difference(X3,X4),difference(X4,X3)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(15,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[14]) ).
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)],[4]) ).
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(31,plain,
! [X1,X2,X3] :
( ( ~ member(X3,difference(X1,X2))
| ( member(X3,X1)
& ~ member(X3,X2) ) )
& ( ~ member(X3,X1)
| member(X3,X2)
| member(X3,difference(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(32,plain,
! [X4,X5,X6] :
( ( ~ member(X6,difference(X4,X5))
| ( member(X6,X4)
& ~ member(X6,X5) ) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X5)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(distribute,[status(thm)],[32]) ).
cnf(34,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(36,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(37,negated_conjecture,
? [X1,X2,X3] :
( ( ~ member(X1,symmetric_difference(X2,X3))
| ( ( ~ member(X1,X2)
| member(X1,X3) )
& ( ~ member(X1,X3)
| member(X1,X2) ) ) )
& ( member(X1,symmetric_difference(X2,X3))
| ( ( ~ member(X1,X2)
| ~ member(X1,X3) )
& ( member(X1,X2)
| member(X1,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(38,negated_conjecture,
? [X4,X5,X6] :
( ( ~ member(X4,symmetric_difference(X5,X6))
| ( ( ~ member(X4,X5)
| member(X4,X6) )
& ( ~ member(X4,X6)
| member(X4,X5) ) ) )
& ( member(X4,symmetric_difference(X5,X6))
| ( ( ~ member(X4,X5)
| ~ member(X4,X6) )
& ( member(X4,X5)
| member(X4,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[37]) ).
fof(39,negated_conjecture,
( ( ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0))
| ( ( ~ member(esk2_0,esk3_0)
| member(esk2_0,esk4_0) )
& ( ~ member(esk2_0,esk4_0)
| member(esk2_0,esk3_0) ) ) )
& ( member(esk2_0,symmetric_difference(esk3_0,esk4_0))
| ( ( ~ member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0) )
& ( member(esk2_0,esk3_0)
| member(esk2_0,esk4_0) ) ) ) ),
inference(skolemize,[status(esa)],[38]) ).
fof(40,negated_conjecture,
( ( ~ member(esk2_0,esk3_0)
| member(esk2_0,esk4_0)
| ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0)) )
& ( ~ member(esk2_0,esk4_0)
| member(esk2_0,esk3_0)
| ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0)) )
& ( ~ member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0)
| member(esk2_0,symmetric_difference(esk3_0,esk4_0)) )
& ( member(esk2_0,esk3_0)
| member(esk2_0,esk4_0)
| member(esk2_0,symmetric_difference(esk3_0,esk4_0)) ) ),
inference(distribute,[status(thm)],[39]) ).
cnf(41,negated_conjecture,
( member(esk2_0,symmetric_difference(esk3_0,esk4_0))
| member(esk2_0,esk4_0)
| member(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(42,negated_conjecture,
( member(esk2_0,symmetric_difference(esk3_0,esk4_0))
| ~ member(esk2_0,esk4_0)
| ~ member(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(43,negated_conjecture,
( member(esk2_0,esk3_0)
| ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0))
| ~ member(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(44,negated_conjecture,
( member(esk2_0,esk4_0)
| ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0))
| ~ member(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(46,negated_conjecture,
( member(esk2_0,esk3_0)
| member(esk2_0,esk4_0)
| member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) ),
inference(rw,[status(thm)],[41,15,theory(equality)]),
[unfolding] ).
cnf(47,negated_conjecture,
( member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0)
| ~ member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) ),
inference(rw,[status(thm)],[43,15,theory(equality)]),
[unfolding] ).
cnf(48,negated_conjecture,
( member(esk2_0,esk4_0)
| ~ member(esk2_0,esk3_0)
| ~ member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) ),
inference(rw,[status(thm)],[44,15,theory(equality)]),
[unfolding] ).
cnf(49,negated_conjecture,
( member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)))
| ~ member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0) ),
inference(rw,[status(thm)],[42,15,theory(equality)]),
[unfolding] ).
cnf(62,negated_conjecture,
( member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0)
| ~ member(esk2_0,difference(esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[47,19,theory(equality)]) ).
cnf(67,negated_conjecture,
( member(esk2_0,esk4_0)
| ~ member(esk2_0,esk3_0)
| ~ member(esk2_0,difference(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[48,20,theory(equality)]) ).
cnf(74,negated_conjecture,
( member(esk2_0,difference(esk4_0,esk3_0))
| member(esk2_0,difference(esk3_0,esk4_0))
| member(esk2_0,esk4_0)
| member(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[21,46,theory(equality)]) ).
cnf(82,negated_conjecture,
( member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0) ),
inference(csr,[status(thm)],[62,34]) ).
cnf(84,negated_conjecture,
( member(esk2_0,esk4_0)
| ~ member(esk2_0,esk3_0) ),
inference(csr,[status(thm)],[67,34]) ).
cnf(86,negated_conjecture,
( member(esk2_0,difference(esk4_0,esk3_0))
| member(esk2_0,difference(esk3_0,esk4_0))
| member(esk2_0,esk4_0) ),
inference(csr,[status(thm)],[74,34]) ).
cnf(87,negated_conjecture,
( member(esk2_0,difference(esk3_0,esk4_0))
| member(esk2_0,esk4_0) ),
inference(csr,[status(thm)],[86,36]) ).
cnf(88,negated_conjecture,
( member(esk2_0,esk3_0)
| member(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[36,87,theory(equality)]) ).
cnf(90,negated_conjecture,
member(esk2_0,esk3_0),
inference(csr,[status(thm)],[88,82]) ).
cnf(91,negated_conjecture,
( member(esk2_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[84,90,theory(equality)]) ).
cnf(92,negated_conjecture,
member(esk2_0,esk4_0),
inference(cn,[status(thm)],[91,theory(equality)]) ).
cnf(94,negated_conjecture,
( member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)))
| $false
| ~ member(esk2_0,esk4_0) ),
inference(rw,[status(thm)],[49,90,theory(equality)]) ).
cnf(95,negated_conjecture,
( member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)))
| ~ member(esk2_0,esk4_0) ),
inference(cn,[status(thm)],[94,theory(equality)]) ).
cnf(98,negated_conjecture,
( member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)))
| $false ),
inference(rw,[status(thm)],[95,92,theory(equality)]) ).
cnf(99,negated_conjecture,
member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))),
inference(cn,[status(thm)],[98,theory(equality)]) ).
cnf(100,negated_conjecture,
( member(esk2_0,difference(esk4_0,esk3_0))
| member(esk2_0,difference(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[21,99,theory(equality)]) ).
cnf(102,negated_conjecture,
( member(esk2_0,difference(esk3_0,esk4_0))
| ~ member(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[35,100,theory(equality)]) ).
cnf(104,negated_conjecture,
( member(esk2_0,difference(esk3_0,esk4_0))
| $false ),
inference(rw,[status(thm)],[102,90,theory(equality)]) ).
cnf(105,negated_conjecture,
member(esk2_0,difference(esk3_0,esk4_0)),
inference(cn,[status(thm)],[104,theory(equality)]) ).
cnf(116,negated_conjecture,
~ member(esk2_0,esk4_0),
inference(spm,[status(thm)],[35,105,theory(equality)]) ).
cnf(119,negated_conjecture,
$false,
inference(rw,[status(thm)],[116,92,theory(equality)]) ).
cnf(120,negated_conjecture,
$false,
inference(cn,[status(thm)],[119,theory(equality)]) ).
cnf(121,negated_conjecture,
$false,
120,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET580+3.p
% --creating new selector for []
% -running prover on /tmp/tmp5hobFy/sel_SET580+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET580+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET580+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET580+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
%
%------------------------------------------------------------------------------