TSTP Solution File: SET624+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET624+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 03:04:47 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 10 unt; 0 def)
% Number of atoms : 173 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 186 ( 71 ~; 85 |; 25 &)
% ( 4 <=>; 1 =>; 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 : 96 ( 6 sgn 45 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpA1EXSk/sel_SET624+3.p_1',commutativity_of_union) ).
fof(2,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmpA1EXSk/sel_SET624+3.p_1',union_defn) ).
fof(3,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpA1EXSk/sel_SET624+3.p_1',intersect_defn) ).
fof(4,axiom,
! [X1,X2] :
( intersect(X1,X2)
=> intersect(X2,X1) ),
file('/tmp/tmpA1EXSk/sel_SET624+3.p_1',symmetry_of_intersect) ).
fof(6,conjecture,
! [X1,X2,X3] :
( intersect(X1,union(X2,X3))
<=> ( intersect(X1,X2)
| intersect(X1,X3) ) ),
file('/tmp/tmpA1EXSk/sel_SET624+3.p_1',prove_intersect_with_union) ).
fof(7,negated_conjecture,
~ ! [X1,X2,X3] :
( intersect(X1,union(X2,X3))
<=> ( intersect(X1,X2)
| intersect(X1,X3) ) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(8,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(9,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[8]) ).
fof(10,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(11,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)],[10]) ).
fof(12,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)],[11]) ).
cnf(13,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(15,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[12]) ).
fof(16,plain,
! [X1,X2] :
( ( ~ intersect(X1,X2)
| ? [X3] :
( member(X3,X1)
& member(X3,X2) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| ~ member(X3,X2) )
| intersect(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(17,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ? [X6] :
( member(X6,X4)
& member(X6,X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(variable_rename,[status(thm)],[16]) ).
fof(18,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ( member(esk1_2(X4,X5),X4)
& member(esk1_2(X4,X5),X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(skolemize,[status(esa)],[17]) ).
fof(19,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( ~ intersect(X4,X5)
| ( member(esk1_2(X4,X5),X4)
& member(esk1_2(X4,X5),X5) ) ) ),
inference(shift_quantors,[status(thm)],[18]) ).
fof(20,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| ~ intersect(X4,X5) )
& ( member(esk1_2(X4,X5),X5)
| ~ intersect(X4,X5) ) ),
inference(distribute,[status(thm)],[19]) ).
cnf(21,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(23,plain,
( intersect(X1,X2)
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(24,plain,
! [X1,X2] :
( ~ intersect(X1,X2)
| intersect(X2,X1) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(25,plain,
! [X3,X4] :
( ~ intersect(X3,X4)
| intersect(X4,X3) ),
inference(variable_rename,[status(thm)],[24]) ).
cnf(26,plain,
( intersect(X1,X2)
| ~ intersect(X2,X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(36,negated_conjecture,
? [X1,X2,X3] :
( ( ~ intersect(X1,union(X2,X3))
| ( ~ intersect(X1,X2)
& ~ intersect(X1,X3) ) )
& ( intersect(X1,union(X2,X3))
| intersect(X1,X2)
| intersect(X1,X3) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(37,negated_conjecture,
? [X4,X5,X6] :
( ( ~ intersect(X4,union(X5,X6))
| ( ~ intersect(X4,X5)
& ~ intersect(X4,X6) ) )
& ( intersect(X4,union(X5,X6))
| intersect(X4,X5)
| intersect(X4,X6) ) ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,negated_conjecture,
( ( ~ intersect(esk3_0,union(esk4_0,esk5_0))
| ( ~ intersect(esk3_0,esk4_0)
& ~ intersect(esk3_0,esk5_0) ) )
& ( intersect(esk3_0,union(esk4_0,esk5_0))
| intersect(esk3_0,esk4_0)
| intersect(esk3_0,esk5_0) ) ),
inference(skolemize,[status(esa)],[37]) ).
fof(39,negated_conjecture,
( ( ~ intersect(esk3_0,esk4_0)
| ~ intersect(esk3_0,union(esk4_0,esk5_0)) )
& ( ~ intersect(esk3_0,esk5_0)
| ~ intersect(esk3_0,union(esk4_0,esk5_0)) )
& ( intersect(esk3_0,union(esk4_0,esk5_0))
| intersect(esk3_0,esk4_0)
| intersect(esk3_0,esk5_0) ) ),
inference(distribute,[status(thm)],[38]) ).
cnf(40,negated_conjecture,
( intersect(esk3_0,esk5_0)
| intersect(esk3_0,esk4_0)
| intersect(esk3_0,union(esk4_0,esk5_0)) ),
inference(split_conjunct,[status(thm)],[39]) ).
cnf(41,negated_conjecture,
( ~ intersect(esk3_0,union(esk4_0,esk5_0))
| ~ intersect(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[39]) ).
cnf(42,negated_conjecture,
( ~ intersect(esk3_0,union(esk4_0,esk5_0))
| ~ intersect(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[39]) ).
cnf(48,plain,
( intersect(X1,X2)
| ~ member(esk1_2(X3,X2),X1)
| ~ intersect(X3,X2) ),
inference(spm,[status(thm)],[23,21,theory(equality)]) ).
cnf(49,plain,
( intersect(X1,X2)
| ~ member(esk1_2(X2,X3),X1)
| ~ intersect(X2,X3) ),
inference(spm,[status(thm)],[23,22,theory(equality)]) ).
cnf(56,plain,
( member(esk1_2(X1,union(X2,X3)),X3)
| member(esk1_2(X1,union(X2,X3)),X2)
| ~ intersect(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[15,21,theory(equality)]) ).
cnf(72,plain,
( intersect(union(X1,X2),X3)
| ~ intersect(X4,X3)
| ~ member(esk1_2(X4,X3),X2) ),
inference(spm,[status(thm)],[48,13,theory(equality)]) ).
cnf(112,plain,
( intersect(union(X1,X2),X3)
| ~ intersect(X2,X3) ),
inference(spm,[status(thm)],[72,22,theory(equality)]) ).
cnf(115,plain,
( intersect(union(X2,X1),X3)
| ~ intersect(X2,X3) ),
inference(spm,[status(thm)],[112,9,theory(equality)]) ).
cnf(117,plain,
( intersect(X1,union(X2,X3))
| ~ intersect(X3,X1) ),
inference(spm,[status(thm)],[26,112,theory(equality)]) ).
cnf(122,plain,
( intersect(X1,union(X2,X3))
| ~ intersect(X2,X1) ),
inference(spm,[status(thm)],[26,115,theory(equality)]) ).
cnf(129,negated_conjecture,
( ~ intersect(esk3_0,esk5_0)
| ~ intersect(esk5_0,esk3_0) ),
inference(spm,[status(thm)],[41,117,theory(equality)]) ).
cnf(139,negated_conjecture,
~ intersect(esk3_0,esk5_0),
inference(csr,[status(thm)],[129,26]) ).
cnf(140,negated_conjecture,
( intersect(esk3_0,union(esk4_0,esk5_0))
| intersect(esk3_0,esk4_0) ),
inference(sr,[status(thm)],[40,139,theory(equality)]) ).
cnf(148,negated_conjecture,
( member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0)
| member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk5_0)
| intersect(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[56,140,theory(equality)]) ).
cnf(429,negated_conjecture,
( ~ intersect(esk3_0,esk4_0)
| ~ intersect(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[42,122,theory(equality)]) ).
cnf(442,negated_conjecture,
~ intersect(esk3_0,esk4_0),
inference(csr,[status(thm)],[429,26]) ).
cnf(443,negated_conjecture,
intersect(esk3_0,union(esk4_0,esk5_0)),
inference(sr,[status(thm)],[140,442,theory(equality)]) ).
cnf(446,negated_conjecture,
( member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk5_0)
| member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0) ),
inference(sr,[status(thm)],[148,442,theory(equality)]) ).
cnf(518,negated_conjecture,
( intersect(esk5_0,esk3_0)
| member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0)
| ~ intersect(esk3_0,union(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[49,446,theory(equality)]) ).
cnf(524,negated_conjecture,
( intersect(esk5_0,esk3_0)
| member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0)
| $false ),
inference(rw,[status(thm)],[518,443,theory(equality)]) ).
cnf(525,negated_conjecture,
( intersect(esk5_0,esk3_0)
| member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0) ),
inference(cn,[status(thm)],[524,theory(equality)]) ).
cnf(530,negated_conjecture,
( intersect(esk4_0,esk3_0)
| intersect(esk5_0,esk3_0)
| ~ intersect(esk3_0,union(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[49,525,theory(equality)]) ).
cnf(536,negated_conjecture,
( intersect(esk4_0,esk3_0)
| intersect(esk5_0,esk3_0)
| $false ),
inference(rw,[status(thm)],[530,443,theory(equality)]) ).
cnf(537,negated_conjecture,
( intersect(esk4_0,esk3_0)
| intersect(esk5_0,esk3_0) ),
inference(cn,[status(thm)],[536,theory(equality)]) ).
cnf(540,negated_conjecture,
( intersect(esk3_0,esk5_0)
| intersect(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[26,537,theory(equality)]) ).
cnf(545,negated_conjecture,
intersect(esk4_0,esk3_0),
inference(sr,[status(thm)],[540,139,theory(equality)]) ).
cnf(548,negated_conjecture,
intersect(esk3_0,esk4_0),
inference(spm,[status(thm)],[26,545,theory(equality)]) ).
cnf(553,negated_conjecture,
$false,
inference(sr,[status(thm)],[548,442,theory(equality)]) ).
cnf(554,negated_conjecture,
$false,
553,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET624+3.p
% --creating new selector for []
% -running prover on /tmp/tmpA1EXSk/sel_SET624+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET624+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET624+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET624+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
%
%------------------------------------------------------------------------------