TSTP Solution File: SET638+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET638+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 03:06:25 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 26 unt; 0 def)
% Number of atoms : 53 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 10 ~; 5 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 2 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3] :
( ( subset(X1,union(X2,X3))
& intersection(X1,X3) = empty_set )
=> subset(X1,X2) ),
file('/tmp/tmpAnUcuU/sel_SET638+3.p_1',prove_th120) ).
fof(2,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmpAnUcuU/sel_SET638+3.p_1',commutativity_of_intersection) ).
fof(4,axiom,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/tmp/tmpAnUcuU/sel_SET638+3.p_1',intersection_is_subset) ).
fof(7,axiom,
! [X1,X2] :
( subset(X1,X2)
=> intersection(X1,X2) = X1 ),
file('/tmp/tmpAnUcuU/sel_SET638+3.p_1',subset_intersection) ).
fof(8,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpAnUcuU/sel_SET638+3.p_1',commutativity_of_union) ).
fof(9,axiom,
! [X1,X2,X3] : intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
file('/tmp/tmpAnUcuU/sel_SET638+3.p_1',intersection_distributes_over_union) ).
fof(11,axiom,
! [X1] : union(X1,empty_set) = X1,
file('/tmp/tmpAnUcuU/sel_SET638+3.p_1',union_empty_set) ).
fof(16,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,union(X2,X3))
& intersection(X1,X3) = empty_set )
=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(19,negated_conjecture,
? [X1,X2,X3] :
( subset(X1,union(X2,X3))
& intersection(X1,X3) = empty_set
& ~ subset(X1,X2) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(20,negated_conjecture,
? [X4,X5,X6] :
( subset(X4,union(X5,X6))
& intersection(X4,X6) = empty_set
& ~ subset(X4,X5) ),
inference(variable_rename,[status(thm)],[19]) ).
fof(21,negated_conjecture,
( subset(esk1_0,union(esk2_0,esk3_0))
& intersection(esk1_0,esk3_0) = empty_set
& ~ subset(esk1_0,esk2_0) ),
inference(skolemize,[status(esa)],[20]) ).
cnf(22,negated_conjecture,
~ subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(23,negated_conjecture,
intersection(esk1_0,esk3_0) = empty_set,
inference(split_conjunct,[status(thm)],[21]) ).
cnf(24,negated_conjecture,
subset(esk1_0,union(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[21]) ).
fof(25,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(26,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[25]) ).
fof(35,plain,
! [X3,X4] : subset(intersection(X3,X4),X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(36,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[35]) ).
fof(49,plain,
! [X1,X2] :
( ~ subset(X1,X2)
| intersection(X1,X2) = X1 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(50,plain,
! [X3,X4] :
( ~ subset(X3,X4)
| intersection(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[49]) ).
cnf(51,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[50]) ).
fof(52,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[8]) ).
cnf(53,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[52]) ).
fof(54,plain,
! [X4,X5,X6] : intersection(X4,union(X5,X6)) = union(intersection(X4,X5),intersection(X4,X6)),
inference(variable_rename,[status(thm)],[9]) ).
cnf(55,plain,
intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
inference(split_conjunct,[status(thm)],[54]) ).
fof(65,plain,
! [X2] : union(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[11]) ).
cnf(66,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[65]) ).
cnf(90,negated_conjecture,
subset(esk1_0,union(esk3_0,esk2_0)),
inference(rw,[status(thm)],[24,53,theory(equality)]) ).
cnf(91,plain,
subset(intersection(X2,X1),X1),
inference(spm,[status(thm)],[36,26,theory(equality)]) ).
cnf(130,negated_conjecture,
union(intersection(esk1_0,X1),empty_set) = intersection(esk1_0,union(X1,esk3_0)),
inference(spm,[status(thm)],[55,23,theory(equality)]) ).
cnf(141,negated_conjecture,
intersection(esk1_0,X1) = intersection(esk1_0,union(X1,esk3_0)),
inference(rw,[status(thm)],[130,66,theory(equality)]) ).
cnf(264,negated_conjecture,
( intersection(esk1_0,X1) = esk1_0
| ~ subset(esk1_0,union(X1,esk3_0)) ),
inference(spm,[status(thm)],[51,141,theory(equality)]) ).
cnf(522,negated_conjecture,
( intersection(esk1_0,X1) = esk1_0
| ~ subset(esk1_0,union(esk3_0,X1)) ),
inference(spm,[status(thm)],[264,53,theory(equality)]) ).
cnf(567,negated_conjecture,
intersection(esk1_0,esk2_0) = esk1_0,
inference(spm,[status(thm)],[522,90,theory(equality)]) ).
cnf(579,negated_conjecture,
subset(esk1_0,esk2_0),
inference(spm,[status(thm)],[91,567,theory(equality)]) ).
cnf(592,negated_conjecture,
$false,
inference(sr,[status(thm)],[579,22,theory(equality)]) ).
cnf(593,negated_conjecture,
$false,
592,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET638+3.p
% --creating new selector for []
% -running prover on /tmp/tmpAnUcuU/sel_SET638+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET638+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET638+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET638+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
%
%------------------------------------------------------------------------------