TSTP Solution File: SET635+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET635+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 03:06:16 EST 2010
% Result : Theorem 0.65s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 34 unt; 0 def)
% Number of atoms : 46 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 5 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',commutativity_of_intersection) ).
fof(5,conjecture,
! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',prove_th117) ).
fof(6,axiom,
! [X1] : subset(X1,X1),
file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',reflexivity_of_subset) ).
fof(7,axiom,
! [X1,X2,X3] : difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',difference_and_intersection_and_union) ).
fof(10,axiom,
! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',difference_empty_set) ).
fof(12,axiom,
! [X1] : union(X1,empty_set) = X1,
file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',union_empty_set) ).
fof(14,axiom,
! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',difference_and_intersection) ).
fof(17,negated_conjecture,
~ ! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
inference(assume_negation,[status(cth)],[5]) ).
fof(21,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(22,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[21]) ).
fof(33,negated_conjecture,
? [X1,X2,X3] : intersection(X1,difference(X2,X3)) != difference(intersection(X1,X2),intersection(X1,X3)),
inference(fof_nnf,[status(thm)],[17]) ).
fof(34,negated_conjecture,
? [X4,X5,X6] : intersection(X4,difference(X5,X6)) != difference(intersection(X4,X5),intersection(X4,X6)),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,negated_conjecture,
intersection(esk1_0,difference(esk2_0,esk3_0)) != difference(intersection(esk1_0,esk2_0),intersection(esk1_0,esk3_0)),
inference(skolemize,[status(esa)],[34]) ).
cnf(36,negated_conjecture,
intersection(esk1_0,difference(esk2_0,esk3_0)) != difference(intersection(esk1_0,esk2_0),intersection(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X2] : subset(X2,X2),
inference(variable_rename,[status(thm)],[6]) ).
cnf(38,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X4,X5,X6] : difference(X4,intersection(X5,X6)) = union(difference(X4,X5),difference(X4,X6)),
inference(variable_rename,[status(thm)],[7]) ).
cnf(40,plain,
difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
inference(split_conjunct,[status(thm)],[39]) ).
fof(58,plain,
! [X1,X2] :
( ( difference(X1,X2) != empty_set
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| difference(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(59,plain,
! [X3,X4] :
( ( difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| difference(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[58]) ).
cnf(60,plain,
( difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(68,plain,
! [X2] : union(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[12]) ).
cnf(69,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[68]) ).
fof(76,plain,
! [X4,X5,X6] : intersection(X4,difference(X5,X6)) = difference(intersection(X4,X5),X6),
inference(variable_rename,[status(thm)],[14]) ).
cnf(77,plain,
intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(100,plain,
difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[60,38,theory(equality)]) ).
cnf(126,negated_conjecture,
intersection(esk1_0,difference(esk2_0,intersection(esk1_0,esk3_0))) != intersection(esk1_0,difference(esk2_0,esk3_0)),
inference(rw,[status(thm)],[36,77,theory(equality)]) ).
cnf(182,plain,
union(difference(X1,X2),empty_set) = difference(X1,intersection(X2,X1)),
inference(spm,[status(thm)],[40,100,theory(equality)]) ).
cnf(186,plain,
difference(X1,X2) = difference(X1,intersection(X2,X1)),
inference(rw,[status(thm)],[182,69,theory(equality)]) ).
cnf(480,plain,
union(difference(X1,X2),difference(X1,X3)) = difference(X1,intersection(intersection(X2,X1),X3)),
inference(spm,[status(thm)],[40,186,theory(equality)]) ).
cnf(495,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[186,22,theory(equality)]) ).
cnf(505,plain,
difference(X1,intersection(X2,X3)) = difference(X1,intersection(intersection(X2,X1),X3)),
inference(rw,[status(thm)],[480,40,theory(equality)]) ).
cnf(513,plain,
difference(intersection(X1,X2),X3) = intersection(X1,difference(X2,intersection(intersection(X1,X2),X3))),
inference(spm,[status(thm)],[77,495,theory(equality)]) ).
cnf(538,plain,
intersection(X1,difference(X2,X3)) = intersection(X1,difference(X2,intersection(intersection(X1,X2),X3))),
inference(rw,[status(thm)],[513,77,theory(equality)]) ).
cnf(18884,plain,
intersection(X1,difference(X2,intersection(X1,X3))) = intersection(X1,difference(X2,X3)),
inference(rw,[status(thm)],[538,505,theory(equality)]) ).
cnf(19046,negated_conjecture,
$false,
inference(rw,[status(thm)],[126,18884,theory(equality)]) ).
cnf(19047,negated_conjecture,
$false,
inference(cn,[status(thm)],[19046,theory(equality)]) ).
cnf(19048,negated_conjecture,
$false,
19047,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET635+3.p
% --creating new selector for []
% -running prover on /tmp/tmpZHsWoR/sel_SET635+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET635+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET635+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET635+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
%
%------------------------------------------------------------------------------