TSTP Solution File: SEU328+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU328+1 : TPTP v5.0.0. Released v3.3.0.
% 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 07:23:23 EST 2010
% Result : Theorem 0.56s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 99 ( 48 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 97 ( 43 ~; 38 |; 7 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/tmp/tmpxSs8KT/sel_SEU328+1.p_1',redefinition_k6_subset_1) ).
fof(15,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('/tmp/tmpxSs8KT/sel_SEU328+1.p_1',dt_k2_subset_1) ).
fof(35,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/tmp/tmpxSs8KT/sel_SEU328+1.p_1',d5_subset_1) ).
fof(43,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
file('/tmp/tmpxSs8KT/sel_SEU328+1.p_1',t48_setfam_1) ).
fof(47,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
file('/tmp/tmpxSs8KT/sel_SEU328+1.p_1',dt_k6_setfam_1) ).
fof(52,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
file('/tmp/tmpxSs8KT/sel_SEU328+1.p_1',t12_tops_2) ).
fof(58,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('/tmp/tmpxSs8KT/sel_SEU328+1.p_1',d4_subset_1) ).
fof(60,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[52]) ).
fof(70,plain,
! [X1,X2,X3] :
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(71,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| subset_difference(X4,X5,X6) = set_difference(X5,X6) ),
inference(variable_rename,[status(thm)],[70]) ).
cnf(72,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(111,plain,
! [X2] : element(cast_to_subset(X2),powerset(X2)),
inference(variable_rename,[status(thm)],[15]) ).
cnf(112,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[111]) ).
fof(201,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| subset_complement(X1,X2) = set_difference(X1,X2) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(202,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,X4) = set_difference(X3,X4) ),
inference(variable_rename,[status(thm)],[201]) ).
cnf(203,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[202]) ).
fof(225,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| X2 = empty_set
| union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(226,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| union_of_subsets(X3,complements_of_subsets(X3,X4)) = subset_difference(X3,cast_to_subset(X3),meet_of_subsets(X3,X4)) ),
inference(variable_rename,[status(thm)],[225]) ).
cnf(227,plain,
( union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[226]) ).
fof(243,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| element(meet_of_subsets(X1,X2),powerset(X1)) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(244,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(meet_of_subsets(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[243]) ).
cnf(245,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[244]) ).
fof(261,negated_conjecture,
? [X1,X2] :
( element(X2,powerset(powerset(X1)))
& X2 != empty_set
& union_of_subsets(X1,complements_of_subsets(X1,X2)) != subset_complement(X1,meet_of_subsets(X1,X2)) ),
inference(fof_nnf,[status(thm)],[60]) ).
fof(262,negated_conjecture,
? [X3,X4] :
( element(X4,powerset(powerset(X3)))
& X4 != empty_set
& union_of_subsets(X3,complements_of_subsets(X3,X4)) != subset_complement(X3,meet_of_subsets(X3,X4)) ),
inference(variable_rename,[status(thm)],[261]) ).
fof(263,negated_conjecture,
( element(esk5_0,powerset(powerset(esk4_0)))
& esk5_0 != empty_set
& union_of_subsets(esk4_0,complements_of_subsets(esk4_0,esk5_0)) != subset_complement(esk4_0,meet_of_subsets(esk4_0,esk5_0)) ),
inference(skolemize,[status(esa)],[262]) ).
cnf(264,negated_conjecture,
union_of_subsets(esk4_0,complements_of_subsets(esk4_0,esk5_0)) != subset_complement(esk4_0,meet_of_subsets(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[263]) ).
cnf(265,negated_conjecture,
esk5_0 != empty_set,
inference(split_conjunct,[status(thm)],[263]) ).
cnf(266,negated_conjecture,
element(esk5_0,powerset(powerset(esk4_0))),
inference(split_conjunct,[status(thm)],[263]) ).
fof(287,plain,
! [X2] : cast_to_subset(X2) = X2,
inference(variable_rename,[status(thm)],[58]) ).
cnf(288,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[287]) ).
cnf(297,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[112,288,theory(equality)]),
[unfolding] ).
cnf(298,plain,
( empty_set = X2
| subset_difference(X1,X1,meet_of_subsets(X1,X2)) = union_of_subsets(X1,complements_of_subsets(X1,X2))
| ~ element(X2,powerset(powerset(X1))) ),
inference(rw,[status(thm)],[227,288,theory(equality)]),
[unfolding] ).
cnf(727,plain,
( union_of_subsets(X1,complements_of_subsets(X1,X2)) = set_difference(X1,meet_of_subsets(X1,X2))
| empty_set = X2
| ~ element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X1,powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(spm,[status(thm)],[72,298,theory(equality)]) ).
cnf(730,plain,
( union_of_subsets(X1,complements_of_subsets(X1,X2)) = set_difference(X1,meet_of_subsets(X1,X2))
| empty_set = X2
| ~ element(meet_of_subsets(X1,X2),powerset(X1))
| $false
| ~ element(X2,powerset(powerset(X1))) ),
inference(rw,[status(thm)],[727,297,theory(equality)]) ).
cnf(731,plain,
( union_of_subsets(X1,complements_of_subsets(X1,X2)) = set_difference(X1,meet_of_subsets(X1,X2))
| empty_set = X2
| ~ element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(cn,[status(thm)],[730,theory(equality)]) ).
cnf(6160,plain,
( union_of_subsets(X1,complements_of_subsets(X1,X2)) = set_difference(X1,meet_of_subsets(X1,X2))
| empty_set = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(csr,[status(thm)],[731,245]) ).
cnf(6161,negated_conjecture,
( empty_set = esk5_0
| set_difference(esk4_0,meet_of_subsets(esk4_0,esk5_0)) != subset_complement(esk4_0,meet_of_subsets(esk4_0,esk5_0))
| ~ element(esk5_0,powerset(powerset(esk4_0))) ),
inference(spm,[status(thm)],[264,6160,theory(equality)]) ).
cnf(6206,negated_conjecture,
( empty_set = esk5_0
| set_difference(esk4_0,meet_of_subsets(esk4_0,esk5_0)) != subset_complement(esk4_0,meet_of_subsets(esk4_0,esk5_0))
| $false ),
inference(rw,[status(thm)],[6161,266,theory(equality)]) ).
cnf(6207,negated_conjecture,
( empty_set = esk5_0
| set_difference(esk4_0,meet_of_subsets(esk4_0,esk5_0)) != subset_complement(esk4_0,meet_of_subsets(esk4_0,esk5_0)) ),
inference(cn,[status(thm)],[6206,theory(equality)]) ).
cnf(6208,negated_conjecture,
subset_complement(esk4_0,meet_of_subsets(esk4_0,esk5_0)) != set_difference(esk4_0,meet_of_subsets(esk4_0,esk5_0)),
inference(sr,[status(thm)],[6207,265,theory(equality)]) ).
cnf(6214,negated_conjecture,
~ element(meet_of_subsets(esk4_0,esk5_0),powerset(esk4_0)),
inference(spm,[status(thm)],[6208,203,theory(equality)]) ).
cnf(6226,negated_conjecture,
~ element(esk5_0,powerset(powerset(esk4_0))),
inference(spm,[status(thm)],[6214,245,theory(equality)]) ).
cnf(6231,negated_conjecture,
$false,
inference(rw,[status(thm)],[6226,266,theory(equality)]) ).
cnf(6232,negated_conjecture,
$false,
inference(cn,[status(thm)],[6231,theory(equality)]) ).
cnf(6233,negated_conjecture,
$false,
6232,
[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/SEU/SEU328+1.p
% --creating new selector for []
% -running prover on /tmp/tmpxSs8KT/sel_SEU328+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU328+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU328+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU328+1.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
%
%------------------------------------------------------------------------------