TSTP Solution File: ALG211+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ALG211+1 : TPTP v3.4.2. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 11:23:10 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 82 ( 36 ~; 35 |; 11 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 31 ( 4 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(bg_2_4_3,plain,
! [C,D] :
( ( a_vector_subspace_of(w,v)
| ~ basis_of(C,w) )
& ( a_vector_space(v)
| ~ basis_of(C,w) )
& ( ~ basis_of(union(C,D),v)
| ~ basis_of(C,w) )
& ( a_vector_subspace_of(w,v)
| a_vector_subspace_of(w,v) )
& ( a_vector_space(v)
| a_vector_subspace_of(w,v) )
& ( ~ basis_of(union(C,D),v)
| a_vector_subspace_of(w,v) )
& ( a_vector_subspace_of(w,v)
| a_vector_space(v) )
& ( a_vector_space(v)
| a_vector_space(v) )
& ( ~ basis_of(union(C,D),v)
| a_vector_space(v) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),
[] ).
cnf(159877088,plain,
a_vector_subspace_of(w,v),
inference(rewrite,[status(thm)],[bg_2_4_3]),
[] ).
fof(basis_of,plain,
! [A,B] :
( ( a_subset_of(A,vec_to_class(B))
| ~ basis_of(A,B) )
& ( lin_ind_subset(A,B)
| ~ basis_of(A,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),
[] ).
cnf(159668008,plain,
( a_subset_of(A,vec_to_class(B))
| ~ basis_of(A,B) ),
inference(rewrite,[status(thm)],[basis_of]),
[] ).
fof(bg_remark_63_a,plain,
! [A] :
( ~ a_vector_space(A)
| basis_of(b(A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),
[] ).
cnf(159698688,plain,
( ~ a_vector_space(A)
| basis_of(b(A),A) ),
inference(rewrite,[status(thm)],[bg_remark_63_a]),
[] ).
fof(bg_2_4_a,plain,
! [A,B] :
( ~ a_vector_subspace_of(A,B)
| a_vector_space(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),
[] ).
cnf(159705384,plain,
( ~ a_vector_subspace_of(A,B)
| a_vector_space(A) ),
inference(rewrite,[status(thm)],[bg_2_4_a]),
[] ).
cnf(178264456,plain,
a_vector_space(w),
inference(resolution,[status(thm)],[159705384,159877088]),
[] ).
cnf(178325944,plain,
basis_of(b(w),w),
inference(resolution,[status(thm)],[159698688,178264456]),
[] ).
cnf(178629664,plain,
a_subset_of(b(w),vec_to_class(w)),
inference(resolution,[status(thm)],[159668008,178325944]),
[] ).
fof(bg_2_4_2,plain,
! [C,A,B] :
( ( lin_ind_subset(C,A)
| ~ lin_ind_subset(C,B)
| ~ a_vector_subspace_of(A,B)
| ~ a_subset_of(C,vec_to_class(A)) )
& ( ~ lin_ind_subset(C,A)
| lin_ind_subset(C,B)
| ~ a_vector_subspace_of(A,B)
| ~ a_subset_of(C,vec_to_class(A)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),
[] ).
cnf(159719544,plain,
( ~ lin_ind_subset(C,A)
| lin_ind_subset(C,B)
| ~ a_vector_subspace_of(A,B)
| ~ a_subset_of(C,vec_to_class(A)) ),
inference(rewrite,[status(thm)],[bg_2_4_2]),
[] ).
cnf(159657152,plain,
( lin_ind_subset(A,B)
| ~ basis_of(A,B) ),
inference(rewrite,[status(thm)],[basis_of]),
[] ).
cnf(178620344,plain,
lin_ind_subset(b(w),w),
inference(resolution,[status(thm)],[178325944,159657152]),
[] ).
cnf(179611328,plain,
( lin_ind_subset(b(w),A)
| ~ a_vector_subspace_of(w,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[178629664,159719544,178620344]),
[] ).
fof(bg_2_2_5,plain,
! [A,B,C] :
( ( basis_of(union(A,u(A,B,C)),C)
| ~ lin_ind_subset(A,C)
| ~ basis_of(B,C) )
& ( a_subset_of(u(A,B,C),B)
| ~ lin_ind_subset(A,C)
| ~ basis_of(B,C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),
[] ).
cnf(159692256,plain,
( basis_of(union(A,u(A,B,C)),C)
| ~ lin_ind_subset(A,C)
| ~ basis_of(B,C) ),
inference(rewrite,[status(thm)],[bg_2_2_5]),
[] ).
cnf(159890944,plain,
( ~ basis_of(union(C,D),v)
| ~ basis_of(C,w) ),
inference(rewrite,[status(thm)],[bg_2_4_3]),
[] ).
cnf(178686520,plain,
~ basis_of(union(b(w),C),v),
inference(resolution,[status(thm)],[159890944,178325944]),
[] ).
cnf(179018184,plain,
( ~ lin_ind_subset(b(w),v)
| ~ basis_of(A,v) ),
inference(resolution,[status(thm)],[159692256,178686520]),
[] ).
cnf(159863176,plain,
a_vector_space(v),
inference(rewrite,[status(thm)],[bg_2_4_3]),
[] ).
cnf(178255608,plain,
basis_of(b(v),v),
inference(resolution,[status(thm)],[159698688,159863176]),
[] ).
cnf(179199024,plain,
~ lin_ind_subset(b(w),v),
inference(resolution,[status(thm)],[179018184,178255608]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[159877088,179611328,179199024]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(bg_2_4_3,plain,(((a_vector_subspace_of(w,v)|~basis_of(C,w))&(a_vector_space(v)|~basis_of(C,w))&(~basis_of(union(C,D),v)|~basis_of(C,w))&(a_vector_subspace_of(w,v)|a_vector_subspace_of(w,v))&(a_vector_space(v)|a_vector_subspace_of(w,v))&(~basis_of(union(C,D),v)|a_vector_subspace_of(w,v))&(a_vector_subspace_of(w,v)|a_vector_space(v))&(a_vector_space(v)|a_vector_space(v))&(~basis_of(union(C,D),v)|a_vector_space(v)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),[]).
%
% cnf(159877088,plain,(a_vector_subspace_of(w,v)),inference(rewrite,[status(thm)],[bg_2_4_3]),[]).
%
% fof(basis_of,plain,(((a_subset_of(A,vec_to_class(B))|~basis_of(A,B))&(lin_ind_subset(A,B)|~basis_of(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),[]).
%
% cnf(159668008,plain,(a_subset_of(A,vec_to_class(B))|~basis_of(A,B)),inference(rewrite,[status(thm)],[basis_of]),[]).
%
% fof(bg_remark_63_a,plain,(~a_vector_space(A)|basis_of(b(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),[]).
%
% cnf(159698688,plain,(~a_vector_space(A)|basis_of(b(A),A)),inference(rewrite,[status(thm)],[bg_remark_63_a]),[]).
%
% fof(bg_2_4_a,plain,(~a_vector_subspace_of(A,B)|a_vector_space(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),[]).
%
% cnf(159705384,plain,(~a_vector_subspace_of(A,B)|a_vector_space(A)),inference(rewrite,[status(thm)],[bg_2_4_a]),[]).
%
% cnf(178264456,plain,(a_vector_space(w)),inference(resolution,[status(thm)],[159705384,159877088]),[]).
%
% cnf(178325944,plain,(basis_of(b(w),w)),inference(resolution,[status(thm)],[159698688,178264456]),[]).
%
% cnf(178629664,plain,(a_subset_of(b(w),vec_to_class(w))),inference(resolution,[status(thm)],[159668008,178325944]),[]).
%
% fof(bg_2_4_2,plain,(((lin_ind_subset(C,A)|~lin_ind_subset(C,B)|~a_vector_subspace_of(A,B)|~a_subset_of(C,vec_to_class(A)))&(~lin_ind_subset(C,A)|lin_ind_subset(C,B)|~a_vector_subspace_of(A,B)|~a_subset_of(C,vec_to_class(A))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),[]).
%
% cnf(159719544,plain,(~lin_ind_subset(C,A)|lin_ind_subset(C,B)|~a_vector_subspace_of(A,B)|~a_subset_of(C,vec_to_class(A))),inference(rewrite,[status(thm)],[bg_2_4_2]),[]).
%
% cnf(159657152,plain,(lin_ind_subset(A,B)|~basis_of(A,B)),inference(rewrite,[status(thm)],[basis_of]),[]).
%
% cnf(178620344,plain,(lin_ind_subset(b(w),w)),inference(resolution,[status(thm)],[178325944,159657152]),[]).
%
% cnf(179611328,plain,(lin_ind_subset(b(w),A)|~a_vector_subspace_of(w,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[178629664,159719544,178620344]),[]).
%
% fof(bg_2_2_5,plain,(((basis_of(union(A,u(A,B,C)),C)|~lin_ind_subset(A,C)|~basis_of(B,C))&(a_subset_of(u(A,B,C),B)|~lin_ind_subset(A,C)|~basis_of(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG211+1.tptp',unknown),[]).
%
% cnf(159692256,plain,(basis_of(union(A,u(A,B,C)),C)|~lin_ind_subset(A,C)|~basis_of(B,C)),inference(rewrite,[status(thm)],[bg_2_2_5]),[]).
%
% cnf(159890944,plain,(~basis_of(union(C,D),v)|~basis_of(C,w)),inference(rewrite,[status(thm)],[bg_2_4_3]),[]).
%
% cnf(178686520,plain,(~basis_of(union(b(w),C),v)),inference(resolution,[status(thm)],[159890944,178325944]),[]).
%
% cnf(179018184,plain,(~lin_ind_subset(b(w),v)|~basis_of(A,v)),inference(resolution,[status(thm)],[159692256,178686520]),[]).
%
% cnf(159863176,plain,(a_vector_space(v)),inference(rewrite,[status(thm)],[bg_2_4_3]),[]).
%
% cnf(178255608,plain,(basis_of(b(v),v)),inference(resolution,[status(thm)],[159698688,159863176]),[]).
%
% cnf(179199024,plain,(~lin_ind_subset(b(w),v)),inference(resolution,[status(thm)],[179018184,178255608]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[159877088,179611328,179199024]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------