%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP038-3 : TPTP v3.4.2. Released v1.0.0.
% 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 12:19:06 EDT 2009

% Result   : Unsatisfiable 0.2s
% Output   : Refutation 0.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   11 (   9 unt;   0 def)
%            Number of atoms       :   17 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   14 (   8   ~;   6   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-1 aty)
%            Number of variables   :    6 (   0 sgn   3   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_c_is_in_subgroup,plain,
    ~ subgroup_member(c),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP038-3.tptp',unknown),
    [] ).

cnf(154112368,plain,
    ~ subgroup_member(c),
    inference(rewrite,[status(thm)],[prove_c_is_in_subgroup]),
    [] ).

fof(a_is_in_subgroup,plain,
    subgroup_member(a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP038-3.tptp',unknown),
    [] ).

cnf(154096792,plain,
    subgroup_member(a),
    inference(rewrite,[status(thm)],[a_is_in_subgroup]),
    [] ).

fof(b_is_in_subgroup,plain,
    subgroup_member(b),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP038-3.tptp',unknown),
    [] ).

cnf(154104704,plain,
    subgroup_member(b),
    inference(rewrite,[status(thm)],[b_is_in_subgroup]),
    [] ).

fof(closure_of_product_and_inverse,plain,
    ! [A,B,C] :
      ( ~ subgroup_member(A)
      | ~ subgroup_member(B)
      | ~ product(A,inverse(B),C)
      | subgroup_member(C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP038-3.tptp',unknown),
    [] ).

cnf(154083160,plain,
    ( ~ subgroup_member(A)
    | ~ subgroup_member(B)
    | ~ product(A,inverse(B),C)
    | subgroup_member(C) ),
    inference(rewrite,[status(thm)],[closure_of_product_and_inverse]),
    [] ).

fof(a_times_inverse_b_is_c,plain,
    product(a,inverse(b),c),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP038-3.tptp',unknown),
    [] ).

cnf(154108544,plain,
    product(a,inverse(b),c),
    inference(rewrite,[status(thm)],[a_times_inverse_b_is_c]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[154112368,154096792,154104704,154083160,154108544]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_c_is_in_subgroup,plain,(~subgroup_member(c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP038-3.tptp',unknown),[]).
% 
% cnf(154112368,plain,(~subgroup_member(c)),inference(rewrite,[status(thm)],[prove_c_is_in_subgroup]),[]).
% 
% fof(a_is_in_subgroup,plain,(subgroup_member(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP038-3.tptp',unknown),[]).
% 
% cnf(154096792,plain,(subgroup_member(a)),inference(rewrite,[status(thm)],[a_is_in_subgroup]),[]).
% 
% fof(b_is_in_subgroup,plain,(subgroup_member(b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP038-3.tptp',unknown),[]).
% 
% cnf(154104704,plain,(subgroup_member(b)),inference(rewrite,[status(thm)],[b_is_in_subgroup]),[]).
% 
% fof(closure_of_product_and_inverse,plain,(~subgroup_member(A)|~subgroup_member(B)|~product(A,inverse(B),C)|subgroup_member(C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP038-3.tptp',unknown),[]).
% 
% cnf(154083160,plain,(~subgroup_member(A)|~subgroup_member(B)|~product(A,inverse(B),C)|subgroup_member(C)),inference(rewrite,[status(thm)],[closure_of_product_and_inverse]),[]).
% 
% fof(a_times_inverse_b_is_c,plain,(product(a,inverse(b),c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP038-3.tptp',unknown),[]).
% 
% cnf(154108544,plain,(product(a,inverse(b),c)),inference(rewrite,[status(thm)],[a_times_inverse_b_is_c]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[154112368,154096792,154104704,154083160,154108544]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------