%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP032-3 : 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 12:18:51 EDT 2009

% Result   : Unsatisfiable 0.0s
% Output   : Refutation 0.0s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   10 (   7 unt;   0 def)
%            Number of atoms       :   17 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   16 (   9   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :    9 (   0 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(right_inverse,plain,
    ! [A] : product(A,inverse(A),identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP032-3.tptp',unknown),
    [] ).

cnf(143548416,plain,
    product(A,inverse(A),identity),
    inference(rewrite,[status(thm)],[right_inverse]),
    [] ).

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/GRP032-3.tptp',unknown),
    [] ).

cnf(143587584,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_is_in_subgroup,plain,
    subgroup_member(a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP032-3.tptp',unknown),
    [] ).

cnf(143592296,plain,
    subgroup_member(a),
    inference(rewrite,[status(thm)],[a_is_in_subgroup]),
    [] ).

cnf(151405384,plain,
    ( ~ product(a,inverse(a),A)
    | subgroup_member(A) ),
    inference(resolution,[status(thm)],[143587584,143592296]),
    [] ).

fof(prove_identity_is_in_subgroup,plain,
    ~ subgroup_member(identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP032-3.tptp',unknown),
    [] ).

cnf(143596216,plain,
    ~ subgroup_member(identity),
    inference(rewrite,[status(thm)],[prove_identity_is_in_subgroup]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[143548416,151405384,143596216]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(right_inverse,plain,(product(A,inverse(A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP032-3.tptp',unknown),[]).
% 
% cnf(143548416,plain,(product(A,inverse(A),identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
% 
% 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/GRP032-3.tptp',unknown),[]).
% 
% cnf(143587584,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_is_in_subgroup,plain,(subgroup_member(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP032-3.tptp',unknown),[]).
% 
% cnf(143592296,plain,(subgroup_member(a)),inference(rewrite,[status(thm)],[a_is_in_subgroup]),[]).
% 
% cnf(151405384,plain,(~product(a,inverse(a),A)|subgroup_member(A)),inference(resolution,[status(thm)],[143587584,143592296]),[]).
% 
% fof(prove_identity_is_in_subgroup,plain,(~subgroup_member(identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP032-3.tptp',unknown),[]).
% 
% cnf(143596216,plain,(~subgroup_member(identity)),inference(rewrite,[status(thm)],[prove_identity_is_in_subgroup]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[143548416,151405384,143596216]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------