%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP021-1 : 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 12:18:07 EDT 2009

% Result   : Unsatisfiable 0.2s
% Output   : Refutation 0.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   11 (   8 unt;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   12 (   7   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   17 (   0 sgn   7   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_X_times_inverse_X_is_id,plain,
    ~ $equal(multiply(a,inverse(a)),identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP021-1.tptp',unknown),
    [] ).

cnf(157421472,plain,
    ~ $equal(multiply(a,inverse(a)),identity),
    inference(rewrite,[status(thm)],[prove_X_times_inverse_X_is_id]),
    [] ).

fof(total_function1,plain,
    ! [A,B] : product(A,B,multiply(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP021-1.tptp',unknown),
    [] ).

cnf(157391056,plain,
    product(A,B,multiply(A,B)),
    inference(rewrite,[status(thm)],[total_function1]),
    [] ).

fof(total_function2,plain,
    ! [A,B,C,D] :
      ( ~ product(A,B,C)
      | ~ product(A,B,D)
      | $equal(D,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP021-1.tptp',unknown),
    [] ).

cnf(157402360,plain,
    ( ~ product(A,B,C)
    | ~ product(A,B,D)
    | $equal(D,C) ),
    inference(rewrite,[status(thm)],[total_function2]),
    [] ).

fof(right_inverse,plain,
    ! [A] : product(A,inverse(A),identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP021-1.tptp',unknown),
    [] ).

cnf(157387480,plain,
    product(A,inverse(A),identity),
    inference(rewrite,[status(thm)],[right_inverse]),
    [] ).

cnf(165597984,plain,
    ( ~ product(A,inverse(A),B)
    | $equal(B,identity) ),
    inference(resolution,[status(thm)],[157402360,157387480]),
    [] ).

cnf(171681392,plain,
    $equal(multiply(A,inverse(A)),identity),
    inference(resolution,[status(thm)],[157391056,165597984]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[157421472,171681392]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_X_times_inverse_X_is_id,plain,(~$equal(multiply(a,inverse(a)),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP021-1.tptp',unknown),[]).
% 
% cnf(157421472,plain,(~$equal(multiply(a,inverse(a)),identity)),inference(rewrite,[status(thm)],[prove_X_times_inverse_X_is_id]),[]).
% 
% fof(total_function1,plain,(product(A,B,multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP021-1.tptp',unknown),[]).
% 
% cnf(157391056,plain,(product(A,B,multiply(A,B))),inference(rewrite,[status(thm)],[total_function1]),[]).
% 
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP021-1.tptp',unknown),[]).
% 
% cnf(157402360,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
% 
% fof(right_inverse,plain,(product(A,inverse(A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP021-1.tptp',unknown),[]).
% 
% cnf(157387480,plain,(product(A,inverse(A),identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
% 
% cnf(165597984,plain,(~product(A,inverse(A),B)|$equal(B,identity)),inference(resolution,[status(thm)],[157402360,157387480]),[]).
% 
% cnf(171681392,plain,($equal(multiply(A,inverse(A)),identity)),inference(resolution,[status(thm)],[157391056,165597984]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[157421472,171681392]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------