%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP018-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art09.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 12:18:02 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% 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    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 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(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/GRP018-1.tptp',unknown),
    [] ).

cnf(153158880,plain,
    ( ~ product(A,B,C)
    | ~ product(A,B,D)
    | $equal(D,C) ),
    inference(rewrite,[status(thm)],[total_function2]),
    [] ).

fof(right_identity,plain,
    ! [A] : product(A,identity,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP018-1.tptp',unknown),
    [] ).

cnf(153136512,plain,
    product(A,identity,A),
    inference(rewrite,[status(thm)],[right_identity]),
    [] ).

cnf(161039160,plain,
    ( ~ product(A,identity,B)
    | $equal(B,A) ),
    inference(resolution,[status(thm)],[153158880,153136512]),
    [] ).

fof(total_function1,plain,
    ! [A,B] : product(A,B,multiply(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP018-1.tptp',unknown),
    [] ).

cnf(153147576,plain,
    product(A,B,multiply(A,B)),
    inference(rewrite,[status(thm)],[total_function1]),
    [] ).

cnf(162621080,plain,
    $equal(multiply(A,identity),A),
    inference(resolution,[status(thm)],[161039160,153147576]),
    [] ).

fof(prove_X_times_id_is_X,plain,
    ~ $equal(multiply(a,identity),a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP018-1.tptp',unknown),
    [] ).

cnf(153177992,plain,
    ~ $equal(multiply(a,identity),a),
    inference(rewrite,[status(thm)],[prove_X_times_id_is_X]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[162621080,153177992]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP018-1.tptp',unknown),[]).
% 
% cnf(153158880,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
% 
% fof(right_identity,plain,(product(A,identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP018-1.tptp',unknown),[]).
% 
% cnf(153136512,plain,(product(A,identity,A)),inference(rewrite,[status(thm)],[right_identity]),[]).
% 
% cnf(161039160,plain,(~product(A,identity,B)|$equal(B,A)),inference(resolution,[status(thm)],[153158880,153136512]),[]).
% 
% fof(total_function1,plain,(product(A,B,multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP018-1.tptp',unknown),[]).
% 
% cnf(153147576,plain,(product(A,B,multiply(A,B))),inference(rewrite,[status(thm)],[total_function1]),[]).
% 
% cnf(162621080,plain,($equal(multiply(A,identity),A)),inference(resolution,[status(thm)],[161039160,153147576]),[]).
% 
% fof(prove_X_times_id_is_X,plain,(~$equal(multiply(a,identity),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP018-1.tptp',unknown),[]).
% 
% cnf(153177992,plain,(~$equal(multiply(a,identity),a)),inference(rewrite,[status(thm)],[prove_X_times_id_is_X]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[162621080,153177992]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------