%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP041-2 : 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 12:19:18 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    8 (   6 unt;   0 def)
%            Number of atoms       :   12 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   10 (   6   ~;   4   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   11 (   0 sgn   5   !;   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)
      | equalish(C,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP041-2.tptp',unknown),
    [] ).

cnf(142239848,plain,
    ( ~ product(A,B,C)
    | ~ product(A,B,D)
    | equalish(C,D) ),
    inference(rewrite,[status(thm)],[total_function2]),
    [] ).

fof(left_identity,plain,
    ! [A] : product(identity,A,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP041-2.tptp',unknown),
    [] ).

cnf(142223992,plain,
    product(identity,A,A),
    inference(rewrite,[status(thm)],[left_identity]),
    [] ).

cnf(150045168,plain,
    equalish(A,A),
    inference(resolution,[status(thm)],[142239848,142223992]),
    [] ).

fof(prove_reflexivity,plain,
    ~ equalish(a,a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP041-2.tptp',unknown),
    [] ).

cnf(142266064,plain,
    ~ equalish(a,a),
    inference(rewrite,[status(thm)],[prove_reflexivity]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[150045168,142266064]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP041-2.tptp',unknown),[]).
% 
% cnf(142239848,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[total_function2]),[]).
% 
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP041-2.tptp',unknown),[]).
% 
% cnf(142223992,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
% 
% cnf(150045168,plain,(equalish(A,A)),inference(resolution,[status(thm)],[142239848,142223992]),[]).
% 
% fof(prove_reflexivity,plain,(~equalish(a,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP041-2.tptp',unknown),[]).
% 
% cnf(142266064,plain,(~equalish(a,a)),inference(rewrite,[status(thm)],[prove_reflexivity]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[150045168,142266064]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------