%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP028-1 : 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 12:18:33 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       :   18 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   16 (   9   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   0 con; 1-2 aty)
%            Number of variables   :   27 (   0 sgn  11   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(associativity,plain,
    ! [A,B,C,D,E,F] :
      ( ~ product(A,B,C)
      | ~ product(B,D,E)
      | ~ product(A,E,F)
      | product(C,D,F) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP028-1.tptp',unknown),
    [] ).

cnf(168261184,plain,
    ( ~ product(A,B,C)
    | ~ product(B,D,E)
    | ~ product(A,E,F)
    | product(C,D,F) ),
    inference(rewrite,[status(thm)],[associativity]),
    [] ).

fof(left_soln,plain,
    ! [A,B] : product(left_solution(A,B),A,B),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP028-1.tptp',unknown),
    [] ).

cnf(168265768,plain,
    product(left_solution(A,B),A,B),
    inference(rewrite,[status(thm)],[left_soln]),
    [] ).

cnf(176048688,plain,
    ( ~ product(A,C,A)
    | product(B,C,B) ),
    inference(resolution,[status(thm)],[168261184,168265768]),
    [] ).

fof(right_soln,plain,
    ! [A,B] : product(A,right_solution(A,B),B),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP028-1.tptp',unknown),
    [] ).

cnf(168269648,plain,
    product(A,right_solution(A,B),B),
    inference(rewrite,[status(thm)],[right_soln]),
    [] ).

cnf(176165272,plain,
    product(B,right_solution(A,A),B),
    inference(resolution,[status(thm)],[176048688,168269648]),
    [] ).

fof(prove_there_is_a_right_identity,plain,
    ! [A] : ~ product(not_identity(A),A,not_identity(A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP028-1.tptp',unknown),
    [] ).

cnf(168273400,plain,
    ~ product(not_identity(A),A,not_identity(A)),
    inference(rewrite,[status(thm)],[prove_there_is_a_right_identity]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[176165272,168273400]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(associativity,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP028-1.tptp',unknown),[]).
% 
% cnf(168261184,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity]),[]).
% 
% fof(left_soln,plain,(product(left_solution(A,B),A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP028-1.tptp',unknown),[]).
% 
% cnf(168265768,plain,(product(left_solution(A,B),A,B)),inference(rewrite,[status(thm)],[left_soln]),[]).
% 
% cnf(176048688,plain,(~product(A,C,A)|product(B,C,B)),inference(resolution,[status(thm)],[168261184,168265768]),[]).
% 
% fof(right_soln,plain,(product(A,right_solution(A,B),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP028-1.tptp',unknown),[]).
% 
% cnf(168269648,plain,(product(A,right_solution(A,B),B)),inference(rewrite,[status(thm)],[right_soln]),[]).
% 
% cnf(176165272,plain,(product(B,right_solution(A,A),B)),inference(resolution,[status(thm)],[176048688,168269648]),[]).
% 
% fof(prove_there_is_a_right_identity,plain,(~product(not_identity(A),A,not_identity(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP028-1.tptp',unknown),[]).
% 
% cnf(168273400,plain,(~product(not_identity(A),A,not_identity(A))),inference(rewrite,[status(thm)],[prove_there_is_a_right_identity]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[176165272,168273400]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------