%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : LCL007-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art08.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 13:39:39 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   10 (   7 unt;   0 def)
%            Number of atoms       :   15 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   13 (   8   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   15 (   0 sgn   7   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(ec_5,plain,
    ! [A,B,C] : is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(A,equivalent(B,C)))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL007-1.tptp',unknown),
    [] ).

cnf(171725944,plain,
    is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(A,equivalent(B,C)))),
    inference(rewrite,[status(thm)],[ec_5]),
    [] ).

fof(condensed_detachment,plain,
    ! [A,B] :
      ( ~ is_a_theorem(equivalent(A,B))
      | ~ is_a_theorem(A)
      | is_a_theorem(B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL007-1.tptp',unknown),
    [] ).

cnf(171717016,plain,
    ( ~ is_a_theorem(equivalent(A,B))
    | ~ is_a_theorem(A)
    | is_a_theorem(B) ),
    inference(rewrite,[status(thm)],[condensed_detachment]),
    [] ).

fof(prove_ec_2,plain,
    ~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL007-1.tptp',unknown),
    [] ).

cnf(171729888,plain,
    ~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))),
    inference(rewrite,[status(thm)],[prove_ec_2]),
    [] ).

cnf(179647496,plain,
    ( ~ is_a_theorem(equivalent(A,equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))))
    | ~ is_a_theorem(A) ),
    inference(resolution,[status(thm)],[171717016,171729888]),
    [] ).

fof(ec_4,plain,
    ! [A,B] : is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL007-1.tptp',unknown),
    [] ).

cnf(171721800,plain,
    is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
    inference(rewrite,[status(thm)],[ec_4]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[171725944,179647496,171721800]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(ec_5,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(A,equivalent(B,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL007-1.tptp',unknown),[]).
% 
% cnf(171725944,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(A,equivalent(B,C))))),inference(rewrite,[status(thm)],[ec_5]),[]).
% 
% fof(condensed_detachment,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL007-1.tptp',unknown),[]).
% 
% cnf(171717016,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
% 
% fof(prove_ec_2,plain,(~is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL007-1.tptp',unknown),[]).
% 
% cnf(171729888,plain,(~is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c)))),inference(rewrite,[status(thm)],[prove_ec_2]),[]).
% 
% cnf(179647496,plain,(~is_a_theorem(equivalent(A,equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))))|~is_a_theorem(A)),inference(resolution,[status(thm)],[171717016,171729888]),[]).
% 
% fof(ec_4,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL007-1.tptp',unknown),[]).
% 
% cnf(171721800,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A)))),inference(rewrite,[status(thm)],[ec_4]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[171725944,179647496,171721800]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------