%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COL120-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.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 11:35:26 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    7 (   5 unt;   0 def)
%            Number of atoms       :    9 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    6 (   4   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-4 aty)
%            Number of variables   :    8 (   1 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_1,plain,
    c_in(c_pair(v_y,v_x,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL120-2.tptp',unknown),
    [] ).

cnf(160345672,plain,
    c_in(c_pair(v_y,v_x,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
    inference(rewrite,[status(thm)],[cls_conjecture_1]),
    [] ).

fof(cls_conjecture_2,plain,
    ! [A] :
      ( ~ c_in(c_pair(v_x,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_pair(v_y,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL120-2.tptp',unknown),
    [] ).

cnf(160352648,plain,
    ( ~ c_in(c_pair(v_x,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))
    | ~ c_in(c_pair(v_y,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
    inference(rewrite,[status(thm)],[cls_conjecture_2]),
    [] ).

fof(cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0,plain,
    ! [A,B,C] : c_in(c_pair(A,A,B,B),c_transitive__closure_ortrancl(C,B),tc_prod(B,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL120-2.tptp',unknown),
    [] ).

cnf(160361040,plain,
    c_in(c_pair(A,A,B,B),c_transitive__closure_ortrancl(C,B),tc_prod(B,B)),
    inference(rewrite,[status(thm)],[cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[160345672,160352648,160361040]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_1,plain,(c_in(c_pair(v_y,v_x,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL120-2.tptp',unknown),[]).
% 
% cnf(160345672,plain,(c_in(c_pair(v_y,v_x,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
% 
% fof(cls_conjecture_2,plain,(~c_in(c_pair(v_x,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_y,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL120-2.tptp',unknown),[]).
% 
% cnf(160352648,plain,(~c_in(c_pair(v_x,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_pair(v_y,A,t_a,t_a),c_transitive__closure_ortrancl(v_r,t_a),tc_prod(t_a,t_a))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
% 
% fof(cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0,plain,(c_in(c_pair(A,A,B,B),c_transitive__closure_ortrancl(C,B),tc_prod(B,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL120-2.tptp',unknown),[]).
% 
% cnf(160361040,plain,(c_in(c_pair(A,A,B,B),c_transitive__closure_ortrancl(C,B),tc_prod(B,B))),inference(rewrite,[status(thm)],[cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[160345672,160352648,160361040]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------