%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET850-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art04.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 15:39:29 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    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :   16 (   2 sgn   7   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_Set_Osubset__trans_0,plain,
    ! [A,B,C,D] :
      ( ~ c_lessequals(A,B,tc_set(C))
      | ~ c_lessequals(D,A,tc_set(C))
      | c_lessequals(D,B,tc_set(C)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET850-2.tptp',unknown),
    [] ).

cnf(147166752,plain,
    ( ~ c_lessequals(A,B,tc_set(C))
    | ~ c_lessequals(D,A,tc_set(C))
    | c_lessequals(D,B,tc_set(C)) ),
    inference(rewrite,[status(thm)],[cls_Set_Osubset__trans_0]),
    [] ).

fof(cls_conjecture_0,plain,
    c_lessequals(v_x,v_y,tc_set(tc_set(t_a))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET850-2.tptp',unknown),
    [] ).

cnf(147175480,plain,
    c_lessequals(v_x,v_y,tc_set(tc_set(t_a))),
    inference(rewrite,[status(thm)],[cls_conjecture_0]),
    [] ).

cnf(157618128,plain,
    ( ~ c_lessequals(v_y,A,tc_set(tc_set(t_a)))
    | c_lessequals(v_x,A,tc_set(tc_set(t_a))) ),
    inference(resolution,[status(thm)],[147166752,147175480]),
    [] ).

fof(cls_Zorn_OAbrial__axiom1_0,plain,
    ! [A,B,C] : c_lessequals(A,c_zorn_osucc(B,A,C),tc_set(tc_set(C))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET850-2.tptp',unknown),
    [] ).

cnf(147171520,plain,
    c_lessequals(A,c_zorn_osucc(B,A,C),tc_set(tc_set(C))),
    inference(rewrite,[status(thm)],[cls_Zorn_OAbrial__axiom1_0]),
    [] ).

cnf(157633224,plain,
    c_lessequals(v_x,c_zorn_osucc(A,v_y,t_a),tc_set(tc_set(t_a))),
    inference(resolution,[status(thm)],[157618128,147171520]),
    [] ).

fof(cls_conjecture_1,plain,
    ~ c_lessequals(v_x,c_zorn_osucc(v_s,v_y,t_a),tc_set(tc_set(t_a))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET850-2.tptp',unknown),
    [] ).

cnf(147179720,plain,
    ~ c_lessequals(v_x,c_zorn_osucc(v_s,v_y,t_a),tc_set(tc_set(t_a))),
    inference(rewrite,[status(thm)],[cls_conjecture_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[157633224,147179720]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Set_Osubset__trans_0,plain,(~c_lessequals(A,B,tc_set(C))|~c_lessequals(D,A,tc_set(C))|c_lessequals(D,B,tc_set(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET850-2.tptp',unknown),[]).
% 
% cnf(147166752,plain,(~c_lessequals(A,B,tc_set(C))|~c_lessequals(D,A,tc_set(C))|c_lessequals(D,B,tc_set(C))),inference(rewrite,[status(thm)],[cls_Set_Osubset__trans_0]),[]).
% 
% fof(cls_conjecture_0,plain,(c_lessequals(v_x,v_y,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET850-2.tptp',unknown),[]).
% 
% cnf(147175480,plain,(c_lessequals(v_x,v_y,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
% 
% cnf(157618128,plain,(~c_lessequals(v_y,A,tc_set(tc_set(t_a)))|c_lessequals(v_x,A,tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[147166752,147175480]),[]).
% 
% fof(cls_Zorn_OAbrial__axiom1_0,plain,(c_lessequals(A,c_zorn_osucc(B,A,C),tc_set(tc_set(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET850-2.tptp',unknown),[]).
% 
% cnf(147171520,plain,(c_lessequals(A,c_zorn_osucc(B,A,C),tc_set(tc_set(C)))),inference(rewrite,[status(thm)],[cls_Zorn_OAbrial__axiom1_0]),[]).
% 
% cnf(157633224,plain,(c_lessequals(v_x,c_zorn_osucc(A,v_y,t_a),tc_set(tc_set(t_a)))),inference(resolution,[status(thm)],[157618128,147171520]),[]).
% 
% fof(cls_conjecture_1,plain,(~c_lessequals(v_x,c_zorn_osucc(v_s,v_y,t_a),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET850-2.tptp',unknown),[]).
% 
% cnf(147179720,plain,(~c_lessequals(v_x,c_zorn_osucc(v_s,v_y,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[157633224,147179720]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------