%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : LCL431-2 : 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 13:49:49 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 (   8 unt;   0 def)
%            Number of atoms       :   12 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   5   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   14 (   4 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_0,plain,
    c_proplog_osat(c_emptyset,v_p,t_a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL431-2.tptp',unknown),
    [] ).

cnf(153401272,plain,
    c_proplog_osat(c_emptyset,v_p,t_a),
    inference(rewrite,[status(thm)],[cls_conjecture_0]),
    [] ).

fof(cls_PropLog_Ocompleteness__0__lemma__dest_0,plain,
    ! [A,B,C,D] :
      ( ~ c_proplog_osat(c_emptyset,A,B)
      | c_in(A,c_proplog_othms(c_minus(c_proplog_ohyps(A,C,B),c_proplog_ohyps(A,D,B),tc_set(tc_proplog_opl(B))),B),tc_proplog_opl(B)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL431-2.tptp',unknown),
    [] ).

cnf(153452504,plain,
    ( ~ c_proplog_osat(c_emptyset,A,B)
    | c_in(A,c_proplog_othms(c_minus(c_proplog_ohyps(A,C,B),c_proplog_ohyps(A,D,B),tc_set(tc_proplog_opl(B))),B),tc_proplog_opl(B)) ),
    inference(rewrite,[status(thm)],[cls_PropLog_Ocompleteness__0__lemma__dest_0]),
    [] ).

fof(cls_conjecture_1,plain,
    ~ c_in(v_p,c_proplog_othms(c_emptyset,t_a),tc_proplog_opl(t_a)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL431-2.tptp',unknown),
    [] ).

cnf(153406288,plain,
    ~ c_in(v_p,c_proplog_othms(c_emptyset,t_a),tc_proplog_opl(t_a)),
    inference(rewrite,[status(thm)],[cls_conjecture_1]),
    [] ).

fof(cls_Set_ODiff__cancel_0,plain,
    ! [A,B] : $equal(c_minus(A,A,tc_set(B)),c_emptyset),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL431-2.tptp',unknown),
    [] ).

cnf(153461640,plain,
    $equal(c_minus(A,A,tc_set(B)),c_emptyset),
    inference(rewrite,[status(thm)],[cls_Set_ODiff__cancel_0]),
    [] ).

cnf(163950464,plain,
    ~ c_in(v_p,c_proplog_othms(c_minus(A,A,tc_set(B)),t_a),tc_proplog_opl(t_a)),
    inference(paramodulation,[status(thm)],[153406288,153461640,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[153401272,153452504,163950464]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_0,plain,(c_proplog_osat(c_emptyset,v_p,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL431-2.tptp',unknown),[]).
% 
% cnf(153401272,plain,(c_proplog_osat(c_emptyset,v_p,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
% 
% fof(cls_PropLog_Ocompleteness__0__lemma__dest_0,plain,(~c_proplog_osat(c_emptyset,A,B)|c_in(A,c_proplog_othms(c_minus(c_proplog_ohyps(A,C,B),c_proplog_ohyps(A,D,B),tc_set(tc_proplog_opl(B))),B),tc_proplog_opl(B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL431-2.tptp',unknown),[]).
% 
% cnf(153452504,plain,(~c_proplog_osat(c_emptyset,A,B)|c_in(A,c_proplog_othms(c_minus(c_proplog_ohyps(A,C,B),c_proplog_ohyps(A,D,B),tc_set(tc_proplog_opl(B))),B),tc_proplog_opl(B))),inference(rewrite,[status(thm)],[cls_PropLog_Ocompleteness__0__lemma__dest_0]),[]).
% 
% fof(cls_conjecture_1,plain,(~c_in(v_p,c_proplog_othms(c_emptyset,t_a),tc_proplog_opl(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL431-2.tptp',unknown),[]).
% 
% cnf(153406288,plain,(~c_in(v_p,c_proplog_othms(c_emptyset,t_a),tc_proplog_opl(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
% 
% fof(cls_Set_ODiff__cancel_0,plain,($equal(c_minus(A,A,tc_set(B)),c_emptyset)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL431-2.tptp',unknown),[]).
% 
% cnf(153461640,plain,($equal(c_minus(A,A,tc_set(B)),c_emptyset)),inference(rewrite,[status(thm)],[cls_Set_ODiff__cancel_0]),[]).
% 
% cnf(163950464,plain,(~c_in(v_p,c_proplog_othms(c_minus(A,A,tc_set(B)),t_a),tc_proplog_opl(t_a))),inference(paramodulation,[status(thm)],[153406288,153461640,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[153401272,153452504,163950464]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------