TSTP Solution File: LCL077-2 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : LCL077-2 : 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 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 13:41:21 EDT 2009

% Result   : Unsatisfiable 0.6s
% Output   : Refutation 0.6s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   28 (  17 unt;   0 def)
%            Number of atoms       :   43 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   32 (  17   ~;  15   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   57 (  11 sgn  12   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_cn_39,plain,
    ~ is_a_theorem(implies(not(not(a)),a)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),
    [] ).

cnf(155194280,plain,
    ~ is_a_theorem(implies(not(not(a)),a)),
    inference(rewrite,[status(thm)],[prove_cn_39]),
    [] ).

fof(transitivity,plain,
    ! [A,B,C] :
      ( ~ is_a_theorem(implies(A,B))
      | ~ is_a_theorem(implies(B,C))
      | is_a_theorem(implies(A,C)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),
    [] ).

cnf(155190728,plain,
    ( ~ is_a_theorem(implies(A,B))
    | ~ is_a_theorem(implies(B,C))
    | is_a_theorem(implies(A,C)) ),
    inference(rewrite,[status(thm)],[transitivity]),
    [] ).

fof(cn_18,plain,
    ! [A,B] : is_a_theorem(implies(A,implies(B,A))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),
    [] ).

cnf(155172984,plain,
    is_a_theorem(implies(A,implies(B,A))),
    inference(rewrite,[status(thm)],[cn_18]),
    [] ).

cnf(162991360,plain,
    ( ~ is_a_theorem(implies(implies(C,A),B))
    | is_a_theorem(implies(A,B)) ),
    inference(resolution,[status(thm)],[155190728,155172984]),
    [] ).

fof(cn_49,plain,
    ! [A,B] : is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),
    [] ).

cnf(155181016,plain,
    is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
    inference(rewrite,[status(thm)],[cn_49]),
    [] ).

cnf(165816360,plain,
    is_a_theorem(implies(not(B),implies(B,A))),
    inference(resolution,[status(thm)],[162991360,155181016]),
    [] ).

cnf(166270640,plain,
    ( ~ is_a_theorem(implies(implies(B,A),C))
    | is_a_theorem(implies(not(B),C)) ),
    inference(resolution,[status(thm)],[165816360,155190728]),
    [] ).

cnf(174701128,plain,
    is_a_theorem(implies(not(not(A)),implies(B,A))),
    inference(resolution,[status(thm)],[166270640,155181016]),
    [] ).

cnf(175367752,plain,
    ( ~ is_a_theorem(implies(implies(C,B),A))
    | is_a_theorem(implies(not(not(B)),A)) ),
    inference(resolution,[status(thm)],[155190728,174701128]),
    [] ).

fof(condensed_detachment,plain,
    ! [A,B] :
      ( ~ is_a_theorem(implies(A,B))
      | ~ is_a_theorem(A)
      | is_a_theorem(B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),
    [] ).

cnf(155168232,plain,
    ( ~ is_a_theorem(implies(A,B))
    | ~ is_a_theorem(A)
    | is_a_theorem(B) ),
    inference(rewrite,[status(thm)],[condensed_detachment]),
    [] ).

cnf(162971976,plain,
    ( ~ is_a_theorem(implies(implies(B,implies(C,B)),A))
    | is_a_theorem(A) ),
    inference(resolution,[status(thm)],[155168232,155172984]),
    [] ).

fof(cn_35,plain,
    ! [A,B,C] : is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),
    [] ).

cnf(155177112,plain,
    is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
    inference(rewrite,[status(thm)],[cn_35]),
    [] ).

cnf(163743920,plain,
    is_a_theorem(implies(implies(A,B),implies(A,A))),
    inference(resolution,[status(thm)],[162971976,155177112]),
    [] ).

cnf(163821392,plain,
    is_a_theorem(implies(A,A)),
    inference(resolution,[status(thm)],[163743920,162971976]),
    [] ).

cnf(162952600,plain,
    ( ~ is_a_theorem(A)
    | is_a_theorem(implies(B,A)) ),
    inference(resolution,[status(thm)],[155168232,155172984]),
    [] ).

cnf(163835736,plain,
    is_a_theorem(implies(B,implies(A,A))),
    inference(resolution,[status(thm)],[163821392,162952600]),
    [] ).

cnf(163921712,plain,
    ( ~ is_a_theorem(implies(implies(B,implies(A,A)),C))
    | is_a_theorem(C) ),
    inference(resolution,[status(thm)],[163835736,155168232]),
    [] ).

cnf(163855712,plain,
    ( ~ is_a_theorem(implies(implies(A,A),B))
    | is_a_theorem(B) ),
    inference(resolution,[status(thm)],[163821392,155168232]),
    [] ).

cnf(164600280,plain,
    is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
    inference(resolution,[status(thm)],[163855712,155177112]),
    [] ).

cnf(176501080,plain,
    is_a_theorem(implies(implies(implies(A,A),B),B)),
    inference(resolution,[status(thm)],[163921712,164600280]),
    [] ).

cnf(178089600,plain,
    is_a_theorem(implies(not(not(A)),A)),
    inference(resolution,[status(thm)],[175367752,176501080]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[155194280,178089600]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_cn_39,plain,(~is_a_theorem(implies(not(not(a)),a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),[]).
% 
% cnf(155194280,plain,(~is_a_theorem(implies(not(not(a)),a))),inference(rewrite,[status(thm)],[prove_cn_39]),[]).
% 
% fof(transitivity,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(implies(B,C))|is_a_theorem(implies(A,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),[]).
% 
% cnf(155190728,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(implies(B,C))|is_a_theorem(implies(A,C))),inference(rewrite,[status(thm)],[transitivity]),[]).
% 
% fof(cn_18,plain,(is_a_theorem(implies(A,implies(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),[]).
% 
% cnf(155172984,plain,(is_a_theorem(implies(A,implies(B,A)))),inference(rewrite,[status(thm)],[cn_18]),[]).
% 
% cnf(162991360,plain,(~is_a_theorem(implies(implies(C,A),B))|is_a_theorem(implies(A,B))),inference(resolution,[status(thm)],[155190728,155172984]),[]).
% 
% fof(cn_49,plain,(is_a_theorem(implies(implies(not(A),not(B)),implies(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),[]).
% 
% cnf(155181016,plain,(is_a_theorem(implies(implies(not(A),not(B)),implies(B,A)))),inference(rewrite,[status(thm)],[cn_49]),[]).
% 
% cnf(165816360,plain,(is_a_theorem(implies(not(B),implies(B,A)))),inference(resolution,[status(thm)],[162991360,155181016]),[]).
% 
% cnf(166270640,plain,(~is_a_theorem(implies(implies(B,A),C))|is_a_theorem(implies(not(B),C))),inference(resolution,[status(thm)],[165816360,155190728]),[]).
% 
% cnf(174701128,plain,(is_a_theorem(implies(not(not(A)),implies(B,A)))),inference(resolution,[status(thm)],[166270640,155181016]),[]).
% 
% cnf(175367752,plain,(~is_a_theorem(implies(implies(C,B),A))|is_a_theorem(implies(not(not(B)),A))),inference(resolution,[status(thm)],[155190728,174701128]),[]).
% 
% fof(condensed_detachment,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),[]).
% 
% cnf(155168232,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
% 
% cnf(162971976,plain,(~is_a_theorem(implies(implies(B,implies(C,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[155168232,155172984]),[]).
% 
% fof(cn_35,plain,(is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),[]).
% 
% cnf(155177112,plain,(is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))),inference(rewrite,[status(thm)],[cn_35]),[]).
% 
% cnf(163743920,plain,(is_a_theorem(implies(implies(A,B),implies(A,A)))),inference(resolution,[status(thm)],[162971976,155177112]),[]).
% 
% cnf(163821392,plain,(is_a_theorem(implies(A,A))),inference(resolution,[status(thm)],[163743920,162971976]),[]).
% 
% cnf(162952600,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[155168232,155172984]),[]).
% 
% cnf(163835736,plain,(is_a_theorem(implies(B,implies(A,A)))),inference(resolution,[status(thm)],[163821392,162952600]),[]).
% 
% cnf(163921712,plain,(~is_a_theorem(implies(implies(B,implies(A,A)),C))|is_a_theorem(C)),inference(resolution,[status(thm)],[163835736,155168232]),[]).
% 
% cnf(163855712,plain,(~is_a_theorem(implies(implies(A,A),B))|is_a_theorem(B)),inference(resolution,[status(thm)],[163821392,155168232]),[]).
% 
% cnf(164600280,plain,(is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B)))),inference(resolution,[status(thm)],[163855712,155177112]),[]).
% 
% cnf(176501080,plain,(is_a_theorem(implies(implies(implies(A,A),B),B))),inference(resolution,[status(thm)],[163921712,164600280]),[]).
% 
% cnf(178089600,plain,(is_a_theorem(implies(not(not(A)),A))),inference(resolution,[status(thm)],[175367752,176501080]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[155194280,178089600]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------