TSTP Solution File: LCL398-1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : LCL398-1 : TPTP v3.4.2. Released v2.3.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art03.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 13:49:13 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   17 (  12 unt;   0 def)
%            Number of atoms       :   24 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   20 (  13   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   23 (   2 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/LCL398-1.tptp',unknown),
    [] ).

cnf(143219864,plain,
    ( ~ is_a_theorem(implies(A,B))
    | ~ is_a_theorem(A)
    | is_a_theorem(B) ),
    inference(rewrite,[status(thm)],[condensed_detachment]),
    [] ).

fof(cn_3,plain,
    ! [A,B] : is_a_theorem(implies(A,implies(not(A),B))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),
    [] ).

cnf(143232688,plain,
    is_a_theorem(implies(A,implies(not(A),B))),
    inference(rewrite,[status(thm)],[cn_3]),
    [] ).

cnf(151041448,plain,
    ( ~ is_a_theorem(A)
    | is_a_theorem(implies(not(A),B)) ),
    inference(resolution,[status(thm)],[143219864,143232688]),
    [] ).

fof(prove_cn_64,plain,
    ~ is_a_theorem(implies(not(implies(x,x)),y)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),
    [] ).

cnf(143240456,plain,
    ~ is_a_theorem(implies(not(implies(x,x)),y)),
    inference(rewrite,[status(thm)],[prove_cn_64]),
    [] ).

cnf(151115360,plain,
    ~ is_a_theorem(implies(x,x)),
    inference(resolution,[status(thm)],[151041448,143240456]),
    [] ).

cnf(151135568,plain,
    ( ~ is_a_theorem(implies(A,implies(x,x)))
    | ~ is_a_theorem(A) ),
    inference(resolution,[status(thm)],[143219864,151115360]),
    [] ).

fof(cn_2,plain,
    ! [A] : is_a_theorem(implies(implies(not(A),A),A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),
    [] ).

cnf(143228712,plain,
    is_a_theorem(implies(implies(not(A),A),A)),
    inference(rewrite,[status(thm)],[cn_2]),
    [] ).

cnf(151587904,plain,
    ~ is_a_theorem(implies(implies(implies(not(A),A),A),implies(x,x))),
    inference(resolution,[status(thm)],[151135568,143228712]),
    [] ).

fof(cn_1,plain,
    ! [A,B,C] : is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),
    [] ).

cnf(143224720,plain,
    is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
    inference(rewrite,[status(thm)],[cn_1]),
    [] ).

cnf(151276224,plain,
    ( ~ is_a_theorem(implies(A,B))
    | is_a_theorem(implies(implies(B,C),implies(A,C))) ),
    inference(resolution,[status(thm)],[143219864,143224720]),
    [] ).

cnf(154438640,plain,
    ~ is_a_theorem(implies(x,implies(not(x),x))),
    inference(resolution,[status(thm)],[151587904,151276224]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[154438640,143232688]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% 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/LCL398-1.tptp',unknown),[]).
% 
% cnf(143219864,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
% 
% fof(cn_3,plain,(is_a_theorem(implies(A,implies(not(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),[]).
% 
% cnf(143232688,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(rewrite,[status(thm)],[cn_3]),[]).
% 
% cnf(151041448,plain,(~is_a_theorem(A)|is_a_theorem(implies(not(A),B))),inference(resolution,[status(thm)],[143219864,143232688]),[]).
% 
% fof(prove_cn_64,plain,(~is_a_theorem(implies(not(implies(x,x)),y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),[]).
% 
% cnf(143240456,plain,(~is_a_theorem(implies(not(implies(x,x)),y))),inference(rewrite,[status(thm)],[prove_cn_64]),[]).
% 
% cnf(151115360,plain,(~is_a_theorem(implies(x,x))),inference(resolution,[status(thm)],[151041448,143240456]),[]).
% 
% cnf(151135568,plain,(~is_a_theorem(implies(A,implies(x,x)))|~is_a_theorem(A)),inference(resolution,[status(thm)],[143219864,151115360]),[]).
% 
% fof(cn_2,plain,(is_a_theorem(implies(implies(not(A),A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),[]).
% 
% cnf(143228712,plain,(is_a_theorem(implies(implies(not(A),A),A))),inference(rewrite,[status(thm)],[cn_2]),[]).
% 
% cnf(151587904,plain,(~is_a_theorem(implies(implies(implies(not(A),A),A),implies(x,x)))),inference(resolution,[status(thm)],[151135568,143228712]),[]).
% 
% fof(cn_1,plain,(is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),[]).
% 
% cnf(143224720,plain,(is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))),inference(rewrite,[status(thm)],[cn_1]),[]).
% 
% cnf(151276224,plain,(~is_a_theorem(implies(A,B))|is_a_theorem(implies(implies(B,C),implies(A,C)))),inference(resolution,[status(thm)],[143219864,143224720]),[]).
% 
% cnf(154438640,plain,(~is_a_theorem(implies(x,implies(not(x),x)))),inference(resolution,[status(thm)],[151587904,151276224]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[154438640,143232688]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------