TSTP Solution File: LCL397-1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : LCL397-1 : 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 13:49:11 EDT 2009

% Result   : Unsatisfiable 1.2s
% Output   : Refutation 1.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   23 (  16 unt;   0 def)
%            Number of atoms       :   32 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   20 (  11   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    6 (   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   :   47 (  12 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_cn_63,plain,
    ~ is_a_theorem(implies(x,implies(y,y))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),
    [] ).

cnf(162389920,plain,
    ~ is_a_theorem(implies(x,implies(y,y))),
    inference(rewrite,[status(thm)],[prove_cn_63]),
    [] ).

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/LCL397-1.tptp',unknown),
    [] ).

cnf(162369416,plain,
    ( ~ is_a_theorem(implies(A,B))
    | ~ is_a_theorem(A)
    | is_a_theorem(B) ),
    inference(rewrite,[status(thm)],[condensed_detachment]),
    [] ).

fof(cn_2,plain,
    ! [A] : is_a_theorem(implies(implies(not(A),A),A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),
    [] ).

cnf(162378264,plain,
    is_a_theorem(implies(implies(not(A),A),A)),
    inference(rewrite,[status(thm)],[cn_2]),
    [] ).

cnf(170180488,plain,
    ( ~ is_a_theorem(implies(implies(implies(not(B),B),B),A))
    | is_a_theorem(A) ),
    inference(resolution,[status(thm)],[162369416,162378264]),
    [] ).

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/LCL397-1.tptp',unknown),
    [] ).

cnf(162374272,plain,
    is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
    inference(rewrite,[status(thm)],[cn_1]),
    [] ).

cnf(170385536,plain,
    ( ~ is_a_theorem(implies(A,B))
    | is_a_theorem(implies(implies(B,C),implies(A,C))) ),
    inference(resolution,[status(thm)],[162369416,162374272]),
    [] ).

fof(cn_3,plain,
    ! [A,B] : is_a_theorem(implies(A,implies(not(A),B))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),
    [] ).

cnf(162382240,plain,
    is_a_theorem(implies(A,implies(not(A),B))),
    inference(rewrite,[status(thm)],[cn_3]),
    [] ).

cnf(170319560,plain,
    ( ~ is_a_theorem(implies(implies(B,implies(not(B),C)),A))
    | is_a_theorem(A) ),
    inference(resolution,[status(thm)],[162369416,162382240]),
    [] ).

cnf(171479856,plain,
    is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),
    inference(resolution,[status(thm)],[170319560,162374272]),
    [] ).

cnf(176058456,plain,
    ( ~ is_a_theorem(implies(implies(not(A),B),C))
    | is_a_theorem(implies(A,C)) ),
    inference(resolution,[status(thm)],[171479856,162369416]),
    [] ).

cnf(176129312,plain,
    is_a_theorem(implies(A,A)),
    inference(resolution,[status(thm)],[171479856,170180488]),
    [] ).

cnf(170296248,plain,
    ( ~ is_a_theorem(A)
    | is_a_theorem(implies(not(A),B)) ),
    inference(resolution,[status(thm)],[162369416,162382240]),
    [] ).

cnf(176454056,plain,
    is_a_theorem(implies(not(implies(A,A)),B)),
    inference(resolution,[status(thm)],[176129312,170296248]),
    [] ).

cnf(176901920,plain,
    is_a_theorem(implies(implies(B,C),implies(not(implies(A,A)),C))),
    inference(resolution,[status(thm)],[176454056,170385536]),
    [] ).

cnf(180287720,plain,
    is_a_theorem(implies(A,implies(not(implies(C,C)),B))),
    inference(resolution,[status(thm)],[176058456,176901920]),
    [] ).

cnf(180389232,plain,
    is_a_theorem(implies(implies(implies(not(implies(D,D)),C),B),implies(A,B))),
    inference(resolution,[status(thm)],[170385536,180287720]),
    [] ).

cnf(192309496,plain,
    is_a_theorem(implies(A,implies(B,B))),
    inference(resolution,[status(thm)],[170180488,180389232]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[162389920,192309496]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(prove_cn_63,plain,(~is_a_theorem(implies(x,implies(y,y)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),[]).
% 
% cnf(162389920,plain,(~is_a_theorem(implies(x,implies(y,y)))),inference(rewrite,[status(thm)],[prove_cn_63]),[]).
% 
% 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/LCL397-1.tptp',unknown),[]).
% 
% cnf(162369416,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
% 
% fof(cn_2,plain,(is_a_theorem(implies(implies(not(A),A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),[]).
% 
% cnf(162378264,plain,(is_a_theorem(implies(implies(not(A),A),A))),inference(rewrite,[status(thm)],[cn_2]),[]).
% 
% cnf(170180488,plain,(~is_a_theorem(implies(implies(implies(not(B),B),B),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162369416,162378264]),[]).
% 
% 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/LCL397-1.tptp',unknown),[]).
% 
% cnf(162374272,plain,(is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))),inference(rewrite,[status(thm)],[cn_1]),[]).
% 
% cnf(170385536,plain,(~is_a_theorem(implies(A,B))|is_a_theorem(implies(implies(B,C),implies(A,C)))),inference(resolution,[status(thm)],[162369416,162374272]),[]).
% 
% fof(cn_3,plain,(is_a_theorem(implies(A,implies(not(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL397-1.tptp',unknown),[]).
% 
% cnf(162382240,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(rewrite,[status(thm)],[cn_3]),[]).
% 
% cnf(170319560,plain,(~is_a_theorem(implies(implies(B,implies(not(B),C)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162369416,162382240]),[]).
% 
% cnf(171479856,plain,(is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C)))),inference(resolution,[status(thm)],[170319560,162374272]),[]).
% 
% cnf(176058456,plain,(~is_a_theorem(implies(implies(not(A),B),C))|is_a_theorem(implies(A,C))),inference(resolution,[status(thm)],[171479856,162369416]),[]).
% 
% cnf(176129312,plain,(is_a_theorem(implies(A,A))),inference(resolution,[status(thm)],[171479856,170180488]),[]).
% 
% cnf(170296248,plain,(~is_a_theorem(A)|is_a_theorem(implies(not(A),B))),inference(resolution,[status(thm)],[162369416,162382240]),[]).
% 
% cnf(176454056,plain,(is_a_theorem(implies(not(implies(A,A)),B))),inference(resolution,[status(thm)],[176129312,170296248]),[]).
% 
% cnf(176901920,plain,(is_a_theorem(implies(implies(B,C),implies(not(implies(A,A)),C)))),inference(resolution,[status(thm)],[176454056,170385536]),[]).
% 
% cnf(180287720,plain,(is_a_theorem(implies(A,implies(not(implies(C,C)),B)))),inference(resolution,[status(thm)],[176058456,176901920]),[]).
% 
% cnf(180389232,plain,(is_a_theorem(implies(implies(implies(not(implies(D,D)),C),B),implies(A,B)))),inference(resolution,[status(thm)],[170385536,180287720]),[]).
% 
% cnf(192309496,plain,(is_a_theorem(implies(A,implies(B,B)))),inference(resolution,[status(thm)],[170180488,180389232]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[162389920,192309496]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------