TSTP Solution File: COL100-1 by Faust---1.0

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%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COL100-1 : TPTP v3.4.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art06.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 11:34:28 EDT 2009

% Result   : Unsatisfiable 144.4s
% Output   : Refutation 144.4s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   31 (  13 unt;   0 def)
%            Number of atoms       :   61 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   63 (  33   ~;  30   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-4 aty)
%            Number of variables   :   42 (   1 sgn  19   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(diamond_trancl_2h4,plain,
    ! [A] :
      ( ~ member(pair(y,A),trancl(r))
      | member(pair(ya,sk1(A)),trancl(r)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
    [] ).

cnf(155150976,plain,
    ( ~ member(pair(y,A),trancl(r))
    | member(pair(ya,sk1(A)),trancl(r)) ),
    inference(rewrite,[status(thm)],[diamond_trancl_2h4]),
    [] ).

fof(diamond_trancl_2c1,plain,
    member(pair(y,yp),trancl(r)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
    [] ).

cnf(155162864,plain,
    member(pair(y,yp),trancl(r)),
    inference(rewrite,[status(thm)],[diamond_trancl_2c1]),
    [] ).

cnf(167099576,plain,
    member(pair(ya,sk1(yp)),trancl(r)),
    inference(resolution,[status(thm)],[155150976,155162864]),
    [] ).

fof(diamond_trancl_2c2,plain,
    ! [A] :
      ( ~ member(pair(z,A),trancl(r))
      | ~ member(pair(yp,A),trancl(r)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
    [] ).

cnf(155168480,plain,
    ( ~ member(pair(z,A),trancl(r))
    | ~ member(pair(yp,A),trancl(r)) ),
    inference(rewrite,[status(thm)],[diamond_trancl_2c2]),
    [] ).

fof(diamond_trancl_2h1,plain,
    diamond(r),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
    [] ).

cnf(155131840,plain,
    diamond(r),
    inference(rewrite,[status(thm)],[diamond_trancl_2h1]),
    [] ).

fof(diamond_strip_lemmaD1,plain,
    ! [A,B,C,D] :
      ( ~ diamond(A)
      | ~ member(pair(B,C),trancl(A))
      | ~ member(pair(B,D),A)
      | member(pair(D,diamond_strip_lemmad_sk1(B,C,D,A)),trancl(A)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
    [] ).

cnf(155097272,plain,
    ( ~ diamond(A)
    | ~ member(pair(B,C),trancl(A))
    | ~ member(pair(B,D),A)
    | member(pair(D,diamond_strip_lemmad_sk1(B,C,D,A)),trancl(A)) ),
    inference(rewrite,[status(thm)],[diamond_strip_lemmaD1]),
    [] ).

fof(diamond_trancl_2h3,plain,
    member(pair(ya,z),r),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
    [] ).

cnf(155145248,plain,
    member(pair(ya,z),r),
    inference(rewrite,[status(thm)],[diamond_trancl_2h3]),
    [] ).

cnf(165823144,plain,
    ( ~ member(pair(ya,A),trancl(r))
    | member(pair(z,diamond_strip_lemmad_sk1(ya,A,z,r)),trancl(r)) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[155131840,155097272,155145248]),
    [] ).

cnf(170753944,plain,
    member(pair(z,diamond_strip_lemmad_sk1(ya,sk1(yp),z,r)),trancl(r)),
    inference(resolution,[status(thm)],[165823144,167099576]),
    [] ).

cnf(284290032,plain,
    ~ member(pair(yp,diamond_strip_lemmad_sk1(ya,sk1(yp),z,r)),trancl(r)),
    inference(resolution,[status(thm)],[155168480,170753944]),
    [] ).

fof(diamond_strip_lemmaD2,plain,
    ! [A,B,C,D] :
      ( ~ diamond(A)
      | ~ member(pair(B,C),trancl(A))
      | ~ member(pair(B,D),A)
      | member(pair(C,diamond_strip_lemmad_sk1(B,C,D,A)),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
    [] ).

cnf(155123376,plain,
    ( ~ diamond(A)
    | ~ member(pair(B,C),trancl(A))
    | ~ member(pair(B,D),A)
    | member(pair(C,diamond_strip_lemmad_sk1(B,C,D,A)),A) ),
    inference(rewrite,[status(thm)],[diamond_strip_lemmaD2]),
    [] ).

cnf(165806648,plain,
    ( ~ member(pair(ya,A),trancl(r))
    | member(pair(A,diamond_strip_lemmad_sk1(ya,A,z,r)),r) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[155131840,155123376,155145248]),
    [] ).

fof(trans_trancl,plain,
    ! [A] : trans(trancl(A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
    [] ).

cnf(155051216,plain,
    trans(trancl(A)),
    inference(rewrite,[status(thm)],[trans_trancl]),
    [] ).

fof(transD,plain,
    ! [A,B,C,D] :
      ( ~ trans(A)
      | ~ member(pair(B,C),A)
      | ~ member(pair(C,D),A)
      | member(pair(B,D),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
    [] ).

cnf(155061560,plain,
    ( ~ trans(A)
    | ~ member(pair(B,C),A)
    | ~ member(pair(C,D),A)
    | member(pair(B,D),A) ),
    inference(rewrite,[status(thm)],[transD]),
    [] ).

fof(diamond_trancl_2h5,plain,
    ! [A] :
      ( ~ member(pair(y,A),trancl(r))
      | member(pair(A,sk1(A)),trancl(r)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
    [] ).

cnf(155159248,plain,
    ( ~ member(pair(y,A),trancl(r))
    | member(pair(A,sk1(A)),trancl(r)) ),
    inference(rewrite,[status(thm)],[diamond_trancl_2h5]),
    [] ).

cnf(167246976,plain,
    member(pair(yp,sk1(yp)),trancl(r)),
    inference(resolution,[status(thm)],[155159248,155162864]),
    [] ).

cnf(170847592,plain,
    ( ~ member(pair(sk1(yp),A),trancl(r))
    | member(pair(yp,A),trancl(r)) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[155051216,155061560,167246976]),
    [] ).

fof(r_into_trancl,plain,
    ! [A,B,C] :
      ( ~ member(pair(A,B),C)
      | member(pair(A,B),trancl(C)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
    [] ).

cnf(155042024,plain,
    ( ~ member(pair(A,B),C)
    | member(pair(A,B),trancl(C)) ),
    inference(rewrite,[status(thm)],[r_into_trancl]),
    [] ).

cnf(199901488,plain,
    ( member(pair(yp,A),trancl(r))
    | ~ member(pair(sk1(yp),A),r) ),
    inference(resolution,[status(thm)],[170847592,155042024]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[167099576,284290032,165806648,199901488]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 143 seconds
% START OF PROOF SEQUENCE
% fof(diamond_trancl_2h4,plain,(~member(pair(y,A),trancl(r))|member(pair(ya,sk1(A)),trancl(r))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
% 
% cnf(155150976,plain,(~member(pair(y,A),trancl(r))|member(pair(ya,sk1(A)),trancl(r))),inference(rewrite,[status(thm)],[diamond_trancl_2h4]),[]).
% 
% fof(diamond_trancl_2c1,plain,(member(pair(y,yp),trancl(r))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
% 
% cnf(155162864,plain,(member(pair(y,yp),trancl(r))),inference(rewrite,[status(thm)],[diamond_trancl_2c1]),[]).
% 
% cnf(167099576,plain,(member(pair(ya,sk1(yp)),trancl(r))),inference(resolution,[status(thm)],[155150976,155162864]),[]).
% 
% fof(diamond_trancl_2c2,plain,(~member(pair(z,A),trancl(r))|~member(pair(yp,A),trancl(r))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
% 
% cnf(155168480,plain,(~member(pair(z,A),trancl(r))|~member(pair(yp,A),trancl(r))),inference(rewrite,[status(thm)],[diamond_trancl_2c2]),[]).
% 
% fof(diamond_trancl_2h1,plain,(diamond(r)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
% 
% cnf(155131840,plain,(diamond(r)),inference(rewrite,[status(thm)],[diamond_trancl_2h1]),[]).
% 
% fof(diamond_strip_lemmaD1,plain,(~diamond(A)|~member(pair(B,C),trancl(A))|~member(pair(B,D),A)|member(pair(D,diamond_strip_lemmad_sk1(B,C,D,A)),trancl(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
% 
% cnf(155097272,plain,(~diamond(A)|~member(pair(B,C),trancl(A))|~member(pair(B,D),A)|member(pair(D,diamond_strip_lemmad_sk1(B,C,D,A)),trancl(A))),inference(rewrite,[status(thm)],[diamond_strip_lemmaD1]),[]).
% 
% fof(diamond_trancl_2h3,plain,(member(pair(ya,z),r)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
% 
% cnf(155145248,plain,(member(pair(ya,z),r)),inference(rewrite,[status(thm)],[diamond_trancl_2h3]),[]).
% 
% cnf(165823144,plain,(~member(pair(ya,A),trancl(r))|member(pair(z,diamond_strip_lemmad_sk1(ya,A,z,r)),trancl(r))),inference(forward_subsumption_resolution__resolution,[status(thm)],[155131840,155097272,155145248]),[]).
% 
% cnf(170753944,plain,(member(pair(z,diamond_strip_lemmad_sk1(ya,sk1(yp),z,r)),trancl(r))),inference(resolution,[status(thm)],[165823144,167099576]),[]).
% 
% cnf(284290032,plain,(~member(pair(yp,diamond_strip_lemmad_sk1(ya,sk1(yp),z,r)),trancl(r))),inference(resolution,[status(thm)],[155168480,170753944]),[]).
% 
% fof(diamond_strip_lemmaD2,plain,(~diamond(A)|~member(pair(B,C),trancl(A))|~member(pair(B,D),A)|member(pair(C,diamond_strip_lemmad_sk1(B,C,D,A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
% 
% cnf(155123376,plain,(~diamond(A)|~member(pair(B,C),trancl(A))|~member(pair(B,D),A)|member(pair(C,diamond_strip_lemmad_sk1(B,C,D,A)),A)),inference(rewrite,[status(thm)],[diamond_strip_lemmaD2]),[]).
% 
% cnf(165806648,plain,(~member(pair(ya,A),trancl(r))|member(pair(A,diamond_strip_lemmad_sk1(ya,A,z,r)),r)),inference(forward_subsumption_resolution__resolution,[status(thm)],[155131840,155123376,155145248]),[]).
% 
% fof(trans_trancl,plain,(trans(trancl(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
% 
% cnf(155051216,plain,(trans(trancl(A))),inference(rewrite,[status(thm)],[trans_trancl]),[]).
% 
% fof(transD,plain,(~trans(A)|~member(pair(B,C),A)|~member(pair(C,D),A)|member(pair(B,D),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
% 
% cnf(155061560,plain,(~trans(A)|~member(pair(B,C),A)|~member(pair(C,D),A)|member(pair(B,D),A)),inference(rewrite,[status(thm)],[transD]),[]).
% 
% fof(diamond_trancl_2h5,plain,(~member(pair(y,A),trancl(r))|member(pair(A,sk1(A)),trancl(r))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
% 
% cnf(155159248,plain,(~member(pair(y,A),trancl(r))|member(pair(A,sk1(A)),trancl(r))),inference(rewrite,[status(thm)],[diamond_trancl_2h5]),[]).
% 
% cnf(167246976,plain,(member(pair(yp,sk1(yp)),trancl(r))),inference(resolution,[status(thm)],[155159248,155162864]),[]).
% 
% cnf(170847592,plain,(~member(pair(sk1(yp),A),trancl(r))|member(pair(yp,A),trancl(r))),inference(forward_subsumption_resolution__resolution,[status(thm)],[155051216,155061560,167246976]),[]).
% 
% fof(r_into_trancl,plain,(~member(pair(A,B),C)|member(pair(A,B),trancl(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
% 
% cnf(155042024,plain,(~member(pair(A,B),C)|member(pair(A,B),trancl(C))),inference(rewrite,[status(thm)],[r_into_trancl]),[]).
% 
% cnf(199901488,plain,(member(pair(yp,A),trancl(r))|~member(pair(sk1(yp),A),r)),inference(resolution,[status(thm)],[170847592,155042024]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[167099576,284290032,165806648,199901488]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------