%------------------------------------------------------------------------------
% File     : SYO748+1 : TPTP v8.2.0. Released v7.4.0.
% Domain   : Syntactic
% Problem  : SuperPostulates problem sp410R2
% Version  : Especial.
% English  :

% Refs     : [Lam20] Lampert (2020), Email to Geoff Sutcliffe
%          : [LN20]  Lampert & Nakano (2020), Deciding Simple Infinity Axio
% Source   : [Lam20]
% Names    : sp410R2.p [Lam20]

% Status   : Satisfiable
% Rating   : 1.00 v7.4.0
% Syntax   : Number of formulae    :    8 (   0 unt;   0 def)
%            Number of atoms       :   30 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   37 (  15   ~;  13   |;   9   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   28 (  17   !;  11   ?)
% SPC      : FOF_SAT_RFO_NEQ

% Comments : Has only infinite models.
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
    ? [Y1] :
      ( ? [Y2] :
          ( f(Y1,Y2)
          & ? [Y3] : ~ f(Y3,Y2) )
      & ! [X1] :
          ( ~ f(Y1,X1)
          | f(X1,X1) ) ) ).

fof(axiom_2,axiom,
    ? [Y1] :
      ( f(Y1,Y1)
      & ! [X1] :
          ( ! [X2] : f(X2,X1)
          | ~ f(Y1,X1) ) ) ).

fof(axiom_3,axiom,
    ! [X1] :
    ? [Y1] :
      ( ? [Y2] : ~ f(Y1,Y2)
      & f(Y1,X1) ) ).

fof(axiom_4,axiom,
    ! [X1] :
    ? [Y1] :
      ( ~ f(Y1,Y1)
      & f(Y1,X1) ) ).

fof(axiom_5,axiom,
    ! [X1,X2,X3] :
      ( ~ f(X2,X1)
      | ~ f(X3,X2)
      | f(X3,X1) ) ).

fof(axiom_6,axiom,
    ! [X1,X2] :
      ( f(X2,X1)
      | ! [X3] :
          ( f(X3,X2)
          | ~ f(X3,X1) ) ) ).

fof(axiom_7,axiom,
    ! [X1] :
      ( ? [Y1] :
          ( ? [Y2] :
              ( ? [Y4] :
                  ( ~ f(Y1,Y4)
                  & f(Y2,Y4) )
              & ~ f(Y2,X1) )
          & ! [X2] :
              ( ! [X3] :
                  ( ~ f(X2,X3)
                  | f(Y1,X3) )
              | ? [Y3] :
                  ( f(X2,Y3)
                  & ~ f(Y3,Y3) ) ) )
      | f(X1,X1) ) ).

fof(axiom_8,axiom,
    ! [X1] :
      ( ! [X2] :
          ( ~ f(X1,X2)
          | f(X2,X2) )
      | ! [X3] :
          ( ~ f(X3,X1)
          | f(X3,X3) )
      | ~ f(X1,X1) ) ).

%------------------------------------------------------------------------------