%------------------------------------------------------------------------------
% File     : SYO886_7.212 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Syntactic
% Problem  : Barcan scheme instance, with added axioms, conjecture removed
% Version  : Especial.
% English  : If for all x necessarily f(x), then it is necessary that for
%            all x f(x), with domain size 2.

% Refs     : [Bar46] Barcan (1946), A Functional Calculus of First Order Ba
%          : [Sar25] Sariyanto (2025), Email to Geoff Sutcliffe
% Source   : [Sar25]
% Names    : fun_test_2.txt [Sar25]

% Status   : Satisfiable
% Rating   : ? v9.3.0
% Syntax   : Number of formulae    :    4 (   1 unt;   3 typ;   0 def)
%            Number of atoms       :    1 (   1 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    1 (   1   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :    4 (   0   !;   4   ?;   4   :)
% SPC      : NX0_SAT_EQU_NAR_NDT

% Comments :
%------------------------------------------------------------------------------
tff(logic_specs,logic,
    $modal == 
      [ $domains == $constant,
        $designation == $flexible,
        $terms == $local,
        $modalities == $modal_system_S5 ] ).

tff(test_sort_decl,type,
    t: $tType ).

tff(f_decl,type,
    f: $i > $o ).

tff(test_s_decl,type,
    s: ( $i * t ) > $i ).

tff(test_axiom_decl,axiom,
    ? [X1: $i,X2: t,Y1: $i,Y2: t] : ( s(X1,X2) != s(Y1,Y2) ) ).

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