%------------------------------------------------------------------------------
% File     : SYO886_6.212 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Syntactic
% Problem  : Barcan scheme instance, with added axioms.
% 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_1.txt [Sar25]

% Status   : CounterSatisfiable
% Rating   : ? v9.3.0
% Syntax   : Number of formulae    :    5 (   1 unt;   3 typ;   0 def)
%            Number of atoms       :    5 (   1 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :    6 (   1   ~;   0   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   2 {.};   0 {#})
%            Maximal formula depth :    6 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number of X terms     :    2 (   2  [];   0 ite;   0 let;   0 dis)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :    6 (   2   !;   4   ?;   6   :)
% SPC      : NX0_CSA_EQU_NAR_NDT

% Comments :
%------------------------------------------------------------------------------
tff(logic_specs,logic,
    $modal == 
      [ $domains == $varying,
        $designation == $rigid,
        $terms == $global,
        $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) ) ).

tff(con,conjecture,
    ( ! [X: $i] : ( {$box} @ (f(X)) )
   => ( {$box}
      @ ( ! [X: $i] : f(X) ) ) ) ).

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