## TPTP Problem File: SYO564^7.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO564^7 : TPTP v7.0.0. Released v5.5.0.
% Domain   : Syntactic
% Problem  : Barcan scheme instance. (Ted Sider's qml wwf 1)
% Version  : [Ben12] axioms.
% English  :

% Refs     : [Bar46] Barcan (1946), A Functional Calculus of First Order Ba
%          : [Sid09] Sider (2009), Logic for Philosophy
%          : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source   : [Ben12]
% Names    : s4-cumul-SYM001+1 [Ben12]

% Status   : CounterSatisfiable
% Rating   : 0.33 v5.5.0
% Syntax   : Number of formulae    :   74 (   0 unit;  37 type;  32 defn)
%            Number of atoms       :  259 (  36 equality; 145 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :  155 (   5   ~;   5   |;   9   &; 126   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  182 ( 182   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   41 (  37   :;   0   =)
%            Number of variables   :   92 (   2 sgn;  34   !;   7   ?;  51   ^)
%                                         (  92   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_NAR

% Comments :
%------------------------------------------------------------------------------
%----Include axioms for Modal logic S4 under cumulative domains
include('Axioms/LCL015^0.ax').
include('Axioms/LCL013^5.ax').
include('Axioms/LCL015^1.ax').
%------------------------------------------------------------------------------
thf(f_type,type,(
f: mu > \$i > \$o )).

thf(con,conjecture,
( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X: mu] :
( mbox_s4 @ ( f @ X ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] :
( f @ X ) ) ) ) )).

%------------------------------------------------------------------------------
```