## TPTP Problem File: SYO056^1.p

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```%------------------------------------------------------------------------------
% File     : SYO056^1 : TPTP v7.0.0. Released v4.0.0.
% Domain   : Logic Calculi (Quantified multimodal logic)
% Problem  : Simple textbook example 13
% Version  : [Ben09] axioms.
% English  :

% Refs     : [Gol92] Goldblatt (1992), Logics of Time and Computation
%          : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% Source   : [Ben09]
% Names    : ex13.p [Ben09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v6.4.0, 0.00 v6.3.0, 0.33 v5.4.0, 0.00 v5.0.0, 0.67 v4.1.0, 0.50 v4.0.0
% Syntax   : Number of formulae    :   64 (   0 unit;  32 type;  31 defn)
%            Number of atoms       :  238 (  36 equality; 137 variable)
%            Maximal formula depth :   12 (   6 average)
%            Number of connectives :  138 (   4   ~;   4   |;   8   &; 114   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  172 ( 172   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   36 (  32   :;   0   =)
%            Number of variables   :   87 (   3 sgn;  30   !;   6   ?;  51   ^)
%                                         (  87   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_NAR

% Comments :
%------------------------------------------------------------------------------
%----Include embedding of quantified multimodal logic in simple type theory
include('Axioms/LCL013^0.ax').
%------------------------------------------------------------------------------
thf(conj,conjecture,(
! [R: \$i > \$i > \$o] :
( mvalid
@ ( mforall_prop
@ ^ [A: \$i > \$o] :
( mforall_prop
@ ^ [B: \$i > \$o] :
( mimplies @ ( mbox @ R @ ( mor @ A @ B ) ) @ ( mor @ ( mbox @ R @ A ) @ ( mbox @ R @ B ) ) ) ) ) ) )).

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