TPTP Problem File: SYO055^2.p

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%------------------------------------------------------------------------------
% File     : SYO055^2 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Logic Calculi (Quantified multimodal logic)
% Problem  : Simple textbook example 12
% Version  : [Ben09] axioms.
%          : Theorem formulation : Accessibility relation not valid
% English  :

% Refs     : [Gol92] Goldblatt (1992), Logics of Time and Computation
%          : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% Source   : [Ben09]
% Names    : ex12a.p [Ben09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :   64 (   0 unit;  32 type;  31 defn)
%            Number of atoms       :  240 (  36 equality; 138 variable)
%            Maximal formula depth :   15 (   6 average)
%            Number of connectives :  141 (   5   ~;   4   |;   8   &; 116   @)
%                                         (   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;  29   !;   7   ?;  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] :
                  ( mor @ ( mbox @ R @ ( mimplies @ ( mbox @ R @ A ) @ B ) ) @ ( mbox @ R @ ( mimplies @ ( mbox @ R @ B ) @ A ) ) ) ) ) ) )).

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