## TPTP Problem File: AGT032^2.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : AGT032^2 : TPTP v7.1.0. Released v5.2.0.
% Domain   : Agents
% Problem  : Someone likes someone else
% Version  : [Ben11] axioms : Reduced > Complete.
% English  :

% Refs     : [Ben11] Benzmueller (2011), Email to Geoff Sutcliffe
%          : [Ben11] Benzmueller (2011), Combining and Automating Classical
% Source   : [Ben11]
% Names    : Ex_12_2_K [Ben11]

% Status   : Theorem
% Rating   : 0.25 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.80 v5.2.0
% Syntax   : Number of formulae    :   93 (   0 unit;  43 type;  31 defn)
%            Number of atoms       :  408 (  36 equality; 168 variable)
%            Maximal formula depth :   15 (   6 average)
%            Number of connectives :  290 (   4   ~;   4   |;   8   &; 266   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  183 ( 183   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   47 (  43   :;   0   =)
%            Number of variables   :  102 (   3 sgn;  29   !;   6   ?;  67   ^)
%                                         ( 102   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

%------------------------------------------------------------------------------
%----Include embedding of quantified multimodal logic in simple type theory
include('Axioms/LCL013^0.ax').
%------------------------------------------------------------------------------
thf(a1,type,(
a1: \$i > \$i > \$o )).

thf(a2,type,(
a2: \$i > \$i > \$o )).

thf(a3,type,(
a3: \$i > \$i > \$o )).

thf(jan,type,(
jan: mu )).

thf(piotr,type,(
piotr: mu )).

thf(cola,type,(
cola: mu )).

thf(pepsi,type,(
pepsi: mu )).

thf(beer,type,(
beer: mu )).

thf(likes,type,(
likes: mu > mu > \$i > \$o )).

thf(very_much_likes,type,(
very_much_likes: mu > mu > \$i > \$o )).

thf(possibly_likes,type,(
possibly_likes: mu > mu > \$i > \$o )).

thf(axiom_a1_1,axiom,
( mvalid @ ( mbox @ a1 @ ( likes @ jan @ cola ) ) )).

thf(axiom_a1_2,axiom,
( mvalid @ ( mbox @ a1 @ ( likes @ piotr @ pepsi ) ) )).

thf(axiom_a1_3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mbox @ a1 @ ( mimplies @ ( mdia @ a1 @ ( likes @ X @ pepsi ) ) @ ( likes @ X @ cola ) ) ) ) )).

thf(axiom_a1_4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mbox @ a1 @ ( mimplies @ ( mdia @ a1 @ ( likes @ X @ cola ) ) @ ( likes @ X @ pepsi ) ) ) ) )).

thf(axiom_a2_1,axiom,
( mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ) )).

thf(axiom_a2_2,axiom,
( mvalid @ ( mbox @ a1 @ ( likes @ piotr @ cola ) ) )).

thf(axiom_a2_3,axiom,
( mvalid @ ( mbox @ a1 @ ( likes @ piotr @ beer ) ) )).

thf(axiom_a2_4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mbox @ a2 @ ( mimplies @ ( likes @ X @ pepsi ) @ ( likes @ X @ cola ) ) ) ) )).

thf(axiom_a2_5,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mbox @ a2 @ ( mimplies @ ( likes @ X @ cola ) @ ( likes @ X @ pepsi ) ) ) ) )).

thf(axiom_a3_1,axiom,
( mvalid @ ( mbox @ a3 @ ( likes @ jan @ cola ) ) )).

thf(axiom_a3_2,axiom,
( mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ) )).

thf(axiom_a3_3,axiom,
( mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ) )).

thf(axiom_a3_4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mbox @ a3 @ ( mimplies @ ( mand @ ( likes @ X @ Y ) @ ( mand @ ( mbox @ a1 @ ( likes @ X @ Y ) ) @ ( mbox @ a2 @ ( likes @ X @ Y ) ) ) ) @ ( very_much_likes @ X @ Y ) ) ) ) ) )).

thf(axiom_user_communication_1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mimplies @ ( mbox @ a3 @ ( very_much_likes @ X @ Y ) ) @ ( very_much_likes @ X @ Y ) ) ) ) )).

thf(axiom_user_communication_2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mimplies @ ( mdia @ a3 @ ( very_much_likes @ X @ Y ) ) @ ( likes @ X @ Y ) ) ) ) )).

thf(axiom_user_communication_3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mimplies @ ( mdia @ a1 @ ( likes @ X @ Y ) ) @ ( possibly_likes @ X @ Y ) ) ) ) )).

thf(axiom_user_communication_4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mimplies @ ( mdia @ a2 @ ( likes @ X @ Y ) ) @ ( possibly_likes @ X @ Y ) ) ) ) )).

thf(axiom_user_communication_5,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mimplies @ ( mdia @ a3 @ ( likes @ X @ Y ) ) @ ( possibly_likes @ X @ Y ) ) ) ) )).

thf(conj,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X: mu] :
( mexists_ind
@ ^ [Y: mu] :
( likes @ X @ Y ) ) ) )).

```