## TPTP Problem File: AGT040^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : AGT040^1 : TPTP v7.2.0. Bugfixed v5.4.0.
% Domain   : Agents
% Problem  : Piotr possibly likes cola
% Version  : [Ben11] axioms.
% English  :

% Refs     : [Ben11] Benzmueller (2011), Email to Geoff Sutcliffe
%          : [Ben11] Benzmueller (2011), Combining and Automating Classical
% Source   : [Ben11]
% Names    : Ex_12_10 [Ben11]

% Status   : Theorem
% Rating   : 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0
% Syntax   : Number of formulae    :  118 (   0 unit;  45 type;  33 defn)
%            Number of atoms       :  479 (  38 equality; 181 variable)
%            Maximal formula depth :   15 (   6 average)
%            Number of connectives :  334 (   4   ~;   4   |;   9   &; 307   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  203 ( 203   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   49 (  45   :;   0   =)
%            Number of variables   :  109 (   3 sgn;  34   !;   6   ?;  69   ^)
%                                         ( 109   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Bugfixes : v5.4.0 - Added missing axioms for symmetry of B
%------------------------------------------------------------------------------
%----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(axioms_B_a1,axiom,
( msymmetric @ a1 )).

thf(axioms_B_a2,axiom,
( msymmetric @ a2 )).

thf(axioms_B_a3,axiom,
( msymmetric @ a3 )).

thf(axioms_D_a1,axiom,
( mserial @ a1 )).

thf(axioms_D_a2,axiom,
( mserial @ a2 )).

thf(axioms_D_a3,axiom,
( mserial @ a3 )).

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

thf(subrel_def,definition,
( subrel
= ( ^ [R1: \$i > \$i > \$o,R2: \$i > \$i > \$o] :
! [X: \$i,Y: \$i] :
( ( R1 @ X @ Y )
=> ( R2 @ X @ Y ) ) ) )).

thf(axiom_I_a1_a2,axiom,
( subrel @ a1 @ a2 )).

thf(axiom_I_a1_a3,axiom,
( subrel @ a1 @ a3 )).

thf(axiom_I_a2_a3,axiom,
( subrel @ a2 @ a3 )).

thf(cond4s,type,(
cond4s: ( \$i > \$i > \$o ) > ( \$i > \$i > \$o ) > \$o )).

thf(cond4s_def,definition,
( cond4s
= ( ^ [R1: \$i > \$i > \$o,R2: \$i > \$i > \$o] :
! [U: \$i,V: \$i,W: \$i] :
( ( ( R1 @ U @ V )
& ( R2 @ V @ W ) )
=> ( R2 @ U @ W ) ) ) )).

thf(axioms_Is_a1_a1,axiom,
( cond4s @ a1 @ a1 )).

thf(axioms_Is_a1_a2,axiom,
( cond4s @ a1 @ a2 )).

thf(axioms_Is_a1_a3,axiom,
( cond4s @ a1 @ a3 )).

thf(axioms_Is_a2_a1,axiom,
( cond4s @ a2 @ a1 )).

thf(axioms_Is_a2_a2,axiom,
( cond4s @ a2 @ a2 )).

thf(axioms_Is_a2_a3,axiom,
( cond4s @ a2 @ a3 )).

thf(axioms_Is_a3_a1,axiom,
( cond4s @ a1 @ a1 )).

thf(axioms_Is_a3_a2,axiom,
( cond4s @ a2 @ a2 )).

thf(axioms_Is_a3_a3,axiom,
( cond4s @ a3 @ a3 )).

thf(axioms_5_a1,axiom,
( meuclidean @ a1 )).

thf(axioms_5_a2,axiom,
( meuclidean @ a2 )).

thf(axioms_5_a3,axiom,
( meuclidean @ a3 )).

thf(conj,conjecture,
( mvalid @ ( possibly_likes @ piotr @ cola ) )).

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