TPTP Problem File: AGT041^1.p
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% File : AGT041^1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Domain : Agents
% Problem : Piotr possibly likes beer
% Version : [Ben11] axioms.
% English :
% Refs : [Ben11] Benzmueller (2011), Email to Geoff Sutcliffe
% : [Ben11] Benzmueller (2011), Combining and Automating Classical
% Source : [Ben11]
% Names : Ex_12_11 [Ben11]
% Status : Theorem
% Rating : 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 .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 ( 33 unt; 45 typ; 33 def)
% Number of atoms : 272 ( 38 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 334 ( 4 ~; 4 |; 9 &; 307 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 203 ( 203 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 53 usr; 15 con; 0-3 aty)
% Number of variables : 109 ( 69 ^; 34 !; 6 ?; 109 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
% Bugfixes : v5.4.0 - Added missing axioms for symmetry of B
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%----Include embedding of quantified multimodal logic in simple type theory
include('Axioms/LCL013^0.ax').
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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 @ beer ) ).
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