TPTP Problem File: PUZ085^1.p
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% File : PUZ085^1 : TPTP v9.0.0. Released v4.0.0.
% Domain : Logic Calculi (Espistemic logic)
% Problem : The friends puzzle - transitivity for Peter's wife
% Version : [Ben09] axioms.
% English : (i) Peter is a friend of John, so if Peter knows that John knows
% something then John knows that Peter knows the same thing.
% (ii) Peter is married, so if Peter's wife knows something, then
% Peter knows the same thing. John and Peter have an appointment,
% let us consider the following situation: (a) Peter knows the time
% of their appointment. (b) Peter also knows that John knows the
% place of their appointment. Moreover, (c) Peter's wife knows that
% if Peter knows the time of their appointment, then John knows
% that too (since John and Peter are friends). Finally, (d) Peter
% knows that if John knows the place and the time of their
% appointment, then John knows that he has an appointment. From
% this situation we want to prove (e) that each of the two friends
% knows that the other one knows that he has an appointment.
% Refs : [Gol92] Goldblatt (1992), Logics of Time and Computation
% : [Bal98] Baldoni (1998), Normal Multimodal Logics: Automatic De
% : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% Source : [Ben09]
% Names : mmex2.p [Ben09]
% Status : Theorem
% Rating : 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.33 v4.0.0
% Syntax : Number of formulae : 73 ( 31 unt; 35 typ; 31 def)
% Number of atoms : 118 ( 36 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 144 ( 4 ~; 4 |; 8 &; 120 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 178 ( 178 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 7 con; 0-3 aty)
% Number of variables : 85 ( 50 ^; 29 !; 6 ?; 85 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
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%----Include embedding of quantified multimodal logic in simple type theory
include('Axioms/LCL013^0.ax').
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thf(peter,type,
peter: $i > $i > $o ).
thf(john,type,
john: $i > $i > $o ).
thf(wife,type,
wife: ( $i > $i > $o ) > $i > $i > $o ).
thf(refl_peter,axiom,
mreflexive @ peter ).
thf(refl_john,axiom,
mreflexive @ john ).
thf(refl_wife_peter,axiom,
mreflexive @ ( wife @ peter ) ).
thf(trans_peter,axiom,
mtransitive @ peter ).
thf(trans_john,axiom,
mtransitive @ john ).
thf(trans_wife_peter,axiom,
mtransitive @ ( wife @ peter ) ).
thf(conj,conjecture,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ A ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ A ) ) ) ) ) ).
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