TPTP Problem File: SYO460^3.p
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% File : SYO460^3 : TPTP v9.0.0. Released v4.0.0.
% Domain : Syntactic
% Problem : Ted Sider's propositional modal logic wff 11
% Version : Especial.
% : Theorem formulation : Uses system M axioms.
% English :
% Refs : [Sid09] Sider (2009), Logic for Philosophy
% Source : [Sid09]
% Names :
% 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, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.0
% Syntax : Number of formulae : 73 ( 33 unt; 38 typ; 33 def)
% Number of atoms : 115 ( 38 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 144 ( 5 ~; 5 |; 8 &; 118 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 181 ( 181 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 6 con; 0-3 aty)
% Number of variables : 88 ( 52 ^; 30 !; 6 ?; 88 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
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%----Include axioms for Modal logic M
include('Axioms/LCL013^0.ax').
include('Axioms/LCL013^3.ax').
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thf(p_type,type,
p: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(r_type,type,
r: $i > $o ).
thf(prove,conjecture,
mvalid @ ( mimplies @ ( mor @ ( mdia_m @ ( mand @ p @ q ) ) @ ( mdia_m @ ( mand @ p @ r ) ) ) @ ( mdia_m @ p ) ) ).
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