TPTP Problem File: SYO573^7.p
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% File : SYO573^7 : TPTP v8.2.0. Released v5.5.0.
% Domain : Syntactic
% Problem : Quantified modal logics wwfs. problem 15.
% Version : [Ben12] axioms.
% English :
% Refs : [Sid09] Sider (2009), Logic for Philosophy
% : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source : [Ben12]
% Names : s4-cumul-SYM076+1 [Ben12]
% Status : CounterSatisfiable
% Rating : 0.25 v8.2.0, 0.50 v8.1.0, 0.60 v7.5.0, 0.40 v7.4.0, 0.50 v7.2.0, 0.33 v6.2.0, 0.00 v6.0.0, 0.33 v5.5.0
% Syntax : Number of formulae : 77 ( 34 unt; 39 typ; 32 def)
% Number of atoms : 118 ( 36 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 162 ( 5 ~; 5 |; 9 &; 133 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 184 ( 184 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 7 con; 0-3 aty)
% Number of variables : 91 ( 49 ^; 35 !; 7 ?; 91 :)
% SPC : TH0_CSA_EQU_NAR
% Comments :
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%----Include axioms for Modal logic S4 under cumulative domains
include('Axioms/LCL015^0.ax').
include('Axioms/LCL013^5.ax').
include('Axioms/LCL015^1.ax').
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thf(g_type,type,
g: mu > $i > $o ).
thf(f_type,type,
f: mu > $i > $o ).
thf(a_type,type,
a: mu ).
thf(existence_of_a_ax,axiom,
! [V: $i] : ( exists_in_world @ a @ V ) ).
thf(con,conjecture,
mvalid @ ( mimplies @ ( mand @ ( mdia_s4 @ ( f @ a ) ) @ ( mdia_s4 @ ( g @ a ) ) ) @ ( mdia_s4 @ ( mand @ ( f @ a ) @ ( g @ a ) ) ) ) ).
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