%------------------------------------------------------------------------------
% File : SYO923_1.010 : TPTP v9.0.0. Released v9.0.0.
% Domain : Syntactic
% Problem : KSP problem k45_t4p_p.0010
% Version : Especial.
% English :
% Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
% : [NH+22] Nalon et al. (2022), Local Reductions for the Modal Cu
% : [Nal22] Nalon (2022), Email to Geoff Sutcliffe
% : [NH+23] Nalon et al. (2023), Buy One Get 14 Free: Evaluating L
% Source : [Nal22]
% Names : k45_t4p_p.0010 [Nal22]
% Status : Theorem
% Rating : 1.00 v9.0.0
% Syntax : Number of formulae : 13 ( 0 unt; 12 typ; 0 def)
% Number of atoms : 485 ( 0 equ)
% Maximal formula atoms : 485 ( 485 avg)
% Number of connectives : 1445 ( 247 ~; 229 |; 255 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% ( 714 {.}; 0 {#})
% Maximal formula depth : 53 ( 53 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 12 usr; 12 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 (; 0 !; 0 ?; 0 :)
% SPC : NX0_THM_PRP_NEQ_NAR
% Comments : Uses instances of T and 4 to produce the formula.
%------------------------------------------------------------------------------
tff('k45_t4p_p.0010',logic,
$modal ==
[ $modalities == $modal_system_K45 ] ).
tff(p0_decl,type,
p0: $o ).
tff(p1_decl,type,
p1: $o ).
tff(p3_decl,type,
p3: $o ).
tff(p4_decl,type,
p4: $o ).
tff(y0_decl,type,
y0: $o ).
tff(y1_decl,type,
y1: $o ).
tff(y3_decl,type,
y3: $o ).
tff(y4_decl,type,
y4: $o ).
tff(z0_decl,type,
z0: $o ).
tff(z1_decl,type,
z1: $o ).
tff(z3_decl,type,
z3: $o ).
tff(z4_decl,type,
z4: $o ).
tff(prove,conjecture,
~ ( [.] ( <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& <.> ( [.] ( <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& <.> ( [.] ( <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& <.> ( [.] ( <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& <.> ( [.] ( <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& <.> ( [.] ( <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& <.> ( [.] ( <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& <.> ( [.] ( <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& <.> ( [.] ( <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& <.> ( [.] ( <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& <.> [.] <.> ( ~ p0
| ( [.] z0
& <.> [.] y0
& <.> <.> ( ~ z0
| ~ y0 ) ) )
& <.> ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& <.> [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& <.> ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& <.> [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& <.> ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& <.> [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& <.> ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& <.> [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& <.> ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& <.> [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& <.> ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& <.> [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& <.> ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& <.> [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& <.> ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& <.> [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& <.> ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& <.> [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& <.> ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& <.> [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( [.] ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( [.] ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( [.] ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( [.] ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( [.] ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( [.] ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( [.] ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( [.] ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( [.] ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( ( <.> [.] ( ~ p0
| ( [.] z0
& <.> [.] y0
& <.> <.> ( ~ z0
| ~ y0 ) ) )
| <.> ( ( p0
| ( [.] z0
& <.> [.] y0
& <.> <.> ( ~ z0
| ~ y0 ) ) )
& <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) ) )
& [.] ( <.> [.] <.> ( ( p0
| ( [.] z0
& <.> [.] y0
& <.> <.> ( ~ z0
| ~ y0 ) ) )
& <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
| <.> [.] ( ~ p0
| ( [.] z0
& <.> [.] y0
& <.> <.> ( ~ z0
| ~ y0 ) ) ) )
& ( <.> [.] ( ~ p0
| ( [.] z0
& <.> [.] y0
& <.> <.> ( ~ z0
| ~ y0 ) ) )
| [.] [.] <.> ( ( p0
| ( [.] z0
& <.> [.] y0
& <.> <.> ( ~ z0
| ~ y0 ) ) )
& <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) ) )
& [.] ( [.] <.> [.] ( ~ p0
| ( [.] z0
& <.> [.] y0
& <.> <.> ( ~ z0
| ~ y0 ) ) )
| ~ p0
| ( [.] z0
& <.> [.] y0
& <.> <.> ( ~ z0
| ~ y0 ) )
| [.] ( ( p0
| ( [.] z0
& <.> [.] y0
& <.> <.> ( ~ z0
| ~ y0 ) ) )
& <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) ) )
& [.] <.> ( ( p0
| ( [.] z0
& <.> [.] y0
& <.> <.> ( ~ z0
| ~ y0 ) ) )
& <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) ) )
& [.] ( <.> [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& [.] ( <.> [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& [.] ( <.> [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& [.] ( <.> [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& [.] ( <.> [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& [.] ( <.> [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& [.] ( <.> [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& [.] ( <.> [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& [.] ( <.> [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& [.] ( <.> [.] ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
| [.] [.] <.> ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) ) ).
%------------------------------------------------------------------------------