%------------------------------------------------------------------------------
% File : SYO920_1.014 : TPTP v9.0.0. Released v9.0.0.
% Domain : Syntactic
% Problem : KSP problem k_t4p_p.0014
% 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 : k_t4p_p.0014 [Nal22]
% Status : Theorem
% Rating : 0.50 v9.0.0
% Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 129 ( 129 avg)
% Number of connectives : 542 ( 105 ~; 67 |; 33 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% ( 309 {.}; 0 {#})
% Maximal formula depth : 58 ( 58 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 : 4 ( 4 usr; 4 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('k_t4p_p.0014',logic,
$modal ==
[ $modalities == $modal_system_K ] ).
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(prove,conjecture,
~ ~ ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] ( <.> ~ ( [.] ~ p1
=> [.] [.] ~ p1 )
| [.] <.> [.] p0
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 ) )
| [.] ( ~ [.] p1
=> [.] ~ [.] p1 )
| <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( <.> ( [.] p1
& <.> <.> ~ p1 )
| <.> ( ( [.] <.> p0
& [.] ( ~ p0
| [.] p3 ) )
| <.> ( [.] <.> [.] ( ~ p0
| [.] p3 )
& [.] <.> p0 )
| ( [.] <.> p0
& <.> <.> [.] ( ~ p0
| [.] p3 ) )
| <.> ( <.> [.] <.> p0
& p0
& <.> ( ~ p0
| [.] p3 ) )
| <.> [.] ( ~ p0
| [.] p3 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 ) )
| <.> ( [.] <.> p1
& <.> <.> [.] ~ p1 )
| <.> p4 ) ).
%------------------------------------------------------------------------------