%------------------------------------------------------------------------------
% File : SYP017_1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Syntactic
% Problem : Logic K, problem k_lin, size 10
% Version : Especial.
% English :
% Refs : [BHS98] Balsiger et al. (1998), Logics Workbench 1.0
% : [Ste24] Steen (2024), Email to Geoff Sutcliffe
% Source : [Ste24]
% Names : K/k_lin_p/10.p
% Status : Theorem
% Rating : 0.00 v9.3.0
% Syntax : Number of formulae : 12 ( 0 unt; 11 typ; 0 def)
% Number of atoms : 286 ( 0 equ)
% Maximal formula atoms : 286 ( 286 avg)
% Number of connectives : 529 ( 90 ~; 51 |; 142 &)
% ( 0 <=>; 92 =>; 0 <=; 0 <~>)
% ( 154 {.}; 0 {#})
% Maximal formula depth : 23 ( 23 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 : 11 ( 11 usr; 11 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_NDT
% Comments :
%------------------------------------------------------------------------------
tff(simple_k,logic,
$modal ==
[ $domains == $constant,
$designation == $rigid,
$terms == $local,
$modalities == $modal_system_K ] ).
tff(p10_type,type,
p10: $o ).
tff(p3_type,type,
p3: $o ).
tff(p11_type,type,
p11: $o ).
tff(p2_type,type,
p2: $o ).
tff(p9_type,type,
p9: $o ).
tff(p1_type,type,
p1: $o ).
tff(p4_type,type,
p4: $o ).
tff(p7_type,type,
p7: $o ).
tff(p5_type,type,
p5: $o ).
tff(p6_type,type,
p6: $o ).
tff(p8_type,type,
p8: $o ).
tff(10,conjecture,
( ~ ( ( [.] ( ( ( p1
& [.] p1
& p1 )
=> p2 )
| ( ~ p1
=> ~ ( [.] p2
& p2 ) ) )
& [.] ( [.] ( ( p1
& [.] p1
& p1 )
=> p2 )
| ( ~ p1
=> ~ ( [.] p2
& p2 ) ) )
& [.] ( ( ( p1
& [.] p1
& p1 )
=> p2 )
| [.] ( ~ p1
=> ~ ( [.] p2
& p2 ) ) ) )
=> ( [.] ( ( p1
& [.] p1
& p1 )
=> p2 )
| [.] ( ~ p1
=> ~ ( [.] p2
& p2 ) ) ) )
| ~ ( ( [.] ( ( ( p2
& [.] p2
& p2 )
=> p3 )
| ( ~ p2
=> ~ ( [.] p3
& p3 ) ) )
& [.] ( [.] ( ( p2
& [.] p2
& p2 )
=> p3 )
| ( ~ p2
=> ~ ( [.] p3
& p3 ) ) )
& [.] ( ( ( p2
& [.] p2
& p2 )
=> p3 )
| [.] ( ~ p2
=> ~ ( [.] p3
& p3 ) ) ) )
=> ( [.] ( ( p2
& [.] p2
& p2 )
=> p3 )
| [.] ( ~ p2
=> ~ ( [.] p3
& p3 ) ) ) )
| ~ ( ( [.] ( ( ( p3
& [.] p3
& p3 )
=> p4 )
| ( ~ p3
=> ~ ( [.] p4
& p4 ) ) )
& [.] ( [.] ( ( p3
& [.] p3
& p3 )
=> p4 )
| ( ~ p3
=> ~ ( [.] p4
& p4 ) ) )
& [.] ( ( ( p3
& [.] p3
& p3 )
=> p4 )
| [.] ( ~ p3
=> ~ ( [.] p4
& p4 ) ) ) )
=> ( [.] ( ( p3
& [.] p3
& p3 )
=> p4 )
| [.] ( ~ p3
=> ~ ( [.] p4
& p4 ) ) ) )
| [.] ( ( p10
& [.] p10 )
=> p10 )
| [.] ( ( p10
& [.] p10 )
=> p10 )
| ~ ( ( [.] ( ( ( p4
& [.] p4
& p4 )
=> p5 )
| ( ~ p4
=> ~ ( [.] p5
& p5 ) ) )
& [.] ( [.] ( ( p4
& [.] p4
& p4 )
=> p5 )
| ( ~ p4
=> ~ ( [.] p5
& p5 ) ) )
& [.] ( ( ( p4
& [.] p4
& p4 )
=> p5 )
| [.] ( ~ p4
=> ~ ( [.] p5
& p5 ) ) ) )
=> ( [.] ( ( p4
& [.] p4
& p4 )
=> p5 )
| [.] ( ~ p4
=> ~ ( [.] p5
& p5 ) ) ) )
| ~ ( ( [.] ( ( ( p5
& [.] p5
& p5 )
=> p6 )
| ( ~ p5
=> ~ ( [.] p6
& p6 ) ) )
& [.] ( [.] ( ( p5
& [.] p5
& p5 )
=> p6 )
| ( ~ p5
=> ~ ( [.] p6
& p6 ) ) )
& [.] ( ( ( p5
& [.] p5
& p5 )
=> p6 )
| [.] ( ~ p5
=> ~ ( [.] p6
& p6 ) ) ) )
=> ( [.] ( ( p5
& [.] p5
& p5 )
=> p6 )
| [.] ( ~ p5
=> ~ ( [.] p6
& p6 ) ) ) )
| ~ ( ( [.] ( ( ( p6
& [.] p6
& p6 )
=> p7 )
| ( ~ p6
=> ~ ( [.] p7
& p7 ) ) )
& [.] ( [.] ( ( p6
& [.] p6
& p6 )
=> p7 )
| ( ~ p6
=> ~ ( [.] p7
& p7 ) ) )
& [.] ( ( ( p6
& [.] p6
& p6 )
=> p7 )
| [.] ( ~ p6
=> ~ ( [.] p7
& p7 ) ) ) )
=> ( [.] ( ( p6
& [.] p6
& p6 )
=> p7 )
| [.] ( ~ p6
=> ~ ( [.] p7
& p7 ) ) ) )
| ~ ( ( [.] ( ( ( p7
& [.] p7
& p7 )
=> p8 )
| ( ~ p7
=> ~ ( [.] p8
& p8 ) ) )
& [.] ( [.] ( ( p7
& [.] p7
& p7 )
=> p8 )
| ( ~ p7
=> ~ ( [.] p8
& p8 ) ) )
& [.] ( ( ( p7
& [.] p7
& p7 )
=> p8 )
| [.] ( ~ p7
=> ~ ( [.] p8
& p8 ) ) ) )
=> ( [.] ( ( p7
& [.] p7
& p7 )
=> p8 )
| [.] ( ~ p7
=> ~ ( [.] p8
& p8 ) ) ) )
| ~ ( ( [.] ( ( ( p8
& [.] p8
& p8 )
=> p9 )
| ( ~ p8
=> ~ ( [.] p9
& p9 ) ) )
& [.] ( [.] ( ( p8
& [.] p8
& p8 )
=> p9 )
| ( ~ p8
=> ~ ( [.] p9
& p9 ) ) )
& [.] ( ( ( p8
& [.] p8
& p8 )
=> p9 )
| [.] ( ~ p8
=> ~ ( [.] p9
& p9 ) ) ) )
=> ( [.] ( ( p8
& [.] p8
& p8 )
=> p9 )
| [.] ( ~ p8
=> ~ ( [.] p9
& p9 ) ) ) )
| ~ ( ( [.] ( ( ( p9
& [.] p9
& p9 )
=> p10 )
| ( ~ p9
=> ~ ( [.] p10
& p10 ) ) )
& [.] ( [.] ( ( p9
& [.] p9
& p9 )
=> p10 )
| ( ~ p9
=> ~ ( [.] p10
& p10 ) ) )
& [.] ( ( ( p9
& [.] p9
& p9 )
=> p10 )
| [.] ( ~ p9
=> ~ ( [.] p10
& p10 ) ) ) )
=> ( [.] ( ( p9
& [.] p9
& p9 )
=> p10 )
| [.] ( ~ p9
=> ~ ( [.] p10
& p10 ) ) ) )
| ~ ( ( [.] ( ( ( p10
& [.] p10
& p10 )
=> p11 )
| ( ~ p10
=> ~ ( [.] p11
& p11 ) ) )
& [.] ( [.] ( ( p10
& [.] p10
& p10 )
=> p11 )
| ( ~ p10
=> ~ ( [.] p11
& p11 ) ) )
& [.] ( ( ( p10
& [.] p10
& p10 )
=> p11 )
| [.] ( ~ p10
=> ~ ( [.] p11
& p11 ) ) ) )
=> ( [.] ( ( p10
& [.] p10
& p10 )
=> p11 )
| [.] ( ~ p10
=> ~ ( [.] p11
& p11 ) ) ) ) ) ).
%------------------------------------------------------------------------------