TPTP Problem File: PLA055_1.010.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : PLA055_1.010 : TPTP v9.1.0. Released v9.0.0.
% Domain : Planning
% Problem : Path from the entry to the exit of a labyrinth 10
% Version : Especial.
% English : The formula is the path from the entry to the exit of a
% labyrinth. It makes no difference whether one starts at the
% entry or at the exit.
% 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_path_p.0010 [Nal22]
% Status : Theorem
% Rating : 0.50 v9.0.0
% Syntax : Number of formulae : 8 ( 0 unt; 7 typ; 0 def)
% Number of atoms : 351 ( 0 equ)
% Maximal formula atoms : 351 ( 351 avg)
% Number of connectives : 1387 ( 147 ~; 209 |; 141 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% ( 890 {.}; 0 {#})
% Maximal formula depth : 223 ( 223 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 : 7 ( 7 usr; 7 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 :
%------------------------------------------------------------------------------
tff('k_path_p.0010',logic,
$modal ==
[ $modalities == $modal_system_K ] ).
tff(false_decl,type,
false: $o ).
tff(p1_decl,type,
p1: $o ).
tff(p2_decl,type,
p2: $o ).
tff(p3_decl,type,
p3: $o ).
tff(p4_decl,type,
p4: $o ).
tff(p5_decl,type,
p5: $o ).
tff(p6_decl,type,
p6: $o ).
tff(prove,conjecture,
~ ~ ( [.] p1
| [.] p2
| [.] p3
| [.] p5
| <.> ( ~ p1
& [.] p3 )
| <.> ( ~ p1
& [.] p5 )
| false
| <.> ( ~ p2
& [.] p1 )
| false
| <.> ( ~ p3
& [.] p3 )
| <.> ( ~ p3
& [.] p5 )
| false
| false
| false
| <.> ( ~ p5
& [.] p3 )
| <.> ( ~ p5
& [.] p5 )
| false
| false
| false
| <.> <.> ( ~ p1
& [.] p1 )
| <.> <.> ( ~ p1
& [.] p3 )
| <.> <.> ( ~ p1
& [.] p6 )
| <.> <.> ( ~ p1
& [.] p5 )
| false
| false
| <.> ( ~ p4
& [.] p2 )
| <.> ( ~ p6
& [.] p2 )
| <.> <.> ( ~ p3
& [.] p1 )
| <.> <.> ( ~ p3
& [.] p3 )
| <.> <.> ( ~ p3
& [.] p5 )
| false
| false
| <.> ( ~ p4
& [.] p4 )
| <.> ( ~ p6
& [.] p4 )
| <.> <.> ( ~ p5
& [.] p1 )
| <.> <.> ( ~ p5
& [.] p3 )
| <.> <.> ( ~ p5
& [.] p5 )
| false
| false
| <.> ( ~ p4
& [.] p6 )
| <.> ( ~ p6
& [.] p6 )
| <.> <.> <.> ( ~ p1
& [.] p1 )
| <.> <.> <.> ( ~ p1
& [.] p3 )
| false
| false
| <.> <.> ( ~ p2
& [.] p2 )
| <.> <.> ( ~ p4
& [.] p2 )
| <.> <.> ( ~ p6
& [.] p2 )
| <.> <.> <.> ( ~ p3
& [.] p1 )
| <.> <.> <.> ( ~ p3
& [.] p3 )
| false
| false
| <.> <.> ( ~ p2
& [.] p4 )
| <.> <.> ( ~ p4
& [.] p4 )
| <.> <.> ( ~ p6
& [.] p4 )
| <.> <.> <.> ( ~ p5
& [.] p1 )
| <.> <.> <.> ( ~ p5
& [.] p3 )
| false
| <.> <.> <.> ( ~ p6
& [.] p5 )
| <.> <.> ( ~ p2
& [.] p6 )
| <.> <.> ( ~ p4
& [.] p6 )
| <.> <.> ( ~ p6
& [.] p6 )
| <.> <.> <.> <.> ( ~ p1
& [.] p1 )
| <.> <.> <.> <.> ( ~ p1
& [.] p3 )
| <.> <.> <.> <.> ( ~ p1
& [.] p5 )
| false
| false
| <.> <.> <.> ( ~ p2
& [.] p2 )
| <.> <.> <.> ( ~ p4
& [.] p2 )
| <.> <.> <.> <.> ( ~ p3
& [.] p1 )
| <.> <.> <.> <.> ( ~ p3
& [.] p3 )
| <.> <.> <.> <.> ( ~ p3
& [.] p5 )
| false
| false
| <.> <.> <.> ( ~ p2
& [.] p4 )
| <.> <.> <.> ( ~ p4
& [.] p4 )
| <.> <.> <.> <.> ( ~ p5
& [.] p1 )
| <.> <.> <.> <.> ( ~ p5
& [.] p3 )
| <.> <.> <.> <.> ( ~ p5
& [.] p4 )
| <.> <.> <.> <.> ( ~ p5
& [.] p5 )
| false
| false
| <.> <.> <.> ( ~ p2
& [.] p6 )
| <.> <.> <.> ( ~ p4
& [.] p6 )
| <.> <.> <.> <.> <.> ( ~ p1
& [.] p3 )
| <.> <.> <.> <.> <.> ( ~ p1
& [.] p5 )
| false
| false
| <.> <.> <.> <.> ( ~ p2
& [.] p2 )
| <.> <.> <.> <.> ( ~ p4
& [.] p2 )
| <.> <.> <.> <.> ( ~ p6
& [.] p2 )
| <.> <.> <.> <.> <.> ( ~ p3
& [.] p3 )
| <.> <.> <.> <.> <.> ( ~ p3
& [.] p5 )
| false
| <.> <.> <.> <.> <.> ( ~ p4
& [.] p1 )
| <.> <.> <.> <.> ( ~ p2
& [.] p4 )
| <.> <.> <.> <.> ( ~ p4
& [.] p4 )
| <.> <.> <.> <.> ( ~ p6
& [.] p4 )
| <.> <.> <.> <.> <.> ( ~ p5
& [.] p3 )
| <.> <.> <.> <.> <.> ( ~ p5
& [.] p5 )
| false
| false
| <.> <.> <.> <.> ( ~ p2
& [.] p6 )
| <.> <.> <.> <.> ( ~ p4
& [.] p6 )
| <.> <.> <.> <.> ( ~ p6
& [.] p6 )
| <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p1 )
| <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p3 )
| <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p4 )
| <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p5 )
| false
| false
| <.> <.> <.> <.> <.> ( ~ p2
& [.] p2 )
| <.> <.> <.> <.> <.> ( ~ p6
& [.] p2 )
| <.> <.> <.> <.> <.> <.> ( ~ p3
& [.] p1 )
| <.> <.> <.> <.> <.> <.> ( ~ p3
& [.] p3 )
| <.> <.> <.> <.> <.> <.> ( ~ p3
& [.] p5 )
| false
| false
| <.> <.> <.> <.> <.> ( ~ p2
& [.] p4 )
| <.> <.> <.> <.> <.> ( ~ p6
& [.] p4 )
| <.> <.> <.> <.> <.> <.> ( ~ p5
& [.] p1 )
| <.> <.> <.> <.> <.> <.> ( ~ p5
& [.] p3 )
| <.> <.> <.> <.> <.> <.> ( ~ p5
& [.] p5 )
| false
| false
| <.> <.> <.> <.> <.> ( ~ p2
& [.] p6 )
| <.> <.> <.> <.> <.> ( ~ p6
& [.] p6 )
| <.> <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p3 )
| <.> <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p5 )
| false
| false
| <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p2 )
| <.> <.> <.> <.> <.> <.> ( ~ p4
& [.] p2 )
| <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p2 )
| <.> <.> <.> <.> <.> <.> <.> ( ~ p3
& [.] p3 )
| <.> <.> <.> <.> <.> <.> <.> ( ~ p3
& [.] p5 )
| false
| <.> <.> <.> <.> <.> <.> <.> ( ~ p4
& [.] p1 )
| <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p4 )
| <.> <.> <.> <.> <.> <.> ( ~ p4
& [.] p4 )
| <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p4 )
| <.> <.> <.> <.> <.> <.> <.> ( ~ p5
& [.] p3 )
| <.> <.> <.> <.> <.> <.> <.> ( ~ p5
& [.] p5 )
| false
| false
| <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p6 )
| <.> <.> <.> <.> <.> <.> ( ~ p4
& [.] p6 )
| <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p6 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p1 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p3 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p4 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p5 )
| false
| false
| <.> <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p2 )
| <.> <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p2 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p3
& [.] p1 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p3
& [.] p3 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p3
& [.] p5 )
| false
| false
| <.> <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p4 )
| <.> <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p4 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p5
& [.] p1 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p5
& [.] p3 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p5
& [.] p5 )
| false
| false
| <.> <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p6 )
| <.> <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p6 )
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p3 )
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p1
& [.] p5 )
| false
| false
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p2 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p4
& [.] p2 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p2 )
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p3
& [.] p3 )
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p3
& [.] p5 )
| false
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p4
& [.] p1 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p4 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p4
& [.] p4 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p4 )
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p5
& [.] p3 )
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p5
& [.] p5 )
| false
| false
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p6 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p4
& [.] p6 )
| <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p6 )
| false
| false
| false
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p2 )
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p2 )
| false
| false
| false
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p4 )
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p4 )
| false
| false
| false
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p2
& [.] p6 )
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p6
& [.] p6 )
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ~ p2
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ~ p4
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ~ p1
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ~ p6 ) ).
%------------------------------------------------------------------------------