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%------------------------------------------------------------------------------
% File : DAT001=1 : TPTP v5.5.0. Released v5.0.0.
% Domain : Data Structures
% Problem : Recursive list sort
% Version : Especial.
% English :
% Refs :
% Source : [TPTP]
% Names :
% Status : Theorem
% Rating : 0.12 v5.5.0, 0.25 v5.4.0, 0.38 v5.3.0, 0.29 v5.2.0, 0.20 v5.1.0, 0.25 v5.0.0
% Syntax : Number of formulae : 8 ( 5 unit; 4 type)
% Number of atoms : 13 ( 0 equality)
% Maximal formula depth : 6 ( 3 average)
% Number of connectives : 2 ( 0 ~; 0 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% ( 0 ~|; 0 ~&)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 propositional; 0-2 arity)
% Number of functors : 7 ( 6 constant; 0-2 arity)
% Number of variables : 4 ( 0 sgn; 4 !; 0 ?)
% Maximal term depth : 6 ( 2 average)
% Arithmetic symbols : 7 ( 2 pred; 0 func; 5 numbers)
% SPC : TFF_THM_NEQ_ARI
% Comments :
%------------------------------------------------------------------------------
tff(list_type,type,(
list: $tType )).
tff(nil_type,type,(
nil: list )).
tff(mycons_type,type,(
mycons: ( $int * list ) > list )).
tff(sorted_type,type,(
sorted: list > $o )).
tff(empty_is_sorted,axiom,(
sorted(nil) )).
tff(single_is_sorted,axiom,(
! [X: $int] : sorted(mycons(X,nil)) )).
tff(recursive_sort,axiom,(
! [X: $int,Y: $int,R: list] :
( ( $less(X,Y)
& sorted(mycons(Y,R)) )
=> sorted(mycons(X,mycons(Y,R))) ) )).
tff(check_list,conjecture,(
sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil)))))) )).
%------------------------------------------------------------------------------
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