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%------------------------------------------------------------------------------
% File : SYN000_1 : TPTP v5.5.0. Released v5.0.0.
% Domain : Syntactic
% Problem : Basic TPTP TFF syntax without arithmetic
% Version : Biased.
% English : Basic TPTP TFF syntax that you can't survive without parsing.
% Refs :
% Source : [TPTP]
% Names :
% Status : Theorem
% Rating : 0.40 v5.5.0, 0.25 v5.4.0, 0.33 v5.2.0, 0.67 v5.0.0
% Syntax : Number of formulae : 38 ( 21 unit; 25 type)
% Number of atoms : 74 ( 3 equality)
% Maximal formula depth : 7 ( 3 average)
% Number of connectives : 28 ( 9 ~; 10 |; 3 &)
% ( 1 <=>; 3 =>; 1 <=; 1 <~>)
% ( 0 ~|; 0 ~&)
% Number of type conns : 17 ( 10 >; 7 *; 0 +; 0 <<)
% Number of predicates : 37 ( 30 propositional; 0-3 arity)
% Number of functors : 10 ( 6 constant; 0-3 arity)
% Number of variables : 14 ( 1 sgn; 6 !; 8 ?)
% Maximal term depth : 4 ( 2 average)
% SPC : TFF_THM_EQU_NAR
% Comments :
%------------------------------------------------------------------------------
%----Propositional
tff(p0_type,type,(
p0: $o )).
tff(q0_type,type,(
q0: $o )).
tff(r0_type,type,(
r0: $o )).
tff(s0_type,type,(
s0: $o )).
tff(propositional,axiom,
( ( p0
& ~ q0 )
=> ( r0
| ~ s0 ) )).
%----First-order
tff(a_type,type,(
a: $i )).
tff(b_type,type,(
b: $i )).
tff(h_type,type,(
h: $i )).
tff(f_type,type,(
f: $i > $i )).
tff(g_type,type,(
g: ( $i * $i * $i ) > $i )).
tff(p_type,type,(
p: $i > $o )).
tff(q_type,type,(
q: ( $i * $i ) > $o )).
tff(r_type,type,(
r: ( $i * $i * $i ) > $o )).
tff(s_type,type,(
s: $i > $o )).
tff(first_order,axiom,(
! [X: $i] :
( ( p(X)
| ~ q(X,a) )
=> ? [Y: $i,Z: $i] :
( r(X,f(Y),g(X,f(Y),Z))
& ~ s(f(f(f(b)))) ) ) )).
%----Equality
tff(equality,axiom,(
? [Y: $i] :
! [X: $i,Z: $i] :
( f(Y) = g(X,f(Y),Z)
| f(f(f(b))) != a
| X = f(Y) ) )).
%----True and false
tff(true_false,axiom,
( $true
| $false )).
tff(quoted_proposition_type,type,(
'A proposition': $o )).
tff(quoted_predicate_type,type,(
'A predicate': $i > $o )).
tff(quoted_constant_type,type,(
'A constant': $i )).
tff(quoted_function_type,type,(
'A function': $i > $i )).
tff(quoted_escape_type,type,(
'A \'quoted \\ escape\'': $i )).
%----Quoted symbols
tff(single_quoted,axiom,
( 'A proposition'
| 'A predicate'(a)
| p('A constant')
| p('A function'(a))
| p('A \'quoted \\ escape\'') )).
%----Connectives - seen |, &, =>, ~ already
tff(useful_connectives,axiom,(
! [X: $i] :
( ( p(X)
<= ~ q(X,a) )
<=> ? [Y: $i,Z: $i] :
( r(X,f(Y),g(X,f(Y),Z))
<~> ~ s(f(f(f(b)))) ) ) )).
%----New types
tff(new_type,type,(
new: $tType )).
tff(newc_type,type,(
newc: new )).
tff(newf_type,type,(
newf: ( new * $i ) > new )).
tff(newp_type,type,(
newp: ( new * $i ) > $o )).
tff(new_axiom,axiom,(
! [X: new] : newp(newf(newc,a),a) )).
%----Annotated formula names
tff(123,axiom,(
! [X: $i] :
( ( p(X)
| ~ q(X,a) )
=> ? [Y: $i,Z: $i] :
( r(X,f(Y),g(X,f(Y),Z))
& ~ s(f(f(f(b)))) ) ) )).
%----Roles
tff(role_hypothesis,hypothesis,(
p(h) )).
tff(role_conjecture,conjecture,(
? [X: $i] : p(X) )).
%----Include directive
include('Axioms/SYN000_0.ax').
%----Comments
/* This
is a block
comment.
*/
%------------------------------------------------------------------------------
|
