## TPTP Problem File: SYN000+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYN000+1 : TPTP v8.1.2. Released v4.0.0.
% Domain   : Syntactic
% Problem  : Basic TPTP FOF syntax
% Version  : Biased.
% English  : Basic TPTP FOF syntax that you can't survive without parsing.

% Refs     :
% Source   : [TPTP]
% Names    :

% Status   : Theorem
% Rating   : 0.17 v8.1.0, 0.19 v7.4.0, 0.17 v7.0.0, 0.20 v6.4.0, 0.19 v6.3.0, 0.25 v6.2.0, 0.28 v6.1.0, 0.33 v6.0.0, 0.43 v5.5.0, 0.48 v5.4.0, 0.46 v5.3.0, 0.52 v5.2.0, 0.40 v5.1.0, 0.43 v5.0.0, 0.54 v4.1.0, 0.57 v4.0.1, 0.78 v4.0.0
% Syntax   : Number of formulae    :   12 (   5 unt;   0 def)
%            Number of atoms       :   31 (   3 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   28 (   9   ~;  10   |;   3   &)
%                                         (   1 <=>;   3  =>;   1  <=;   1 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   16 (  13 usr;  10 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :   13 (   5   !;   8   ?)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
%----Propositional
fof(propositional,axiom,
( ( p0
& ~ q0 )
=> ( r0
| ~ s0 ) ) ).

%----First-order
fof(first_order,axiom,
! [X] :
( ( p(X)
| ~ q(X,a) )
=> ? [Y,Z] :
( r(X,f(Y),g(X,f(Y),Z))
& ~ s(f(f(f(b)))) ) ) ).

%----Equality
fof(equality,axiom,
? [Y] :
! [X,Z] :
( f(Y) = g(X,f(Y),Z)
| f(f(f(b))) != a
| X = f(Y) ) ).

%----True and false
fof(true_false,axiom,
( \$true
| \$false ) ).

%----Quoted symbols
fof(single_quoted,axiom,
( 'A proposition'
| 'A predicate'(a)
| p('A constant')
| p('A function'(a))
| p('A \'quoted \\ escape\'') ) ).

%----Connectives - seen |, &, =>, ~ already
fof(useful_connectives,axiom,
! [X] :
( ( p(X)
<= ~ q(X,a) )
<=> ? [Y,Z] :
( r(X,f(Y),g(X,f(Y),Z))
<~> ~ s(f(f(f(b)))) ) ) ).

%----Annotated formula names
fof(123,axiom,
! [X] :
( ( p(X)
| ~ q(X,a) )
=> ? [Y,Z] :
( r(X,f(Y),g(X,f(Y),Z))
& ~ s(f(f(f(b)))) ) ) ).

%----Roles
fof(role_hypothesis,hypothesis,
p(h) ).

fof(role_conjecture,conjecture,
? [X] : p(X) ).

%----Include directive
include('Axioms/SYN000+0.ax').