TPTP Axioms File: SYN002+0.ax


%------------------------------------------------------------------------------
% File     : SYN002+0 : TPTP v7.5.0. Released v3.6.0.
% Domain   : Syntactic
% Axioms   : Orevkov formula
% Version  : [TS00] axioms : Especial.
% English  : r(x,y,z)=y+2^x=z

% Refs     : [TS00]  Troelska & Schwichtenberg (2000), Basic Proof Theory
%          : [Rat08] Raths (2008), Email to G. Sutcliffe
% Source   : [Rat08]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    2 (   1 unit)
%            Number of atoms       :    4 (   0 equality)
%            Maximal formula depth :    7 (   4 average)
%            Number of connectives :    2 (   0 ~  ;   0  |;   0  &)
%                                         (   0 <=>;   2 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    1 (   0 propositional; 3-3 arity)
%            Number of functors    :    2 (   1 constant; 0-1 arity)
%            Number of variables   :    5 (   0 singleton;   5 !;   0 ?)
%            Maximal term depth    :    2 (   1 average)
% SPC      : 

% Comments :
%------------------------------------------------------------------------------
fof(hyp1,axiom,(
    ! [Y] : r(Y,zero,succ(Y)) )).

fof(hyp2,axiom,(
    ! [Y,X,Z,Z1] :
      ( r(Y,X,Z)
     => ( r(Z,X,Z1)
       => r(Y,succ(X),Z1) ) ) )).

%------------------------------------------------------------------------------