## TPTP Problem File: SYN079+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN079+1 : TPTP v8.1.0. Released v2.0.0.
% Domain   : Syntactic
% Problem  : Pelletier Problem 57
% Version  : Especial.
% English  :

% Refs     : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
%          : [Hah94] Haehnle (1994), Email to G. Sutcliffe
% Source   : [Hah94]
% Names    : Pelletier 57 [Pel86]

% Status   : Theorem
% Rating   : 0.00 v5.3.0, 0.09 v5.2.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    4 (   3 unt;   0 def)
%            Number of atoms       :    6 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :    2 (   0   ~;   0   |;   1   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :    3 (   3   !;   0   ?)
% SPC      : FOF_THM_RFO_NEQ

%--------------------------------------------------------------------------
fof(pel57_1,axiom,
big_f(f(a,b),f(b,c)) ).

fof(pel57_2,axiom,
big_f(f(b,c),f(a,c)) ).

fof(pel57_3,axiom,
! [X,Y,Z] :
( ( big_f(X,Y)
& big_f(Y,Z) )
=> big_f(X,Z) ) ).

fof(pel57,conjecture,
big_f(f(a,b),f(a,c)) ).

%--------------------------------------------------------------------------
```