## TPTP Problem File: SYN069-1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN069-1 : TPTP v8.1.0. Released v1.0.0.
% Domain   : Syntactic
% Problem  : Pelletier Problem 45
% Version  : Especial.
% English  :

% Refs     : [KM64]  Kalish & Montegue (1964), Logic: Techniques of Formal
%          : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% Source   : [Pel86]
% Names    : Pelletier 45 [Pel86]
%          : p45.in [ANL]

% Status   : Unsatisfiable
% Rating   : 0.00 v2.0.0
% Syntax   : Number of clauses     :    9 (   1 unt;   2 nHn;   9 RR)
%            Number of literals    :   27 (   0 equ;  17 neg)
%            Maximal clause size   :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   6 usr;   0 prp; 1-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   11 (   0 sgn)
% SPC      : CNF_UNS_RFO_NEQ_NHN

%--------------------------------------------------------------------------
cnf(clause_1,axiom,
( ~ big_f(X)
| big_g(f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) ) ).

cnf(clause_2,axiom,
( ~ big_f(X)
| big_h(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) ) ).

cnf(clause_3,axiom,
( ~ big_f(X)
| ~ big_j(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) ) ).

cnf(clause_4,axiom,
( ~ big_l(X)
| ~ big_k(X) ) ).

cnf(clause_5,axiom,
big_f(a) ).

cnf(clause_6,axiom,
( ~ big_h(a,X)
| big_l(X) ) ).

cnf(clause_7,axiom,
( ~ big_g(X)
| ~ big_h(a,X)
| big_j(a,X) ) ).

cnf(clause_8,negated_conjecture,
( ~ big_f(X)
| big_g(g(X)) ) ).

cnf(clause_9,negated_conjecture,
( ~ big_f(X)
| big_h(X,g(X)) ) ).

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