#--------------------------------------------------------------------------
# File     : COL038-1 : TPTP v2.1.0. Released v1.0.0.
# Domain   : Combinatory Logic
# Problem  : Strong fixed point for B, M, and V
# Version  : [WM88] (equality) axioms.
# English  : The strong fixed point property holds for the set 
#            P consisting of the combinators B, M, and V, where ((Bx)y)z 
#            = x(yz), Mx = xx, ((Vx)y)z = (zx)y.

# Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
#          : [MW87]  McCune & Wos (1987), A Case Study in Automated Theorem
#          : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq
#          : [MW88]  McCune & Wos (1988), Some Fixed Point Problems in Comb
# Source   : [MW88]
# Names    : - [MW88]

# Status   : unsatisfiable
# Rating   : 0.83 v2.1.0, 0.88 v2.0.0
# Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   1 RR)
#            Number of literals   :    4 (   4 equality)
#            Maximal clause size  :    1 (   1 average)
#            Number of predicates :    1 (   0 propositional; 2-2 arity)
#            Number of functors   :    5 (   3 constant; 0-2 arity)
#            Number of variables  :    8 (   0 singleton)
#            Maximal term depth   :    4 (   3 average)

# Comments : 
#          : tptp2X -f setheo:sign -t rm_equality:rstfp COL038-1.p 
#--------------------------------------------------------------------------
# b_definition, axiom.
equal(apply(apply(apply(b, X), Y), Z), apply(X, apply(Y, Z))) <- .

# m_definition, axiom.
equal(apply(m, X), apply(X, X)) <- .

# v_definition, axiom.
equal(apply(apply(apply(v, X), Y), Z), apply(apply(Z, X), Y)) <- .

# prove_fixed_point, conjecture.
 <- equal(apply(Y, f(Y)), apply(f(Y), apply(Y, f(Y)))).

#--------------------------------------------------------------------------