#--------------------------------------------------------------------------
# File     : COL042-8 : TPTP v2.1.0. Released v2.1.0.
# Domain   : Combinatory Logic
# Problem  : Strong fixed point for B and W1
# Version  : [WM88] (equality) axioms.
#            Theorem formulation : The fixed point is provided and checked.
# English  : The strong fixed point property holds for the set 
#            P consisting of the combinators B and W1, where ((Bx)y)z 
#            = x(yz), (W1x)y = (yx)x.

# Refs     : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq
#          : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St
# Source   : [TPTP]
# Names    : 

# Status   : unsatisfiable
# Rating   : ? v2.1.0
# Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   2 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 (   4 constant; 0-2 arity)
#            Number of variables  :    5 (   0 singleton)
#            Maximal term depth   :    7 (   3 average)

# Comments : 
#          : tptp2X -f setheo:sign -t rm_equality:rstfp COL042-8.p 
#--------------------------------------------------------------------------
# b_definition, axiom.
equal(apply(apply(apply(b, X), Y), Z), apply(X, apply(Y, Z))) <- .

# w1_definition, axiom.
equal(apply(apply(w1, X), Y), apply(apply(Y, X), X)) <- .

# strong_fixed_point, axiom.
equal(strong_fixed_point, apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)) <- .

# prove_strong_fixed_point, conjecture.
 <- equal(apply(strong_fixed_point, fixed_pt), apply(fixed_pt, apply(strong_fixed_point, fixed_pt))).

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