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# File     : COL064-7 : TPTP v2.1.0. Bugfixed v1.2.0.
# Domain   : Combinatory Logic
# Problem  : Find combinator equivalent to V from B and T
# Version  : [WM88] (equality) axioms.
#            Theorem formulation : The combinator is provided and checked.
# English  : Construct from B and T alone a combinator that behaves as the 
#            combinator V does, where ((Bx)y)z = x(yz), (Tx)y = yx, 
#            ((Vx)y)z = (zx)y.

# Refs     : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq
#          : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to 
# Source   : [TPTP]
# Names    : 

# Status   : unsatisfiable
# Rating   : 0.40 v2.1.0, 0.71 v2.0.0
# Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   1 RR)
#            Number of literals   :    3 (   3 equality)
#            Maximal clause size  :    1 (   1 average)
#            Number of predicates :    1 (   0 propositional; 2-2 arity)
#            Number of functors   :    6 (   5 constant; 0-2 arity)
#            Number of variables  :    5 (   0 singleton)
#            Maximal term depth   :    9 (   4 average)

# Comments : 
#          : tptp2X -f setheo:sign -t rm_equality:rstfp COL064-7.p 
# Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed.
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# b_definition, axiom.
equal(apply(apply(apply(b, X), Y), Z), apply(X, apply(Y, Z))) <- .

# t_definition, axiom.
equal(apply(apply(t, X), Y), apply(Y, X)) <- .

# prove_v_combinator, conjecture.
 <- equal(apply(apply(apply(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, t), t))), x), y), z), apply(apply(z, x), y)).

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