#--------------------------------------------------------------------------
# File     : CAT018-4 : TPTP v2.1.0. Released v1.0.0.
# Domain   : Category Theory
# Problem  : If xy and yz exist, then so does x(yz)
# Version  : [Sco79] axioms : Reduced > Complete.
# English  : 

# Refs     : [Sco79] Scott (1979), Identity and Existence in Intuitionist L
# Source   : [TPTP]
# Names    : 

# Status   : unsatisfiable
# Rating   : 0.83 v2.1.0, 0.80 v2.0.0
# Syntax   : Number of clauses    :   14 (   0 non-Horn;   6 unit;  11 RR)
#            Number of literals   :   24 (   7 equality)
#            Maximal clause size  :    3 (   1 average)
#            Number of predicates :    3 (   0 propositional; 1-2 arity)
#            Number of functors   :    6 (   3 constant; 0-2 arity)
#            Number of variables  :   19 (   2 singleton)
#            Maximal term depth   :    3 (   1 average)

# Comments : The dependent axioms have been removed.
#          : tptp2X -f setheo:sign -t rm_equality:rstfp CAT018-4.p 
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# equivalence_implies_existence1, axiom.
there_exists(X) <- 
    equivalent(X, Y).

# equivalence_implies_existence2, axiom.
equal(X, Y) <- 
    equivalent(X, Y).

# existence_and_equality_implies_equivalence1, axiom.
equivalent(X, Y) <- 
    there_exists(X),
    equal(X, Y).

# domain_has_elements, axiom.
there_exists(X) <- 
    there_exists(domain(X)).

# codomain_has_elements, axiom.
there_exists(X) <- 
    there_exists(codomain(X)).

# composition_implies_domain, axiom.
there_exists(domain(X)) <- 
    there_exists(compose(X, Y)).

# domain_codomain_composition1, axiom.
equal(domain(X), codomain(Y)) <- 
    there_exists(compose(X, Y)).

# domain_codomain_composition2, axiom.
there_exists(compose(X, Y)) <- 
    there_exists(domain(X)),
    equal(domain(X), codomain(Y)).

# associativity_of_compose, axiom.
equal(compose(X, compose(Y, Z)), compose(compose(X, Y), Z)) <- .

# compose_domain, axiom.
equal(compose(X, domain(X)), X) <- .

# compose_codomain, axiom.
equal(compose(codomain(X), X), X) <- .

# assume_ab_exists, hypothesis.
there_exists(compose(a, b)) <- .

# assume_bc_exists, hypothesis.
there_exists(compose(b, c)) <- .

# prove_a_bc_exists, conjecture.
 <- there_exists(compose(a, compose(b, c))).

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