How can I know if it is possible to logically infer both sentences from the given database? (Using first order logic)

My basic assumptions are that(because of dealing with AI): Closed world assumptions, Domain closure and Unique names assumptions.

the database i have:

  1. every professor counsels at least one student

$\forall x,y(C(x,y) \land \forall x,y -> (x=p \land y=(\exists S(s)))$

  1. every student has a counselor, who is a professor

$\forall x,y(H(x,y) \land \forall x,y(x=s \land y=c) \land c -> p)$

  1. Eric is a professor

$\exists x(P(x) \land x-> x='Eric')$

  1. counseling meeting occur at the campus

$\exists x,y(occurs(x,y) \land \forall x,y ((x=m \land i) \land y = u)$

  1. Rachel is a student

$\exists x(S(x) \land x -> x = s \land x = 'Rachel')$

  1. every counselor meets with all of his counselees(the ones he counsels)

$\forall x,y(M(x,y) \land x=c \land M(x,y) -> y=h )$ (Every counselor meets with all of his counselees, and if he meets with someone he must be his counselee)


S(x) - x is a student

P(x) - x is a professor

C(x,y) - x counsels y

M(x,y) - x meets with y

O(x,y) - x occurs at y

H(x,y) - x has y

p - a professor

s - a student

c - a counselor

m - a meeting

h - a counselee

i - a counseling

u - a campus

what i don't understand is how is it possible to infer:

1)Eric counsels Rachel

2)Eric was at the campus

Very much struggling with it and spent so much time without being able to infer neither of those


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