# Logically infering using resolutions

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)

where:

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