| (1) | If p1 = p2, then C1 = C2. |
| (2) | If p is the proposition that a is F, and q the proposition that b is G and p = q, then a = b and being F = being G. |
| (3) | ∀x (Prop(x) ∧ x ∈ C →True(x)) |
| (4) | ∀p (Op → p) |
| (5) | ∀p, q ∀F, G ∀a, b (p ≡ F (a) ∧ q ≡ G(b) ∧ p ≡ q → F ≡ G ∧ a = b) |
| (6) | ∃p p |
| (7) | For some way things may be said to be, things are that way. |
| (8) | Some facts about dinosaurs are rather surprising. |
| (9) | John believes that dinosaurs are extinct. |
| (10) | That dinosaurs are extinct is what John believes. |
| (11) | Dinosaurs are extinct is what John believes that. |
| (12) | I want you visit me. |
| (13) | I want you to visit me. |
| (14) | Some facts are surprising. |
| (15) | Some cars are expensive. |
| (16) | Something is surprising, namely the fact that I won at chess. |
| (17) | Something is expensive, namely the Tesla. |
| (18) | Something is disgusting. |
| (19) | There are two things that bother John: his ulcer and the fact that I won at chess. |
| (20) | Everything that is disgusting to either Jay or Jess is appealing to Joe. |
| (21) | ∀p(p ∨ ¬p) |
| (22) | ∀p(True(p) ∨ True(¬p)) |
| (23) | English Target: Is reality structured? |
| (24) | HOL Target: ∀p, q ∀F, G ∀a, b (p ≡ F (a) ∧ q ≡ G(b) ∧ p ≡ q → F ≡ G ∧ a = b)? |