Conjunctive-binding first-order logic positive-properties conjecture

Let $cb$ denote the conjunctive-binding fragment of first-order logic, whose binding-form grammar permits conjunctions but not disjunctions. Its satisfiability problem asks whether a sentence has a model, and the finite-model property means that every satisfiable sentence has a finite model.

Conjunctive-binding positive-properties conjecture. The fragment $cb$ enjoys the finite-model property and has a decidable satisfiability problem.

This is proposed as the positive counterpart to the negative properties of the unrestricted binding fragment and as an analogue of the corresponding established properties of the one-binding fragment. The source gives no resolution.