Some more recent books in this area: David Corfield "Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy" Fernando Zalamea "Synthetic Philo

Some more recent books in this area: David Corfield "Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy" Fernando Zalamea "Synthetic Philosophy of Contemporary Mathematics" (though the book is a bit convoluted in the language it uses) also recent translation from French: Albert Lautman "Mathematics, Ideas and the Physical Real" also a book that uses category theory for purposes of philosophy: Rocco Gangle "Diagrammatic Immanence: Category Theory and Philosophy" I also would guess, that nowadays such a book should include chapters about automatic theorem provers, but don't know them