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 1d revised Satisfiability proof of formulas with pure literals added 1 character in body 1d comment Satisfiability proof of formulas with pure literals Hi thx for your reply. Yes, I understand the principle, but I have problems in formulating a precise (structural) induction proof. 1d comment Satisfiability proof of formulas with pure literals Thx for the comment, I've edited my question and included the case for $\psi := \varphi \land \ell$. Is this going in the right direction? 1d revised Satisfiability proof of formulas with pure literals added 290 characters in body 2d revised Satisfiability proof of formulas with pure literals edited title 2d revised Satisfiability proof of formulas with pure literals edited body 2d revised Satisfiability proof of formulas with pure literals added 2 characters in body 2d asked Satisfiability proof of formulas with pure literals 2d comment Validity of a first-order formula yay! Can I ask you yet another question, just to be sure: If I replace $r$ in $\varphi$ by $\doteq$ (equality), so now I am considering also the theory of equality and its axioms, then the formula becomes valid. So, each instance of $r(x,y)$ gets replaced by $x \doteq y$. My assumption is that, then the formula is valid. because $x$ and $y$ are equal and according to the predicate substitution axioms of equality theory $p(x)$ and $p(y)$ always evaluates to the same truth value. Is this kind of the right (formal) argument? 2d comment Validity of a first-order formula Thank you for your reply. So, I choose $\mathbb N_0$ as my Domain. $I(x) = 0$, $I(y)=1$. Moreover the meaning of predicate $p$ is "is even". The meaning of the predicate $r(x,y)$ is $y$ is greater than $x$, and I am done? 2d asked Validity of a first-order formula Jan29 accepted Get rid of an existential quantifier Jan29 awarded Editor Jan29 comment Get rid of an existential quantifier yeah thank you. i've edited my question Jan29 revised Get rid of an existential quantifier edited body Jan29 asked Get rid of an existential quantifier Jan23 awarded Student Jan23 accepted Number of triangles in a graph Jan23 awarded Supporter Jan23 asked Number of triangles in a graph