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 Apr 23 revised Satisfiability proof of formulas with pure literals added 1 character in body Apr 23 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. Apr 23 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? Apr 23 revised Satisfiability proof of formulas with pure literals added 290 characters in body Apr 22 revised Satisfiability proof of formulas with pure literals edited title Apr 22 revised Satisfiability proof of formulas with pure literals edited body Apr 22 revised Satisfiability proof of formulas with pure literals added 2 characters in body Apr 22 asked Satisfiability proof of formulas with pure literals Apr 22 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? Apr 22 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? Apr 22 asked Validity of a first-order formula Jan 29 accepted Get rid of an existential quantifier Jan 29 awarded Editor Jan 29 comment Get rid of an existential quantifier yeah thank you. i've edited my question Jan 29 revised Get rid of an existential quantifier edited body Jan 29 asked Get rid of an existential quantifier Jan 23 awarded Student Jan 23 accepted Number of triangles in a graph Jan 23 awarded Supporter Jan 23 asked Number of triangles in a graph