$\neg P(x,y)\vee P(S,y)$ (1)
$\neg P(x,f(x))\vee P(S,f(x))$ (2)
$\neg P(S,f(x))\vee P(x,f(x))$ (3)
Is, this set of formulas, consistent? I think so, because I could not to obtain a contradiction. What do you think?
$\neg P(x,y)\vee P(S,y)$ (1)
$\neg P(x,f(x))\vee P(S,f(x))$ (2)
$\neg P(S,f(x))\vee P(x,f(x))$ (3)
Is, this set of formulas, consistent? I think so, because I could not to obtain a contradiction. What do you think?
If $P$ is interpreted to always be true, then (no matter how $S$ and $f$ are interpreted), all three sentences are true. Thus the set has a model and hence is consistent.