Differences

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+====== On substitutions ======
+Let t1[x:=t0] denote the result of substituting all occurrences of variable x in term t1 with the term t0.  These rules define substitution recursively:
+  x[x:=t0] = t2
+  y[x:=t0] = y   (for any variable y distinct from x)
+  c[x:=t0] = c   (for any constant symbol c)
+  f(t1,...,tn)[x:=t0] = f(t1[x:=t0],...,tn[x:=t0])
+The first cases are base cases and the last case is recursive case.
+For quantifier-free formulas, we similarly substitute recursively.  We rename quantified variables along the way to make them distinct from other variables (this avoides accidental "variable capture"):
+  R(t1,...,tn)[x:=t0] = R(t1[x:=t0],...,tn[x:=t0])
+  (t1=t2)[x:=t0] = (t1[x:=t0] = t2[x:=t0])
+  (F1 & F2)[x:=t0] = (F1[x:=t0] & F2[x:=t0])
+  (~F)[x:=t0] = ~(F[x:=t0])
+  (forall y. F) [x:=t0]  =  forall y. (F[x:=t0]),   if y does not occur in t (otherwise, rename y as a bound variable)
+  (exists y. F) [x:=t0]  =  exists y. (F[x:=t0]),   if y does not occur in t (otherwise, rename y as a bound variable)