In special symbols:

Let p = ($S)($rf)($r)($w)($x)($y)($t) & symbol_1r(S,t,r,R) & symbol_0r(S,t,w,a) & symbol_0r(S,t,x,b) & symbol_0r(S,t,y,c)}

So fz = {(R,a,z,c)| ($S)($v)($r)($w)($y)($t)symbol_1r(S,t,r,R) & symbol_0r(S,t,w,a) & variable_0r(S,t,z,v) & symbol_0r(S,t,y,c)}

Let gz = {(R2,a,z,c)| ($S)($v)($r)($w)($y)($t)symbol_1r(S,t,r,R2) & symbol_0r(S,t,w,a) & variable_0r(S,t,z,v) & symbol_0r(S,t,y,c)}

Suppose (x) (R(a,x,z) ó R2(a,x,c))

But R ~= R2

Then S believes fz is ($v)($r)($w)($y)($t) belief_r(S,t,r,w,z,y) & symbol_1r(S,t,r,R) & symbol_0r(S,t,w,a) & variable_0r(S,t,z,v) & symbol0-r(S,y,c,t)}

And S believes gz is ($v)($r2)($w)($y)($t) belief_r(S,t,r,w,z,y) & symbol_1r(S,t,r2,R2) & symbol_0r(S,t,w,a) & variable_0r(S,t,z,v) & symbol0-r(S,y,c,t)}

In Plain Symbols:

Let p = (ES)(Erf)(Er)(Ew)(Ex)(Ey)(Et) & symbol_1r(S,t,r,R) & symbol_0r(S,t,w,a) & symbol_0r(S,t,x,b) & symbol_0r(S,t,y,c)}

So fz = {(R,a,z,c)| (ES)(Ev)(Er)(Ew)(Ey)(Et)symbol_1r(S,t,r,R) & symbol_0r(S,t,w,a) & variable_0r(S,t,z,v) & symbol_0r(S,t,y,c)}

Let gz = {(R2,a,z,c)| (ES)(Ev)(Er)(Ew)(Ey)(Et)symbol_1r(S,t,r,R2) & symbol_0r(S,t,w,a) & variable_0r(S,t,z,v) & symbol_0r(S,t,y,c)}

Suppose (x) (R(a,x,z) ó R2(a,x,c))

But R ~= R2

Then S believes fz is (Ev)(Er)(Ew)(Ey)(Et) belief_r(S,t,r,w,z,y) & symbol_1r(S,t,r,R) & symbol_0r(S,t,w,a) & variable_0r(S,t,z,v) & symbol0-r(S,y,c,t)}

And S believes gz is (Ev)(Er2)(Ew)(Ey)(Et) belief_r(S,t,r,w,z,y) & symbol_1r(S,t,r2,R2) & symbol_0r(S,t,w,a) & variable_0r(S,t,z,v) & symbol0-r(S,y,c,t)}

Conclusion:

So S believes R(a,z,c) essentially involves R, not just the values of R(a,z,c).