F=\
lambda t,y:next((b for a,b in t if all(c(a,p(y)[0],{}))),0)
T=type
def p(s,c=0):
 q,n=[],0
 while s and(c<1or')'!=s[0]):
  S=s[0];n+=S=='!'
  if S.isalpha():q+=[n,S],;n=0
  if'('==S:t,s=p(s[1:],1);q+=(n,t),;n=0
  s=s[1:]
 return q,s
def c(a,b,d):
 if T(a)==T(b):
  for x,y in zip(a,b):
   p,q=x;n,m=y;z=p<1or p%2==n%2
   if T(x)==list:yield all([d.get(q,m)==m,z]);d[q]=m
   if T(x)==tuple:yield all([T(y)==tuple,z,*c(q,m,d)])
 
axioms="""a>(b>a); A
(a>(b>c))>((a>b)>(a>c)); B
(!a>!b)>(b>a); C""" 
cases="""
(b>!c)>(c>(b>!c)); A
(a>(a>a))>((a>a)>(a>a)); B
(a>(b>!!!!!c))>((a>b)>(a>!!!!!c)); B
(!a>!b)>(b>a); C
a>(b>c); 0
(!(a>(b>!c))>!(c>c))>((c>c)>(a>(b>!c))); C"""
def a_temp(d):
	return [[p((t:=i.split('; '))[0])[0], t[1]] for i in filter(None, d.split('\n'))]
 
for i in filter(None, cases.split('\n')):
	x, y = i.split('; ')
	print(F(a_temp(axioms), x), y)

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