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from itertools import product
V='∀'
E='∃'


def tt(f,n) :
  xss=product((0,1),repeat=n)
  print('function:',f.__name__)
  for xs in xss : print(*xs,':',int(f(*xs)))
  print('')

# p \/ (q /\ r) = (p \/ q) /\ (p \/ r)

def prob1(p,q,r) :
  x=p or (q and r)
  y= (p or q) and (p or r)
  return x==y

tt(prob1,3)

# p/\(q\/r)=(p/\q)\/(p/\r)

def prob2(p,q,r) :
  x=p and ( q or r )
  y=(p and q) or (p and r)
  return x==y

tt(prob2,3)

#~(p/\q)=(~p\/~q)

def prob3(p,q) :
  x=not (p and q)
  y=(not p) or (not q)
  return x==y
tt(prob3,2)

#(~(p\/q))=((~p)/\~q)

def prob4(p, q):
   x = not(p or q)
   y = not p and not q
   return x == y

tt(prob4, 2)

#(p/\(p=>q)=>q)

def prob5(p,q):
  x= p and ( not p or q)
  return not x or q
    
tt(prob5,2)

# (p=>q)=((p\/q)=q)

def prob6(p,q) :
  x = (not p or q)
  y=((p or q) == q)
  return x==y
 
tt(prob6,2)


#((p=>q)=(p\/q))=q
def prob7(p,q):
  if ((not p or q)==(p or q))==q:
    return 1
 
tt(prob7,2)



#(p=>q)=((p/\q)=p)
def prob8(p,q):
  if (not p or q)==((p and q)==p):
    return 1
 
tt(prob8,2)


#((p=>q)=(p/\q))=p

def prob9(p,q):
  if ((not p or q)==(p and q))==p:
    return '1'

tt(prob9,2)



#(p=>q)/\(q=>r)=>(p=>r)
def prob10(p,q,r) :
  x = not ((not p or q) and (not q or r)) or (not p or r)
  return x
 
tt(prob10, 3)


# (p = q) /\ (q => r)  => (p => r)
#answer 1
def prob11(p,q,r) :
  x = not((p is q) and (not q or r)) or (not p or r)
  return x
 
tt(prob11, 3)

#(p=q)/\(q=>r)=>(p=>r)
#answer 2
def prob11(p,q,r):
  x=(p==q) and (not q or r)
  y=not p or r
  return not x or y

tt(prob11,3)

#((p=>q)/\(q=r))=>(p=>r)

def prob12(p,q,r):
  x=(not p or q) and ( q==r )
  y=not p or r
  return not x or y

tt(prob12,3)

#(p=>q)=>((p/\r)=>(q/\r))

def prob13(p,q,r):
  x=not p or q
  y=(not(p and r) or ( q and r))
  return not x or y

tt(prob13,3)

#Question#2----------------------------------------

#(p=>q)=>r=p=>(q=>r)

def prob14(p,q,r):
  x=(not(not p or q) or r)
  y=(not p or (not q or r))
  return x==y

tt(prob14,3) 


def prob15(p, q):
    x = not(p and q)
    y = not p and not q
    return x == y

tt(prob15, 2)


def prob16(p, q):
    x = not(p or q)
    y = not p or not q
    return x == y

tt(prob16, 2)



def prob17(p):
    x = p
    y = not p
    return x == y

tt(prob17, 1)
import re

def _map_ikev2_vendor_capabilities(message_type, input_string):
    # List of acceptable message types
    valid_message_types = ['IKE_SA_INIT', 'IKE_AUTH']
    
    # Validate message type
    if message_type not in valid_message_types:
        raise ValueError(f"Invalid message type: {message_type}. Must be one of {valid_message_types}")
    
    # Mapping dictionary for IKE values with RFC references
    value_map = {
        # IKE_SA_INIT capabilities
        'FRAG_SUP': 'IKE Fragmentation',  # RFC 7383, Section 3
        'REDIR_SUP': 'IKE Redirection',  # RFC 5685, Section 3
        'HASH_ALG': 'Hash Algorithms',  # RFC 7296, Section 3.3.2
        'NATD_S_IP': 'NAT Detection (Source IP)',  # RFC 7296, Section 2.23
        'NATD_D_IP': 'NAT Detection (Destination IP)',  # RFC 7296, Section 2.23
        'SIGN_HASH_ALGS': 'Signature Hash Algorithms',  # RFC 7296, Section 2.15
        'NON_FIRST_FRAGMENTS': 'Non-First IKE Fragments',  # RFC 7383, Section 3
        'CHILDLESS_IKEV2_SUP': 'Childless IKEv2',  # RFC 6023, Section 3
        'INTERMEDIATE': 'Intermediate Exchange',  # RFC 9242, Section 3
        'COOKIE': 'Cookie-Based DoS Protection',  # RFC 7296, Section 2.6
        # IKE_AUTH capabilities
        'ESP_TFC_PAD_N': 'ESPv3 TFC Padding Disabled',  # RFC 7296, Section 3.3.1
        'MOBIKE_SUP': 'MOBIKE',  # RFC 4555, Section 3
        'MULT_AUTH': 'Multiple Auth',  # RFC 4739, Section 3
        'EAP_ONLY': 'EAP-Only Auth',  # RFC 5998, Section 3
        'MSG_ID_SYN_SUP': 'Message ID Synchronization',  # RFC 6311, Section 3
        'IPCOMP_SUPPORTED': 'IP Payload Compression Support',  # RFC 7296, Section 3.3.2
        'ADD_4_ADDR': 'Additional IPv4 Addresses',  # RFC 4555, Section 3.2
        'ADD_6_ADDR': 'Additional IPv6 Addresses',  # RFC 4555, Section 3.2
        'INIT_CONTACT': 'Initial Contact',  # RFC 7296, Section 3.16
        'HTTP_CERT_LOOKUP_SUP': 'HTTP Certificate Lookup',  # RFC 7296, Section 3.7
    }
        
    # Regex to capture N(...) patterns
    pattern = r'N\([^)]+\)'
    matches = re.findall(pattern, input_string)
    
    # Parse matches and create result list
    result = []
    for match in matches:
        key = match[2:-1]  # Extract content inside N(...)
        # Only include keys valid for the message type
        if key in value_map:
            result.append(value_map[key])
    
    return ', '.join(result)

# Example usage
ike_sa_init_string = '2025-07-18 20:16:22.839 15[ENC] <4> parsed IKE_SA_INIT request 0 [ SA KE No N(NATD_S_IP) N(NATD_D_IP) N(FRAG_SUP) N(HASH_ALG) N(MULT_AUTH) ]'
ike_auth_string = '2025-07-18 20:16:22.898 07[ENC] <4> parsed IKE_AUTH request 1 [ IDi N(INIT_CONTACT) IDr AUTH N(ESP_TFC_PAD_N) SA TSi TSr N(MOBIKE_SUP) N(ADD_4_ADDR)N(MULT_AUTH) N(EAP_ONLY) N(MSG_ID_SYN_SUP) ]'

# Test with IKE_SA_INIT
print("IKE_SA_INIT Results:")
print(_map_ikev2_vendor_capabilities("IKE_SA_INIT", ike_sa_init_string))

# Test with IKE_AUTH
print("\nIKE_AUTH Results:")
print(_map_ikev2_vendor_capabilities("IKE_AUTH", ike_auth_string))