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def parse_ike_proposal(proposal):
    """
    Parse an IKE or ESP proposal string to extract encryption, hash, and DH group in human-readable format.
    
    Args:
        proposal (str): IKE or ESP proposal string, e.g., 'IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_1024',
                        'AES_GCM_16_256/PRF_HMAC_SHA2_256/ECP_384', or 'ESP:AES_CBC_256/HMAC_SHA1_96/NO_EXT_SEQ'
    
    Returns:
        dict: Dictionary with encryption, hash, and DH group in human-readable format
    """
    dh_mapping = {
        'MODP_768': '1',
        'MODP_1024': '2',
        'MODP_1536': '5',
        'MODP_2048': '14',
        'MODP_3072': '15',
        'MODP_4096': '16',
        'MODP_6144': '17',
        'MODP_8192': '18',
        'ECP_256': '19',
        'ECP_384': '20',
        'ECP_521': '21',
        'ECP_192': '25',
        'ECP_224': '26',
        'MODP_1024_160': '22',
        'MODP_2048_224': '23',
        'MODP_2048_256': '24',
        'FFDHE_2048': '256',
        'FFDHE_3072': '257',
        'FFDHE_4096': '258',
        'FFDHE_6144': '259',
        'FFDHE_8192': '260',
        'ECP_224_BP': '27',
        'ECP_256_BP': '28',
        'ECP_384_BP': '29',
        'ECP_512_BP': '30',
        'CURVE_25519': '31',
        'CURVE_448': '32',
    }
    
    enc_mapping = {
        'AES_CBC_128': 'AES-128',
        'AES_CBC_192': 'AES-192',
        'AES_CBC_256': 'AES-256',
        'AES_GCM_16_128': 'AES-GCM-128',
        'AES_GCM_16_192': 'AES-GCM-192',
        'AES_GCM_16_256': 'AES-GCM-256',
        'AES_GCM_8_128': 'AES-GCM-128-8',
        'AES_GCM_8_256': 'AES-GCM-256-8',
        'AES_GCM_12_128': 'AES-GCM-128-12',
        'AES_GCM_12_256': 'AES-GCM-256-12',
        'AES_CCM_16_128': 'AES-CCM-128',
        'AES_CCM_16_256': 'AES-CCM-256',
        'AES_CTR_128': 'AES-CTR-128',
        'AES_CTR_192': 'AES-CTR-192',
        'AES_CTR_256': 'AES-CTR-256',
        '3DES_CBC': '3DES',
        'DES_CBC': 'DES',
        'CAMELLIA_CBC_128': 'CAMELLIA-128',
        'CAMELLIA_CBC_256': 'CAMELLIA-256',
        'CHACHA20_POLY1305': 'CHACHA20-POLY1305',
        'BLOWFISH_CBC': 'BLOWFISH',
        'CAST5_CBC': 'CAST5',
        'NULL': 'NULL'
    }
    
    hash_mapping = {
        'HMAC_MD5': 'MD5',
        'HMAC_MD5_96': 'MD5',
        'HMAC_SHA1': 'SHA1',
        'HMAC_SHA1_96': 'SHA1',
        'HMAC_SHA2_256': 'SHA2-256',
        'HMAC_SHA2_256_128': 'SHA2-256',
        'HMAC_SHA2_384': 'SHA2-384',
        'HMAC_SHA2_384_192': 'SHA2-384',
        'HMAC_SHA2_512': 'SHA2-512',
        'HMAC_SHA2_512_256': 'SHA2-512',
        'HMAC_SHA3_224': 'SHA3-224',
        'HMAC_SHA3_256': 'SHA3-256',
        'HMAC_SHA3_384': 'SHA3-384',
        'HMAC_SHA3_512': 'SHA3-512',
        'AES_GMAC_128': 'GMAC-128',
        'AES_GMAC_192': 'GMAC-192',
        'AES_GMAC_256': 'GMAC-256',
        'POLY1305': 'POLY1305',
        'NONE': 'NULL'
    }
    
    components = proposal.split('/')
    
    result = {
        'encryption': "Unknown",
        'hash': 'None',
        'dh_group': 'None'
    }
    
    is_ike = proposal.startswith('IKE:')
    is_esp = proposal.startswith('ESP:')
    
    if is_ike or is_esp:
        components[0] = components[0].replace('IKE:', '').replace('ESP:', '')
    
    if len(components) == 4:
        result['encryption'] = enc_mapping.get(components[0], 'Unknown')
        result['hash'] = hash_mapping.get(components[1], 'Unknown')
        result['dh_group'] = dh_mapping.get(components[3], 'None')
    elif len(components) == 3:
        result['encryption'] = enc_mapping.get(components[0], 'Unknown')
        if (is_ike or not is_esp) and components[1].startswith('PRF_'):
            result['hash'] = 'None'
            result['dh_group'] = dh_mapping.get(components[2], 'None')
        else:
            result['hash'] = hash_mapping.get(components[1], 'Unknown')
            result['dh_group'] = 'None'
    
    if result['encryption'] == 'Unknown':
        print(f"Unrecognized proposal: {proposal}")
    
    return result

def process_proposals(proposal_list):
    """
    Process a list of IKE or ESP proposals, concatenating encryption and hash values, and listing all unique DH groups.
    
    Args:
        proposal_list (str): Comma-separated string of IKE or ESP proposals
    
    Returns:
        str: Formatted string with concatenated encryption, hash, and DH groups
    """
    proposal_list = proposal_list.replace(',', ', ')
    proposals = proposal_list.strip().split(', ')
    
    # Collect unique encryption, hash, and DH groups
    enc_set = set()
    hash_set = set()
    dh_set = set()
    
    for proposal in proposals:
        parsed = parse_ike_proposal(proposal.strip())
        enc_set.add(parsed['encryption'])
        if parsed['hash'] != 'None':
            hash_set.add(parsed['hash'])
        if parsed['dh_group'] != 'None':
            dh_set.add(parsed['dh_group'])
    
    # Convert sets to sorted lists
    enc_list = sorted(list(enc_set))
    hash_list = sorted(list(hash_set))
    dh_list = sorted(list(dh_set), key=lambda x: int(x))
    
    # Format output as a single concatenated string
    enc_part = f"Encryption {' '.join(enc_list)}" if enc_list else "Encryption None"
    hash_part = f" Hash {' '.join(hash_list)}" if hash_list else " Hash None"
    dh_part = f" DH Group(s) {' '.join(dh_list)}" if dh_list else " DH Group(s) None"
    
    return f"{enc_part}{hash_part}{dh_part}"

# Example usage
if __name__ == "__main__":
    #IKEv1 DEFAULT AWS WORKING
    #proposals = """IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_1024, IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_2048, IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_3072, IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_4096, IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_6144, IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_8192, IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/ECP_256, IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/ECP_384, IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/ECP_521, IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_1024_160, IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_2048_224, IKE:AES_CBC_128/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_2048_256, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_1024, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_2048, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_3072, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_4096, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_6144, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_8192, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/ECP_256, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/ECP_384, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/ECP_521, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_1024_160, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_2048_224, IKE:AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_2048_256, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_1024, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_2048, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_3072, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_4096, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_6144, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_8192, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/ECP_256, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/ECP_384, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/ECP_521, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_1024_160, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_2048_224, IKE:AES_CBC_128/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_2048_256, IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_1024, IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_2048,IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_3072, IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_4096, IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_6144, IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_8192, IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/ECP_256, IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/ECP_384, IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/ECP_521, IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_1024_160, IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_2048_224, IKE:AES_CBC_128/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_2048_256, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_1024, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_2048, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_3072, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_4096, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_6144, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_8192, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/ECP_256, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/ECP_384, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/ECP_521, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_1024_160, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_2048_224, IKE:AES_CBC_256/HMAC_SHA1_96/PRF_HMAC_SHA1/MODP_2048_256, IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_1024, IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_2048, IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_3072, IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_4096, IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_6144, IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_8192,IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/ECP_256, IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/ECP_384, IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/ECP_521, IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_1024_160, IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_2048_224, IKE:AES_CBC_256/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/MODP_2048_256, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_1024, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_2048, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_3072, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_4096, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_6144, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_8192, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/ECP_256, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/ECP_384, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/ECP_521, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_1024_160, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_2048_224, IKE:AES_CBC_256/HMAC_SHA2_384_192/PRF_HMAC_SHA2_384/MODP_2048_256, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_1024, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_2048, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_3072, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_4096, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_6144, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_8192, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/ECP_256, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/ECP_384, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/ECP_521, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_1024_160, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_2048_224, IKE:AES_CBC_256/HMAC_SHA2_512_256/PRF_HMAC_SHA2_512/MODP_2048_256"""
    
    #IKEv2 DEFAULT AWS NOT WORKING
    proposals = """IKE:AES_CBC_128/AES_CBC_256/HMAC_SHA1_96/HMAC_SHA2_256_128/HMAC_SHA2_384_192/HMAC_SHA2_512_256/PRF_HMAC_SHA1/PRF_HMAC_SHA2_256/PRF_HMAC_SHA2_384/PRF_HMAC_SHA2_512/MODP_1024/MODP_2048/MODP_3072/MODP_4096/MODP_6144/MODP_8192/ECP_256/ECP_384/ECP_521/MODP_1024_160/MODP_2048_224/MODP_2048_256, IKE:AES_GCM_16_128/AES_GCM_16_256/PRF_HMAC_SHA1/PRF_HMAC_SHA2_256/PRF_HMAC_SHA2_384/PRF_HMAC_SHA2_512/MODP_1024/MODP_2048/MODP_3072/MODP_4096/MODP_6144/MODP_8192/ECP_256/ECP_384/ECP_521/MODP_1024_160/MODP_2048_224/MODP_2048_256"""

    print(process_proposals(proposals))
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)