# -*- coding: utf-8 -*-
from parser_ import Parser_
parser = Parser_()
axioms = ["a=b->a'=b'", "a=b->a=c->b=c", "a'=b'->a=b", "!a'=0", "a+b'=(a+b)'", "a+0=a", "a*0=a", "a*b'=a*b+a"]
axioms = [parser.parse(axiom) for axiom in axioms]
scheme_axiom = [
"A->B->A", # 1
"(A->B)->(A->B->C)->(A->C)", # 2
"A->B->A&B", # 3
"A&B->A", # 4
"A&B->B", # 5
"A->A|B", # 6
"B->A|B", # 7
"(A->B)->(C->B)->(A|C->B)", # 8
"(A->B)->(A->!B)->!A", # 9
"!!A->A",
] # 10
semi_cons = ["A->A->A", "(A->A->A)->(A->(A->A)->A)->(A->A)", "(A->(A->A)->A)->(A->A)", "A->(A->A)->A", "A->A"]
semi_cons = [parser.parse(line) for line in semi_cons]
axiom_induction = "F(0)&@x(F(x)->F(x'))->F(x)"
axiom_universal = "@xF(x)->F(o)"
axiom_existence = "F(o)->?xF(x)"
axiom_induction = parser.parse(axiom_induction)
axiom_universal = parser.parse(axiom_universal)
axiom_existence = parser.parse(axiom_existence)
tmp.append(
assumption_pop([Negation(t) if i & (1 << (ind + 1)) == 0 else t for ind, t in enumerate(popped)],
alpha,
formula,
masked_proofs[i],
masked_proofs[i + 1])
)
masked_proofs = tmp
variables = popped
# debug_test()
# return
return masked_proofs[0]
t = time.time()
parser.set_formula('')
line = fr.read()
ex = parser.parse(line)
q = disproof_test(ex)
if q != {}:
fw.write('Высказывание ложно при ')
for key in q:
fw.write('{0}={1} '.format(str(key), 'И' if q[key] else 'Л'))
else:
l = proove(ex)
fw.write('|-{}\n'.format(str(ex)))
for line in l:
fw.write(str(line) + '\n')
print('prooving time: {} sec.'.format(str(time.time() - t)))
if len(ans) > 0 and assump[last_pos] == ',':
ans.append(assump[last_pos:])
if len(ans) > 1:
for i in range(1, len(ans)):
ans[i] = ans[i][1:]
return ans
parser = Parser_()
proof = []
deduction = []
annot = []
cache = {}
assumptions, formula = read.readline().split('|-')
formula = parser.parse(formula)
assumptions = [parser.parse(assumption) for assumption in split_by_comma(assumptions)]
uni_rule = [parser.parse(line) for line in uni_rule]
exist_rule = [parser.parse(line) for line in exist_rule]
if assumptions != []:
alpha = assumptions.pop()
else:
alpha = None
def axiom_deduct(epression):
cons = subst_pred(scheme_axiom[0], {'A': expression, 'B': alpha})
deduction.append(cons)
deduction.append(expression)
deduction.append(cons.args[1])
"((!(A|!A)->(!A->!(A|!A)))->((!(A|!A)->((!A->!(A|!A))->!!A))->(!(A|!A)->!!A)))",
"((!(A|!A)->((!A->!(A|!A))->!!A))->(!(A|!A)->!!A))",
"(!(A|!A)->!!A)",
"(!(A|!A)->!A)->(!(A|!A)->!!A)->!!(A|!A)",
"(!(A|!A)->!!A)->!!(A|!A)",
"!!(A|!A)",
"!!(A|!A)->(A|!A)",
"A|!A"
]
simpleProves = {
'!A,!B|-!(A|B)': FF_F_OR,
'!A,B|-(A|B)': FT_T_OR,
'A,!B|-(A|B)': TF_T_OR,
'A,B|-(A|B)': TT_T_OR,
'!A,!B|-!(A&B)': FF_F_AND,
'!A,B|-!(A&B)': FT_F_AND,
'A,!B|-!(A&B)': TF_F_AND,
'A,B|-(A&B)': TT_T_AND,
'!A,!B|-(A->B)': FF_T_CONS,
'!A,B|-(A->B)': FT_T_CONS,
'A,!B|-!(A->B)': TF_F_CONS,
'A,B|-(A->B)': TT_T_CONS,
'|-A|!A': T_F_OR,
'!A|-!A': F_F_NOT,
'A|-!!A': T_F_NOT
}
for key in simpleProves:
simpleProves[key] = [parser.parse(line) for line in simpleProves[key]]
