# -*- 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)
from proofs import simpleProves
import re
import time
import sys
read = 'test.in'
write = 'test.out'
if len(sys.argv) > 1:
read = sys.argv[1]
if len(sys.argv) > 2:
write = sys.argv[2]
fr = open(read)
fw = open(write, 'w')
parser = Parser_()
def assumption_pop(assumptions, alpha, formula, old_proof_negated, old_proof):
proof = deduction(assumptions, alpha, old_proof) # Вывод Г |- alpha -> formula - (1)
proof.extend(deduction(assumptions, Negation(alpha), old_proof_negated)) # Вывод Г |- !alpha -> formula - (2)
proof.extend(
[eval_by_mapping(line, {'A': alpha}) for line in simpleProves['|-A|!A']]
) # док-во alpha|!alpha - (3)
mapping = {'A': alpha, 'B': formula, 'C': Negation(alpha)}
proof.append(eval_by_mapping(parsed_axioms[7][0], mapping)) # сх. аксиом 8 - (4)
proof.append(eval_by_mapping(parsed_axioms[7][0].right, mapping)) # M.P. последнее выражение в (1), (4) - (5)
proof.append(eval_by_mapping(parsed_axioms[7][0].right.right, mapping)) # M.P. последнее выражение в (2), (5) - (6)
proof.append(eval_by_mapping(parsed_axioms[7][0].right.right.right, mapping)) # M.P. последнее выражение в (3), (6)
return proof
from axioms import axioms, scheme_axiom, axiom_induction, axiom_universal, axiom_existence, semi_cons
from substitute import subst, find_mismatch, subst_pred
from math_expressions import Variable, Zero, Increment
from logic_expressions import Consequence, Universal, Existence, Predicate
from util import ConnectedEntryException
from copy import copy
import sys
import time
read = 'test.in'
write = 'test.out'
if len(sys.argv) > 1:
read = sys.argv[1]
if len(sys.argv) > 2:
write = sys.argv[2]
parser = Parser_()
read = open(read)
write = open(write, 'w')
uni_rule = open('uni_quantifier.proof')
exist_rule = open('exist_quantifier.proof')
def split_by_comma(assump):
sum = 0
last_pos = 0
ans = []
for i, a in enumerate(assump):
if a == '(':
sum += 1
# -*- coding: utf-8 -*-
from parser_ import Parser_
parser = Parser_()
# !a,b|-(a->b)
FT_T_CONS = [
"B->A->B",
"B",
"A->B"
]
# a,!b|-!(a&b)
TF_F_AND = [
"((A&B)->B)->((A&B)->!B)->!(A&B)",
"(A&B)->B ",
"(A&B->!B)->!(A&B)",
"!B->A&B->!B",
"!B",
"A&B->!B",
"!(A&B)"
]
# !a,b|-!(a&b)
FT_F_AND = [
"((A&B)->A)->((A&B)->!A)->!(A&B)",
"(A&B)->A ",
"(A&B->!A)->!(A&B)",
"!A->A&B->!A",
"!A",
"A&B->!A",
"!(A&B)"
]
# a->b|-(!b->!a)
