def _check_antecedents(g1, g2, x):
    from sympy import re, Eq, Ne, cos, I, exp, sin, sign, unpolarify
    from sympy import arg as arg_, unbranched_argument as arg
    #  Yes, this is madness.
    # XXX TODO this is a testing *nightmare*
    # NOTE if you update these conditions, please update the documentation as well

    # The following conditions are found in
    # [P], Section 2.24.1
    #
    # They are also reproduced (verbatim!) at
    # http://functions.wolfram.com/HypergeometricFunctions/MeijerG/21/02/03/
    #
    # Note: k=l=r=alpha=1
    sigma, _ = _get_coeff_exp(g1.argument, x)
    omega, _ = _get_coeff_exp(g2.argument, x)
    s, t, u, v = S([len(g1.bm), len(g1.an), len(g1.ap), len(g1.bq)])
    m, n, p, q = S([len(g2.bm), len(g2.an), len(g2.ap), len(g2.bq)])
    bstar = s + t - (u + v)/2
    cstar = m + n - (p + q)/2
    rho = g1.nu + (u - v)/2 + 1
    mu = g2.nu + (p - q)/2 + 1
    phi = q - p - (v - u)
    eta = 1 - (v - u) - mu - rho
    psi = (pi*(q - m - n) + abs(arg(omega)))/(q - p)
    theta = (pi*(v - s - t) + abs(arg(sigma)))/(v - u)

    _debug('Checking antecedents:')
    _debug('  sigma=%s, s=%s, t=%s, u=%s, v=%s, b*=%s, rho=%s'
           % (sigma, s, t, u, v, bstar, rho))
    _debug('  omega=%s, m=%s, n=%s, p=%s, q=%s, c*=%s, mu=%s,'
           % (omega, m, n, p, q, cstar, mu))
    _debug('  phi=%s, eta=%s, psi=%s, theta=%s' % (phi, eta, psi, theta))

    def _c1():
        for g in [g1, g2]:
            for i in g.an:
                for j in g.bm:
                    diff = i - j
                    if diff.is_integer and diff.is_positive:
                        return False
        return True
    c1 = _c1()
    c2 = And(*[re(1 + i + j) > 0 for i in g1.bm for j in g2.bm])
    c3 = And(*[re(1 + i + j) < 1 + 1 for i in g1.an for j in g2.an])
    c4 = And(*[(p - q)*re(1 + i - 1) - re(mu) > -S(3)/2 for i in g1.an])
    c5 = And(*[(p - q)*re(1 + i) - re(mu) > -S(3)/2 for i in g1.bm])
    c6 = And(*[(u - v)*re(1 + i - 1) - re(rho) > -S(3)/2 for i in g2.an])
    c7 = And(*[(u - v)*re(1 + i) - re(rho) > -S(3)/2 for i in g2.bm])
    c8 = (abs(phi) + 2*re((rho - 1)*(q - p) + (v - u)*(q - p) + (mu -
          1)*(v - u)) > 0)
    c9 = (abs(phi) - 2*re((rho - 1)*(q - p) + (v - u)*(q - p) + (mu -
          1)*(v - u)) > 0)
    c10 = (abs(arg(sigma)) < bstar*pi)
    c11 = Eq(abs(arg(sigma)), bstar*pi)
    c12 = (abs(arg(omega)) < cstar*pi)
    c13 = Eq(abs(arg(omega)), cstar*pi)

    # The following condition is *not* implemented as stated on the wolfram
    # function site. In the book of Prudnikov there is an additional part
    # (the And involving re()). However, I only have this book in russian, and
    # I don't read any russian. The following condition is what other people
    # have told me it means.
    # Worryingly, it is different from the condition implemented in REDUCE.
    # The REDUCE implementation:
    #   https://reduce-algebra.svn.sourceforge.net/svnroot/reduce-algebra/trunk/packages/defint/definta.red
    #   (search for tst14)
    # The Wolfram alpha version:
    #   http://functions.wolfram.com/HypergeometricFunctions/MeijerG/21/02/03/03/0014/
    z0 = exp(-(bstar + cstar)*pi*I)
    zos = unpolarify(z0*omega/sigma)
    zso = unpolarify(z0*sigma/omega)
    if zos == 1/zso:
        c14 = And(Eq(phi, 0), bstar + cstar <= 1,
                  Or(Ne(zos, 1), re(mu + rho + v - u) < 1,
                     re(mu + rho + q - p) < 1))
    else:
        c14 = And(Eq(phi, 0), bstar - 1 + cstar <= 0,
                  Or(And(Ne(zos, 1), abs(arg_(1 - zos)) < pi),
                     And(re(mu + rho + v - u) < 1, Eq(zos, 1))))

        def _cond():
            '''
            Note: if `zso` is 1 then tmp will be NaN.  This raises a
            TypeError on `NaN < pi`.  Previously this gave `False` so
            this behavior has been hardcoded here but someone should
            check if this NaN is more serious! This NaN is triggered by
            test_meijerint() in test_meijerint.py:
            `meijerint_definite(exp(x), x, 0, I)`
            '''
            tmp = abs(arg_(1 - zso))
            return False if tmp is S.NaN else tmp < pi
        c14_alt = And(Eq(phi, 0), cstar - 1 + bstar <= 0,
                  Or(And(Ne(zso, 1), _cond()),
                     And(re(mu + rho + q - p) < 1, Eq(zso, 1))))

        # Since r=k=l=1, in our case there is c14_alt which is the same as calling
        # us with (g1, g2) = (g2, g1). The conditions below enumerate all cases
        # (i.e. we don't have to try arguments reversed by hand), and indeed try
        # all symmetric cases. (i.e. whenever there is a condition involving c14,
        # there is also a dual condition which is exactly what we would get when g1,
        # g2 were interchanged, *but c14 was unaltered*).
        # Hence the following seems correct:
        c14 = Or(c14, c14_alt)

    '''
    When `c15` is NaN (e.g. from `psi` being NaN as happens during
    'test_issue_4992' and/or `theta` is NaN as in 'test_issue_6253',
    both in `test_integrals.py`) the comparison to 0 formerly gave False
    whereas now an error is raised. To keep the old behavior, the value
    of NaN is replaced with False but perhaps a closer look at this condition
    should be made: XXX how should conditions leading to c15=NaN be handled?
    '''
    try:
        lambda_c = (q - p)*abs(omega)**(1/(q - p))*cos(psi) \
            + (v - u)*abs(sigma)**(1/(v - u))*cos(theta)
        # the TypeError might be raised here, e.g. if lambda_c is NaN
        if _eval_cond(lambda_c > 0) != False:
            c15 = (lambda_c > 0)
        else:
            def lambda_s0(c1, c2):
                return c1*(q - p)*abs(omega)**(1/(q - p))*sin(psi) \
                    + c2*(v - u)*abs(sigma)**(1/(v - u))*sin(theta)
            lambda_s = Piecewise(
                ((lambda_s0(+1, +1)*lambda_s0(-1, -1)),
                 And(Eq(arg(sigma), 0), Eq(arg(omega), 0))),
                (lambda_s0(sign(arg(omega)), +1)*lambda_s0(sign(arg(omega)), -1),
                 And(Eq(arg(sigma), 0), Ne(arg(omega), 0))),
                (lambda_s0(+1, sign(arg(sigma)))*lambda_s0(-1, sign(arg(sigma))),
                 And(Ne(arg(sigma), 0), Eq(arg(omega), 0))),
                (lambda_s0(sign(arg(omega)), sign(arg(sigma))), True))
            tmp = [lambda_c > 0,
                   And(Eq(lambda_c, 0), Ne(lambda_s, 0), re(eta) > -1),
                   And(Eq(lambda_c, 0), Eq(lambda_s, 0), re(eta) > 0)]
            c15 = Or(*tmp)
    except TypeError:
        c15 = False
    for cond, i in [(c1, 1), (c2, 2), (c3, 3), (c4, 4), (c5, 5), (c6, 6),
                    (c7, 7), (c8, 8), (c9, 9), (c10, 10), (c11, 11),
                    (c12, 12), (c13, 13), (c14, 14), (c15, 15)]:
        _debug('  c%s:' % i, cond)

    # We will return Or(*conds)
    conds = []

    def pr(count):
        _debug('  case %s:' % count, conds[-1])
    conds += [And(m*n*s*t != 0, bstar.is_positive is True, cstar.is_positive is True, c1, c2, c3, c10,
                  c12)]  # 1
    pr(1)
    conds += [And(Eq(u, v), Eq(bstar, 0), cstar.is_positive is True, sigma.is_positive is True, re(rho) < 1,
                  c1, c2, c3, c12)]  # 2
    pr(2)
    conds += [And(Eq(p, q), Eq(cstar, 0), bstar.is_positive is True, omega.is_positive is True, re(mu) < 1,
                  c1, c2, c3, c10)]  # 3
    pr(3)
    conds += [And(Eq(p, q), Eq(u, v), Eq(bstar, 0), Eq(cstar, 0),
                  sigma.is_positive is True, omega.is_positive is True, re(mu) < 1, re(rho) < 1,
                  Ne(sigma, omega), c1, c2, c3)]  # 4
    pr(4)
    conds += [And(Eq(p, q), Eq(u, v), Eq(bstar, 0), Eq(cstar, 0),
                  sigma.is_positive is True, omega.is_positive is True, re(mu + rho) < 1,
                  Ne(omega, sigma), c1, c2, c3)]  # 5
    pr(5)
    conds += [And(p > q, s.is_positive is True, bstar.is_positive is True, cstar >= 0,
                  c1, c2, c3, c5, c10, c13)]  # 6
    pr(6)
    conds += [And(p < q, t.is_positive is True, bstar.is_positive is True, cstar >= 0,
                  c1, c2, c3, c4, c10, c13)]  # 7
    pr(7)
    conds += [And(u > v, m.is_positive is True, cstar.is_positive is True, bstar >= 0,
                  c1, c2, c3, c7, c11, c12)]  # 8
    pr(8)
    conds += [And(u < v, n.is_positive is True, cstar.is_positive is True, bstar >= 0,
                  c1, c2, c3, c6, c11, c12)]  # 9
    pr(9)
    conds += [And(p > q, Eq(u, v), Eq(bstar, 0), cstar >= 0, sigma.is_positive is True,
                  re(rho) < 1, c1, c2, c3, c5, c13)]  # 10
    pr(10)
    conds += [And(p < q, Eq(u, v), Eq(bstar, 0), cstar >= 0, sigma.is_positive is True,
                  re(rho) < 1, c1, c2, c3, c4, c13)]  # 11
    pr(11)
    conds += [And(Eq(p, q), u > v, bstar >= 0, Eq(cstar, 0), omega.is_positive is True,
                  re(mu) < 1, c1, c2, c3, c7, c11)]  # 12
    pr(12)
    conds += [And(Eq(p, q), u < v, bstar >= 0, Eq(cstar, 0), omega.is_positive is True,
                  re(mu) < 1, c1, c2, c3, c6, c11)]  # 13
    pr(13)
    conds += [And(p < q, u > v, bstar >= 0, cstar >= 0,
                  c1, c2, c3, c4, c7, c11, c13)]  # 14
    pr(14)
    conds += [And(p > q, u < v, bstar >= 0, cstar >= 0,
                  c1, c2, c3, c5, c6, c11, c13)]  # 15
    pr(15)
    conds += [And(p > q, u > v, bstar >= 0, cstar >= 0,
                  c1, c2, c3, c5, c7, c8, c11, c13, c14)]  # 16
    pr(16)
    conds += [And(p < q, u < v, bstar >= 0, cstar >= 0,
                  c1, c2, c3, c4, c6, c9, c11, c13, c14)]  # 17
    pr(17)
    conds += [And(Eq(t, 0), s.is_positive is True, bstar.is_positive is True, phi.is_positive is True, c1, c2, c10)]  # 18
    pr(18)
    conds += [And(Eq(s, 0), t.is_positive is True, bstar.is_positive is True, phi.is_negative is True, c1, c3, c10)]  # 19
    pr(19)
    conds += [And(Eq(n, 0), m.is_positive is True, cstar.is_positive is True, phi.is_negative is True, c1, c2, c12)]  # 20
    pr(20)
    conds += [And(Eq(m, 0), n.is_positive is True, cstar.is_positive is True, phi.is_positive is True, c1, c3, c12)]  # 21
    pr(21)
    conds += [And(Eq(s*t, 0), bstar.is_positive is True, cstar.is_positive is True,
                  c1, c2, c3, c10, c12)]  # 22
    pr(22)
    conds += [And(Eq(m*n, 0), bstar.is_positive is True, cstar.is_positive is True,
                  c1, c2, c3, c10, c12)]  # 23
    pr(23)

    # The following case is from [Luke1969]. As far as I can tell, it is *not*
    # covered by Prudnikov's.
    # Let G1 and G2 be the two G-functions. Suppose the integral exists from
    # 0 to a > 0 (this is easy the easy part), that G1 is exponential decay at
    # infinity, and that the mellin transform of G2 exists.
    # Then the integral exists.
    mt1_exists = _check_antecedents_1(g1, x, helper=True)
    mt2_exists = _check_antecedents_1(g2, x, helper=True)
    conds += [And(mt2_exists, Eq(t, 0), u < s, bstar.is_positive is True, c10, c1, c2, c3)]
    pr('E1')
    conds += [And(mt2_exists, Eq(s, 0), v < t, bstar.is_positive is True, c10, c1, c2, c3)]
    pr('E2')
    conds += [And(mt1_exists, Eq(n, 0), p < m, cstar.is_positive is True, c12, c1, c2, c3)]
    pr('E3')
    conds += [And(mt1_exists, Eq(m, 0), q < n, cstar.is_positive is True, c12, c1, c2, c3)]
    pr('E4')

    # Let's short-circuit if this worked ...
    # the rest is corner-cases and terrible to read.
    r = Or(*conds)
    if _eval_cond(r) != False:
        return r

    conds += [And(m + n > p, Eq(t, 0), Eq(phi, 0), s.is_positive is True, bstar.is_positive is True, cstar.is_negative is True,
                  abs(arg(omega)) < (m + n - p + 1)*pi,
                  c1, c2, c10, c14, c15)]  # 24
    pr(24)
    conds += [And(m + n > q, Eq(s, 0), Eq(phi, 0), t.is_positive is True, bstar.is_positive is True, cstar.is_negative is True,
                  abs(arg(omega)) < (m + n - q + 1)*pi,
                  c1, c3, c10, c14, c15)]  # 25
    pr(25)
    conds += [And(Eq(p, q - 1), Eq(t, 0), Eq(phi, 0), s.is_positive is True, bstar.is_positive is True,
                  cstar >= 0, cstar*pi < abs(arg(omega)),
                  c1, c2, c10, c14, c15)]  # 26
    pr(26)
    conds += [And(Eq(p, q + 1), Eq(s, 0), Eq(phi, 0), t.is_positive is True, bstar.is_positive is True,
                  cstar >= 0, cstar*pi < abs(arg(omega)),
                  c1, c3, c10, c14, c15)]  # 27
    pr(27)
    conds += [And(p < q - 1, Eq(t, 0), Eq(phi, 0), s.is_positive is True, bstar.is_positive is True,
                  cstar >= 0, cstar*pi < abs(arg(omega)),
                  abs(arg(omega)) < (m + n - p + 1)*pi,
                  c1, c2, c10, c14, c15)]  # 28
    pr(28)
    conds += [And(
        p > q + 1, Eq(s, 0), Eq(phi, 0), t.is_positive is True, bstar.is_positive is True, cstar >= 0,
                  cstar*pi < abs(arg(omega)),
                  abs(arg(omega)) < (m + n - q + 1)*pi,
                  c1, c3, c10, c14, c15)]  # 29
    pr(29)
    conds += [And(Eq(n, 0), Eq(phi, 0), s + t > 0, m.is_positive is True, cstar.is_positive is True, bstar.is_negative is True,
                  abs(arg(sigma)) < (s + t - u + 1)*pi,
                  c1, c2, c12, c14, c15)]  # 30
    pr(30)
    conds += [And(Eq(m, 0), Eq(phi, 0), s + t > v, n.is_positive is True, cstar.is_positive is True, bstar.is_negative is True,
                  abs(arg(sigma)) < (s + t - v + 1)*pi,
                  c1, c3, c12, c14, c15)]  # 31
    pr(31)
    conds += [And(Eq(n, 0), Eq(phi, 0), Eq(u, v - 1), m.is_positive is True, cstar.is_positive is True,
                  bstar >= 0, bstar*pi < abs(arg(sigma)),
                  abs(arg(sigma)) < (bstar + 1)*pi,
                  c1, c2, c12, c14, c15)]  # 32
    pr(32)
    conds += [And(Eq(m, 0), Eq(phi, 0), Eq(u, v + 1), n.is_positive is True, cstar.is_positive is True,
                  bstar >= 0, bstar*pi < abs(arg(sigma)),
                  abs(arg(sigma)) < (bstar + 1)*pi,
                  c1, c3, c12, c14, c15)]  # 33
    pr(33)
    conds += [And(
        Eq(n, 0), Eq(phi, 0), u < v - 1, m.is_positive is True, cstar.is_positive is True, bstar >= 0,
        bstar*pi < abs(arg(sigma)),
        abs(arg(sigma)) < (s + t - u + 1)*pi,
        c1, c2, c12, c14, c15)]  # 34
    pr(34)
    conds += [And(
        Eq(m, 0), Eq(phi, 0), u > v + 1, n.is_positive is True, cstar.is_positive is True, bstar >= 0,
        bstar*pi < abs(arg(sigma)),
        abs(arg(sigma)) < (s + t - v + 1)*pi,
        c1, c3, c12, c14, c15)]  # 35
    pr(35)

    return Or(*conds)

    # NOTE An alternative, but as far as I can tell weaker, set of conditions
    #      can be found in [L, section 5.6.2].
Return a condition under which the integral theorem applies.
dataset/ETHPy150Open sympy/sympy/sympy/integrals/meijerint.py/_check_antecedents