# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X1))))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X2))))))<=>(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))|~(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/real/lt__int_c1', ch4s_reals_ltu_u_intu_c1)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/real/lt__int_c1', aHLu_FALSITY)).
fof(14, axiom,![X5]:((p(s(t_bool,X5))=>p(s(t_bool,f)))<=>s(t_bool,X5)=s(t_bool,f)),file('i/f/real/lt__int_c1', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(27, axiom,![X1]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))),file('i/f/real/lt__int_c1', ah4s_primu_u_recs_LESSu_u_0)).
fof(32, axiom,![X7]:s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X7))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X7))),file('i/f/real/lt__int_c1', ah4s_reals_REALu_u_NEGu_u_LT0)).
fof(33, axiom,![X7]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X7))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X7))),file('i/f/real/lt__int_c1', ah4s_reals_REALu_u_NEGu_u_LE0)).
fof(34, axiom,![X1]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))),file('i/f/real/lt__int_c1', ah4s_reals_REALu_u_POS)).
fof(35, axiom,![X1]:![X2]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))),file('i/f/real/lt__int_c1', ah4s_arithmetics_LESSu_u_EQ)).
fof(36, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))),file('i/f/real/lt__int_c1', ah4s_arithmetics_NOTu_u_LESS)).
fof(39, axiom,![X1]:![X2]:(~(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2)))))),file('i/f/real/lt__int_c1', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(40, axiom,![X1]:![X2]:s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X2))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),file('i/f/real/lt__int_c1', ah4s_reals_REALu_u_LT)).
fof(41, axiom,p(s(t_bool,t)),file('i/f/real/lt__int_c1', aHLu_TRUTH)).
fof(47, axiom,![X5]:(s(t_bool,t)=s(t_bool,X5)<=>p(s(t_bool,X5))),file('i/f/real/lt__int_c1', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(49, axiom,![X16]:![X9]:![X7]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X9))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X9),s(t_h4s_realaxs_real,X16)))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X16))))),file('i/f/real/lt__int_c1', ah4s_reals_REALu_u_LETu_u_TRANS)).
# SZS output end CNFRefutation
