# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(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/eq__ints_c1', ch4s_reals_equ_u_intsu_c1)).
fof(21, axiom,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))),file('i/f/real/eq__ints_c1', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(22, axiom,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))),file('i/f/real/eq__ints_c1', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(23, axiom,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,h4s_nums_0)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/real/eq__ints_c1', ah4s_reals_REALu_u_NEGu_u_0)).
fof(24, axiom,![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/real/eq__ints_c1', ah4s_arithmetics_SUBu_u_EQUALu_u_0)).
fof(26, axiom,![X1]:(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))=>p(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,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X1))))))),file('i/f/real/eq__ints_c1', ah4s_reals_REALu_u_NZu_u_IMPu_u_LT)).
fof(32, axiom,![X1]:~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/real/eq__ints_c1', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(34, axiom,![X10]:![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X10)<=>(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X10)))|(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,X10),s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/real/eq__ints_c1', ah4s_arithmetics_SUBu_u_RIGHTu_u_EQ)).
fof(35, axiom,![X5]:s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X5)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/real/eq__ints_c1', ah4s_reals_REALu_u_SUBu_u_REFL)).
fof(38, axiom,![X1]:![X2]:(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_h4s_nums_num,X2)=s(t_h4s_nums_num,X1)),file('i/f/real/eq__ints_c1', ah4s_reals_REALu_u_INJ)).
fof(41, axiom,![X1]:![X2]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(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_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))),file('i/f/real/eq__ints_c1', ah4s_reals_REALu_u_ADD)).
fof(48, 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,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))),file('i/f/real/eq__ints_c1', ah4s_reals_REALu_u_LT)).
fof(53, axiom,![X5]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X5)))))=s(t_h4s_realaxs_real,X5),file('i/f/real/eq__ints_c1', ah4s_reals_REALu_u_NEGNEG)).
fof(65, axiom,![X4]:![X5]:s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X4)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X4))))),file('i/f/real/eq__ints_c1', ah4s_reals_realu_u_sub0)).
fof(66, axiom,~(p(s(t_bool,f))),file('i/f/real/eq__ints_c1', aHLu_FALSITY)).
fof(68, axiom,![X8]:((p(s(t_bool,X8))=>p(s(t_bool,f)))<=>s(t_bool,X8)=s(t_bool,f)),file('i/f/real/eq__ints_c1', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
# SZS output end CNFRefutation
