# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(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,X1))),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,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/le__int_c2', ch4s_reals_leu_u_intu_c2)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/real/le__int_c2', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/real/le__int_c2', aHLu_FALSITY)).
fof(6, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/real/le__int_c2', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/real/le__int_c2', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X3]:(s(t_bool,f)=s(t_bool,X3)<=>~(p(s(t_bool,X3)))),file('i/f/real/le__int_c2', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(14, 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/le__int_c2', ah4s_reals_REALu_u_POS)).
fof(16, 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/le__int_c2', ah4s_primu_u_recs_LESSu_u_0)).
fof(17, axiom,![X2]:(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/real/le__int_c2', ah4s_arithmetics_numu_u_CASES)).
fof(18, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0))))<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/real/le__int_c2', ah4s_arithmetics_LESSu_u_EQu_u_0)).
fof(19, 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/le__int_c2', ah4s_reals_REALu_u_NEGu_u_LT0)).
fof(20, 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/le__int_c2', ah4s_reals_REALu_u_NEGu_u_0)).
fof(21, axiom,![X1]:![X2]: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,X2))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),file('i/f/real/le__int_c2', ah4s_reals_REALu_u_LE)).
fof(22, 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/le__int_c2', ah4s_reals_REALu_u_LT)).
fof(23, axiom,![X8]:![X7]:(~(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X8)))))<=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X7))))),file('i/f/real/le__int_c2', ah4s_reals_REALu_u_NOTu_u_LE)).
fof(24, axiom,![X9]:![X8]:![X7]:((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X8))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X9)))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X9))))),file('i/f/real/le__int_c2', ah4s_reals_REALu_u_LTEu_u_TRANS)).
# SZS output end CNFRefutation
