# 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,h4s_nums_0))),s(t_h4s_realaxs_real,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_transcs_root(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_realaxs_real,X1))))))),file('i/f/transc/ROOT__POS', ch4s_transcs_ROOTu_u_POS)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/transc/ROOT__POS', aHLu_FALSITY)).
fof(3, axiom,![X3]:![X1]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X3))))<=>(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X3))))|s(t_h4s_realaxs_real,X1)=s(t_h4s_realaxs_real,X3))),file('i/f/transc/ROOT__POS', ah4s_reals_REALu_u_LEu_u_LT)).
fof(4, 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/transc/ROOT__POS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(8, axiom,![X1]:~(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X1))))),file('i/f/transc/ROOT__POS', ah4s_reals_REALu_u_LTu_u_REFL)).
fof(11, axiom,![X3]:![X1]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X3))))<=>(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X3))))&~(s(t_h4s_realaxs_real,X1)=s(t_h4s_realaxs_real,X3)))),file('i/f/transc/ROOT__POS', ah4s_reals_REALu_u_LTu_u_LE)).
fof(14, axiom,![X3]:![X1]:(s(t_h4s_realaxs_real,X1)=s(t_h4s_realaxs_real,X3)|(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X3))))|p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1)))))),file('i/f/transc/ROOT__POS', ah4s_reals_REALu_u_LTu_u_TOTAL)).
fof(15, axiom,![X3]:![X1]:(~(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X3)))))<=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1))))),file('i/f/transc/ROOT__POS', ah4s_reals_REALu_u_NOTu_u_LT)).
fof(16, axiom,![X3]:![X1]:(~(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X3)))))<=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1))))),file('i/f/transc/ROOT__POS', ah4s_reals_REALu_u_NOTu_u_LE)).
fof(20, axiom,![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,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X2)))))),file('i/f/transc/ROOT__POS', ah4s_reals_REALu_u_POS)).
fof(21, axiom,![X8]:![X3]:![X1]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X3))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X8)))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X8))))),file('i/f/transc/ROOT__POS', ah4s_reals_REALu_u_LEu_u_TRANS)).
fof(22, axiom,![X8]:![X3]:![X1]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X3))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X8)))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X8))))),file('i/f/transc/ROOT__POS', ah4s_reals_REALu_u_LETu_u_TRANS)).
fof(25, axiom,(p(s(t_bool,f))<=>![X6]:p(s(t_bool,X6))),file('i/f/transc/ROOT__POS', ah4s_bools_Fu_u_DEF)).
fof(54, axiom,![X2]:![X17]: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,X17))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X2)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2))),file('i/f/transc/ROOT__POS', ah4s_reals_REALu_u_LE)).
fof(56, axiom,![X1]:![X2]:(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,X1))))=>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_transcs_root(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_realaxs_real,X1))))))),file('i/f/transc/ROOT__POS', ah4s_transcs_ROOTu_u_POSu_u_LT)).
fof(57, axiom,![X2]:s(t_h4s_realaxs_real,h4s_transcs_root(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),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/transc/ROOT__POS', ah4s_transcs_ROOTu_u_0)).
fof(73, axiom,![X2]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/transc/ROOT__POS', ah4s_nums_NOTu_u_SUC)).
fof(75, axiom,![X17]:(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_nums_0)|?[X2]:s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))),file('i/f/transc/ROOT__POS', ah4s_arithmetics_numu_u_CASES)).
fof(76, axiom,![X2]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))),file('i/f/transc/ROOT__POS', ah4s_primu_u_recs_LESSu_u_SUCu_u_REFL)).
fof(77, axiom,![X2]:![X17]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2)))))<=>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,X17))))),file('i/f/transc/ROOT__POS', ah4s_arithmetics_NOTu_u_LEQ)).
fof(79, axiom,![X2]:![X17]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,X2))),file('i/f/transc/ROOT__POS', ah4s_arithmetics_LESSu_u_EQ)).
fof(80, axiom,![X17]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/transc/ROOT__POS', ah4s_arithmetics_ADD1)).
fof(81, axiom,![X2]:![X17]: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,X17))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X2)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2))),file('i/f/transc/ROOT__POS', ah4s_reals_REALu_u_LT)).
# SZS output end CNFRefutation
