# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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,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_realaxs_inv(s(t_h4s_realaxs_real,X1))))))),file('i/f/real/REAL__INV__POS', ch4s_reals_REALu_u_INVu_u_POS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/real/REAL__INV__POS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/real/REAL__INV__POS', aHLu_FALSITY)).
fof(5, axiom,![X2]:![X3]:((p(s(t_bool,X3))=>p(s(t_bool,X2)))=>((p(s(t_bool,X2))=>p(s(t_bool,X3)))=>s(t_bool,X3)=s(t_bool,X2))),file('i/f/real/REAL__INV__POS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,![X5]:![X1]:(s(t_h4s_realaxs_real,X1)=s(t_h4s_realaxs_real,X5)|(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X5))))|p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X1)))))),file('i/f/real/REAL__INV__POS', ah4s_reals_REALu_u_LTu_u_TOTAL)).
fof(10, axiom,![X5]:![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,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,X5)))))=>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_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X5))))))),file('i/f/real/REAL__INV__POS', ah4s_reals_REALu_u_LTu_u_MUL)).
fof(11, axiom,![X5]:![X1]:~((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X5))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X1)))))),file('i/f/real/REAL__INV__POS', ah4s_reals_REALu_u_LTu_u_ANTISYM)).
fof(12, axiom,![X5]:![X1]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X5))))=>~(s(t_h4s_realaxs_real,X1)=s(t_h4s_realaxs_real,X5))),file('i/f/real/REAL__INV__POS', ah4s_reals_REALu_u_LTu_u_IMPu_u_NE)).
fof(13, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/real/REAL__INV__POS', aHLu_BOOLu_CASES)).
fof(15, axiom,![X1]: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_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X1)))))=s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/real/REAL__INV__POS', ah4s_reals_REALu_u_NEGu_u_GT0)).
fof(16, axiom,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,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))),file('i/f/real/REAL__INV__POS', ah4s_reals_REALu_u_LTu_u_01)).
fof(17, axiom,![X1]:(~(s(t_h4s_realaxs_real,X1)=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_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,X1)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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/real/REAL__INV__POS', ah4s_reals_REALu_u_MULu_u_LINV)).
fof(18, axiom,![X1]:(~(s(t_h4s_realaxs_real,X1)=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_realaxs_inv(s(t_h4s_realaxs_real,X1)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/real/REAL__INV__POS', ah4s_reals_REALu_u_INVu_u_NZ)).
fof(19, axiom,![X5]:![X1]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X5)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,X5))),file('i/f/real/REAL__INV__POS', ah4s_reals_REALu_u_NEGu_u_LMUL)).
# SZS output end CNFRefutation
