# 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_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,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,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,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,X1)))),file('i/f/real/REAL__LT__LMUL__0', ch4s_reals_REALu_u_LTu_u_LMULu_u_0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/real/REAL__LT__LMUL__0', aHLu_TRUTH)).
fof(4, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/real/REAL__LT__LMUL__0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(8, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/real/REAL__LT__LMUL__0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X7]:![X1]:![X2]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X7)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,X7))),file('i/f/real/REAL__LT__LMUL__0', ah4s_reals_REALu_u_MULu_u_ASSOC)).
fof(10, 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,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_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))))))),file('i/f/real/REAL__LT__LMUL__0', ah4s_reals_REALu_u_LTu_u_MUL)).
fof(11, axiom,![X1]:![X2]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))))=>~(s(t_h4s_realaxs_real,X2)=s(t_h4s_realaxs_real,X1))),file('i/f/real/REAL__LT__LMUL__0', ah4s_reals_REALu_u_LTu_u_IMPu_u_NE)).
fof(12, axiom,![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,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,h4s_realaxs_inv(s(t_h4s_realaxs_real,X2))))))),file('i/f/real/REAL__LT__LMUL__0', ah4s_reals_REALu_u_INVu_u_POS)).
fof(13, axiom,![X2]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(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))))))),s(t_h4s_realaxs_real,X2)))=s(t_h4s_realaxs_real,X2),file('i/f/real/REAL__LT__LMUL__0', ah4s_reals_REALu_u_MULu_u_LID)).
fof(14, axiom,![X2]:(~(s(t_h4s_realaxs_real,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_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,X2)))=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__LT__LMUL__0', ah4s_reals_REALu_u_MULu_u_LINV)).
fof(15, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/real/REAL__LT__LMUL__0', aHLu_BOOLu_CASES)).
fof(16, axiom,~(p(s(t_bool,f))),file('i/f/real/REAL__LT__LMUL__0', aHLu_FALSITY)).
# SZS output end CNFRefutation
