# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_transcs_division(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))))),file('i/f/transc/DIVISION__LE', ch4s_transcs_DIVISIONu_u_LE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/transc/DIVISION__LE', aHLu_TRUTH)).
fof(6, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/transc/DIVISION__LE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X5]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X5)))))),file('i/f/transc/DIVISION__LE', ah4s_primu_u_recs_LESSu_u_SUCu_u_REFL)).
fof(8, axiom,![X6]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X6)))),file('i/f/transc/DIVISION__LE', ah4s_reals_REALu_u_LEu_u_REFL)).
fof(9, axiom,![X7]:![X6]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))))),file('i/f/transc/DIVISION__LE', ah4s_reals_REALu_u_LTu_u_IMPu_u_LE)).
fof(10, axiom,![X8]:(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_nums_0)|?[X5]:s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X5)))),file('i/f/transc/DIVISION__LE', ah4s_arithmetics_numu_u_CASES)).
fof(11, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_transcs_division(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))<=>(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_realaxs_real,X2)&(![X5]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,X5))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X5)))))))))&![X5]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))))=>s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,X5)))=s(t_h4s_realaxs_real,X1))))),file('i/f/transc/DIVISION__LE', ah4s_transcs_DIVISIONu_u_THM)).
fof(12, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_transcs_division(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))=>![X5]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X5)))))))))),file('i/f/transc/DIVISION__LE', ah4s_transcs_DIVISIONu_u_LT)).
fof(16, axiom,![X8]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X8)))),file('i/f/transc/DIVISION__LE', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(17, axiom,![X5]:![X8]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X8)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X5))),file('i/f/transc/DIVISION__LE', ah4s_arithmetics_GREATERu_u_EQ)).
fof(18, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/transc/DIVISION__LE', aHLu_BOOLu_CASES)).
fof(19, axiom,~(p(s(t_bool,f))),file('i/f/transc/DIVISION__LE', aHLu_FALSITY)).
# SZS output end CNFRefutation
