# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((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,X4),s(t_h4s_realaxs_real,X3))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))))&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),X2),s(t_h4s_nums_num,X1))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))))))),file('i/f/integral/DIVISION__DSIZE__GE', ch4s_integrals_DIVISIONu_u_DSIZEu_u_GE)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/integral/DIVISION__DSIZE__GE', aHLu_FALSITY)).
fof(29, axiom,![X1]:![X18]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X1)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,X1))),file('i/f/integral/DIVISION__DSIZE__GE', ah4s_arithmetics_LESSu_u_EQ)).
fof(30, axiom,![X1]:![X18]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X18))))),file('i/f/integral/DIVISION__DSIZE__GE', ah4s_arithmetics_NOTu_u_LESS)).
fof(31, axiom,![X1]:![X18]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X18)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X1))),file('i/f/integral/DIVISION__DSIZE__GE', ah4s_arithmetics_GREATERu_u_EQ)).
fof(33, axiom,![X1]:![X18]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))))<=>(s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X1)))))),file('i/f/integral/DIVISION__DSIZE__GE', ah4s_arithmetics_LEu_c1)).
fof(34, axiom,![X3]:![X4]:![X19]:(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,X4),s(t_h4s_realaxs_real,X3))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X19))))<=>(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X19),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_realaxs_real,X4)&(![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X19))))))=>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),X19),s(t_h4s_nums_num,X1))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X19),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))))))&![X1]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X19))))))=>s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X19),s(t_h4s_nums_num,X1)))=s(t_h4s_realaxs_real,X3))))),file('i/f/integral/DIVISION__DSIZE__GE', ah4s_transcs_DIVISIONu_u_THM)).
fof(37, axiom,![X9]:~(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X9),s(t_h4s_realaxs_real,X9))))),file('i/f/integral/DIVISION__DSIZE__GE', ah4s_reals_REALu_u_LTu_u_REFL)).
fof(38, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/integral/DIVISION__DSIZE__GE', aHLu_BOOLu_CASES)).
fof(39, axiom,p(s(t_bool,t)),file('i/f/integral/DIVISION__DSIZE__GE', aHLu_TRUTH)).
fof(42, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)<=>p(s(t_bool,X8))),file('i/f/integral/DIVISION__DSIZE__GE', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
