# 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))))&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)))))=s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_nums_num,X1))))),file('i/f/integral/DIVISION__DSIZE__LE', ch4s_integrals_DIVISIONu_u_DSIZEu_u_LE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/integral/DIVISION__DSIZE__LE', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/integral/DIVISION__DSIZE__LE', aHLu_FALSITY)).
fof(19, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/integral/DIVISION__DSIZE__LE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(20, axiom,![X7]:(s(t_bool,X7)=s(t_bool,f)<=>~(p(s(t_bool,X7)))),file('i/f/integral/DIVISION__DSIZE__LE', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(41, axiom,![X1]:![X16]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),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,X16))))),file('i/f/integral/DIVISION__DSIZE__LE', ah4s_arithmetics_NOTu_u_LESS)).
fof(42, axiom,![X3]:![X4]:![X17]:(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),X17))))<=>(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X17),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),X17))))))=>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),X17),s(t_h4s_nums_num,X1))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X17),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),X17))))))=>s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X17),s(t_h4s_nums_num,X1)))=s(t_h4s_realaxs_real,X3))))),file('i/f/integral/DIVISION__DSIZE__LE', ah4s_transcs_DIVISIONu_u_THM)).
fof(45, 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__LE', ah4s_reals_REALu_u_LTu_u_REFL)).
# SZS output end CNFRefutation
