# 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,X3),s(t_h4s_realaxs_real,X2))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))))=>![X4]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1),s(t_h4s_nums_num,X4))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4))))))))),file('i/f/integral/DIVISION__LE__SUC', ch4s_integrals_DIVISIONu_u_LEu_u_SUC)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/integral/DIVISION__LE__SUC', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/integral/DIVISION__LE__SUC', aHLu_FALSITY)).
fof(20, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/integral/DIVISION__LE__SUC', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(21, axiom,![X7]:(s(t_bool,X7)=s(t_bool,f)<=>~(p(s(t_bool,X7)))),file('i/f/integral/DIVISION__LE__SUC', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(41, axiom,![X9]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X9),s(t_h4s_realaxs_real,X9)))),file('i/f/integral/DIVISION__LE__SUC', ah4s_reals_REALu_u_LEu_u_REFL)).
fof(42, axiom,![X17]:![X9]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X9),s(t_h4s_realaxs_real,X17))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X9),s(t_h4s_realaxs_real,X17))))),file('i/f/integral/DIVISION__LE__SUC', ah4s_reals_REALu_u_LTu_u_IMPu_u_LE)).
fof(46, axiom,![X2]:![X3]:![X24]:(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,X3),s(t_h4s_realaxs_real,X2))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X24))))<=>(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X24),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_realaxs_real,X3)&(![X4]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X24))))))=>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),X24),s(t_h4s_nums_num,X4))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X24),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4)))))))))&![X4]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X24))))))=>s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X24),s(t_h4s_nums_num,X4)))=s(t_h4s_realaxs_real,X2))))),file('i/f/integral/DIVISION__LE__SUC', ah4s_transcs_DIVISIONu_u_THM)).
fof(47, axiom,![X4]:![X25]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4))))))<=>(s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4)))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X4)))))),file('i/f/integral/DIVISION__LE__SUC', ah4s_arithmetics_LEu_c1)).
fof(48, axiom,![X4]:![X25]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X4))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X25))))),file('i/f/integral/DIVISION__LE__SUC', ah4s_arithmetics_LESSu_u_CASES)).
fof(49, axiom,![X4]:![X25]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X25)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X4))),file('i/f/integral/DIVISION__LE__SUC', ah4s_arithmetics_GREATERu_u_EQ)).
fof(51, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/integral/DIVISION__LE__SUC', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
