# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat))),happ(s(t_fun(t_h4s_rats_rat,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)))),h4s_ratrings_ratu_u_ru_u_monomu_u_insert),s(t_h4s_rats_rat,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_lists_list(t_h4s_quotes_index),X2))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,happ(s(t_fun(t_h4s_rats_rat,t_h4s_rats_rat),happ(s(t_fun(t_h4s_rats_rat,t_fun(t_h4s_rats_rat,t_h4s_rats_rat)),h4s_rats_ratu_u_add),s(t_h4s_rats_rat,X5))),s(t_h4s_rats_rat,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat))),happ(s(t_fun(t_h4s_rats_rat,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)))),h4s_ratrings_ratu_u_ru_u_monomu_u_insert),s(t_h4s_rats_rat,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X1))))))),file('i/f/ratRing/rat__ring__thms_c18', ch4s_ratRings_ratu_u_ringu_u_thmsu_c18)).
fof(4, axiom,![X11]:![X13]:![X14]:![X8]:![X15]:![X16]:s(t_fun(X11,t_fun(X11,X11)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X11),h4s_rings_ring0(s(X11,X16),s(X11,X15),s(t_fun(X11,t_fun(X11,X11)),X8),s(t_fun(X11,t_fun(X11,X11)),X14),s(t_fun(X11,X11),X13)))))=s(t_fun(X11,t_fun(X11,X11)),X8),file('i/f/ratRing/rat__ring__thms_c18', ah4s_rings_ringu_u_accessorsu_c2)).
fof(5, axiom,![X11]:![X1]:![X17]:![X2]:![X3]:![X4]:![X5]:s(t_h4s_canonicals_canonicalu_u_sum(X11),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X11),t_h4s_canonicals_canonicalu_u_sum(X11)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X11),t_h4s_canonicals_canonicalu_u_sum(X11))),happ(s(t_fun(X11,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X11),t_h4s_canonicals_canonicalu_u_sum(X11)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(X11),X17))),s(X11,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X11),h4s_canonicals_consu_u_monom(s(X11,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X11),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X11),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_lists_list(t_h4s_quotes_index),X2))),s(t_h4s_canonicals_canonicalu_u_sum(X11),h4s_canonicals_consu_u_monom(s(X11,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X11),h4s_canonicals_consu_u_monom(s(X11,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X11),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(X11),h4s_canonicals_consu_u_monom(s(X11,happ(s(t_fun(X11,X11),happ(s(t_fun(X11,t_fun(X11,X11)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X11),X17))),s(X11,X5))),s(X11,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X11),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X11),h4s_canonicals_consu_u_monom(s(X11,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X11),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X11),t_h4s_canonicals_canonicalu_u_sum(X11)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X11),t_h4s_canonicals_canonicalu_u_sum(X11))),happ(s(t_fun(X11,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X11),t_h4s_canonicals_canonicalu_u_sum(X11)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(X11),X17))),s(X11,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X11),X1))))))),file('i/f/ratRing/rat__ring__thms_c18', ah4s_ringNorms_monomu_u_insertu_u_defu_c0)).
fof(8, axiom,s(t_fun(t_h4s_rats_rat,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)))),h4s_ratrings_ratu_u_ru_u_monomu_u_insert)=s(t_fun(t_h4s_rats_rat,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(t_h4s_rats_rat),h4s_rings_ring0(s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_rats_rat,h4s_rats_ratu_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_fun(t_h4s_rats_rat,t_fun(t_h4s_rats_rat,t_h4s_rats_rat)),h4s_rats_ratu_u_add),s(t_fun(t_h4s_rats_rat,t_fun(t_h4s_rats_rat,t_h4s_rats_rat)),h4s_rats_ratu_u_mul),s(t_fun(t_h4s_rats_rat,t_h4s_rats_rat),h4s_rats_ratu_u_ainv))))),file('i/f/ratRing/rat__ring__thms_c18', ah4s_ratRings_ratu_u_ru_u_monomu_u_insertu_u_def)).
# SZS output end CNFRefutation
