# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]: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))),h4s_ratrings_ratu_u_ru_u_varlistu_u_insert),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_varlist(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_varlist(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_varlist(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,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_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_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_varlist(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))),h4s_ratrings_ratu_u_ru_u_varlistu_u_insert),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_c22', ch4s_ratRings_ratu_u_ringu_u_thmsu_c22)).
fof(5, axiom,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))),h4s_ratrings_ratu_u_ru_u_varlistu_u_insert)=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))),h4s_ringnorms_ru_u_varlistu_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_c22', ah4s_ratRings_ratu_u_ru_u_varlistu_u_insertu_u_def)).
fof(9, axiom,![X4]:![X1]:![X14]:![X2]:![X3]:s(t_h4s_canonicals_canonicalu_u_sum(X4),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4))),h4s_ringnorms_ru_u_varlistu_u_insert(s(t_h4s_rings_ring(X4),X14))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X4),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X4),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X4),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(X4),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X4),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X4),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(X4),h4s_canonicals_consu_u_monom(s(X4,happ(s(t_fun(X4,X4),happ(s(t_fun(X4,t_fun(X4,X4)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X4),X14))),s(X4,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X4),X14))))),s(X4,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X4),X14))))),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X4),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X4),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X4),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4))),h4s_ringnorms_ru_u_varlistu_u_insert(s(t_h4s_rings_ring(X4),X14))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X4),X1))))))),file('i/f/ratRing/rat__ring__thms_c22', ah4s_ringNorms_varlistu_u_insertu_u_defu_c1)).
fof(13, axiom,![X4]:![X15]:![X16]:![X9]:![X17]:![X18]:s(X4,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X4),h4s_rings_ring0(s(X4,X18),s(X4,X17),s(t_fun(X4,t_fun(X4,X4)),X9),s(t_fun(X4,t_fun(X4,X4)),X16),s(t_fun(X4,X4),X15)))))=s(X4,X17),file('i/f/ratRing/rat__ring__thms_c22', ah4s_rings_ringu_u_accessorsu_c1)).
fof(14, axiom,![X4]:![X15]:![X16]:![X9]:![X17]:![X18]:s(t_fun(X4,t_fun(X4,X4)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X4),h4s_rings_ring0(s(X4,X18),s(X4,X17),s(t_fun(X4,t_fun(X4,X4)),X9),s(t_fun(X4,t_fun(X4,X4)),X16),s(t_fun(X4,X4),X15)))))=s(t_fun(X4,t_fun(X4,X4)),X9),file('i/f/ratRing/rat__ring__thms_c22', ah4s_rings_ringu_u_accessorsu_c2)).
# SZS output end CNFRefutation
