# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),h4s_numrings_numu_u_spolynomu_u_normalize),s(t_h4s_canonicals_spolynom(t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_h4s_canonicals_spolynom(t_h4s_nums_num)),h4s_canonicals_spconst),s(t_h4s_nums_num,X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)))),h4s_canonicals_consu_u_monom),s(t_h4s_nums_num,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_nilu_u_monom))),file('i/f/numRing/num__ring__thms_c51', ch4s_numRings_numu_u_ringu_u_thmsu_c51)).
fof(9, axiom,![X2]:![X14]:![X1]:s(t_h4s_canonicals_canonicalu_u_sum(X2),happ(s(t_fun(t_h4s_canonicals_spolynom(X2),t_h4s_canonicals_canonicalu_u_sum(X2)),h4s_canonicals_spolynomu_u_normalize(s(t_h4s_semiu_u_rings_semiu_u_ring(X2),X14))),s(t_h4s_canonicals_spolynom(X2),happ(s(t_fun(X2,t_h4s_canonicals_spolynom(X2)),h4s_canonicals_spconst),s(X2,X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X2),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X2),t_h4s_canonicals_canonicalu_u_sum(X2)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X2),t_h4s_canonicals_canonicalu_u_sum(X2))),happ(s(t_fun(X2,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X2),t_h4s_canonicals_canonicalu_u_sum(X2)))),h4s_canonicals_consu_u_monom),s(X2,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))),s(t_h4s_canonicals_canonicalu_u_sum(X2),h4s_canonicals_nilu_u_monom))),file('i/f/numRing/num__ring__thms_c51', ah4s_canonicals_spolynomu_u_normalizeu_u_defu_c1)).
fof(12, axiom,s(t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),h4s_numrings_numu_u_spolynomu_u_normalize)=s(t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),h4s_canonicals_spolynomu_u_normalize(s(t_h4s_semiu_u_rings_semiu_u_ring(t_h4s_nums_num),h4s_semiu_u_rings_semiu_u_ring0(s(t_h4s_nums_num,h4s_nums_0),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_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a))))),file('i/f/numRing/num__ring__thms_c51', ah4s_numRings_numu_u_spolynomu_u_normalizeu_u_def)).
fof(21, axiom,![X35]:s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,X35))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X35),file('i/f/numRing/num__ring__thms_c51', ah4s_numerals_numeralu_u_distribu_c1)).
fof(22, axiom,![X35]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X35)))=s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),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_nums_num,X35))),file('i/f/numRing/num__ring__thms_c51', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
# SZS output end CNFRefutation
