# 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_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_numrings_numu_u_monomu_u_insert),s(t_h4s_nums_num,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_consu_u_monom(s(t_h4s_nums_num,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),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_nums_num),h4s_canonicals_consu_u_monom(s(t_h4s_nums_num,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_consu_u_monom(s(t_h4s_nums_num,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_consu_u_monom(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,X5))),s(t_h4s_nums_num,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_consu_u_monom(s(t_h4s_nums_num,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),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_numrings_numu_u_monomu_u_insert),s(t_h4s_nums_num,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X1))))))),file('i/f/numRing/num__ring__thms_c17', ch4s_numRings_numu_u_ringu_u_thmsu_c17)).
fof(4, axiom,![X11]:![X13]:![X8]:![X14]:![X15]:s(t_fun(X11,t_fun(X11,X11)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X11),h4s_semiu_u_rings_semiu_u_ring0(s(X11,X15),s(X11,X14),s(t_fun(X11,t_fun(X11,X11)),X8),s(t_fun(X11,t_fun(X11,X11)),X13)))))=s(t_fun(X11,t_fun(X11,X11)),X8),file('i/f/numRing/num__ring__thms_c17', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c2)).
fof(5, axiom,![X11]:![X1]:![X16]:![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_canonicals_monomu_u_insert(s(t_h4s_semiu_u_rings_semiu_u_ring(X11),X16))),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_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X11),X16))),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_canonicals_monomu_u_insert(s(t_h4s_semiu_u_rings_semiu_u_ring(X11),X16))),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/numRing/num__ring__thms_c17', ah4s_canonicals_monomu_u_insertu_u_defu_c0)).
fof(8, axiom,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_numrings_numu_u_monomu_u_insert)=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_monomu_u_insert(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_c17', ah4s_numRings_numu_u_monomu_u_insertu_u_def)).
# SZS output end CNFRefutation
