# 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_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))),h4s_numrings_numu_u_varlistu_u_insert),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_varlist(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_varlist(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_varlist(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,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),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_nums_num),X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_consu_u_varlist(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))),h4s_numrings_numu_u_varlistu_u_insert),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_c21', ch4s_numRings_numu_u_ringu_u_thmsu_c21)).
fof(4, axiom,![X9]:![X11]:![X6]:![X12]:![X13]:s(X9,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(X9),h4s_semiu_u_rings_semiu_u_ring0(s(X9,X13),s(X9,X12),s(t_fun(X9,t_fun(X9,X9)),X6),s(t_fun(X9,t_fun(X9,X9)),X11)))))=s(X9,X12),file('i/f/numRing/num__ring__thms_c21', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c1)).
fof(5, axiom,![X9]:![X11]:![X6]:![X12]:![X13]:s(t_fun(X9,t_fun(X9,X9)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X9),h4s_semiu_u_rings_semiu_u_ring0(s(X9,X13),s(X9,X12),s(t_fun(X9,t_fun(X9,X9)),X6),s(t_fun(X9,t_fun(X9,X9)),X11)))))=s(t_fun(X9,t_fun(X9,X9)),X6),file('i/f/numRing/num__ring__thms_c21', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c2)).
fof(7, axiom,![X9]:![X1]:![X14]:![X2]:![X3]:s(t_h4s_canonicals_canonicalu_u_sum(X9),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X9),t_h4s_canonicals_canonicalu_u_sum(X9)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X9),t_h4s_canonicals_canonicalu_u_sum(X9))),h4s_canonicals_varlistu_u_insert(s(t_h4s_semiu_u_rings_semiu_u_ring(X9),X14))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X9),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X9),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X9),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(X9),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X9),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X9),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(X9),h4s_canonicals_consu_u_monom(s(X9,happ(s(t_fun(X9,X9),happ(s(t_fun(X9,t_fun(X9,X9)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X9),X14))),s(X9,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(X9),X14))))),s(X9,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(X9),X14))))),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X9),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X9),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X9),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X9),t_h4s_canonicals_canonicalu_u_sum(X9)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X9),t_h4s_canonicals_canonicalu_u_sum(X9))),h4s_canonicals_varlistu_u_insert(s(t_h4s_semiu_u_rings_semiu_u_ring(X9),X14))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X9),X1))))))),file('i/f/numRing/num__ring__thms_c21', ah4s_canonicals_varlistu_u_insertu_u_defu_c1)).
fof(9, axiom,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))),h4s_numrings_numu_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_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_canonicals_varlistu_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_c21', ah4s_numRings_numu_u_varlistu_u_insertu_u_def)).
# SZS output end CNFRefutation
