# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]: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_canonicals_canonicalu_u_sum(t_h4s_nums_num),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_canonicalu_u_sumu_u_merge),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),X4),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),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),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),X4),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),X4),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_canonicals_canonicalu_u_sum(t_h4s_nums_num),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_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),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),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),X4),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_canonicals_canonicalu_u_sum(t_h4s_nums_num),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_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),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_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),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_canonicals_canonicalu_u_sum(t_h4s_nums_num),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_canonicalu_u_sumu_u_merge),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),X4),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X1))))))),file('i/f/numRing/num__ring__thms_c13', ch4s_numRings_numu_u_ringu_u_thmsu_c13)).
fof(7, axiom,![X10]:![X1]:![X2]:![X12]:![X3]:![X4]:s(t_h4s_canonicals_canonicalu_u_sum(X10),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),h4s_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X12))),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X10),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X10),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X10),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),X4),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X10),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),h4s_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X12))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X2))),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X10),X1))))))),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_monom(s(X10,happ(s(t_fun(X10,X10),happ(s(t_fun(X10,t_fun(X10,X10)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X12))),s(X10,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X12))))),s(X10,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X12))))),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X10),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),h4s_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X12))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X2))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X10),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),h4s_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X12))),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X10),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X1))))))),file('i/f/numRing/num__ring__thms_c13', ah4s_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c3)).
fof(11, axiom,s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),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_canonicalu_u_sumu_u_merge)=s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_canonicals_canonicalu_u_sumu_u_merge(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_c13', ah4s_numRings_numu_u_canonicalu_u_sumu_u_mergeu_u_def)).
fof(12, axiom,![X10]:![X21]:![X7]:![X22]:![X23]:s(X10,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),h4s_semiu_u_rings_semiu_u_ring0(s(X10,X23),s(X10,X22),s(t_fun(X10,t_fun(X10,X10)),X7),s(t_fun(X10,t_fun(X10,X10)),X21)))))=s(X10,X22),file('i/f/numRing/num__ring__thms_c13', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c1)).
fof(13, axiom,![X10]:![X21]:![X7]:![X22]:![X23]:s(t_fun(X10,t_fun(X10,X10)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),h4s_semiu_u_rings_semiu_u_ring0(s(X10,X23),s(X10,X22),s(t_fun(X10,t_fun(X10,X10)),X7),s(t_fun(X10,t_fun(X10,X10)),X21)))))=s(t_fun(X10,t_fun(X10,X10)),X7),file('i/f/numRing/num__ring__thms_c13', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c2)).
# SZS output end CNFRefutation
