# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(t_h4s_nums_num,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num))),h4s_numrings_numu_u_icsu_u_aux),s(t_h4s_quotes_varmap(t_h4s_nums_num),X1))),s(t_h4s_nums_num,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_canonicals_consu_u_monom),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),X2)))))=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,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num))),h4s_numrings_numu_u_icsu_u_aux),s(t_h4s_quotes_varmap(t_h4s_nums_num),X1))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num))),h4s_numrings_numu_u_interpu_u_m),s(t_h4s_quotes_varmap(t_h4s_nums_num),X1))),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),X2))))),file('i/f/numRing/num__ring__thms_c46', ch4s_numRings_numu_u_ringu_u_thmsu_c46)).
fof(6, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num))),h4s_numrings_numu_u_interpu_u_m)=s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num))),h4s_canonicals_interpu_u_m(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_c46', ah4s_numRings_numu_u_interpu_u_mu_u_def)).
fof(9, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num))),h4s_numrings_numu_u_icsu_u_aux)=s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num))),h4s_canonicals_icsu_u_aux(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_c46', ah4s_numRings_numu_u_icsu_u_auxu_u_def)).
fof(14, axiom,![X6]:![X1]:![X2]:![X14]:![X3]:![X4]:![X5]:s(X6,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6),happ(s(t_fun(X6,t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6)),happ(s(t_fun(t_h4s_quotes_varmap(X6),t_fun(X6,t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(X6),X14))),s(t_h4s_quotes_varmap(X6),X1))),s(X6,X5))),s(t_h4s_canonicals_canonicalu_u_sum(X6),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6))),happ(s(t_fun(X6,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6)))),h4s_canonicals_consu_u_monom),s(X6,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X6),X2)))))=s(X6,happ(s(t_fun(X6,X6),happ(s(t_fun(X6,t_fun(X6,X6)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X6),X14))),s(X6,X5))),s(X6,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6),happ(s(t_fun(X6,t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6)),happ(s(t_fun(t_h4s_quotes_varmap(X6),t_fun(X6,t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(X6),X14))),s(t_h4s_quotes_varmap(X6),X1))),s(X6,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X6),happ(s(t_fun(X6,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X6)),happ(s(t_fun(t_h4s_quotes_varmap(X6),t_fun(X6,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X6))),h4s_canonicals_interpu_u_m(s(t_h4s_semiu_u_rings_semiu_u_ring(X6),X14))),s(t_h4s_quotes_varmap(X6),X1))),s(X6,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))))),s(t_h4s_canonicals_canonicalu_u_sum(X6),X2))))),file('i/f/numRing/num__ring__thms_c46', ah4s_canonicals_icsu_u_auxu_u_defu_c2)).
fof(29, axiom,![X6]:![X17]:![X11]:![X18]:![X5]:s(t_fun(X6,t_fun(X6,X6)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X6),h4s_semiu_u_rings_semiu_u_ring0(s(X6,X5),s(X6,X18),s(t_fun(X6,t_fun(X6,X6)),X11),s(t_fun(X6,t_fun(X6,X6)),X17)))))=s(t_fun(X6,t_fun(X6,X6)),X11),file('i/f/numRing/num__ring__thms_c46', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c2)).
# SZS output end CNFRefutation
