# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]: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_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_cs),s(t_h4s_quotes_varmap(t_h4s_nums_num),X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_nilu_u_monom)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numRing/num__ring__thms_c47', ch4s_numRings_numu_u_ringu_u_thmsu_c47)).
fof(4, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_cs)=s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num)),h4s_canonicals_interpu_u_cs(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_c47', ah4s_numRings_numu_u_interpu_u_csu_u_def)).
fof(8, axiom,![X7]:![X1]:![X9]:s(X7,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X7),X7),happ(s(t_fun(t_h4s_quotes_varmap(X7),t_fun(t_h4s_canonicals_canonicalu_u_sum(X7),X7)),h4s_canonicals_interpu_u_cs(s(t_h4s_semiu_u_rings_semiu_u_ring(X7),X9))),s(t_h4s_quotes_varmap(X7),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X7),h4s_canonicals_nilu_u_monom)))=s(X7,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(X7),X9))),file('i/f/numRing/num__ring__thms_c47', ah4s_canonicals_interpu_u_csu_u_defu_c0)).
fof(11, axiom,![X7]:![X13]:![X4]:![X14]:![X15]:s(X7,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(X7),h4s_semiu_u_rings_semiu_u_ring0(s(X7,X15),s(X7,X14),s(t_fun(X7,t_fun(X7,X7)),X4),s(t_fun(X7,t_fun(X7,X7)),X13)))))=s(X7,X15),file('i/f/numRing/num__ring__thms_c47', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c0)).
# SZS output end CNFRefutation
