# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:s(X1,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1),happ(s(t_fun(X1,t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1)),happ(s(t_fun(t_h4s_quotes_varmap(X1),t_fun(X1,t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1))),h4s_ringnorms_ru_u_icsu_u_aux(s(t_h4s_rings_ring(X1),X4))),s(t_h4s_quotes_varmap(X1),X2))),s(X1,X6))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X5),s(t_h4s_canonicals_canonicalu_u_sum(X1),X3)))))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X4))),s(X1,X6))),s(X1,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1),happ(s(t_fun(X1,t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1)),happ(s(t_fun(t_h4s_quotes_varmap(X1),t_fun(X1,t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1))),h4s_ringnorms_ru_u_icsu_u_aux(s(t_h4s_rings_ring(X1),X4))),s(t_h4s_quotes_varmap(X1),X2))),s(X1,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X1),happ(s(t_fun(t_h4s_quotes_varmap(X1),t_fun(t_h4s_lists_list(t_h4s_quotes_index),X1)),h4s_ringnorms_ru_u_interpu_u_vl(s(t_h4s_rings_ring(X1),X4))),s(t_h4s_quotes_varmap(X1),X2))),s(t_h4s_lists_list(t_h4s_quotes_index),X5))))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X3))))),file('i/f/ringNorm/ics__aux__def_c1', ch4s_ringNorms_icsu_u_auxu_u_defu_c1)).
fof(5, axiom,![X1]:![X2]:![X3]:![X13]:![X5]:![X6]:s(X1,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1),happ(s(t_fun(X1,t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1)),happ(s(t_fun(t_h4s_quotes_varmap(X1),t_fun(X1,t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X13))),s(t_h4s_quotes_varmap(X1),X2))),s(X1,X6))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X5),s(t_h4s_canonicals_canonicalu_u_sum(X1),X3)))))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X13))),s(X1,X6))),s(X1,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1),happ(s(t_fun(X1,t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1)),happ(s(t_fun(t_h4s_quotes_varmap(X1),t_fun(X1,t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X13))),s(t_h4s_quotes_varmap(X1),X2))),s(X1,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X1),happ(s(t_fun(t_h4s_quotes_varmap(X1),t_fun(t_h4s_lists_list(t_h4s_quotes_index),X1)),h4s_canonicals_interpu_u_vl(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X13))),s(t_h4s_quotes_varmap(X1),X2))),s(t_h4s_lists_list(t_h4s_quotes_index),X5))))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X3))))),file('i/f/ringNorm/ics__aux__def_c1', ah4s_canonicals_icsu_u_auxu_u_defu_c1)).
fof(7, axiom,![X1]:![X4]:s(t_fun(t_h4s_quotes_varmap(X1),t_fun(X1,t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1))),h4s_ringnorms_ru_u_icsu_u_aux(s(t_h4s_rings_ring(X1),X4)))=s(t_fun(t_h4s_quotes_varmap(X1),t_fun(X1,t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),X1))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),h4s_rings_semiu_u_ringu_u_of(s(t_h4s_rings_ring(X1),X4))))),file('i/f/ringNorm/ics__aux__def_c1', ah4s_ringNorms_ru_u_icsu_u_auxu_u_def)).
fof(9, axiom,![X1]:![X4]:s(t_fun(t_h4s_quotes_varmap(X1),t_fun(t_h4s_lists_list(t_h4s_quotes_index),X1)),h4s_ringnorms_ru_u_interpu_u_vl(s(t_h4s_rings_ring(X1),X4)))=s(t_fun(t_h4s_quotes_varmap(X1),t_fun(t_h4s_lists_list(t_h4s_quotes_index),X1)),h4s_canonicals_interpu_u_vl(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),h4s_rings_semiu_u_ringu_u_of(s(t_h4s_rings_ring(X1),X4))))),file('i/f/ringNorm/ics__aux__def_c1', ah4s_ringNorms_ru_u_interpu_u_vlu_u_def)).
fof(10, axiom,![X1]:![X4]:s(t_h4s_semiu_u_rings_semiu_u_ring(X1),h4s_rings_semiu_u_ringu_u_of(s(t_h4s_rings_ring(X1),X4)))=s(t_h4s_semiu_u_rings_semiu_u_ring(X1),h4s_semiu_u_rings_semiu_u_ring0(s(X1,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X1),X4))),s(X1,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X1),X4))),s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X4))),s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X4))))),file('i/f/ringNorm/ics__aux__def_c1', ah4s_rings_semiu_u_ringu_u_ofu_u_def)).
fof(11, axiom,![X1]:![X15]:![X9]:![X16]:![X6]:s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),h4s_semiu_u_rings_semiu_u_ring0(s(X1,X6),s(X1,X16),s(t_fun(X1,t_fun(X1,X1)),X9),s(t_fun(X1,t_fun(X1,X1)),X15)))))=s(t_fun(X1,t_fun(X1,X1)),X9),file('i/f/ringNorm/ics__aux__def_c1', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c2)).
# SZS output end CNFRefutation
