# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]: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,X4))),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),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,X4))),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_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_vl),s(t_h4s_quotes_varmap(t_h4s_nums_num),X1))),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_c45', ch4s_numRings_numu_u_ringu_u_thmsu_c45)).
fof(4, axiom,![X10]:![X12]:![X7]:![X13]:![X4]: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,X4),s(X10,X13),s(t_fun(X10,t_fun(X10,X10)),X7),s(t_fun(X10,t_fun(X10,X10)),X12)))))=s(t_fun(X10,t_fun(X10,X10)),X7),file('i/f/numRing/num__ring__thms_c45', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c2)).
fof(6, axiom,![X10]:![X1]:![X2]:![X14]:![X3]:![X4]:s(X10,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),X10),happ(s(t_fun(X10,t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),X10)),happ(s(t_fun(t_h4s_quotes_varmap(X10),t_fun(X10,t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),X10))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X14))),s(t_h4s_quotes_varmap(X10),X1))),s(X10,X4))),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),X2)))))=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),X14))),s(X10,X4))),s(X10,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),X10),happ(s(t_fun(X10,t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),X10)),happ(s(t_fun(t_h4s_quotes_varmap(X10),t_fun(X10,t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),X10))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X14))),s(t_h4s_quotes_varmap(X10),X1))),s(X10,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10),happ(s(t_fun(t_h4s_quotes_varmap(X10),t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10)),h4s_canonicals_interpu_u_vl(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X14))),s(t_h4s_quotes_varmap(X10),X1))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X2))))),file('i/f/numRing/num__ring__thms_c45', ah4s_canonicals_icsu_u_auxu_u_defu_c1)).
fof(8, 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_c45', ah4s_numRings_numu_u_icsu_u_auxu_u_def)).
fof(10, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_vl)=s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num)),h4s_canonicals_interpu_u_vl(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_c45', ah4s_numRings_numu_u_interpu_u_vlu_u_def)).
# SZS output end CNFRefutation
