# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_nums_num,h4s_numeralu_u_bits_fdub(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numeralu_u_bits_idiv2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numeralu_u_bits_idiv2),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numeralu_u_bits_idiv2),s(t_h4s_nums_num,X1))))),file('i/f/numeral_bit/FDUB__iDIV2', ch4s_numeralu_u_bits_FDUBu_u_iDIV2)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/numeral_bit/FDUB__iDIV2', aHLu_TRUTH)).
fof(11, axiom,![X11]:s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_div2),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/numeral_bit/FDUB__iDIV2', ah4s_arithmetics_DIV2u_u_def)).
fof(12, axiom,![X11]:![X4]:s(t_h4s_nums_num,h4s_numeralu_u_bits_fdub(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X4),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11)))))=s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X4),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X4),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11))))))),file('i/f/numeral_bit/FDUB__iDIV2', ah4s_numeralu_u_bits_FDUBu_u_defu_c1)).
fof(13, axiom,![X4]:s(t_h4s_nums_num,h4s_numeralu_u_bits_fdub(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X4),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral_bit/FDUB__iDIV2', ah4s_numeralu_u_bits_FDUBu_u_defu_c0)).
fof(14, axiom,s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numeralu_u_bits_idiv2)=s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_div2),file('i/f/numeral_bit/FDUB__iDIV2', ah4s_numeralu_u_bits_iDIV20)).
fof(15, axiom,~(p(s(t_bool,f))),file('i/f/numeral_bit/FDUB__iDIV2', aHLu_FALSITY)).
fof(17, axiom,![X12]:![X11]:![X13]:(?[X14]:(s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X14)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X11)))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,X12)),file('i/f/numeral_bit/FDUB__iDIV2', ah4s_arithmetics_DIVu_u_UNIQUE)).
fof(18, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/numeral_bit/FDUB__iDIV2', aHLu_BOOLu_CASES)).
fof(20, axiom,![X11]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X11)))))=s(t_bool,t),file('i/f/numeral_bit/FDUB__iDIV2', ah4s_numerals_numeralu_u_ltu_c1)).
fof(21, axiom,![X11]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X11))),file('i/f/numeral_bit/FDUB__iDIV2', ah4s_numerals_numeralu_u_distribu_c21)).
fof(22, axiom,![X15]:(s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_nums_0)|?[X11]:s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11)))),file('i/f/numeral_bit/FDUB__iDIV2', ah4s_arithmetics_numu_u_CASES)).
fof(23, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X11),file('i/f/numeral_bit/FDUB__iDIV2', ah4s_numerals_numeralu_u_distribu_c1)).
fof(24, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral_bit/FDUB__iDIV2', ah4s_numerals_numeralu_u_distribu_c3)).
# SZS output end CNFRefutation
