# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(t_h4s_options_option(X1),h4s_sptrees_lookup(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_sptrees_spt(X1),happ(s(t_fun(t_h4s_sptrees_spt(X1),t_h4s_sptrees_spt(X1)),happ(s(t_fun(X1,t_fun(t_h4s_sptrees_spt(X1),t_h4s_sptrees_spt(X1))),happ(s(t_fun(t_h4s_sptrees_spt(X1),t_fun(X1,t_fun(t_h4s_sptrees_spt(X1),t_h4s_sptrees_spt(X1)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(X1),X3))),s(X1,X4))),s(t_h4s_sptrees_spt(X1),X2)))))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4))),file('i/f/sptree/lookup__compute_c8', ch4s_sptrees_lookupu_u_computeu_c8)).
fof(4, axiom,![X1]:![X2]:![X3]:![X4]:s(t_h4s_options_option(X1),h4s_sptrees_lookup(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_sptrees_spt(X1),happ(s(t_fun(t_h4s_sptrees_spt(X1),t_h4s_sptrees_spt(X1)),happ(s(t_fun(X1,t_fun(t_h4s_sptrees_spt(X1),t_h4s_sptrees_spt(X1))),happ(s(t_fun(t_h4s_sptrees_spt(X1),t_fun(X1,t_fun(t_h4s_sptrees_spt(X1),t_h4s_sptrees_spt(X1)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(X1),X3))),s(X1,X4))),s(t_h4s_sptrees_spt(X1),X2)))))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4))),file('i/f/sptree/lookup__compute_c8', ah4s_sptrees_lookupu_u_computeu_c4)).
fof(9, axiom,![X22]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/sptree/lookup__compute_c8', ah4s_numerals_numeralu_u_distribu_c27)).
fof(10, axiom,![X22]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X22)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X22)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/sptree/lookup__compute_c8', ah4s_numerals_numeralu_u_distribu_c17)).
fof(14, axiom,s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,t),file('i/f/sptree/lookup__compute_c8', ah4s_arithmetics_EVEN0u_c0)).
fof(16, axiom,p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/sptree/lookup__compute_c8', ah4s_numerals_numeralu_u_distribu_c35)).
fof(27, axiom,![X2]:![X3]:((p(s(t_bool,X3))=>p(s(t_bool,X2)))=>((p(s(t_bool,X2))=>p(s(t_bool,X3)))=>s(t_bool,X3)=s(t_bool,X2))),file('i/f/sptree/lookup__compute_c8', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(49, axiom,![X28]:![X22]:![X25]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X22)))=s(t_h4s_nums_num,X28)<=>(s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X28)))|(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X22))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X28),s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/sptree/lookup__compute_c8', ah4s_arithmetics_SUBu_u_RIGHTu_u_EQ)).
fof(50, axiom,![X34]:![X4]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X34))),s(t_h4s_nums_num,X34)))=s(t_h4s_nums_num,X4),file('i/f/sptree/lookup__compute_c8', ah4s_arithmetics_ADDu_u_SUB)).
fof(53, axiom,![X22]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X22),file('i/f/sptree/lookup__compute_c8', ah4s_numerals_numeralu_u_distribu_c1)).
fof(54, axiom,![X25]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X25)))=s(t_h4s_nums_num,X25),file('i/f/sptree/lookup__compute_c8', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(56, axiom,![X22]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X22)))),file('i/f/sptree/lookup__compute_c8', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
