# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:?[X4]:((p(s(t_bool,X4))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0))&s(X1,h4s_lists_el(s(t_h4s_nums_num,X2),s(t_h4s_lists_list(X1),X3)))=s(X1,h4s_bools_cond(s(t_bool,X4),s(X1,h4s_lists_hd(s(t_h4s_lists_list(X1),X3))),s(X1,h4s_lists_el(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,X2))),s(t_h4s_lists_list(X1),h4s_lists_tl(s(t_h4s_lists_list(X1),X3)))))))),file('i/f/list/EL__compute', ch4s_lists_ELu_u_compute)).
fof(3, axiom,![X10]:![X11]:((p(s(t_bool,X11))=>p(s(t_bool,X10)))=>((p(s(t_bool,X10))=>p(s(t_bool,X11)))=>s(t_bool,X11)=s(t_bool,X10))),file('i/f/list/EL__compute', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(27, axiom,![X1]:![X10]:![X11]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X11),s(X1,X10)))=s(X1,X11),file('i/f/list/EL__compute', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(28, axiom,![X1]:![X10]:![X11]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X11),s(X1,X10)))=s(X1,X10),file('i/f/list/EL__compute', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(29, axiom,![X1]:![X3]:s(X1,h4s_lists_el(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(X1),X3)))=s(X1,h4s_lists_hd(s(t_h4s_lists_list(X1),X3))),file('i/f/list/EL__compute', ah4s_lists_EL0u_c0)).
fof(30, axiom,![X1]:![X2]:![X3]:s(X1,h4s_lists_el(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_lists_list(X1),X3)))=s(X1,h4s_lists_el(s(t_h4s_nums_num,X2),s(t_h4s_lists_list(X1),h4s_lists_tl(s(t_h4s_lists_list(X1),X3))))),file('i/f/list/EL__compute', ah4s_lists_EL0u_c1)).
fof(45, axiom,![X1]:s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),h4s_lists_nil)))=s(t_bool,t),file('i/f/list/EL__compute', ah4s_lists_NULLu_u_DEFu_c0)).
fof(46, axiom,![X1]:![X13]:![X32]:s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X32))),s(t_h4s_lists_list(X1),X13)))))=s(t_bool,f),file('i/f/list/EL__compute', ah4s_lists_NULLu_u_DEFu_c1)).
fof(50, axiom,![X37]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X37)))))=s(t_h4s_nums_num,X37),file('i/f/list/EL__compute', ah4s_primu_u_recs_PRE0u_c1)).
fof(51, axiom,s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/list/EL__compute', ah4s_primu_u_recs_PRE0u_c0)).
fof(62, axiom,![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))),file('i/f/list/EL__compute', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(63, axiom,![X37]:(s(t_h4s_nums_num,X37)=s(t_h4s_nums_num,h4s_nums_0)|?[X2]:s(t_h4s_nums_num,X37)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))),file('i/f/list/EL__compute', ah4s_arithmetics_numu_u_CASES)).
fof(68, axiom,~(p(s(t_bool,f))),file('i/f/list/EL__compute', aHLu_FALSITY)).
fof(81, axiom,p(s(t_bool,t)),file('i/f/list/EL__compute', aHLu_TRUTH)).
# SZS output end CNFRefutation
