# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(X1,h4s_richu_u_lists_ell(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_lists_list(X1),h4s_lists_snoc(s(X1,X2),s(t_h4s_lists_list(X1),X4)))))=s(X1,h4s_richu_u_lists_ell(s(t_h4s_nums_num,X3),s(t_h4s_lists_list(X1),X4))),file('i/f/rich_list/ELL__SUC__SNOC', ch4s_richu_u_lists_ELLu_u_SUCu_u_SNOC)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/rich_list/ELL__SUC__SNOC', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/rich_list/ELL__SUC__SNOC', aHLu_FALSITY)).
fof(4, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/rich_list/ELL__SUC__SNOC', aHLu_BOOLu_CASES)).
fof(5, axiom,![X3]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3)))))),file('i/f/rich_list/ELL__SUC__SNOC', ah4s_primu_u_recs_LESSu_u_0)).
fof(6, axiom,![X6]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6)))))=s(t_h4s_nums_num,X6),file('i/f/rich_list/ELL__SUC__SNOC', ah4s_primu_u_recs_PRE0u_c1)).
fof(7, axiom,![X1]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3))))=>![X2]:![X4]:s(X1,h4s_richu_u_lists_ell(s(t_h4s_nums_num,X3),s(t_h4s_lists_list(X1),h4s_lists_snoc(s(X1,X2),s(t_h4s_lists_list(X1),X4)))))=s(X1,h4s_richu_u_lists_ell(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,X3))),s(t_h4s_lists_list(X1),X4)))),file('i/f/rich_list/ELL__SUC__SNOC', ah4s_richu_u_lists_ELLu_u_SNOC)).
# SZS output end CNFRefutation
