# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X1),X2)))=s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X2),s(t_h4s_lists_list(X1),h4s_lists_setu_u_tou_u_list(s(t_fun(X1,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X1),X2))))))),file('i/f/sorting/ALL__DISTINCT__PERM__LIST__TO__SET__TO__LIST', ch4s_sortings_ALLu_u_DISTINCTu_u_PERMu_u_LISTu_u_TOu_u_SETu_u_TOu_u_LIST)).
fof(4, axiom,![X6]:![X7]:(s(t_bool,X7)=s(t_bool,X6)<=>((p(s(t_bool,X7))=>p(s(t_bool,X6)))&(p(s(t_bool,X6))=>p(s(t_bool,X7))))),file('i/f/sorting/ALL__DISTINCT__PERM__LIST__TO__SET__TO__LIST', ah4s_bools_EQu_u_IMPu_u_THM)).
fof(6, axiom,![X1]:![X10]:![X11]:(p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X11),s(t_h4s_lists_list(X1),X10))))=>s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X1),X11)))=s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X1),X10)))),file('i/f/sorting/ALL__DISTINCT__PERM__LIST__TO__SET__TO__LIST', ah4s_sortings_ALLu_u_DISTINCTu_u_PERM)).
fof(7, axiom,![X1]:![X10]:![X11]:((p(s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X1),X11))))&(p(s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X1),X10))))&![X4]:s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X1),X11)))))=s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X1),X10)))))))=>p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X11),s(t_h4s_lists_list(X1),X10))))),file('i/f/sorting/ALL__DISTINCT__PERM__LIST__TO__SET__TO__LIST', ah4s_sortings_PERMu_u_ALLu_u_DISTINCT)).
fof(8, axiom,![X1]:![X12]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X12))))=>![X4]:s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X1),h4s_lists_setu_u_tou_u_list(s(t_fun(X1,t_bool),X12)))))))=s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X12)))),file('i/f/sorting/ALL__DISTINCT__PERM__LIST__TO__SET__TO__LIST', ah4s_lists_MEMu_u_SETu_u_TOu_u_LIST)).
fof(9, axiom,![X1]:![X12]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X12))))=>p(s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X1),h4s_lists_setu_u_tou_u_list(s(t_fun(X1,t_bool),X12))))))),file('i/f/sorting/ALL__DISTINCT__PERM__LIST__TO__SET__TO__LIST', ah4s_lists_ALLu_u_DISTINCTu_u_SETu_u_TOu_u_LIST)).
fof(10, axiom,![X1]:![X13]:p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X1),X13)))))),file('i/f/sorting/ALL__DISTINCT__PERM__LIST__TO__SET__TO__LIST', ah4s_lists_FINITEu_u_LISTu_u_TOu_u_SET)).
# SZS output end CNFRefutation
