# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X4),s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X3))))&p(s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X1),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(X1,X2),X1),h4s_pairs_fst),s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X4)))))))=>s(t_h4s_finiteu_u_maps_fmap(X1,X2),h4s_alists_alistu_u_tou_u_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X4)))=s(t_h4s_finiteu_u_maps_fmap(X1,X2),h4s_alists_alistu_u_tou_u_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X3)))),file('i/f/alist/alist__to__fmap__PERM', ch4s_alists_alistu_u_tou_u_fmapu_u_PERM)).
fof(5, axiom,![X9]:![X10]:![X11]:((p(s(t_bool,X11))<=>s(t_bool,X10)=s(t_bool,X9))<=>((p(s(t_bool,X11))|(p(s(t_bool,X10))|p(s(t_bool,X9))))&((p(s(t_bool,X11))|(~(p(s(t_bool,X9)))|~(p(s(t_bool,X10)))))&((p(s(t_bool,X10))|(~(p(s(t_bool,X9)))|~(p(s(t_bool,X11)))))&(p(s(t_bool,X9))|(~(p(s(t_bool,X10)))|~(p(s(t_bool,X11))))))))),file('i/f/alist/alist__to__fmap__PERM', ah4s_sats_dcu_u_eq)).
fof(12, axiom,![X1]:![X2]:![X12]:(p(s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X1),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(X1,X2),X1),h4s_pairs_fst),s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X12))))))=>p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),h4s_alists_fmapu_u_tou_u_alist(s(t_h4s_finiteu_u_maps_fmap(X1,X2),h4s_alists_alistu_u_tou_u_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X12))))),s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X12))))),file('i/f/alist/alist__to__fmap__PERM', ah4s_alists_alistu_u_tou_u_fmapu_u_tou_u_alistu_u_PERM)).
fof(13, axiom,![X1]:![X13]:![X14]:![X15]:((p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X15),s(t_h4s_lists_list(X1),X14))))&p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X14),s(t_h4s_lists_list(X1),X13)))))=>p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X15),s(t_h4s_lists_list(X1),X13))))),file('i/f/alist/alist__to__fmap__PERM', ah4s_sortings_PERMu_u_TRANS)).
fof(14, axiom,![X1]:![X3]:![X4]:s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X4),s(t_h4s_lists_list(X1),X3)))=s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X3),s(t_h4s_lists_list(X1),X4))),file('i/f/alist/alist__to__fmap__PERM', ah4s_sortings_PERMu_u_SYM)).
fof(15, axiom,![X1]:![X3]:![X4]:(p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X4),s(t_h4s_lists_list(X1),X3))))=>s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X1),X4)))=s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X1),X3)))),file('i/f/alist/alist__to__fmap__PERM', ah4s_sortings_ALLu_u_DISTINCTu_u_PERM)).
fof(16, axiom,![X2]:![X1]:![X3]:![X4]:![X16]:(p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X4),s(t_h4s_lists_list(X1),X3))))=>p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X2),h4s_lists_map(s(t_fun(X1,X2),X16),s(t_h4s_lists_list(X1),X4))),s(t_h4s_lists_list(X2),h4s_lists_map(s(t_fun(X1,X2),X16),s(t_h4s_lists_list(X1),X3))))))),file('i/f/alist/alist__to__fmap__PERM', ah4s_sortings_PERMu_u_MAP)).
fof(17, axiom,![X1]:![X2]:![X17]:![X18]:(p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),h4s_alists_fmapu_u_tou_u_alist(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X18))),s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),h4s_alists_fmapu_u_tou_u_alist(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X17))))))<=>s(t_h4s_finiteu_u_maps_fmap(X1,X2),X18)=s(t_h4s_finiteu_u_maps_fmap(X1,X2),X17)),file('i/f/alist/alist__to__fmap__PERM', ah4s_alists_PERMu_u_fmapu_u_tou_u_alist)).
# SZS output end CNFRefutation
