# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(~(s(X2,X4)=s(X2,X3))=>s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),h4s_finiteu_u_maps_fdomsub(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X5),s(X2,X4))),s(X2,X3)))=s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X5),s(X2,X3)))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ch4s_finiteu_u_maps_DOMSUBu_u_FAPPLYu_u_NEQ)).
fof(3, axiom,![X1]:![X2]:![X8]:![X5]:s(t_h4s_finiteu_u_maps_fmap(X2,X1),h4s_finiteu_u_maps_fdomsub(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X5),s(X2,X8)))=s(t_h4s_finiteu_u_maps_fmap(X2,X1),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X5),s(t_fun(X2,t_bool),h4s_predu_u_sets_compl(s(t_fun(X2,t_bool),h4s_predu_u_sets_insert(s(X2,X8),s(t_fun(X2,t_bool),h4s_predu_u_sets_empty))))))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_finiteu_u_maps_fmapu_u_domsub)).
fof(4, axiom,![X1]:![X2]:![X7]:![X9]:![X10]:s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X10),s(t_fun(X2,t_bool),X9))),s(X2,X7)))=s(X1,h4s_bools_cond(s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),h4s_predu_u_sets_inter(s(t_fun(X2,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X10))),s(t_fun(X2,t_bool),X9))))),s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X10),s(X2,X7))),s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),h4s_finiteu_u_maps_fempty),s(X2,X7))))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_finiteu_u_maps_DRESTRICTu_u_DEFu_c1)).
fof(5, axiom,![X2]:![X7]:![X11]:(p(s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),h4s_predu_u_sets_compl(s(t_fun(X2,t_bool),X11))))))<=>~(p(s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),X11)))))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_predu_u_sets_INu_u_COMPL)).
fof(6, axiom,![X2]:![X6]:![X7]:![X11]:(p(s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),h4s_predu_u_sets_insert(s(X2,X6),s(t_fun(X2,t_bool),X11))))))<=>(s(X2,X7)=s(X2,X6)|p(s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),X11)))))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_predu_u_sets_INu_u_INSERT)).
fof(7, axiom,![X2]:![X7]:~(p(s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),h4s_predu_u_sets_empty))))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(8, axiom,![X2]:![X12]:![X13]:s(X2,h4s_bools_cond(s(t_bool,t),s(X2,X13),s(X2,X12)))=s(X2,X13),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(9, axiom,![X2]:![X12]:![X13]:s(X2,h4s_bools_cond(s(t_bool,f),s(X2,X13),s(X2,X12)))=s(X2,X12),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(11, axiom,![X1]:![X2]:![X7]:![X10]:(~(p(s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X10)))))))=>s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X10),s(X2,X7)))=s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),h4s_finiteu_u_maps_fempty),s(X2,X7)))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_finiteu_u_maps_NOTu_u_FDOMu_u_FAPPLYu_u_FEMPTY)).
fof(12, axiom,![X2]:![X7]:![X18]:![X11]:(p(s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),h4s_predu_u_sets_inter(s(t_fun(X2,t_bool),X11),s(t_fun(X2,t_bool),X18))))))<=>(p(s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),X11))))&p(s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),X18)))))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_predu_u_sets_INu_u_INTER)).
fof(13, axiom,![X12]:![X13]:((p(s(t_bool,X13))=>p(s(t_bool,X12)))=>((p(s(t_bool,X12))=>p(s(t_bool,X13)))=>s(t_bool,X13)=s(t_bool,X12))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(17, axiom,p(s(t_bool,t)),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', aHLu_TRUTH)).
fof(22, axiom,![X18]:(s(t_bool,X18)=s(t_bool,t)<=>p(s(t_bool,X18))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(23, axiom,~(p(s(t_bool,f))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', aHLu_FALSITY)).
fof(25, axiom,(p(s(t_bool,f))<=>![X18]:p(s(t_bool,X18))),file('i/f/finite_map/DOMSUB__FAPPLY__NEQ', ah4s_bools_Fu_u_DEF)).
# SZS output end CNFRefutation
