# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:![X4]:s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(t_bool,t_fun(X1,t_bool)),X2),s(t_bool,X3))),s(X1,X4)))=s(t_bool,X3)=>![X5]:![X3]:(p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),X5),s(t_fun(X1,t_bool),happ(s(t_fun(t_bool,t_fun(X1,t_bool)),X2),s(t_bool,X3))))))<=>(s(t_fun(X1,t_bool),X5)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)|p(s(t_bool,X3))))),file('i/f/res_quan/RES__FORALL__NULL', ch4s_resu_u_quans_RESu_u_FORALLu_u_NULL)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/res_quan/RES__FORALL__NULL', aHLu_FALSITY)).
fof(3, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/res_quan/RES__FORALL__NULL', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(8, axiom,(p(s(t_bool,f))<=>![X8]:p(s(t_bool,X8))),file('i/f/res_quan/RES__FORALL__NULL', ah4s_bools_Fu_u_DEF)).
fof(9, axiom,![X1]:![X4]:~(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/res_quan/RES__FORALL__NULL', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(12, axiom,![X8]:(s(t_bool,X8)=s(t_bool,f)<=>~(p(s(t_bool,X8)))),file('i/f/res_quan/RES__FORALL__NULL', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(55, axiom,![X1]:![X4]:s(t_fun(X1,t_bool),h4s_predu_u_sets_rest(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),file('i/f/res_quan/RES__FORALL__NULL', ah4s_predu_u_sets_RESTu_u_SING)).
fof(57, axiom,![X1]:![X4]:![X28]:(p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X28))))<=>![X29]:(p(s(t_bool,h4s_bools_in(s(X1,X29),s(t_fun(X1,t_bool),X4))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X28),s(X1,X29)))))),file('i/f/res_quan/RES__FORALL__NULL', ah4s_bools_RESu_u_FORALLu_u_DEF)).
fof(59, axiom,![X1]:![X4]:![X18]:s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X18)))=s(t_bool,happ(s(t_fun(X1,t_bool),X18),s(X1,X4))),file('i/f/res_quan/RES__FORALL__NULL', ah4s_predu_u_sets_SPECIFICATION)).
fof(67, axiom,![X1]:![X8]:![X26]:(s(t_fun(X1,t_bool),X26)=s(t_fun(X1,t_bool),X8)<=>![X4]:s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X26)))=s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X8)))),file('i/f/res_quan/RES__FORALL__NULL', ah4s_predu_u_sets_EXTENSION)).
fof(68, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/res_quan/RES__FORALL__NULL', aHLu_BOOLu_CASES)).
fof(70, axiom,![X8]:((p(s(t_bool,f))=>p(s(t_bool,X8)))<=>p(s(t_bool,t))),file('i/f/res_quan/RES__FORALL__NULL', ah4s_bools_IMPu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
