# 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_fun(X1,t_bool),t_fun(X1,t_bool)),X2),s(t_fun(X1,t_bool),X3))),s(X1,X4)))=s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X4)))=>![X5]:(![X6]:![X7]:![X8]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool))),X5),s(t_fun(X1,t_bool),X6))),s(t_fun(X1,t_bool),X7))),s(X1,X8))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),X6),s(X1,X8))))|p(s(t_bool,happ(s(t_fun(X1,t_bool),X7),s(X1,X8))))))=>![X3]:![X7]:![X6]:(p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool))),X5),s(t_fun(X1,t_bool),X6))),s(t_fun(X1,t_bool),X7))),s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2),s(t_fun(X1,t_bool),X3))))))<=>(p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),X6),s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2),s(t_fun(X1,t_bool),X3))))))&p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),X7),s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2),s(t_fun(X1,t_bool),X3)))))))))),file('i/f/res_quan/RES__FORALL__DISJ__DIST', ch4s_resu_u_quans_RESu_u_FORALLu_u_DISJu_u_DIST)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/res_quan/RES__FORALL__DISJ__DIST', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/res_quan/RES__FORALL__DISJ__DIST', aHLu_FALSITY)).
fof(4, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/res_quan/RES__FORALL__DISJ__DIST', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(5, axiom,![X1]:![X11]:![X6]:(p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),X6),s(t_fun(X1,t_bool),X11))))<=>![X12]:(p(s(t_bool,h4s_bools_in(s(X1,X12),s(t_fun(X1,t_bool),X6))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X11),s(X1,X12)))))),file('i/f/res_quan/RES__FORALL__DISJ__DIST', ah4s_resu_u_quans_RESu_u_FORALL)).
fof(6, axiom,![X13]:(s(t_bool,X13)=s(t_bool,t)|s(t_bool,X13)=s(t_bool,f)),file('i/f/res_quan/RES__FORALL__DISJ__DIST', aHLu_BOOLu_CASES)).
fof(7, axiom,![X14]:![X15]:![X11]:![X16]:(![X12]:s(X15,happ(s(t_fun(X14,X15),X11),s(X14,X12)))=s(X15,happ(s(t_fun(X14,X15),X16),s(X14,X12)))=>s(t_fun(X14,X15),X11)=s(t_fun(X14,X15),X16)),file('i/f/res_quan/RES__FORALL__DISJ__DIST', aHLu_EXT)).
fof(8, axiom,![X1]:![X12]:![X6]:s(t_bool,h4s_bools_in(s(X1,X12),s(t_fun(X1,t_bool),X6)))=s(t_bool,happ(s(t_fun(X1,t_bool),X6),s(X1,X12))),file('i/f/res_quan/RES__FORALL__DISJ__DIST', ah4s_predu_u_sets_SPECIFICATION)).
# SZS output end CNFRefutation
