# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(![X5]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),X2),s(X1,X5))))=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),X4),s(X1,X5))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X5))))))=>(p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X4))))=>p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X3)))))),file('i/f/quotient/RES__FORALL__REGULAR', ch4s_quotients_RESu_u_FORALLu_u_REGULAR)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/quotient/RES__FORALL__REGULAR', aHLu_FALSITY)).
fof(11, axiom,(p(s(t_bool,f))<=>![X8]:p(s(t_bool,X8))),file('i/f/quotient/RES__FORALL__REGULAR', ah4s_bools_Fu_u_DEF)).
fof(30, axiom,![X8]:(s(t_bool,X8)=s(t_bool,f)<=>~(p(s(t_bool,X8)))),file('i/f/quotient/RES__FORALL__REGULAR', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(58, axiom,![X1]:![X5]:![X30]:(p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),X5),s(t_fun(X1,t_bool),X30))))<=>![X31]:(p(s(t_bool,h4s_bools_in(s(X1,X31),s(t_fun(X1,t_bool),X5))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X30),s(X1,X31)))))),file('i/f/quotient/RES__FORALL__REGULAR', ah4s_bools_RESu_u_FORALLu_u_DEF)).
fof(64, axiom,![X1]:![X5]:![X4]:s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),X4)))=s(t_bool,happ(s(t_fun(X1,t_bool),X4),s(X1,X5))),file('i/f/quotient/RES__FORALL__REGULAR', ah4s_predu_u_sets_SPECIFICATION)).
fof(65, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/quotient/RES__FORALL__REGULAR', aHLu_BOOLu_CASES)).
fof(74, axiom,p(s(t_bool,t)),file('i/f/quotient/RES__FORALL__REGULAR', aHLu_TRUTH)).
fof(76, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)<=>p(s(t_bool,X8))),file('i/f/quotient/RES__FORALL__REGULAR', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
