# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,X2))))<=>(p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,t))))&p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,f)))))),file('i/f/bool/FORALL__BOOL', ch4s_bools_FORALLu_u_BOOL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bool/FORALL__BOOL', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bool/FORALL__BOOL', aHLu_FALSITY)).
fof(4, axiom,![X1]:((p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,t))))&p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,f)))))=>![X2]:p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,X2))))),file('i/f/bool/FORALL__BOOL', ah4s_bools_boolu_u_INDUCT)).
fof(7, axiom,(p(s(t_bool,f))<=>![X3]:p(s(t_bool,X3))),file('i/f/bool/FORALL__BOOL', ah4s_bools_Fu_u_DEF)).
fof(8, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/bool/FORALL__BOOL', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X3]:(s(t_bool,f)=s(t_bool,X3)<=>~(p(s(t_bool,X3)))),file('i/f/bool/FORALL__BOOL', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(26, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/bool/FORALL__BOOL', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
