# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/bool/ONE__ONE__THM', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f0))),file('i/f/bool/ONE__ONE__THM', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f0)),file('i/f/bool/ONE__ONE__THM', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:![X8]:![X6]:(p(s(t_bool,h4s_bools_oneu_u_one(s(t_fun(X8,X7),X6))))<=>![X9]:![X10]:(s(X7,happ(s(t_fun(X8,X7),X6),s(X8,X9)))=s(X7,happ(s(t_fun(X8,X7),X6),s(X8,X10)))=>s(X8,X9)=s(X8,X10))),file('i/f/bool/ONE__ONE__THM', ah4s_bools_ONEu_u_ONEu_u_DEF)).
fof(21, axiom,(p(s(t_bool,f0))<=>![X1]:p(s(t_bool,X1))),file('i/f/bool/ONE__ONE__THM', ah4s_bools_Fu_u_DEF)).
fof(34, axiom,~(s(t_bool,f0)=s(t_bool,t)),file('i/f/bool/ONE__ONE__THM', ah4s_bools_BOOLu_u_EQu_u_DISTINCTu_c1)).
fof(36, axiom,![X1]:(s(t_bool,t)=s(t_bool,X1)<=>p(s(t_bool,X1))),file('i/f/bool/ONE__ONE__THM', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(37, axiom,![X8]:![X15]:![X16]:s(X8,h4s_bools_cond(s(t_bool,t),s(X8,X16),s(X8,X15)))=s(X8,X16),file('i/f/bool/ONE__ONE__THM', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(53, axiom,![X1]:(s(t_bool,f0)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/bool/ONE__ONE__THM', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(133, conjecture,![X7]:![X8]:![X4]:(p(s(t_bool,h4s_bools_oneu_u_one(s(t_fun(X8,X7),X4))))<=>![X9]:![X10]:(s(X7,happ(s(t_fun(X8,X7),X4),s(X8,X9)))=s(X7,happ(s(t_fun(X8,X7),X4),s(X8,X10)))=>s(X8,X9)=s(X8,X10))),file('i/f/bool/ONE__ONE__THM', ch4s_bools_ONEu_u_ONEu_u_THM)).
# SZS output end CNFRefutation
