# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:(p(s(t_bool,h4s_quotients_equiv(s(t_fun(X1,t_fun(X1,t_bool)),X6))))=>((p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X6),s(X1,X5))),s(X1,X4))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X6),s(X1,X3))),s(X1,X2)))))=>(s(X1,X5)=s(X1,X3)=>p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X6),s(X1,X4))),s(X1,X2))))))),file('i/f/quotient/EQUALS__EQUIV__IMPLIES', ch4s_quotients_EQUALSu_u_EQUIVu_u_IMPLIES)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/quotient/EQUALS__EQUIV__IMPLIES', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/quotient/EQUALS__EQUIV__IMPLIES', aHLu_FALSITY)).
fof(4, axiom,![X1]:![X7]:(p(s(t_bool,h4s_quotients_equiv(s(t_fun(X1,t_fun(X1,t_bool)),X7))))<=>![X8]:![X9]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X7),s(X1,X8))),s(X1,X9))))<=>s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X7),s(X1,X8)))=s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X7),s(X1,X9))))),file('i/f/quotient/EQUALS__EQUIV__IMPLIES', ah4s_quotients_EQUIVu_u_def)).
fof(6, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)|s(t_bool,X11)=s(t_bool,f)),file('i/f/quotient/EQUALS__EQUIV__IMPLIES', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
