# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(t_fun(X4,X1),X6),s(t_fun(X1,X4),X5))))=>![X8]:![X9]:![X10]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X8),s(t_fun(X3,X2),X9),s(t_fun(X2,X3),X10))))=>![X11]:![X12]:![X13]:![X14]:((p(s(t_bool,happ(s(t_fun(t_fun(X4,X3),t_bool),happ(s(t_fun(t_fun(X4,X3),t_fun(t_fun(X4,X3),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(t_fun(X3,t_fun(X3,t_bool)),X8))),s(t_fun(X4,X3),X11))),s(t_fun(X4,X3),X12))))&p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(X4,X13))),s(X4,X14)))))=>p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X8),s(X3,h4s_bools_literalu_u_case(s(t_fun(X4,X3),X11),s(X4,X13))))),s(X3,h4s_bools_literalu_u_case(s(t_fun(X4,X3),X12),s(X4,X14))))))))),file('i/f/quotient/literal__case__RSP', ch4s_quotients_literalu_u_caseu_u_RSP)).
fof(3, axiom,![X16]:![X17]:((p(s(t_bool,X17))=>p(s(t_bool,X16)))=>((p(s(t_bool,X16))=>p(s(t_bool,X17)))=>s(t_bool,X17)=s(t_bool,X16))),file('i/f/quotient/literal__case__RSP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(26, axiom,![X3]:![X4]:![X13]:![X33]:s(X3,h4s_bools_literalu_u_case(s(t_fun(X4,X3),X13),s(X4,X33)))=s(X3,happ(s(t_fun(X4,X3),X13),s(X4,X33))),file('i/f/quotient/literal__case__RSP', ah4s_bools_literalu_u_caseu_u_DEF)).
fof(31, axiom,![X3]:![X4]:![X12]:![X11]:![X8]:![X7]:(p(s(t_bool,happ(s(t_fun(t_fun(X4,X3),t_bool),happ(s(t_fun(t_fun(X4,X3),t_fun(t_fun(X4,X3),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(t_fun(X3,t_fun(X3,t_bool)),X8))),s(t_fun(X4,X3),X11))),s(t_fun(X4,X3),X12))))<=>![X13]:![X14]:(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(X4,X13))),s(X4,X14))))=>p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X8),s(X3,happ(s(t_fun(X4,X3),X11),s(X4,X13))))),s(X3,happ(s(t_fun(X4,X3),X12),s(X4,X14)))))))),file('i/f/quotient/literal__case__RSP', ah4s_quotients_FUNu_u_REL)).
fof(36, axiom,![X3]:![X4]:![X41]:![X42]:![X43]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X4,t_fun(X4,t_bool)),X43),s(t_fun(X4,X3),X42),s(t_fun(X3,X4),X41))))=>![X25]:![X44]:(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X43),s(X4,X25))),s(X4,X44))))<=>(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X43),s(X4,X25))),s(X4,X25))))&(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X43),s(X4,X44))),s(X4,X44))))&s(X3,happ(s(t_fun(X4,X3),X42),s(X4,X25)))=s(X3,happ(s(t_fun(X4,X3),X42),s(X4,X44))))))),file('i/f/quotient/literal__case__RSP', ah4s_quotients_QUOTIENTu_u_REL)).
# SZS output end CNFRefutation
