# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:![X8]:![X9]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X5,t_fun(X5,t_bool)),X9),s(t_fun(X5,X6),X8),s(t_fun(X6,X5),X7))))=>![X10]:![X11]:![X12]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X10),s(t_fun(X3,X4),X11),s(t_fun(X4,X3),X12))))=>![X13]:![X14]:![X15]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X13),s(t_fun(X1,X2),X14),s(t_fun(X2,X1),X15))))=>![X16]:![X17]:![X18]:s(X2,happ(s(t_fun(X6,X2),happ(s(t_fun(X4,t_fun(X6,X2)),happ(s(t_fun(t_fun(X6,t_fun(X4,X2)),t_fun(X4,t_fun(X6,X2))),h4s_combins_c),s(t_fun(X6,t_fun(X4,X2)),X16))),s(X4,X17))),s(X6,X18)))=s(X2,happ(s(t_fun(X1,X2),X14),s(X1,happ(s(t_fun(X5,X1),happ(s(t_fun(X3,t_fun(X5,X1)),happ(s(t_fun(t_fun(X5,t_fun(X3,X1)),t_fun(X3,t_fun(X5,X1))),h4s_combins_c),s(t_fun(X5,t_fun(X3,X1)),happ(s(t_fun(t_fun(X6,t_fun(X4,X2)),t_fun(X5,t_fun(X3,X1))),h4s_quotients_u_2du_2du_3e(s(t_fun(X5,X6),X8),s(t_fun(t_fun(X4,X2),t_fun(X3,X1)),h4s_quotients_u_2du_2du_3e(s(t_fun(X3,X4),X11),s(t_fun(X2,X1),X15))))),s(t_fun(X6,t_fun(X4,X2)),X16))))),s(X3,happ(s(t_fun(X4,X3),X12),s(X4,X17))))),s(X5,happ(s(t_fun(X6,X5),X7),s(X6,X18)))))))))),file('i/f/quotient/C__PRS', ch4s_quotients_Cu_u_PRS)).
fof(5, axiom,![X27]:![X28]:((p(s(t_bool,X28))=>p(s(t_bool,X27)))=>((p(s(t_bool,X27))=>p(s(t_bool,X28)))=>s(t_bool,X28)=s(t_bool,X27))),file('i/f/quotient/C__PRS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(7, axiom,![X3]:![X5]:![X22]:![X23]:![X24]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X5,t_fun(X5,t_bool)),X24),s(t_fun(X5,X3),X23),s(t_fun(X3,X5),X22))))<=>(![X25]:s(X3,happ(s(t_fun(X5,X3),X23),s(X5,happ(s(t_fun(X3,X5),X22),s(X3,X25)))))=s(X3,X25)&(![X25]:p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X24),s(X5,happ(s(t_fun(X3,X5),X22),s(X3,X25))))),s(X5,happ(s(t_fun(X3,X5),X22),s(X3,X25))))))&![X29]:![X30]:(p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X24),s(X5,X29))),s(X5,X30))))<=>(p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X24),s(X5,X29))),s(X5,X29))))&(p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X24),s(X5,X30))),s(X5,X30))))&s(X3,happ(s(t_fun(X5,X3),X23),s(X5,X29)))=s(X3,happ(s(t_fun(X5,X3),X23),s(X5,X30))))))))),file('i/f/quotient/C__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(31, axiom,![X6]:![X3]:![X1]:![X5]:![X21]:![X16]:![X17]:![X42]:s(X6,happ(s(t_fun(X5,X6),happ(s(t_fun(t_fun(X1,X3),t_fun(X5,X6)),h4s_quotients_u_2du_2du_3e(s(t_fun(X5,X1),X16),s(t_fun(X3,X6),X21))),s(t_fun(X1,X3),X17))),s(X5,X42)))=s(X6,happ(s(t_fun(X3,X6),X21),s(X3,happ(s(t_fun(X1,X3),X17),s(X1,happ(s(t_fun(X5,X1),X16),s(X5,X42))))))),file('i/f/quotient/C__PRS', ah4s_quotients_FUNu_u_MAP)).
fof(47, axiom,![X1]:![X5]:![X3]:![X17]:![X42]:![X50]:s(X1,happ(s(t_fun(X5,X1),happ(s(t_fun(X3,t_fun(X5,X1)),happ(s(t_fun(t_fun(X5,t_fun(X3,X1)),t_fun(X3,t_fun(X5,X1))),h4s_combins_c),s(t_fun(X5,t_fun(X3,X1)),X17))),s(X3,X42))),s(X5,X50)))=s(X1,happ(s(t_fun(X3,X1),happ(s(t_fun(X5,t_fun(X3,X1)),X17),s(X5,X50))),s(X3,X42))),file('i/f/quotient/C__PRS', ah4s_combins_Cu_u_DEF)).
# SZS output end CNFRefutation
