# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(![X6]:![X7]:![X8]:![X9]:s(X2,happ(s(t_fun(X1,X2),happ(s(t_fun(t_fun(X4,X3),t_fun(X1,X2)),happ(s(t_fun(t_fun(X3,X2),t_fun(t_fun(X4,X3),t_fun(X1,X2))),happ(s(t_fun(t_fun(X1,X4),t_fun(t_fun(X3,X2),t_fun(t_fun(X4,X3),t_fun(X1,X2)))),X5),s(t_fun(X1,X4),X6))),s(t_fun(X3,X2),X7))),s(t_fun(X4,X3),X8))),s(X1,X9)))=s(X2,happ(s(t_fun(X1,X2),happ(s(t_fun(t_fun(X4,X3),t_fun(X1,X2)),h4s_quotients_u_2du_2du_3e(s(t_fun(X1,X4),X6),s(t_fun(X3,X2),X7))),s(t_fun(X4,X3),X8))),s(X1,X9)))=>![X10]:![X6]:![X11]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X11),s(t_fun(X1,X4),X6),s(t_fun(X4,X1),X10))))=>![X12]:![X13]:![X7]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X12),s(t_fun(X2,X3),X13),s(t_fun(X3,X2),X7))))=>![X8]:![X9]:s(X3,happ(s(t_fun(X4,X3),X8),s(X4,X9)))=s(X3,happ(s(t_fun(X4,X3),happ(s(t_fun(t_fun(X1,X2),t_fun(X4,X3)),h4s_quotients_u_2du_2du_3e(s(t_fun(X4,X1),X10),s(t_fun(X2,X3),X13))),s(t_fun(X1,X2),happ(s(t_fun(t_fun(X4,X3),t_fun(X1,X2)),happ(s(t_fun(t_fun(X3,X2),t_fun(t_fun(X4,X3),t_fun(X1,X2))),happ(s(t_fun(t_fun(X1,X4),t_fun(t_fun(X3,X2),t_fun(t_fun(X4,X3),t_fun(X1,X2)))),X5),s(t_fun(X1,X4),X6))),s(t_fun(X3,X2),X7))),s(t_fun(X4,X3),X8))))),s(X4,X9)))))),file('i/f/quotient/LAMBDA__PRS1', ch4s_quotients_LAMBDAu_u_PRS1)).
fof(34, axiom,![X2]:![X1]:![X31]:![X32]:![X33]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X33),s(t_fun(X1,X2),X32),s(t_fun(X2,X1),X31))))<=>(![X30]:s(X2,happ(s(t_fun(X1,X2),X32),s(X1,happ(s(t_fun(X2,X1),X31),s(X2,X30)))))=s(X2,X30)&(![X30]:p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X33),s(X1,happ(s(t_fun(X2,X1),X31),s(X2,X30))))),s(X1,happ(s(t_fun(X2,X1),X31),s(X2,X30))))))&![X22]:![X34]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X33),s(X1,X22))),s(X1,X34))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X33),s(X1,X22))),s(X1,X22))))&(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X33),s(X1,X34))),s(X1,X34))))&s(X2,happ(s(t_fun(X1,X2),X32),s(X1,X22)))=s(X2,happ(s(t_fun(X1,X2),X32),s(X1,X34))))))))),file('i/f/quotient/LAMBDA__PRS1', ah4s_quotients_QUOTIENTu_u_def)).
fof(38, axiom,![X3]:![X2]:![X4]:![X1]:![X16]:![X8]:![X9]:![X35]:s(X3,happ(s(t_fun(X1,X3),happ(s(t_fun(t_fun(X4,X2),t_fun(X1,X3)),h4s_quotients_u_2du_2du_3e(s(t_fun(X1,X4),X8),s(t_fun(X2,X3),X16))),s(t_fun(X4,X2),X9))),s(X1,X35)))=s(X3,happ(s(t_fun(X2,X3),X16),s(X2,happ(s(t_fun(X4,X2),X9),s(X4,happ(s(t_fun(X1,X4),X8),s(X1,X35))))))),file('i/f/quotient/LAMBDA__PRS1', ah4s_quotients_FUNu_u_MAP)).
fof(76, axiom,p(s(t_bool,t)),file('i/f/quotient/LAMBDA__PRS1', aHLu_TRUTH)).
fof(78, axiom,![X20]:(s(t_bool,X20)=s(t_bool,t)<=>p(s(t_bool,X20))),file('i/f/quotient/LAMBDA__PRS1', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
