# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(![X6]:![X7]:![X8]:![X9]:s(X1,happ(s(t_fun(X3,X1),happ(s(t_fun(t_fun(X3,X4),t_fun(X3,X1)),happ(s(t_fun(t_fun(X4,X2),t_fun(t_fun(X3,X4),t_fun(X3,X1))),happ(s(t_fun(t_fun(X2,X1),t_fun(t_fun(X4,X2),t_fun(t_fun(X3,X4),t_fun(X3,X1)))),X5),s(t_fun(X2,X1),X6))),s(t_fun(X4,X2),X7))),s(t_fun(X3,X4),X8))),s(X3,X9)))=s(X1,happ(s(t_fun(X2,X1),X6),s(X2,happ(s(t_fun(X4,X2),X7),s(X4,happ(s(t_fun(X3,X4),X8),s(X3,X9)))))))=>![X10]:![X8]:![X11]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X11),s(t_fun(X3,X4),X8),s(t_fun(X4,X3),X10))))=>![X12]:![X13]:![X6]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X12),s(t_fun(X1,X2),X13),s(t_fun(X2,X1),X6))))=>![X7]:![X9]:s(X2,happ(s(t_fun(X4,X2),X7),s(X4,X9)))=s(X2,happ(s(t_fun(X4,X2),happ(s(t_fun(t_fun(X3,X1),t_fun(X4,X2)),h4s_quotients_u_2du_2du_3e(s(t_fun(X4,X3),X10),s(t_fun(X1,X2),X13))),s(t_fun(X3,X1),happ(s(t_fun(t_fun(X3,X4),t_fun(X3,X1)),happ(s(t_fun(t_fun(X4,X2),t_fun(t_fun(X3,X4),t_fun(X3,X1))),happ(s(t_fun(t_fun(X2,X1),t_fun(t_fun(X4,X2),t_fun(t_fun(X3,X4),t_fun(X3,X1)))),X5),s(t_fun(X2,X1),X6))),s(t_fun(X4,X2),X7))),s(t_fun(X3,X4),X8))))),s(X4,X9)))))),file('i/f/quotient/LAMBDA__PRS', ch4s_quotients_LAMBDAu_u_PRS)).
fof(26, axiom,![X1]:![X3]:![X34]:![X35]:![X36]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X36),s(t_fun(X3,X1),X35),s(t_fun(X1,X3),X34))))<=>(![X37]:s(X1,happ(s(t_fun(X3,X1),X35),s(X3,happ(s(t_fun(X1,X3),X34),s(X1,X37)))))=s(X1,X37)&(![X37]:p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X36),s(X3,happ(s(t_fun(X1,X3),X34),s(X1,X37))))),s(X3,happ(s(t_fun(X1,X3),X34),s(X1,X37))))))&![X26]:![X38]:(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X36),s(X3,X26))),s(X3,X38))))<=>(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X36),s(X3,X26))),s(X3,X26))))&(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X36),s(X3,X38))),s(X3,X38))))&s(X1,happ(s(t_fun(X3,X1),X35),s(X3,X26)))=s(X1,happ(s(t_fun(X3,X1),X35),s(X3,X38))))))))),file('i/f/quotient/LAMBDA__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(38, axiom,![X2]:![X1]:![X4]:![X3]:![X16]:![X7]:![X9]:![X44]:s(X2,happ(s(t_fun(X3,X2),happ(s(t_fun(t_fun(X4,X1),t_fun(X3,X2)),h4s_quotients_u_2du_2du_3e(s(t_fun(X3,X4),X7),s(t_fun(X1,X2),X16))),s(t_fun(X4,X1),X9))),s(X3,X44)))=s(X2,happ(s(t_fun(X1,X2),X16),s(X1,happ(s(t_fun(X4,X1),X9),s(X4,happ(s(t_fun(X3,X4),X7),s(X3,X44))))))),file('i/f/quotient/LAMBDA__PRS', ah4s_quotients_FUNu_u_MAP)).
fof(69, axiom,p(s(t_bool,t)),file('i/f/quotient/LAMBDA__PRS', aHLu_TRUTH)).
fof(73, axiom,![X17]:(s(t_bool,X17)=s(t_bool,t)<=>p(s(t_bool,X17))),file('i/f/quotient/LAMBDA__PRS', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
