# 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(X3,t_fun(X3,t_bool)),X7),s(t_fun(X3,X4),X6),s(t_fun(X4,X3),X5))))=>![X8]:![X9]:![X10]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X8),s(t_fun(X1,X2),X9),s(t_fun(X2,X1),X10))))=>![X11]:![X12]:s(X2,happ(s(t_fun(X4,X2),X11),s(X4,X12)))=s(X2,happ(s(t_fun(X1,X2),X9),s(X1,happ(s(t_fun(X3,X1),happ(s(t_fun(t_fun(X4,X2),t_fun(X3,X1)),h4s_quotients_u_2du_2du_3e(s(t_fun(X3,X4),X6),s(t_fun(X2,X1),X10))),s(t_fun(X4,X2),X11))),s(X3,happ(s(t_fun(X4,X3),X5),s(X4,X12))))))))),file('i/f/quotient/APPLY__PRS', ch4s_quotients_APPLYu_u_PRS)).
fof(5, axiom,![X1]:![X3]:![X16]:![X17]:![X18]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X18),s(t_fun(X3,X1),X17),s(t_fun(X1,X3),X16))))<=>(![X19]:s(X1,happ(s(t_fun(X3,X1),X17),s(X3,happ(s(t_fun(X1,X3),X16),s(X1,X19)))))=s(X1,X19)&(![X19]:p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X18),s(X3,happ(s(t_fun(X1,X3),X16),s(X1,X19))))),s(X3,happ(s(t_fun(X1,X3),X16),s(X1,X19))))))&![X22]:![X23]:(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X18),s(X3,X22))),s(X3,X23))))<=>(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X18),s(X3,X22))),s(X3,X22))))&(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X18),s(X3,X23))),s(X3,X23))))&s(X1,happ(s(t_fun(X3,X1),X17),s(X3,X22)))=s(X1,happ(s(t_fun(X3,X1),X17),s(X3,X23))))))))),file('i/f/quotient/APPLY__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(32, axiom,![X2]:![X1]:![X4]:![X3]:![X15]:![X11]:![X12]:![X37]: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),X11),s(t_fun(X1,X2),X15))),s(t_fun(X4,X1),X12))),s(X3,X37)))=s(X2,happ(s(t_fun(X1,X2),X15),s(X1,happ(s(t_fun(X4,X1),X12),s(X4,happ(s(t_fun(X3,X4),X11),s(X3,X37))))))),file('i/f/quotient/APPLY__PRS', ah4s_quotients_FUNu_u_MAP)).
fof(70, axiom,p(s(t_bool,t)),file('i/f/quotient/APPLY__PRS', aHLu_TRUTH)).
fof(75, axiom,![X24]:(s(t_bool,X24)=s(t_bool,t)<=>p(s(t_bool,X24))),file('i/f/quotient/APPLY__PRS', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
