# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(t_fun(X1,X2),X4),s(t_fun(X2,X1),X3))))=>![X6]:![X7]:![X8]:s(X2,h4s_bools_cond(s(t_bool,X6),s(X2,X7),s(X2,X8)))=s(X2,happ(s(t_fun(X1,X2),X4),s(X1,h4s_bools_cond(s(t_bool,X6),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X7))),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X8)))))))),file('i/f/quotient/COND__PRS', ch4s_quotients_CONDu_u_PRS)).
fof(3, axiom,![X2]:![X1]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(t_fun(X1,X2),X4),s(t_fun(X2,X1),X3))))<=>(![X6]:s(X2,happ(s(t_fun(X1,X2),X4),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X6)))))=s(X2,X6)&(![X6]:p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X6))))),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X6))))))&![X14]:![X15]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X14))),s(X1,X15))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X14))),s(X1,X14))))&(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X15))),s(X1,X15))))&s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X14)))=s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X15))))))))),file('i/f/quotient/COND__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(54, axiom,![X2]:![X1]:![X19]:![X13]:![X11]:![X7]:s(X2,happ(s(t_fun(X1,X2),X11),s(X1,h4s_bools_cond(s(t_bool,X7),s(X1,X13),s(X1,X19)))))=s(X2,h4s_bools_cond(s(t_bool,X7),s(X2,happ(s(t_fun(X1,X2),X11),s(X1,X13))),s(X2,happ(s(t_fun(X1,X2),X11),s(X1,X19))))),file('i/f/quotient/COND__PRS', ah4s_bools_CONDu_u_RAND)).
fof(71, axiom,~(p(s(t_bool,f))),file('i/f/quotient/COND__PRS', aHLu_FALSITY)).
fof(72, axiom,![X18]:(s(t_bool,X18)=s(t_bool,t)|s(t_bool,X18)=s(t_bool,f)),file('i/f/quotient/COND__PRS', aHLu_BOOLu_CASES)).
fof(81, axiom,(~(p(s(t_bool,t)))<=>p(s(t_bool,f))),file('i/f/quotient/COND__PRS', ah4s_bools_NOTu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
