# 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]: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))))))),file('i/f/quotient/QUOTIENT__REP__REFL', ch4s_quotients_QUOTIENTu_u_REPu_u_REFL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/quotient/QUOTIENT__REP__REFL', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/quotient/QUOTIENT__REP__REFL', aHLu_FALSITY)).
fof(4, 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))))))&![X7]:![X8]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X7))),s(X1,X8))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X7))),s(X1,X7))))&(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X8))),s(X1,X8))))&s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X7)))=s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X8))))))))),file('i/f/quotient/QUOTIENT__REP__REFL', ah4s_quotients_QUOTIENTu_u_def)).
fof(5, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/quotient/QUOTIENT__REP__REFL', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
