# 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]:s(X2,happ(s(t_fun(X2,X2),h4s_combins_i),s(X2,X6)))=s(X2,happ(s(t_fun(X1,X2),X4),s(X1,happ(s(t_fun(X1,X1),h4s_combins_i),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X6)))))))),file('i/f/quotient/I__PRS', ch4s_quotients_Iu_u_PRS)).
fof(25, 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))))<=>(![X27]:s(X2,happ(s(t_fun(X1,X2),X4),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X27)))))=s(X2,X27)&(![X27]: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,X27))))),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X27))))))&![X21]:![X28]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X21))),s(X1,X28))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X21))),s(X1,X21))))&(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X28))),s(X1,X28))))&s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X21)))=s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X28))))))))),file('i/f/quotient/I__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(28, axiom,![X1]:![X11]:s(X1,happ(s(t_fun(X1,X1),h4s_combins_i),s(X1,X11)))=s(X1,X11),file('i/f/quotient/I__PRS', ah4s_combins_Iu_u_THM)).
fof(45, axiom,~(p(s(t_bool,f))),file('i/f/quotient/I__PRS', aHLu_FALSITY)).
fof(68, axiom,![X14]:(s(t_bool,X14)=s(t_bool,t)|s(t_bool,X14)=s(t_bool,f)),file('i/f/quotient/I__PRS', aHLu_BOOLu_CASES)).
fof(69, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/quotient/I__PRS', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
