# 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(X1,t_fun(X1,t_bool)),X7),s(t_fun(X1,X2),X6),s(t_fun(X2,X1),X5))))=>![X8]:![X9]:![X10]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X8),s(t_fun(X3,X4),X9),s(t_fun(X4,X3),X10))))=>![X11]:![X12]:s(X2,happ(s(t_fun(X4,X2),happ(s(t_fun(X2,t_fun(X4,X2)),h4s_combins_k),s(X2,X11))),s(X4,X12)))=s(X2,happ(s(t_fun(X1,X2),X6),s(X1,happ(s(t_fun(X3,X1),happ(s(t_fun(X1,t_fun(X3,X1)),h4s_combins_k),s(X1,happ(s(t_fun(X2,X1),X5),s(X2,X11))))),s(X3,happ(s(t_fun(X4,X3),X10),s(X4,X12))))))))),file('i/f/quotient/K__PRS', ch4s_quotients_Ku_u_PRS)).
fof(33, axiom,![X3]:![X1]:![X32]:![X33]:![X34]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X34),s(t_fun(X1,X3),X33),s(t_fun(X3,X1),X32))))<=>(![X35]:s(X3,happ(s(t_fun(X1,X3),X33),s(X1,happ(s(t_fun(X3,X1),X32),s(X3,X35)))))=s(X3,X35)&(![X35]:p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X34),s(X1,happ(s(t_fun(X3,X1),X32),s(X3,X35))))),s(X1,happ(s(t_fun(X3,X1),X32),s(X3,X35))))))&![X26]:![X36]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X34),s(X1,X26))),s(X1,X36))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X34),s(X1,X26))),s(X1,X26))))&(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X34),s(X1,X36))),s(X1,X36))))&s(X3,happ(s(t_fun(X1,X3),X33),s(X1,X26)))=s(X3,happ(s(t_fun(X1,X3),X33),s(X1,X36))))))))),file('i/f/quotient/K__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(34, axiom,![X3]:![X1]:![X11]:![X37]:s(X1,happ(s(t_fun(X3,X1),happ(s(t_fun(X1,t_fun(X3,X1)),h4s_combins_k),s(X1,X11))),s(X3,X37)))=s(X1,X11),file('i/f/quotient/K__PRS', ah4s_combins_Ku_u_DEF)).
fof(38, axiom,~(p(s(t_bool,f))),file('i/f/quotient/K__PRS', aHLu_FALSITY)).
fof(73, axiom,![X17]:(s(t_bool,X17)=s(t_bool,t)|s(t_bool,X17)=s(t_bool,f)),file('i/f/quotient/K__PRS', aHLu_BOOLu_CASES)).
fof(74, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/quotient/K__PRS', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
