# 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]:s(t_bool,h4s_bools_in(s(X2,X6),s(t_fun(X2,t_bool),X7)))=s(t_bool,h4s_bools_in(s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X6))),s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X2,t_bool),t_fun(X1,t_bool)),h4s_quotients_u_2du_2du_3e(s(t_fun(X1,X2),X4),s(t_fun(t_bool,t_bool),h4s_combins_i))),s(t_fun(X2,t_bool),X7)))))),file('i/f/quotient_pred_set/IN__PRS', ch4s_quotientu_u_predu_u_sets_INu_u_PRS)).
fof(5, 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))))<=>(![X12]:s(X2,happ(s(t_fun(X1,X2),X4),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X12)))))=s(X2,X12)&(![X12]: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,X12))))),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X12))))))&![X15]:![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,X15))),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,X15))),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,X7))),s(X1,X7))))&s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X15)))=s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X7))))))))),file('i/f/quotient_pred_set/IN__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(36, axiom,![X1]:![X6]:![X25]:s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X25)))=s(t_bool,happ(s(t_fun(X1,t_bool),X25),s(X1,X6))),file('i/f/quotient_pred_set/IN__PRS', ah4s_predu_u_sets_SPECIFICATION)).
fof(40, axiom,![X30]:![X2]:![X31]:![X1]:![X6]:![X32]:![X11]:![X10]:s(X30,happ(s(t_fun(X1,X30),happ(s(t_fun(t_fun(X31,X2),t_fun(X1,X30)),h4s_quotients_u_2du_2du_3e(s(t_fun(X1,X31),X10),s(t_fun(X2,X30),X11))),s(t_fun(X31,X2),X32))),s(X1,X6)))=s(X30,happ(s(t_fun(X2,X30),X11),s(X2,happ(s(t_fun(X31,X2),X32),s(X31,happ(s(t_fun(X1,X31),X10),s(X1,X6))))))),file('i/f/quotient_pred_set/IN__PRS', ah4s_quotients_FUNu_u_MAPu_u_THM)).
fof(41, axiom,![X1]:![X6]:s(X1,happ(s(t_fun(X1,X1),h4s_combins_i),s(X1,X6)))=s(X1,X6),file('i/f/quotient_pred_set/IN__PRS', ah4s_combins_Iu_u_THM)).
fof(53, axiom,~(p(s(t_bool,f))),file('i/f/quotient_pred_set/IN__PRS', aHLu_FALSITY)).
fof(77, axiom,![X16]:(s(t_bool,X16)=s(t_bool,t)|s(t_bool,X16)=s(t_bool,f)),file('i/f/quotient_pred_set/IN__PRS', aHLu_BOOLu_CASES)).
fof(78, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/quotient_pred_set/IN__PRS', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
