# 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(X2,t_fun(X2,t_bool)),X5),s(t_fun(X2,X1),X4),s(t_fun(X1,X2),X3))))=>![X6]:![X7]:![X8]:![X9]:((p(s(t_bool,happ(s(t_fun(t_fun(X2,t_bool),t_bool),happ(s(t_fun(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_equals))),s(t_fun(X2,t_bool),X6))),s(t_fun(X2,t_bool),X7))))&p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X8))),s(X2,X9)))))=>s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X6)))=s(t_bool,h4s_bools_in(s(X2,X9),s(t_fun(X2,t_bool),X7))))),file('i/f/quotient_pred_set/SET__REL__MP', ch4s_quotientu_u_predu_u_sets_SETu_u_RELu_u_MP)).
fof(4, axiom,![X2]:![X8]:![X10]:s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X10)))=s(t_bool,happ(s(t_fun(X2,t_bool),X10),s(X2,X8))),file('i/f/quotient_pred_set/SET__REL__MP', ah4s_predu_u_sets_SPECIFICATION)).
fof(5, axiom,![X2]:![X7]:![X6]:![X5]:(p(s(t_bool,happ(s(t_fun(t_fun(X2,t_bool),t_bool),happ(s(t_fun(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_equals))),s(t_fun(X2,t_bool),X6))),s(t_fun(X2,t_bool),X7))))<=>![X8]:![X9]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X8))),s(X2,X9))))=>s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X6)))=s(t_bool,h4s_bools_in(s(X2,X9),s(t_fun(X2,t_bool),X7))))),file('i/f/quotient_pred_set/SET__REL__MP', ah4s_quotientu_u_predu_u_sets_SETu_u_REL)).
fof(6, axiom,![X11]:![X12]:((p(s(t_bool,X12))=>p(s(t_bool,X11)))=>((p(s(t_bool,X11))=>p(s(t_bool,X12)))=>s(t_bool,X12)=s(t_bool,X11))),file('i/f/quotient_pred_set/SET__REL__MP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(43, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_fun(X2,X1),X4),s(t_fun(X1,X2),X3))))<=>(![X26]:s(X1,happ(s(t_fun(X2,X1),X4),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X26)))))=s(X1,X26)&(![X26]:p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X26))))),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X26))))))&![X13]:![X6]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X13))),s(X2,X6))))<=>(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X13))),s(X2,X13))))&(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X6))),s(X2,X6))))&s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X13)))=s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X6))))))))),file('i/f/quotient_pred_set/SET__REL__MP', ah4s_quotients_QUOTIENTu_u_def)).
# SZS output end CNFRefutation
