# 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(X4,t_fun(X4,t_bool)),X7),s(t_fun(X4,X1),X6),s(t_fun(X1,X4),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,X2),X9),s(t_fun(X2,X3),X10))))=>![X11]:![X12]:((p(s(t_bool,happ(s(t_fun(t_fun(X4,X3),t_bool),happ(s(t_fun(t_fun(t_fun(X4,X3),t_fun(t_fun(X4,X3),t_bool)),t_fun(t_fun(X4,X3),t_bool)),h4s_quotients_respects),s(t_fun(t_fun(X4,X3),t_fun(t_fun(X4,X3),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(t_fun(X3,t_fun(X3,t_bool)),X8))))),s(t_fun(X4,X3),X11))))&p(s(t_bool,happ(s(t_fun(t_fun(X4,X3),t_bool),happ(s(t_fun(t_fun(t_fun(X4,X3),t_fun(t_fun(X4,X3),t_bool)),t_fun(t_fun(X4,X3),t_bool)),h4s_quotients_respects),s(t_fun(t_fun(X4,X3),t_fun(t_fun(X4,X3),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(t_fun(X3,t_fun(X3,t_bool)),X8))))),s(t_fun(X4,X3),X12)))))=>(s(t_fun(X1,X2),happ(s(t_fun(t_fun(X4,X3),t_fun(X1,X2)),h4s_quotients_u_2du_2du_3e(s(t_fun(X1,X4),X5),s(t_fun(X3,X2),X9))),s(t_fun(X4,X3),X11)))=s(t_fun(X1,X2),happ(s(t_fun(t_fun(X4,X3),t_fun(X1,X2)),h4s_quotients_u_2du_2du_3e(s(t_fun(X1,X4),X5),s(t_fun(X3,X2),X9))),s(t_fun(X4,X3),X12)))<=>![X13]:![X14]:(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(X4,X13))),s(X4,X14))))=>p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X8),s(X3,happ(s(t_fun(X4,X3),X11),s(X4,X13))))),s(X3,happ(s(t_fun(X4,X3),X12),s(X4,X14))))))))))),file('i/f/quotient/FUN__REL__EQUALS', ch4s_quotients_FUNu_u_RELu_u_EQUALS)).
fof(4, axiom,![X4]:![X1]:![X2]:![X3]:![X5]:![X6]:![X7]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(t_fun(X4,X1),X6),s(t_fun(X1,X4),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,X2),X9),s(t_fun(X2,X3),X10))))=>p(s(t_bool,h4s_quotients_quotient(s(t_fun(t_fun(X4,X3),t_fun(t_fun(X4,X3),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(t_fun(X3,t_fun(X3,t_bool)),X8))),s(t_fun(t_fun(X4,X3),t_fun(X1,X2)),h4s_quotients_u_2du_2du_3e(s(t_fun(X1,X4),X5),s(t_fun(X3,X2),X9))),s(t_fun(t_fun(X1,X2),t_fun(X4,X3)),h4s_quotients_u_2du_2du_3e(s(t_fun(X4,X1),X6),s(t_fun(X2,X3),X10)))))))),file('i/f/quotient/FUN__REL__EQUALS', ah4s_quotients_FUNu_u_QUOTIENT)).
fof(5, axiom,![X3]:![X4]:![X12]:![X11]:![X8]:![X7]:(p(s(t_bool,happ(s(t_fun(t_fun(X4,X3),t_bool),happ(s(t_fun(t_fun(X4,X3),t_fun(t_fun(X4,X3),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(t_fun(X3,t_fun(X3,t_bool)),X8))),s(t_fun(X4,X3),X11))),s(t_fun(X4,X3),X12))))<=>![X13]:![X14]:(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X7),s(X4,X13))),s(X4,X14))))=>p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X8),s(X3,happ(s(t_fun(X4,X3),X11),s(X4,X13))))),s(X3,happ(s(t_fun(X4,X3),X12),s(X4,X14)))))))),file('i/f/quotient/FUN__REL__EQUALS', ah4s_quotients_FUNu_u_REL)).
fof(6, axiom,![X4]:![X3]:s(t_fun(t_fun(X4,t_fun(X4,X3)),t_fun(X4,X3)),h4s_quotients_respects)=s(t_fun(t_fun(X4,t_fun(X4,X3)),t_fun(X4,X3)),h4s_combins_w),file('i/f/quotient/FUN__REL__EQUALS', ah4s_quotients_respectsu_u_def)).
fof(7, axiom,![X3]:![X4]:![X17]:![X18]:![X19]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X4,t_fun(X4,t_bool)),X19),s(t_fun(X4,X3),X18),s(t_fun(X3,X4),X17))))=>![X20]:![X21]:(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X19),s(X4,X20))),s(X4,X20))))=>(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X19),s(X4,X21))),s(X4,X21))))=>(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X19),s(X4,X20))),s(X4,X21))))<=>s(X3,happ(s(t_fun(X4,X3),X18),s(X4,X20)))=s(X3,happ(s(t_fun(X4,X3),X18),s(X4,X21))))))),file('i/f/quotient/FUN__REL__EQUALS', ah4s_quotients_QUOTIENTu_u_RELu_u_ABSu_u_EQ)).
fof(8, axiom,![X3]:![X4]:![X13]:![X11]:s(X3,happ(s(t_fun(X4,X3),happ(s(t_fun(t_fun(X4,t_fun(X4,X3)),t_fun(X4,X3)),h4s_combins_w),s(t_fun(X4,t_fun(X4,X3)),X11))),s(X4,X13)))=s(X3,happ(s(t_fun(X4,X3),happ(s(t_fun(X4,t_fun(X4,X3)),X11),s(X4,X13))),s(X4,X13))),file('i/f/quotient/FUN__REL__EQUALS', ah4s_combins_Wu_u_THM)).
# SZS output end CNFRefutation
