# 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(X3,t_fun(X3,t_bool)),X7),s(t_fun(X3,X4),X6),s(t_fun(X4,X3),X5))))=>![X8]:![X9]:![X10]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X8),s(t_fun(X2,X1),X9),s(t_fun(X1,X2),X10))))=>![X11]:s(t_h4s_sums_sum(X4,X1),happ(s(t_fun(X4,t_h4s_sums_sum(X4,X1)),h4s_sums_inl),s(X4,X11)))=s(t_h4s_sums_sum(X4,X1),happ(s(t_fun(t_h4s_sums_sum(X3,X2),t_h4s_sums_sum(X4,X1)),h4s_sums_u_2bu_2b(s(t_fun(X3,X4),X6),s(t_fun(X2,X1),X9))),s(t_h4s_sums_sum(X3,X2),happ(s(t_fun(X3,t_h4s_sums_sum(X3,X2)),h4s_sums_inl),s(X3,happ(s(t_fun(X4,X3),X5),s(X4,X11))))))))),file('i/f/quotient_sum/INL__PRS', ch4s_quotientu_u_sums_INLu_u_PRS)).
fof(4, axiom,![X2]:![X3]:![X17]:![X18]:![X19]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X19),s(t_fun(X3,X2),X18),s(t_fun(X2,X3),X17))))<=>(![X11]:s(X2,happ(s(t_fun(X3,X2),X18),s(X3,happ(s(t_fun(X2,X3),X17),s(X2,X11)))))=s(X2,X11)&(![X11]:p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X19),s(X3,happ(s(t_fun(X2,X3),X17),s(X2,X11))))),s(X3,happ(s(t_fun(X2,X3),X17),s(X2,X11))))))&![X20]:![X21]:(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X19),s(X3,X20))),s(X3,X21))))<=>(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X19),s(X3,X20))),s(X3,X20))))&(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X19),s(X3,X21))),s(X3,X21))))&s(X2,happ(s(t_fun(X3,X2),X18),s(X3,X20)))=s(X2,happ(s(t_fun(X3,X2),X18),s(X3,X21))))))))),file('i/f/quotient_sum/INL__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(33, axiom,![X2]:![X1]:![X4]:![X3]:![X15]:![X14]:![X11]:s(t_h4s_sums_sum(X4,X1),happ(s(t_fun(t_h4s_sums_sum(X3,X2),t_h4s_sums_sum(X4,X1)),h4s_sums_u_2bu_2b(s(t_fun(X3,X4),X14),s(t_fun(X2,X1),X15))),s(t_h4s_sums_sum(X3,X2),happ(s(t_fun(X3,t_h4s_sums_sum(X3,X2)),h4s_sums_inl),s(X3,X11)))))=s(t_h4s_sums_sum(X4,X1),happ(s(t_fun(X4,t_h4s_sums_sum(X4,X1)),h4s_sums_inl),s(X4,happ(s(t_fun(X3,X4),X14),s(X3,X11))))),file('i/f/quotient_sum/INL__PRS', ah4s_sums_SUMu_u_MAPu_u_defu_c0)).
fof(46, axiom,~(p(s(t_bool,f))),file('i/f/quotient_sum/INL__PRS', aHLu_FALSITY)).
fof(78, axiom,![X22]:(s(t_bool,X22)=s(t_bool,t)|s(t_bool,X22)=s(t_bool,f)),file('i/f/quotient_sum/INL__PRS', aHLu_BOOLu_CASES)).
fof(79, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/quotient_sum/INL__PRS', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
