# 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(X2,t_fun(X2,t_bool)),X7),s(t_fun(X2,X1),X6),s(t_fun(X1,X2),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]:s(t_h4s_sums_sum(X1,X4),happ(s(t_fun(X4,t_h4s_sums_sum(X1,X4)),h4s_sums_inr),s(X4,X11)))=s(t_h4s_sums_sum(X1,X4),happ(s(t_fun(t_h4s_sums_sum(X2,X3),t_h4s_sums_sum(X1,X4)),h4s_sums_u_2bu_2b(s(t_fun(X2,X1),X6),s(t_fun(X3,X4),X9))),s(t_h4s_sums_sum(X2,X3),happ(s(t_fun(X3,t_h4s_sums_sum(X2,X3)),h4s_sums_inr),s(X3,happ(s(t_fun(X4,X3),X10),s(X4,X11))))))))),file('i/f/quotient_sum/INR__PRS', ch4s_quotientu_u_sums_INRu_u_PRS)).
fof(5, axiom,![X22]:![X23]:((p(s(t_bool,X23))=>p(s(t_bool,X22)))=>((p(s(t_bool,X22))=>p(s(t_bool,X23)))=>s(t_bool,X23)=s(t_bool,X22))),file('i/f/quotient_sum/INR__PRS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,![X3]:![X2]:![X17]:![X18]:![X19]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X19),s(t_fun(X2,X3),X18),s(t_fun(X3,X2),X17))))<=>(![X20]:s(X3,happ(s(t_fun(X2,X3),X18),s(X2,happ(s(t_fun(X3,X2),X17),s(X3,X20)))))=s(X3,X20)&(![X20]:p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X19),s(X2,happ(s(t_fun(X3,X2),X17),s(X3,X20))))),s(X2,happ(s(t_fun(X3,X2),X17),s(X3,X20))))))&![X25]:![X26]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X19),s(X2,X25))),s(X2,X26))))<=>(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X19),s(X2,X25))),s(X2,X25))))&(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X19),s(X2,X26))),s(X2,X26))))&s(X3,happ(s(t_fun(X2,X3),X18),s(X2,X25)))=s(X3,happ(s(t_fun(X2,X3),X18),s(X2,X26))))))))),file('i/f/quotient_sum/INR__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(36, axiom,![X2]:![X1]:![X4]:![X3]:![X15]:![X14]:![X11]:s(t_h4s_sums_sum(X1,X4),happ(s(t_fun(t_h4s_sums_sum(X2,X3),t_h4s_sums_sum(X1,X4)),h4s_sums_u_2bu_2b(s(t_fun(X2,X1),X14),s(t_fun(X3,X4),X15))),s(t_h4s_sums_sum(X2,X3),happ(s(t_fun(X3,t_h4s_sums_sum(X2,X3)),h4s_sums_inr),s(X3,X11)))))=s(t_h4s_sums_sum(X1,X4),happ(s(t_fun(X4,t_h4s_sums_sum(X1,X4)),h4s_sums_inr),s(X4,happ(s(t_fun(X3,X4),X15),s(X3,X11))))),file('i/f/quotient_sum/INR__PRS', ah4s_sums_SUMu_u_MAPu_u_defu_c1)).
# SZS output end CNFRefutation
