# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:(s(t_h4s_sums_sum(X1,X2),h4s_bools_cond(s(t_bool,X6),s(t_h4s_sums_sum(X1,X2),happ(s(t_fun(X1,t_h4s_sums_sum(X1,X2)),h4s_sums_inl),s(X1,X5))),s(t_h4s_sums_sum(X1,X2),happ(s(t_fun(X2,t_h4s_sums_sum(X1,X2)),h4s_sums_inr),s(X2,X4)))))=s(t_h4s_sums_sum(X1,X2),happ(s(t_fun(X2,t_h4s_sums_sum(X1,X2)),h4s_sums_inr),s(X2,X3)))<=>(~(p(s(t_bool,X6)))&s(X2,X3)=s(X2,X4))),file('i/f/sum/cond__sum__expand_c3', ch4s_sums_condu_u_sumu_u_expandu_c3)).
fof(5, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/sum/cond__sum__expand_c3', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(31, axiom,![X8]:![X7]:![X30]:(?[X5]:s(t_h4s_sums_sum(X8,X7),X30)=s(t_h4s_sums_sum(X8,X7),happ(s(t_fun(X8,t_h4s_sums_sum(X8,X7)),h4s_sums_inl),s(X8,X5)))|?[X4]:s(t_h4s_sums_sum(X8,X7),X30)=s(t_h4s_sums_sum(X8,X7),happ(s(t_fun(X7,t_h4s_sums_sum(X8,X7)),h4s_sums_inr),s(X7,X4)))),file('i/f/sum/cond__sum__expand_c3', ah4s_sums_sumu_u_CASES)).
fof(34, axiom,![X8]:![X7]:![X4]:![X5]:(s(t_h4s_sums_sum(X8,X7),happ(s(t_fun(X7,t_h4s_sums_sum(X8,X7)),h4s_sums_inr),s(X7,X5)))=s(t_h4s_sums_sum(X8,X7),happ(s(t_fun(X7,t_h4s_sums_sum(X8,X7)),h4s_sums_inr),s(X7,X4)))<=>s(X7,X5)=s(X7,X4)),file('i/f/sum/cond__sum__expand_c3', ah4s_sums_INRu_u_11)).
fof(39, axiom,![X7]:![X8]:![X32]:![X33]:~(s(t_h4s_sums_sum(X8,X7),happ(s(t_fun(X7,t_h4s_sums_sum(X8,X7)),h4s_sums_inr),s(X7,X32)))=s(t_h4s_sums_sum(X8,X7),happ(s(t_fun(X8,t_h4s_sums_sum(X8,X7)),h4s_sums_inl),s(X8,X33)))),file('i/f/sum/cond__sum__expand_c3', ah4s_sums_INRu_u_nequ_u_INL)).
fof(40, axiom,![X34]:![X35]:![X3]:![X4]:![X5]:![X6]:(s(t_h4s_sums_sum(X35,X34),h4s_bools_cond(s(t_bool,X6),s(t_h4s_sums_sum(X35,X34),happ(s(t_fun(X35,t_h4s_sums_sum(X35,X34)),h4s_sums_inl),s(X35,X5))),s(t_h4s_sums_sum(X35,X34),happ(s(t_fun(X34,t_h4s_sums_sum(X35,X34)),h4s_sums_inr),s(X34,X4)))))=s(t_h4s_sums_sum(X35,X34),happ(s(t_fun(X35,t_h4s_sums_sum(X35,X34)),h4s_sums_inl),s(X35,X3)))<=>(p(s(t_bool,X6))&s(X35,X3)=s(X35,X5))),file('i/f/sum/cond__sum__expand_c3', ah4s_sums_condu_u_sumu_u_expandu_c2)).
fof(42, axiom,![X8]:![X9]:![X10]:s(X8,h4s_bools_cond(s(t_bool,t),s(X8,X10),s(X8,X9)))=s(X8,X10),file('i/f/sum/cond__sum__expand_c3', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(43, axiom,![X8]:![X9]:![X10]:s(X8,h4s_bools_cond(s(t_bool,f),s(X8,X10),s(X8,X9)))=s(X8,X9),file('i/f/sum/cond__sum__expand_c3', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
fof(48, axiom,![X9]:![X10]:![X36]:(p(s(t_bool,h4s_bools_cond(s(t_bool,X36),s(t_bool,X10),s(t_bool,X9))))<=>((p(s(t_bool,X36))&p(s(t_bool,X10)))|(~(p(s(t_bool,X36)))&p(s(t_bool,X9))))),file('i/f/sum/cond__sum__expand_c3', ah4s_bools_CONDu_u_EXPANDu_u_OR)).
fof(60, axiom,p(s(t_bool,t)),file('i/f/sum/cond__sum__expand_c3', aHLu_TRUTH)).
fof(61, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)|s(t_bool,X12)=s(t_bool,f)),file('i/f/sum/cond__sum__expand_c3', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
