# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:(s(t_h4s_sums_sum(X2,X1),h4s_bools_cond(s(t_bool,X6),s(t_h4s_sums_sum(X2,X1),happ(s(t_fun(X1,t_h4s_sums_sum(X2,X1)),h4s_sums_inr),s(X1,X5))),s(t_h4s_sums_sum(X2,X1),happ(s(t_fun(X2,t_h4s_sums_sum(X2,X1)),h4s_sums_inl),s(X2,X4)))))=s(t_h4s_sums_sum(X2,X1),happ(s(t_fun(X2,t_h4s_sums_sum(X2,X1)),h4s_sums_inl),s(X2,X3)))<=>(~(p(s(t_bool,X6)))&s(X2,X3)=s(X2,X4))),file('i/f/sum/cond__sum__expand_c1', ch4s_sums_condu_u_sumu_u_expandu_c1)).
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_c1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(33, axiom,![X8]:![X7]:![X28]:![X29]:~(s(t_h4s_sums_sum(X7,X8),happ(s(t_fun(X8,t_h4s_sums_sum(X7,X8)),h4s_sums_inr),s(X8,X28)))=s(t_h4s_sums_sum(X7,X8),happ(s(t_fun(X7,t_h4s_sums_sum(X7,X8)),h4s_sums_inl),s(X7,X29)))),file('i/f/sum/cond__sum__expand_c1', ah4s_sums_INRu_u_nequ_u_INL)).
fof(35, axiom,![X8]:![X7]:![X4]:![X5]:(s(t_h4s_sums_sum(X7,X8),happ(s(t_fun(X7,t_h4s_sums_sum(X7,X8)),h4s_sums_inl),s(X7,X5)))=s(t_h4s_sums_sum(X7,X8),happ(s(t_fun(X7,t_h4s_sums_sum(X7,X8)),h4s_sums_inl),s(X7,X4)))<=>s(X7,X5)=s(X7,X4)),file('i/f/sum/cond__sum__expand_c1', ah4s_sums_INLu_u_11)).
fof(44, axiom,![X7]:![X9]:![X10]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X10),s(X7,X9)))=s(X7,X10),file('i/f/sum/cond__sum__expand_c1', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(45, axiom,![X7]:![X9]:![X10]:s(X7,h4s_bools_cond(s(t_bool,f),s(X7,X10),s(X7,X9)))=s(X7,X9),file('i/f/sum/cond__sum__expand_c1', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(61, axiom,p(s(t_bool,t)),file('i/f/sum/cond__sum__expand_c1', aHLu_TRUTH)).
# SZS output end CNFRefutation
