# 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(X2,t_h4s_sums_sum(X1,X2)),h4s_sums_inr),s(X2,X5))),s(t_h4s_sums_sum(X1,X2),happ(s(t_fun(X1,t_h4s_sums_sum(X1,X2)),h4s_sums_inl),s(X1,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,X5))),file('i/f/sum/cond__sum__expand_c0', ch4s_sums_condu_u_sumu_u_expandu_c0)).
fof(28, axiom,![X2]:![X1]:![X4]:![X5]:(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(X1,t_h4s_sums_sum(X2,X1)),h4s_sums_inr),s(X1,X4)))<=>s(X1,X5)=s(X1,X4)),file('i/f/sum/cond__sum__expand_c0', ah4s_sums_INRu_u_11)).
fof(31, axiom,![X1]:![X2]:![X22]:![X23]:~(s(t_h4s_sums_sum(X2,X1),happ(s(t_fun(X1,t_h4s_sums_sum(X2,X1)),h4s_sums_inr),s(X1,X22)))=s(t_h4s_sums_sum(X2,X1),happ(s(t_fun(X2,t_h4s_sums_sum(X2,X1)),h4s_sums_inl),s(X2,X23)))),file('i/f/sum/cond__sum__expand_c0', ah4s_sums_INRu_u_nequ_u_INL)).
fof(34, axiom,![X2]:![X7]:![X8]:s(X2,h4s_bools_cond(s(t_bool,t),s(X2,X8),s(X2,X7)))=s(X2,X8),file('i/f/sum/cond__sum__expand_c0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(35, axiom,![X2]:![X7]:![X8]:s(X2,h4s_bools_cond(s(t_bool,f),s(X2,X8),s(X2,X7)))=s(X2,X7),file('i/f/sum/cond__sum__expand_c0', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(52, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)|s(t_bool,X10)=s(t_bool,f)),file('i/f/sum/cond__sum__expand_c0', aHLu_BOOLu_CASES)).
fof(54, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)<=>p(s(t_bool,X10))),file('i/f/sum/cond__sum__expand_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
