# 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),h4s_sums_inr(s(X1,X5))),s(t_h4s_sums_sum(X2,X1),h4s_sums_inl(s(X2,X4)))))=s(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(2, axiom,p(s(t_bool,t)),file('i/f/sum/cond__sum__expand_c1', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/sum/cond__sum__expand_c1', aHLu_FALSITY)).
fof(4, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/sum/cond__sum__expand_c1', aHLu_BOOLu_CASES)).
fof(18, axiom,![X7]:(s(t_bool,f)=s(t_bool,X7)<=>~(p(s(t_bool,X7)))),file('i/f/sum/cond__sum__expand_c1', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(22, axiom,![X14]:![X10]:![X4]:![X5]:(s(t_h4s_sums_sum(X10,X14),h4s_sums_inl(s(X10,X5)))=s(t_h4s_sums_sum(X10,X14),h4s_sums_inl(s(X10,X4)))<=>s(X10,X5)=s(X10,X4)),file('i/f/sum/cond__sum__expand_c1', ah4s_sums_INRu_u_INLu_u_11u_c0)).
fof(23, axiom,![X10]:![X14]:![X4]:![X5]:~(s(t_h4s_sums_sum(X10,X14),h4s_sums_inl(s(X10,X5)))=s(t_h4s_sums_sum(X10,X14),h4s_sums_inr(s(X14,X4)))),file('i/f/sum/cond__sum__expand_c1', ah4s_sums_sumu_u_distinct)).
fof(25, axiom,![X10]:![X8]:![X9]:s(X10,h4s_bools_cond(s(t_bool,t),s(X10,X9),s(X10,X8)))=s(X10,X9),file('i/f/sum/cond__sum__expand_c1', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(26, axiom,![X10]:![X8]:![X9]:s(X10,h4s_bools_cond(s(t_bool,f),s(X10,X9),s(X10,X8)))=s(X10,X8),file('i/f/sum/cond__sum__expand_c1', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
# SZS output end CNFRefutation
