# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:p(s(t_bool,happ(s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),X3),s(t_h4s_sums_sum(X1,X2),X4))))<=>(![X5]:p(s(t_bool,happ(s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),X3),s(t_h4s_sums_sum(X1,X2),h4s_sums_inl(s(X1,X5))))))&![X6]:p(s(t_bool,happ(s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),X3),s(t_h4s_sums_sum(X1,X2),h4s_sums_inr(s(X2,X6)))))))),file('i/f/sum/FORALL__SUM', ch4s_sums_FORALLu_u_SUM)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/sum/FORALL__SUM', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/sum/FORALL__SUM', aHLu_FALSITY)).
fof(8, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)<=>p(s(t_bool,X9))),file('i/f/sum/FORALL__SUM', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X1]:![X2]:![X3]:((![X5]:p(s(t_bool,happ(s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),X3),s(t_h4s_sums_sum(X1,X2),h4s_sums_inl(s(X1,X5))))))&![X6]:p(s(t_bool,happ(s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),X3),s(t_h4s_sums_sum(X1,X2),h4s_sums_inr(s(X2,X6)))))))=>![X4]:p(s(t_bool,happ(s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),X3),s(t_h4s_sums_sum(X1,X2),X4))))),file('i/f/sum/FORALL__SUM', ah4s_sums_sumu_u_INDUCT)).
fof(11, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/sum/FORALL__SUM', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
