# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X2),X3),s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_setu_u_relations_relu_u_tou_u_reln(s(t_fun(X1,t_fun(X2,t_bool)),X4)))))=s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X1,t_fun(X2,t_bool)),X4),s(X1,happ(s(t_fun(t_h4s_pairs_prod(X1,X2),X1),h4s_pairs_fst),s(t_h4s_pairs_prod(X1,X2),X3))))),s(X2,happ(s(t_fun(t_h4s_pairs_prod(X1,X2),X2),h4s_pairs_snd),s(t_h4s_pairs_prod(X1,X2),X3))))),file('i/f/set_relation/reln__rel__conv__thms_c0', ch4s_setu_u_relations_relnu_u_relu_u_convu_u_thmsu_c0)).
fof(27, axiom,![X1]:![X2]:![X3]:![X4]:s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X2),X3),s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_setu_u_relations_relu_u_tou_u_reln(s(t_fun(X1,t_fun(X2,t_bool)),X4)))))=s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X1,t_fun(X2,t_bool)),X4),s(X1,happ(s(t_fun(t_h4s_pairs_prod(X1,X2),X1),h4s_pairs_fst),s(t_h4s_pairs_prod(X1,X2),X3))))),s(X2,happ(s(t_fun(t_h4s_pairs_prod(X1,X2),X2),h4s_pairs_snd),s(t_h4s_pairs_prod(X1,X2),X3))))),file('i/f/set_relation/reln__rel__conv__thms_c0', ah4s_setu_u_relations_inu_u_relu_u_tou_u_reln)).
fof(34, axiom,![X1]:![X9]:![X23]:s(t_bool,h4s_bools_in(s(X1,X9),s(t_fun(X1,t_bool),X23)))=s(t_bool,happ(s(t_fun(X1,t_bool),X23),s(X1,X9))),file('i/f/set_relation/reln__rel__conv__thms_c0', ah4s_bools_INu_u_DEF)).
fof(49, axiom,![X1]:![X2]:![X32]:![X18]:![X7]:s(X1,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(X2,X32),X18),s(t_fun(X2,t_fun(X32,X1)),X7)))=s(X1,happ(s(t_fun(X32,X1),happ(s(t_fun(X2,t_fun(X32,X1)),X7),s(X2,happ(s(t_fun(t_h4s_pairs_prod(X2,X32),X2),h4s_pairs_fst),s(t_h4s_pairs_prod(X2,X32),X18))))),s(X32,happ(s(t_fun(t_h4s_pairs_prod(X2,X32),X32),h4s_pairs_snd),s(t_h4s_pairs_prod(X2,X32),X18))))),file('i/f/set_relation/reln__rel__conv__thms_c0', ah4s_pairs_pairu_u_CASEu_u_def)).
# SZS output end CNFRefutation
