# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))))<=>s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/PSUBSET__SING', ch4s_predu_u_sets_PSUBSETu_u_SING)).
fof(32, axiom,![X1]:![X2]:~(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/PSUBSET__SING', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(34, axiom,![X1]:![X9]:![X2]:(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X9),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))))<=>s(X1,X2)=s(X1,X9)),file('i/f/pred_set/PSUBSET__SING', ah4s_predu_u_sets_INu_u_SING)).
fof(36, axiom,![X1]:![X6]:![X3]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X6))))<=>(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X6))))&~(s(t_fun(X1,t_bool),X3)=s(t_fun(X1,t_bool),X6)))),file('i/f/pred_set/PSUBSET__SING', ah4s_predu_u_sets_PSUBSETu_u_DEF)).
fof(37, axiom,![X1]:![X6]:![X3]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X6))))<=>?[X2]:(~(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X3)))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_bool),X6)))))),file('i/f/pred_set/PSUBSET__SING', ah4s_predu_u_sets_PSUBSETu_u_INSERTu_u_SUBSET)).
fof(38, axiom,![X1]:![X20]:![X21]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X21),s(t_fun(X1,t_bool),X20))))<=>(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X21),s(t_fun(X1,t_bool),X20))))&~(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X20),s(t_fun(X1,t_bool),X21))))))),file('i/f/pred_set/PSUBSET__SING', ah4s_predu_u_sets_PSUBSETu_u_EQN)).
fof(43, axiom,![X1]:![X22]:![X6]:![X3]:((p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X6))))&p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X6),s(t_fun(X1,t_bool),X22)))))=>p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X22))))),file('i/f/pred_set/PSUBSET__SING', ah4s_predu_u_sets_SUBSETu_u_PSUBSETu_u_TRANS)).
fof(45, axiom,![X1]:![X2]:![X6]:![X3]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_bool),X6))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X6))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X6)))))),file('i/f/pred_set/PSUBSET__SING', ah4s_predu_u_sets_INSERTu_u_SUBSET)).
fof(47, axiom,![X1]:![X6]:![X3]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X6))))<=>![X2]:(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X3))))=>p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X6)))))),file('i/f/pred_set/PSUBSET__SING', ah4s_predu_u_sets_SUBSETu_u_DEF)).
# SZS output end CNFRefutation
