# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2))))=>p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X4),s(t_fun(X1,t_bool),X2))))))),file('i/f/pred_set/SUBSET__INSERT__RIGHT', ch4s_predu_u_sets_SUBSETu_u_INSERTu_u_RIGHT)).
fof(3, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/pred_set/SUBSET__INSERT__RIGHT', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(30, axiom,![X1]:![X7]:![X6]:(~(p(s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X6)))))=>![X5]:s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X6),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X7),s(t_fun(X1,t_bool),X5)))))=s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X6),s(t_fun(X1,t_bool),X5)))),file('i/f/pred_set/SUBSET__INSERT__RIGHT', ah4s_predu_u_sets_SUBSETu_u_INSERT)).
fof(31, axiom,![X1]:![X7]:![X5]:![X6]:s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X6),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X7),s(t_fun(X1,t_bool),X5)))))=s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X6),s(X1,X7))),s(t_fun(X1,t_bool),X5))),file('i/f/pred_set/SUBSET__INSERT__RIGHT', ah4s_predu_u_sets_SUBSETu_u_INSERTu_u_DELETE)).
fof(32, axiom,![X1]:![X7]:![X5]:![X6]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X7),s(t_fun(X1,t_bool),X6))),s(t_fun(X1,t_bool),X5))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X5))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X6),s(t_fun(X1,t_bool),X5)))))),file('i/f/pred_set/SUBSET__INSERT__RIGHT', ah4s_predu_u_sets_INSERTu_u_SUBSET)).
fof(40, axiom,![X1]:![X7]:![X6]:(p(s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X6))))=>s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X7),s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X6),s(X1,X7)))))=s(t_fun(X1,t_bool),X6)),file('i/f/pred_set/SUBSET__INSERT__RIGHT', ah4s_predu_u_sets_INSERTu_u_DELETE)).
fof(60, axiom,![X1]:![X7]:![X21]:s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X21)))=s(t_bool,happ(s(t_fun(X1,t_bool),X21),s(X1,X7))),file('i/f/pred_set/SUBSET__INSERT__RIGHT', ah4s_predu_u_sets_SPECIFICATION)).
# SZS output end CNFRefutation
