# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t0)),file('i/f/pred_set/SUBSET__INSERT', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/SUBSET__INSERT', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t0)|s(t_bool,X1)=s(t_bool,f)),file('i/f/pred_set/SUBSET__INSERT', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/pred_set/SUBSET__INSERT', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(7, axiom,![X9]:![X1]:![X10]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X9,t_bool),X10),s(t_fun(X9,t_bool),X1))))<=>![X6]:(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X10))))=>p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X1)))))),file('i/f/pred_set/SUBSET__INSERT', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(8, axiom,![X9]:![X11]:![X6]:![X10]:(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),h4s_predu_u_sets_insert(s(X9,X11),s(t_fun(X9,t_bool),X10))))))<=>(s(X9,X6)=s(X9,X11)|p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X10)))))),file('i/f/pred_set/SUBSET__INSERT', ah4s_predu_u_sets_INu_u_INSERT)).
fof(9, conjecture,![X9]:![X6]:![X10]:(~(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X10)))))=>![X1]:s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X9,t_bool),X10),s(t_fun(X9,t_bool),h4s_predu_u_sets_insert(s(X9,X6),s(t_fun(X9,t_bool),X1)))))=s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X9,t_bool),X10),s(t_fun(X9,t_bool),X1)))),file('i/f/pred_set/SUBSET__INSERT', ch4s_predu_u_sets_SUBSETu_u_INSERT)).
# SZS output end CNFRefutation
