# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2))))=>![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X3))))=>p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X2)))))),file('i/f/util_prob/SUBSET__THM', ch4s_utilu_u_probs_SUBSETu_u_THM)).
fof(6, axiom,![X1]:![X12]:![X3]:(?[X4]:(s(X1,X4)=s(X1,X12)&p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X4)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X12))))),file('i/f/util_prob/SUBSET__THM', ah4s_bools_UNWINDu_u_THM2)).
fof(40, axiom,![X1]:![X11]:![X23]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X23),s(t_fun(X1,t_bool),X11))))<=>![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X23))))=>p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X11)))))),file('i/f/util_prob/SUBSET__THM', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(43, axiom,![X1]:![X4]:![X26]:s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X26)))=s(t_bool,happ(s(t_fun(X1,t_bool),X26),s(X1,X4))),file('i/f/util_prob/SUBSET__THM', ah4s_bools_INu_u_DEF)).
fof(53, axiom,p(s(t_bool,t)),file('i/f/util_prob/SUBSET__THM', aHLu_TRUTH)).
fof(54, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)|s(t_bool,X11)=s(t_bool,f)),file('i/f/util_prob/SUBSET__THM', aHLu_BOOLu_CASES)).
fof(56, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)<=>p(s(t_bool,X11))),file('i/f/util_prob/SUBSET__THM', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(71, axiom,~(p(s(t_bool,f))),file('i/f/util_prob/SUBSET__THM', aHLu_FALSITY)).
# SZS output end CNFRefutation
