# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:((p(s(t_bool,h4s_bools_in(s(t_fun(X1,X2),X6),s(t_fun(t_fun(X1,X2),t_bool),h4s_utilu_u_probs_funset(s(t_fun(X1,t_bool),X5),s(t_fun(X2,t_bool),X4))))))&p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X5)))))=>p(s(t_bool,h4s_bools_in(s(X2,happ(s(t_fun(X1,X2),X6),s(X1,X3))),s(t_fun(X2,t_bool),X4))))),file('i/f/util_prob/FUNSET__THM', ch4s_utilu_u_probs_FUNSETu_u_THM)).
fof(2, axiom,~(p(s(t_bool,f0))),file('i/f/util_prob/FUNSET__THM', aHLu_FALSITY)).
fof(5, axiom,![X11]:![X12]:((p(s(t_bool,X12))=>p(s(t_bool,X11)))=>((p(s(t_bool,X11))=>p(s(t_bool,X12)))=>s(t_bool,X12)=s(t_bool,X11))),file('i/f/util_prob/FUNSET__THM', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(28, axiom,(p(s(t_bool,f0))<=>![X4]:p(s(t_bool,X4))),file('i/f/util_prob/FUNSET__THM', ah4s_bools_Fu_u_DEF)).
fof(63, axiom,![X1]:![X3]:![X20]:s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X20)))=s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X3))),file('i/f/util_prob/FUNSET__THM', ah4s_predu_u_sets_SPECIFICATION)).
fof(68, axiom,![X1]:![X2]:![X6]:![X19]:![X20]:(p(s(t_bool,h4s_bools_in(s(t_fun(X1,X2),X6),s(t_fun(t_fun(X1,X2),t_bool),h4s_utilu_u_probs_funset(s(t_fun(X1,t_bool),X20),s(t_fun(X2,t_bool),X19))))))<=>![X3]:(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X20))))=>p(s(t_bool,h4s_bools_in(s(X2,happ(s(t_fun(X1,X2),X6),s(X1,X3))),s(t_fun(X2,t_bool),X19)))))),file('i/f/util_prob/FUNSET__THM', ah4s_utilu_u_probs_INu_u_FUNSET)).
fof(80, axiom,p(s(t_bool,t0)),file('i/f/util_prob/FUNSET__THM', aHLu_TRUTH)).
# SZS output end CNFRefutation
