# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(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_univ))))<=>?[X3]:~(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X2)))))),file('i/f/pred_set/PSUBSET__UNIV', ch4s_predu_u_sets_PSUBSETu_u_UNIV)).
fof(2, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/pred_set/PSUBSET__UNIV', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(25, axiom,![X1]:![X19]:![X20]:(![X3]:(s(X1,X3)=s(X1,X19)=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X3)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X19))))),file('i/f/pred_set/PSUBSET__UNIV', ah4s_bools_UNWINDu_u_FORALLu_u_THM2)).
fof(31, axiom,![X1]:![X3]:![X10]:s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X10)))=s(t_bool,happ(s(t_fun(X1,t_bool),X10),s(X1,X3))),file('i/f/pred_set/PSUBSET__UNIV', ah4s_predu_u_sets_SPECIFICATION)).
fof(37, axiom,![X1]:![X2]:(![X3]:p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X2))))<=>s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_univ)),file('i/f/pred_set/PSUBSET__UNIV', ah4s_predu_u_sets_EQu_u_UNIV)).
fof(41, axiom,![X1]:![X6]:![X2]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X6))))<=>(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X6))))&~(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),X6)))),file('i/f/pred_set/PSUBSET__UNIV', ah4s_predu_u_sets_PSUBSETu_u_DEF)).
fof(43, axiom,![X1]:![X2]:~(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X2))))),file('i/f/pred_set/PSUBSET__UNIV', ah4s_predu_u_sets_PSUBSETu_u_IRREFL)).
fof(44, axiom,![X1]:![X2]:~(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_empty))))),file('i/f/pred_set/PSUBSET__UNIV', ah4s_predu_u_sets_NOTu_u_PSUBSETu_u_EMPTY)).
fof(48, axiom,![X1]:![X2]:p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_univ)))),file('i/f/pred_set/PSUBSET__UNIV', ah4s_predu_u_sets_SUBSETu_u_UNIV)).
fof(56, axiom,p(s(t_bool,t)),file('i/f/pred_set/PSUBSET__UNIV', aHLu_TRUTH)).
fof(59, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/pred_set/PSUBSET__UNIV', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(72, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/PSUBSET__UNIV', aHLu_FALSITY)).
fof(75, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/pred_set/PSUBSET__UNIV', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(77, axiom,(p(s(t_bool,f))<=>![X6]:p(s(t_bool,X6))),file('i/f/pred_set/PSUBSET__UNIV', ah4s_bools_Fu_u_DEF)).
# SZS output end CNFRefutation
