# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t0)),file('i/f/pred_set/SUBSET__EQ__CARD', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/SUBSET__EQ__CARD', 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__EQ__CARD', aHLu_BOOLu_CASES)).
fof(15, axiom,![X7]:![X8]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X7,t_bool),X8))))=>![X1]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X7,t_bool),X1),s(t_fun(X7,t_bool),X8))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X7,t_bool),X1))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X7,t_bool),X8)))))))),file('i/f/pred_set/SUBSET__EQ__CARD', ah4s_predu_u_sets_CARDu_u_PSUBSET)).
fof(41, axiom,![X13]:![X14]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X13))),file('i/f/pred_set/SUBSET__EQ__CARD', ah4s_arithmetics_LESSu_u_EQ)).
fof(44, axiom,![X7]:![X1]:![X8]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X7,t_bool),X8),s(t_fun(X7,t_bool),X1))))<=>(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X7,t_bool),X8),s(t_fun(X7,t_bool),X1))))&~(s(t_fun(X7,t_bool),X8)=s(t_fun(X7,t_bool),X1)))),file('i/f/pred_set/SUBSET__EQ__CARD', ah4s_predu_u_sets_PSUBSETu_u_DEF)).
fof(50, axiom,![X14]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X14)))),file('i/f/pred_set/SUBSET__EQ__CARD', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(93, axiom,![X13]:![X14]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,X14))))),file('i/f/pred_set/SUBSET__EQ__CARD', ah4s_arithmetics_NOTu_u_LEQ)).
fof(133, conjecture,![X7]:![X8]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X7,t_bool),X8))))=>![X1]:((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X7,t_bool),X1))))&(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X7,t_bool),X8)))=s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X7,t_bool),X1)))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X7,t_bool),X8),s(t_fun(X7,t_bool),X1))))))=>s(t_fun(X7,t_bool),X8)=s(t_fun(X7,t_bool),X1))),file('i/f/pred_set/SUBSET__EQ__CARD', ch4s_predu_u_sets_SUBSETu_u_EQu_u_CARD)).
# SZS output end CNFRefutation
