# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X2))))=>![X3]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X3))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X2)))))))),file('i/f/pred_set/CARD__PSUBSET', ch4s_predu_u_sets_CARDu_u_PSUBSET)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/CARD__PSUBSET', aHLu_FALSITY)).
fof(3, 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/CARD__PSUBSET', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(5, axiom,![X6]:![X7]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X6))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X6))))|s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,X6))),file('i/f/pred_set/CARD__PSUBSET', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(6, axiom,![X1]:![X3]:![X2]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X3))))<=>(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X3))))&~(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),X3)))),file('i/f/pred_set/CARD__PSUBSET', ah4s_predu_u_sets_PSUBSETu_u_DEF)).
fof(8, axiom,![X1]:![X3]:![X2]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X3))))<=>?[X8]:(~(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X2)))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X8),s(t_fun(X1,t_bool),X2))),s(t_fun(X1,t_bool),X3)))))),file('i/f/pred_set/CARD__PSUBSET', ah4s_predu_u_sets_PSUBSETu_u_INSERTu_u_SUBSET)).
fof(9, axiom,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),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))))=>p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X3)))))),file('i/f/pred_set/CARD__PSUBSET', ah4s_predu_u_sets_SUBSETu_u_FINITE)).
fof(10, axiom,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),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))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X3))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X2)))))))),file('i/f/pred_set/CARD__PSUBSET', ah4s_predu_u_sets_CARDu_u_SUBSET)).
fof(11, axiom,![X6]:![X7]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X6)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X6))),file('i/f/pred_set/CARD__PSUBSET', ah4s_arithmetics_LESSu_u_EQ)).
fof(12, axiom,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X2))))=>![X8]:s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X8),s(t_fun(X1,t_bool),X2)))))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X2))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X2))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X2)))))))),file('i/f/pred_set/CARD__PSUBSET', ah4s_predu_u_sets_CARDu_u_INSERT)).
fof(13, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t0)|s(t_bool,X3)=s(t_bool,f)),file('i/f/pred_set/CARD__PSUBSET', aHLu_BOOLu_CASES)).
fof(14, axiom,![X1]:![X4]:![X5]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X5),s(X1,X4)))=s(X1,X4),file('i/f/pred_set/CARD__PSUBSET', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(15, axiom,p(s(t_bool,t0)),file('i/f/pred_set/CARD__PSUBSET', aHLu_TRUTH)).
# SZS output end CNFRefutation
