# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),file('i/f/pred_set/CARD__SING', ch4s_predu_u_sets_CARDu_u_SING)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/CARD__SING', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/CARD__SING', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/pred_set/CARD__SING', aHLu_BOOLu_CASES)).
fof(6, 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__SING', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/pred_set/CARD__SING', ah4s_arithmetics_ONE)).
fof(10, axiom,![X1]:s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/pred_set/CARD__SING', ah4s_predu_u_sets_CARDu_u_DEFu_c0)).
fof(11, axiom,![X1]:![X6]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X6))))=>![X2]:s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),X6)))))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X6))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X6))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X6)))))))),file('i/f/pred_set/CARD__SING', ah4s_predu_u_sets_CARDu_u_DEFu_c1)).
fof(13, axiom,![X1]:![X2]:~(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/CARD__SING', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(14, axiom,![X1]:p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))),file('i/f/pred_set/CARD__SING', ah4s_predu_u_sets_FINITEu_u_EMPTY)).
fof(15, 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__SING', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
