# 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_finite(s(t_fun(X1,t_bool),X3))))=>(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),X2))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X3))))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2))))))))))),file('i/f/pred_set/LESS__CARD__DIFF', ch4s_predu_u_sets_LESSu_u_CARDu_u_DIFF)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/pred_set/LESS__CARD__DIFF', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/LESS__CARD__DIFF', aHLu_FALSITY)).
fof(5, axiom,![X4]:![X5]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X4))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X4))))|s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,X4))),file('i/f/pred_set/LESS__CARD__DIFF', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(6, axiom,![X4]:![X5]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X4)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X5))))),file('i/f/pred_set/LESS__CARD__DIFF', ah4s_arithmetics_NOTu_u_LESS)).
fof(7, axiom,![X1]:![X3]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X3))))=>![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),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2))))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X3))))))),file('i/f/pred_set/LESS__CARD__DIFF', ah4s_predu_u_sets_CARDu_u_INTERu_u_LESSu_u_EQ)).
fof(8, 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_finite(s(t_fun(X1,t_bool),X3))))=>s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(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),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2))))))))),file('i/f/pred_set/LESS__CARD__DIFF', ah4s_predu_u_sets_CARDu_u_DIFF)).
fof(10, axiom,![X1]:![X2]:![X3]:s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X3))),file('i/f/pred_set/LESS__CARD__DIFF', ah4s_predu_u_sets_INTERu_u_COMM)).
fof(11, axiom,![X4]:![X5]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X4)))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X5))))),file('i/f/pred_set/LESS__CARD__DIFF', ah4s_arithmetics_SUBu_u_LESSu_u_0)).
fof(13, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t0)|s(t_bool,X2)=s(t_bool,f)),file('i/f/pred_set/LESS__CARD__DIFF', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
