# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X2))))&p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X2)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X3),s(X1,X4))),s(t_h4s_nums_num,h4s_predu_u_sets_sumu_u_image(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_bool),X2))))))),file('i/f/pred_set/SUM__IMAGE__IN__LE', ch4s_predu_u_sets_SUMu_u_IMAGEu_u_INu_u_LE)).
fof(2, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/pred_set/SUM__IMAGE__IN__LE', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(23, axiom,![X1]:![X7]:![X2]:![X3]:((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X2))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X7),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_sumu_u_image(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_bool),X7))),s(t_h4s_nums_num,h4s_predu_u_sets_sumu_u_image(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_bool),X2))))))),file('i/f/pred_set/SUM__IMAGE__IN__LE', ah4s_predu_u_sets_SUMu_u_IMAGEu_u_SUBSETu_u_LE)).
fof(24, axiom,![X1]:![X3]:![X4]:s(t_h4s_nums_num,h4s_predu_u_sets_sumu_u_image(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))))=s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X3),s(X1,X4))),file('i/f/pred_set/SUM__IMAGE__IN__LE', ah4s_predu_u_sets_SUMu_u_IMAGEu_u_SING)).
fof(26, axiom,![X1]:![X7]:![X2]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X7))))<=>![X8]:(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X2))))=>p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X7)))))),file('i/f/pred_set/SUM__IMAGE__IN__LE', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(27, axiom,![X1]:![X14]:![X8]:![X2]:(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X14),s(t_fun(X1,t_bool),X2))))))<=>(s(X1,X8)=s(X1,X14)|p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X2)))))),file('i/f/pred_set/SUM__IMAGE__IN__LE', ah4s_predu_u_sets_INu_u_INSERT)).
fof(28, axiom,![X1]:![X8]:~(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/SUM__IMAGE__IN__LE', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
# SZS output end CNFRefutation
