# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_nums_num,h4s_predu_u_sets_sumu_u_image(s(t_fun(X1,t_h4s_nums_num),X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X3),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),X2),s(X1,X3))),file('i/f/pred_set/SUM__IMAGE__SING', ch4s_predu_u_sets_SUMu_u_IMAGEu_u_SING)).
fof(7, axiom,![X1]:![X9]:![X2]:![X3]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X9))))=>s(t_h4s_nums_num,h4s_predu_u_sets_sumu_u_image(s(t_fun(X1,t_h4s_nums_num),X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X3),s(t_fun(X1,t_bool),X9)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X2),s(X1,X3))),s(t_h4s_nums_num,h4s_predu_u_sets_sumu_u_image(s(t_fun(X1,t_h4s_nums_num),X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X9),s(X1,X3)))))))),file('i/f/pred_set/SUM__IMAGE__SING', ah4s_predu_u_sets_SUMu_u_IMAGEu_u_THMu_c1)).
fof(8, axiom,![X1]:![X7]:s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),s(X1,X7)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),file('i/f/pred_set/SUM__IMAGE__SING', ah4s_predu_u_sets_EMPTYu_u_DELETE)).
fof(9, 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/SUM__IMAGE__SING', ah4s_predu_u_sets_FINITEu_u_EMPTY)).
fof(10, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_predu_u_sets_sumu_u_image(s(t_fun(X1,t_h4s_nums_num),X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/pred_set/SUM__IMAGE__SING', ah4s_predu_u_sets_SUMu_u_IMAGEu_u_THMu_c0)).
fof(11, axiom,![X10]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X10),file('i/f/pred_set/SUM__IMAGE__SING', ah4s_arithmetics_ADDu_u_0)).
# SZS output end CNFRefutation
