# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:![X4]:![X5]:![X6]:s(t_h4s_realaxs_real,happ(s(t_fun(X1,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(X1,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(X1,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(X1,t_h4s_realaxs_real))),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(X1,t_h4s_realaxs_real)))),X2),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_h4s_realaxs_real),X4))),s(t_h4s_realaxs_real,X5))),s(X1,X6)))=s(t_h4s_realaxs_real,h4s_bools_cond(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X3))),s(t_h4s_realaxs_real,happ(s(t_fun(X1,t_h4s_realaxs_real),X4),s(X1,X6))),s(t_h4s_realaxs_real,X5)))=>![X5]:![X3]:![X4]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X3))))=>s(t_h4s_realaxs_real,h4s_realu_u_sigmas_realu_u_sumu_u_image(s(t_fun(X1,t_h4s_realaxs_real),X4),s(t_fun(X1,t_bool),X3)))=s(t_h4s_realaxs_real,h4s_realu_u_sigmas_realu_u_sumu_u_image(s(t_fun(X1,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(X1,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(X1,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(X1,t_h4s_realaxs_real))),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(X1,t_h4s_realaxs_real)))),X2),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_h4s_realaxs_real),X4))),s(t_h4s_realaxs_real,X5))),s(t_fun(X1,t_bool),X3))))),file('i/f/real_sigma/REAL__SUM__IMAGE__IN__IF__ALT', ch4s_realu_u_sigmas_REALu_u_SUMu_u_IMAGEu_u_INu_u_IFu_u_ALT)).
fof(3, axiom,![X1]:![X3]:![X8]:![X4]:((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X3))))&![X6]:(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X3))))=>s(t_h4s_realaxs_real,happ(s(t_fun(X1,t_h4s_realaxs_real),X4),s(X1,X6)))=s(t_h4s_realaxs_real,happ(s(t_fun(X1,t_h4s_realaxs_real),X8),s(X1,X6)))))=>s(t_h4s_realaxs_real,h4s_realu_u_sigmas_realu_u_sumu_u_image(s(t_fun(X1,t_h4s_realaxs_real),X4),s(t_fun(X1,t_bool),X3)))=s(t_h4s_realaxs_real,h4s_realu_u_sigmas_realu_u_sumu_u_image(s(t_fun(X1,t_h4s_realaxs_real),X8),s(t_fun(X1,t_bool),X3)))),file('i/f/real_sigma/REAL__SUM__IMAGE__IN__IF__ALT', ah4s_realu_u_sigmas_REALu_u_SUMu_u_IMAGEu_u_EQ)).
fof(7, axiom,![X1]:![X15]:![X7]:![X16]:![X6]:![X17]:![X18]:((s(t_bool,X18)=s(t_bool,X17)&((p(s(t_bool,X17))=>s(X1,X6)=s(X1,X16))&(~(p(s(t_bool,X17)))=>s(X1,X7)=s(X1,X15))))=>s(X1,h4s_bools_cond(s(t_bool,X18),s(X1,X6),s(X1,X7)))=s(X1,h4s_bools_cond(s(t_bool,X17),s(X1,X16),s(X1,X15)))),file('i/f/real_sigma/REAL__SUM__IMAGE__IN__IF__ALT', ah4s_bools_CONDu_u_CONG)).
fof(8, axiom,![X1]:![X13]:![X14]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X14),s(X1,X13)))=s(X1,X14),file('i/f/real_sigma/REAL__SUM__IMAGE__IN__IF__ALT', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(9, axiom,p(s(t_bool,t)),file('i/f/real_sigma/REAL__SUM__IMAGE__IN__IF__ALT', aHLu_TRUTH)).
fof(13, axiom,![X19]:(s(t_bool,X19)=s(t_bool,t)<=>p(s(t_bool,X19))),file('i/f/real_sigma/REAL__SUM__IMAGE__IN__IF__ALT', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
