# 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]:![X4]:(![X5]:s(t_h4s_realaxs_real,happ(s(t_fun(X1,t_h4s_realaxs_real),X3),s(X1,X5)))=s(t_h4s_realaxs_real,X4)=>s(t_h4s_realaxs_real,h4s_realu_u_sigmas_realu_u_sumu_u_image(s(t_fun(X1,t_h4s_realaxs_real),X3),s(t_fun(X1,t_bool),X2)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X2))))),s(t_h4s_realaxs_real,X4))))),file('i/f/real_sigma/REAL__SUM__IMAGE__FINITE__CONST', ch4s_realu_u_sigmas_REALu_u_SUMu_u_IMAGEu_u_FINITEu_u_CONST)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/real_sigma/REAL__SUM__IMAGE__FINITE__CONST', aHLu_TRUTH)).
fof(11, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/real_sigma/REAL__SUM__IMAGE__FINITE__CONST', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(15, axiom,![X4]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X4)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/real_sigma/REAL__SUM__IMAGE__FINITE__CONST', ah4s_reals_REALu_u_MULu_u_LZERO)).
fof(16, axiom,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X2))))=>![X3]:![X14]:((p(s(t_bool,h4s_bools_in(s(X1,X14),s(t_fun(X1,t_bool),X2))))&![X15]:(p(s(t_bool,h4s_bools_in(s(X1,X15),s(t_fun(X1,t_bool),X2))))=>s(t_h4s_realaxs_real,happ(s(t_fun(X1,t_h4s_realaxs_real),X3),s(X1,X14)))=s(t_h4s_realaxs_real,happ(s(t_fun(X1,t_h4s_realaxs_real),X3),s(X1,X15)))))=>s(t_h4s_realaxs_real,h4s_realu_u_sigmas_realu_u_sumu_u_image(s(t_fun(X1,t_h4s_realaxs_real),X3),s(t_fun(X1,t_bool),X2)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X2))))),s(t_h4s_realaxs_real,happ(s(t_fun(X1,t_h4s_realaxs_real),X3),s(X1,X14))))))),file('i/f/real_sigma/REAL__SUM__IMAGE__FINITE__CONST', ah4s_realu_u_sigmas_REALu_u_SUMu_u_IMAGEu_u_FINITEu_u_SAME)).
fof(17, axiom,![X1]:![X3]:s(t_h4s_realaxs_real,h4s_realu_u_sigmas_realu_u_sumu_u_image(s(t_fun(X1,t_h4s_realaxs_real),X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/real_sigma/REAL__SUM__IMAGE__FINITE__CONST', ah4s_realu_u_sigmas_REALu_u_SUMu_u_IMAGEu_u_THMu_c0)).
fof(18, 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/real_sigma/REAL__SUM__IMAGE__FINITE__CONST', ah4s_predu_u_sets_CARDu_u_EMPTY)).
fof(20, axiom,![X1]:![X5]:![X4]:![X19]:(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X5),s(t_fun(X1,t_bool),X19))))))<=>(s(X1,X4)=s(X1,X5)|p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X19)))))),file('i/f/real_sigma/REAL__SUM__IMAGE__FINITE__CONST', ah4s_predu_u_sets_INu_u_INSERT)).
fof(21, axiom,![X1]:![X19]:(s(t_fun(X1,t_bool),X19)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)|?[X4]:?[X6]:(s(t_fun(X1,t_bool),X19)=s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X4),s(t_fun(X1,t_bool),X6)))&~(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X6))))))),file('i/f/real_sigma/REAL__SUM__IMAGE__FINITE__CONST', ah4s_predu_u_sets_SETu_u_CASES)).
fof(22, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f0)),file('i/f/real_sigma/REAL__SUM__IMAGE__FINITE__CONST', aHLu_BOOLu_CASES)).
fof(23, axiom,~(p(s(t_bool,f0))),file('i/f/real_sigma/REAL__SUM__IMAGE__FINITE__CONST', aHLu_FALSITY)).
# SZS output end CNFRefutation
