# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:s(t_h4s_pairs_prod(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_bool)),X1),s(t_h4s_nums_num,X2)))=s(t_h4s_pairs_prod(t_h4s_nums_num,t_bool),h4s_pairs_u_2c(s(t_h4s_nums_num,X2),s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0)))))=>s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_gspec(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_bool)),X1)))=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty)),file('i/f/float/FLOAT__COUNTINDUCT_c0', ch4s_floats_FLOATu_u_COUNTINDUCTu_c0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/float/FLOAT__COUNTINDUCT_c0', aHLu_TRUTH)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/float/FLOAT__COUNTINDUCT_c0', aHLu_BOOLu_CASES)).
fof(14, axiom,![X3]:(s(t_bool,f)=s(t_bool,X3)<=>~(p(s(t_bool,X3)))),file('i/f/float/FLOAT__COUNTINDUCT_c0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(15, axiom,![X6]:![X2]:~(p(s(t_bool,h4s_bools_in(s(X6,X2),s(t_fun(X6,t_bool),h4s_predu_u_sets_empty))))),file('i/f/float/FLOAT__COUNTINDUCT_c0', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(18, axiom,![X6]:![X3]:![X14]:(s(t_fun(X6,t_bool),X14)=s(t_fun(X6,t_bool),X3)<=>![X2]:s(t_bool,h4s_bools_in(s(X6,X2),s(t_fun(X6,t_bool),X14)))=s(t_bool,h4s_bools_in(s(X6,X2),s(t_fun(X6,t_bool),X3)))),file('i/f/float/FLOAT__COUNTINDUCT_c0', ah4s_predu_u_sets_EXTENSION)).
fof(19, axiom,![X6]:![X15]:![X16]:![X10]:(p(s(t_bool,h4s_bools_in(s(X6,X16),s(t_fun(X6,t_bool),h4s_predu_u_sets_gspec(s(t_fun(X15,t_h4s_pairs_prod(X6,t_bool)),X10))))))<=>?[X2]:s(t_h4s_pairs_prod(X6,t_bool),h4s_pairs_u_2c(s(X6,X16),s(t_bool,t)))=s(t_h4s_pairs_prod(X6,t_bool),happ(s(t_fun(X15,t_h4s_pairs_prod(X6,t_bool)),X10),s(X15,X2)))),file('i/f/float/FLOAT__COUNTINDUCT_c0', ah4s_predu_u_sets_GSPECIFICATION)).
fof(20, axiom,![X17]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/float/FLOAT__COUNTINDUCT_c0', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(22, axiom,![X6]:![X15]:![X7]:![X2]:![X19]:![X12]:(s(t_h4s_pairs_prod(X6,X15),h4s_pairs_u_2c(s(X6,X2),s(X15,X7)))=s(t_h4s_pairs_prod(X6,X15),h4s_pairs_u_2c(s(X6,X12),s(X15,X19)))<=>(s(X6,X2)=s(X6,X12)&s(X15,X7)=s(X15,X19))),file('i/f/float/FLOAT__COUNTINDUCT_c0', ah4s_pairs_CLOSEDu_u_PAIRu_u_EQ)).
# SZS output end CNFRefutation
