# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(?[X3]:(p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,X3),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,t),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_ltx(s(t_h4s_integers_int,X1))))))))&p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),X2),s(t_h4s_integers_int,X3)))))<=>p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),X2),s(t_h4s_integers_int,X1))))),file('i/f/DeepSyntax/in__bset_c7', ch4s_DeepSyntaxs_inu_u_bsetu_c7)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/DeepSyntax/in__bset_c7', aHLu_TRUTH)).
fof(19, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/DeepSyntax/in__bset_c7', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(20, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/DeepSyntax/in__bset_c7', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(32, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/DeepSyntax/in__bset_c7', aHLu_BOOLu_CASES)).
fof(40, axiom,![X21]:![X1]:s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,X21),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_ltx(s(t_h4s_integers_int,X1)))))=s(t_fun(t_h4s_integers_int,t_bool),h4s_bools_cond(s(t_bool,X21),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_insert(s(t_h4s_integers_int,X1),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty))),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty))),file('i/f/DeepSyntax/in__bset_c7', ah4s_DeepSyntaxs_Bsetu_u_defu_c5)).
fof(42, axiom,![X7]:![X14]:![X8]:(p(s(t_bool,h4s_bools_in(s(X7,X8),s(t_fun(X7,t_bool),h4s_predu_u_sets_insert(s(X7,X14),s(t_fun(X7,t_bool),h4s_predu_u_sets_empty))))))<=>s(X7,X8)=s(X7,X14)),file('i/f/DeepSyntax/in__bset_c7', ah4s_predu_u_sets_INu_u_SING)).
fof(44, axiom,![X7]:![X4]:![X5]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X5),s(X7,X4)))=s(X7,X5),file('i/f/DeepSyntax/in__bset_c7', ah4s_bools_CONDu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
