# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_fcps_cart(t_bool,X1),t_bool),t_bool),X2),s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_bool),h4s_predu_u_sets_empty))))&![X3]:(p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_fcps_cart(t_bool,X1),t_bool),t_bool),X2),s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_bool),X3))))=>![X4]:(~(p(s(t_bool,h4s_bools_in(s(t_h4s_fcps_cart(t_bool,X1),X4),s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_bool),X3)))))=>p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_fcps_cart(t_bool,X1),t_bool),t_bool),X2),s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_bool),h4s_predu_u_sets_insert(s(t_h4s_fcps_cart(t_bool,X1),X4),s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_bool),X3)))))))))=>![X3]:p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_fcps_cart(t_bool,X1),t_bool),t_bool),X2),s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_bool),X3))))),file('i/f/words/WORD__SET__INDUCT', ch4s_wordss_WORDu_u_SETu_u_INDUCT)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/words/WORD__SET__INDUCT', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/words/WORD__SET__INDUCT', aHLu_FALSITY)).
fof(6, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/words/WORD__SET__INDUCT', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X1]:![X2]:((p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))&![X3]:((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X3))))&p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),X2),s(t_fun(X1,t_bool),X3)))))=>![X4]:(~(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X3)))))=>p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X4),s(t_fun(X1,t_bool),X3)))))))))=>![X3]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X3))))=>p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),X2),s(t_fun(X1,t_bool),X3)))))),file('i/f/words/WORD__SET__INDUCT', ah4s_predu_u_sets_FINITEu_u_INDUCT)).
fof(8, axiom,![X1]:![X3]:p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_bool),X3)))),file('i/f/words/WORD__SET__INDUCT', ah4s_wordss_WORDu_u_FINITE)).
fof(9, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/words/WORD__SET__INDUCT', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
