# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:![X5]:p(s(t_bool,happ(s(t_fun(t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2),t_bool),X3),s(t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2),happ(s(t_fun(t_h4s_patricias_ptree(X2),t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2)),happ(s(t_fun(t_fun(X1,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(X2),t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2))),h4s_patriciau_u_castss_wordu_u_ptree),s(t_fun(X1,t_h4s_ones_one),X4))),s(t_h4s_patricias_ptree(X2),X5))))))=>![X6]:p(s(t_bool,happ(s(t_fun(t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2),t_bool),X3),s(t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2),X6))))),file('i/f/patricia_casts/word__ptree__induction', ch4s_patriciau_u_castss_wordu_u_ptreeu_u_induction)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/patricia_casts/word__ptree__induction', aHLu_FALSITY)).
fof(33, axiom,![X9]:(s(t_bool,f0)=s(t_bool,X9)<=>~(p(s(t_bool,X9)))),file('i/f/patricia_casts/word__ptree__induction', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(48, axiom,![X1]:![X2]:![X34]:?[X4]:?[X5]:s(t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2),X34)=s(t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2),happ(s(t_fun(t_h4s_patricias_ptree(X2),t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2)),happ(s(t_fun(t_fun(X1,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(X2),t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2))),h4s_patriciau_u_castss_wordu_u_ptree),s(t_fun(X1,t_h4s_ones_one),X4))),s(t_h4s_patricias_ptree(X2),X5))),file('i/f/patricia_casts/word__ptree__induction', ah4s_patriciau_u_castss_wordu_u_ptreeu_u_nchotomy)).
fof(53, axiom,![X1]:![X2]:s(t_fun(t_fun(X1,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(X2),t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2))),h4s_patriciau_u_castss_wordu_u_ptree)=s(t_fun(t_fun(X1,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(X2),t_h4s_patriciau_u_castss_wordu_u_ptree(X1,X2))),h4s_patriciau_u_castss_u_20u_40indu_u_typepatriciau_u_casts0),file('i/f/patricia_casts/word__ptree__induction', ah4s_patriciau_u_castss_Wordu_u_ptree0)).
# SZS output end CNFRefutation
