# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),h4s_patricias_peek(s(t_h4s_patricias_ptree(X1),happ(s(t_fun(X1,t_h4s_patricias_ptree(X1)),happ(s(t_fun(t_h4s_nums_num,t_fun(X1,t_h4s_patricias_ptree(X1))),h4s_patricias_leaf),s(t_h4s_nums_num,X3))),s(X1,X4))),s(t_h4s_nums_num,X2))))))<=>s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,X2)),file('i/f/patricia/IS__PTREE__PEEK_c1', ch4s_patricias_ISu_u_PTREEu_u_PEEKu_c1)).
fof(34, axiom,p(s(t_bool,t)),file('i/f/patricia/IS__PTREE__PEEK_c1', aHLu_TRUTH)).
fof(35, axiom,~(p(s(t_bool,f))),file('i/f/patricia/IS__PTREE__PEEK_c1', aHLu_FALSITY)).
fof(40, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)<=>p(s(t_bool,X10))),file('i/f/patricia/IS__PTREE__PEEK_c1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(58, axiom,![X11]:![X9]:(~(p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X11),X9)))))<=>s(t_h4s_options_option(X11),X9)=s(t_h4s_options_option(X11),h4s_options_none)),file('i/f/patricia/IS__PTREE__PEEK_c1', ah4s_options_NOTu_u_ISu_u_SOMEu_u_EQu_u_NONE)).
fof(59, axiom,![X11]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X11),h4s_options_none)))=s(t_bool,f),file('i/f/patricia/IS__PTREE__PEEK_c1', ah4s_options_ISu_u_SOMEu_u_DEFu_c1)).
fof(60, axiom,![X11]:![X9]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X11),h4s_options_some(s(X11,X9)))))=s(t_bool,t),file('i/f/patricia/IS__PTREE__PEEK_c1', ah4s_options_ISu_u_SOMEu_u_DEFu_c0)).
fof(61, axiom,![X11]:![X2]:![X3]:![X29]:?[X30]:((p(s(t_bool,X30))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X3))&s(t_h4s_options_option(X11),h4s_patricias_peek(s(t_h4s_patricias_ptree(X11),happ(s(t_fun(X11,t_h4s_patricias_ptree(X11)),happ(s(t_fun(t_h4s_nums_num,t_fun(X11,t_h4s_patricias_ptree(X11))),h4s_patricias_leaf),s(t_h4s_nums_num,X3))),s(X11,X29))),s(t_h4s_nums_num,X2)))=s(t_h4s_options_option(X11),h4s_bools_cond(s(t_bool,X30),s(t_h4s_options_option(X11),h4s_options_some(s(X11,X29))),s(t_h4s_options_option(X11),h4s_options_none)))),file('i/f/patricia/IS__PTREE__PEEK_c1', ah4s_patricias_PEEKu_u_defu_c1)).
fof(70, axiom,![X11]:s(t_fun(t_h4s_nums_num,t_fun(X11,t_h4s_patricias_ptree(X11))),h4s_patricias_leaf)=s(t_fun(t_h4s_nums_num,t_fun(X11,t_h4s_patricias_ptree(X11))),h4s_patricias_u_20u_40indu_u_typepatricia1),file('i/f/patricia/IS__PTREE__PEEK_c1', ah4s_patricias_Leaf0)).
fof(73, axiom,![X11]:![X9]:![X16]:(s(t_h4s_options_option(X11),h4s_bools_cond(s(t_bool,X16),s(t_h4s_options_option(X11),h4s_options_some(s(X11,X9))),s(t_h4s_options_option(X11),h4s_options_none)))=s(t_h4s_options_option(X11),h4s_options_none)<=>~(p(s(t_bool,X16)))),file('i/f/patricia/IS__PTREE__PEEK_c1', ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c0)).
# SZS output end CNFRefutation
