# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))))<=>?[X4]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X4),s(t_h4s_nums_num,X1))))&(![X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X4),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))))&(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X4),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))))))))&?[X3]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X4),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))))))),file('i/f/Omega_Automata/BOREL__HIERARCHY__G_c0', ch4s_Omegau_u_Automatas_BORELu_u_HIERARCHYu_u_Gu_c0)).
fof(2, axiom,p(s(t_bool,t1)),file('i/f/Omega_Automata/BOREL__HIERARCHY__G_c0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/Omega_Automata/BOREL__HIERARCHY__G_c0', aHLu_FALSITY)).
fof(20, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t1)|s(t_bool,X3)=s(t_bool,f)),file('i/f/Omega_Automata/BOREL__HIERARCHY__G_c0', aHLu_BOOLu_CASES)).
fof(23, axiom,![X10]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10))))),file('i/f/Omega_Automata/BOREL__HIERARCHY__G_c0', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(24, axiom,![X10]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),file('i/f/Omega_Automata/BOREL__HIERARCHY__G_c0', ah4s_arithmetics_ADDu_u_SYM)).
fof(29, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,X11),file('i/f/Omega_Automata/BOREL__HIERARCHY__G_c0', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
