# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:~((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2)))))),file('i/f/arithmetic/LESS__ANTISYM', ch4s_arithmetics_LESSu_u_ANTISYM)).
fof(2, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/arithmetic/LESS__ANTISYM', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(3, axiom,![X1]:~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/LESS__ANTISYM', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(9, axiom,![X7]:![X1]:![X2]:((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X7)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X7))))),file('i/f/arithmetic/LESS__ANTISYM', ah4s_arithmetics_LESSu_u_TRANS)).
fof(18, axiom,![X1]:~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/LESS__ANTISYM', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(32, axiom,![X8]:![X15]:![X5]:(?[X10]:(s(X8,X10)=s(X8,X15)&p(s(t_bool,happ(s(t_fun(X8,t_bool),X5),s(X8,X10)))))<=>p(s(t_bool,happ(s(t_fun(X8,t_bool),X5),s(X8,X15))))),file('i/f/arithmetic/LESS__ANTISYM', ah4s_bools_UNWINDu_u_THM2)).
fof(80, axiom,p(s(t_bool,t)),file('i/f/arithmetic/LESS__ANTISYM', aHLu_TRUTH)).
fof(81, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/arithmetic/LESS__ANTISYM', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
