# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/X__LE__X__EXP', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/X__LE__X__EXP', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/arithmetic/X__LE__X__EXP', aHLu_BOOLu_CASES)).
fof(6, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X9]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/X__LE__X__EXP', ah4s_nums_NOTu_u_SUC)).
fof(14, axiom,![X9]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X9))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(15, axiom,![X9]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9)))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_primu_u_recs_LESSu_u_0)).
fof(16, axiom,![X10]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_EXP0u_c0)).
fof(17, axiom,![X9]:![X10]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_EXP0u_c1)).
fof(18, axiom,![X10]:(s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_nums_0)|?[X9]:s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9)))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_numu_u_CASES)).
fof(20, axiom,![X9]:![X10]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9))))))<=>(s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_nums_0)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X9)))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_LEu_u_MULTu_u_CANCELu_u_LBAREu_c0)).
fof(21, axiom,![X11]:![X6]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X11))))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X6))))|s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_ZEROu_u_LTu_u_EXP)).
fof(22, conjecture,![X6]:![X9]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X9))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X9))))))),file('i/f/arithmetic/X__LE__X__EXP', ch4s_arithmetics_Xu_u_LEu_u_Xu_u_EXP)).
# SZS output end CNFRefutation
