# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X2))))|s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ch4s_arithmetics_Xu_u_LTu_u_EXPu_u_Xu_u_IFF)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/X__LT__EXP__X__IFF', aHLu_TRUTH)).
fof(4, 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/X__LT__EXP__X__IFF', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X11]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(14, axiom,![X11]: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,X11)))))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_primu_u_recs_LESSu_u_0)).
fof(15, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_ALTu_u_ZERO)).
fof(16, axiom,![X12]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X12),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__LT__EXP__X__IFF', ah4s_arithmetics_EXP0u_c0)).
fof(17, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_ONE)).
fof(18, axiom,![X11]:~(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11)))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_SUCu_u_NOT)).
fof(19, axiom,![X12]:(s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_nums_0)|?[X11]:s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11)))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_numu_u_CASES)).
fof(20, axiom,![X1]:?[X13]:((p(s(t_bool,X13))<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))&s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,X13),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_ZEROu_u_EXP)).
fof(21, axiom,![X11]:![X12]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11))))))<=>(s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,X11)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_primu_u_recs_LESSu_u_THM)).
fof(22, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X1),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(23, axiom,![X11]:![X12]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_LESSu_u_MONOu_u_EQ)).
fof(24, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X11)))=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__LT__EXP__X__IFF', ah4s_arithmetics_EXPu_u_1u_c0)).
fof(25, axiom,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X2))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_Xu_u_LTu_u_EXPu_u_X)).
fof(26, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/X__LT__EXP__X__IFF', aHLu_FALSITY)).
fof(32, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/arithmetic/X__LT__EXP__X__IFF', aHLu_BOOLu_CASES)).
fof(34, axiom,![X6]:![X3]:![X4]:s(X6,h4s_bools_cond(s(t_bool,f),s(X6,X4),s(X6,X3)))=s(X6,X3),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
