# 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,h4s_nums_0),s(t_h4s_nums_num,X2))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))))),file('i/f/arithmetic/X__LE__X__EXP', ch4s_arithmetics_Xu_u_LEu_u_Xu_u_EXP)).
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/X__LE__X__EXP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(25, axiom,![X2]:![X17]:![X18]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X18))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X2))))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_EXPu_u_BASEu_u_LEQu_u_MONOu_u_IMP)).
fof(26, axiom,![X2]:![X17]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_LESSu_u_EQ)).
fof(27, axiom,![X2]:![X17]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2))))|s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X2))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(33, axiom,![X2]:![X17]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X17))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_LESSu_u_CASES)).
fof(35, axiom,![X2]:![X17]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X17))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
fof(37, axiom,![X2]:![X17]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2))))))<=>(s(t_h4s_nums_num,X17)=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,X2)))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_LEu_u_MULTu_u_CANCELu_u_LBAREu_c0)).
fof(40, axiom,![X8]:![X2]:![X17]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X8)))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X8))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_LESSu_u_LESSu_u_EQu_u_TRANS)).
fof(41, axiom,![X2]:![X17]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_EXP0u_c1)).
fof(43, axiom,![X2]:![X17]:(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X2)=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,X17)))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_EXPu_u_EQu_u_0)).
fof(44, axiom,![X14]:![X1]:(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,X1),s(t_h4s_nums_num,X14))))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))|s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_ZEROu_u_LTu_u_EXP)).
fof(48, axiom,![X2]:(~(s(t_h4s_nums_num,X2)=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,X2))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(49, axiom,![X2]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(53, axiom,![X17]:(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_nums_0)|?[X2]:s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_numu_u_CASES)).
fof(55, axiom,![X2]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/X__LE__X__EXP', ah4s_nums_NOTu_u_SUC)).
fof(56, axiom,![X2]:![X17]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_LESSu_u_MONOu_u_EQ)).
fof(66, axiom,![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/X__LE__X__EXP', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
