# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),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/LE__LT1', ch4s_arithmetics_LEu_u_LT1)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/LE__LT1', 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/LE__LT1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/arithmetic/LE__LT1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(10, axiom,![X7]:![X8]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))))))=>(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X7)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))),file('i/f/arithmetic/LE__LT1', ah4s_primu_u_recs_LESSu_u_LEMMA1)).
fof(11, axiom,![X7]:![X8]:((s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X7)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))))))),file('i/f/arithmetic/LE__LT1', ah4s_primu_u_recs_LESSu_u_LEMMA2)).
fof(12, axiom,![X7]:![X8]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))|s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X7))),file('i/f/arithmetic/LE__LT1', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(13, axiom,![X8]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),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/LE__LT1', ah4s_arithmetics_ADD1)).
fof(14, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/arithmetic/LE__LT1', aHLu_BOOLu_CASES)).
fof(15, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/LE__LT1', aHLu_FALSITY)).
# SZS output end CNFRefutation
