# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(p(s(t_bool,h4s_seqs_subseq(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1))))=>![X2]:![X3]:?[X4]:(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_arithmetics_u_3eu_3d),s(t_h4s_nums_num,X4))),s(t_h4s_nums_num,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_arithmetics_u_3eu_3d),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,X4))))),s(t_h4s_nums_num,X3)))))),file('i/f/seq/SEQ__DIRECT', ch4s_seqs_SEQu_u_DIRECT)).
fof(2, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/seq/SEQ__DIRECT', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(40, axiom,![X4]:![X8]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X4)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X8))))),file('i/f/seq/SEQ__DIRECT', ah4s_arithmetics_NOTu_u_LESS)).
fof(42, axiom,![X8]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X8)))),file('i/f/seq/SEQ__DIRECT', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(45, axiom,![X4]:![X8]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X4))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X4))))|s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X4))),file('i/f/seq/SEQ__DIRECT', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(48, axiom,![X7]:![X4]:![X8]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X4))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),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/seq/SEQ__DIRECT', ah4s_arithmetics_LESSu_u_EQu_u_LESSu_u_TRANS)).
fof(56, axiom,![X4]:![X8]: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_arithmetics_u_3eu_3d),s(t_h4s_nums_num,X4))),s(t_h4s_nums_num,X8)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X4))),file('i/f/seq/SEQ__DIRECT', ah4s_arithmetics_GREATERu_u_EQ)).
fof(61, axiom,![X1]:(p(s(t_bool,h4s_seqs_subseq(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1))))=>![X4]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,X4))))))),file('i/f/seq/SEQ__DIRECT', ah4s_seqs_SEQu_u_SUBLE)).
# SZS output end CNFRefutation
