# 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,X2))))=>![X3]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))))))),file('i/f/arithmetic/LESS__IMP__LESS__ADD', ch4s_arithmetics_LESSu_u_IMPu_u_LESSu_u_ADD)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/LESS__IMP__LESS__ADD', aHLu_TRUTH)).
fof(7, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)<=>p(s(t_bool,X9))),file('i/f/arithmetic/LESS__IMP__LESS__ADD', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(8, axiom,![X10]:![X11]:((p(s(t_bool,X11))=>p(s(t_bool,X10)))=>((p(s(t_bool,X10))=>p(s(t_bool,X11)))=>s(t_bool,X11)=s(t_bool,X10))),file('i/f/arithmetic/LESS__IMP__LESS__ADD', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,X2),s(t_h4s_nums_num,X1))))|s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1))),file('i/f/arithmetic/LESS__IMP__LESS__ADD', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(13, axiom,![X3]:![X1]:![X2]:((p(s(t_bool,h4s_primu_u_recs_u_3c(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,X1),s(t_h4s_nums_num,X3)))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))))),file('i/f/arithmetic/LESS__IMP__LESS__ADD', ah4s_arithmetics_LESSu_u_TRANS)).
fof(23, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/LESS__IMP__LESS__ADD', ah4s_arithmetics_NOTu_u_LESS)).
fof(30, axiom,![X1]:![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/LESS__IMP__LESS__ADD', ah4s_arithmetics_LESSu_u_EQu_u_ADD)).
fof(53, axiom,![X1]:![X2]:((~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))&~(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,X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/LESS__IMP__LESS__ADD', ah4s_arithmetics_LESSu_u_CASESu_u_IMP)).
fof(59, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/LESS__IMP__LESS__ADD', ah4s_arithmetics_ADDu_u_SYM)).
# SZS output end CNFRefutation
