# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_primu_u_recs_u_3c(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,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/SUB__LESS__0', ch4s_arithmetics_SUBu_u_LESSu_u_0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/SUB__LESS__0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/SUB__LESS__0', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/SUB__LESS__0', aHLu_BOOLu_CASES)).
fof(6, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/arithmetic/SUB__LESS__0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/arithmetic/SUB__LESS__0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X1]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/SUB__LESS__0', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(14, 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/SUB__LESS__0', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(15, 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/SUB__LESS__0', ah4s_arithmetics_NOTu_u_LESS)).
fof(17, axiom,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/SUB__LESS__0', ah4s_arithmetics_SUBu_u_EQu_u_0)).
# SZS output end CNFRefutation
