# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),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_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/SUB__LEFT__ADD', ch4s_arithmetics_SUBu_u_LEFTu_u_ADD)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/SUB__LEFT__ADD', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/SUB__LEFT__ADD', aHLu_FALSITY)).
fof(4, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/arithmetic/SUB__LEFT__ADD', aHLu_BOOLu_CASES)).
fof(6, 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/arithmetic/SUB__LEFT__ADD', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(11, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X7]:![X5]:![X6]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X6),s(X7,X5)))=s(X7,X6),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(13, axiom,![X7]:![X5]:![X6]:s(X7,h4s_bools_cond(s(t_bool,f),s(X7,X6),s(X7,X5)))=s(X7,X5),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(14, axiom,![X2]:![X3]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(15, axiom,![X9]:![X10]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X10))))=>![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X9)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9)))))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_LESSu_u_EQu_u_ADDu_u_SUB)).
fof(16, axiom,![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X3),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(17, axiom,![X2]:![X3]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),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,X3))))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_NOTu_u_LESS)).
fof(18, axiom,![X2]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_LESSu_u_IMPu_u_LESSu_u_ORu_u_EQ)).
# SZS output end CNFRefutation
