# 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(3, axiom,![X2]:![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_SUBu_c1)).
fof(4, axiom,![X4]:![X7]:![X8]:s(X4,h4s_bools_cond(s(t_bool,t),s(X4,X8),s(X4,X7)))=s(X4,X8),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(5, axiom,![X4]:![X7]:![X8]:s(X4,h4s_bools_cond(s(t_bool,f),s(X4,X8),s(X4,X7)))=s(X4,X7),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(7, axiom,![X13]:![X14]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X14))))=>![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_LESSu_u_EQu_u_ADDu_u_SUB)).
fof(10, 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(12, axiom,![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_SUBu_u_EQUALu_u_0)).
fof(16, axiom,![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_SUBu_c0)).
fof(20, axiom,![X2]:![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_nums_suc(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,X3))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_SUBu_u_MONOu_u_EQ)).
fof(27, axiom,![X2]:![X3]: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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_ADDu_u_SYM)).
fof(30, axiom,![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,X3),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(31, axiom,![X2]:![X3]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_LESSu_u_EQu_u_ADD)).
fof(33, 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(35, axiom,![X2]:![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(40, axiom,![X2]:![X3]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_LESSu_u_ADDu_u_SUC)).
fof(51, axiom,![X2]:![X3]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))|s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,X2))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(53, 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(55, axiom,![X2]:![X3]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X2))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_arithmetics_ORu_u_LESS)).
fof(58, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/arithmetic/SUB__LEFT__ADD', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
# SZS output end CNFRefutation
