# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/LESS__EQ__ADD__SUB', aHLu_TRUTH)).
fof(9, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/LESS__EQ__ADD__SUB', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(10, axiom,![X9]:![X10]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9))))|s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,X9))),file('i/f/arithmetic/LESS__EQ__ADD__SUB', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(11, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/LESS__EQ__ADD__SUB', ah4s_arithmetics_ONE)).
fof(12, axiom,![X9]:![X10]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X9),s(t_h4s_nums_num,X10))),file('i/f/arithmetic/LESS__EQ__ADD__SUB', ah4s_arithmetics_ADDu_u_SYM)).
fof(13, axiom,![X11]:![X9]:![X10]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X11)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X11))),file('i/f/arithmetic/LESS__EQ__ADD__SUB', ah4s_arithmetics_ADDu_u_ASSOC)).
fof(14, axiom,![X9]:![X10]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9))))),file('i/f/arithmetic/LESS__EQ__ADD__SUB', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(15, axiom,![X9]:![X10]:(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9)))=s(t_h4s_nums_num,X10)<=>s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/LESS__EQ__ADD__SUB', ah4s_arithmetics_ADDu_u_INVu_u_0u_u_EQ)).
fof(16, axiom,![X10]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X10)))),file('i/f/arithmetic/LESS__EQ__ADD__SUB', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(17, axiom,![X9]:![X10]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X10))))=>?[X11]:s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))),file('i/f/arithmetic/LESS__EQ__ADD__SUB', ah4s_arithmetics_LESSu_u_ADDu_u_1)).
fof(18, axiom,![X12]:![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,X12)))=s(t_h4s_nums_num,X13),file('i/f/arithmetic/LESS__EQ__ADD__SUB', ah4s_arithmetics_ADDu_u_SUB)).
fof(19, conjecture,![X12]:![X14]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X14))))=>![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X12)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X12)))))),file('i/f/arithmetic/LESS__EQ__ADD__SUB', ch4s_arithmetics_LESSu_u_EQu_u_ADDu_u_SUB)).
# SZS output end CNFRefutation
