# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/bit/BITS__SUC__THM', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bit/BITS__SUC__THM', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/bit/BITS__SUC__THM', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:![X8]:![X9]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9))))))=>s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_bits_sbit(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X8))))),s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))=s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))),file('i/f/bit/BITS__SUC__THM', ah4s_bits_BITSu_u_SUC)).
fof(16, axiom,![X7]:![X15]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7))))|s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,X7))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(29, axiom,![X7]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X15))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_ADDu_u_SYM)).
fof(32, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_0)))=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/bit/BITS__SUC__THM', ah4s_arithmetics_EXP0u_c0)).
fof(33, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X15),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_ADDu_u_0)).
fof(39, axiom,![X10]:![X13]:![X14]:s(X10,h4s_bools_cond(s(t_bool,f),s(X10,X14),s(X10,X13)))=s(X10,X13),file('i/f/bit/BITS__SUC__THM', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(40, axiom,![X10]:![X13]:![X14]:s(X10,h4s_bools_cond(s(t_bool,t),s(X10,X14),s(X10,X13)))=s(X10,X14),file('i/f/bit/BITS__SUC__THM', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(47, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,X15),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(65, axiom,![X7]:![X15]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X15))))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_NOTu_u_LESS)).
fof(66, axiom,![X7]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X7)))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(67, axiom,![X1]:((p(s(t_bool,X1))=>p(s(t_bool,f)))<=>s(t_bool,X1)=s(t_bool,f)),file('i/f/bit/BITS__SUC__THM', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(77, axiom,![X7]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X7)))))=s(t_h4s_nums_num,X7),file('i/f/bit/BITS__SUC__THM', ah4s_numerals_numeralu_u_addu_c0)).
fof(81, axiom,![X7]:![X15]:(~(s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,X7))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X7))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X15)))))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(83, axiom,![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_SUBu_u_EQUALu_u_0)).
fof(84, axiom,![X7]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X15))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_SUBu_u_MONOu_u_EQ)).
fof(88, axiom,![X7]:![X8]:![X9]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))))=>s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/bit/BITS__SUC__THM', ah4s_bits_BITSu_u_ZERO)).
fof(96, axiom,![X7]:![X15]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7)))))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X7))))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_SUBu_u_LEFTu_u_SUC)).
fof(98, axiom,![X15]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),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/bit/BITS__SUC__THM', ah4s_arithmetics_ADD1)).
fof(100, axiom,![X7]:![X15]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X7))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_LESSu_u_EQ)).
fof(113, axiom,![X7]:![X15]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7))))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(116, axiom,![X7]:![X15]:(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_nums_0)&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15)))))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_EXPu_u_EQu_u_0)).
fof(118, axiom,![X7]:![X15]:(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_nums_0)|s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_MULTu_u_EQu_u_0)).
fof(122, axiom,![X7]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7))))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_EXP0u_c1)).
fof(133, conjecture,![X7]:![X8]:![X9]:s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_bits_sbit(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X8))))),s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))))),file('i/f/bit/BITS__SUC__THM', ch4s_bits_BITSu_u_SUCu_u_THM)).
# SZS output end CNFRefutation
