# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),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,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X1))))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_bits_log2(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1)))))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ch4s_bits_TWOEXPu_u_LEu_u_IMPu_u_LEu_u_LOG2u_c1)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', aHLu_FALSITY)).
fof(8, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X4]:((p(s(t_bool,X4))=>p(s(t_bool,f)))<=>s(t_bool,X4)=s(t_bool,f)),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(12, axiom,![X10]:![X11]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_arithmetics_NOTu_u_LESS)).
fof(13, axiom,![X11]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X11)))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(15, axiom,![X12]:(p(s(t_bool,h4s_primu_u_recs_u_3c(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,X12))))=>![X10]:![X11]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X10)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_arithmetics_EXPu_u_BASEu_u_LTu_u_MONO)).
fof(17, axiom,![X10]:![X11]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_numerals_numeralu_u_distribu_c22)).
fof(18, axiom,![X10]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_numerals_numeralu_u_ltu_c2)).
fof(19, axiom,![X10]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_numerals_numeralu_u_lteu_c1)).
fof(20, axiom,![X13]:![X10]:![X11]:s(t_bool,h4s_arithmetics_u_3cu_3d(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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X13)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X13))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(21, axiom,![X10]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_numerals_numeralu_u_distribu_c27)).
fof(22, axiom,![X13]:![X10]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,X10))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))))))))=>s(t_h4s_nums_num,h4s_bits_log2(s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,X13)),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_bits_LOG2u_u_UNIQUE)).
fof(23, axiom,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),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,X1))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_bits_log2(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_bits_log2(s(t_h4s_nums_num,X1)))))))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_bits_LOG2u_u_LEu_u_MONO)).
fof(24, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,X11),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(25, axiom,![X10]:![X11]: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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_arithmetics_ADDu_u_SYM)).
fof(26, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', aHLu_BOOLu_CASES)).
fof(27, axiom,![X10]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X10))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(28, axiom,![X10]:![X11]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X11))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))))),file('i/f/bit/TWOEXP__LE__IMP__LE__LOG2_c1', ah4s_numerals_numeralu_u_ltu_c5)).
# SZS output end CNFRefutation
