%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP388_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:33:46 AM UTC 2026
% Result : Theorem 3.48s 1.47s
% Output : Refutation 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 22 unt; 0 typ; 7 def)
% Number of atoms : 70 ( 27 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 57 ( 28 ~; 24 |; 0 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 58 ( 56 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 32 ( 30 usr; 5 prp; 0-2 aty)
% Number of functors : 355 ( 355 usr; 44 con; 0-3 aty)
% Number of variables : 22 ( 20 !; 2 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Nat_set_set$': $tType ).
tff(type_def_6,type,
'A_a_prod_ell2$': $tType ).
tff(type_def_7,type,
'A_b_prod_ell2_set$': $tType ).
tff(type_def_8,type,
'Int_bool_fun$': $tType ).
tff(type_def_9,type,
'A_b_prod_a_prod_ell2$': $tType ).
tff(type_def_10,type,
'Nat_a_b_prod_ell2_fun$': $tType ).
tff(type_def_11,type,
'B_ell2_b_ell2_fun$': $tType ).
tff(type_def_12,type,
'A_b_prod_ell2_b_ell2_fun$': $tType ).
tff(type_def_13,type,
'A_ell2_a_b_prod_ell2_fun$': $tType ).
tff(type_def_14,type,
'Num_num_fun$': $tType ).
tff(type_def_15,type,
'Num_enat_fun$': $tType ).
tff(type_def_16,type,
'B_a_prod_ell2$': $tType ).
tff(type_def_17,type,
'Int_set$': $tType ).
tff(type_def_18,type,
'Enat$': $tType ).
tff(type_def_19,type,
'Int_int_fun$': $tType ).
tff(type_def_20,type,
'B_ell2_set_a_b_prod_ell2_set_fun$': $tType ).
tff(type_def_21,type,
'Enat_int_fun$': $tType ).
tff(type_def_22,type,
'Num_bool_fun$': $tType ).
tff(type_def_23,type,
'Enat_set$': $tType ).
tff(type_def_24,type,
'A_ell2_set$': $tType ).
tff(type_def_25,type,
'A_b_prod_ell2_a_a_b_prod_prod_ell2_fun$': $tType ).
tff(type_def_26,type,
'Nat_nat_fun$': $tType ).
tff(type_def_27,type,
'A_b_prod_ell2$': $tType ).
tff(type_def_28,type,
'Nat$': $tType ).
tff(type_def_29,type,
'A_b_prod_ell2_bool_fun$': $tType ).
tff(type_def_30,type,
'Nat_b_ell2_fun$': $tType ).
tff(type_def_31,type,
'Enat_enat_fun$': $tType ).
tff(type_def_32,type,
'B_ell2_b_a_prod_ell2_fun$': $tType ).
tff(type_def_33,type,
'Num$': $tType ).
tff(type_def_34,type,
'A_b_prod_ell2_a_b_prod_a_prod_ell2_fun$': $tType ).
tff(type_def_35,type,
'Nat_set_nat_set_fun$': $tType ).
tff(type_def_36,type,
'Enat_bool_fun$': $tType ).
tff(type_def_37,type,
'A_b_prod_ell2_a_b_prod_ell2_fun$': $tType ).
tff(type_def_38,type,
'B_ell2_set$': $tType ).
tff(type_def_39,type,
'Int_enat_fun$': $tType ).
tff(type_def_40,type,
'A_b_prod_ell2_set_bool_fun$': $tType ).
tff(type_def_41,type,
'B_ell2_bool_fun$': $tType ).
tff(type_def_42,type,
'Enat_num_fun$': $tType ).
tff(type_def_43,type,
'Nat_set_bool_fun$': $tType ).
tff(type_def_44,type,
'A_ell2$': $tType ).
tff(type_def_45,type,
'A_b_prod_ell2_set_a_b_prod_ell2_fun$': $tType ).
tff(type_def_46,type,
'B_ell2_a_b_prod_ell2_fun$': $tType ).
tff(type_def_47,type,
'Enat_enat_bool_fun_fun$': $tType ).
tff(type_def_48,type,
'B_ell2_set_set$': $tType ).
tff(type_def_49,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_50,type,
'B_ell2_nat_fun$': $tType ).
tff(type_def_51,type,
'A_b_prod_ell2_set_set$': $tType ).
tff(type_def_52,type,
'Nat_nat_fun_bool_fun$': $tType ).
tff(type_def_53,type,
'Nat_bool_fun$': $tType ).
tff(type_def_54,type,
'Nat_set$': $tType ).
tff(type_def_55,type,
'A_ell2_a_ell2_fun$': $tType ).
tff(type_def_56,type,
'A_b_prod_ell2_nat_fun$': $tType ).
tff(type_def_57,type,
'B_ell2$': $tType ).
tff(type_def_58,type,
'Int_num_fun$': $tType ).
tff(type_def_59,type,
'Num_int_fun$': $tType ).
tff(type_def_60,type,
'Num_num_bool_fun_fun$': $tType ).
tff(func_def_0,type,
'uum$': ( 'Nat_nat_fun$' * 'Nat_set$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_1,type,
'the_inv_into$c': ( 'B_ell2_set$' * 'B_ell2_nat_fun$' ) > 'Nat_b_ell2_fun$' ).
tff(func_def_2,type,
'one$b': 'Enat$' ).
tff(func_def_3,type,
'zero$e': 'Enat$' ).
tff(func_def_4,type,
'fun_app$q': ( 'B_ell2_nat_fun$' * 'B_ell2$' ) > 'Nat$' ).
tff(func_def_5,type,
'dbl_inc$': 'Int_int_fun$' ).
tff(func_def_6,type,
'image$': 'B_ell2_a_b_prod_ell2_fun$' > 'B_ell2_set_a_b_prod_ell2_set_fun$' ).
tff(func_def_7,type,
'collect$b': 'Nat_bool_fun$' > 'Nat_set$' ).
tff(func_def_8,type,
'fun_app$aa': ( 'Num_enat_fun$' * 'Num$' ) > 'Enat$' ).
tff(func_def_9,type,
'uut$': ( 'Nat_set$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_10,type,
'inj_on$i': 'A_b_prod_ell2_b_ell2_fun$' > 'A_b_prod_ell2_set_bool_fun$' ).
tff(func_def_11,type,
'minus$h': 'Enat$' > 'Enat_enat_fun$' ).
tff(func_def_12,type,
'fun_app$h': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_13,type,
'fun_app$x': ( 'Enat_enat_bool_fun_fun$' * 'Enat$' ) > 'Enat_bool_fun$' ).
tff(func_def_14,type,
'image$g': ( 'Int_int_fun$' * 'Int_set$' ) > 'Int_set$' ).
tff(func_def_15,type,
'collect$a': 'A_b_prod_ell2_bool_fun$' > 'A_b_prod_ell2_set$' ).
tff(func_def_16,type,
'uuw$': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_17,type,
'comp$c': ( 'A_b_prod_ell2_a_b_prod_ell2_fun$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_18,type,
'comp$g': ( 'B_ell2_b_ell2_fun$' * 'A_b_prod_ell2_b_ell2_fun$' ) > 'A_b_prod_ell2_b_ell2_fun$' ).
tff(func_def_19,type,
'plus$a': 'Enat$' > 'Enat_enat_fun$' ).
tff(func_def_20,type,
'dbl$': 'Int_int_fun$' ).
tff(func_def_21,type,
'eps$a': 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_22,type,
'uus$': ( 'Nat_set$' * 'Nat_set$' ) > 'Nat_bool_fun$' ).
tff(func_def_23,type,
'fun_app$e': ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2$' ) > 'A_b_prod_ell2$' ).
tff(func_def_24,type,
'dbl_dec$a': 'Int_int_fun$' ).
tff(func_def_25,type,
'fun_app$y': ( 'A_ell2_a_ell2_fun$' * 'A_ell2$' ) > 'A_ell2$' ).
tff(func_def_26,type,
'comp$e': ( 'B_ell2_b_ell2_fun$' * 'B_ell2_b_ell2_fun$' ) > 'B_ell2_b_ell2_fun$' ).
tff(func_def_27,type,
'sub$a': ( 'Num$' * 'Num$' ) > 'A_ell2$' ).
tff(func_def_28,type,
'fun_app$ac': ( 'Enat_num_fun$' * 'Enat$' ) > 'Num$' ).
tff(func_def_29,type,
'uug$': 'Nat_set$' > 'Nat_bool_fun$' ).
tff(func_def_30,type,
'tensor_ell2$': 'A_ell2$' > 'B_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_31,type,
'uuq$': 'A_b_prod_ell2$' > 'A_b_prod_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_32,type,
'the_inv_into$': ( 'A_b_prod_ell2_set$' * 'A_b_prod_ell2_b_ell2_fun$' ) > 'B_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_33,type,
'uuf$': 'B_ell2$' > 'A_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_34,type,
'inc$': 'Num_num_fun$' ).
tff(func_def_35,type,
'zero$b': 'A_b_prod_ell2$' ).
tff(func_def_36,type,
'psi$': 'A_ell2$' ).
tff(func_def_37,type,
'uuh$': 'B_ell2_bool_fun$' ).
tff(func_def_38,type,
'minus$d': ( 'A_b_prod_ell2_set$' * 'A_b_prod_ell2_set$' ) > 'A_b_prod_ell2_set$' ).
tff(func_def_39,type,
'the_inv_into$d': ( 'A_b_prod_ell2_set$' * 'A_b_prod_ell2_nat_fun$' ) > 'Nat_a_b_prod_ell2_fun$' ).
tff(func_def_40,type,
'uun$': 'Nat_nat_fun$' > 'Nat_bool_fun$' ).
tff(func_def_41,type,
'bitM$': 'Num_num_fun$' ).
tff(func_def_42,type,
'comp$n': ( 'A_b_prod_ell2_nat_fun$' * 'Nat_a_b_prod_ell2_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_43,type,
'uuv$': 'Nat_nat_fun_bool_fun$' ).
tff(func_def_44,type,
'dbl_inc$a': 'A_ell2$' > 'A_ell2$' ).
tff(func_def_45,type,
'of_nat$': 'Nat$' > $int ).
tff(func_def_46,type,
'fun_app$g': ( 'B_ell2_b_a_prod_ell2_fun$' * 'B_ell2$' ) > 'B_a_prod_ell2$' ).
tff(func_def_47,type,
'zero$a': 'B_ell2$' ).
tff(func_def_48,type,
'minus$g': ( 'Nat_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_49,type,
'minus$b': ( 'Nat_set$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_50,type,
'uuc$': 'Nat_nat_fun$' ).
tff(func_def_51,type,
'tensor_ell2$b': ( 'B_ell2$' * 'A_ell2$' ) > 'B_a_prod_ell2$' ).
tff(func_def_52,type,
'uminus$d': 'Int_set$' > 'Int_set$' ).
tff(func_def_53,type,
'uur$': $int > 'Int_int_fun$' ).
tff(func_def_54,type,
'image$b': ( 'B_ell2_nat_fun$' * 'B_ell2_set$' ) > 'Nat_set$' ).
tff(func_def_55,type,
'uminus$c': 'A_ell2$' > 'A_ell2$' ).
tff(func_def_56,type,
'fun_app$s': ( 'A_b_prod_ell2_set_a_b_prod_ell2_fun$' * 'A_b_prod_ell2_set$' ) > 'A_b_prod_ell2$' ).
tff(func_def_57,type,
'comp$a': ( 'A_b_prod_ell2_b_ell2_fun$' * 'Nat_a_b_prod_ell2_fun$' ) > 'Nat_b_ell2_fun$' ).
tff(func_def_58,type,
'uuj$': ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' * 'A_b_prod_ell2_bool_fun$' ) > 'A_b_prod_ell2_bool_fun$' ).
tff(func_def_59,type,
'top$e': 'A_ell2_set$' ).
tff(func_def_60,type,
'sub$': 'Num$' > 'Num_int_fun$' ).
tff(func_def_61,type,
'fun_app$v': ( 'Num_num_bool_fun_fun$' * 'Num$' ) > 'Num_bool_fun$' ).
tff(func_def_62,type,
'comp$m': ( 'B_ell2_nat_fun$' * 'Nat_b_ell2_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_63,type,
'image$a': 'Nat_nat_fun$' > 'Nat_set_nat_set_fun$' ).
tff(func_def_64,type,
'comp$j': ( 'A_b_prod_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2_a_b_prod_ell2_fun$' ) > 'A_b_prod_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_65,type,
'comp$b': ( 'Nat_nat_fun$' * 'Nat_nat_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_66,type,
'uminus$': 'Nat_set$' > 'Nat_set$' ).
tff(func_def_67,type,
'minus$e': 'A_ell2$' > 'A_ell2_a_ell2_fun$' ).
tff(func_def_68,type,
'uu$': ( 'A_b_prod_ell2_a_b_prod_ell2_fun$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_69,type,
'fun_app$j': ( 'B_ell2_b_ell2_fun$' * 'B_ell2$' ) > 'B_ell2$' ).
tff(func_def_70,type,
'less_eq$b': 'A_b_prod_ell2_set$' > 'A_b_prod_ell2_set_bool_fun$' ).
tff(func_def_71,type,
'uuo$': $int > 'Int_int_fun$' ).
tff(func_def_72,type,
'top$a': 'B_ell2_set$' ).
tff(func_def_73,type,
'dbl$a': 'A_ell2$' > 'A_ell2$' ).
tff(func_def_74,type,
'to_nat$': 'Nat_nat_fun$' ).
tff(func_def_75,type,
'eps$': 'Nat_nat_fun_bool_fun$' > 'Nat_nat_fun$' ).
tff(func_def_76,type,
'uue$': 'A_ell2$' > 'A_b_prod_ell2_a_b_prod_a_prod_ell2_fun$' ).
tff(func_def_77,type,
'uminus$a': 'B_ell2_set$' > 'B_ell2_set$' ).
tff(func_def_78,type,
'inj_on$k': 'A_b_prod_ell2_a_b_prod_ell2_fun$' > 'A_b_prod_ell2_set_bool_fun$' ).
tff(func_def_79,type,
'member$a': 'A_b_prod_ell2$' > 'A_b_prod_ell2_set_bool_fun$' ).
tff(func_def_80,type,
'fun_app$ae': ( 'Enat_int_fun$' * 'Enat$' ) > $int ).
tff(func_def_81,type,
'one$a': 'Nat$' ).
tff(func_def_82,type,
'tensor_ell2$a': ( 'A_b_prod_ell2$' * 'A_ell2$' ) > 'A_b_prod_a_prod_ell2$' ).
tff(func_def_83,type,
'uminus$e': 'Nat_bool_fun$' > 'Nat_bool_fun$' ).
tff(func_def_84,type,
'numeral$b': 'Num$' > 'A_ell2$' ).
tff(func_def_85,type,
'fun_app$ag': ( 'Int_enat_fun$' * $int ) > 'Enat$' ).
tff(func_def_86,type,
'tensor_ell2$d': 'A_ell2$' > 'A_b_prod_ell2_a_a_b_prod_prod_ell2_fun$' ).
tff(func_def_87,type,
'top$g': 'Int_set$' ).
tff(func_def_88,type,
'top$i': 'Enat$' ).
tff(func_def_89,type,
'uud$': 'A_ell2$' > 'B_ell2_b_a_prod_ell2_fun$' ).
tff(func_def_90,type,
'numeral$': 'Num_int_fun$' ).
tff(func_def_91,type,
'member$': 'Nat$' > 'Nat_set_bool_fun$' ).
tff(func_def_92,type,
'comp$k': ( 'Nat_nat_fun$' * 'B_ell2_nat_fun$' ) > 'B_ell2_nat_fun$' ).
tff(func_def_93,type,
'fun_app$d': ( 'A_ell2_a_b_prod_ell2_fun$' * 'A_ell2$' ) > 'A_b_prod_ell2$' ).
tff(func_def_94,type,
'top$c': 'B_ell2_bool_fun$' ).
tff(func_def_95,type,
'comp$i': ( 'A_b_prod_ell2_b_ell2_fun$' * 'A_b_prod_ell2_a_b_prod_ell2_fun$' ) > 'A_b_prod_ell2_b_ell2_fun$' ).
tff(func_def_96,type,
'fun_app$z': ( 'Num_num_fun$' * 'Num$' ) > 'Num$' ).
tff(func_def_97,type,
'fun_app$i': ( 'A_b_prod_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2$' ) > 'A_b_prod_ell2$' ).
tff(func_def_98,type,
'less_eq$a': 'Nat_set$' > 'Nat_set_bool_fun$' ).
tff(func_def_99,type,
'fun_app$k': ( 'A_b_prod_ell2_b_ell2_fun$' * 'A_b_prod_ell2$' ) > 'B_ell2$' ).
tff(func_def_100,type,
'comp$f': ( 'A_b_prod_ell2_b_ell2_fun$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2_b_ell2_fun$' ).
tff(func_def_101,type,
'comp$d': ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_b_ell2_fun$' ) > 'B_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_102,type,
'fun_app$af': ( 'Int_num_fun$' * $int ) > 'Num$' ).
tff(func_def_103,type,
'image$d': ( 'A_b_prod_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2_set$' ) > 'A_b_prod_ell2_set$' ).
tff(func_def_104,type,
'numeral$a': 'Num_enat_fun$' ).
tff(func_def_105,type,
'uminus$b': 'A_b_prod_ell2_set$' > 'A_b_prod_ell2_set$' ).
tff(func_def_106,type,
'fun_app$o': ( 'Nat_set_nat_set_fun$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_107,type,
'the_inv_into$a': ( 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'A_b_prod_ell2_b_ell2_fun$' ).
tff(func_def_108,type,
'inj_on$j': 'Nat_b_ell2_fun$' > 'Nat_set_bool_fun$' ).
tff(func_def_109,type,
'fun_app$f': ( 'A_b_prod_ell2_a_b_prod_a_prod_ell2_fun$' * 'A_b_prod_ell2$' ) > 'A_b_prod_a_prod_ell2$' ).
tff(func_def_110,type,
'fun_app$c': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_111,type,
'top$b': 'A_b_prod_ell2_set$' ).
tff(func_def_112,type,
'image$h': ( 'B_ell2_set_a_b_prod_ell2_set_fun$' * 'B_ell2_set_set$' ) > 'A_b_prod_ell2_set_set$' ).
tff(func_def_113,type,
'fpow$': 'B_ell2_set$' > 'B_ell2_set_set$' ).
tff(func_def_114,type,
'fun_app$n': ( 'B_ell2_set_a_b_prod_ell2_set_fun$' * 'B_ell2_set$' ) > 'A_b_prod_ell2_set$' ).
tff(func_def_115,type,
'minus$': 'A_b_prod_ell2$' > 'A_b_prod_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_116,type,
'the_inv_into$b': ( 'Nat_set$' * 'Nat_nat_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_117,type,
'zero$': 'A_ell2$' ).
tff(func_def_118,type,
'uui$': 'A_b_prod_ell2_bool_fun$' ).
tff(func_def_119,type,
'uub$': ( 'B_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2_b_ell2_fun$' ) > 'A_b_prod_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_120,type,
'inj_on$d': 'A_b_prod_ell2_nat_fun$' > 'A_b_prod_ell2_set_bool_fun$' ).
tff(func_def_121,type,
'top$f': 'Enat_set$' ).
tff(func_def_122,type,
'fpow$b': 'A_b_prod_ell2_set$' > 'A_b_prod_ell2_set_set$' ).
tff(func_def_123,type,
'minus$f': ( 'Int_set$' * 'Int_set$' ) > 'Int_set$' ).
tff(func_def_124,type,
'minus$c': ( 'B_ell2_set$' * 'B_ell2_set$' ) > 'B_ell2_set$' ).
tff(func_def_125,type,
'nat$': $int > 'Nat$' ).
tff(func_def_126,type,
'image$c': ( 'A_b_prod_ell2_nat_fun$' * 'A_b_prod_ell2_set$' ) > 'Nat_set$' ).
tff(func_def_127,type,
'uua$': ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_b_ell2_fun$' ) > 'B_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_128,type,
'comp$': ( 'A_b_prod_ell2_nat_fun$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2_nat_fun$' ).
tff(func_def_129,type,
'fun_app$ai': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_130,type,
'image$f': ( 'A_b_prod_ell2_b_ell2_fun$' * 'A_b_prod_ell2_set$' ) > 'B_ell2_set$' ).
tff(func_def_131,type,
'fun_app$ab': ( 'Num_int_fun$' * 'Num$' ) > $int ).
tff(func_def_132,type,
'uul$': ( 'Nat_nat_fun$' * 'Nat_set$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_133,type,
'fun_app$t': ( 'Nat_b_ell2_fun$' * 'Nat$' ) > 'B_ell2$' ).
tff(func_def_134,type,
'tensor_ell2$c': ( 'A_ell2$' * 'A_ell2$' ) > 'A_a_prod_ell2$' ).
tff(func_def_135,type,
'top$h': 'Nat_bool_fun$' ).
tff(func_def_136,type,
'one$c': 'Num$' ).
tff(func_def_137,type,
'minus$a': 'B_ell2$' > 'B_ell2_b_ell2_fun$' ).
tff(func_def_138,type,
'one$': 'A_ell2$' ).
tff(func_def_139,type,
'uuu$': 'Nat_set$' > 'Nat_bool_fun$' ).
tff(func_def_140,type,
'plus$': ( 'A_ell2$' * 'A_ell2$' ) > 'A_ell2$' ).
tff(func_def_141,type,
'inj_on$e': 'A_b_prod_ell2_a_a_b_prod_prod_ell2_fun$' > 'A_b_prod_ell2_set_bool_fun$' ).
tff(func_def_142,type,
'fun_app$ad': ( 'Enat_enat_fun$' * 'Enat$' ) > 'Enat$' ).
tff(func_def_143,type,
'dbl_dec$': 'A_ell2$' > 'A_ell2$' ).
tff(func_def_144,type,
'image$e': ( 'B_ell2_b_ell2_fun$' * 'B_ell2_set$' ) > 'B_ell2_set$' ).
tff(func_def_145,type,
'inj_on$': 'Nat_nat_fun$' > 'Nat_set_bool_fun$' ).
tff(func_def_146,type,
'less_eq$c': 'Num_num_bool_fun_fun$' ).
tff(func_def_147,type,
'fun_app$r': ( 'A_b_prod_ell2_nat_fun$' * 'A_b_prod_ell2$' ) > 'Nat$' ).
tff(func_def_148,type,
'zero$d': 'Nat$' ).
tff(func_def_149,type,
'top$': 'Nat_set$' ).
tff(func_def_150,type,
'comp$l': ( 'Nat_nat_fun$' * 'A_b_prod_ell2_nat_fun$' ) > 'A_b_prod_ell2_nat_fun$' ).
tff(func_def_151,type,
'inj_on$g': 'A_b_prod_ell2_a_b_prod_a_prod_ell2_fun$' > 'A_b_prod_ell2_set_bool_fun$' ).
tff(func_def_152,type,
'collect$': 'B_ell2_bool_fun$' > 'B_ell2_set$' ).
tff(func_def_153,type,
'zero$c': 'A_a_prod_ell2$' ).
tff(func_def_154,type,
'uup$': 'B_ell2$' > 'B_ell2_b_ell2_fun$' ).
tff(func_def_155,type,
'comp$h': ( 'B_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2_b_ell2_fun$' ) > 'A_b_prod_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_156,type,
'bit1$': 'Num_num_fun$' ).
tff(func_def_157,type,
'less_eq$d': 'Enat_enat_bool_fun_fun$' ).
tff(func_def_158,type,
'bit0$': 'Num_num_fun$' ).
tff(func_def_159,type,
'uuk$': ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' * 'A_b_prod_ell2_bool_fun$' ) > 'B_ell2_bool_fun$' ).
tff(func_def_160,type,
'inj_on$l': 'Nat_a_b_prod_ell2_fun$' > 'Nat_set_bool_fun$' ).
tff(func_def_161,type,
'fpow$a': 'Nat_set$' > 'Nat_set_set$' ).
tff(func_def_162,type,
'top$d': 'A_b_prod_ell2_bool_fun$' ).
tff(func_def_170,type,
sK0: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_171,type,
sK1: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_172,type,
sK2: 'Num_bool_fun$' > 'Num$' ).
tff(func_def_173,type,
sK3: 'Int_num_fun$' > $int ).
tff(func_def_174,type,
sK4: 'Int_num_fun$' > $int ).
tff(func_def_175,type,
sK5: ( 'B_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2_b_ell2_fun$' ) > 'A_b_prod_ell2$' ).
tff(func_def_176,type,
sK6: 'Num_int_fun$' > 'Num$' ).
tff(func_def_177,type,
sK7: 'Num_int_fun$' > 'Num$' ).
tff(func_def_178,type,
sK8: ( 'A_b_prod_ell2_b_ell2_fun$' * 'B_ell2$' ) > 'A_b_prod_ell2$' ).
tff(func_def_179,type,
sK9: 'Num_int_fun$' > 'Num$' ).
tff(func_def_180,type,
sK10: 'Num_int_fun$' > 'Num$' ).
tff(func_def_181,type,
sK11: 'Int_enat_fun$' > $int ).
tff(func_def_182,type,
sK12: 'Int_enat_fun$' > $int ).
tff(func_def_183,type,
sK13: ( 'A_b_prod_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2$' ) > 'A_b_prod_ell2$' ).
tff(func_def_184,type,
sK14: ( 'B_ell2_b_ell2_fun$' * 'B_ell2_b_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_185,type,
sK15: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_186,type,
sK16: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_187,type,
sK17: 'Num$' > 'Num$' ).
tff(func_def_188,type,
sK18: 'Num$' > 'Num$' ).
tff(func_def_189,type,
sK19: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_190,type,
sK20: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_191,type,
sK21: 'Int_int_fun$' > $int ).
tff(func_def_192,type,
sK22: 'Int_int_fun$' > $int ).
tff(func_def_193,type,
sK23: ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' * 'A_b_prod_ell2_bool_fun$' ) > 'B_ell2$' ).
tff(func_def_194,type,
sK24: ( 'B_ell2_b_ell2_fun$' * 'B_ell2$' ) > 'B_ell2$' ).
tff(func_def_195,type,
sK25: 'B_ell2_b_ell2_fun$' > 'B_ell2$' ).
tff(func_def_196,type,
sK26: ( 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_197,type,
sK27: ( 'Nat_set$' * 'Nat_nat_fun$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_198,type,
sK28: 'Int_enat_fun$' > $int ).
tff(func_def_199,type,
sK29: 'Int_enat_fun$' > $int ).
tff(func_def_200,type,
sK30: 'B_ell2$' ).
tff(func_def_201,type,
sK31: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_202,type,
sK32: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_203,type,
sK33: 'A_b_prod_ell2$' > 'B_ell2$' ).
tff(func_def_204,type,
sK34: ( 'A_b_prod_ell2_set_bool_fun$' * 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2_set$' ).
tff(func_def_205,type,
sK35: ( 'A_b_prod_ell2_set_bool_fun$' * 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'A_b_prod_ell2_set$' ).
tff(func_def_206,type,
sK36: 'Nat_nat_fun$' ).
tff(func_def_207,type,
sK37: ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_208,type,
sK38: ( 'Nat_set$' * 'Nat_nat_fun$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_209,type,
sK39: ( 'Nat_nat_fun$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_210,type,
sK40: ( 'Nat_nat_fun$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_211,type,
sK41: 'Num_int_fun$' > 'Num$' ).
tff(func_def_212,type,
sK42: 'Num_int_fun$' > 'Num$' ).
tff(func_def_213,type,
sK43: ( 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_214,type,
sK44: ( 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_215,type,
sK45: ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' * 'B_ell2_b_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_216,type,
sK46: ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' * 'B_ell2_b_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_217,type,
sK47: ( 'A_b_prod_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2$' ) > 'A_b_prod_ell2$' ).
tff(func_def_218,type,
sK48: 'A_b_prod_ell2_a_b_prod_ell2_fun$' > 'A_b_prod_ell2$' ).
tff(func_def_219,type,
sK49: 'Num_num_fun$' > 'Num$' ).
tff(func_def_220,type,
sK50: 'Num_num_fun$' > 'Num$' ).
tff(func_def_221,type,
sK51: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_222,type,
sK52: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_223,type,
sK53: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_224,type,
sK54: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_225,type,
sK55: ( 'B_ell2$' * 'A_b_prod_ell2_b_ell2_fun$' ) > 'A_b_prod_ell2$' ).
tff(func_def_226,type,
sK56: 'Int_num_fun$' > $int ).
tff(func_def_227,type,
sK57: 'Int_num_fun$' > $int ).
tff(func_def_228,type,
sK58: ( 'A_b_prod_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2_a_b_prod_ell2_fun$' ) > 'A_b_prod_ell2$' ).
tff(func_def_229,type,
sK59: ( 'A_b_prod_ell2_nat_fun$' * 'Nat$' * 'A_b_prod_ell2$' ) > 'A_b_prod_ell2$' ).
tff(func_def_230,type,
sK60: ( 'A_b_prod_ell2_nat_fun$' * 'Nat$' ) > 'A_b_prod_ell2$' ).
tff(func_def_231,type,
sK61: ( 'A_b_prod_ell2_b_ell2_fun$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_232,type,
sK62: ( 'Nat$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_233,type,
sK63: 'Nat_set$' > 'Nat$' ).
tff(func_def_234,type,
sK64: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_235,type,
sK65: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_236,type,
sK66: ( 'Nat$' * 'B_ell2_nat_fun$' ) > 'B_ell2$' ).
tff(func_def_237,type,
sK67: 'Int_num_fun$' > $int ).
tff(func_def_238,type,
sK68: 'Int_num_fun$' > $int ).
tff(func_def_239,type,
sK69: ( 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_240,type,
sK70: ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_241,type,
sK71: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_242,type,
sK72: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_243,type,
sK73: ( 'B_ell2_nat_fun$' * 'Nat$' * 'B_ell2$' ) > 'B_ell2$' ).
tff(func_def_244,type,
sK74: ( 'B_ell2_nat_fun$' * 'Nat$' ) > 'B_ell2$' ).
tff(func_def_245,type,
sK75: 'Enat_enat_fun$' > 'Enat$' ).
tff(func_def_246,type,
sK76: 'Enat_enat_fun$' > 'Enat$' ).
tff(func_def_247,type,
sK77: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_248,type,
sK78: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_249,type,
sK79: 'A_b_prod_ell2$' ).
tff(func_def_250,type,
sK80: ( 'Nat_nat_fun$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_251,type,
sK81: 'Int_int_fun$' > $int ).
tff(func_def_252,type,
sK82: 'Int_int_fun$' > $int ).
tff(func_def_253,type,
sK83: ( 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_254,type,
sK84: ( 'Nat_set$' * 'Nat$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_255,type,
sK85: ( 'Nat_bool_fun$' * 'Nat_set$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_256,type,
sK86: ( 'A_b_prod_ell2$' * 'A_b_prod_ell2_a_b_prod_ell2_fun$' ) > 'A_b_prod_ell2$' ).
tff(func_def_257,type,
sK87: ( 'B_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2$' * 'B_ell2_set$' ) > 'B_ell2$' ).
tff(func_def_258,type,
sK88: ( 'B_ell2$' * 'B_ell2_b_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_259,type,
sK89: ( 'A_b_prod_ell2_set$' * 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2_set$' ).
tff(func_def_260,type,
sK90: ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' * 'A_b_prod_ell2_bool_fun$' ) > 'A_b_prod_ell2$' ).
tff(func_def_261,type,
sK91: ( 'A_b_prod_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' ) > 'B_ell2_set$' ).
tff(func_def_262,type,
sK92: ( 'A_b_prod_ell2$' * 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_263,type,
sK93: ( 'Nat_nat_fun$' * 'Nat_set_bool_fun$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_264,type,
sK94: ( 'Nat_nat_fun$' * 'Nat_set_bool_fun$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_265,type,
sK95: ( 'Nat_nat_fun$' * 'Nat_set$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_266,type,
sK96: ( 'Nat_nat_fun$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_267,type,
sK97: ( 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2_set_bool_fun$' ) > 'A_b_prod_ell2_set$' ).
tff(func_def_268,type,
sK98: ( 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2_set_bool_fun$' ) > 'B_ell2_set$' ).
tff(func_def_269,type,
sK99: ( 'Nat_set$' * 'Nat_nat_fun$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_270,type,
sK100: 'A_b_prod_ell2_set$' > 'A_b_prod_ell2$' ).
tff(func_def_271,type,
sK101: 'Num_num_fun$' > 'Num$' ).
tff(func_def_272,type,
sK102: 'Num_num_fun$' > 'Num$' ).
tff(func_def_273,type,
sK103: 'Int_int_fun$' > $int ).
tff(func_def_274,type,
sK104: 'Int_int_fun$' > $int ).
tff(func_def_275,type,
sK105: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_276,type,
sK106: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_277,type,
sK107: ( 'A_b_prod_ell2_set_bool_fun$' * 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'A_b_prod_ell2_set$' ).
tff(func_def_278,type,
sK108: ( 'A_b_prod_ell2_set_bool_fun$' * 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2_set$' ).
tff(func_def_279,type,
sK109: ( 'Nat_nat_fun$' * 'Nat_set$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_280,type,
sK110: ( 'Nat_nat_fun$' * 'Nat_set$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_281,type,
sK111: ( 'Nat$' * 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_282,type,
sK112: ( 'Nat$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_283,type,
sK113: 'Nat$' ).
tff(func_def_284,type,
sK114: ( 'Nat_set$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_285,type,
sK115: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_286,type,
sK116: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_287,type,
sK117: ( 'Nat_set$' * 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_288,type,
sK118: 'Enat_enat_fun$' > 'Enat$' ).
tff(func_def_289,type,
sK119: 'Enat_enat_fun$' > 'Enat$' ).
tff(func_def_290,type,
sK120: ( 'B_ell2_bool_fun$' * 'B_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2_set$' ) > 'B_ell2$' ).
tff(func_def_291,type,
sK121: 'Int_int_fun$' > $int ).
tff(func_def_292,type,
sK122: 'Int_int_fun$' > $int ).
tff(func_def_293,type,
sK123: ( 'A_b_prod_ell2$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_294,type,
sK124: ( 'A_b_prod_ell2$' * 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2$' ) > 'B_ell2$' ).
tff(func_def_295,type,
sK125: ( 'A_b_prod_ell2$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_296,type,
sK126: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_297,type,
sK127: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_298,type,
sK128: 'Enat_enat_fun$' > 'Enat$' ).
tff(func_def_299,type,
sK129: 'Enat_enat_fun$' > 'Enat$' ).
tff(func_def_300,type,
sK130: 'A_b_prod_ell2_b_ell2_fun$' > 'B_ell2$' ).
tff(func_def_301,type,
sK131: ( 'A_b_prod_ell2_b_ell2_fun$' * 'B_ell2$' ) > 'A_b_prod_ell2$' ).
tff(func_def_302,type,
sK132: 'Int_num_fun$' > $int ).
tff(func_def_303,type,
sK133: 'Int_num_fun$' > $int ).
tff(func_def_304,type,
sK134: 'B_ell2_set$' > 'B_ell2$' ).
tff(func_def_305,type,
sK135: ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' * 'A_b_prod_ell2_set$' ) > 'B_ell2$' ).
tff(func_def_306,type,
sK136: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_307,type,
sK137: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_308,type,
sK138: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_309,type,
sK139: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_310,type,
sK140: ( 'Nat_set$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_311,type,
sK141: ( 'Nat_set$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_312,type,
sK142: ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' * 'A_b_prod_ell2_set$' ) > 'B_ell2$' ).
tff(func_def_313,type,
sK143: ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' ) > 'B_ell2$' ).
tff(func_def_314,type,
sK144: ( 'Nat_set_bool_fun$' * 'Nat_nat_fun$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_315,type,
sK145: ( 'Nat_set_bool_fun$' * 'Nat_nat_fun$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_316,type,
sK146: 'Num_num_fun$' > 'Num$' ).
tff(func_def_317,type,
sK147: 'Num_num_fun$' > 'Num$' ).
tff(func_def_318,type,
sK148: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_319,type,
sK149: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_320,type,
sK150: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_321,type,
sK151: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_322,type,
sK152: 'Enat_enat_fun$' > 'Enat$' ).
tff(func_def_323,type,
sK153: 'Enat_enat_fun$' > 'Enat$' ).
tff(func_def_324,type,
sK154: ( 'Nat_set$' * 'Nat_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_325,type,
sK155: ( 'A_b_prod_ell2_nat_fun$' * 'Nat$' ) > 'A_b_prod_ell2$' ).
tff(func_def_326,type,
sK156: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_327,type,
sK157: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_328,type,
sK158: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_329,type,
sK159: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_330,type,
sK160: ( 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_331,type,
sK161: ( 'Nat_set$' * 'Nat_nat_fun$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_332,type,
sK162: 'Num_num_fun$' > 'Num$' ).
tff(func_def_333,type,
sK163: 'Num_num_fun$' > 'Num$' ).
tff(func_def_334,type,
sK164: ( 'A_b_prod_ell2_set$' * 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2_set$' ).
tff(func_def_335,type,
sK165: 'Num_int_fun$' > 'Num$' ).
tff(func_def_336,type,
sK166: 'Num_int_fun$' > 'Num$' ).
tff(func_def_337,type,
sK167: ( 'A_b_prod_ell2$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_338,type,
sK168: 'B_ell2_a_b_prod_ell2_fun$' > 'B_ell2$' ).
tff(func_def_339,type,
sK169: 'B_ell2_a_b_prod_ell2_fun$' > 'B_ell2$' ).
tff(func_def_340,type,
sK170: ( 'A_b_prod_ell2_b_ell2_fun$' * 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' ) > 'B_ell2$' ).
tff(func_def_341,type,
sK171: ( 'B_ell2_b_ell2_fun$' * 'B_ell2$' ) > 'B_ell2$' ).
tff(func_def_342,type,
sK172: 'B_ell2_a_b_prod_ell2_fun$' > 'B_ell2$' ).
tff(func_def_343,type,
sK173: 'B_ell2_a_b_prod_ell2_fun$' > 'B_ell2$' ).
tff(func_def_344,type,
sK174: ( 'B_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2$' ) > 'B_ell2$' ).
tff(func_def_345,type,
sK175: 'B_ell2_a_b_prod_ell2_fun$' > 'A_b_prod_ell2$' ).
tff(func_def_346,type,
sK176: ( 'A_b_prod_ell2$' * 'B_ell2_a_b_prod_ell2_fun$' ) > 'B_ell2$' ).
tff(func_def_347,type,
sK177: 'Int_enat_fun$' > $int ).
tff(func_def_348,type,
sK178: 'Int_enat_fun$' > $int ).
tff(func_def_349,type,
sK179: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_350,type,
sK180: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_351,type,
sK181: 'Enat_enat_bool_fun_fun$' > 'Enat$' ).
tff(func_def_352,type,
sK182: 'Enat_enat_bool_fun_fun$' > 'Enat$' ).
tff(func_def_353,type,
sK183: 'Enat_enat_bool_fun_fun$' > 'Enat$' ).
tff(func_def_354,type,
sK184: 'Enat_enat_bool_fun_fun$' > 'Enat$' ).
tff(func_def_355,type,
sK185: ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' ) > 'B_ell2$' ).
tff(func_def_356,type,
sK186: ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' ) > 'B_ell2$' ).
tff(func_def_357,type,
sK187: 'Int_enat_fun$' > $int ).
tff(func_def_358,type,
sK188: 'Int_enat_fun$' > $int ).
tff(func_def_359,type,
sF189: 'B_ell2_a_b_prod_ell2_fun$' ).
tff(func_def_360,type,
sF190: 'B_ell2_set_a_b_prod_ell2_set_fun$' ).
tff(func_def_361,type,
sF191: 'A_b_prod_ell2_set$' ).
tff(pred_def_1,type,
'inj_on$c': ( 'B_ell2_nat_fun$' * 'B_ell2_set$' ) > $o ).
tff(pred_def_2,type,
'fun_app$u': ( 'Num_bool_fun$' * 'Num$' ) > $o ).
tff(pred_def_3,type,
'fun_app$a': ( 'Nat_set_bool_fun$' * 'Nat_set$' ) > $o ).
tff(pred_def_4,type,
'less_eq$': ( 'B_ell2_set$' * 'B_ell2_set$' ) > $o ).
tff(pred_def_5,type,
'member$d': ( 'Enat$' * 'Enat_set$' ) > $o ).
tff(pred_def_6,type,
'member$b': ( 'B_ell2$' * 'B_ell2_set$' ) > $o ).
tff(pred_def_7,type,
'inj_on$o': ( 'Nat_set_nat_set_fun$' * 'Nat_set_set$' ) > $o ).
tff(pred_def_8,type,
'inj_on$h': ( 'A_ell2_a_b_prod_ell2_fun$' * 'A_ell2_set$' ) > $o ).
tff(pred_def_9,type,
'folding_insort_key_axioms$a': ( 'Nat_set$' * 'Nat_nat_fun$' ) > $o ).
tff(pred_def_10,type,
'inj_on$a': ( 'B_ell2_a_b_prod_ell2_fun$' * 'B_ell2_set$' ) > $o ).
tff(pred_def_11,type,
'inj_on$n': ( 'B_ell2_set_a_b_prod_ell2_set_fun$' * 'B_ell2_set_set$' ) > $o ).
tff(pred_def_12,type,
'folding_insort_key_axioms$': ( 'B_ell2_set$' * 'B_ell2_a_b_prod_ell2_fun$' ) > $o ).
tff(pred_def_13,type,
'fun_app$b': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_14,type,
'fun_app$m': ( 'A_b_prod_ell2_set_bool_fun$' * 'A_b_prod_ell2_set$' ) > $o ).
tff(pred_def_15,type,
'inj_on$m': ( 'Int_int_fun$' * 'Int_set$' ) > $o ).
tff(pred_def_16,type,
'less_eq$f': ( 'A_b_prod_ell2_set_set$' * 'A_b_prod_ell2_set_set$' ) > $o ).
tff(pred_def_17,type,
'inj_on$f': ( 'B_ell2_b_a_prod_ell2_fun$' * 'B_ell2_set$' ) > $o ).
tff(pred_def_18,type,
'fun_app$p': ( 'B_ell2_bool_fun$' * 'B_ell2$' ) > $o ).
tff(pred_def_19,type,
'member$c': ( 'A_ell2$' * 'A_ell2_set$' ) > $o ).
tff(pred_def_20,type,
'fun_app$ah': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_21,type,
'fun_app$l': ( 'A_b_prod_ell2_bool_fun$' * 'A_b_prod_ell2$' ) > $o ).
tff(pred_def_22,type,
'member$e': ( $int * 'Int_set$' ) > $o ).
tff(pred_def_23,type,
'less_eq$e': ( 'Nat_bool_fun$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_24,type,
'inj_on$b': ( 'B_ell2_b_ell2_fun$' * 'B_ell2_set$' ) > $o ).
tff(pred_def_25,type,
'fun_app$w': ( 'Enat_bool_fun$' * 'Enat$' ) > $o ).
tff(pred_def_26,type,
'fun_app$': ( 'Nat_nat_fun_bool_fun$' * 'Nat_nat_fun$' ) > $o ).
tff(f25,conjecture,
'fun_app$n'('image$'('tensor_ell2$'('psi$')),'top$a') = 'top$b',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture24) ).
tff(f26,negated_conjecture,
( ( ~ 'fun_app$n'('image$'('tensor_ell2$'('psi$')),'top$a') ) = 'top$b' ),
inference(negated_conjecture,[status(cth)],[f25]) ).
tff(f27,axiom,
! [X0: 'A_b_prod_ell2$'] :
? [X1: 'B_ell2$'] : ( 'fun_app$e'('tensor_ell2$'('psi$'),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom25) ).
tff(f56,axiom,
! [X1: 'B_ell2$',X0: 'B_ell2_a_b_prod_ell2_fun$'] : 'fun_app$m'('member$a'('fun_app$e'(X0,X1)),'fun_app$n'('image$'(X0),'top$a')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom54) ).
tff(f110,axiom,
! [X0: 'A_b_prod_ell2_set$'] :
( ! [X1: 'A_b_prod_ell2$'] : 'fun_app$m'('member$a'(X1),X0)
=> ( 'top$b' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom108) ).
tff(f838,plain,
! [X1: 'B_ell2_a_b_prod_ell2_fun$',X0: 'B_ell2$'] : 'fun_app$m'('member$a'('fun_app$e'(X1,X0)),'fun_app$n'('image$'(X1),'top$a')),
inference(rectify,[],[f56]) ).
tff(f1098,plain,
'fun_app$n'('image$'('tensor_ell2$'('psi$')),'top$a') != 'top$b',
inference(flattening,[],[f26]) ).
tff(f1334,plain,
! [X0: 'A_b_prod_ell2_set$'] :
( ? [X1: 'A_b_prod_ell2$'] : ~ 'fun_app$m'('member$a'(X1),X0)
| ( 'top$b' = X0 ) ),
inference(ennf_transformation,[],[f110]) ).
tff(f1723,plain,
! [X0: 'A_b_prod_ell2$'] : ( 'fun_app$e'('tensor_ell2$'('psi$'),sK33(X0)) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(X1,sK33(X0))],[f27]) ).
tff(f1973,plain,
! [X0: 'A_b_prod_ell2_set$'] :
( ~ 'fun_app$m'('member$a'(sK100(X0)),X0)
| ( 'top$b' = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(X1,sK100(X0))],[f1334]) ).
tff(f1982,plain,
! [X0: 'B_ell2_a_b_prod_ell2_fun$',X1: 'B_ell2$'] : 'fun_app$m'('member$a'('fun_app$e'(X0,X1)),'fun_app$n'('image$'(X0),'top$a')),
inference(rectify,[],[f838]) ).
tff(f2543,plain,
! [X0: 'A_b_prod_ell2$'] : ( 'fun_app$e'('tensor_ell2$'('psi$'),sK33(X0)) = X0 ),
inference(cnf_transformation,[],[f1723]) ).
tff(f3155,plain,
! [X0: 'A_b_prod_ell2_set$'] :
( ~ 'fun_app$m'('member$a'(sK100(X0)),X0)
| ( 'top$b' = X0 ) ),
inference(cnf_transformation,[],[f1973]) ).
tff(f3169,plain,
! [X0: 'B_ell2_a_b_prod_ell2_fun$',X1: 'B_ell2$'] : 'fun_app$m'('member$a'('fun_app$e'(X0,X1)),'fun_app$n'('image$'(X0),'top$a')),
inference(cnf_transformation,[],[f1982]) ).
tff(f3392,plain,
'fun_app$n'('image$'('tensor_ell2$'('psi$')),'top$a') != 'top$b',
inference(cnf_transformation,[],[f1098]) ).
tff(f3844,definition,
sF189 = 'tensor_ell2$'('psi$'),
introduced(definition,[new_symbols(definition,[sF189])],[function_definition]) ).
tff(f3845,plain,
'tensor_ell2$'('psi$') = sF189,
inference(reorient_equations,[],[f3844]) ).
tff(f3846,definition,
sF190 = 'image$'(sF189),
introduced(definition,[new_symbols(definition,[sF190])],[function_definition]) ).
tff(f3847,plain,
'image$'(sF189) = sF190,
inference(reorient_equations,[],[f3846]) ).
tff(f3848,definition,
sF191 = 'fun_app$n'(sF190,'top$a'),
introduced(definition,[new_symbols(definition,[sF191])],[function_definition]) ).
tff(f3849,plain,
'top$b' != sF191,
inference(definition_folding,[],[f3392,f3848,f3847,f3845]) ).
tff(f4385,definition,
( spl192_23
<=> ( 'image$'(sF189) = sF190 ) ),
introduced(definition,[new_symbols(definition,[spl192_23])],[avatar_definition]) ).
tff(f4387,plain,
( ( 'image$'(sF189) = sF190 )
| ~ spl192_23 ),
inference(avatar_component_clause,[],[f4385]) ).
tff(f4388,plain,
spl192_23,
inference(avatar_split_clause,[],[f3847,f4385]) ).
tff(f4461,definition,
( spl192_38
<=> ( sF191 = 'fun_app$n'(sF190,'top$a') ) ),
introduced(definition,[new_symbols(definition,[spl192_38])],[avatar_definition]) ).
tff(f4463,plain,
( ( sF191 = 'fun_app$n'(sF190,'top$a') )
| ~ spl192_38 ),
inference(avatar_component_clause,[],[f4461]) ).
tff(f4464,plain,
spl192_38,
inference(avatar_split_clause,[],[f3848,f4461]) ).
tff(f4491,definition,
( spl192_44
<=> ( 'top$b' = sF191 ) ),
introduced(definition,[new_symbols(definition,[spl192_44])],[avatar_definition]) ).
tff(f4493,plain,
( ( 'top$b' != sF191 )
| spl192_44 ),
inference(avatar_component_clause,[],[f4491]) ).
tff(f4494,plain,
~ spl192_44,
inference(avatar_split_clause,[],[f3849,f4491]) ).
tff(f4531,definition,
( spl192_52
<=> ( 'tensor_ell2$'('psi$') = sF189 ) ),
introduced(definition,[new_symbols(definition,[spl192_52])],[avatar_definition]) ).
tff(f4533,plain,
( ( 'tensor_ell2$'('psi$') = sF189 )
| ~ spl192_52 ),
inference(avatar_component_clause,[],[f4531]) ).
tff(f4534,plain,
spl192_52,
inference(avatar_split_clause,[],[f3845,f4531]) ).
tff(f4598,plain,
( ! [X0: 'A_b_prod_ell2$'] : ( 'fun_app$e'(sF189,sK33(X0)) = X0 )
| ~ spl192_52 ),
inference(forward_demodulation,[],[f2543,f4533]) ).
tff(f5127,plain,
( ! [X0: 'A_b_prod_ell2$'] : 'fun_app$m'('member$a'(X0),'fun_app$n'('image$'(sF189),'top$a'))
| ~ spl192_52 ),
inference(superposition,[],[f3169,f4598]) ).
tff(f5136,plain,
( ! [X0: 'A_b_prod_ell2$'] : 'fun_app$m'('member$a'(X0),'fun_app$n'(sF190,'top$a'))
| ~ spl192_23
| ~ spl192_52 ),
inference(forward_demodulation,[],[f5127,f4387]) ).
tff(f5138,plain,
( ! [X0: 'A_b_prod_ell2$'] : 'fun_app$m'('member$a'(X0),sF191)
| ~ spl192_23
| ~ spl192_38
| ~ spl192_52 ),
inference(forward_demodulation,[],[f5136,f4463]) ).
tff(f5144,plain,
( ( 'top$b' = sF191 )
| ~ spl192_23
| ~ spl192_38
| ~ spl192_52 ),
inference(resolution,[],[f5138,f3155]) ).
tff(f5145,plain,
( $false
| ~ spl192_23
| ~ spl192_38
| spl192_44
| ~ spl192_52 ),
inference(forward_subsumption_resolution,[],[f5144,f4493]) ).
tff(f5146,plain,
( ~ spl192_23
| ~ spl192_38
| spl192_44
| ~ spl192_52 ),
inference(avatar_contradiction_clause,[],[f5145]) ).
tff(f5147,plain,
$false,
inference(avatar_smt_refutation,[],[f5146,f4534,f4494,f4464,f4388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP388_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 12:59:56 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.48/1.47 % (2823983)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.48/1.47 % (2823994)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3052012339:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.48/1.47 % (2823994)Instruction limit reached!
% 3.48/1.47 % (2823994)------------------------------
% 3.48/1.47 % (2823994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2823994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2823994)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2823994)Termination reason: Instruction limit
% 3.48/1.47 % (2823994)Termination phase: Preprocessing 3
% 3.48/1.47 % (2823994)Time elapsed: 0.011 s
% 3.48/1.47 % (2823994)Peak memory usage: 88 MB
% 3.48/1.47 % (2823994)Instructions burned: 34 (million)
% 3.48/1.47 % (2823988)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3816024896:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.48/1.47 % (2823992)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3893925111:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.48/1.47 % (2823989)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3740309235:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.48/1.47 % (2823990)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=853871481:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.48/1.47 % (2823991)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=564532602:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.48/1.47 % (2823992)Instruction limit reached!
% 3.48/1.47 % (2823992)------------------------------
% 3.48/1.47 % (2823992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2823992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2823992)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2823992)Termination reason: Instruction limit
% 3.48/1.47 % (2823992)Termination phase: Property scanning
% 3.48/1.47 % (2823992)Time elapsed: 0.004 s
% 3.48/1.47 % (2823992)Peak memory usage: 85 MB
% 3.48/1.47 % (2823992)Instructions burned: 6 (million)
% 3.48/1.47 % (2823991)Instruction limit reached!
% 3.48/1.47 % (2823991)------------------------------
% 3.48/1.47 % (2823991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2823991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2823991)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2823991)Termination reason: Instruction limit
% 3.48/1.47 % (2823991)Termination phase: Property scanning
% 3.48/1.47 % (2823991)Time elapsed: 0.004 s
% 3.48/1.47 % (2823991)Peak memory usage: 86 MB
% 3.48/1.47 % (2823991)Instructions burned: 7 (million)
% 3.48/1.47 % (2823988)Instruction limit reached!
% 3.48/1.47 % (2823988)------------------------------
% 3.48/1.47 % (2823988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2823988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2823988)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2823988)Termination reason: Instruction limit
% 3.48/1.47 % (2823988)Termination phase: Property scanning
% 3.48/1.47 % (2823988)Time elapsed: 0.007 s
% 3.48/1.47 % (2823988)Peak memory usage: 85 MB
% 3.48/1.47 % (2823988)Instructions burned: 13 (million)
% 3.48/1.47 % (2823993)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2851032854:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.48/1.47 % (2823993)Instruction limit reached!
% 3.48/1.47 % (2823993)------------------------------
% 3.48/1.47 % (2823993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2823993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2823993)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2823993)Termination reason: Instruction limit
% 3.48/1.47 % (2823993)Termination phase: Function definition elimination
% 3.48/1.47 % (2823993)Time elapsed: 0.026 s
% 3.48/1.47 % (2823993)Peak memory usage: 88 MB
% 3.48/1.47 % (2823993)Instructions burned: 46 (million)
% 3.48/1.47 % (2823996)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=4237118879:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.48/1.47 % (2823996)Instruction limit reached!
% 3.48/1.47 % (2823996)------------------------------
% 3.48/1.47 % (2823996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2823996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2823996)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2823996)Termination reason: Instruction limit
% 3.48/1.47 % (2823996)Termination phase: Preprocessing 1
% 3.48/1.47 % (2823996)Time elapsed: 0.005 s
% 3.48/1.47 % (2823996)Peak memory usage: 86 MB
% 3.48/1.47 % (2823996)Instructions burned: 16 (million)
% 3.48/1.47 % (2823989)First to succeed.
% 3.48/1.47 % (2823989)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2823983"
% 3.48/1.47 % (2824003)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=2470424080:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 3.48/1.47 % (2824004)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2218511164:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.48/1.47 % (2824005)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=157813215:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.48/1.47 % (2823990)Instruction limit reached!
% 3.48/1.47 % (2823990)------------------------------
% 3.48/1.47 % (2823990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2823990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2823990)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2823990)Termination reason: Instruction limit
% 3.48/1.47 % (2823990)Termination phase: Saturation
% 3.48/1.47 % (2823990)Time elapsed: 0.159 s
% 3.48/1.47 % (2823990)Peak memory usage: 119 MB
% 3.48/1.47 % (2823990)Instructions burned: 201 (million)
% 3.48/1.47 % (2824004)Instruction limit reached!
% 3.48/1.47 % (2824004)------------------------------
% 3.48/1.47 % (2824004)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2824004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2824004)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2824004)Termination reason: Instruction limit
% 3.48/1.47 % (2824004)Termination phase: Preprocessing 2
% 3.48/1.47 % (2824004)Time elapsed: 0.009 s
% 3.48/1.47 % (2824004)Peak memory usage: 86 MB
% 3.48/1.47 % (2824004)Instructions burned: 16 (million)
% 3.48/1.47 % (2824005)Instruction limit reached!
% 3.48/1.47 % (2824005)------------------------------
% 3.48/1.47 % (2824005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2824005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2824005)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2824005)Termination reason: Instruction limit
% 3.48/1.47 % (2824005)Termination phase: Preprocessing 2
% 3.48/1.47 % (2824005)Time elapsed: 0.014 s
% 3.48/1.47 % (2824005)Peak memory usage: 87 MB
% 3.48/1.47 % (2824005)Instructions burned: 25 (million)
% 3.48/1.47 % (2824003)Instruction limit reached!
% 3.48/1.47 % (2824003)------------------------------
% 3.48/1.47 % (2824003)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2824003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2824003)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2824003)Termination reason: Instruction limit
% 3.48/1.47 % (2824003)Termination phase: Preprocessing 3
% 3.48/1.47 % (2824003)Time elapsed: 0.017 s
% 3.48/1.47 % (2824003)Peak memory usage: 87 MB
% 3.48/1.47 % (2824003)Instructions burned: 29 (million)
% 3.48/1.47 % (2824006)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=3861560184:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.48/1.47 % (2824006)Instruction limit reached!
% 3.48/1.47 % (2824006)------------------------------
% 3.48/1.47 % (2824006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2824006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2824006)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2824006)Termination reason: Instruction limit
% 3.48/1.47 % (2824006)Termination phase: Preprocessing 3
% 3.48/1.47 % (2824006)Time elapsed: 0.016 s
% 3.48/1.47 % (2824006)Peak memory usage: 87 MB
% 3.48/1.47 % (2824006)Instructions burned: 27 (million)
% 3.48/1.47 % (2824008)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=686124440:i=85:gtgl=4:rtra=on:gtg=exists_sym_2997 on theBenchmark for (2997ds/85Mi)
% 3.48/1.47 % (2824014)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=1089149491:i=4:ep=RST:ins=2:rtra=on_2996 on theBenchmark for (2996ds/4Mi)
% 3.48/1.47 % (2824014)Instruction limit reached!
% 3.48/1.47 % (2824014)------------------------------
% 3.48/1.47 % (2824014)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2824014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2824014)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2824014)Termination reason: Instruction limit
% 3.48/1.47 % (2824014)Termination phase: Property scanning
% 3.48/1.47 % (2824014)Time elapsed: 0.002 s
% 3.48/1.47 % (2824014)Peak memory usage: 86 MB
% 3.48/1.47 % (2824014)Instructions burned: 5 (million)
% 3.48/1.47 % (2824008)Instruction limit reached!
% 3.48/1.47 % (2824008)------------------------------
% 3.48/1.47 % (2824008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2824008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2824008)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2824008)Termination reason: Instruction limit
% 3.48/1.47 % (2824008)Termination phase: Property scanning
% 3.48/1.47 % (2824008)Time elapsed: 0.045 s
% 3.48/1.47 % (2824008)Peak memory usage: 89 MB
% 3.48/1.47 % (2824008)Instructions burned: 85 (million)
% 3.48/1.47 % (2824013)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=1172085008:i=181:rtra=on:ss=axioms:ev=cautious_2996 on theBenchmark for (2996ds/181Mi)
% 3.48/1.47 % (2824012)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=3546095815:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2996 on theBenchmark for (2996ds/2Mi)
% 3.48/1.47 % (2824012)Instruction limit reached!
% 3.48/1.47 % (2824012)------------------------------
% 3.48/1.47 % (2824012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2824012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2824012)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2824012)Termination reason: Instruction limit
% 3.48/1.47 % (2824012)Termination phase: shuffling
% 3.48/1.47 % (2824012)Time elapsed: 0.002 s
% 3.48/1.47 % (2824012)Peak memory usage: 85 MB
% 3.48/1.47 % (2824012)Instructions burned: 2 (million)
% 3.48/1.47 % (2824013)Also succeeded, but the first one will report.
% 3.48/1.47 % (2824015)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=3908997982:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2996 on theBenchmark for (2996ds/66Mi)
% 3.48/1.47 % (2824015)Instruction limit reached!
% 3.48/1.47 % (2824015)------------------------------
% 3.48/1.47 % (2824015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (2824015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (2824015)CaDiCaL version: 2.1.3
% 3.48/1.47 % (2824015)Termination reason: Instruction limit
% 3.48/1.47 % (2824015)Termination phase: Property scanning
% 3.48/1.47 % (2824015)Time elapsed: 0.037 s
% 3.48/1.47 % (2824015)Peak memory usage: 88 MB
% 3.48/1.47 % (2824015)Instructions burned: 66 (million)
% 3.48/1.47 % (2824017)lrs+10_1_thi=all:si=on:fd=off:random_seed=3640053590:i=53:rtra=on:gtg=all_2995 on theBenchmark for (2995ds/53Mi)
% 3.48/1.47 % (2823989)Refutation found. Thanks to Tanya!
% 3.48/1.47 % SZS status Theorem for theBenchmark
% 3.48/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 4.55/1.66 % (2823989)------------------------------
% 4.55/1.66 % (2823989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.66 % (2823989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.66 % (2823989)CaDiCaL version: 2.1.3
% 4.55/1.66 % (2823989)Termination reason: Refutation
% 4.55/1.66 % (2823989)Time elapsed: 0.123 s
% 4.55/1.66 % (2823989)Peak memory usage: 119 MB
% 4.55/1.66 % (2823989)Instructions burned: 167 (million)
% 4.55/1.66 % (2823989)------------------------------
% 4.55/1.66 % (2823989)------------------------------
% 4.55/1.66 % (2823983)Success in time 0.591 s
% 4.55/1.66 % Vampire exiting
%------------------------------------------------------------------------------