TSTP Solution File: ITP388_1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 06:56:15 EDT 2024
% Result : Theorem 0.63s 0.83s
% Output : Refutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 260
% Syntax : Number of formulae : 273 ( 10 unt; 254 typ; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 8 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 58 ( 56 usr; 1 ari)
% Number of type conns : 267 ( 161 >; 106 *; 0 +; 0 <<)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-2 aty)
% Number of functors : 172 ( 172 usr; 37 con; 0-3 aty)
% Number of variables : 34 ( 25 !; 9 ?; 34 :)
% 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$' ).
tff(func_def_170,type,
sK0: 'A_b_prod_ell2$' > 'B_ell2$' ).
tff(func_def_171,type,
sK1: 'B_ell2_a_b_prod_ell2_fun$' > 'A_b_prod_ell2$' ).
tff(func_def_172,type,
sK2: ( 'B_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2$' ) > 'B_ell2$' ).
tff(func_def_173,type,
sK3: 'B_ell2_a_b_prod_ell2_fun$' > 'B_ell2$' ).
tff(func_def_174,type,
sK4: 'B_ell2_a_b_prod_ell2_fun$' > 'B_ell2$' ).
tff(func_def_175,type,
sK5: 'B_ell2_a_b_prod_ell2_fun$' > 'B_ell2$' ).
tff(func_def_176,type,
sK6: 'B_ell2_a_b_prod_ell2_fun$' > 'B_ell2$' ).
tff(func_def_177,type,
sK7: ( 'B_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2$' ) > 'B_ell2$' ).
tff(func_def_178,type,
sK8: ( 'B_ell2_a_b_prod_ell2_fun$' * 'A_b_prod_ell2$' ) > 'B_ell2$' ).
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(f897,plain,
$false,
inference(equality_resolution,[],[f893]) ).
tff(f893,plain,
! [X0: 'A_b_prod_ell2$'] : ( sK1('tensor_ell2$'('psi$')) != X0 ),
inference(superposition,[],[f892,f869]) ).
tff(f869,plain,
! [X0: 'A_b_prod_ell2$'] : ( 'fun_app$e'('tensor_ell2$'('psi$'),sK0(X0)) = X0 ),
inference(cnf_transformation,[],[f846]) ).
tff(f846,plain,
! [X0: 'A_b_prod_ell2$'] : ( 'fun_app$e'('tensor_ell2$'('psi$'),sK0(X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f27,f845]) ).
tff(f845,plain,
! [X0: 'A_b_prod_ell2$'] :
( ? [X1: 'B_ell2$'] : ( 'fun_app$e'('tensor_ell2$'('psi$'),X1) = X0 )
=> ( 'fun_app$e'('tensor_ell2$'('psi$'),sK0(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f27,axiom,
! [X0: 'A_b_prod_ell2$'] :
? [X1: 'B_ell2$'] : ( 'fun_app$e'('tensor_ell2$'('psi$'),X1) = X0 ),
file('/export/starexec/sandbox/tmp/tmp.lzTtX2N5mS/Vampire---4.8_29055',axiom25) ).
tff(f892,plain,
! [X0: 'B_ell2$'] : ( 'fun_app$e'('tensor_ell2$'('psi$'),X0) != sK1('tensor_ell2$'('psi$')) ),
inference(trivial_inequality_removal,[],[f891]) ).
tff(f891,plain,
! [X0: 'B_ell2$'] :
( ( 'top$b' != 'top$b' )
| ( 'fun_app$e'('tensor_ell2$'('psi$'),X0) != sK1('tensor_ell2$'('psi$')) ) ),
inference(superposition,[],[f865,f876]) ).
tff(f876,plain,
! [X2: 'B_ell2$',X0: 'B_ell2_a_b_prod_ell2_fun$'] :
( ( 'top$b' = 'fun_app$n'('image$'(X0),'top$a') )
| ( 'fun_app$e'(X0,X2) != sK1(X0) ) ),
inference(cnf_transformation,[],[f853]) ).
tff(f853,plain,
! [X0: 'B_ell2_a_b_prod_ell2_fun$'] :
( ( ( 'top$b' = 'fun_app$n'('image$'(X0),'top$a') )
| ! [X2: 'B_ell2$'] : ( 'fun_app$e'(X0,X2) != sK1(X0) ) )
& ( ! [X3: 'A_b_prod_ell2$'] : ( 'fun_app$e'(X0,sK2(X0,X3)) = X3 )
| ( 'top$b' != 'fun_app$n'('image$'(X0),'top$a') ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f850,f852,f851]) ).
tff(f851,plain,
! [X0: 'B_ell2_a_b_prod_ell2_fun$'] :
( ? [X1: 'A_b_prod_ell2$'] :
! [X2: 'B_ell2$'] : ( 'fun_app$e'(X0,X2) != X1 )
=> ! [X2: 'B_ell2$'] : ( 'fun_app$e'(X0,X2) != sK1(X0) ) ),
introduced(choice_axiom,[]) ).
tff(f852,plain,
! [X0: 'B_ell2_a_b_prod_ell2_fun$',X3: 'A_b_prod_ell2$'] :
( ? [X4: 'B_ell2$'] : ( 'fun_app$e'(X0,X4) = X3 )
=> ( 'fun_app$e'(X0,sK2(X0,X3)) = X3 ) ),
introduced(choice_axiom,[]) ).
tff(f850,plain,
! [X0: 'B_ell2_a_b_prod_ell2_fun$'] :
( ( ( 'top$b' = 'fun_app$n'('image$'(X0),'top$a') )
| ? [X1: 'A_b_prod_ell2$'] :
! [X2: 'B_ell2$'] : ( 'fun_app$e'(X0,X2) != X1 ) )
& ( ! [X3: 'A_b_prod_ell2$'] :
? [X4: 'B_ell2$'] : ( 'fun_app$e'(X0,X4) = X3 )
| ( 'top$b' != 'fun_app$n'('image$'(X0),'top$a') ) ) ),
inference(rectify,[],[f849]) ).
tff(f849,plain,
! [X0: 'B_ell2_a_b_prod_ell2_fun$'] :
( ( ( 'top$b' = 'fun_app$n'('image$'(X0),'top$a') )
| ? [X1: 'A_b_prod_ell2$'] :
! [X2: 'B_ell2$'] : ( 'fun_app$e'(X0,X2) != X1 ) )
& ( ! [X1: 'A_b_prod_ell2$'] :
? [X2: 'B_ell2$'] : ( 'fun_app$e'(X0,X2) = X1 )
| ( 'top$b' != 'fun_app$n'('image$'(X0),'top$a') ) ) ),
inference(nnf_transformation,[],[f136]) ).
tff(f136,axiom,
! [X0: 'B_ell2_a_b_prod_ell2_fun$'] :
( ( 'top$b' = 'fun_app$n'('image$'(X0),'top$a') )
<=> ! [X1: 'A_b_prod_ell2$'] :
? [X2: 'B_ell2$'] : ( 'fun_app$e'(X0,X2) = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.lzTtX2N5mS/Vampire---4.8_29055',axiom134) ).
tff(f865,plain,
'fun_app$n'('image$'('tensor_ell2$'('psi$')),'top$a') != 'top$b',
inference(cnf_transformation,[],[f833]) ).
tff(f833,plain,
'fun_app$n'('image$'('tensor_ell2$'('psi$')),'top$a') != 'top$b',
inference(flattening,[],[f26]) ).
tff(f26,negated_conjecture,
( ~ 'fun_app$n'('image$'('tensor_ell2$'('psi$')),'top$a') = 'top$b' ),
inference(negated_conjecture,[],[f25]) ).
tff(f25,conjecture,
'fun_app$n'('image$'('tensor_ell2$'('psi$')),'top$a') = 'top$b',
file('/export/starexec/sandbox/tmp/tmp.lzTtX2N5mS/Vampire---4.8_29055',conjecture24) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.30 % Computer : n028.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri May 3 18:55:53 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 This is a TF0_THM_EQU_ARI problem
% 0.10/0.30 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.lzTtX2N5mS/Vampire---4.8_29055
% 0.63/0.82 % (29169)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2994ds/78Mi)
% 0.63/0.82 % (29168)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2994ds/51Mi)
% 0.63/0.82 % (29170)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2994ds/33Mi)
% 0.63/0.82 % (29167)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2994ds/34Mi)
% 0.63/0.82 % (29171)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2994ds/34Mi)
% 0.63/0.82 % (29172)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2994ds/45Mi)
% 0.63/0.82 % (29173)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2994ds/83Mi)
% 0.63/0.82 % (29174)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2994ds/56Mi)
% 0.63/0.83 % (29170)Refutation not found, incomplete strategy% (29170)------------------------------
% 0.63/0.83 % (29170)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.83 % (29170)Termination reason: Refutation not found, incomplete strategy
% 0.63/0.83
% 0.63/0.83 % (29170)Memory used [KB]: 1672
% 0.63/0.83 % (29170)Time elapsed: 0.015 s
% 0.63/0.83 % (29170)Instructions burned: 31 (million)
% 0.63/0.83 % (29174)Refutation not found, incomplete strategy% (29174)------------------------------
% 0.63/0.83 % (29174)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.83 % (29174)Termination reason: Refutation not found, incomplete strategy
% 0.63/0.83
% 0.63/0.83 % (29174)Memory used [KB]: 1681
% 0.63/0.83 % (29170)------------------------------
% 0.63/0.83 % (29170)------------------------------
% 0.63/0.83 % (29174)Time elapsed: 0.015 s
% 0.63/0.83 % (29174)Instructions burned: 32 (million)
% 0.63/0.83 % (29172)First to succeed.
% 0.63/0.83 % (29174)------------------------------
% 0.63/0.83 % (29174)------------------------------
% 0.63/0.83 % (29167)Instruction limit reached!
% 0.63/0.83 % (29167)------------------------------
% 0.63/0.83 % (29167)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.83 % (29167)Termination reason: Unknown
% 0.63/0.83 % (29167)Termination phase: Property scanning
% 0.63/0.83
% 0.63/0.83 % (29167)Memory used [KB]: 1682
% 0.63/0.83 % (29167)Time elapsed: 0.016 s
% 0.63/0.83 % (29167)Instructions burned: 34 (million)
% 0.63/0.83 % (29167)------------------------------
% 0.63/0.83 % (29167)------------------------------
% 0.63/0.83 % (29171)Instruction limit reached!
% 0.63/0.83 % (29171)------------------------------
% 0.63/0.83 % (29171)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.83 % (29171)Termination reason: Unknown
% 0.63/0.83 % (29171)Termination phase: Preprocessing 2
% 0.63/0.83
% 0.63/0.83 % (29171)Memory used [KB]: 1729
% 0.63/0.83 % (29171)Time elapsed: 0.016 s
% 0.63/0.83 % (29171)Instructions burned: 35 (million)
% 0.63/0.83 % (29171)------------------------------
% 0.63/0.83 % (29171)------------------------------
% 0.63/0.83 % (29172)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-29163"
% 0.63/0.83 % (29173)Also succeeded, but the first one will report.
% 0.63/0.83 % (29169)Also succeeded, but the first one will report.
% 0.63/0.83 % (29172)Refutation found. Thanks to Tanya!
% 0.63/0.83 % SZS status Theorem for Vampire---4
% 0.63/0.83 % SZS output start Proof for Vampire---4
% See solution above
% 0.63/0.83 % (29172)------------------------------
% 0.63/0.83 % (29172)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.83 % (29172)Termination reason: Refutation
% 0.63/0.83
% 0.63/0.83 % (29172)Memory used [KB]: 1688
% 0.63/0.83 % (29172)Time elapsed: 0.016 s
% 0.63/0.83 % (29172)Instructions burned: 33 (million)
% 0.63/0.83 % (29163)Success in time 0.525 s
% 0.63/0.83 % Vampire---4.8 exiting
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