TSTP Solution File: SWW619_2 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWW619_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n017.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 : Tue May 21 07:01:48 EDT 2024

% Result   : Theorem 0.62s 0.81s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   82
% Syntax   : Number of formulae    :  100 (   8 unt;  77 typ;   0 def)
%            Number of atoms       :  218 (  25 equ)
%            Maximal formula atoms :   30 (   9 avg)
%            Number of connectives :  282 (  87   ~;  41   |; 122   &)
%                                         (   0 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   8 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number arithmetic     :  471 ( 144 atm; 172 fun;  83 num;  72 var)
%            Number of types       :    9 (   7 usr;   1 ari)
%            Number of type conns  :  155 (  54   >; 101   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  17 usr;   1 prp; 0-7 aty)
%            Number of functors    :   57 (  53 usr;  18 con; 0-6 aty)
%            Number of variables   :  102 (  56   !;  46   ?; 102   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    uni: $tType ).

tff(type_def_6,type,
    ty: $tType ).

tff(type_def_7,type,
    bool1: $tType ).

tff(type_def_8,type,
    tuple02: $tType ).

tff(type_def_9,type,
    elt4: $tType ).

tff(type_def_10,type,
    array_elt2: $tType ).

tff(type_def_11,type,
    map_int_elt2: $tType ).

tff(func_def_0,type,
    witness1: ty > uni ).

tff(func_def_1,type,
    int: ty ).

tff(func_def_2,type,
    real: ty ).

tff(func_def_3,type,
    bool: ty ).

tff(func_def_4,type,
    true1: bool1 ).

tff(func_def_5,type,
    false1: bool1 ).

tff(func_def_6,type,
    match_bool1: ( ty * bool1 * uni * uni ) > uni ).

tff(func_def_7,type,
    tuple0: ty ).

tff(func_def_8,type,
    tuple03: tuple02 ).

tff(func_def_9,type,
    qtmark: ty ).

tff(func_def_12,type,
    map: ( ty * ty ) > ty ).

tff(func_def_13,type,
    get: ( ty * ty * uni * uni ) > uni ).

tff(func_def_14,type,
    set: ( ty * ty * uni * uni * uni ) > uni ).

tff(func_def_15,type,
    const: ( ty * ty * uni ) > uni ).

tff(func_def_16,type,
    array: ty > ty ).

tff(func_def_17,type,
    mk_array1: ( ty * $int * uni ) > uni ).

tff(func_def_18,type,
    length1: ( ty * uni ) > $int ).

tff(func_def_19,type,
    elts: ( ty * uni ) > uni ).

tff(func_def_20,type,
    get2: ( ty * uni * $int ) > uni ).

tff(func_def_21,type,
    t2tb: $int > uni ).

tff(func_def_22,type,
    tb2t: uni > $int ).

tff(func_def_23,type,
    set2: ( ty * uni * $int * uni ) > uni ).

tff(func_def_24,type,
    make1: ( ty * $int * uni ) > uni ).

tff(func_def_25,type,
    elt5: ty ).

tff(func_def_26,type,
    t2tb7: elt4 > uni ).

tff(func_def_27,type,
    tb2t7: uni > elt4 ).

tff(func_def_28,type,
    t2tb8: array_elt2 > uni ).

tff(func_def_29,type,
    tb2t8: uni > array_elt2 ).

tff(func_def_30,type,
    ref: ty > ty ).

tff(func_def_31,type,
    mk_ref: ( ty * uni ) > uni ).

tff(func_def_32,type,
    contents: ( ty * uni ) > uni ).

tff(func_def_33,type,
    occ1: ( ty * uni * uni * $int * $int ) > $int ).

tff(func_def_37,type,
    abs: $int > $int ).

tff(func_def_39,type,
    div: ( $int * $int ) > $int ).

tff(func_def_40,type,
    mod: ( $int * $int ) > $int ).

tff(func_def_41,type,
    min: ( $int * $int ) > $int ).

tff(func_def_42,type,
    max: ( $int * $int ) > $int ).

tff(func_def_43,type,
    t2tb9: map_int_elt2 > uni ).

tff(func_def_44,type,
    tb2t9: uni > map_int_elt2 ).

tff(func_def_45,type,
    sK0: $int ).

tff(func_def_46,type,
    sK1: map_int_elt2 ).

tff(func_def_47,type,
    sK2: $int ).

tff(func_def_48,type,
    sK3: map_int_elt2 ).

tff(func_def_49,type,
    sK4: $int ).

tff(func_def_50,type,
    sK5: map_int_elt2 ).

tff(func_def_51,type,
    sK6: $int ).

tff(func_def_52,type,
    sK7: ( array_elt2 * $int * $int ) > $int ).

tff(func_def_53,type,
    sK8: ( array_elt2 * $int * $int ) > $int ).

tff(func_def_54,type,
    sK9: ( ty * uni * uni * $int * $int * $int ) > $int ).

tff(func_def_55,type,
    sK10: ( ty * uni * uni * $int * $int ) > uni ).

tff(func_def_56,type,
    sK11: ( ty * uni * uni * $int * $int ) > $int ).

tff(func_def_57,type,
    sK12: ( ty * uni * uni * $int * $int ) > $int ).

tff(func_def_58,type,
    sK13: ( ty * uni * uni * $int * $int ) > $int ).

tff(pred_def_1,type,
    sort1: ( ty * uni ) > $o ).

tff(pred_def_3,type,
    le3: ( elt4 * elt4 ) > $o ).

tff(pred_def_4,type,
    sorted_sub3: ( array_elt2 * $int * $int ) > $o ).

tff(pred_def_6,type,
    sorted3: array_elt2 > $o ).

tff(pred_def_7,type,
    permut2: ( ty * uni * uni * $int * $int ) > $o ).

tff(pred_def_8,type,
    map_eq_sub1: ( ty * uni * uni * $int * $int ) > $o ).

tff(pred_def_9,type,
    array_eq_sub1: ( ty * uni * uni * $int * $int ) > $o ).

tff(pred_def_10,type,
    array_eq: ( ty * uni * uni ) > $o ).

tff(pred_def_11,type,
    exchange2: ( ty * uni * uni * $int * $int * $int * $int ) > $o ).

tff(pred_def_12,type,
    exchange3: ( ty * uni * uni * $int * $int ) > $o ).

tff(pred_def_13,type,
    permut3: ( ty * uni * uni * $int * $int ) > $o ).

tff(pred_def_14,type,
    permut_sub1: ( ty * uni * uni * $int * $int ) > $o ).

tff(pred_def_15,type,
    permut_all: ( ty * uni * uni ) > $o ).

tff(pred_def_16,type,
    sQ14_eqProxy: ( elt4 * elt4 ) > $o ).

tff(pred_def_17,type,
    sQ15_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_18,type,
    sQ16_eqProxy: ( uni * uni ) > $o ).

tff(pred_def_19,type,
    sQ17_eqProxy: ( array_elt2 * array_elt2 ) > $o ).

tff(f433,plain,
    $false,
    inference(subsumption_resolution,[],[f432,f279]) ).

tff(f279,plain,
    ~ $less($product(sK6,sK4),0),
    inference(cnf_transformation,[],[f256]) ).

tff(f256,plain,
    ( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(sK6,sK4),min(sK0,$sum($product(sK6,sK4),sK4)))
    & $less($product(sK6,sK4),sK0)
    & ~ $less($product(sK6,sK4),0)
    & $less(sK4,sK0)
    & ! [X7: $int] :
        ( sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(X7,sK4),min(sK0,$sum($product(X7,sK4),sK4)))
        | ~ $less($product(X7,sK4),sK0)
        | $less($product(X7,sK4),0) )
    & permut_all(elt5,mk_array1(elt5,sK0,t2tb9(sK1)),mk_array1(elt5,sK0,t2tb9(sK5)))
    & ~ $less(sK4,1)
    & ! [X8: $int] :
        ( ( tb2t7(get(elt5,int,t2tb9(sK1),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb(X8))) )
        | ~ $less(X8,sK2)
        | $less(X8,0) )
    & ( sK0 = sK2 )
    & ~ $less(sK2,0)
    & ~ $less(sK0,0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f251,f255,f254,f253,f252]) ).

tff(f252,plain,
    ( ? [X0: $int,X1: map_int_elt2] :
        ( ? [X2: $int,X3: map_int_elt2] :
            ( ? [X4: $int,X5: map_int_elt2] :
                ( ? [X6: $int] :
                    ( ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X6,X4),min(X0,$sum($product(X6,X4),X4)))
                    & $less($product(X6,X4),X0)
                    & ~ $less($product(X6,X4),0) )
                & $less(X4,X0)
                & ! [X7: $int] :
                    ( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X4),min(X0,$sum($product(X7,X4),X4)))
                    | ~ $less($product(X7,X4),X0)
                    | $less($product(X7,X4),0) )
                & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5)))
                & ~ $less(X4,1) )
            & ! [X8: $int] :
                ( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X8))) )
                | ~ $less(X8,X2)
                | $less(X8,0) )
            & ( X0 = X2 )
            & ~ $less(X2,0) )
        & ~ $less(X0,0) )
   => ( ? [X3: map_int_elt2,X2: $int] :
          ( ? [X5: map_int_elt2,X4: $int] :
              ( ? [X6: $int] :
                  ( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(X5))),$product(X6,X4),min(sK0,$sum($product(X6,X4),X4)))
                  & $less($product(X6,X4),sK0)
                  & ~ $less($product(X6,X4),0) )
              & $less(X4,sK0)
              & ! [X7: $int] :
                  ( sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(X5))),$product(X7,X4),min(sK0,$sum($product(X7,X4),X4)))
                  | ~ $less($product(X7,X4),sK0)
                  | $less($product(X7,X4),0) )
              & permut_all(elt5,mk_array1(elt5,sK0,t2tb9(sK1)),mk_array1(elt5,sK0,t2tb9(X5)))
              & ~ $less(X4,1) )
          & ! [X8: $int] :
              ( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK1),t2tb(X8))) )
              | ~ $less(X8,X2)
              | $less(X8,0) )
          & ( sK0 = X2 )
          & ~ $less(X2,0) )
      & ~ $less(sK0,0) ) ),
    introduced(choice_axiom,[]) ).

tff(f253,plain,
    ( ? [X3: map_int_elt2,X2: $int] :
        ( ? [X5: map_int_elt2,X4: $int] :
            ( ? [X6: $int] :
                ( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(X5))),$product(X6,X4),min(sK0,$sum($product(X6,X4),X4)))
                & $less($product(X6,X4),sK0)
                & ~ $less($product(X6,X4),0) )
            & $less(X4,sK0)
            & ! [X7: $int] :
                ( sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(X5))),$product(X7,X4),min(sK0,$sum($product(X7,X4),X4)))
                | ~ $less($product(X7,X4),sK0)
                | $less($product(X7,X4),0) )
            & permut_all(elt5,mk_array1(elt5,sK0,t2tb9(sK1)),mk_array1(elt5,sK0,t2tb9(X5)))
            & ~ $less(X4,1) )
        & ! [X8: $int] :
            ( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK1),t2tb(X8))) )
            | ~ $less(X8,X2)
            | $less(X8,0) )
        & ( sK0 = X2 )
        & ~ $less(X2,0) )
   => ( ? [X5: map_int_elt2,X4: $int] :
          ( ? [X6: $int] :
              ( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(X5))),$product(X6,X4),min(sK0,$sum($product(X6,X4),X4)))
              & $less($product(X6,X4),sK0)
              & ~ $less($product(X6,X4),0) )
          & $less(X4,sK0)
          & ! [X7: $int] :
              ( sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(X5))),$product(X7,X4),min(sK0,$sum($product(X7,X4),X4)))
              | ~ $less($product(X7,X4),sK0)
              | $less($product(X7,X4),0) )
          & permut_all(elt5,mk_array1(elt5,sK0,t2tb9(sK1)),mk_array1(elt5,sK0,t2tb9(X5)))
          & ~ $less(X4,1) )
      & ! [X8: $int] :
          ( ( tb2t7(get(elt5,int,t2tb9(sK1),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb(X8))) )
          | ~ $less(X8,sK2)
          | $less(X8,0) )
      & ( sK0 = sK2 )
      & ~ $less(sK2,0) ) ),
    introduced(choice_axiom,[]) ).

tff(f254,plain,
    ( ? [X5: map_int_elt2,X4: $int] :
        ( ? [X6: $int] :
            ( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(X5))),$product(X6,X4),min(sK0,$sum($product(X6,X4),X4)))
            & $less($product(X6,X4),sK0)
            & ~ $less($product(X6,X4),0) )
        & $less(X4,sK0)
        & ! [X7: $int] :
            ( sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(X5))),$product(X7,X4),min(sK0,$sum($product(X7,X4),X4)))
            | ~ $less($product(X7,X4),sK0)
            | $less($product(X7,X4),0) )
        & permut_all(elt5,mk_array1(elt5,sK0,t2tb9(sK1)),mk_array1(elt5,sK0,t2tb9(X5)))
        & ~ $less(X4,1) )
   => ( ? [X6: $int] :
          ( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(X6,sK4),min(sK0,$sum($product(X6,sK4),sK4)))
          & $less($product(X6,sK4),sK0)
          & ~ $less($product(X6,sK4),0) )
      & $less(sK4,sK0)
      & ! [X7: $int] :
          ( sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(X7,sK4),min(sK0,$sum($product(X7,sK4),sK4)))
          | ~ $less($product(X7,sK4),sK0)
          | $less($product(X7,sK4),0) )
      & permut_all(elt5,mk_array1(elt5,sK0,t2tb9(sK1)),mk_array1(elt5,sK0,t2tb9(sK5)))
      & ~ $less(sK4,1) ) ),
    introduced(choice_axiom,[]) ).

tff(f255,plain,
    ( ? [X6: $int] :
        ( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(X6,sK4),min(sK0,$sum($product(X6,sK4),sK4)))
        & $less($product(X6,sK4),sK0)
        & ~ $less($product(X6,sK4),0) )
   => ( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(sK6,sK4),min(sK0,$sum($product(sK6,sK4),sK4)))
      & $less($product(sK6,sK4),sK0)
      & ~ $less($product(sK6,sK4),0) ) ),
    introduced(choice_axiom,[]) ).

tff(f251,plain,
    ? [X0: $int,X1: map_int_elt2] :
      ( ? [X2: $int,X3: map_int_elt2] :
          ( ? [X4: $int,X5: map_int_elt2] :
              ( ? [X6: $int] :
                  ( ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X6,X4),min(X0,$sum($product(X6,X4),X4)))
                  & $less($product(X6,X4),X0)
                  & ~ $less($product(X6,X4),0) )
              & $less(X4,X0)
              & ! [X7: $int] :
                  ( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X4),min(X0,$sum($product(X7,X4),X4)))
                  | ~ $less($product(X7,X4),X0)
                  | $less($product(X7,X4),0) )
              & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5)))
              & ~ $less(X4,1) )
          & ! [X8: $int] :
              ( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X8))) )
              | ~ $less(X8,X2)
              | $less(X8,0) )
          & ( X0 = X2 )
          & ~ $less(X2,0) )
      & ~ $less(X0,0) ),
    inference(rectify,[],[f208]) ).

tff(f208,plain,
    ? [X0: $int,X1: map_int_elt2] :
      ( ? [X2: $int,X3: map_int_elt2] :
          ( ? [X5: $int,X6: map_int_elt2] :
              ( ? [X8: $int] :
                  ( ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5)))
                  & $less($product(X8,X5),X0)
                  & ~ $less($product(X8,X5),0) )
              & $less(X5,X0)
              & ! [X7: $int] :
                  ( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5)))
                  | ~ $less($product(X7,X5),X0)
                  | $less($product(X7,X5),0) )
              & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
              & ~ $less(X5,1) )
          & ! [X4: $int] :
              ( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) )
              | ~ $less(X4,X2)
              | $less(X4,0) )
          & ( X0 = X2 )
          & ~ $less(X2,0) )
      & ~ $less(X0,0) ),
    inference(flattening,[],[f207]) ).

tff(f207,plain,
    ? [X0: $int,X1: map_int_elt2] :
      ( ? [X2: $int,X3: map_int_elt2] :
          ( ? [X5: $int,X6: map_int_elt2] :
              ( ? [X8: $int] :
                  ( ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5)))
                  & $less($product(X8,X5),X0)
                  & ~ $less($product(X8,X5),0) )
              & $less(X5,X0)
              & ! [X7: $int] :
                  ( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5)))
                  | ~ $less($product(X7,X5),X0)
                  | $less($product(X7,X5),0) )
              & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
              & ~ $less(X5,1) )
          & ! [X4: $int] :
              ( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) )
              | ~ $less(X4,X2)
              | $less(X4,0) )
          & ( X0 = X2 )
          & ~ $less(X2,0) )
      & ~ $less(X0,0) ),
    inference(ennf_transformation,[],[f160]) ).

tff(f160,plain,
    ~ ! [X0: $int,X1: map_int_elt2] :
        ( ~ $less(X0,0)
       => ! [X2: $int,X3: map_int_elt2] :
            ( ( ! [X4: $int] :
                  ( ( $less(X4,X2)
                    & ~ $less(X4,0) )
                 => ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) ) )
              & ( X0 = X2 )
              & ~ $less(X2,0) )
           => ! [X5: $int,X6: map_int_elt2] :
                ( ( ! [X7: $int] :
                      ( ( $less($product(X7,X5),X0)
                        & ~ $less($product(X7,X5),0) )
                     => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))) )
                  & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
                  & ~ $less(X5,1) )
               => ( $less(X5,X0)
                 => ! [X8: $int] :
                      ( ( $less($product(X8,X5),X0)
                        & ~ $less($product(X8,X5),0) )
                     => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5))) ) ) ) ) ),
    inference(rectify,[],[f141]) ).

tff(f141,plain,
    ~ ! [X0: $int,X10: map_int_elt2] :
        ( ~ $less(X0,0)
       => ! [X29: $int,X30: map_int_elt2] :
            ( ( ! [X14: $int] :
                  ( ( $less(X14,X29)
                    & ~ $less(X14,0) )
                 => ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) )
              & ( X0 = X29 )
              & ~ $less(X29,0) )
           => ! [X31: $int,X11: map_int_elt2] :
                ( ( ! [X25: $int] :
                      ( ( $less($product(X25,X31),X0)
                        & ~ $less($product(X25,X31),0) )
                     => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) )
                  & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
                  & ~ $less(X31,1) )
               => ( $less(X31,X0)
                 => ! [X25: $int] :
                      ( ( $less($product(X25,X31),X0)
                        & ~ $less($product(X25,X31),0) )
                     => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) ) ) ) ),
    inference(theory_normalization,[],[f99]) ).

tff(f99,negated_conjecture,
    ~ ! [X0: $int,X10: map_int_elt2] :
        ( $lesseq(0,X0)
       => ! [X29: $int,X30: map_int_elt2] :
            ( ( ! [X14: $int] :
                  ( ( $less(X14,X29)
                    & $lesseq(0,X14) )
                 => ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) )
              & ( X0 = X29 )
              & $lesseq(0,X29) )
           => ! [X31: $int,X11: map_int_elt2] :
                ( ( ! [X25: $int] :
                      ( ( $less($product(X25,X31),X0)
                        & $lesseq(0,$product(X25,X31)) )
                     => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) )
                  & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
                  & $lesseq(1,X31) )
               => ( $less(X31,X0)
                 => ! [X25: $int] :
                      ( ( $less($product(X25,X31),X0)
                        & $lesseq(0,$product(X25,X31)) )
                     => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) ) ) ) ),
    inference(negated_conjecture,[],[f98]) ).

tff(f98,conjecture,
    ! [X0: $int,X10: map_int_elt2] :
      ( $lesseq(0,X0)
     => ! [X29: $int,X30: map_int_elt2] :
          ( ( ! [X14: $int] :
                ( ( $less(X14,X29)
                  & $lesseq(0,X14) )
               => ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) )
            & ( X0 = X29 )
            & $lesseq(0,X29) )
         => ! [X31: $int,X11: map_int_elt2] :
              ( ( ! [X25: $int] :
                    ( ( $less($product(X25,X31),X0)
                      & $lesseq(0,$product(X25,X31)) )
                   => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) )
                & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
                & $lesseq(1,X31) )
             => ( $less(X31,X0)
               => ! [X25: $int] :
                    ( ( $less($product(X25,X31),X0)
                      & $lesseq(0,$product(X25,X31)) )
                   => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_bottom_up_mergesort) ).

tff(f432,plain,
    $less($product(sK6,sK4),0),
    inference(subsumption_resolution,[],[f430,f341]) ).

tff(f341,plain,
    $less($product(sK6,sK4),sK2),
    inference(definition_unfolding,[],[f280,f273]) ).

tff(f273,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f256]) ).

tff(f280,plain,
    $less($product(sK6,sK4),sK0),
    inference(cnf_transformation,[],[f256]) ).

tff(f430,plain,
    ( ~ $less($product(sK6,sK4),sK2)
    | $less($product(sK6,sK4),0) ),
    inference(resolution,[],[f343,f340]) ).

tff(f340,plain,
    ~ sorted_sub3(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4))),
    inference(definition_unfolding,[],[f281,f273,f273]) ).

tff(f281,plain,
    ~ sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(sK6,sK4),min(sK0,$sum($product(sK6,sK4),sK4))),
    inference(cnf_transformation,[],[f256]) ).

tff(f343,plain,
    ! [X7: $int] :
      ( sorted_sub3(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(X7,sK4),min(sK2,$sum($product(X7,sK4),sK4)))
      | ~ $less($product(X7,sK4),sK2)
      | $less($product(X7,sK4),0) ),
    inference(definition_unfolding,[],[f277,f273,f273,f273]) ).

tff(f277,plain,
    ! [X7: $int] :
      ( sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(X7,sK4),min(sK0,$sum($product(X7,sK4),sK4)))
      | ~ $less($product(X7,sK4),sK0)
      | $less($product(X7,sK4),0) ),
    inference(cnf_transformation,[],[f256]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWW619_2 : TPTP v8.2.0. Released v6.1.0.
% 0.12/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat May 18 19:35:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a TF0_THM_EQU_ARI problem
% 0.14/0.35  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.62/0.80  % (18153)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2995ds/56Mi)
% 0.62/0.80  % (18146)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 theBenchmark for (2995ds/34Mi)
% 0.62/0.80  % (18148)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2995ds/78Mi)
% 0.62/0.80  % (18147)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 theBenchmark for (2995ds/51Mi)
% 0.62/0.80  % (18151)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2995ds/45Mi)
% 0.62/0.80  % (18149)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2995ds/33Mi)
% 0.62/0.80  % (18150)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 theBenchmark for (2995ds/34Mi)
% 0.62/0.80  % (18152)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 theBenchmark for (2995ds/83Mi)
% 0.62/0.80  % (18153)First to succeed.
% 0.62/0.80  % (18153)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18144"
% 0.62/0.81  % (18153)Refutation found. Thanks to Tanya!
% 0.62/0.81  % SZS status Theorem for theBenchmark
% 0.62/0.81  % SZS output start Proof for theBenchmark
% See solution above
% 0.62/0.81  % (18153)------------------------------
% 0.62/0.81  % (18153)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.81  % (18153)Termination reason: Refutation
% 0.62/0.81  
% 0.62/0.81  % (18153)Memory used [KB]: 1290
% 0.62/0.81  % (18153)Time elapsed: 0.006 s
% 0.62/0.81  % (18153)Instructions burned: 17 (million)
% 0.62/0.81  % (18144)Success in time 0.443 s
% 0.62/0.81  % Vampire---4.8 exiting
%------------------------------------------------------------------------------