TSTP Solution File: SWW619_2 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SWW619_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n005.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 : Mon Jun 24 18:35:15 EDT 2024

% Result   : Theorem 0.24s 0.52s
% Output   : Refutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   19 (   5 unt;   0 typ;   0 def)
%            Number of atoms       :  212 (  24 equ)
%            Maximal formula atoms :   30 (  11 avg)
%            Number of connectives :  279 (  86   ~;  39   |; 122   &)
%                                         (   0 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (  11 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number arithmetic     :  456 ( 141 atm; 163 fun;  81 num;  71 var)
%            Number of types       :    9 (   7 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  14 usr;   1 prp; 0-7 aty)
%            Number of functors    :   59 (  55 usr;  18 con; 0-7 aty)
%            Number of variables   :  101 (  55   !;  46   ?; 101   :)

% 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,
    sK1: ( ty * $int * $int * uni * uni ) > $int ).

tff(func_def_46,type,
    sK2: ( ty * $int * uni * $int * uni ) > uni ).

tff(func_def_47,type,
    sK3: $int ).

tff(func_def_48,type,
    sK4: map_int_elt2 ).

tff(func_def_49,type,
    sK5: map_int_elt2 ).

tff(func_def_50,type,
    sK6: $int ).

tff(func_def_51,type,
    sK7: map_int_elt2 ).

tff(func_def_52,type,
    sK8: $int ).

tff(func_def_53,type,
    sK9: $int ).

tff(func_def_54,type,
    sK10: ( uni * $int * $int * uni * ty ) > $int ).

tff(func_def_55,type,
    sK11: ( $int * $int * uni * ty * uni ) > $int ).

tff(func_def_56,type,
    sK12: ( array_elt2 * $int * $int ) > $int ).

tff(func_def_57,type,
    sK13: ( array_elt2 * $int * $int ) > $int ).

tff(func_def_58,type,
    sK14: ( $int * uni * $int * ty * uni ) > $int ).

tff(func_def_59,type,
    sK15: ( $int * $int * $int * uni * ty * uni ) > $int ).

tff(func_def_60,type,
    sK16: ( $int * uni * ty * $int * 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,
    sP0: ( $int * uni * ty * $int * uni * $int * $int ) > $o ).

tff(f655,plain,
    $false,
    inference(subsumption_resolution,[],[f654,f461]) ).

tff(f461,plain,
    $less($product(sK9,sK8),sK3),
    inference(cnf_transformation,[],[f359]) ).

tff(f359,plain,
    ( ( sK3 = sK6 )
    & ! [X4: $int] :
        ( ( tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(sK5),t2tb(X4))) )
        | ~ $less(X4,sK6)
        | $less(X4,0) )
    & permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(sK7)))
    & $less(sK8,sK3)
    & ! [X7: $int] :
        ( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(X7,sK8),min(sK3,$sum($product(X7,sK8),sK8)))
        | $less($product(X7,sK8),0)
        | ~ $less($product(X7,sK8),sK3) )
    & ~ $less(sK8,1)
    & ~ $less($product(sK9,sK8),0)
    & $less($product(sK9,sK8),sK3)
    & ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(sK9,sK8),min(sK3,$sum($product(sK9,sK8),sK8)))
    & ~ $less(sK6,0)
    & ~ $less(sK3,0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8,sK9])],[f354,f358,f357,f356,f355]) ).

tff(f355,plain,
    ( ? [X0: $int,X1: map_int_elt2] :
        ( ? [X2: map_int_elt2,X3: $int] :
            ( ( X0 = X3 )
            & ! [X4: $int] :
                ( ( tb2t7(get(elt5,int,t2tb9(X2),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) )
                | ~ $less(X4,X3)
                | $less(X4,0) )
            & ? [X5: map_int_elt2,X6: $int] :
                ( permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5)))
                & $less(X6,X0)
                & ! [X7: $int] :
                    ( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X6),min(X0,$sum($product(X7,X6),X6)))
                    | $less($product(X7,X6),0)
                    | ~ $less($product(X7,X6),X0) )
                & ~ $less(X6,1)
                & ? [X8: $int] :
                    ( ~ $less($product(X8,X6),0)
                    & $less($product(X8,X6),X0)
                    & ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X8,X6),min(X0,$sum($product(X8,X6),X6))) ) )
            & ~ $less(X3,0) )
        & ~ $less(X0,0) )
   => ( ? [X3: $int,X2: map_int_elt2] :
          ( ( sK3 = X3 )
          & ! [X4: $int] :
              ( ( tb2t7(get(elt5,int,t2tb9(X2),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X4))) )
              | ~ $less(X4,X3)
              | $less(X4,0) )
          & ? [X6: $int,X5: map_int_elt2] :
              ( permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(X5)))
              & $less(X6,sK3)
              & ! [X7: $int] :
                  ( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X7,X6),min(sK3,$sum($product(X7,X6),X6)))
                  | $less($product(X7,X6),0)
                  | ~ $less($product(X7,X6),sK3) )
              & ~ $less(X6,1)
              & ? [X8: $int] :
                  ( ~ $less($product(X8,X6),0)
                  & $less($product(X8,X6),sK3)
                  & ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X8,X6),min(sK3,$sum($product(X8,X6),X6))) ) )
          & ~ $less(X3,0) )
      & ~ $less(sK3,0) ) ),
    introduced(choice_axiom,[]) ).

tff(f356,plain,
    ( ? [X3: $int,X2: map_int_elt2] :
        ( ( sK3 = X3 )
        & ! [X4: $int] :
            ( ( tb2t7(get(elt5,int,t2tb9(X2),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X4))) )
            | ~ $less(X4,X3)
            | $less(X4,0) )
        & ? [X6: $int,X5: map_int_elt2] :
            ( permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(X5)))
            & $less(X6,sK3)
            & ! [X7: $int] :
                ( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X7,X6),min(sK3,$sum($product(X7,X6),X6)))
                | $less($product(X7,X6),0)
                | ~ $less($product(X7,X6),sK3) )
            & ~ $less(X6,1)
            & ? [X8: $int] :
                ( ~ $less($product(X8,X6),0)
                & $less($product(X8,X6),sK3)
                & ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X8,X6),min(sK3,$sum($product(X8,X6),X6))) ) )
        & ~ $less(X3,0) )
   => ( ( sK3 = sK6 )
      & ! [X4: $int] :
          ( ( tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(sK5),t2tb(X4))) )
          | ~ $less(X4,sK6)
          | $less(X4,0) )
      & ? [X6: $int,X5: map_int_elt2] :
          ( permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(X5)))
          & $less(X6,sK3)
          & ! [X7: $int] :
              ( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X7,X6),min(sK3,$sum($product(X7,X6),X6)))
              | $less($product(X7,X6),0)
              | ~ $less($product(X7,X6),sK3) )
          & ~ $less(X6,1)
          & ? [X8: $int] :
              ( ~ $less($product(X8,X6),0)
              & $less($product(X8,X6),sK3)
              & ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X8,X6),min(sK3,$sum($product(X8,X6),X6))) ) )
      & ~ $less(sK6,0) ) ),
    introduced(choice_axiom,[]) ).

tff(f357,plain,
    ( ? [X6: $int,X5: map_int_elt2] :
        ( permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(X5)))
        & $less(X6,sK3)
        & ! [X7: $int] :
            ( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X7,X6),min(sK3,$sum($product(X7,X6),X6)))
            | $less($product(X7,X6),0)
            | ~ $less($product(X7,X6),sK3) )
        & ~ $less(X6,1)
        & ? [X8: $int] :
            ( ~ $less($product(X8,X6),0)
            & $less($product(X8,X6),sK3)
            & ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X8,X6),min(sK3,$sum($product(X8,X6),X6))) ) )
   => ( permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(sK7)))
      & $less(sK8,sK3)
      & ! [X7: $int] :
          ( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(X7,sK8),min(sK3,$sum($product(X7,sK8),sK8)))
          | $less($product(X7,sK8),0)
          | ~ $less($product(X7,sK8),sK3) )
      & ~ $less(sK8,1)
      & ? [X8: $int] :
          ( ~ $less($product(X8,sK8),0)
          & $less($product(X8,sK8),sK3)
          & ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(X8,sK8),min(sK3,$sum($product(X8,sK8),sK8))) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f358,plain,
    ( ? [X8: $int] :
        ( ~ $less($product(X8,sK8),0)
        & $less($product(X8,sK8),sK3)
        & ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(X8,sK8),min(sK3,$sum($product(X8,sK8),sK8))) )
   => ( ~ $less($product(sK9,sK8),0)
      & $less($product(sK9,sK8),sK3)
      & ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(sK9,sK8),min(sK3,$sum($product(sK9,sK8),sK8))) ) ),
    introduced(choice_axiom,[]) ).

tff(f354,plain,
    ? [X0: $int,X1: map_int_elt2] :
      ( ? [X2: map_int_elt2,X3: $int] :
          ( ( X0 = X3 )
          & ! [X4: $int] :
              ( ( tb2t7(get(elt5,int,t2tb9(X2),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) )
              | ~ $less(X4,X3)
              | $less(X4,0) )
          & ? [X5: map_int_elt2,X6: $int] :
              ( permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5)))
              & $less(X6,X0)
              & ! [X7: $int] :
                  ( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X6),min(X0,$sum($product(X7,X6),X6)))
                  | $less($product(X7,X6),0)
                  | ~ $less($product(X7,X6),X0) )
              & ~ $less(X6,1)
              & ? [X8: $int] :
                  ( ~ $less($product(X8,X6),0)
                  & $less($product(X8,X6),X0)
                  & ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X8,X6),min(X0,$sum($product(X8,X6),X6))) ) )
          & ~ $less(X3,0) )
      & ~ $less(X0,0) ),
    inference(rectify,[],[f330]) ).

tff(f330,plain,
    ? [X1: $int,X0: map_int_elt2] :
      ( ? [X3: map_int_elt2,X2: $int] :
          ( ( X1 = X2 )
          & ! [X4: $int] :
              ( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X0),t2tb(X4))) )
              | ~ $less(X4,X2)
              | $less(X4,0) )
          & ? [X5: map_int_elt2,X6: $int] :
              ( permut_all(elt5,mk_array1(elt5,X1,t2tb9(X0)),mk_array1(elt5,X1,t2tb9(X5)))
              & $less(X6,X1)
              & ! [X7: $int] :
                  ( sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X7,X6),min(X1,$sum($product(X7,X6),X6)))
                  | $less($product(X7,X6),0)
                  | ~ $less($product(X7,X6),X1) )
              & ~ $less(X6,1)
              & ? [X8: $int] :
                  ( ~ $less($product(X8,X6),0)
                  & $less($product(X8,X6),X1)
                  & ~ sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X8,X6),min(X1,$sum($product(X8,X6),X6))) ) )
          & ~ $less(X2,0) )
      & ~ $less(X1,0) ),
    inference(flattening,[],[f329]) ).

tff(f329,plain,
    ? [X1: $int,X0: map_int_elt2] :
      ( ? [X2: $int,X3: map_int_elt2] :
          ( ? [X6: $int,X5: map_int_elt2] :
              ( ? [X8: $int] :
                  ( ~ sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X8,X6),min(X1,$sum($product(X8,X6),X6)))
                  & ~ $less($product(X8,X6),0)
                  & $less($product(X8,X6),X1) )
              & $less(X6,X1)
              & ! [X7: $int] :
                  ( sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X7,X6),min(X1,$sum($product(X7,X6),X6)))
                  | ~ $less($product(X7,X6),X1)
                  | $less($product(X7,X6),0) )
              & ~ $less(X6,1)
              & permut_all(elt5,mk_array1(elt5,X1,t2tb9(X0)),mk_array1(elt5,X1,t2tb9(X5))) )
          & ! [X4: $int] :
              ( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X0),t2tb(X4))) )
              | $less(X4,0)
              | ~ $less(X4,X2) )
          & ( X1 = X2 )
          & ~ $less(X2,0) )
      & ~ $less(X1,0) ),
    inference(ennf_transformation,[],[f242]) ).

tff(f242,plain,
    ~ ! [X1: $int,X0: map_int_elt2] :
        ( ~ $less(X1,0)
       => ! [X2: $int,X3: map_int_elt2] :
            ( ( ! [X4: $int] :
                  ( ( ~ $less(X4,0)
                    & $less(X4,X2) )
                 => ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X0),t2tb(X4))) ) )
              & ( X1 = X2 )
              & ~ $less(X2,0) )
           => ! [X6: $int,X5: map_int_elt2] :
                ( ( ! [X7: $int] :
                      ( ( $less($product(X7,X6),X1)
                        & ~ $less($product(X7,X6),0) )
                     => sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X7,X6),min(X1,$sum($product(X7,X6),X6))) )
                  & ~ $less(X6,1)
                  & permut_all(elt5,mk_array1(elt5,X1,t2tb9(X0)),mk_array1(elt5,X1,t2tb9(X5))) )
               => ( $less(X6,X1)
                 => ! [X8: $int] :
                      ( ( ~ $less($product(X8,X6),0)
                        & $less($product(X8,X6),X1) )
                     => sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X8,X6),min(X1,$sum($product(X8,X6),X6))) ) ) ) ) ),
    inference(rectify,[],[f135]) ).

tff(f135,plain,
    ~ ! [X10: map_int_elt2,X0: $int] :
        ( ~ $less(X0,0)
       => ! [X29: $int,X30: map_int_elt2] :
            ( ( ( X0 = X29 )
              & ~ $less(X29,0)
              & ! [X14: $int] :
                  ( ( ~ $less(X14,0)
                    & $less(X14,X29) )
                 => ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) ) )
           => ! [X11: map_int_elt2,X31: $int] :
                ( ( ~ $less(X31,1)
                  & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
                  & ! [X25: $int] :
                      ( ( ~ $less($product(X25,X31),0)
                        & $less($product(X25,X31),X0) )
                     => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) )
               => ( $less(X31,X0)
                 => ! [X25: $int] :
                      ( ( ~ $less($product(X25,X31),0)
                        & $less($product(X25,X31),X0) )
                     => 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,
    ~ ! [X10: map_int_elt2,X0: $int] :
        ( $lesseq(0,X0)
       => ! [X29: $int,X30: map_int_elt2] :
            ( ( ( X0 = X29 )
              & $lesseq(0,X29)
              & ! [X14: $int] :
                  ( ( $lesseq(0,X14)
                    & $less(X14,X29) )
                 => ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) ) )
           => ! [X11: map_int_elt2,X31: $int] :
                ( ( $lesseq(1,X31)
                  & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
                  & ! [X25: $int] :
                      ( ( $lesseq(0,$product(X25,X31))
                        & $less($product(X25,X31),X0) )
                     => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) )
               => ( $less(X31,X0)
                 => ! [X25: $int] :
                      ( ( $lesseq(0,$product(X25,X31))
                        & $less($product(X25,X31),X0) )
                     => 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,
    ! [X10: map_int_elt2,X0: $int] :
      ( $lesseq(0,X0)
     => ! [X29: $int,X30: map_int_elt2] :
          ( ( ( X0 = X29 )
            & $lesseq(0,X29)
            & ! [X14: $int] :
                ( ( $lesseq(0,X14)
                  & $less(X14,X29) )
               => ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) ) )
         => ! [X11: map_int_elt2,X31: $int] :
              ( ( $lesseq(1,X31)
                & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
                & ! [X25: $int] :
                    ( ( $lesseq(0,$product(X25,X31))
                      & $less($product(X25,X31),X0) )
                   => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) )
             => ( $less(X31,X0)
               => ! [X25: $int] :
                    ( ( $lesseq(0,$product(X25,X31))
                      & $less($product(X25,X31),X0) )
                   => 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',unknown) ).

tff(f654,plain,
    ~ $less($product(sK9,sK8),sK3),
    inference(subsumption_resolution,[],[f645,f462]) ).

tff(f462,plain,
    ~ $less($product(sK9,sK8),0),
    inference(cnf_transformation,[],[f359]) ).

tff(f645,plain,
    ( $less($product(sK9,sK8),0)
    | ~ $less($product(sK9,sK8),sK3) ),
    inference(resolution,[],[f464,f460]) ).

tff(f460,plain,
    ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(sK9,sK8),min(sK3,$sum($product(sK9,sK8),sK8))),
    inference(cnf_transformation,[],[f359]) ).

tff(f464,plain,
    ! [X7: $int] :
      ( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(X7,sK8),min(sK3,$sum($product(X7,sK8),sK8)))
      | $less($product(X7,sK8),0)
      | ~ $less($product(X7,sK8),sK3) ),
    inference(cnf_transformation,[],[f359]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SWW619_2 : TPTP v8.2.0. Released v6.1.0.
% 0.03/0.13  % Command    : run_vampire %s %d THM
% 0.13/0.36  % Computer : n005.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Wed Jun 19 06:08:09 EDT 2024
% 0.13/0.36  % CPUTime    : 
% 0.23/0.38  This is a TF0_THM_EQU_ARI problem
% 0.23/0.38  Running first-order theorem proving
% 0.23/0.38  Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.44  % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44  % (1242)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/34Mi)
% 0.23/0.44  % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44  % (1245)ott+1011_1:2_br=off:bs=unit_only:bsr=unit_only:nwc=5.0:s2a=on:s2agt=32:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.23/0.44  % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44  % (1243)dis+1011_1:64_drc=off:flr=on:nwc=2.0:sac=on:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/8Mi)
% 0.23/0.45  % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45  % (1241)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59848Mi)
% 0.23/0.45  % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45  % (1247)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/32Mi)
% 0.23/0.45  % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45  % (1244)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.23/0.45  % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45  % (1246)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/15Mi)
% 0.23/0.45  % (1244)Instruction limit reached!
% 0.23/0.45  % (1244)------------------------------
% 0.23/0.45  % (1244)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.23/0.45  % (1244)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.23/0.45  % (1244)Termination reason: Time limit
% 0.23/0.45  % (1244)Termination phase: shuffling
% 0.23/0.45  
% 0.23/0.45  % (1244)Memory used [KB]: 857
% 0.23/0.45  % (1244)Time elapsed: 0.002 s
% 0.23/0.45  % (1244)Instructions burned: 2 (million)
% 0.23/0.45  % (1243)Instruction limit reached!
% 0.23/0.45  % (1243)------------------------------
% 0.23/0.45  % (1243)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.23/0.45  % (1243)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.23/0.45  % (1243)Termination reason: Time limit
% 0.23/0.45  % (1243)Termination phase: Preprocessing 3
% 0.23/0.45  
% 0.23/0.45  % (1243)Memory used [KB]: 1091
% 0.23/0.45  % (1243)Time elapsed: 0.007 s
% 0.23/0.45  % (1243)Instructions burned: 8 (million)
% 0.24/0.45  % (1246)Instruction limit reached!
% 0.24/0.45  % (1246)------------------------------
% 0.24/0.45  % (1246)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.45  % (1246)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.45  % (1246)Termination reason: Time limit
% 0.24/0.45  % (1246)Termination phase: Saturation
% 0.24/0.45  
% 0.24/0.45  % (1246)Memory used [KB]: 1136
% 0.24/0.45  % (1246)Time elapsed: 0.010 s
% 0.24/0.45  % (1246)Instructions burned: 16 (million)
% 0.24/0.46  % (1242)Instruction limit reached!
% 0.24/0.46  % (1242)------------------------------
% 0.24/0.46  % (1242)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.46  % (1242)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.46  % (1242)Termination reason: Time limit
% 0.24/0.46  % (1242)Termination phase: Saturation
% 0.24/0.46  
% 0.24/0.46  % (1242)Memory used [KB]: 1497
% 0.24/0.46  % (1242)Time elapsed: 0.021 s
% 0.24/0.46  % (1242)Instructions burned: 34 (million)
% 0.24/0.47  % (1247)Instruction limit reached!
% 0.24/0.47  % (1247)------------------------------
% 0.24/0.47  % (1247)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.47  % (1247)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.47  % (1247)Termination reason: Time limit
% 0.24/0.47  % (1247)Termination phase: Saturation
% 0.24/0.47  
% 0.24/0.47  % (1247)Memory used [KB]: 1382
% 0.24/0.47  % (1247)Time elapsed: 0.022 s
% 0.24/0.47  % (1247)Instructions burned: 33 (million)
% 0.24/0.47  % (1245)Instruction limit reached!
% 0.24/0.47  % (1245)------------------------------
% 0.24/0.47  % (1245)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.47  % (1245)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.47  % (1245)Termination reason: Time limit
% 0.24/0.47  % (1245)Termination phase: Saturation
% 0.24/0.47  
% 0.24/0.47  % (1245)Memory used [KB]: 1543
% 0.24/0.47  % (1245)Time elapsed: 0.026 s
% 0.24/0.47  % (1245)Instructions burned: 37 (million)
% 0.24/0.51  % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.51  % (1248)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=36:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/36Mi)
% 0.24/0.51  % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.51  % (1249)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/26Mi)
% 0.24/0.51  % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.51  % (1250)lrs+10_1:8_ep=R:erd=off:fs=off:fsr=off:gve=force:nwc=2.0:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.24/0.52  % (1250)Instruction limit reached!
% 0.24/0.52  % (1250)------------------------------
% 0.24/0.52  % (1250)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.52  % (1250)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.52  % (1250)Termination reason: Time limit
% 0.24/0.52  % (1250)Termination phase: Property scanning
% 0.24/0.52  
% 0.24/0.52  % (1250)Memory used [KB]: 861
% 0.24/0.52  % (1250)Time elapsed: 0.003 s
% 0.24/0.52  % (1250)Instructions burned: 3 (million)
% 0.24/0.52  % (1248)First to succeed.
% 0.24/0.52  % (1248)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1240"
% 0.24/0.52  % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.52  % (1248)Refutation found. Thanks to Tanya!
% 0.24/0.52  % SZS status Theorem for theBenchmark
% 0.24/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.52  % (1248)------------------------------
% 0.24/0.52  % (1248)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.52  % (1248)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.52  % (1248)Termination reason: Refutation
% 0.24/0.52  
% 0.24/0.52  % (1248)Memory used [KB]: 1343
% 0.24/0.52  % (1248)Time elapsed: 0.015 s
% 0.24/0.52  % (1248)Instructions burned: 23 (million)
% 0.24/0.52  % (1248)------------------------------
% 0.24/0.52  % (1248)------------------------------
% 0.24/0.52  % (1240)Success in time 0.128 s
%------------------------------------------------------------------------------