TSTP Solution File: LCL768_5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : LCL768_5 : TPTP v8.1.2. Released v6.0.0.
% 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 : n008.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 07:42:19 EDT 2024

% Result   : Theorem 0.60s 0.82s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   71
% Syntax   : Number of formulae    :  104 (  16 unt;  61 typ;   0 def)
%            Number of atoms       :  137 (  23 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  145 (  51   ~;  49   |;  36   &)
%                                         (   8 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   78 (  46   >;  32   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   3 prp; 0-3 aty)
%            Number of functors    :   53 (  53 usr;   9 con; 0-5 aty)
%            Number of variables   :  155 (  87   !;  12   ?; 155   :)
%                                         (  56  !>;   0  ?*;   0  @-;   0  @+)

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

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

tff(type_def_7,type,
    list: $tType > $tType ).

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

tff(type_def_9,type,
    fun: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    combb: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).

tff(func_def_1,type,
    combc: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(X1,fun(X0,X2)) ) ).

tff(func_def_2,type,
    combk: 
      !>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).

tff(func_def_3,type,
    combs: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).

tff(func_def_4,type,
    it: fun(dB,bool) ).

tff(func_def_5,type,
    app: fun(dB,fun(dB,dB)) ).

tff(func_def_6,type,
    var: nat > dB ).

tff(func_def_7,type,
    dB_case: 
      !>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).

tff(func_def_8,type,
    substn: ( dB * dB * nat ) > dB ).

tff(func_def_9,type,
    append: 
      !>[X0: $tType] : fun(list(X0),fun(list(X0),list(X0))) ).

tff(func_def_10,type,
    butlast: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_11,type,
    foldl: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).

tff(func_def_12,type,
    hd: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_13,type,
    insert: 
      !>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).

tff(func_def_14,type,
    last: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_15,type,
    cons: 
      !>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).

tff(func_def_16,type,
    nil: 
      !>[X0: $tType] : list(X0) ).

tff(func_def_17,type,
    list_case: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).

tff(func_def_18,type,
    maps: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,list(X1)) * list(X0) ) > list(X1) ) ).

tff(func_def_19,type,
    rev: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_20,type,
    rotate1: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_21,type,
    splice: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_22,type,
    tl: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_23,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_24,type,
    fFalse: bool ).

tff(func_def_25,type,
    fNot: fun(bool,bool) ).

tff(func_def_26,type,
    fTrue: bool ).

tff(func_def_27,type,
    fconj: fun(bool,fun(bool,bool)) ).

tff(func_def_28,type,
    fdisj: fun(bool,fun(bool,bool)) ).

tff(func_def_29,type,
    fequal: 
      !>[X0: $tType] : ( X0 > fun(X0,bool) ) ).

tff(func_def_30,type,
    i: nat ).

tff(func_def_31,type,
    rs: list(dB) ).

tff(func_def_32,type,
    sK0: 
      !>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).

tff(func_def_33,type,
    sK1: 
      !>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > list(X0) ) ).

tff(func_def_34,type,
    sK2: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_35,type,
    sK3: 
      !>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).

tff(func_def_36,type,
    sK4: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_37,type,
    sK5: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_38,type,
    sK6: 
      !>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).

tff(func_def_39,type,
    sK7: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_40,type,
    sK8: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_41,type,
    sK9: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_42,type,
    sK10: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_43,type,
    sK11: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_44,type,
    sK12: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_45,type,
    sK13: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_46,type,
    sK14: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_47,type,
    sK15: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).

tff(func_def_48,type,
    sK16: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_49,type,
    sK17: 
      !>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_50,type,
    sK18: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(pred_def_1,type,
    list_all: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_2,type,
    list_ex1: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_3,type,
    listsp: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_4,type,
    pp: bool > $o ).

tff(pred_def_5,type,
    sQ19_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f598,plain,
    $false,
    inference(avatar_sat_refutation,[],[f563,f592,f597]) ).

tff(f597,plain,
    spl20_2,
    inference(avatar_contradiction_clause,[],[f596]) ).

tff(f596,plain,
    ( $false
    | spl20_2 ),
    inference(subsumption_resolution,[],[f595,f280]) ).

tff(f280,plain,
    ! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
    inference(cnf_transformation,[],[f132]) ).

tff(f132,plain,
    ! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ! [X4: nat] : pp(aa(dB,bool,it,var(X4))),
    file('/export/starexec/sandbox2/tmp/tmp.dauGutawue/Vampire---4.8_19363',fact_0_Var__IT) ).

tff(f595,plain,
    ( ~ pp(aa(dB,bool,it,var(i)))
    | spl20_2 ),
    inference(subsumption_resolution,[],[f594,f275]) ).

tff(f275,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
    inference(cnf_transformation,[],[f129]) ).

tff(f129,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X2: $tType,X9: fun(X2,bool)] : listsp(X2,X9,nil(X2)),
    file('/export/starexec/sandbox2/tmp/tmp.dauGutawue/Vampire---4.8_19363',fact_3_listsp_ONil) ).

tff(f594,plain,
    ( ~ listsp(dB,it,nil(dB))
    | ~ pp(aa(dB,bool,it,var(i)))
    | spl20_2 ),
    inference(resolution,[],[f562,f372]) ).

tff(f372,plain,
    ! [X0: $tType,X2: fun(X0,bool),X3: X0,X4: list(X0)] :
      ( listsp(X0,X2,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4))
      | ~ listsp(X0,X2,X4)
      | ~ pp(aa(X0,bool,X2,X3)) ),
    inference(equality_resolution,[],[f274]) ).

tff(f274,plain,
    ! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: list(X0),X4: list(X0)] :
      ( listsp(X0,X2,X1)
      | ~ listsp(X0,X2,X4)
      | ~ pp(aa(X0,bool,X2,X3))
      | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 ) ),
    inference(cnf_transformation,[],[f199]) ).

tff(f199,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( ( listsp(X0,X2,X1)
        | ( ! [X3: X0,X4: list(X0)] :
              ( ~ listsp(X0,X2,X4)
              | ~ pp(aa(X0,bool,X2,X3))
              | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 ) )
          & ( nil(X0) != X1 ) ) )
      & ( ( listsp(X0,X2,sK1(X0,X1,X2))
          & pp(aa(X0,bool,X2,sK0(X0,X1,X2)))
          & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK0(X0,X1,X2)),sK1(X0,X1,X2)) = X1 ) )
        | ( nil(X0) = X1 )
        | ~ listsp(X0,X2,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f197,f198]) ).

tff(f198,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( ? [X5: X0,X6: list(X0)] :
          ( listsp(X0,X2,X6)
          & pp(aa(X0,bool,X2,X5))
          & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) = X1 ) )
     => ( listsp(X0,X2,sK1(X0,X1,X2))
        & pp(aa(X0,bool,X2,sK0(X0,X1,X2)))
        & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK0(X0,X1,X2)),sK1(X0,X1,X2)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f197,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( ( listsp(X0,X2,X1)
        | ( ! [X3: X0,X4: list(X0)] :
              ( ~ listsp(X0,X2,X4)
              | ~ pp(aa(X0,bool,X2,X3))
              | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 ) )
          & ( nil(X0) != X1 ) ) )
      & ( ? [X5: X0,X6: list(X0)] :
            ( listsp(X0,X2,X6)
            & pp(aa(X0,bool,X2,X5))
            & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) = X1 ) )
        | ( nil(X0) = X1 )
        | ~ listsp(X0,X2,X1) ) ),
    inference(rectify,[],[f196]) ).

tff(f196,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( ( listsp(X0,X2,X1)
        | ( ! [X3: X0,X4: list(X0)] :
              ( ~ listsp(X0,X2,X4)
              | ~ pp(aa(X0,bool,X2,X3))
              | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 ) )
          & ( nil(X0) != X1 ) ) )
      & ( ? [X3: X0,X4: list(X0)] :
            ( listsp(X0,X2,X4)
            & pp(aa(X0,bool,X2,X3))
            & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) = X1 ) )
        | ( nil(X0) = X1 )
        | ~ listsp(X0,X2,X1) ) ),
    inference(flattening,[],[f195]) ).

tff(f195,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( ( listsp(X0,X2,X1)
        | ( ! [X3: X0,X4: list(X0)] :
              ( ~ listsp(X0,X2,X4)
              | ~ pp(aa(X0,bool,X2,X3))
              | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 ) )
          & ( nil(X0) != X1 ) ) )
      & ( ? [X3: X0,X4: list(X0)] :
            ( listsp(X0,X2,X4)
            & pp(aa(X0,bool,X2,X3))
            & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) = X1 ) )
        | ( nil(X0) = X1 )
        | ~ listsp(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f128]) ).

tff(f128,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( listsp(X0,X2,X1)
    <=> ( ? [X3: X0,X4: list(X0)] :
            ( listsp(X0,X2,X4)
            & pp(aa(X0,bool,X2,X3))
            & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) = X1 ) )
        | ( nil(X0) = X1 ) ) ),
    inference(rectify,[],[f29]) ).

tff(f29,axiom,
    ! [X2: $tType,X20: list(X2),X9: fun(X2,bool)] :
      ( listsp(X2,X9,X20)
    <=> ( ? [X28: X2,X29: list(X2)] :
            ( listsp(X2,X9,X29)
            & pp(aa(X2,bool,X9,X28))
            & ( aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X28),X29) = X20 ) )
        | ( nil(X2) = X20 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.dauGutawue/Vampire---4.8_19363',fact_28_listsp_Osimps) ).

tff(f562,plain,
    ( ~ listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))
    | spl20_2 ),
    inference(avatar_component_clause,[],[f560]) ).

tff(f560,plain,
    ( spl20_2
  <=> listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl20_2])]) ).

tff(f592,plain,
    spl20_1,
    inference(avatar_split_clause,[],[f589,f556]) ).

tff(f556,plain,
    ( spl20_1
  <=> listsp(dB,it,rs) ),
    introduced(avatar_definition,[new_symbols(naming,[spl20_1])]) ).

tff(f589,plain,
    listsp(dB,it,rs),
    inference(resolution,[],[f254,f264]) ).

tff(f264,plain,
    ! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
      ( ~ listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3)
      | listsp(X0,X2,X3) ),
    inference(cnf_transformation,[],[f194]) ).

tff(f194,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
      ( ( listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3)
        | ~ listsp(X0,X1,X3)
        | ~ listsp(X0,X2,X3) )
      & ( ( listsp(X0,X1,X3)
          & listsp(X0,X2,X3) )
        | ~ listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3) ) ),
    inference(flattening,[],[f193]) ).

tff(f193,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
      ( ( listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3)
        | ~ listsp(X0,X1,X3)
        | ~ listsp(X0,X2,X3) )
      & ( ( listsp(X0,X1,X3)
          & listsp(X0,X2,X3) )
        | ~ listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3) ) ),
    inference(nnf_transformation,[],[f124]) ).

tff(f124,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
      ( listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3)
    <=> ( listsp(X0,X1,X3)
        & listsp(X0,X2,X3) ) ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X2: $tType,X13: fun(X2,bool),X9: fun(X2,bool),X14: list(X2)] :
      ( listsp(X2,combs(X2,bool,bool,combb(bool,fun(bool,bool),X2,fconj,X9),X13),X14)
    <=> ( listsp(X2,X13,X14)
        & listsp(X2,X9,X14) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.dauGutawue/Vampire---4.8_19363',fact_11_listsp__conj__eq) ).

tff(f254,plain,
    listsp(dB,combs(dB,bool,bool,combb(bool,fun(bool,bool),dB,fconj,it),combb(dB,bool,dB,it,aa(dB,fun(dB,dB),combc(dB,dB,dB,app),var(i)))),rs),
    inference(cnf_transformation,[],[f117]) ).

tff(f117,axiom,
    listsp(dB,combs(dB,bool,bool,combb(bool,fun(bool,bool),dB,fconj,it),combb(dB,bool,dB,it,aa(dB,fun(dB,dB),combc(dB,dB,dB,app),var(i)))),rs),
    file('/export/starexec/sandbox2/tmp/tmp.dauGutawue/Vampire---4.8_19363',conj_0) ).

tff(f563,plain,
    ( ~ spl20_1
    | ~ spl20_2 ),
    inference(avatar_split_clause,[],[f549,f560,f556]) ).

tff(f549,plain,
    ( ~ listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))
    | ~ listsp(dB,it,rs) ),
    inference(resolution,[],[f278,f255]) ).

tff(f255,plain,
    ~ listsp(dB,it,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
    inference(cnf_transformation,[],[f120]) ).

tff(f120,plain,
    ~ listsp(dB,it,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
    inference(flattening,[],[f119]) ).

tff(f119,negated_conjecture,
    ~ listsp(dB,it,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
    inference(negated_conjecture,[],[f118]) ).

tff(f118,conjecture,
    listsp(dB,it,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
    file('/export/starexec/sandbox2/tmp/tmp.dauGutawue/Vampire---4.8_19363',conj_1) ).

tff(f278,plain,
    ! [X0: $tType,X2: list(X0),X3: fun(X0,bool),X1: list(X0)] :
      ( listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))
      | ~ listsp(X0,X3,X1)
      | ~ listsp(X0,X3,X2) ),
    inference(cnf_transformation,[],[f201]) ).

tff(f201,plain,
    ! [X0: $tType,X1: list(X0),X2: list(X0),X3: fun(X0,bool)] :
      ( ( listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))
        | ~ listsp(X0,X3,X1)
        | ~ listsp(X0,X3,X2) )
      & ( ( listsp(X0,X3,X1)
          & listsp(X0,X3,X2) )
        | ~ listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) ) ),
    inference(flattening,[],[f200]) ).

tff(f200,plain,
    ! [X0: $tType,X1: list(X0),X2: list(X0),X3: fun(X0,bool)] :
      ( ( listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))
        | ~ listsp(X0,X3,X1)
        | ~ listsp(X0,X3,X2) )
      & ( ( listsp(X0,X3,X1)
          & listsp(X0,X3,X2) )
        | ~ listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) ) ),
    inference(nnf_transformation,[],[f130]) ).

tff(f130,plain,
    ! [X0: $tType,X1: list(X0),X2: list(X0),X3: fun(X0,bool)] :
      ( listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))
    <=> ( listsp(X0,X3,X1)
        & listsp(X0,X3,X2) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X2: $tType,X6: list(X2),X8: list(X2),X9: fun(X2,bool)] :
      ( listsp(X2,X9,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X8),X6))
    <=> ( listsp(X2,X9,X6)
        & listsp(X2,X9,X8) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.dauGutawue/Vampire---4.8_19363',fact_2_append__in__listsp__conv) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : LCL768_5 : TPTP v8.1.2. Released v6.0.0.
% 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
% 0.14/0.36  % Computer : n008.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 13:59:12 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a TF1_THM_EQU_NAR problem
% 0.14/0.36  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/tmp/tmp.dauGutawue/Vampire---4.8_19363
% 0.60/0.81  % (19478)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 (2995ds/56Mi)
% 0.60/0.81  % (19471)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 (2995ds/34Mi)
% 0.60/0.81  % (19473)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.60/0.81  % (19474)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.60/0.81  % (19472)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 (2995ds/51Mi)
% 0.60/0.81  % (19475)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 (2995ds/34Mi)
% 0.60/0.81  % (19476)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.60/0.81  % (19477)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 (2995ds/83Mi)
% 0.60/0.81  % (19477)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
% 0.60/0.81  % (19478)Refutation not found, incomplete strategy% (19478)------------------------------
% 0.60/0.81  % (19478)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.81  % (19478)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.81  
% 0.60/0.81  % (19478)Memory used [KB]: 1255
% 0.60/0.81  % (19478)Time elapsed: 0.006 s
% 0.60/0.81  % (19478)Instructions burned: 20 (million)
% 0.60/0.81  % (19478)------------------------------
% 0.60/0.81  % (19478)------------------------------
% 0.60/0.82  % (19479)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2995ds/55Mi)
% 0.60/0.82  % (19477)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.60/0.82  % (19476)Refutation not found, incomplete strategy% (19476)------------------------------
% 0.60/0.82  % (19476)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.82  % (19476)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.82  
% 0.60/0.82  % (19476)Memory used [KB]: 1313
% 0.60/0.82  % (19476)Time elapsed: 0.011 s
% 0.60/0.82  % (19476)Instructions burned: 21 (million)
% 0.60/0.82  % (19476)------------------------------
% 0.60/0.82  % (19476)------------------------------
% 0.60/0.82  % (19471)First to succeed.
% 0.60/0.82  % (19475)Also succeeded, but the first one will report.
% 0.60/0.82  % (19471)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19470"
% 0.60/0.82  % (19471)Refutation found. Thanks to Tanya!
% 0.60/0.82  % SZS status Theorem for Vampire---4
% 0.60/0.82  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.82  % (19471)------------------------------
% 0.60/0.82  % (19471)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.82  % (19471)Termination reason: Refutation
% 0.60/0.82  
% 0.60/0.82  % (19471)Memory used [KB]: 1337
% 0.60/0.82  % (19471)Time elapsed: 0.016 s
% 0.60/0.82  % (19471)Instructions burned: 27 (million)
% 0.60/0.82  % (19470)Success in time 0.448 s
% 0.60/0.82  % Vampire---4.8 exiting
%------------------------------------------------------------------------------