TSTP Solution File: DAT067_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT067_1 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n006.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 Apr 30 11:03:57 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   72
% Syntax   : Number of formulae    :  162 (  65 unt;  11 typ;   0 def)
%            Number of atoms       :  294 ( 123 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  237 (  94   ~;  83   |;  16   &)
%                                         (  37 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :  275 (  29 atm;  70 fun;  44 num; 132 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   37 (  34 usr;  34 prp; 0-2 aty)
%            Number of functors    :   13 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  236 ( 230   !;   6   ?; 236   :)

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

tff(func_def_0,type,
    empty: heap ).

tff(func_def_1,type,
    toop: heap > $int ).

tff(func_def_2,type,
    sel: ( heap * $int ) > $int ).

tff(func_def_3,type,
    length: heap > $int ).

tff(func_def_4,type,
    app: ( heap * $int ) > heap ).

tff(func_def_5,type,
    get: heap > heap ).

tff(func_def_10,type,
    sK0: $int ).

tff(func_def_11,type,
    sK1: $int ).

tff(func_def_12,type,
    sK2: heap ).

tff(pred_def_1,type,
    lsls: ( heap * heap ) > $o ).

tff(f299,plain,
    $false,
    inference(avatar_sat_refutation,[],[f81,f86,f90,f94,f98,f103,f107,f111,f115,f119,f123,f127,f131,f135,f139,f143,f147,f151,f162,f166,f170,f174,f178,f192,f196,f200,f204,f208,f212,f216,f262,f266,f292,f298]) ).

tff(f298,plain,
    ( spl3_1
    | spl3_2
    | ~ spl3_33 ),
    inference(avatar_split_clause,[],[f297,f290,f83,f78]) ).

tff(f78,plain,
    ( spl3_1
  <=> ( sK1 = $sum(1,length(sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

tff(f83,plain,
    ( spl3_2
  <=> ( sel(app(sK2,sK0),sK1) = sel(sK2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

tff(f290,plain,
    ( spl3_33
  <=> ! [X2: $int,X0: $int,X1: heap] :
        ( ( sel(app(X1,X0),X2) = sel(X1,X2) )
        | ( $sum(1,length(X1)) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).

tff(f297,plain,
    ( ( sK1 = $sum(1,length(sK2)) )
    | spl3_2
    | ~ spl3_33 ),
    inference(trivial_inequality_removal,[],[f295]) ).

tff(f295,plain,
    ( ( sel(sK2,sK1) != sel(sK2,sK1) )
    | ( sK1 = $sum(1,length(sK2)) )
    | spl3_2
    | ~ spl3_33 ),
    inference(superposition,[],[f85,f291]) ).

tff(f291,plain,
    ( ! [X2: $int,X0: $int,X1: heap] :
        ( ( sel(app(X1,X0),X2) = sel(X1,X2) )
        | ( $sum(1,length(X1)) = X2 ) )
    | ~ spl3_33 ),
    inference(avatar_component_clause,[],[f290]) ).

tff(f85,plain,
    ( ( sel(app(sK2,sK0),sK1) != sel(sK2,sK1) )
    | spl3_2 ),
    inference(avatar_component_clause,[],[f83]) ).

tff(f292,plain,
    spl3_33,
    inference(avatar_split_clause,[],[f64,f290]) ).

tff(f64,plain,
    ! [X2: $int,X0: $int,X1: heap] :
      ( ( sel(app(X1,X0),X2) = sel(X1,X2) )
      | ( $sum(1,length(X1)) = X2 ) ),
    inference(cnf_transformation,[],[f43]) ).

tff(f43,plain,
    ! [X0: $int,X1: heap,X2: $int] :
      ( ( sel(app(X1,X0),X2) = sel(X1,X2) )
      | ( $sum(1,length(X1)) = X2 ) ),
    inference(ennf_transformation,[],[f37]) ).

tff(f37,plain,
    ! [X0: $int,X1: heap,X2: $int] :
      ( ( $sum(1,length(X1)) != X2 )
     => ( sel(app(X1,X0),X2) = sel(X1,X2) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X2: $int,X1: heap,X0: $int] :
      ( ( $sum(1,length(X1)) != X0 )
     => ( sel(app(X1,X2),X0) = sel(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_3) ).

tff(f266,plain,
    spl3_32,
    inference(avatar_split_clause,[],[f67,f264]) ).

tff(f264,plain,
    ( spl3_32
  <=> ! [X2: heap,X0: $int,X1: heap] :
        ( lsls(X1,X2)
        | ( X1 = X2 )
        | ~ lsls(X1,app(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).

tff(f67,plain,
    ! [X2: heap,X0: $int,X1: heap] :
      ( lsls(X1,X2)
      | ( X1 = X2 )
      | ~ lsls(X1,app(X2,X0)) ),
    inference(cnf_transformation,[],[f50]) ).

tff(f50,plain,
    ! [X0: $int,X1: heap,X2: heap] :
      ( ( lsls(X1,app(X2,X0))
        | ( ~ lsls(X1,X2)
          & ( X1 != X2 ) ) )
      & ( lsls(X1,X2)
        | ( X1 = X2 )
        | ~ lsls(X1,app(X2,X0)) ) ),
    inference(flattening,[],[f49]) ).

tff(f49,plain,
    ! [X0: $int,X1: heap,X2: heap] :
      ( ( lsls(X1,app(X2,X0))
        | ( ~ lsls(X1,X2)
          & ( X1 != X2 ) ) )
      & ( lsls(X1,X2)
        | ( X1 = X2 )
        | ~ lsls(X1,app(X2,X0)) ) ),
    inference(nnf_transformation,[],[f40]) ).

tff(f40,plain,
    ! [X0: $int,X1: heap,X2: heap] :
      ( lsls(X1,app(X2,X0))
    <=> ( lsls(X1,X2)
        | ( X1 = X2 ) ) ),
    inference(rectify,[],[f14]) ).

tff(f14,axiom,
    ! [X2: $int,X3: heap,X1: heap] :
      ( lsls(X3,app(X1,X2))
    <=> ( lsls(X3,X1)
        | ( X1 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_30) ).

tff(f262,plain,
    spl3_31,
    inference(avatar_split_clause,[],[f18,f260]) ).

tff(f260,plain,
    ( spl3_31
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).

tff(f18,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
    introduced(theory_axiom_136,[]) ).

tff(f216,plain,
    spl3_30,
    inference(avatar_split_clause,[],[f73,f214]) ).

tff(f214,plain,
    ( spl3_30
  <=> ! [X2: $int,X0: heap] : ( sel(app(X0,X2),$sum(1,length(X0))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).

tff(f73,plain,
    ! [X2: $int,X0: heap] : ( sel(app(X0,X2),$sum(1,length(X0))) = X2 ),
    inference(equality_resolution,[],[f65]) ).

tff(f65,plain,
    ! [X2: $int,X0: heap,X1: $int] :
      ( ( sel(app(X0,X2),X1) = X2 )
      | ( $sum(1,length(X0)) != X1 ) ),
    inference(cnf_transformation,[],[f44]) ).

tff(f44,plain,
    ! [X0: heap,X1: $int,X2: $int] :
      ( ( sel(app(X0,X2),X1) = X2 )
      | ( $sum(1,length(X0)) != X1 ) ),
    inference(ennf_transformation,[],[f38]) ).

tff(f38,plain,
    ! [X0: heap,X1: $int,X2: $int] :
      ( ( $sum(1,length(X0)) = X1 )
     => ( sel(app(X0,X2),X1) = X2 ) ),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X1: heap,X0: $int,X2: $int] :
      ( ( $sum(1,length(X1)) = X0 )
     => ( sel(app(X1,X2),X0) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_2) ).

tff(f212,plain,
    spl3_29,
    inference(avatar_split_clause,[],[f71,f210]) ).

tff(f210,plain,
    ( spl3_29
  <=> ! [X2: $int,X0: heap,X1: heap,X3: $int] :
        ( ( X2 = X3 )
        | ( app(X0,X2) != app(X1,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).

tff(f71,plain,
    ! [X2: $int,X3: $int,X0: heap,X1: heap] :
      ( ( X2 = X3 )
      | ( app(X0,X2) != app(X1,X3) ) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f52,plain,
    ! [X0: heap,X1: heap,X2: $int,X3: $int] :
      ( ( ( app(X0,X2) = app(X1,X3) )
        | ( X2 != X3 )
        | ( X0 != X1 ) )
      & ( ( ( X2 = X3 )
          & ( X0 = X1 ) )
        | ( app(X0,X2) != app(X1,X3) ) ) ),
    inference(flattening,[],[f51]) ).

tff(f51,plain,
    ! [X0: heap,X1: heap,X2: $int,X3: $int] :
      ( ( ( app(X0,X2) = app(X1,X3) )
        | ( X2 != X3 )
        | ( X0 != X1 ) )
      & ( ( ( X2 = X3 )
          & ( X0 = X1 ) )
        | ( app(X0,X2) != app(X1,X3) ) ) ),
    inference(nnf_transformation,[],[f41]) ).

tff(f41,plain,
    ! [X0: heap,X1: heap,X2: $int,X3: $int] :
      ( ( app(X0,X2) = app(X1,X3) )
    <=> ( ( X2 = X3 )
        & ( X0 = X1 ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X1: heap,X3: heap,X2: $int,X4: $int] :
      ( ( app(X1,X2) = app(X3,X4) )
    <=> ( ( X2 = X4 )
        & ( X1 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_22) ).

tff(f208,plain,
    spl3_28,
    inference(avatar_split_clause,[],[f70,f206]) ).

tff(f206,plain,
    ( spl3_28
  <=> ! [X0: heap,X3: $int,X2: $int,X1: heap] :
        ( ( X0 = X1 )
        | ( app(X0,X2) != app(X1,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).

tff(f70,plain,
    ! [X2: $int,X3: $int,X0: heap,X1: heap] :
      ( ( X0 = X1 )
      | ( app(X0,X2) != app(X1,X3) ) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f204,plain,
    spl3_27,
    inference(avatar_split_clause,[],[f59,f202]) ).

tff(f202,plain,
    ( spl3_27
  <=> ! [X0: heap] :
        ( ( app(get(X0),toop(X0)) = X0 )
        | ( empty = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).

tff(f59,plain,
    ! [X0: heap] :
      ( ( app(get(X0),toop(X0)) = X0 )
      | ( empty = X0 ) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: heap] :
      ( ( app(get(X0),toop(X0)) = X0 )
      | ( empty = X0 ) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X1: heap] :
      ( ( app(get(X1),toop(X1)) = X1 )
      | ( empty = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_24) ).

tff(f200,plain,
    ( spl3_26
    | ~ spl3_4
    | ~ spl3_18 ),
    inference(avatar_split_clause,[],[f158,f149,f92,f198]) ).

tff(f198,plain,
    ( spl3_26
  <=> ! [X0: heap,X1: $int] : ~ lsls(app(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).

tff(f92,plain,
    ( spl3_4
  <=> ! [X0: heap] : ~ lsls(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

tff(f149,plain,
    ( spl3_18
  <=> ! [X2: heap,X0: $int,X1: heap] :
        ( lsls(X1,app(X2,X0))
        | ~ lsls(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).

tff(f158,plain,
    ( ! [X0: heap,X1: $int] : ~ lsls(app(X0,X1),X0)
    | ~ spl3_4
    | ~ spl3_18 ),
    inference(resolution,[],[f150,f93]) ).

tff(f93,plain,
    ( ! [X0: heap] : ~ lsls(X0,X0)
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f92]) ).

tff(f150,plain,
    ( ! [X2: heap,X0: $int,X1: heap] :
        ( lsls(X1,app(X2,X0))
        | ~ lsls(X1,X2) )
    | ~ spl3_18 ),
    inference(avatar_component_clause,[],[f149]) ).

tff(f196,plain,
    spl3_25,
    inference(avatar_split_clause,[],[f25,f194]) ).

tff(f194,plain,
    ( spl3_25
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | $less($sum(X0,X2),$sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).

tff(f25,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less($sum(X0,X2),$sum(X1,X2)) ),
    introduced(theory_axiom_145,[]) ).

tff(f192,plain,
    spl3_24,
    inference(avatar_split_clause,[],[f20,f190]) ).

tff(f190,plain,
    ( spl3_24
  <=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).

tff(f20,plain,
    ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
    introduced(theory_axiom_139,[]) ).

tff(f178,plain,
    spl3_23,
    inference(avatar_split_clause,[],[f66,f176]) ).

tff(f176,plain,
    ( spl3_23
  <=> ! [X2: heap,X0: heap,X1: heap] :
        ( lsls(X1,X2)
        | ~ lsls(X0,X2)
        | ~ lsls(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).

tff(f66,plain,
    ! [X2: heap,X0: heap,X1: heap] :
      ( lsls(X1,X2)
      | ~ lsls(X0,X2)
      | ~ lsls(X1,X0) ),
    inference(cnf_transformation,[],[f46]) ).

tff(f46,plain,
    ! [X0: heap,X1: heap,X2: heap] :
      ( lsls(X1,X2)
      | ~ lsls(X0,X2)
      | ~ lsls(X1,X0) ),
    inference(flattening,[],[f45]) ).

tff(f45,plain,
    ! [X0: heap,X1: heap,X2: heap] :
      ( lsls(X1,X2)
      | ~ lsls(X0,X2)
      | ~ lsls(X1,X0) ),
    inference(ennf_transformation,[],[f39]) ).

tff(f39,plain,
    ! [X0: heap,X1: heap,X2: heap] :
      ( ( lsls(X0,X2)
        & lsls(X1,X0) )
     => lsls(X1,X2) ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X3: heap,X1: heap,X5: heap] :
      ( ( lsls(X3,X5)
        & lsls(X1,X3) )
     => lsls(X1,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_28) ).

tff(f174,plain,
    spl3_22,
    inference(avatar_split_clause,[],[f63,f172]) ).

tff(f172,plain,
    ( spl3_22
  <=> ! [X0: $int,X1: heap] : ( $sum(1,length(X1)) = length(app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).

tff(f63,plain,
    ! [X0: $int,X1: heap] : ( $sum(1,length(X1)) = length(app(X1,X0)) ),
    inference(cnf_transformation,[],[f36]) ).

tff(f36,plain,
    ! [X0: $int,X1: heap] : ( $sum(1,length(X1)) = length(app(X1,X0)) ),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X2: $int,X1: heap] : ( $sum(1,length(X1)) = length(app(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_26) ).

tff(f170,plain,
    spl3_21,
    inference(avatar_split_clause,[],[f24,f168]) ).

tff(f168,plain,
    ( spl3_21
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,X0)
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).

tff(f24,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f166,plain,
    spl3_20,
    inference(avatar_split_clause,[],[f23,f164]) ).

tff(f164,plain,
    ( spl3_20
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,X2)
        | $less(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).

tff(f23,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X2)
      | $less(X0,X2) ),
    introduced(theory_axiom_143,[]) ).

tff(f162,plain,
    ( spl3_19
    | ~ spl3_3
    | ~ spl3_16 ),
    inference(avatar_split_clause,[],[f152,f141,f88,f160]) ).

tff(f160,plain,
    ( spl3_19
  <=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).

tff(f88,plain,
    ( spl3_3
  <=> ! [X0: $int] : ~ $less(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

tff(f141,plain,
    ( spl3_16
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).

tff(f152,plain,
    ( ! [X0: $int] : $less(X0,$sum(X0,1))
    | ~ spl3_3
    | ~ spl3_16 ),
    inference(resolution,[],[f142,f89]) ).

tff(f89,plain,
    ( ! [X0: $int] : ~ $less(X0,X0)
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f88]) ).

tff(f142,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(X0,1))
        | $less(X0,X1) )
    | ~ spl3_16 ),
    inference(avatar_component_clause,[],[f141]) ).

tff(f151,plain,
    spl3_18,
    inference(avatar_split_clause,[],[f69,f149]) ).

tff(f69,plain,
    ! [X2: heap,X0: $int,X1: heap] :
      ( lsls(X1,app(X2,X0))
      | ~ lsls(X1,X2) ),
    inference(cnf_transformation,[],[f50]) ).

tff(f147,plain,
    spl3_17,
    inference(avatar_split_clause,[],[f28,f145]) ).

tff(f145,plain,
    ( spl3_17
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).

tff(f28,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_161,[]) ).

tff(f143,plain,
    spl3_16,
    inference(avatar_split_clause,[],[f26,f141]) ).

tff(f26,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_147,[]) ).

tff(f139,plain,
    spl3_15,
    inference(avatar_split_clause,[],[f17,f137]) ).

tff(f137,plain,
    ( spl3_15
  <=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).

tff(f17,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f135,plain,
    spl3_14,
    inference(avatar_split_clause,[],[f62,f133]) ).

tff(f133,plain,
    ( spl3_14
  <=> ! [X0: heap,X1: $int] : ( toop(app(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

tff(f62,plain,
    ! [X0: heap,X1: $int] : ( toop(app(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f35]) ).

tff(f35,plain,
    ! [X0: heap,X1: $int] : ( toop(app(X0,X1)) = X1 ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X1: heap,X2: $int] : ( toop(app(X1,X2)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_21) ).

tff(f131,plain,
    spl3_13,
    inference(avatar_split_clause,[],[f61,f129]) ).

tff(f129,plain,
    ( spl3_13
  <=> ! [X0: $int,X1: heap] : ( get(app(X1,X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

tff(f61,plain,
    ! [X0: $int,X1: heap] : ( get(app(X1,X0)) = X1 ),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0: $int,X1: heap] : ( get(app(X1,X0)) = X1 ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X2: $int,X1: heap] : ( get(app(X1,X2)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_20) ).

tff(f127,plain,
    spl3_12,
    inference(avatar_split_clause,[],[f21,f125]) ).

tff(f125,plain,
    ( spl3_12
  <=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

tff(f21,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f123,plain,
    spl3_11,
    inference(avatar_split_clause,[],[f74,f121]) ).

tff(f121,plain,
    ( spl3_11
  <=> ! [X2: heap,X0: $int] : lsls(X2,app(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

tff(f74,plain,
    ! [X2: heap,X0: $int] : lsls(X2,app(X2,X0)),
    inference(equality_resolution,[],[f68]) ).

tff(f68,plain,
    ! [X2: heap,X0: $int,X1: heap] :
      ( lsls(X1,app(X2,X0))
      | ( X1 != X2 ) ),
    inference(cnf_transformation,[],[f50]) ).

tff(f119,plain,
    spl3_10,
    inference(avatar_split_clause,[],[f60,f117]) ).

tff(f117,plain,
    ( spl3_10
  <=> ! [X0: heap,X1: $int] : ( empty != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

tff(f60,plain,
    ! [X0: heap,X1: $int] : ( empty != app(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f33,plain,
    ! [X0: heap,X1: $int] : ( empty != app(X0,X1) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X1: heap,X2: $int] : ( empty != app(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_23) ).

tff(f115,plain,
    spl3_9,
    inference(avatar_split_clause,[],[f58,f113]) ).

tff(f113,plain,
    ( spl3_9
  <=> ! [X0: $int] : ( sel(empty,X0) = 0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

tff(f58,plain,
    ! [X0: $int] : ( sel(empty,X0) = 0 ),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $int] : ( sel(empty,X0) = 0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_1) ).

tff(f111,plain,
    spl3_8,
    inference(avatar_split_clause,[],[f27,f109]) ).

tff(f109,plain,
    ( spl3_8
  <=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

tff(f27,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f107,plain,
    spl3_7,
    inference(avatar_split_clause,[],[f19,f105]) ).

tff(f105,plain,
    ( spl3_7
  <=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

tff(f19,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f103,plain,
    spl3_6,
    inference(avatar_split_clause,[],[f55,f100]) ).

tff(f100,plain,
    ( spl3_6
  <=> ( 0 = length(empty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

tff(f55,plain,
    0 = length(empty),
    inference(cnf_transformation,[],[f9]) ).

tff(f9,axiom,
    0 = length(empty),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_25) ).

tff(f98,plain,
    spl3_5,
    inference(avatar_split_clause,[],[f57,f96]) ).

tff(f96,plain,
    ( spl3_5
  <=> ! [X0: heap] : ~ lsls(X0,empty) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

tff(f57,plain,
    ! [X0: heap] : ~ lsls(X0,empty),
    inference(cnf_transformation,[],[f31]) ).

tff(f31,plain,
    ! [X0: heap] : ~ lsls(X0,empty),
    inference(rectify,[],[f13]) ).

tff(f13,axiom,
    ! [X1: heap] : ~ lsls(X1,empty),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_29) ).

tff(f94,plain,
    spl3_4,
    inference(avatar_split_clause,[],[f56,f92]) ).

tff(f56,plain,
    ! [X0: heap] : ~ lsls(X0,X0),
    inference(cnf_transformation,[],[f30]) ).

tff(f30,plain,
    ! [X0: heap] : ~ lsls(X0,X0),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X1: heap] : ~ lsls(X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_27) ).

tff(f90,plain,
    spl3_3,
    inference(avatar_split_clause,[],[f22,f88]) ).

tff(f22,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f86,plain,
    ~ spl3_2,
    inference(avatar_split_clause,[],[f53,f83]) ).

tff(f53,plain,
    sel(app(sK2,sK0),sK1) != sel(sK2,sK1),
    inference(cnf_transformation,[],[f48]) ).

tff(f48,plain,
    ( ( sK1 != $sum(1,length(sK2)) )
    & ( sel(app(sK2,sK0),sK1) != sel(sK2,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f42,f47]) ).

tff(f47,plain,
    ( ? [X0: $int,X1: $int,X2: heap] :
        ( ( $sum(1,length(X2)) != X1 )
        & ( sel(app(X2,X0),X1) != sel(X2,X1) ) )
   => ( ( sK1 != $sum(1,length(sK2)) )
      & ( sel(app(sK2,sK0),sK1) != sel(sK2,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f42,plain,
    ? [X0: $int,X1: $int,X2: heap] :
      ( ( $sum(1,length(X2)) != X1 )
      & ( sel(app(X2,X0),X1) != sel(X2,X1) ) ),
    inference(ennf_transformation,[],[f29]) ).

tff(f29,plain,
    ~ ! [X0: $int,X1: $int,X2: heap] :
        ( ( $sum(1,length(X2)) = X1 )
        | ( sel(app(X2,X0),X1) = sel(X2,X1) ) ),
    inference(rectify,[],[f16]) ).

tff(f16,negated_conjecture,
    ~ ! [X2: $int,X0: $int,X1: heap] :
        ( ( $sum(1,length(X1)) = X0 )
        | ( sel(app(X1,X2),X0) = sel(X1,X0) ) ),
    inference(negated_conjecture,[],[f15]) ).

tff(f15,conjecture,
    ! [X2: $int,X0: $int,X1: heap] :
      ( ( $sum(1,length(X1)) = X0 )
      | ( sel(app(X1,X2),X0) = sel(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',th_2) ).

tff(f81,plain,
    ~ spl3_1,
    inference(avatar_split_clause,[],[f54,f78]) ).

tff(f54,plain,
    sK1 != $sum(1,length(sK2)),
    inference(cnf_transformation,[],[f48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : DAT067_1 : TPTP v8.1.2. Released v5.5.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Apr 29 22:02:35 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (29573)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (29577)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  % (29577)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36  % (29577)Terminated due to inappropriate strategy.
% 0.13/0.36  % (29577)------------------------------
% 0.13/0.36  % (29577)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.36  % (29577)Termination reason: Inappropriate
% 0.13/0.36  
% 0.13/0.36  % (29577)Memory used [KB]: 749
% 0.13/0.36  % (29577)Time elapsed: 0.002 s
% 0.13/0.36  % (29577)Instructions burned: 3 (million)
% 0.13/0.36  % (29577)------------------------------
% 0.13/0.36  % (29577)------------------------------
% 0.13/0.37  % (29576)WARNING: value z3 for option sas not known
% 0.13/0.37  % (29574)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (29575)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (29578)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.37  % (29579)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.37  % (29580)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.37  % (29576)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37  % (29574)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37  % (29575)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37  % (29574)Terminated due to inappropriate strategy.
% 0.13/0.37  % (29574)------------------------------
% 0.13/0.37  % (29574)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37  % (29574)Termination reason: Inappropriate
% 0.13/0.37  
% 0.13/0.37  % (29574)Memory used [KB]: 749
% 0.13/0.37  % (29574)Time elapsed: 0.002 s
% 0.13/0.37  % (29574)Instructions burned: 3 (million)
% 0.13/0.37  % (29575)Terminated due to inappropriate strategy.
% 0.13/0.37  % (29575)------------------------------
% 0.13/0.37  % (29575)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37  % (29574)------------------------------
% 0.13/0.37  % (29574)------------------------------
% 0.13/0.37  % (29575)Termination reason: Inappropriate
% 0.13/0.37  
% 0.13/0.37  % (29575)Memory used [KB]: 749
% 0.13/0.37  % (29575)Time elapsed: 0.002 s
% 0.13/0.37  % (29575)Instructions burned: 3 (million)
% 0.13/0.37  % (29575)------------------------------
% 0.13/0.37  % (29575)------------------------------
% 0.13/0.38  % (29578)First to succeed.
% 0.13/0.38  % (29581)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.38  % (29581)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.38  % (29581)Terminated due to inappropriate strategy.
% 0.13/0.38  % (29581)------------------------------
% 0.13/0.38  % (29581)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38  % (29581)Termination reason: Inappropriate
% 0.13/0.38  
% 0.13/0.38  % (29581)Memory used [KB]: 748
% 0.13/0.38  % (29581)Time elapsed: 0.002 s
% 0.13/0.38  % (29581)Instructions burned: 3 (million)
% 0.13/0.38  % (29581)------------------------------
% 0.13/0.38  % (29581)------------------------------
% 0.13/0.38  % (29578)Refutation found. Thanks to Tanya!
% 0.13/0.38  % SZS status Theorem for theBenchmark
% 0.13/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38  % (29578)------------------------------
% 0.13/0.38  % (29578)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38  % (29578)Termination reason: Refutation
% 0.13/0.38  
% 0.13/0.38  % (29578)Memory used [KB]: 921
% 0.13/0.38  % (29578)Time elapsed: 0.012 s
% 0.13/0.38  % (29578)Instructions burned: 15 (million)
% 0.13/0.38  % (29578)------------------------------
% 0.13/0.38  % (29578)------------------------------
% 0.13/0.38  % (29573)Success in time 0.026 s
%------------------------------------------------------------------------------