TSTP Solution File: DAT030_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT030_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n012.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 05:05:41 EDT 2024

% Result   : Theorem 0.22s 0.53s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   59
%            Number of leaves      :   69
% Syntax   : Number of formulae    :  434 (  50 unt;  10 typ;   0 def)
%            Number of atoms       : 1090 ( 125 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives : 1210 ( 544   ~; 547   |;  58   &)
%                                         (  42 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     : 1792 ( 514 atm; 310 fun; 625 num; 343 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   43 (  39 usr;  39 prp; 0-2 aty)
%            Number of functors    :   44 (   8 usr;  38 con; 0-2 aty)
%            Number of variables   :  381 ( 347   !;  34   ?; 381   :)

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

tff(func_def_0,type,
    empty: collection ).

tff(func_def_1,type,
    add: ( $int * collection ) > collection ).

tff(func_def_2,type,
    remove: ( $int * collection ) > collection ).

tff(func_def_7,type,
    sK0: collection ).

tff(func_def_8,type,
    sK1: collection ).

tff(func_def_9,type,
    sK2: $int ).

tff(func_def_10,type,
    sK3: $int > $int ).

tff(func_def_11,type,
    sK4: $int > $int ).

tff(pred_def_1,type,
    in: ( $int * collection ) > $o ).

tff(f3892,plain,
    $false,
    inference(avatar_sat_refutation,[],[f195,f215,f250,f266,f289,f338,f468,f2772,f2783,f2975,f2977,f2979,f2991,f3018,f3079,f3106,f3183,f3258,f3396,f3423,f3508,f3617,f3703,f3731,f3765,f3804,f3871]) ).

tff(f3871,plain,
    ( ~ spl5_2
    | ~ spl5_4 ),
    inference(avatar_contradiction_clause,[],[f3870]) ).

tff(f3870,plain,
    ( $false
    | ~ spl5_2
    | ~ spl5_4 ),
    inference(subsumption_resolution,[],[f3869,f122]) ).

tff(f122,plain,
    ~ $less(sK4(sK2),1),
    inference(resolution,[],[f116,f58]) ).

tff(f58,plain,
    $less(0,sK4(sK2)),
    inference(resolution,[],[f55,f41]) ).

tff(f41,plain,
    in(sK2,sK0),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,plain,
    ( ~ $less(1,sK2)
    & in(sK2,sK0)
    & ! [X3: $int] :
        ( ( ( $sum(sK3(X3),sK4(X3)) = X3 )
          & in(sK4(X3),sK1)
          & in(sK3(X3),sK1) )
        | ~ in(X3,sK0) )
    & ! [X6: $int] :
        ( $less(0,X6)
        | ~ in(X6,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f28,f31,f30,f29]) ).

tff(f29,plain,
    ( ? [X0: collection,X1: collection] :
        ( ? [X2: $int] :
            ( ~ $less(1,X2)
            & in(X2,X0) )
        & ! [X3: $int] :
            ( ? [X4: $int,X5: $int] :
                ( ( $sum(X4,X5) = X3 )
                & in(X5,X1)
                & in(X4,X1) )
            | ~ in(X3,X0) )
        & ! [X6: $int] :
            ( $less(0,X6)
            | ~ in(X6,X1) ) )
   => ( ? [X2: $int] :
          ( ~ $less(1,X2)
          & in(X2,sK0) )
      & ! [X3: $int] :
          ( ? [X5: $int,X4: $int] :
              ( ( $sum(X4,X5) = X3 )
              & in(X5,sK1)
              & in(X4,sK1) )
          | ~ in(X3,sK0) )
      & ! [X6: $int] :
          ( $less(0,X6)
          | ~ in(X6,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f30,plain,
    ( ? [X2: $int] :
        ( ~ $less(1,X2)
        & in(X2,sK0) )
   => ( ~ $less(1,sK2)
      & in(sK2,sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f31,plain,
    ! [X3: $int] :
      ( ? [X5: $int,X4: $int] :
          ( ( $sum(X4,X5) = X3 )
          & in(X5,sK1)
          & in(X4,sK1) )
     => ( ( $sum(sK3(X3),sK4(X3)) = X3 )
        & in(sK4(X3),sK1)
        & in(sK3(X3),sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f28,plain,
    ? [X0: collection,X1: collection] :
      ( ? [X2: $int] :
          ( ~ $less(1,X2)
          & in(X2,X0) )
      & ! [X3: $int] :
          ( ? [X4: $int,X5: $int] :
              ( ( $sum(X4,X5) = X3 )
              & in(X5,X1)
              & in(X4,X1) )
          | ~ in(X3,X0) )
      & ! [X6: $int] :
          ( $less(0,X6)
          | ~ in(X6,X1) ) ),
    inference(rectify,[],[f27]) ).

tff(f27,plain,
    ? [X0: collection,X1: collection] :
      ( ? [X6: $int] :
          ( ~ $less(1,X6)
          & in(X6,X0) )
      & ! [X2: $int] :
          ( ? [X3: $int,X4: $int] :
              ( ( $sum(X3,X4) = X2 )
              & in(X4,X1)
              & in(X3,X1) )
          | ~ in(X2,X0) )
      & ! [X5: $int] :
          ( $less(0,X5)
          | ~ in(X5,X1) ) ),
    inference(flattening,[],[f26]) ).

tff(f26,plain,
    ? [X0: collection,X1: collection] :
      ( ? [X6: $int] :
          ( ~ $less(1,X6)
          & in(X6,X0) )
      & ! [X2: $int] :
          ( ? [X3: $int,X4: $int] :
              ( ( $sum(X3,X4) = X2 )
              & in(X4,X1)
              & in(X3,X1) )
          | ~ in(X2,X0) )
      & ! [X5: $int] :
          ( $less(0,X5)
          | ~ in(X5,X1) ) ),
    inference(ennf_transformation,[],[f21]) ).

tff(f21,plain,
    ~ ! [X0: collection,X1: collection] :
        ( ( ! [X2: $int] :
              ( in(X2,X0)
             => ? [X3: $int,X4: $int] :
                  ( ( $sum(X3,X4) = X2 )
                  & in(X4,X1)
                  & in(X3,X1) ) )
          & ! [X5: $int] :
              ( in(X5,X1)
             => $less(0,X5) ) )
       => ! [X6: $int] :
            ( in(X6,X0)
           => $less(1,X6) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,plain,
    ~ ! [X0: collection,X1: collection] :
        ( ( ! [X3: $int] :
              ( in(X3,X0)
             => ? [X4: $int,X5: $int] :
                  ( ( $sum(X4,X5) = X3 )
                  & in(X5,X1)
                  & in(X4,X1) ) )
          & ! [X2: $int] :
              ( in(X2,X1)
             => $less(0,X2) ) )
       => ! [X6: $int] :
            ( in(X6,X0)
           => $less(1,X6) ) ),
    inference(theory_normalization,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ! [X0: collection,X1: collection] :
        ( ( ! [X3: $int] :
              ( in(X3,X0)
             => ? [X4: $int,X5: $int] :
                  ( ( $sum(X4,X5) = X3 )
                  & in(X5,X1)
                  & in(X4,X1) ) )
          & ! [X2: $int] :
              ( in(X2,X1)
             => $greater(X2,0) ) )
       => ! [X6: $int] :
            ( in(X6,X0)
           => $greater(X6,1) ) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ! [X0: collection,X1: collection] :
      ( ( ! [X3: $int] :
            ( in(X3,X0)
           => ? [X4: $int,X5: $int] :
                ( ( $sum(X4,X5) = X3 )
                & in(X5,X1)
                & in(X4,X1) ) )
        & ! [X2: $int] :
            ( in(X2,X1)
           => $greater(X2,0) ) )
     => ! [X6: $int] :
          ( in(X6,X0)
         => $greater(X6,1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f55,plain,
    ! [X0: $int] :
      ( ~ in(X0,sK0)
      | $less(0,sK4(X0)) ),
    inference(resolution,[],[f39,f37]) ).

tff(f37,plain,
    ! [X6: $int] :
      ( ~ in(X6,sK1)
      | $less(0,X6) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f39,plain,
    ! [X3: $int] :
      ( in(sK4(X3),sK1)
      | ~ in(X3,sK0) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f116,plain,
    ! [X0: $int] :
      ( ~ $less(0,X0)
      | ~ $less(X0,1) ),
    inference(superposition,[],[f86,f11]) ).

tff(f11,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f86,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$sum(1,X0))
      | ~ $less(X0,X1) ),
    inference(superposition,[],[f20,f9]) ).

tff(f9,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f20,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$sum(X0,1))
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_161,[]) ).

tff(f3869,plain,
    ( $less(sK4(sK2),1)
    | ~ spl5_2
    | ~ spl5_4 ),
    inference(subsumption_resolution,[],[f3824,f214]) ).

tff(f214,plain,
    ( $less(1,sK3(sK2))
    | ~ spl5_4 ),
    inference(avatar_component_clause,[],[f212]) ).

tff(f212,plain,
    ( spl5_4
  <=> $less(1,sK3(sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

tff(f3824,plain,
    ( ~ $less(1,sK3(sK2))
    | $less(sK4(sK2),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f308,f1134]) ).

tff(f1134,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(1,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1132]) ).

tff(f1132,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-1),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1124,f386]) ).

tff(f386,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
    inference(evaluation,[],[f365]) ).

tff(f365,plain,
    ! [X0: $int,X1: $int] : ( $sum(0,X1) = $sum(X0,$sum($uminus(X0),X1)) ),
    inference(superposition,[],[f10,f13]) ).

tff(f13,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f10,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
    introduced(theory_axiom_136,[]) ).

tff(f1124,plain,
    ( ! [X0: $int] :
        ( $less($sum(-1,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1080,f9]) ).

tff(f1080,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-1),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f508]) ).

tff(f508,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-1,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f499,f15]) ).

tff(f15,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X2)
      | ~ $less(X0,X1)
      | $less(X0,X2) ),
    introduced(theory_axiom_143,[]) ).

tff(f499,plain,
    ( $less($sum(-1,sK2),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f492,f470]) ).

tff(f470,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f194,f15]) ).

tff(f194,plain,
    ( $less(sK2,1)
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f192]) ).

tff(f192,plain,
    ( spl5_2
  <=> $less(sK2,1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

tff(f492,plain,
    ! [X0: $int] : $less($sum(-1,X0),X0),
    inference(evaluation,[],[f491]) ).

tff(f491,plain,
    ! [X0: $int] : $less($sum($uminus(1),X0),X0),
    inference(superposition,[],[f76,f386]) ).

tff(f76,plain,
    ! [X0: $int] : $less(X0,$sum(1,X0)),
    inference(superposition,[],[f71,f9]) ).

tff(f71,plain,
    ! [X0: $int] : $less(X0,$sum(X0,1)),
    inference(resolution,[],[f18,f14]) ).

tff(f14,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f18,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,1))
      | $less(X0,X1) ),
    introduced(theory_axiom_147,[]) ).

tff(f304,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($sum(X2,X1),$sum(X1,X0))
      | ~ $less(X2,X0) ),
    inference(superposition,[],[f17,f9]) ).

tff(f17,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($sum(X0,X2),$sum(X1,X2))
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_145,[]) ).

tff(f308,plain,
    ! [X0: $int] :
      ( $less($sum(X0,sK4(sK2)),sK2)
      | ~ $less(X0,sK3(sK2)) ),
    inference(superposition,[],[f17,f70]) ).

tff(f70,plain,
    sK2 = $sum(sK3(sK2),sK4(sK2)),
    inference(resolution,[],[f40,f41]) ).

tff(f40,plain,
    ! [X3: $int] :
      ( ~ in(X3,sK0)
      | ( $sum(sK3(X3),sK4(X3)) = X3 ) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f3804,plain,
    ( ~ spl5_37
    | spl5_38
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2746,f192,f3801,f3797]) ).

tff(f3797,plain,
    ( spl5_37
  <=> $less(16,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_37])]) ).

tff(f3801,plain,
    ( spl5_38
  <=> ( sK2 = 17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_38])]) ).

tff(f2746,plain,
    ( ( sK2 = 17 )
    | ~ $less(16,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2698]) ).

tff(f2698,plain,
    ( ( sK2 = $sum(16,1) )
    | ~ $less(16,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f2101]) ).

tff(f2101,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(16,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f2096]) ).

tff(f2096,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-16),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f2075,f386]) ).

tff(f2075,plain,
    ( ! [X0: $int] :
        ( $less($sum(-16,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1095,f9]) ).

tff(f1095,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-16),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f937]) ).

tff(f937,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-16,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f935,f15]) ).

tff(f935,plain,
    ( $less($sum(-16,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f933]) ).

tff(f933,plain,
    ( $less($sum($sum(-15,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f916,f500]) ).

tff(f500,plain,
    ! [X0: $int] : $less($sum(X0,-1),X0),
    inference(superposition,[],[f492,f9]) ).

tff(f916,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-15,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f914,f15]) ).

tff(f914,plain,
    ( $less($sum(-15,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f912]) ).

tff(f912,plain,
    ( $less($sum($sum(-14,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f895,f500]) ).

tff(f895,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-14,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f893,f15]) ).

tff(f893,plain,
    ( $less($sum(-14,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f891]) ).

tff(f891,plain,
    ( $less($sum($sum(-13,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f874,f500]) ).

tff(f874,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-13,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f872,f15]) ).

tff(f872,plain,
    ( $less($sum(-13,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f870]) ).

tff(f870,plain,
    ( $less($sum($sum(-12,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f853,f500]) ).

tff(f853,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-12,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f851,f15]) ).

tff(f851,plain,
    ( $less($sum(-12,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f849]) ).

tff(f849,plain,
    ( $less($sum($sum(-11,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f832,f500]) ).

tff(f832,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-11,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f830,f15]) ).

tff(f830,plain,
    ( $less($sum(-11,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f828]) ).

tff(f828,plain,
    ( $less($sum($sum(-10,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f773,f500]) ).

tff(f773,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-10,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f771,f15]) ).

tff(f771,plain,
    ( $less($sum(-10,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f769]) ).

tff(f769,plain,
    ( $less($sum($sum(-9,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f752,f500]) ).

tff(f752,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-9,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f750,f15]) ).

tff(f750,plain,
    ( $less($sum(-9,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f748]) ).

tff(f748,plain,
    ( $less($sum($sum(-8,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f700,f500]) ).

tff(f700,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-8,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f698,f15]) ).

tff(f698,plain,
    ( $less($sum(-8,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f696]) ).

tff(f696,plain,
    ( $less($sum($sum(-7,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f679,f500]) ).

tff(f679,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-7,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f677,f15]) ).

tff(f677,plain,
    ( $less($sum(-7,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f675]) ).

tff(f675,plain,
    ( $less($sum($sum(-6,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f635,f500]) ).

tff(f635,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-6,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f633,f15]) ).

tff(f633,plain,
    ( $less($sum(-6,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f631]) ).

tff(f631,plain,
    ( $less($sum($sum(-5,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f614,f500]) ).

tff(f614,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-5,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f612,f15]) ).

tff(f612,plain,
    ( $less($sum(-5,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f610]) ).

tff(f610,plain,
    ( $less($sum($sum(-4,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f583,f500]) ).

tff(f583,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-4,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f581,f15]) ).

tff(f581,plain,
    ( $less($sum(-4,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f579]) ).

tff(f579,plain,
    ( $less($sum($sum(-3,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f562,f500]) ).

tff(f562,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-3,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f548,f15]) ).

tff(f548,plain,
    ( $less($sum(-3,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f546]) ).

tff(f546,plain,
    ( $less($sum($sum(-2,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f535,f500]) ).

tff(f535,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(-2,sK2))
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f533,f15]) ).

tff(f533,plain,
    ( $less($sum(-2,sK2),1)
    | ~ spl5_2 ),
    inference(evaluation,[],[f531]) ).

tff(f531,plain,
    ( $less($sum($sum(-1,sK2),-1),1)
    | ~ spl5_2 ),
    inference(resolution,[],[f508,f500]) ).

tff(f163,plain,
    ! [X0: $int,X1: $int] :
      ( $less($sum(X0,1),X1)
      | ( $sum(X0,1) = X1 )
      | ~ $less(X0,X1) ),
    inference(resolution,[],[f16,f20]) ).

tff(f16,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f3765,plain,
    ( ~ spl5_35
    | spl5_36
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2747,f192,f3762,f3758]) ).

tff(f3758,plain,
    ( spl5_35
  <=> $less(15,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_35])]) ).

tff(f3762,plain,
    ( spl5_36
  <=> ( sK2 = 16 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_36])]) ).

tff(f2747,plain,
    ( ( sK2 = 16 )
    | ~ $less(15,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2697]) ).

tff(f2697,plain,
    ( ( sK2 = $sum(15,1) )
    | ~ $less(15,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f2065]) ).

tff(f2065,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(15,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f2060]) ).

tff(f2060,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-15),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f2039,f386]) ).

tff(f2039,plain,
    ( ! [X0: $int] :
        ( $less($sum(-15,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1094,f9]) ).

tff(f1094,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-15),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f916]) ).

tff(f3731,plain,
    ( ~ spl5_33
    | spl5_34
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2748,f192,f3728,f3724]) ).

tff(f3724,plain,
    ( spl5_33
  <=> $less(14,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_33])]) ).

tff(f3728,plain,
    ( spl5_34
  <=> ( sK2 = 15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_34])]) ).

tff(f2748,plain,
    ( ( sK2 = 15 )
    | ~ $less(14,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2696]) ).

tff(f2696,plain,
    ( ( sK2 = $sum(14,1) )
    | ~ $less(14,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f2029]) ).

tff(f2029,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(14,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f2024]) ).

tff(f2024,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-14),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f2003,f386]) ).

tff(f2003,plain,
    ( ! [X0: $int] :
        ( $less($sum(-14,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1093,f9]) ).

tff(f1093,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-14),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f895]) ).

tff(f3703,plain,
    ( ~ spl5_31
    | spl5_32
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2749,f192,f3700,f3696]) ).

tff(f3696,plain,
    ( spl5_31
  <=> $less(13,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_31])]) ).

tff(f3700,plain,
    ( spl5_32
  <=> ( sK2 = 14 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_32])]) ).

tff(f2749,plain,
    ( ( sK2 = 14 )
    | ~ $less(13,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2695]) ).

tff(f2695,plain,
    ( ( sK2 = $sum(13,1) )
    | ~ $less(13,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1993]) ).

tff(f1993,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(13,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1988]) ).

tff(f1988,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-13),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1763,f386]) ).

tff(f1763,plain,
    ( ! [X0: $int] :
        ( $less($sum(-13,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1092,f9]) ).

tff(f1092,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-13),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f874]) ).

tff(f3617,plain,
    ( ~ spl5_29
    | spl5_30
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2750,f192,f3614,f3610]) ).

tff(f3610,plain,
    ( spl5_29
  <=> $less(12,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_29])]) ).

tff(f3614,plain,
    ( spl5_30
  <=> ( sK2 = 13 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_30])]) ).

tff(f2750,plain,
    ( ( sK2 = 13 )
    | ~ $less(12,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2694]) ).

tff(f2694,plain,
    ( ( sK2 = $sum(12,1) )
    | ~ $less(12,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1753]) ).

tff(f1753,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(12,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1750]) ).

tff(f1750,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-12),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1731,f386]) ).

tff(f1731,plain,
    ( ! [X0: $int] :
        ( $less($sum(-12,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1091,f9]) ).

tff(f1091,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-12),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f853]) ).

tff(f3508,plain,
    ( ~ spl5_27
    | spl5_28
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2751,f192,f3505,f3501]) ).

tff(f3501,plain,
    ( spl5_27
  <=> $less(11,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_27])]) ).

tff(f3505,plain,
    ( spl5_28
  <=> ( sK2 = 12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_28])]) ).

tff(f2751,plain,
    ( ( sK2 = 12 )
    | ~ $less(11,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2693]) ).

tff(f2693,plain,
    ( ( sK2 = $sum(11,1) )
    | ~ $less(11,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1721]) ).

tff(f1721,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(11,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1718]) ).

tff(f1718,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-11),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1699,f386]) ).

tff(f1699,plain,
    ( ! [X0: $int] :
        ( $less($sum(-11,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1090,f9]) ).

tff(f1090,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-11),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f832]) ).

tff(f3423,plain,
    ( ~ spl5_25
    | spl5_26
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2752,f192,f3420,f3416]) ).

tff(f3416,plain,
    ( spl5_25
  <=> $less(10,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_25])]) ).

tff(f3420,plain,
    ( spl5_26
  <=> ( sK2 = 11 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_26])]) ).

tff(f2752,plain,
    ( ( sK2 = 11 )
    | ~ $less(10,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2692]) ).

tff(f2692,plain,
    ( ( sK2 = $sum(10,1) )
    | ~ $less(10,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1689]) ).

tff(f1689,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(10,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1686]) ).

tff(f1686,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-10),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1667,f386]) ).

tff(f1667,plain,
    ( ! [X0: $int] :
        ( $less($sum(-10,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1089,f9]) ).

tff(f1089,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-10),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f773]) ).

tff(f3396,plain,
    ( ~ spl5_23
    | spl5_24
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2753,f192,f3393,f3389]) ).

tff(f3389,plain,
    ( spl5_23
  <=> $less(9,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).

tff(f3393,plain,
    ( spl5_24
  <=> ( sK2 = 10 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).

tff(f2753,plain,
    ( ( sK2 = 10 )
    | ~ $less(9,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2691]) ).

tff(f2691,plain,
    ( ( sK2 = $sum(9,1) )
    | ~ $less(9,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1567]) ).

tff(f1567,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(9,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1564]) ).

tff(f1564,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-9),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1546,f386]) ).

tff(f1546,plain,
    ( ! [X0: $int] :
        ( $less($sum(-9,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1088,f9]) ).

tff(f1088,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-9),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f752]) ).

tff(f3258,plain,
    ( ~ spl5_21
    | spl5_22
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2754,f192,f3255,f3251]) ).

tff(f3251,plain,
    ( spl5_21
  <=> $less(8,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).

tff(f3255,plain,
    ( spl5_22
  <=> ( sK2 = 9 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).

tff(f2754,plain,
    ( ( sK2 = 9 )
    | ~ $less(8,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2690]) ).

tff(f2690,plain,
    ( ( sK2 = $sum(8,1) )
    | ~ $less(8,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1398]) ).

tff(f1398,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(8,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1395]) ).

tff(f1395,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-8),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1378,f386]) ).

tff(f1378,plain,
    ( ! [X0: $int] :
        ( $less($sum(-8,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1087,f9]) ).

tff(f1087,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-8),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f700]) ).

tff(f3183,plain,
    ( ~ spl5_19
    | spl5_20
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2755,f192,f3180,f3176]) ).

tff(f3176,plain,
    ( spl5_19
  <=> $less(7,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).

tff(f3180,plain,
    ( spl5_20
  <=> ( sK2 = 8 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).

tff(f2755,plain,
    ( ( sK2 = 8 )
    | ~ $less(7,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2689]) ).

tff(f2689,plain,
    ( ( sK2 = $sum(7,1) )
    | ~ $less(7,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1370]) ).

tff(f1370,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(7,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1367]) ).

tff(f1367,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-7),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1350,f386]) ).

tff(f1350,plain,
    ( ! [X0: $int] :
        ( $less($sum(-7,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1086,f9]) ).

tff(f1086,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-7),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f679]) ).

tff(f3106,plain,
    ( ~ spl5_17
    | spl5_18
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2756,f192,f3103,f3099]) ).

tff(f3099,plain,
    ( spl5_17
  <=> $less(6,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).

tff(f3103,plain,
    ( spl5_18
  <=> ( sK2 = 7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).

tff(f2756,plain,
    ( ( sK2 = 7 )
    | ~ $less(6,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2688]) ).

tff(f2688,plain,
    ( ( sK2 = $sum(6,1) )
    | ~ $less(6,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1342]) ).

tff(f1342,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(6,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1339]) ).

tff(f1339,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-6),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1322,f386]) ).

tff(f1322,plain,
    ( ! [X0: $int] :
        ( $less($sum(-6,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1085,f9]) ).

tff(f1085,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-6),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f635]) ).

tff(f3079,plain,
    ( ~ spl5_15
    | spl5_16
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2757,f192,f3076,f3072]) ).

tff(f3072,plain,
    ( spl5_15
  <=> $less(5,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).

tff(f3076,plain,
    ( spl5_16
  <=> ( sK2 = 6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).

tff(f2757,plain,
    ( ( sK2 = 6 )
    | ~ $less(5,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2687]) ).

tff(f2687,plain,
    ( ( sK2 = $sum(5,1) )
    | ~ $less(5,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1314]) ).

tff(f1314,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(5,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1311]) ).

tff(f1311,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-5),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1214,f386]) ).

tff(f1214,plain,
    ( ! [X0: $int] :
        ( $less($sum(-5,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1084,f9]) ).

tff(f1084,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-5),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f614]) ).

tff(f3018,plain,
    ( ~ spl5_13
    | spl5_14
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2758,f192,f3015,f3011]) ).

tff(f3011,plain,
    ( spl5_13
  <=> $less(4,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).

tff(f3015,plain,
    ( spl5_14
  <=> ( sK2 = 5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).

tff(f2758,plain,
    ( ( sK2 = 5 )
    | ~ $less(4,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2686]) ).

tff(f2686,plain,
    ( ( sK2 = $sum(4,1) )
    | ~ $less(4,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1206]) ).

tff(f1206,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(4,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1204]) ).

tff(f1204,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-4),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1188,f386]) ).

tff(f1188,plain,
    ( ! [X0: $int] :
        ( $less($sum(-4,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1083,f9]) ).

tff(f1083,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-4),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f583]) ).

tff(f2991,plain,
    ( ~ spl5_11
    | spl5_12
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2759,f192,f2988,f2984]) ).

tff(f2984,plain,
    ( spl5_11
  <=> $less(3,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).

tff(f2988,plain,
    ( spl5_12
  <=> ( sK2 = 4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).

tff(f2759,plain,
    ( ( sK2 = 4 )
    | ~ $less(3,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2685]) ).

tff(f2685,plain,
    ( ( sK2 = $sum(3,1) )
    | ~ $less(3,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1180]) ).

tff(f1180,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(3,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1178]) ).

tff(f1178,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-3),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1162,f386]) ).

tff(f1162,plain,
    ( ! [X0: $int] :
        ( $less($sum(-3,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1082,f9]) ).

tff(f1082,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-3),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f562]) ).

tff(f2979,plain,
    ~ spl5_9,
    inference(avatar_contradiction_clause,[],[f2978]) ).

tff(f2978,plain,
    ( $false
    | ~ spl5_9 ),
    inference(evaluation,[],[f2785]) ).

tff(f2785,plain,
    ( ~ $less(1,2)
    | ~ spl5_9 ),
    inference(superposition,[],[f42,f2778]) ).

tff(f2778,plain,
    ( ( sK2 = 2 )
    | ~ spl5_9 ),
    inference(avatar_component_clause,[],[f2776]) ).

tff(f2776,plain,
    ( spl5_9
  <=> ( sK2 = 2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).

tff(f42,plain,
    ~ $less(1,sK2),
    inference(cnf_transformation,[],[f32]) ).

tff(f2977,plain,
    ( ~ spl5_2
    | ~ spl5_9 ),
    inference(avatar_contradiction_clause,[],[f2976]) ).

tff(f2976,plain,
    ( $false
    | ~ spl5_2
    | ~ spl5_9 ),
    inference(evaluation,[],[f2801]) ).

tff(f2801,plain,
    ( $less(2,1)
    | ~ spl5_2
    | ~ spl5_9 ),
    inference(superposition,[],[f194,f2778]) ).

tff(f2975,plain,
    ( ~ spl5_2
    | ~ spl5_9 ),
    inference(avatar_contradiction_clause,[],[f2974]) ).

tff(f2974,plain,
    ( $false
    | ~ spl5_2
    | ~ spl5_9 ),
    inference(evaluation,[],[f2810]) ).

tff(f2810,plain,
    ( $less($sum(-1,2),1)
    | ~ spl5_2
    | ~ spl5_9 ),
    inference(superposition,[],[f499,f2778]) ).

tff(f2783,plain,
    ( spl5_9
    | spl5_10
    | spl5_7 ),
    inference(avatar_split_clause,[],[f2773,f2765,f2780,f2776]) ).

tff(f2780,plain,
    ( spl5_10
  <=> $less(sK2,2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).

tff(f2765,plain,
    ( spl5_7
  <=> $less(2,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

tff(f2773,plain,
    ( $less(sK2,2)
    | ( sK2 = 2 )
    | spl5_7 ),
    inference(resolution,[],[f2767,f16]) ).

tff(f2767,plain,
    ( ~ $less(2,sK2)
    | spl5_7 ),
    inference(avatar_component_clause,[],[f2765]) ).

tff(f2772,plain,
    ( ~ spl5_7
    | spl5_8
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f2760,f192,f2769,f2765]) ).

tff(f2769,plain,
    ( spl5_8
  <=> ( sK2 = 3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).

tff(f2760,plain,
    ( ( sK2 = 3 )
    | ~ $less(2,sK2)
    | ~ spl5_2 ),
    inference(evaluation,[],[f2684]) ).

tff(f2684,plain,
    ( ( sK2 = $sum(2,1) )
    | ~ $less(2,sK2)
    | $less(1,1)
    | ~ spl5_2 ),
    inference(resolution,[],[f163,f1154]) ).

tff(f1154,plain,
    ( ! [X0: $int] :
        ( ~ $less($sum(2,X0),sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(evaluation,[],[f1152]) ).

tff(f1152,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less($sum($uminus(-2),X0),sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1136,f386]) ).

tff(f1136,plain,
    ( ! [X0: $int] :
        ( $less($sum(-2,X0),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(superposition,[],[f1081,f9]) ).

tff(f1081,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-2),1)
        | ~ $less(X0,sK2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f304,f535]) ).

tff(f468,plain,
    ~ spl5_1,
    inference(avatar_contradiction_clause,[],[f467]) ).

tff(f467,plain,
    ( $false
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f466,f316]) ).

tff(f316,plain,
    ( $less(0,sK3(1))
    | ~ spl5_1 ),
    inference(superposition,[],[f57,f190]) ).

tff(f190,plain,
    ( ( 1 = sK2 )
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f188]) ).

tff(f188,plain,
    ( spl5_1
  <=> ( 1 = sK2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

tff(f57,plain,
    $less(0,sK3(sK2)),
    inference(resolution,[],[f54,f41]) ).

tff(f54,plain,
    ! [X0: $int] :
      ( ~ in(X0,sK0)
      | $less(0,sK3(X0)) ),
    inference(resolution,[],[f38,f37]) ).

tff(f38,plain,
    ! [X3: $int] :
      ( in(sK3(X3),sK1)
      | ~ in(X3,sK0) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f466,plain,
    ( ~ $less(0,sK3(1))
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f462,f320]) ).

tff(f320,plain,
    ( ~ $less(sK4(1),1)
    | ~ spl5_1 ),
    inference(superposition,[],[f122,f190]) ).

tff(f462,plain,
    ( $less(sK4(1),1)
    | ~ $less(0,sK3(1))
    | ~ spl5_1 ),
    inference(superposition,[],[f444,f11]) ).

tff(f444,plain,
    ( ! [X0: $int] :
        ( $less($sum(sK4(1),X0),1)
        | ~ $less(X0,sK3(1)) )
    | ~ spl5_1 ),
    inference(superposition,[],[f340,f9]) ).

tff(f340,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,sK4(1)),1)
        | ~ $less(X0,sK3(1)) )
    | ~ spl5_1 ),
    inference(forward_demodulation,[],[f339,f190]) ).

tff(f339,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,sK4(1)),1)
        | ~ $less(X0,sK3(sK2)) )
    | ~ spl5_1 ),
    inference(forward_demodulation,[],[f308,f190]) ).

tff(f338,plain,
    ( ~ spl5_1
    | ~ spl5_5 ),
    inference(avatar_contradiction_clause,[],[f337]) ).

tff(f337,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_5 ),
    inference(global_subsumption,[],[f10,f52,f46,f51,f53,f41,f42,f14,f43,f37,f11,f19,f44,f45,f38,f39,f13,f54,f57,f55,f58,f56,f9,f40,f70,f18,f73,f71,f77,f76,f20,f87,f75,f92,f89,f94,f47,f49,f72,f100,f101,f109,f86,f110,f115,f116,f124,f127,f121,f15,f133,f134,f135,f136,f137,f138,f139,f140,f122,f131,f143,f146,f142,f147,f132,f151,f154,f150,f155,f149,f159,f158,f16,f163,f164,f165,f166,f173,f175,f176,f177,f178,f180,f183,f185,f167,f157,f202,f201,f168,f12,f228,f229,f232,f233,f236,f237,f171,f261,f270,f273,f276,f268,f279,f280,f281,f283,f284,f285,f282,f287,f179,f17,f291,f293,f295,f296,f297,f298,f299,f312,f301,f303,f304,f305,f306,f307,f313,f309,f190,f314,f316,f317,f318,f319,f320,f321,f322,f323,f324,f325,f326,f327,f328,f329,f330,f334,f335,f336]) ).

tff(f336,plain,
    ( $less(sK3(1),1)
    | ~ spl5_1
    | ~ spl5_5 ),
    inference(superposition,[],[f282,f190]) ).

tff(f335,plain,
    ( ( 1 = $sum(sK3(1),1) )
    | ~ spl5_1
    | ~ spl5_5 ),
    inference(superposition,[],[f268,f190]) ).

tff(f334,plain,
    ( ( 1 = sK4(1) )
    | ~ spl5_1
    | ~ spl5_5 ),
    inference(superposition,[],[f261,f190]) ).

tff(f330,plain,
    ( ~ $less(sK4(1),-1)
    | ~ spl5_1 ),
    inference(superposition,[],[f201,f190]) ).

tff(f329,plain,
    ( ~ $less(sK3(1),-1)
    | ~ spl5_1 ),
    inference(superposition,[],[f158,f190]) ).

tff(f328,plain,
    ( ! [X0: $int] :
        ( $less(X0,sK4(1))
        | ~ $less(X0,-1) )
    | ~ spl5_1 ),
    inference(superposition,[],[f157,f190]) ).

tff(f327,plain,
    ( $less(-1,sK4(1))
    | ~ spl5_1 ),
    inference(superposition,[],[f155,f190]) ).

tff(f326,plain,
    ( ~ $less(sK4(1),0)
    | ~ spl5_1 ),
    inference(superposition,[],[f150,f190]) ).

tff(f325,plain,
    ( ! [X0: $int] :
        ( $less(X0,sK3(1))
        | ~ $less(X0,-1) )
    | ~ spl5_1 ),
    inference(superposition,[],[f149,f190]) ).

tff(f324,plain,
    ( $less(-1,sK3(1))
    | ~ spl5_1 ),
    inference(superposition,[],[f147,f190]) ).

tff(f323,plain,
    ( ~ $less(sK3(1),0)
    | ~ spl5_1 ),
    inference(superposition,[],[f142,f190]) ).

tff(f322,plain,
    ( ! [X0: $int] :
        ( $less(X0,sK4(1))
        | ~ $less(X0,0) )
    | ~ spl5_1 ),
    inference(superposition,[],[f132,f190]) ).

tff(f321,plain,
    ( ! [X0: $int] :
        ( $less(X0,sK3(1))
        | ~ $less(X0,0) )
    | ~ spl5_1 ),
    inference(superposition,[],[f131,f190]) ).

tff(f319,plain,
    ( ~ $less(sK3(1),1)
    | ~ spl5_1 ),
    inference(superposition,[],[f121,f190]) ).

tff(f318,plain,
    ( ( 1 = $sum(sK3(1),sK4(1)) )
    | ~ spl5_1 ),
    inference(superposition,[],[f70,f190]) ).

tff(f317,plain,
    ( $less(0,sK4(1))
    | ~ spl5_1 ),
    inference(superposition,[],[f58,f190]) ).

tff(f314,plain,
    ( in(1,sK0)
    | ~ spl5_1 ),
    inference(superposition,[],[f41,f190]) ).

tff(f309,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,1),sK2)
        | ~ $less(X0,sK3(sK2)) )
    | ~ spl5_5 ),
    inference(superposition,[],[f17,f268]) ).

tff(f313,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,1),sK2)
        | ~ $less(X0,sK3(sK2)) )
    | ~ spl5_5 ),
    inference(forward_demodulation,[],[f308,f261]) ).

tff(f307,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
      | ~ $less(X2,$uminus(X0)) ),
    inference(superposition,[],[f17,f12]) ).

tff(f306,plain,
    ! [X0: $int,X1: $int] :
      ( $less($sum(X1,X0),0)
      | ~ $less(X1,$uminus(X0)) ),
    inference(superposition,[],[f17,f56]) ).

tff(f305,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($sum(X2,X1),$sum(X1,X0))
      | ~ $less(X2,X0) ),
    inference(superposition,[],[f17,f9]) ).

tff(f303,plain,
    ! [X0: $int,X1: $int] :
      ( $less($sum(X1,$uminus(X0)),0)
      | ~ $less(X1,X0) ),
    inference(superposition,[],[f17,f13]) ).

tff(f301,plain,
    ( ! [X0: $int] :
        ( $less(sK2,$sum(X0,1))
        | ~ $less(sK3(sK2),X0) )
    | ~ spl5_5 ),
    inference(superposition,[],[f17,f268]) ).

tff(f312,plain,
    ( ! [X0: $int] :
        ( $less(sK2,$sum(X0,1))
        | ~ $less(sK3(sK2),X0) )
    | ~ spl5_5 ),
    inference(forward_demodulation,[],[f300,f261]) ).

tff(f300,plain,
    ! [X0: $int] :
      ( $less(sK2,$sum(X0,sK4(sK2)))
      | ~ $less(sK3(sK2),X0) ),
    inference(superposition,[],[f17,f70]) ).

tff(f299,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
      | ~ $less($uminus(X0),X2) ),
    inference(superposition,[],[f17,f12]) ).

tff(f298,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,$sum(X1,X0))
      | ~ $less($uminus(X0),X1) ),
    inference(superposition,[],[f17,f56]) ).

tff(f297,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($sum(X1,X0),$sum(X2,X1))
      | ~ $less(X0,X2) ),
    inference(superposition,[],[f17,f9]) ).

tff(f296,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($sum(X1,X0),$sum(X2,X1))
      | ~ $less(X0,X2) ),
    inference(superposition,[],[f17,f9]) ).

tff(f295,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,$sum(X1,$uminus(X0)))
      | ~ $less(X0,X1) ),
    inference(superposition,[],[f17,f13]) ).

tff(f293,plain,
    ! [X2: $int,X3: $int,X0: $int,X1: $int] :
      ( ~ $less(X2,$sum(X0,X3))
      | ~ $less(X0,X1)
      | $less(X2,$sum(X1,X3)) ),
    inference(resolution,[],[f17,f15]) ).

tff(f291,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,1)
      | ~ $less(X1,$sum(X0,X1)) ),
    inference(resolution,[],[f17,f86]) ).

tff(f179,plain,
    ( $less(sK2,1)
    | ( 1 = sK2 ) ),
    inference(resolution,[],[f16,f42]) ).

tff(f287,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,sK3(sK2))
        | $less(X0,sK2) )
    | ~ spl5_5 ),
    inference(resolution,[],[f282,f15]) ).

tff(f282,plain,
    ( $less(sK3(sK2),sK2)
    | ~ spl5_5 ),
    inference(superposition,[],[f71,f268]) ).

tff(f285,plain,
    ( ( sK2 = $sum(1,sK3(sK2)) )
    | ~ spl5_5 ),
    inference(superposition,[],[f9,f268]) ).

tff(f284,plain,
    ( ( sK2 = $sum(1,sK3(sK2)) )
    | ~ spl5_5 ),
    inference(superposition,[],[f9,f268]) ).

tff(f283,plain,
    ( ! [X0: $int] :
        ( $less(X0,sK2)
        | $less(sK3(sK2),X0) )
    | ~ spl5_5 ),
    inference(superposition,[],[f18,f268]) ).

tff(f281,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,sK2)
        | ~ $less(sK3(sK2),X0) )
    | ~ spl5_5 ),
    inference(superposition,[],[f20,f268]) ).

tff(f280,plain,
    ( ( sK2 = $sum(1,sK3(sK2)) )
    | ~ spl5_5 ),
    inference(superposition,[],[f268,f9]) ).

tff(f279,plain,
    ( ( sK2 = $sum(1,sK3(sK2)) )
    | ~ spl5_5 ),
    inference(superposition,[],[f268,f9]) ).

tff(f268,plain,
    ( ( sK2 = $sum(sK3(sK2),1) )
    | ~ spl5_5 ),
    inference(superposition,[],[f70,f261]) ).

tff(f276,plain,
    ( in(1,sK1)
    | ~ spl5_5 ),
    inference(subsumption_resolution,[],[f275,f41]) ).

tff(f275,plain,
    ( in(1,sK1)
    | ~ in(sK2,sK0)
    | ~ spl5_5 ),
    inference(superposition,[],[f39,f261]) ).

tff(f273,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less(X0,-1) )
    | ~ spl5_5 ),
    inference(superposition,[],[f157,f261]) ).

tff(f270,plain,
    ( ! [X0: $int] :
        ( $less(X0,1)
        | ~ $less(X0,0) )
    | ~ spl5_5 ),
    inference(superposition,[],[f132,f261]) ).

tff(f261,plain,
    ( ( 1 = sK4(sK2) )
    | ~ spl5_5 ),
    inference(avatar_component_clause,[],[f259]) ).

tff(f259,plain,
    ( spl5_5
  <=> ( 1 = sK4(sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

tff(f171,plain,
    ( $less(1,sK4(sK2))
    | ( 1 = sK4(sK2) ) ),
    inference(resolution,[],[f16,f122]) ).

tff(f237,plain,
    ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ),
    inference(superposition,[],[f9,f12]) ).

tff(f236,plain,
    ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ),
    inference(superposition,[],[f9,f12]) ).

tff(f233,plain,
    ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ),
    inference(superposition,[],[f12,f9]) ).

tff(f232,plain,
    ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ),
    inference(superposition,[],[f12,f9]) ).

tff(f229,plain,
    ! [X0: $int,X1: $int] : ( $uminus($sum($uminus(X0),X1)) = $sum($uminus(X1),X0) ),
    inference(superposition,[],[f12,f19]) ).

tff(f228,plain,
    ! [X0: $int,X1: $int] : ( $uminus($sum(X1,$uminus(X0))) = $sum(X0,$uminus(X1)) ),
    inference(superposition,[],[f12,f19]) ).

tff(f12,plain,
    ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
    introduced(theory_axiom_139,[]) ).

tff(f168,plain,
    ( $less(1,sK3(sK2))
    | ( 1 = sK3(sK2) ) ),
    inference(resolution,[],[f16,f121]) ).

tff(f201,plain,
    ~ $less(sK4(sK2),-1),
    inference(resolution,[],[f157,f14]) ).

tff(f202,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,-1)
      | ~ $less(X1,X0)
      | $less(X1,sK4(sK2)) ),
    inference(resolution,[],[f157,f15]) ).

tff(f157,plain,
    ! [X0: $int] :
      ( $less(X0,sK4(sK2))
      | ~ $less(X0,-1) ),
    inference(resolution,[],[f155,f15]) ).

tff(f167,plain,
    ( $less(sK2,1)
    | ( 1 = sK2 ) ),
    inference(resolution,[],[f16,f42]) ).

tff(f185,plain,
    ! [X0: $int] :
      ( $less(X0,-1)
      | ( -1 = X0 )
      | ~ $less(X0,0) ),
    inference(resolution,[],[f16,f89]) ).

tff(f183,plain,
    ( $less(1,sK4(sK2))
    | ( 1 = sK4(sK2) ) ),
    inference(resolution,[],[f16,f122]) ).

tff(f180,plain,
    ( $less(1,sK3(sK2))
    | ( 1 = sK3(sK2) ) ),
    inference(resolution,[],[f16,f121]) ).

tff(f178,plain,
    ! [X0: $int] :
      ( $less(X0,0)
      | ( 0 = X0 )
      | ~ $less(X0,1) ),
    inference(resolution,[],[f16,f116]) ).

tff(f177,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X0,X1)
      | ( X0 = X1 )
      | ~ $less(X2,X1)
      | $less(X2,X0) ),
    inference(resolution,[],[f16,f15]) ).

tff(f176,plain,
    ! [X0: $int,X1: $int] :
      ( $less($sum(1,X0),X1)
      | ( $sum(1,X0) = X1 )
      | ~ $less(X0,X1) ),
    inference(resolution,[],[f16,f86]) ).

tff(f175,plain,
    ! [X0: $int,X1: $int] :
      ( $less($sum(X0,1),X1)
      | ( $sum(X0,1) = X1 )
      | ~ $less(X0,X1) ),
    inference(resolution,[],[f16,f20]) ).

tff(f173,plain,
    ! [X0: $int] :
      ( $less(X0,-1)
      | ( -1 = X0 )
      | ~ $less(X0,0) ),
    inference(resolution,[],[f16,f89]) ).

tff(f166,plain,
    ! [X0: $int] :
      ( $less(X0,0)
      | ( 0 = X0 )
      | ~ $less(X0,1) ),
    inference(resolution,[],[f16,f116]) ).

tff(f165,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X2,X1)
      | ( X0 = X1 )
      | $less(X0,X1)
      | $less(X2,X0) ),
    inference(resolution,[],[f16,f15]) ).

tff(f164,plain,
    ! [X0: $int,X1: $int] :
      ( $less($sum(1,X0),X1)
      | ( $sum(1,X0) = X1 )
      | ~ $less(X0,X1) ),
    inference(resolution,[],[f16,f86]) ).

tff(f158,plain,
    ~ $less(sK3(sK2),-1),
    inference(resolution,[],[f149,f14]) ).

tff(f159,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,-1)
      | ~ $less(X1,X0)
      | $less(X1,sK3(sK2)) ),
    inference(resolution,[],[f149,f15]) ).

tff(f149,plain,
    ! [X0: $int] :
      ( $less(X0,sK3(sK2))
      | ~ $less(X0,-1) ),
    inference(resolution,[],[f147,f15]) ).

tff(f155,plain,
    $less(-1,sK4(sK2)),
    inference(resolution,[],[f150,f75]) ).

tff(f150,plain,
    ~ $less(sK4(sK2),0),
    inference(resolution,[],[f132,f14]) ).

tff(f154,plain,
    ~ $less(sK4(sK2),0),
    inference(evaluation,[],[f153]) ).

tff(f153,plain,
    ( ~ $less(-1,0)
    | ~ $less(sK4(sK2),0) ),
    inference(resolution,[],[f132,f89]) ).

tff(f151,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,0)
      | ~ $less(X1,X0)
      | $less(X1,sK4(sK2)) ),
    inference(resolution,[],[f132,f15]) ).

tff(f132,plain,
    ! [X0: $int] :
      ( $less(X0,sK4(sK2))
      | ~ $less(X0,0) ),
    inference(resolution,[],[f15,f58]) ).

tff(f147,plain,
    $less(-1,sK3(sK2)),
    inference(resolution,[],[f142,f75]) ).

tff(f142,plain,
    ~ $less(sK3(sK2),0),
    inference(resolution,[],[f131,f14]) ).

tff(f146,plain,
    ~ $less(sK3(sK2),0),
    inference(evaluation,[],[f145]) ).

tff(f145,plain,
    ( ~ $less(-1,0)
    | ~ $less(sK3(sK2),0) ),
    inference(resolution,[],[f131,f89]) ).

tff(f143,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,0)
      | ~ $less(X1,X0)
      | $less(X1,sK3(sK2)) ),
    inference(resolution,[],[f131,f15]) ).

tff(f131,plain,
    ! [X0: $int] :
      ( $less(X0,sK3(sK2))
      | ~ $less(X0,0) ),
    inference(resolution,[],[f15,f57]) ).

tff(f140,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,-1)
      | $less(X0,X1)
      | $less(X1,0) ),
    inference(resolution,[],[f15,f75]) ).

tff(f139,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less(X0,1)
      | $less(0,X1) ),
    inference(resolution,[],[f15,f101]) ).

tff(f138,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less(X0,0)
      | $less(-1,X1) ),
    inference(resolution,[],[f15,f75]) ).

tff(f137,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less(X0,$sum(1,X2))
      | $less(X2,X1) ),
    inference(resolution,[],[f15,f72]) ).

tff(f136,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less(X0,$sum(1,X1)) ),
    inference(resolution,[],[f15,f76]) ).

tff(f135,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less(X0,$sum(X1,1)) ),
    inference(resolution,[],[f15,f71]) ).

tff(f134,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less(X0,$sum(X2,1))
      | $less(X2,X1) ),
    inference(resolution,[],[f15,f18]) ).

tff(f133,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,0)
      | $less(X0,X1)
      | $less(X1,1) ),
    inference(resolution,[],[f15,f101]) ).

tff(f121,plain,
    ~ $less(sK3(sK2),1),
    inference(resolution,[],[f116,f57]) ).

tff(f127,plain,
    ! [X0: $int] :
      ( ~ $less($sum(1,X0),1)
      | $less(X0,0) ),
    inference(resolution,[],[f116,f72]) ).

tff(f124,plain,
    ! [X0: $int] :
      ( ~ $less($sum(X0,1),1)
      | $less(X0,0) ),
    inference(resolution,[],[f116,f18]) ).

tff(f115,plain,
    ! [X0: $int] :
      ( ~ $less(X0,-1)
      | $less($sum(1,X0),0) ),
    inference(resolution,[],[f86,f75]) ).

tff(f110,plain,
    ! [X0: $int] :
      ( ~ $less(X0,0)
      | $less($sum(1,X0),1) ),
    inference(resolution,[],[f86,f101]) ).

tff(f109,plain,
    ! [X0: $int] :
      ( $less($sum(X0,1),1)
      | ~ $less(X0,0) ),
    inference(resolution,[],[f101,f20]) ).

tff(f101,plain,
    ! [X0: $int] :
      ( $less(X0,1)
      | $less(0,X0) ),
    inference(superposition,[],[f72,f11]) ).

tff(f100,plain,
    ! [X0: $int] :
      ( $less(X0,-1)
      | ~ $less($sum(1,X0),0) ),
    inference(resolution,[],[f72,f89]) ).

tff(f72,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(1,X0))
      | $less(X0,X1) ),
    inference(superposition,[],[f18,f9]) ).

tff(f49,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( in(X0,add(X2,X1))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f36]) ).

tff(f36,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( X0 = X2 )
        | in(X0,X1)
        | ~ in(X0,add(X2,X1)) )
      & ( in(X0,add(X2,X1))
        | ( ( X0 != X2 )
          & ~ in(X0,X1) ) ) ),
    inference(flattening,[],[f35]) ).

tff(f35,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( X0 = X2 )
        | in(X0,X1)
        | ~ in(X0,add(X2,X1)) )
      & ( in(X0,add(X2,X1))
        | ( ( X0 != X2 )
          & ~ in(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f25]) ).

tff(f25,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( X0 = X2 )
        | in(X0,X1) )
    <=> in(X0,add(X2,X1)) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X5: $int,X6: collection,X7: $int] :
      ( ( ( X5 = X7 )
        | in(X5,X6) )
    <=> in(X5,add(X7,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

tff(f47,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( ~ in(X0,remove(X2,X1))
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( ( X0 != X2 )
          & in(X0,X1) )
        | ~ in(X0,remove(X2,X1)) )
      & ( in(X0,remove(X2,X1))
        | ( X0 = X2 )
        | ~ in(X0,X1) ) ),
    inference(flattening,[],[f33]) ).

tff(f33,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( ( X0 != X2 )
          & in(X0,X1) )
        | ~ in(X0,remove(X2,X1)) )
      & ( in(X0,remove(X2,X1))
        | ( X0 = X2 )
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f24]) ).

tff(f24,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( X0 != X2 )
        & in(X0,X1) )
    <=> in(X0,remove(X2,X1)) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X8: $int,X9: collection,X10: $int] :
      ( ( ( X8 != X10 )
        & in(X8,X9) )
    <=> in(X8,remove(X10,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

tff(f94,plain,
    ! [X0: $int] :
      ( ~ $less($sum(X0,1),0)
      | $less(X0,-1) ),
    inference(resolution,[],[f89,f18]) ).

tff(f89,plain,
    ! [X0: $int] :
      ( ~ $less(-1,X0)
      | ~ $less(X0,0) ),
    inference(evaluation,[],[f88]) ).

tff(f88,plain,
    ! [X0: $int] :
      ( ~ $less(X0,0)
      | ~ $less($uminus(1),X0) ),
    inference(superposition,[],[f20,f56]) ).

tff(f92,plain,
    ! [X0: $int] :
      ( $less($sum(X0,1),0)
      | ~ $less(X0,-1) ),
    inference(resolution,[],[f75,f20]) ).

tff(f75,plain,
    ! [X0: $int] :
      ( $less(X0,0)
      | $less(-1,X0) ),
    inference(evaluation,[],[f74]) ).

tff(f74,plain,
    ! [X0: $int] :
      ( $less(X0,0)
      | $less($uminus(1),X0) ),
    inference(superposition,[],[f18,f56]) ).

tff(f87,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$sum(1,X0))
      | ~ $less(X0,X1) ),
    inference(superposition,[],[f20,f9]) ).

tff(f77,plain,
    ! [X0: $int] : $less(X0,$sum(1,X0)),
    inference(superposition,[],[f71,f9]) ).

tff(f73,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(1,X0))
      | $less(X0,X1) ),
    inference(superposition,[],[f18,f9]) ).

tff(f56,plain,
    ! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
    inference(superposition,[],[f13,f19]) ).

tff(f45,plain,
    ! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
    inference(cnf_transformation,[],[f23]) ).

tff(f23,plain,
    ! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X1: $int,X2: collection] : in(X1,add(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

tff(f44,plain,
    ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
    inference(cnf_transformation,[],[f22]) ).

tff(f22,plain,
    ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X3: $int,X4: collection] : ~ in(X3,remove(X3,X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

tff(f19,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f43,plain,
    ! [X0: $int] : ~ in(X0,empty),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $int] : ~ in(X0,empty),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

tff(f53,plain,
    ! [X2: $int,X1: collection] : in(X2,add(X2,X1)),
    inference(equality_resolution,[],[f50]) ).

tff(f50,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( in(X0,add(X2,X1))
      | ( X0 != X2 ) ),
    inference(cnf_transformation,[],[f36]) ).

tff(f51,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( ~ in(X0,add(X2,X1))
      | in(X0,X1)
      | ( X0 = X2 ) ),
    inference(cnf_transformation,[],[f36]) ).

tff(f46,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( in(X0,remove(X2,X1))
      | ( X0 = X2 )
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f52,plain,
    ! [X2: $int,X1: collection] : ~ in(X2,remove(X2,X1)),
    inference(equality_resolution,[],[f48]) ).

tff(f48,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( ( X0 != X2 )
      | ~ in(X0,remove(X2,X1)) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f289,plain,
    ( ~ spl5_2
    | ~ spl5_5 ),
    inference(avatar_contradiction_clause,[],[f288]) ).

tff(f288,plain,
    ( $false
    | ~ spl5_2
    | ~ spl5_5 ),
    inference(subsumption_resolution,[],[f286,f121]) ).

tff(f286,plain,
    ( $less(sK3(sK2),1)
    | ~ spl5_2
    | ~ spl5_5 ),
    inference(resolution,[],[f282,f196]) ).

tff(f196,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,sK2)
        | $less(X0,1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f194,f15]) ).

tff(f266,plain,
    ( spl5_5
    | spl5_6 ),
    inference(avatar_split_clause,[],[f171,f263,f259]) ).

tff(f263,plain,
    ( spl5_6
  <=> $less(1,sK4(sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

tff(f250,plain,
    ( ~ spl5_2
    | ~ spl5_3 ),
    inference(avatar_contradiction_clause,[],[f249]) ).

tff(f249,plain,
    ( $false
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(subsumption_resolution,[],[f247,f122]) ).

tff(f247,plain,
    ( $less(sK4(sK2),1)
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(resolution,[],[f246,f196]) ).

tff(f246,plain,
    ( $less(sK4(sK2),sK2)
    | ~ spl5_3 ),
    inference(superposition,[],[f76,f217]) ).

tff(f217,plain,
    ( ( sK2 = $sum(1,sK4(sK2)) )
    | ~ spl5_3 ),
    inference(superposition,[],[f70,f210]) ).

tff(f210,plain,
    ( ( 1 = sK3(sK2) )
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f208]) ).

tff(f208,plain,
    ( spl5_3
  <=> ( 1 = sK3(sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

tff(f215,plain,
    ( spl5_3
    | spl5_4 ),
    inference(avatar_split_clause,[],[f168,f212,f208]) ).

tff(f195,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f167,f192,f188]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : DAT030_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n012.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 12:53:55 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (14172)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (14175)WARNING: value z3 for option sas not known
% 0.15/0.38  % (14176)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (14174)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (14173)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (14177)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)
% 0.15/0.38  % (14178)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)
% 0.15/0.38  % (14179)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)
% 0.15/0.38  % (14175)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)
% 0.15/0.38  % (14174)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38  % (14176)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38  % (14173)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38  % (14176)Terminated due to inappropriate strategy.
% 0.15/0.38  % (14176)------------------------------
% 0.15/0.38  % (14176)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38  % (14176)Termination reason: Inappropriate
% 0.15/0.38  
% 0.15/0.38  % (14176)Memory used [KB]: 747
% 0.15/0.38  % (14173)Terminated due to inappropriate strategy.
% 0.15/0.38  % (14173)------------------------------
% 0.15/0.38  % (14173)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38  % (14176)Time elapsed: 0.003 s
% 0.15/0.38  % (14173)Termination reason: Inappropriate
% 0.15/0.38  
% 0.15/0.38  % (14176)Instructions burned: 3 (million)
% 0.15/0.38  % (14173)Memory used [KB]: 747
% 0.15/0.38  % (14174)Terminated due to inappropriate strategy.
% 0.15/0.38  % (14174)------------------------------
% 0.15/0.38  % (14174)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38  % (14173)Time elapsed: 0.003 s
% 0.15/0.38  % (14174)Termination reason: Inappropriate
% 0.15/0.38  
% 0.15/0.38  % (14173)Instructions burned: 3 (million)
% 0.15/0.38  % (14174)Memory used [KB]: 747
% 0.15/0.38  % (14174)Time elapsed: 0.003 s
% 0.15/0.38  % (14174)Instructions burned: 3 (million)
% 0.15/0.38  % (14176)------------------------------
% 0.15/0.38  % (14176)------------------------------
% 0.15/0.38  % (14173)------------------------------
% 0.15/0.38  % (14173)------------------------------
% 0.15/0.38  % (14174)------------------------------
% 0.15/0.38  % (14174)------------------------------
% 0.15/0.39  % (14180)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.39  % (14181)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.39  % (14182)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.15/0.39  % (14180)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.39  % (14180)Terminated due to inappropriate strategy.
% 0.15/0.39  % (14180)------------------------------
% 0.15/0.39  % (14180)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39  % (14180)Termination reason: Inappropriate
% 0.15/0.39  
% 0.15/0.39  % (14180)Memory used [KB]: 746
% 0.15/0.39  % (14180)Time elapsed: 0.002 s
% 0.15/0.39  % (14180)Instructions burned: 2 (million)
% 0.15/0.40  % (14180)------------------------------
% 0.15/0.40  % (14180)------------------------------
% 0.22/0.41  % (14183)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.22/0.53  % (14175)First to succeed.
% 0.22/0.53  % (14175)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14172"
% 0.22/0.53  % (14175)Refutation found. Thanks to Tanya!
% 0.22/0.53  % SZS status Theorem for theBenchmark
% 0.22/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.54  % (14175)------------------------------
% 0.22/0.54  % (14175)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.54  % (14175)Termination reason: Refutation
% 0.22/0.54  
% 0.22/0.54  % (14175)Memory used [KB]: 2434
% 0.22/0.54  % (14175)Time elapsed: 0.158 s
% 0.22/0.54  % (14175)Instructions burned: 291 (million)
% 0.22/0.54  % (14172)Success in time 0.174 s
%------------------------------------------------------------------------------