TSTP Solution File: SWW678_1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWW678_1 : TPTP v8.1.0. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n022.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 : Wed Aug 31 19:09:29 EDT 2022

% Result   : Theorem 1.53s 0.57s
% Output   : Refutation 1.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   41
% Syntax   : Number of formulae    :  159 (   7 unt;  16 typ;   0 def)
%            Number of atoms       :  722 ( 203 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  850 ( 271   ~; 323   |; 165   &)
%                                         (  31 <=>;  57  =>;   0  <=;   3 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number arithmetic     :  178 (  96 atm;   0 fun;   0 num;  82 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   18 (  12   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   22 (  16 usr;  14 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :  178 ( 132   !;  46   ?; 178   :)

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

tff(func_def_0,type,
    'empty:Tree': 'Tree' ).

tff(func_def_1,type,
    'left:(Tree)>Tree': 'Tree' > 'Tree' ).

tff(func_def_2,type,
    'val:(Tree)>Int': 'Tree' > $int ).

tff(func_def_3,type,
    'node:(Int*Tree*Tree)>Tree': ( $int * 'Tree' * 'Tree' ) > 'Tree' ).

tff(func_def_4,type,
    'right:(Tree)>Tree': 'Tree' > 'Tree' ).

tff(func_def_9,type,
    sK2: 'Tree' > $int ).

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

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

tff(func_def_12,type,
    sK5: ( 'Tree' * $int ) > 'Tree' ).

tff(func_def_13,type,
    sK6: 'Tree' ).

tff(func_def_14,type,
    sK7: $int ).

tff(pred_def_1,type,
    searchtree: 'Tree' > $o ).

tff(pred_def_2,type,
    in: ( $int * 'Tree' ) > $o ).

tff(pred_def_6,type,
    sP0: 'Tree' > $o ).

tff(pred_def_7,type,
    sP1: ( 'Tree' * $int ) > $o ).

tff(f575,plain,
    $false,
    inference(avatar_sat_refutation,[],[f124,f125,f136,f152,f162,f167,f260,f265,f289,f303,f315,f321,f346,f354,f370,f371,f372,f391,f573,f574]) ).

tff(f574,plain,
    ( spl8_4
    | ~ spl8_24
    | spl8_23
    | ~ spl8_25 ),
    inference(avatar_split_clause,[],[f389,f300,f291,f295,f133]) ).

tff(f133,plain,
    ( spl8_4
  <=> ( 'empty:Tree' = sK6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

tff(f295,plain,
    ( spl8_24
  <=> sP0(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).

tff(f291,plain,
    ( spl8_23
  <=> $less('val:(Tree)>Int'(sK6),sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).

tff(f300,plain,
    ( spl8_25
  <=> in(sK7,'right:(Tree)>Tree'(sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).

tff(f389,plain,
    ( $less('val:(Tree)>Int'(sK6),sK7)
    | ~ sP0(sK6)
    | ( 'empty:Tree' = sK6 )
    | ~ spl8_25 ),
    inference(resolution,[],[f302,f73]) ).

tff(f73,plain,
    ! [X3: $int,X0: 'Tree'] :
      ( ~ in(X3,'right:(Tree)>Tree'(X0))
      | ~ sP0(X0)
      | ( 'empty:Tree' = X0 )
      | $less('val:(Tree)>Int'(X0),X3) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f51,plain,
    ! [X0: 'Tree'] :
      ( ( sP0(X0)
        | ( ( 'empty:Tree' != X0 )
          & ( ~ searchtree('right:(Tree)>Tree'(X0))
            | ( in(sK2(X0),'right:(Tree)>Tree'(X0))
              & ~ $less('val:(Tree)>Int'(X0),sK2(X0)) )
            | ( $less('val:(Tree)>Int'(X0),sK3(X0))
              & in(sK3(X0),'left:(Tree)>Tree'(X0)) )
            | ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
      & ( ( 'empty:Tree' = X0 )
        | ( searchtree('right:(Tree)>Tree'(X0))
          & ! [X3: $int] :
              ( ~ in(X3,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X3) )
          & ! [X4: $int] :
              ( ~ $less('val:(Tree)>Int'(X0),X4)
              | ~ in(X4,'left:(Tree)>Tree'(X0)) )
          & searchtree('left:(Tree)>Tree'(X0)) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f48,f50,f49]) ).

tff(f49,plain,
    ! [X0: 'Tree'] :
      ( ? [X1: $int] :
          ( in(X1,'right:(Tree)>Tree'(X0))
          & ~ $less('val:(Tree)>Int'(X0),X1) )
     => ( in(sK2(X0),'right:(Tree)>Tree'(X0))
        & ~ $less('val:(Tree)>Int'(X0),sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f50,plain,
    ! [X0: 'Tree'] :
      ( ? [X2: $int] :
          ( $less('val:(Tree)>Int'(X0),X2)
          & in(X2,'left:(Tree)>Tree'(X0)) )
     => ( $less('val:(Tree)>Int'(X0),sK3(X0))
        & in(sK3(X0),'left:(Tree)>Tree'(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f48,plain,
    ! [X0: 'Tree'] :
      ( ( sP0(X0)
        | ( ( 'empty:Tree' != X0 )
          & ( ~ searchtree('right:(Tree)>Tree'(X0))
            | ? [X1: $int] :
                ( in(X1,'right:(Tree)>Tree'(X0))
                & ~ $less('val:(Tree)>Int'(X0),X1) )
            | ? [X2: $int] :
                ( $less('val:(Tree)>Int'(X0),X2)
                & in(X2,'left:(Tree)>Tree'(X0)) )
            | ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
      & ( ( 'empty:Tree' = X0 )
        | ( searchtree('right:(Tree)>Tree'(X0))
          & ! [X3: $int] :
              ( ~ in(X3,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X3) )
          & ! [X4: $int] :
              ( ~ $less('val:(Tree)>Int'(X0),X4)
              | ~ in(X4,'left:(Tree)>Tree'(X0)) )
          & searchtree('left:(Tree)>Tree'(X0)) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f47]) ).

tff(f47,plain,
    ! [X0: 'Tree'] :
      ( ( sP0(X0)
        | ( ( 'empty:Tree' != X0 )
          & ( ~ searchtree('right:(Tree)>Tree'(X0))
            | ? [X2: $int] :
                ( in(X2,'right:(Tree)>Tree'(X0))
                & ~ $less('val:(Tree)>Int'(X0),X2) )
            | ? [X1: $int] :
                ( $less('val:(Tree)>Int'(X0),X1)
                & in(X1,'left:(Tree)>Tree'(X0)) )
            | ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
      & ( ( 'empty:Tree' = X0 )
        | ( searchtree('right:(Tree)>Tree'(X0))
          & ! [X2: $int] :
              ( ~ in(X2,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X2) )
          & ! [X1: $int] :
              ( ~ $less('val:(Tree)>Int'(X0),X1)
              | ~ in(X1,'left:(Tree)>Tree'(X0)) )
          & searchtree('left:(Tree)>Tree'(X0)) )
        | ~ sP0(X0) ) ),
    inference(flattening,[],[f46]) ).

tff(f46,plain,
    ! [X0: 'Tree'] :
      ( ( sP0(X0)
        | ( ( 'empty:Tree' != X0 )
          & ( ~ searchtree('right:(Tree)>Tree'(X0))
            | ? [X2: $int] :
                ( in(X2,'right:(Tree)>Tree'(X0))
                & ~ $less('val:(Tree)>Int'(X0),X2) )
            | ? [X1: $int] :
                ( $less('val:(Tree)>Int'(X0),X1)
                & in(X1,'left:(Tree)>Tree'(X0)) )
            | ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
      & ( ( 'empty:Tree' = X0 )
        | ( searchtree('right:(Tree)>Tree'(X0))
          & ! [X2: $int] :
              ( ~ in(X2,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X2) )
          & ! [X1: $int] :
              ( ~ $less('val:(Tree)>Int'(X0),X1)
              | ~ in(X1,'left:(Tree)>Tree'(X0)) )
          & searchtree('left:(Tree)>Tree'(X0)) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f40]) ).

tff(f40,plain,
    ! [X0: 'Tree'] :
      ( sP0(X0)
    <=> ( ( 'empty:Tree' = X0 )
        | ( searchtree('right:(Tree)>Tree'(X0))
          & ! [X2: $int] :
              ( ~ in(X2,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X2) )
          & ! [X1: $int] :
              ( ~ $less('val:(Tree)>Int'(X0),X1)
              | ~ in(X1,'left:(Tree)>Tree'(X0)) )
          & searchtree('left:(Tree)>Tree'(X0)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f302,plain,
    ( in(sK7,'right:(Tree)>Tree'(sK6))
    | ~ spl8_25 ),
    inference(avatar_component_clause,[],[f300]) ).

tff(f573,plain,
    ( ~ spl8_6
    | ~ spl8_23 ),
    inference(avatar_contradiction_clause,[],[f570]) ).

tff(f570,plain,
    ( $false
    | ~ spl8_6
    | ~ spl8_23 ),
    inference(resolution,[],[f538,f16]) ).

tff(f16,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_147,[]) ).

tff(f538,plain,
    ( $less(sK7,sK7)
    | ~ spl8_6
    | ~ spl8_23 ),
    inference(resolution,[],[f401,f292]) ).

tff(f292,plain,
    ( $less('val:(Tree)>Int'(sK6),sK7)
    | ~ spl8_23 ),
    inference(avatar_component_clause,[],[f291]) ).

tff(f401,plain,
    ( ! [X2: $int] :
        ( ~ $less('val:(Tree)>Int'(sK6),X2)
        | $less(sK7,X2) )
    | ~ spl8_6 ),
    inference(resolution,[],[f146,f17]) ).

tff(f17,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less(X0,X2)
      | ~ $less(X1,X2) ),
    introduced(theory_axiom_148,[]) ).

tff(f146,plain,
    ( $less(sK7,'val:(Tree)>Int'(sK6))
    | ~ spl8_6 ),
    inference(avatar_component_clause,[],[f144]) ).

tff(f144,plain,
    ( spl8_6
  <=> $less(sK7,'val:(Tree)>Int'(sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).

tff(f391,plain,
    ( spl8_6
    | spl8_2
    | spl8_4
    | ~ spl8_25 ),
    inference(avatar_split_clause,[],[f388,f300,f133,f121,f144]) ).

tff(f121,plain,
    ( spl8_2
  <=> sP1(sK6,sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

tff(f388,plain,
    ( ( 'empty:Tree' = sK6 )
    | sP1(sK6,sK7)
    | $less(sK7,'val:(Tree)>Int'(sK6))
    | ~ spl8_25 ),
    inference(resolution,[],[f302,f110]) ).

tff(f110,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ~ in(X1,'right:(Tree)>Tree'(X0))
      | sP1(X0,X1)
      | $less(X1,'val:(Tree)>Int'(X0))
      | ( 'empty:Tree' = X0 ) ),
    inference(equality_resolution,[],[f91]) ).

tff(f91,plain,
    ! [X3: 'Tree',X0: 'Tree',X1: $int] :
      ( sP1(X0,X1)
      | ( 'empty:Tree' = X0 )
      | $less(X1,'val:(Tree)>Int'(X0))
      | ( 'right:(Tree)>Tree'(X0) != X3 )
      | ~ in(X1,X3) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f59,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ( sP1(X0,X1)
        | ( 'empty:Tree' = X0 )
        | ( ( 'val:(Tree)>Int'(X0) != X1 )
          & ( ( ! [X2: 'Tree'] :
                  ( ~ in(X1,X2)
                  | ( 'left:(Tree)>Tree'(X0) != X2 ) )
              & $less(X1,'val:(Tree)>Int'(X0)) )
            | ( ! [X3: 'Tree'] :
                  ( ( 'right:(Tree)>Tree'(X0) != X3 )
                  | ~ in(X1,X3) )
              & ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
          & ( 'empty:Tree' != X0 ) ) )
      & ( ( ( 'empty:Tree' != X0 )
          & ( ( 'val:(Tree)>Int'(X0) = X1 )
            | ( ( ( in(X1,sK4(X0,X1))
                  & ( 'left:(Tree)>Tree'(X0) = sK4(X0,X1) ) )
                | ~ $less(X1,'val:(Tree)>Int'(X0)) )
              & ( ( ( 'right:(Tree)>Tree'(X0) = sK5(X0,X1) )
                  & in(X1,sK5(X0,X1)) )
                | $less(X1,'val:(Tree)>Int'(X0)) ) )
            | ( 'empty:Tree' = X0 ) ) )
        | ~ sP1(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f56,f58,f57]) ).

tff(f57,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ? [X4: 'Tree'] :
          ( in(X1,X4)
          & ( 'left:(Tree)>Tree'(X0) = X4 ) )
     => ( in(X1,sK4(X0,X1))
        & ( 'left:(Tree)>Tree'(X0) = sK4(X0,X1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f58,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ? [X5: 'Tree'] :
          ( ( 'right:(Tree)>Tree'(X0) = X5 )
          & in(X1,X5) )
     => ( ( 'right:(Tree)>Tree'(X0) = sK5(X0,X1) )
        & in(X1,sK5(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f56,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ( sP1(X0,X1)
        | ( 'empty:Tree' = X0 )
        | ( ( 'val:(Tree)>Int'(X0) != X1 )
          & ( ( ! [X2: 'Tree'] :
                  ( ~ in(X1,X2)
                  | ( 'left:(Tree)>Tree'(X0) != X2 ) )
              & $less(X1,'val:(Tree)>Int'(X0)) )
            | ( ! [X3: 'Tree'] :
                  ( ( 'right:(Tree)>Tree'(X0) != X3 )
                  | ~ in(X1,X3) )
              & ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
          & ( 'empty:Tree' != X0 ) ) )
      & ( ( ( 'empty:Tree' != X0 )
          & ( ( 'val:(Tree)>Int'(X0) = X1 )
            | ( ( ? [X4: 'Tree'] :
                    ( in(X1,X4)
                    & ( 'left:(Tree)>Tree'(X0) = X4 ) )
                | ~ $less(X1,'val:(Tree)>Int'(X0)) )
              & ( ? [X5: 'Tree'] :
                    ( ( 'right:(Tree)>Tree'(X0) = X5 )
                    & in(X1,X5) )
                | $less(X1,'val:(Tree)>Int'(X0)) ) )
            | ( 'empty:Tree' = X0 ) ) )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f55]) ).

tff(f55,plain,
    ! [X1: 'Tree',X0: $int] :
      ( ( sP1(X1,X0)
        | ( 'empty:Tree' = X1 )
        | ( ( 'val:(Tree)>Int'(X1) != X0 )
          & ( ( ! [X2: 'Tree'] :
                  ( ~ in(X0,X2)
                  | ( 'left:(Tree)>Tree'(X1) != X2 ) )
              & $less(X0,'val:(Tree)>Int'(X1)) )
            | ( ! [X3: 'Tree'] :
                  ( ( 'right:(Tree)>Tree'(X1) != X3 )
                  | ~ in(X0,X3) )
              & ~ $less(X0,'val:(Tree)>Int'(X1)) ) )
          & ( 'empty:Tree' != X1 ) ) )
      & ( ( ( 'empty:Tree' != X1 )
          & ( ( 'val:(Tree)>Int'(X1) = X0 )
            | ( ( ? [X2: 'Tree'] :
                    ( in(X0,X2)
                    & ( 'left:(Tree)>Tree'(X1) = X2 ) )
                | ~ $less(X0,'val:(Tree)>Int'(X1)) )
              & ( ? [X3: 'Tree'] :
                    ( ( 'right:(Tree)>Tree'(X1) = X3 )
                    & in(X0,X3) )
                | $less(X0,'val:(Tree)>Int'(X1)) ) )
            | ( 'empty:Tree' = X1 ) ) )
        | ~ sP1(X1,X0) ) ),
    inference(flattening,[],[f54]) ).

tff(f54,plain,
    ! [X1: 'Tree',X0: $int] :
      ( ( sP1(X1,X0)
        | ( 'empty:Tree' = X1 )
        | ( ( 'val:(Tree)>Int'(X1) != X0 )
          & ( ( ! [X2: 'Tree'] :
                  ( ~ in(X0,X2)
                  | ( 'left:(Tree)>Tree'(X1) != X2 ) )
              & $less(X0,'val:(Tree)>Int'(X1)) )
            | ( ! [X3: 'Tree'] :
                  ( ( 'right:(Tree)>Tree'(X1) != X3 )
                  | ~ in(X0,X3) )
              & ~ $less(X0,'val:(Tree)>Int'(X1)) ) )
          & ( 'empty:Tree' != X1 ) ) )
      & ( ( ( 'empty:Tree' != X1 )
          & ( ( 'val:(Tree)>Int'(X1) = X0 )
            | ( ( ? [X2: 'Tree'] :
                    ( in(X0,X2)
                    & ( 'left:(Tree)>Tree'(X1) = X2 ) )
                | ~ $less(X0,'val:(Tree)>Int'(X1)) )
              & ( ? [X3: 'Tree'] :
                    ( ( 'right:(Tree)>Tree'(X1) = X3 )
                    & in(X0,X3) )
                | $less(X0,'val:(Tree)>Int'(X1)) ) )
            | ( 'empty:Tree' = X1 ) ) )
        | ~ sP1(X1,X0) ) ),
    inference(nnf_transformation,[],[f42]) ).

tff(f42,plain,
    ! [X1: 'Tree',X0: $int] :
      ( sP1(X1,X0)
    <=> ( ( 'empty:Tree' != X1 )
        & ( ( 'val:(Tree)>Int'(X1) = X0 )
          | ( ( ? [X2: 'Tree'] :
                  ( in(X0,X2)
                  & ( 'left:(Tree)>Tree'(X1) = X2 ) )
              | ~ $less(X0,'val:(Tree)>Int'(X1)) )
            & ( ? [X3: 'Tree'] :
                  ( ( 'right:(Tree)>Tree'(X1) = X3 )
                  & in(X0,X3) )
              | $less(X0,'val:(Tree)>Int'(X1)) ) )
          | ( 'empty:Tree' = X1 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f372,plain,
    ( ~ spl8_3
    | spl8_4
    | spl8_2 ),
    inference(avatar_split_clause,[],[f344,f121,f133,f129]) ).

tff(f129,plain,
    ( spl8_3
  <=> ( sK7 = 'val:(Tree)>Int'(sK6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

tff(f344,plain,
    ( ( 'empty:Tree' = sK6 )
    | ( sK7 != 'val:(Tree)>Int'(sK6) )
    | spl8_2 ),
    inference(constrained_resolution,[],[f122,f106]) ).

tff(f106,plain,
    ! [X0: 'Tree'] :
      ( sP1(X0,'val:(Tree)>Int'(X0))
      | ( 'empty:Tree' = X0 ) ),
    inference(equality_resolution,[],[f94]) ).

tff(f94,plain,
    ! [X0: 'Tree',X1: $int] :
      ( sP1(X0,X1)
      | ( 'empty:Tree' = X0 )
      | ( 'val:(Tree)>Int'(X0) != X1 ) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f122,plain,
    ( ~ sP1(sK6,sK7)
    | spl8_2 ),
    inference(avatar_component_clause,[],[f121]) ).

tff(f371,plain,
    ( ~ spl8_23
    | ~ spl8_24
    | spl8_4
    | ~ spl8_29 ),
    inference(avatar_split_clause,[],[f366,f351,f133,f295,f291]) ).

tff(f351,plain,
    ( spl8_29
  <=> in(sK7,'left:(Tree)>Tree'(sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).

tff(f366,plain,
    ( ( 'empty:Tree' = sK6 )
    | ~ sP0(sK6)
    | ~ $less('val:(Tree)>Int'(sK6),sK7)
    | ~ spl8_29 ),
    inference(resolution,[],[f353,f72]) ).

tff(f72,plain,
    ! [X0: 'Tree',X4: $int] :
      ( ~ in(X4,'left:(Tree)>Tree'(X0))
      | ~ sP0(X0)
      | ~ $less('val:(Tree)>Int'(X0),X4)
      | ( 'empty:Tree' = X0 ) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f353,plain,
    ( in(sK7,'left:(Tree)>Tree'(sK6))
    | ~ spl8_29 ),
    inference(avatar_component_clause,[],[f351]) ).

tff(f370,plain,
    ( spl8_2
    | ~ spl8_6
    | spl8_4
    | ~ spl8_29 ),
    inference(avatar_split_clause,[],[f367,f351,f133,f144,f121]) ).

tff(f367,plain,
    ( ( 'empty:Tree' = sK6 )
    | ~ $less(sK7,'val:(Tree)>Int'(sK6))
    | sP1(sK6,sK7)
    | ~ spl8_29 ),
    inference(resolution,[],[f353,f109]) ).

tff(f109,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ~ in(X1,'left:(Tree)>Tree'(X0))
      | ( 'empty:Tree' = X0 )
      | ~ $less(X1,'val:(Tree)>Int'(X0))
      | sP1(X0,X1) ),
    inference(equality_resolution,[],[f92]) ).

tff(f92,plain,
    ! [X2: 'Tree',X0: 'Tree',X1: $int] :
      ( sP1(X0,X1)
      | ( 'empty:Tree' = X0 )
      | ~ in(X1,X2)
      | ( 'left:(Tree)>Tree'(X0) != X2 )
      | ~ $less(X1,'val:(Tree)>Int'(X0)) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f354,plain,
    ( spl8_3
    | spl8_29
    | spl8_25
    | spl8_4
    | ~ spl8_1 ),
    inference(avatar_split_clause,[],[f340,f117,f133,f300,f351,f129]) ).

tff(f117,plain,
    ( spl8_1
  <=> in(sK7,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

tff(f340,plain,
    ( ( 'empty:Tree' = sK6 )
    | in(sK7,'right:(Tree)>Tree'(sK6))
    | in(sK7,'left:(Tree)>Tree'(sK6))
    | ( sK7 = 'val:(Tree)>Int'(sK6) )
    | ~ spl8_1 ),
    inference(resolution,[],[f119,f102]) ).

tff(f102,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ~ in(X1,X0)
      | in(X1,'right:(Tree)>Tree'(X0))
      | in(X1,'left:(Tree)>Tree'(X0))
      | ( 'val:(Tree)>Int'(X0) = X1 )
      | ( 'empty:Tree' = X0 ) ),
    inference(cnf_transformation,[],[f67]) ).

tff(f67,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ( ( ( 'empty:Tree' != X0 )
          & ( ( 'empty:Tree' = X0 )
            | in(X1,'right:(Tree)>Tree'(X0))
            | in(X1,'left:(Tree)>Tree'(X0))
            | ( 'val:(Tree)>Int'(X0) = X1 ) ) )
        | ~ in(X1,X0) )
      & ( in(X1,X0)
        | ( 'empty:Tree' = X0 )
        | ( ( 'empty:Tree' != X0 )
          & ~ in(X1,'right:(Tree)>Tree'(X0))
          & ~ in(X1,'left:(Tree)>Tree'(X0))
          & ( 'val:(Tree)>Int'(X0) != X1 ) ) ) ),
    inference(rectify,[],[f66]) ).

tff(f66,plain,
    ! [X1: 'Tree',X0: $int] :
      ( ( ( ( 'empty:Tree' != X1 )
          & ( ( 'empty:Tree' = X1 )
            | in(X0,'right:(Tree)>Tree'(X1))
            | in(X0,'left:(Tree)>Tree'(X1))
            | ( 'val:(Tree)>Int'(X1) = X0 ) ) )
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | ( 'empty:Tree' = X1 )
        | ( ( 'empty:Tree' != X1 )
          & ~ in(X0,'right:(Tree)>Tree'(X1))
          & ~ in(X0,'left:(Tree)>Tree'(X1))
          & ( 'val:(Tree)>Int'(X1) != X0 ) ) ) ),
    inference(flattening,[],[f65]) ).

tff(f65,plain,
    ! [X1: 'Tree',X0: $int] :
      ( ( ( ( 'empty:Tree' != X1 )
          & ( ( 'empty:Tree' = X1 )
            | in(X0,'right:(Tree)>Tree'(X1))
            | in(X0,'left:(Tree)>Tree'(X1))
            | ( 'val:(Tree)>Int'(X1) = X0 ) ) )
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | ( 'empty:Tree' = X1 )
        | ( ( 'empty:Tree' != X1 )
          & ~ in(X0,'right:(Tree)>Tree'(X1))
          & ~ in(X0,'left:(Tree)>Tree'(X1))
          & ( 'val:(Tree)>Int'(X1) != X0 ) ) ) ),
    inference(nnf_transformation,[],[f39]) ).

tff(f39,plain,
    ! [X1: 'Tree',X0: $int] :
      ( ( ( 'empty:Tree' != X1 )
        & ( ( 'empty:Tree' = X1 )
          | in(X0,'right:(Tree)>Tree'(X1))
          | in(X0,'left:(Tree)>Tree'(X1))
          | ( 'val:(Tree)>Int'(X1) = X0 ) ) )
    <=> in(X0,X1) ),
    inference(flattening,[],[f38]) ).

tff(f38,plain,
    ! [X0: $int,X1: 'Tree'] :
      ( in(X0,X1)
    <=> ( ( in(X0,'left:(Tree)>Tree'(X1))
          | ( 'val:(Tree)>Int'(X1) = X0 )
          | in(X0,'right:(Tree)>Tree'(X1))
          | ( 'empty:Tree' = X1 ) )
        & ( 'empty:Tree' != X1 ) ) ),
    inference(ennf_transformation,[],[f27]) ).

tff(f27,plain,
    ! [X0: $int,X1: 'Tree'] :
      ( in(X0,X1)
    <=> ( ( ( 'empty:Tree' != X1 )
         => ( in(X0,'left:(Tree)>Tree'(X1))
            | ( 'val:(Tree)>Int'(X1) = X0 )
            | in(X0,'right:(Tree)>Tree'(X1)) ) )
        & ( 'empty:Tree' != X1 ) ) ),
    inference(flattening,[],[f26]) ).

tff(f26,plain,
    ! [X0: $int,X1: 'Tree'] :
      ( ( ( ( 'empty:Tree' != X1 )
         => ( in(X0,'left:(Tree)>Tree'(X1))
            | ( 'val:(Tree)>Int'(X1) = X0 )
            | in(X0,'right:(Tree)>Tree'(X1)) ) )
        & ( ( ~ 'empty:Tree' )
          = X1 ) )
    <=> in(X0,X1) ),
    inference(true_and_false_elimination,[],[f25]) ).

tff(f25,plain,
    ! [X0: $int,X1: 'Tree'] :
      ( ( ( ( 'empty:Tree' != X1 )
         => ( in(X0,'left:(Tree)>Tree'(X1))
            | ( 'val:(Tree)>Int'(X1) = X0 )
            | in(X0,'right:(Tree)>Tree'(X1)) ) )
        & ( ( 'empty:Tree' = X1 )
         => $false ) )
    <=> in(X0,X1) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X4: $int,X5: 'Tree'] :
      ( ( ( ( 'empty:Tree' != X5 )
         => ( ( 'val:(Tree)>Int'(X5) = X4 )
            | in(X4,'right:(Tree)>Tree'(X5))
            | in(X4,'left:(Tree)>Tree'(X5)) ) )
        & ( ( 'empty:Tree' = X5 )
         => $false ) )
    <=> in(X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_005) ).

tff(f119,plain,
    ( in(sK7,sK6)
    | ~ spl8_1 ),
    inference(avatar_component_clause,[],[f117]) ).

tff(f346,plain,
    spl8_24,
    inference(avatar_contradiction_clause,[],[f345]) ).

tff(f345,plain,
    ( $false
    | spl8_24 ),
    inference(resolution,[],[f297,f126]) ).

tff(f126,plain,
    sP0(sK6),
    inference(resolution,[],[f95,f81]) ).

tff(f81,plain,
    ! [X0: 'Tree'] :
      ( ~ searchtree(X0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f52,plain,
    ! [X0: 'Tree'] :
      ( ( sP0(X0)
        | ~ searchtree(X0) )
      & ( searchtree(X0)
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f41]) ).

tff(f41,plain,
    ! [X0: 'Tree'] :
      ( sP0(X0)
    <=> searchtree(X0) ),
    inference(definition_folding,[],[f35,f40]) ).

tff(f35,plain,
    ! [X0: 'Tree'] :
      ( ( ( 'empty:Tree' = X0 )
        | ( searchtree('right:(Tree)>Tree'(X0))
          & ! [X2: $int] :
              ( ~ in(X2,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X2) )
          & ! [X1: $int] :
              ( ~ $less('val:(Tree)>Int'(X0),X1)
              | ~ in(X1,'left:(Tree)>Tree'(X0)) )
          & searchtree('left:(Tree)>Tree'(X0)) ) )
    <=> searchtree(X0) ),
    inference(ennf_transformation,[],[f31]) ).

tff(f31,plain,
    ! [X0: 'Tree'] :
      ( searchtree(X0)
    <=> ( ( 'empty:Tree' != X0 )
       => ( searchtree('left:(Tree)>Tree'(X0))
          & searchtree('right:(Tree)>Tree'(X0))
          & ! [X1: $int] :
              ( in(X1,'left:(Tree)>Tree'(X0))
             => ~ $less('val:(Tree)>Int'(X0),X1) )
          & ! [X2: $int] :
              ( in(X2,'right:(Tree)>Tree'(X0))
             => $less('val:(Tree)>Int'(X0),X2) ) ) ) ),
    inference(true_and_false_elimination,[],[f30]) ).

tff(f30,plain,
    ! [X0: 'Tree'] :
      ( searchtree(X0)
    <=> ( ( ( 'empty:Tree' != X0 )
         => ( searchtree('left:(Tree)>Tree'(X0))
            & searchtree('right:(Tree)>Tree'(X0))
            & ! [X1: $int] :
                ( in(X1,'left:(Tree)>Tree'(X0))
               => ~ $less('val:(Tree)>Int'(X0),X1) )
            & ! [X2: $int] :
                ( in(X2,'right:(Tree)>Tree'(X0))
               => $less('val:(Tree)>Int'(X0),X2) ) ) )
        & ( ( 'empty:Tree' = X0 )
         => $true ) ) ),
    inference(rectify,[],[f10]) ).

tff(f10,plain,
    ! [X5: 'Tree'] :
      ( searchtree(X5)
    <=> ( ( ( 'empty:Tree' != X5 )
         => ( searchtree('right:(Tree)>Tree'(X5))
            & ! [X4: $int] :
                ( in(X4,'left:(Tree)>Tree'(X5))
               => ~ $less('val:(Tree)>Int'(X5),X4) )
            & searchtree('left:(Tree)>Tree'(X5))
            & ! [X4: $int] :
                ( in(X4,'right:(Tree)>Tree'(X5))
               => $less('val:(Tree)>Int'(X5),X4) ) ) )
        & ( ( 'empty:Tree' = X5 )
         => $true ) ) ),
    inference(theory_normalization,[],[f7]) ).

tff(f7,axiom,
    ! [X5: 'Tree'] :
      ( searchtree(X5)
    <=> ( ( ( 'empty:Tree' != X5 )
         => ( searchtree('right:(Tree)>Tree'(X5))
            & ! [X4: $int] :
                ( in(X4,'left:(Tree)>Tree'(X5))
               => $lesseq(X4,'val:(Tree)>Int'(X5)) )
            & searchtree('left:(Tree)>Tree'(X5))
            & ! [X4: $int] :
                ( in(X4,'right:(Tree)>Tree'(X5))
               => $greater(X4,'val:(Tree)>Int'(X5)) ) ) )
        & ( ( 'empty:Tree' = X5 )
         => $true ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_006) ).

tff(f95,plain,
    searchtree(sK6),
    inference(cnf_transformation,[],[f64]) ).

tff(f64,plain,
    ( ( ~ sP1(sK6,sK7)
      | ~ in(sK7,sK6) )
    & ( sP1(sK6,sK7)
      | in(sK7,sK6) )
    & searchtree(sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f62,f63]) ).

tff(f63,plain,
    ( ? [X0: 'Tree',X1: $int] :
        ( ( ~ sP1(X0,X1)
          | ~ in(X1,X0) )
        & ( sP1(X0,X1)
          | in(X1,X0) )
        & searchtree(X0) )
   => ( ( ~ sP1(sK6,sK7)
        | ~ in(sK7,sK6) )
      & ( sP1(sK6,sK7)
        | in(sK7,sK6) )
      & searchtree(sK6) ) ),
    introduced(choice_axiom,[]) ).

tff(f62,plain,
    ? [X0: 'Tree',X1: $int] :
      ( ( ~ sP1(X0,X1)
        | ~ in(X1,X0) )
      & ( sP1(X0,X1)
        | in(X1,X0) )
      & searchtree(X0) ),
    inference(rectify,[],[f61]) ).

tff(f61,plain,
    ? [X1: 'Tree',X0: $int] :
      ( ( ~ sP1(X1,X0)
        | ~ in(X0,X1) )
      & ( sP1(X1,X0)
        | in(X0,X1) )
      & searchtree(X1) ),
    inference(flattening,[],[f60]) ).

tff(f60,plain,
    ? [X1: 'Tree',X0: $int] :
      ( ( ~ sP1(X1,X0)
        | ~ in(X0,X1) )
      & ( sP1(X1,X0)
        | in(X0,X1) )
      & searchtree(X1) ),
    inference(nnf_transformation,[],[f43]) ).

tff(f43,plain,
    ? [X1: 'Tree',X0: $int] :
      ( ( in(X0,X1)
      <~> sP1(X1,X0) )
      & searchtree(X1) ),
    inference(definition_folding,[],[f37,f42]) ).

tff(f37,plain,
    ? [X1: 'Tree',X0: $int] :
      ( ( in(X0,X1)
      <~> ( ( 'empty:Tree' != X1 )
          & ( ( 'val:(Tree)>Int'(X1) = X0 )
            | ( ( ? [X2: 'Tree'] :
                    ( in(X0,X2)
                    & ( 'left:(Tree)>Tree'(X1) = X2 ) )
                | ~ $less(X0,'val:(Tree)>Int'(X1)) )
              & ( ? [X3: 'Tree'] :
                    ( ( 'right:(Tree)>Tree'(X1) = X3 )
                    & in(X0,X3) )
                | $less(X0,'val:(Tree)>Int'(X1)) ) )
            | ( 'empty:Tree' = X1 ) ) ) )
      & searchtree(X1) ),
    inference(flattening,[],[f36]) ).

tff(f36,plain,
    ? [X1: 'Tree',X0: $int] :
      ( ( in(X0,X1)
      <~> ( ( ( ( ? [X2: 'Tree'] :
                    ( in(X0,X2)
                    & ( 'left:(Tree)>Tree'(X1) = X2 ) )
                | ~ $less(X0,'val:(Tree)>Int'(X1)) )
              & ( ? [X3: 'Tree'] :
                    ( ( 'right:(Tree)>Tree'(X1) = X3 )
                    & in(X0,X3) )
                | $less(X0,'val:(Tree)>Int'(X1)) ) )
            | ( 'val:(Tree)>Int'(X1) = X0 )
            | ( 'empty:Tree' = X1 ) )
          & ( 'empty:Tree' != X1 ) ) )
      & searchtree(X1) ),
    inference(ennf_transformation,[],[f34]) ).

tff(f34,plain,
    ~ ! [X1: 'Tree',X0: $int] :
        ( searchtree(X1)
       => ( in(X0,X1)
        <=> ( ( ( 'empty:Tree' != X1 )
             => ( ( 'val:(Tree)>Int'(X1) != X0 )
               => ( ( $less(X0,'val:(Tree)>Int'(X1))
                   => ? [X2: 'Tree'] :
                        ( in(X0,X2)
                        & ( 'left:(Tree)>Tree'(X1) = X2 ) ) )
                  & ( ~ $less(X0,'val:(Tree)>Int'(X1))
                   => ? [X3: 'Tree'] :
                        ( ( 'right:(Tree)>Tree'(X1) = X3 )
                        & in(X0,X3) ) ) ) ) )
            & ( 'empty:Tree' != X1 ) ) ) ),
    inference(flattening,[],[f33]) ).

tff(f33,plain,
    ~ ! [X0: $int,X1: 'Tree'] :
        ( searchtree(X1)
       => ( ( ( ( ~ 'empty:Tree' )
              = X1 )
            & ( ( 'empty:Tree' != X1 )
             => ( ( 'val:(Tree)>Int'(X1) != X0 )
               => ( ( $less(X0,'val:(Tree)>Int'(X1))
                   => ? [X2: 'Tree'] :
                        ( in(X0,X2)
                        & ( 'left:(Tree)>Tree'(X1) = X2 ) ) )
                  & ( ~ $less(X0,'val:(Tree)>Int'(X1))
                   => ? [X3: 'Tree'] :
                        ( ( 'right:(Tree)>Tree'(X1) = X3 )
                        & in(X0,X3) ) ) ) ) ) )
        <=> in(X0,X1) ) ),
    inference(true_and_false_elimination,[],[f32]) ).

tff(f32,plain,
    ~ ! [X0: $int,X1: 'Tree'] :
        ( searchtree(X1)
       => ( ( ( ( 'empty:Tree' = X1 )
             => $false )
            & ( ( 'empty:Tree' != X1 )
             => ( ( ( 'val:(Tree)>Int'(X1) = X0 )
                 => $true )
                & ( ( 'val:(Tree)>Int'(X1) != X0 )
                 => ( ( $less(X0,'val:(Tree)>Int'(X1))
                     => ? [X2: 'Tree'] :
                          ( in(X0,X2)
                          & ( 'left:(Tree)>Tree'(X1) = X2 ) ) )
                    & ( ~ $less(X0,'val:(Tree)>Int'(X1))
                     => ? [X3: 'Tree'] :
                          ( ( 'right:(Tree)>Tree'(X1) = X3 )
                          & in(X0,X3) ) ) ) ) ) ) )
        <=> in(X0,X1) ) ),
    inference(rectify,[],[f9]) ).

tff(f9,negated_conjecture,
    ~ ! [X4: $int,X5: 'Tree'] :
        ( searchtree(X5)
       => ( ( ( ( 'empty:Tree' = X5 )
             => $false )
            & ( ( 'empty:Tree' != X5 )
             => ( ( ( 'val:(Tree)>Int'(X5) = X4 )
                 => $true )
                & ( ( 'val:(Tree)>Int'(X5) != X4 )
                 => ( ( $less(X4,'val:(Tree)>Int'(X5))
                     => ? [X6: 'Tree'] :
                          ( ( 'left:(Tree)>Tree'(X5) = X6 )
                          & in(X4,X6) ) )
                    & ( ~ $less(X4,'val:(Tree)>Int'(X5))
                     => ? [X7: 'Tree'] :
                          ( ( 'right:(Tree)>Tree'(X5) = X7 )
                          & in(X4,X7) ) ) ) ) ) ) )
        <=> in(X4,X5) ) ),
    inference(negated_conjecture,[],[f8]) ).

tff(f8,conjecture,
    ! [X4: $int,X5: 'Tree'] :
      ( searchtree(X5)
     => ( ( ( ( 'empty:Tree' = X5 )
           => $false )
          & ( ( 'empty:Tree' != X5 )
           => ( ( ( 'val:(Tree)>Int'(X5) = X4 )
               => $true )
              & ( ( 'val:(Tree)>Int'(X5) != X4 )
               => ( ( $less(X4,'val:(Tree)>Int'(X5))
                   => ? [X6: 'Tree'] :
                        ( ( 'left:(Tree)>Tree'(X5) = X6 )
                        & in(X4,X6) ) )
                  & ( ~ $less(X4,'val:(Tree)>Int'(X5))
                   => ? [X7: 'Tree'] :
                        ( ( 'right:(Tree)>Tree'(X5) = X7 )
                        & in(X4,X7) ) ) ) ) ) ) )
      <=> in(X4,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_007) ).

tff(f297,plain,
    ( ~ sP0(sK6)
    | spl8_24 ),
    inference(avatar_component_clause,[],[f295]) ).

tff(f321,plain,
    ( spl8_4
    | spl8_1
    | ~ spl8_25 ),
    inference(avatar_split_clause,[],[f317,f300,f117,f133]) ).

tff(f317,plain,
    ( in(sK7,sK6)
    | ( 'empty:Tree' = sK6 )
    | ~ spl8_25 ),
    inference(resolution,[],[f302,f100]) ).

tff(f100,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ~ in(X1,'right:(Tree)>Tree'(X0))
      | in(X1,X0)
      | ( 'empty:Tree' = X0 ) ),
    inference(cnf_transformation,[],[f67]) ).

tff(f315,plain,
    ( spl8_3
    | spl8_23
    | spl8_6 ),
    inference(avatar_split_clause,[],[f311,f144,f291,f129]) ).

tff(f311,plain,
    ( $less('val:(Tree)>Int'(sK6),sK7)
    | ( sK7 = 'val:(Tree)>Int'(sK6) )
    | spl8_6 ),
    inference(resolution,[],[f145,f18]) ).

tff(f18,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_149,[]) ).

tff(f145,plain,
    ( ~ $less(sK7,'val:(Tree)>Int'(sK6))
    | spl8_6 ),
    inference(avatar_component_clause,[],[f144]) ).

tff(f303,plain,
    ( spl8_3
    | spl8_4
    | spl8_25
    | spl8_6
    | ~ spl8_2
    | ~ spl8_7 ),
    inference(avatar_split_clause,[],[f186,f149,f121,f144,f300,f133,f129]) ).

tff(f149,plain,
    ( spl8_7
  <=> ( 'right:(Tree)>Tree'(sK6) = sK5(sK6,sK7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).

tff(f186,plain,
    ( $less(sK7,'val:(Tree)>Int'(sK6))
    | in(sK7,'right:(Tree)>Tree'(sK6))
    | ( 'empty:Tree' = sK6 )
    | ( sK7 = 'val:(Tree)>Int'(sK6) )
    | ~ spl8_2
    | ~ spl8_7 ),
    inference(forward_demodulation,[],[f185,f151]) ).

tff(f151,plain,
    ( ( 'right:(Tree)>Tree'(sK6) = sK5(sK6,sK7) )
    | ~ spl8_7 ),
    inference(avatar_component_clause,[],[f149]) ).

tff(f185,plain,
    ( $less(sK7,'val:(Tree)>Int'(sK6))
    | in(sK7,sK5(sK6,sK7))
    | ( 'empty:Tree' = sK6 )
    | ( sK7 = 'val:(Tree)>Int'(sK6) )
    | ~ spl8_2 ),
    inference(resolution,[],[f123,f84]) ).

tff(f84,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ~ sP1(X0,X1)
      | ( 'empty:Tree' = X0 )
      | ( 'val:(Tree)>Int'(X0) = X1 )
      | $less(X1,'val:(Tree)>Int'(X0))
      | in(X1,sK5(X0,X1)) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f123,plain,
    ( sP1(sK6,sK7)
    | ~ spl8_2 ),
    inference(avatar_component_clause,[],[f121]) ).

tff(f289,plain,
    ( spl8_4
    | spl8_1
    | ~ spl8_18
    | ~ spl8_19 ),
    inference(avatar_split_clause,[],[f274,f262,f257,f117,f133]) ).

tff(f257,plain,
    ( spl8_18
  <=> in(sK7,sK4(sK6,sK7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).

tff(f262,plain,
    ( spl8_19
  <=> ( 'left:(Tree)>Tree'(sK6) = sK4(sK6,sK7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).

tff(f274,plain,
    ( in(sK7,sK6)
    | ( 'empty:Tree' = sK6 )
    | ~ spl8_18
    | ~ spl8_19 ),
    inference(resolution,[],[f266,f99]) ).

tff(f99,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ~ in(X1,'left:(Tree)>Tree'(X0))
      | in(X1,X0)
      | ( 'empty:Tree' = X0 ) ),
    inference(cnf_transformation,[],[f67]) ).

tff(f266,plain,
    ( in(sK7,'left:(Tree)>Tree'(sK6))
    | ~ spl8_18
    | ~ spl8_19 ),
    inference(backward_demodulation,[],[f259,f264]) ).

tff(f264,plain,
    ( ( 'left:(Tree)>Tree'(sK6) = sK4(sK6,sK7) )
    | ~ spl8_19 ),
    inference(avatar_component_clause,[],[f262]) ).

tff(f259,plain,
    ( in(sK7,sK4(sK6,sK7))
    | ~ spl8_18 ),
    inference(avatar_component_clause,[],[f257]) ).

tff(f265,plain,
    ( ~ spl8_2
    | spl8_4
    | spl8_19
    | spl8_3
    | ~ spl8_6 ),
    inference(avatar_split_clause,[],[f245,f144,f129,f262,f133,f121]) ).

tff(f245,plain,
    ( ( sK7 = 'val:(Tree)>Int'(sK6) )
    | ( 'left:(Tree)>Tree'(sK6) = sK4(sK6,sK7) )
    | ( 'empty:Tree' = sK6 )
    | ~ sP1(sK6,sK7)
    | ~ spl8_6 ),
    inference(resolution,[],[f146,f86]) ).

tff(f86,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ~ $less(X1,'val:(Tree)>Int'(X0))
      | ( 'val:(Tree)>Int'(X0) = X1 )
      | ~ sP1(X0,X1)
      | ( 'empty:Tree' = X0 )
      | ( 'left:(Tree)>Tree'(X0) = sK4(X0,X1) ) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f260,plain,
    ( ~ spl8_2
    | spl8_3
    | spl8_18
    | spl8_4
    | ~ spl8_6 ),
    inference(avatar_split_clause,[],[f246,f144,f133,f257,f129,f121]) ).

tff(f246,plain,
    ( ( 'empty:Tree' = sK6 )
    | in(sK7,sK4(sK6,sK7))
    | ( sK7 = 'val:(Tree)>Int'(sK6) )
    | ~ sP1(sK6,sK7)
    | ~ spl8_6 ),
    inference(resolution,[],[f146,f87]) ).

tff(f87,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ~ $less(X1,'val:(Tree)>Int'(X0))
      | ~ sP1(X0,X1)
      | ( 'val:(Tree)>Int'(X0) = X1 )
      | ( 'empty:Tree' = X0 )
      | in(X1,sK4(X0,X1)) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f167,plain,
    ( ~ spl8_1
    | ~ spl8_4 ),
    inference(avatar_contradiction_clause,[],[f165]) ).

tff(f165,plain,
    ( $false
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(resolution,[],[f163,f113]) ).

tff(f113,plain,
    ! [X1: $int] : ~ in(X1,'empty:Tree'),
    inference(equality_resolution,[],[f103]) ).

tff(f103,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ( 'empty:Tree' != X0 )
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f67]) ).

tff(f163,plain,
    ( in(sK7,'empty:Tree')
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(forward_demodulation,[],[f119,f135]) ).

tff(f135,plain,
    ( ( 'empty:Tree' = sK6 )
    | ~ spl8_4 ),
    inference(avatar_component_clause,[],[f133]) ).

tff(f162,plain,
    ( ~ spl8_2
    | ~ spl8_4 ),
    inference(avatar_contradiction_clause,[],[f159]) ).

tff(f159,plain,
    ( $false
    | ~ spl8_2
    | ~ spl8_4 ),
    inference(resolution,[],[f156,f112]) ).

tff(f112,plain,
    ! [X1: $int] : ~ sP1('empty:Tree',X1),
    inference(equality_resolution,[],[f88]) ).

tff(f88,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ( 'empty:Tree' != X0 )
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f156,plain,
    ( sP1('empty:Tree',sK7)
    | ~ spl8_2
    | ~ spl8_4 ),
    inference(backward_demodulation,[],[f123,f135]) ).

tff(f152,plain,
    ( spl8_7
    | spl8_4
    | spl8_3
    | spl8_6
    | ~ spl8_2 ),
    inference(avatar_split_clause,[],[f137,f121,f144,f129,f133,f149]) ).

tff(f137,plain,
    ( $less(sK7,'val:(Tree)>Int'(sK6))
    | ( sK7 = 'val:(Tree)>Int'(sK6) )
    | ( 'empty:Tree' = sK6 )
    | ( 'right:(Tree)>Tree'(sK6) = sK5(sK6,sK7) )
    | ~ spl8_2 ),
    inference(resolution,[],[f123,f85]) ).

tff(f85,plain,
    ! [X0: 'Tree',X1: $int] :
      ( ~ sP1(X0,X1)
      | ( 'val:(Tree)>Int'(X0) = X1 )
      | $less(X1,'val:(Tree)>Int'(X0))
      | ( 'empty:Tree' = X0 )
      | ( 'right:(Tree)>Tree'(X0) = sK5(X0,X1) ) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f136,plain,
    ( ~ spl8_3
    | spl8_4
    | spl8_1 ),
    inference(avatar_split_clause,[],[f127,f117,f133,f129]) ).

tff(f127,plain,
    ( ( 'empty:Tree' = sK6 )
    | ( sK7 != 'val:(Tree)>Int'(sK6) )
    | spl8_1 ),
    inference(constrained_resolution,[],[f118,f115]) ).

tff(f115,plain,
    ! [X0: 'Tree'] :
      ( in('val:(Tree)>Int'(X0),X0)
      | ( 'empty:Tree' = X0 ) ),
    inference(equality_resolution,[],[f98]) ).

tff(f98,plain,
    ! [X0: 'Tree',X1: $int] :
      ( in(X1,X0)
      | ( 'empty:Tree' = X0 )
      | ( 'val:(Tree)>Int'(X0) != X1 ) ),
    inference(cnf_transformation,[],[f67]) ).

tff(f118,plain,
    ( ~ in(sK7,sK6)
    | spl8_1 ),
    inference(avatar_component_clause,[],[f117]) ).

tff(f125,plain,
    ( ~ spl8_2
    | ~ spl8_1 ),
    inference(avatar_split_clause,[],[f97,f117,f121]) ).

tff(f97,plain,
    ( ~ in(sK7,sK6)
    | ~ sP1(sK6,sK7) ),
    inference(cnf_transformation,[],[f64]) ).

tff(f124,plain,
    ( spl8_1
    | spl8_2 ),
    inference(avatar_split_clause,[],[f96,f121,f117]) ).

tff(f96,plain,
    ( sP1(sK6,sK7)
    | in(sK7,sK6) ),
    inference(cnf_transformation,[],[f64]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWW678=1 : TPTP v8.1.0. Released v6.4.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 21:01:11 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 1.40/0.54  % (32725)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.40/0.54  % (32724)lrs+22_1:1_amm=sco:fsr=off:gve=force:sos=on:uwa=all:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.40/0.54  % (32726)lrs+10_1:1_ev=force:gve=cautious:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.40/0.54  % (32717)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=36:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/36Mi)
% 1.40/0.54  % (32717)Refutation not found, incomplete strategy% (32717)------------------------------
% 1.40/0.54  % (32717)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.40/0.54  % (32717)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.40/0.54  % (32717)Termination reason: Refutation not found, incomplete strategy
% 1.40/0.54  
% 1.40/0.54  % (32717)Memory used [KB]: 5500
% 1.40/0.54  % (32717)Time elapsed: 0.128 s
% 1.40/0.54  % (32717)Instructions burned: 3 (million)
% 1.40/0.54  % (32717)------------------------------
% 1.40/0.54  % (32717)------------------------------
% 1.40/0.54  % (32718)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/26Mi)
% 1.40/0.54  % (32725)Instruction limit reached!
% 1.40/0.54  % (32725)------------------------------
% 1.40/0.54  % (32725)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.40/0.54  % (32725)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.40/0.54  % (32725)Termination reason: Unknown
% 1.40/0.54  % (32725)Termination phase: Property scanning
% 1.40/0.54  
% 1.40/0.54  % (32725)Memory used [KB]: 895
% 1.40/0.54  % (32725)Time elapsed: 0.003 s
% 1.40/0.54  % (32725)Instructions burned: 2 (million)
% 1.40/0.54  % (32725)------------------------------
% 1.40/0.54  % (32725)------------------------------
% 1.53/0.55  % (32733)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.53/0.55  % (32734)lrs+1_1:10_av=off:drc=off:nwc=2.0:sp=reverse_frequency:thsq=on:thsqc=64:thsql=off:i=47:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/47Mi)
% 1.53/0.55  % (32732)dis+2_1:1_av=off:bsr=on:erd=off:s2pl=on:sgt=16:sos=on:sp=frequency:ss=axioms:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 1.53/0.55  % (32739)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=41:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/41Mi)
% 1.53/0.55  % (32716)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/32Mi)
% 1.53/0.56  % (32713)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.53/0.56  % (32713)Instruction limit reached!
% 1.53/0.56  % (32713)------------------------------
% 1.53/0.56  % (32713)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56  % (32713)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56  % (32713)Termination reason: Unknown
% 1.53/0.56  % (32713)Termination phase: Including theory axioms
% 1.53/0.56  
% 1.53/0.56  % (32713)Memory used [KB]: 895
% 1.53/0.56  % (32713)Time elapsed: 0.002 s
% 1.53/0.56  % (32713)Instructions burned: 2 (million)
% 1.53/0.56  % (32713)------------------------------
% 1.53/0.56  % (32713)------------------------------
% 1.53/0.56  % (32716)Refutation not found, incomplete strategy% (32716)------------------------------
% 1.53/0.56  % (32716)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56  % (32716)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56  % (32716)Termination reason: Refutation not found, incomplete strategy
% 1.53/0.56  
% 1.53/0.56  % (32716)Memory used [KB]: 5500
% 1.53/0.56  % (32716)Time elapsed: 0.133 s
% 1.53/0.56  % (32716)Instructions burned: 4 (million)
% 1.53/0.56  % (32716)------------------------------
% 1.53/0.56  % (32716)------------------------------
% 1.53/0.56  % (32732)Refutation not found, incomplete strategy% (32732)------------------------------
% 1.53/0.56  % (32732)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56  % (32732)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56  % (32732)Termination reason: Refutation not found, incomplete strategy
% 1.53/0.56  
% 1.53/0.56  % (32732)Memory used [KB]: 1023
% 1.53/0.56  % (32732)Time elapsed: 0.133 s
% 1.53/0.56  % (32732)Instructions burned: 4 (million)
% 1.53/0.56  % (32732)------------------------------
% 1.53/0.56  % (32732)------------------------------
% 1.53/0.56  % (32726)Instruction limit reached!
% 1.53/0.56  % (32726)------------------------------
% 1.53/0.56  % (32726)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56  % (32726)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56  % (32726)Termination reason: Unknown
% 1.53/0.56  % (32726)Termination phase: Property scanning
% 1.53/0.56  
% 1.53/0.56  % (32726)Memory used [KB]: 1023
% 1.53/0.56  % (32726)Time elapsed: 0.002 s
% 1.53/0.56  % (32726)Instructions burned: 2 (million)
% 1.53/0.56  % (32726)------------------------------
% 1.53/0.56  % (32726)------------------------------
% 1.53/0.56  % (32738)dis+1011_1:1_bd=off:canc=force:ev=cautious:nwc=5.0:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 1.53/0.56  % (32715)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.53/0.56  % (32729)lrs+10_1:1_sd=10:sos=all:ss=axioms:st=5.0:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.53/0.56  % (32736)lrs+1_3:1_ep=RSTC:sos=on:urr=on:i=43:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/43Mi)
% 1.53/0.56  % (32729)Instruction limit reached!
% 1.53/0.56  % (32729)------------------------------
% 1.53/0.56  % (32729)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56  % (32729)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56  % (32729)Termination reason: Unknown
% 1.53/0.56  % (32729)Termination phase: Saturation
% 1.53/0.56  
% 1.53/0.56  % (32729)Memory used [KB]: 1023
% 1.53/0.56  % (32729)Time elapsed: 0.003 s
% 1.53/0.56  % (32729)Instructions burned: 3 (million)
% 1.53/0.56  % (32729)------------------------------
% 1.53/0.56  % (32729)------------------------------
% 1.53/0.56  % (32722)lrs+10_1:1_ep=R:gve=force:plsq=on:plsqr=32,1:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.53/0.56  % (32722)Instruction limit reached!
% 1.53/0.56  % (32722)------------------------------
% 1.53/0.56  % (32722)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56  % (32722)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56  % (32722)Termination reason: Unknown
% 1.53/0.56  % (32722)Termination phase: Property scanning
% 1.53/0.56  
% 1.53/0.56  % (32722)Memory used [KB]: 1023
% 1.53/0.56  % (32722)Time elapsed: 0.003 s
% 1.53/0.56  % (32722)Instructions burned: 3 (million)
% 1.53/0.56  % (32722)------------------------------
% 1.53/0.56  % (32722)------------------------------
% 1.53/0.57  % (32724)First to succeed.
% 1.53/0.57  % (32724)Refutation found. Thanks to Tanya!
% 1.53/0.57  % SZS status Theorem for theBenchmark
% 1.53/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 1.53/0.57  % (32724)------------------------------
% 1.53/0.57  % (32724)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.57  % (32724)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.57  % (32724)Termination reason: Refutation
% 1.53/0.57  
% 1.53/0.57  % (32724)Memory used [KB]: 6012
% 1.53/0.57  % (32724)Time elapsed: 0.140 s
% 1.53/0.57  % (32724)Instructions burned: 15 (million)
% 1.53/0.57  % (32724)------------------------------
% 1.53/0.57  % (32724)------------------------------
% 1.53/0.57  % (32709)Success in time 0.216 s
%------------------------------------------------------------------------------