TSTP Solution File: SWW679_1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWW679_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_sat --cores 0 -t %d %s

% Computer : n007.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 19:21:05 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   72 (   9 unt;  16 typ;   0 def)
%            Number of atoms       :  298 (  74 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  374 ( 132   ~;  86   |; 102   &)
%                                         (  10 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number arithmetic     :   95 (  59 atm;   0 fun;   0 num;  36 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   12 (   9   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   12 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :   83 (  59   !;  24   ?;  83   :)

% 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,
    sK1: $int ).

tff(func_def_10,type,
    sK2: 'Tree' ).

tff(func_def_11,type,
    sK3: 'Tree' > $int ).

tff(func_def_12,type,
    sK4: 'Tree' > $int ).

tff(func_def_13,type,
    sF5: 'Tree' ).

tff(func_def_14,type,
    sF6: $int ).

tff(func_def_15,type,
    sF7: 'Tree' ).

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(f173,plain,
    $false,
    inference(avatar_sat_refutation,[],[f115,f116,f162,f172]) ).

tff(f172,plain,
    spl8_1,
    inference(avatar_contradiction_clause,[],[f171]) ).

tff(f171,plain,
    ( $false
    | spl8_1 ),
    inference(subsumption_resolution,[],[f170,f118]) ).

tff(f118,plain,
    sP0(sK2),
    inference(resolution,[],[f83,f59]) ).

tff(f59,plain,
    searchtree(sK2),
    inference(cnf_transformation,[],[f43]) ).

tff(f43,plain,
    ( ( ( ! [X2: 'Tree'] :
            ( ( 'right:(Tree)>Tree'(sK2) != X2 )
            | ~ searchtree(X2) )
        & ~ $less(sK1,'val:(Tree)>Int'(sK2)) )
      | ( $less(sK1,'val:(Tree)>Int'(sK2))
        & ! [X3: 'Tree'] :
            ( ( 'left:(Tree)>Tree'(sK2) != X3 )
            | ~ searchtree(X3) ) ) )
    & searchtree(sK2)
    & ( 'empty:Tree' != sK2 )
    & ( 'val:(Tree)>Int'(sK2) != sK1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f41,f42]) ).

tff(f42,plain,
    ( ? [X0: $int,X1: 'Tree'] :
        ( ( ( ! [X2: 'Tree'] :
                ( ( 'right:(Tree)>Tree'(X1) != X2 )
                | ~ searchtree(X2) )
            & ~ $less(X0,'val:(Tree)>Int'(X1)) )
          | ( $less(X0,'val:(Tree)>Int'(X1))
            & ! [X3: 'Tree'] :
                ( ( 'left:(Tree)>Tree'(X1) != X3 )
                | ~ searchtree(X3) ) ) )
        & searchtree(X1)
        & ( 'empty:Tree' != X1 )
        & ( 'val:(Tree)>Int'(X1) != X0 ) )
   => ( ( ( ! [X2: 'Tree'] :
              ( ( 'right:(Tree)>Tree'(sK2) != X2 )
              | ~ searchtree(X2) )
          & ~ $less(sK1,'val:(Tree)>Int'(sK2)) )
        | ( $less(sK1,'val:(Tree)>Int'(sK2))
          & ! [X3: 'Tree'] :
              ( ( 'left:(Tree)>Tree'(sK2) != X3 )
              | ~ searchtree(X3) ) ) )
      & searchtree(sK2)
      & ( 'empty:Tree' != sK2 )
      & ( 'val:(Tree)>Int'(sK2) != sK1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f41,plain,
    ? [X0: $int,X1: 'Tree'] :
      ( ( ( ! [X2: 'Tree'] :
              ( ( 'right:(Tree)>Tree'(X1) != X2 )
              | ~ searchtree(X2) )
          & ~ $less(X0,'val:(Tree)>Int'(X1)) )
        | ( $less(X0,'val:(Tree)>Int'(X1))
          & ! [X3: 'Tree'] :
              ( ( 'left:(Tree)>Tree'(X1) != X3 )
              | ~ searchtree(X3) ) ) )
      & searchtree(X1)
      & ( 'empty:Tree' != X1 )
      & ( 'val:(Tree)>Int'(X1) != X0 ) ),
    inference(rectify,[],[f36]) ).

tff(f36,plain,
    ? [X1: $int,X0: 'Tree'] :
      ( ( ( ! [X3: 'Tree'] :
              ( ( 'right:(Tree)>Tree'(X0) != X3 )
              | ~ searchtree(X3) )
          & ~ $less(X1,'val:(Tree)>Int'(X0)) )
        | ( $less(X1,'val:(Tree)>Int'(X0))
          & ! [X2: 'Tree'] :
              ( ( 'left:(Tree)>Tree'(X0) != X2 )
              | ~ searchtree(X2) ) ) )
      & searchtree(X0)
      & ( 'empty:Tree' != X0 )
      & ( 'val:(Tree)>Int'(X0) != X1 ) ),
    inference(flattening,[],[f35]) ).

tff(f35,plain,
    ? [X0: 'Tree',X1: $int] :
      ( ( ( ! [X3: 'Tree'] :
              ( ( 'right:(Tree)>Tree'(X0) != X3 )
              | ~ searchtree(X3) )
          & ~ $less(X1,'val:(Tree)>Int'(X0)) )
        | ( $less(X1,'val:(Tree)>Int'(X0))
          & ! [X2: 'Tree'] :
              ( ( 'left:(Tree)>Tree'(X0) != X2 )
              | ~ searchtree(X2) ) ) )
      & ( 'val:(Tree)>Int'(X0) != X1 )
      & ( 'empty:Tree' != X0 )
      & searchtree(X0) ),
    inference(ennf_transformation,[],[f25]) ).

tff(f25,plain,
    ~ ! [X0: 'Tree',X1: $int] :
        ( searchtree(X0)
       => ( ( 'empty:Tree' != X0 )
         => ( ( 'val:(Tree)>Int'(X0) != X1 )
           => ( ( $less(X1,'val:(Tree)>Int'(X0))
               => ? [X2: 'Tree'] :
                    ( searchtree(X2)
                    & ( 'left:(Tree)>Tree'(X0) = X2 ) ) )
              & ( ~ $less(X1,'val:(Tree)>Int'(X0))
               => ? [X3: 'Tree'] :
                    ( ( 'right:(Tree)>Tree'(X0) = X3 )
                    & searchtree(X3) ) ) ) ) ) ),
    inference(true_and_false_elimination,[],[f24]) ).

tff(f24,plain,
    ~ ! [X0: 'Tree',X1: $int] :
        ( searchtree(X0)
       => ( ( ( 'empty:Tree' = X0 )
           => $true )
          & ( ( 'empty:Tree' != X0 )
           => ( ( ( 'val:(Tree)>Int'(X0) = X1 )
               => $true )
              & ( ( 'val:(Tree)>Int'(X0) != X1 )
               => ( ( $less(X1,'val:(Tree)>Int'(X0))
                   => ? [X2: 'Tree'] :
                        ( searchtree(X2)
                        & ( 'left:(Tree)>Tree'(X0) = X2 ) ) )
                  & ( ~ $less(X1,'val:(Tree)>Int'(X0))
                   => ? [X3: 'Tree'] :
                        ( ( 'right:(Tree)>Tree'(X0) = X3 )
                        & searchtree(X3) ) ) ) ) ) ) ) ),
    inference(rectify,[],[f9]) ).

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

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

tff(f83,plain,
    ! [X0: 'Tree'] :
      ( ~ searchtree(X0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f54]) ).

tff(f54,plain,
    ! [X0: 'Tree'] :
      ( ( sP0(X0)
        | ~ searchtree(X0) )
      & ( searchtree(X0)
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f40]) ).

tff(f40,plain,
    ! [X0: 'Tree'] :
      ( sP0(X0)
    <=> searchtree(X0) ),
    inference(definition_folding,[],[f34,f39]) ).

tff(f39,plain,
    ! [X0: 'Tree'] :
      ( sP0(X0)
    <=> ( ( 'empty:Tree' = X0 )
        | ( ! [X2: $int] :
              ( ~ in(X2,'left:(Tree)>Tree'(X0))
              | ~ $less('val:(Tree)>Int'(X0),X2) )
          & searchtree('right:(Tree)>Tree'(X0))
          & ! [X1: $int] :
              ( ~ in(X1,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X1) )
          & searchtree('left:(Tree)>Tree'(X0)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f34,plain,
    ! [X0: 'Tree'] :
      ( ( ( 'empty:Tree' = X0 )
        | ( ! [X2: $int] :
              ( ~ in(X2,'left:(Tree)>Tree'(X0))
              | ~ $less('val:(Tree)>Int'(X0),X2) )
          & searchtree('right:(Tree)>Tree'(X0))
          & ! [X1: $int] :
              ( ~ in(X1,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X1) )
          & searchtree('left:(Tree)>Tree'(X0)) ) )
    <=> searchtree(X0) ),
    inference(ennf_transformation,[],[f27]) ).

tff(f27,plain,
    ! [X0: 'Tree'] :
      ( ( ( 'empty:Tree' != X0 )
       => ( ! [X1: $int] :
              ( in(X1,'right:(Tree)>Tree'(X0))
             => $less('val:(Tree)>Int'(X0),X1) )
          & searchtree('left:(Tree)>Tree'(X0))
          & searchtree('right:(Tree)>Tree'(X0))
          & ! [X2: $int] :
              ( in(X2,'left:(Tree)>Tree'(X0))
             => ~ $less('val:(Tree)>Int'(X0),X2) ) ) )
    <=> searchtree(X0) ),
    inference(true_and_false_elimination,[],[f26]) ).

tff(f26,plain,
    ! [X0: 'Tree'] :
      ( searchtree(X0)
    <=> ( ( ( 'empty:Tree' = X0 )
         => $true )
        & ( ( 'empty:Tree' != X0 )
         => ( ! [X1: $int] :
                ( in(X1,'right:(Tree)>Tree'(X0))
               => $less('val:(Tree)>Int'(X0),X1) )
            & searchtree('left:(Tree)>Tree'(X0))
            & searchtree('right:(Tree)>Tree'(X0))
            & ! [X2: $int] :
                ( in(X2,'left:(Tree)>Tree'(X0))
               => ~ $less('val:(Tree)>Int'(X0),X2) ) ) ) ) ),
    inference(rectify,[],[f10]) ).

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

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

tff(f170,plain,
    ( ~ sP0(sK2)
    | spl8_1 ),
    inference(subsumption_resolution,[],[f169,f58]) ).

tff(f58,plain,
    'empty:Tree' != sK2,
    inference(cnf_transformation,[],[f43]) ).

tff(f169,plain,
    ( ( 'empty:Tree' = sK2 )
    | ~ sP0(sK2)
    | spl8_1 ),
    inference(subsumption_resolution,[],[f166,f105]) ).

tff(f105,plain,
    ( ~ searchtree(sF5)
    | spl8_1 ),
    inference(avatar_component_clause,[],[f103]) ).

tff(f103,plain,
    ( spl8_1
  <=> searchtree(sF5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

tff(f166,plain,
    ( searchtree(sF5)
    | ~ sP0(sK2)
    | ( 'empty:Tree' = sK2 ) ),
    inference(superposition,[],[f75,f94]) ).

tff(f94,plain,
    'right:(Tree)>Tree'(sK2) = sF5,
    introduced(function_definition,[]) ).

tff(f75,plain,
    ! [X0: 'Tree'] :
      ( searchtree('right:(Tree)>Tree'(X0))
      | ~ sP0(X0)
      | ( 'empty:Tree' = X0 ) ),
    inference(cnf_transformation,[],[f53]) ).

tff(f53,plain,
    ! [X0: 'Tree'] :
      ( ( sP0(X0)
        | ( ( 'empty:Tree' != X0 )
          & ( ( in(sK3(X0),'left:(Tree)>Tree'(X0))
              & $less('val:(Tree)>Int'(X0),sK3(X0)) )
            | ~ searchtree('right:(Tree)>Tree'(X0))
            | ( in(sK4(X0),'right:(Tree)>Tree'(X0))
              & ~ $less('val:(Tree)>Int'(X0),sK4(X0)) )
            | ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
      & ( ( 'empty:Tree' = X0 )
        | ( ! [X3: $int] :
              ( ~ in(X3,'left:(Tree)>Tree'(X0))
              | ~ $less('val:(Tree)>Int'(X0),X3) )
          & searchtree('right:(Tree)>Tree'(X0))
          & ! [X4: $int] :
              ( ~ in(X4,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X4) )
          & searchtree('left:(Tree)>Tree'(X0)) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f50,f52,f51]) ).

tff(f51,plain,
    ! [X0: 'Tree'] :
      ( ? [X1: $int] :
          ( in(X1,'left:(Tree)>Tree'(X0))
          & $less('val:(Tree)>Int'(X0),X1) )
     => ( in(sK3(X0),'left:(Tree)>Tree'(X0))
        & $less('val:(Tree)>Int'(X0),sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f52,plain,
    ! [X0: 'Tree'] :
      ( ? [X2: $int] :
          ( in(X2,'right:(Tree)>Tree'(X0))
          & ~ $less('val:(Tree)>Int'(X0),X2) )
     => ( in(sK4(X0),'right:(Tree)>Tree'(X0))
        & ~ $less('val:(Tree)>Int'(X0),sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f50,plain,
    ! [X0: 'Tree'] :
      ( ( sP0(X0)
        | ( ( 'empty:Tree' != X0 )
          & ( ? [X1: $int] :
                ( in(X1,'left:(Tree)>Tree'(X0))
                & $less('val:(Tree)>Int'(X0),X1) )
            | ~ searchtree('right:(Tree)>Tree'(X0))
            | ? [X2: $int] :
                ( in(X2,'right:(Tree)>Tree'(X0))
                & ~ $less('val:(Tree)>Int'(X0),X2) )
            | ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
      & ( ( 'empty:Tree' = X0 )
        | ( ! [X3: $int] :
              ( ~ in(X3,'left:(Tree)>Tree'(X0))
              | ~ $less('val:(Tree)>Int'(X0),X3) )
          & searchtree('right:(Tree)>Tree'(X0))
          & ! [X4: $int] :
              ( ~ in(X4,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X4) )
          & searchtree('left:(Tree)>Tree'(X0)) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f49]) ).

tff(f49,plain,
    ! [X0: 'Tree'] :
      ( ( sP0(X0)
        | ( ( 'empty:Tree' != X0 )
          & ( ? [X2: $int] :
                ( in(X2,'left:(Tree)>Tree'(X0))
                & $less('val:(Tree)>Int'(X0),X2) )
            | ~ searchtree('right:(Tree)>Tree'(X0))
            | ? [X1: $int] :
                ( in(X1,'right:(Tree)>Tree'(X0))
                & ~ $less('val:(Tree)>Int'(X0),X1) )
            | ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
      & ( ( 'empty:Tree' = X0 )
        | ( ! [X2: $int] :
              ( ~ in(X2,'left:(Tree)>Tree'(X0))
              | ~ $less('val:(Tree)>Int'(X0),X2) )
          & searchtree('right:(Tree)>Tree'(X0))
          & ! [X1: $int] :
              ( ~ in(X1,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X1) )
          & searchtree('left:(Tree)>Tree'(X0)) )
        | ~ sP0(X0) ) ),
    inference(flattening,[],[f48]) ).

tff(f48,plain,
    ! [X0: 'Tree'] :
      ( ( sP0(X0)
        | ( ( 'empty:Tree' != X0 )
          & ( ? [X2: $int] :
                ( in(X2,'left:(Tree)>Tree'(X0))
                & $less('val:(Tree)>Int'(X0),X2) )
            | ~ searchtree('right:(Tree)>Tree'(X0))
            | ? [X1: $int] :
                ( in(X1,'right:(Tree)>Tree'(X0))
                & ~ $less('val:(Tree)>Int'(X0),X1) )
            | ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
      & ( ( 'empty:Tree' = X0 )
        | ( ! [X2: $int] :
              ( ~ in(X2,'left:(Tree)>Tree'(X0))
              | ~ $less('val:(Tree)>Int'(X0),X2) )
          & searchtree('right:(Tree)>Tree'(X0))
          & ! [X1: $int] :
              ( ~ in(X1,'right:(Tree)>Tree'(X0))
              | $less('val:(Tree)>Int'(X0),X1) )
          & searchtree('left:(Tree)>Tree'(X0)) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f39]) ).

tff(f162,plain,
    spl8_2,
    inference(avatar_contradiction_clause,[],[f161]) ).

tff(f161,plain,
    ( $false
    | spl8_2 ),
    inference(subsumption_resolution,[],[f160,f118]) ).

tff(f160,plain,
    ( ~ sP0(sK2)
    | spl8_2 ),
    inference(subsumption_resolution,[],[f159,f109]) ).

tff(f109,plain,
    ( ~ searchtree(sF7)
    | spl8_2 ),
    inference(avatar_component_clause,[],[f107]) ).

tff(f107,plain,
    ( spl8_2
  <=> searchtree(sF7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

tff(f159,plain,
    ( searchtree(sF7)
    | ~ sP0(sK2) ),
    inference(subsumption_resolution,[],[f157,f58]) ).

tff(f157,plain,
    ( ( 'empty:Tree' = sK2 )
    | searchtree(sF7)
    | ~ sP0(sK2) ),
    inference(superposition,[],[f73,f97]) ).

tff(f97,plain,
    sF7 = 'left:(Tree)>Tree'(sK2),
    introduced(function_definition,[]) ).

tff(f73,plain,
    ! [X0: 'Tree'] :
      ( searchtree('left:(Tree)>Tree'(X0))
      | ( 'empty:Tree' = X0 )
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f53]) ).

tff(f116,plain,
    ( ~ spl8_3
    | ~ spl8_2 ),
    inference(avatar_split_clause,[],[f100,f107,f112]) ).

tff(f112,plain,
    ( spl8_3
  <=> $less(sK1,sF6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

tff(f100,plain,
    ( ~ searchtree(sF7)
    | ~ $less(sK1,sF6) ),
    inference(definition_folding,[],[f89,f97,f95]) ).

tff(f95,plain,
    'val:(Tree)>Int'(sK2) = sF6,
    introduced(function_definition,[]) ).

tff(f89,plain,
    ( ~ $less(sK1,'val:(Tree)>Int'(sK2))
    | ~ searchtree('left:(Tree)>Tree'(sK2)) ),
    inference(equality_resolution,[],[f60]) ).

tff(f60,plain,
    ! [X3: 'Tree'] :
      ( ~ $less(sK1,'val:(Tree)>Int'(sK2))
      | ( 'left:(Tree)>Tree'(sK2) != X3 )
      | ~ searchtree(X3) ),
    inference(cnf_transformation,[],[f43]) ).

tff(f115,plain,
    ( ~ spl8_1
    | spl8_3 ),
    inference(avatar_split_clause,[],[f96,f112,f103]) ).

tff(f96,plain,
    ( $less(sK1,sF6)
    | ~ searchtree(sF5) ),
    inference(definition_folding,[],[f86,f95,f94]) ).

tff(f86,plain,
    ( ~ searchtree('right:(Tree)>Tree'(sK2))
    | $less(sK1,'val:(Tree)>Int'(sK2)) ),
    inference(equality_resolution,[],[f63]) ).

tff(f63,plain,
    ! [X2: 'Tree'] :
      ( ( 'right:(Tree)>Tree'(sK2) != X2 )
      | ~ searchtree(X2)
      | $less(sK1,'val:(Tree)>Int'(sK2)) ),
    inference(cnf_transformation,[],[f43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWW679=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_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 20:45:16 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.50  % (21422)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.51  % (21418)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.51  % (21414)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52  % (21419)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.52  % (21430)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.53  % (21404)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.53  % (21422)First to succeed.
% 0.20/0.53  % (21408)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (21405)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53  % (21422)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (21422)------------------------------
% 0.20/0.53  % (21422)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (21422)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (21422)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (21422)Memory used [KB]: 5500
% 0.20/0.53  % (21422)Time elapsed: 0.121 s
% 0.20/0.53  % (21422)Instructions burned: 7 (million)
% 0.20/0.53  % (21422)------------------------------
% 0.20/0.53  % (21422)------------------------------
% 0.20/0.53  % (21403)Success in time 0.177 s
%------------------------------------------------------------------------------