%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYN082+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : n027.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 19:36:51 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   31 (   2 unt;   0 def)
%            Number of atoms       :   84 (   1 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   95 (  42   ~;  40   |;   3   &)
%                                         (   7 <=>;   2  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   6 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :   21 (  17   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f45,plain,
    $false,
    inference(avatar_sat_refutation,[],[f21,f25,f29,f33,f36,f39]) ).

fof(f39,plain,
    ( spl4_2
    | ~ spl4_1
    | ~ spl4_5 ),
    inference(avatar_split_clause,[],[f38,f31,f14,f18]) ).

fof(f18,plain,
    ( spl4_2
  <=> big_f(sK0,sF3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f14,plain,
    ( spl4_1
  <=> big_f(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f31,plain,
    ( spl4_5
  <=> ! [X2] :
        ( big_f(X2,sF3)
        | ~ big_f(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

fof(f38,plain,
    ( big_f(sK0,sF3)
    | ~ spl4_1
    | ~ spl4_5 ),
    inference(resolution,[],[f32,f16]) ).

fof(f16,plain,
    ( big_f(sK0,sK1)
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f14]) ).

fof(f32,plain,
    ( ! [X2] :
        ( ~ big_f(X2,sK1)
        | big_f(X2,sF3) )
    | ~ spl4_5 ),
    inference(avatar_component_clause,[],[f31]) ).

fof(f36,plain,
    ( ~ spl4_2
    | ~ spl4_3
    | ~ spl4_4 ),
    inference(avatar_split_clause,[],[f35,f27,f23,f18]) ).

fof(f23,plain,
    ( spl4_3
  <=> ! [X1] :
        ( ~ big_f(sK2(X1),sF3)
        | ~ big_f(sK0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f27,plain,
    ( spl4_4
  <=> ! [X1] :
        ( big_f(sK2(X1),X1)
        | ~ big_f(sK0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f35,plain,
    ( ~ big_f(sK0,sF3)
    | ~ spl4_3
    | ~ spl4_4 ),
    inference(duplicate_literal_removal,[],[f34]) ).

fof(f34,plain,
    ( ~ big_f(sK0,sF3)
    | ~ big_f(sK0,sF3)
    | ~ spl4_3
    | ~ spl4_4 ),
    inference(resolution,[],[f28,f24]) ).

fof(f24,plain,
    ( ! [X1] :
        ( ~ big_f(sK2(X1),sF3)
        | ~ big_f(sK0,X1) )
    | ~ spl4_3 ),
    inference(avatar_component_clause,[],[f23]) ).

fof(f28,plain,
    ( ! [X1] :
        ( big_f(sK2(X1),X1)
        | ~ big_f(sK0,X1) )
    | ~ spl4_4 ),
    inference(avatar_component_clause,[],[f27]) ).

fof(f33,plain,
    ( spl4_2
    | spl4_5 ),
    inference(avatar_split_clause,[],[f12,f31,f18]) ).

fof(f12,plain,
    ! [X2] :
      ( big_f(X2,sF3)
      | big_f(sK0,sF3)
      | ~ big_f(X2,sK1) ),
    inference(definition_folding,[],[f4,f8,f8]) ).

fof(f8,plain,
    sF3 = f(sK0),
    introduced(function_definition,[]) ).

fof(f4,plain,
    ! [X2] :
      ( big_f(sK0,f(sK0))
      | ~ big_f(X2,sK1)
      | big_f(X2,f(sK0)) ),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,plain,
    ? [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( big_f(X2,f(X0))
              | ~ big_f(X2,X1) )
          & big_f(X0,X1) )
    <~> big_f(X0,f(X0)) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ! [X0] :
        ( big_f(X0,f(X0))
      <=> ? [X1] :
            ( big_f(X0,X1)
            & ! [X2] :
                ( big_f(X2,X1)
               => big_f(X2,f(X0)) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ! [X0] :
      ( big_f(X0,f(X0))
    <=> ? [X1] :
          ( big_f(X0,X1)
          & ! [X2] :
              ( big_f(X2,X1)
             => big_f(X2,f(X0)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel60) ).

fof(f29,plain,
    ( ~ spl4_2
    | spl4_4 ),
    inference(avatar_split_clause,[],[f11,f27,f18]) ).

fof(f11,plain,
    ! [X1] :
      ( big_f(sK2(X1),X1)
      | ~ big_f(sK0,sF3)
      | ~ big_f(sK0,X1) ),
    inference(definition_folding,[],[f5,f8]) ).

fof(f5,plain,
    ! [X1] :
      ( ~ big_f(sK0,f(sK0))
      | ~ big_f(sK0,X1)
      | big_f(sK2(X1),X1) ),
    inference(cnf_transformation,[],[f3]) ).

fof(f25,plain,
    ( ~ spl4_2
    | spl4_3 ),
    inference(avatar_split_clause,[],[f10,f23,f18]) ).

fof(f10,plain,
    ! [X1] :
      ( ~ big_f(sK2(X1),sF3)
      | ~ big_f(sK0,sF3)
      | ~ big_f(sK0,X1) ),
    inference(definition_folding,[],[f6,f8,f8]) ).

fof(f6,plain,
    ! [X1] :
      ( ~ big_f(sK0,f(sK0))
      | ~ big_f(sK0,X1)
      | ~ big_f(sK2(X1),f(sK0)) ),
    inference(cnf_transformation,[],[f3]) ).

fof(f21,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f9,f18,f14]) ).

fof(f9,plain,
    ( big_f(sK0,sF3)
    | big_f(sK0,sK1) ),
    inference(definition_folding,[],[f7,f8]) ).

fof(f7,plain,
    ( big_f(sK0,f(sK0))
    | big_f(sK0,sK1) ),
    inference(cnf_transformation,[],[f3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem    : SYN082+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13  % 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 : n027.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 21:44:31 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (9687)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.19/0.50  % (9695)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.19/0.50  % (9695)First to succeed.
% 0.19/0.50  % (9695)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Theorem for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (9695)------------------------------
% 0.19/0.50  % (9695)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (9695)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (9695)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (9695)Memory used [KB]: 5373
% 0.19/0.50  % (9695)Time elapsed: 0.107 s
% 0.19/0.50  % (9695)Instructions burned: 1 (million)
% 0.19/0.50  % (9695)------------------------------
% 0.19/0.50  % (9695)------------------------------
% 0.19/0.50  % (9683)Success in time 0.153 s
%------------------------------------------------------------------------------