%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU160+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n011.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 18:26:59 EDT 2022

% Result   : Theorem 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   40 (   6 unt;   0 def)
%            Number of atoms       :  123 (  59 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  132 (  49   ~;  56   |;  18   &)
%                                         (   7 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-1 aty)
%            Number of variables   :   34 (  24   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f54,plain,
    $false,
    inference(avatar_sat_refutation,[],[f41,f46,f47,f50,f53]) ).

fof(f53,plain,
    ( ~ spl2_1
    | spl2_3 ),
    inference(avatar_contradiction_clause,[],[f52]) ).

fof(f52,plain,
    ( $false
    | ~ spl2_1
    | spl2_3 ),
    inference(subsumption_resolution,[],[f51,f26]) ).

fof(f26,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ! [X1] : subset(X1,X1),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f51,plain,
    ( ~ subset(sK1,sK1)
    | ~ spl2_1
    | spl2_3 ),
    inference(forward_demodulation,[],[f45,f36]) ).

fof(f36,plain,
    ( singleton(sK0) = sK1
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f34]) ).

fof(f34,plain,
    ( spl2_1
  <=> singleton(sK0) = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f45,plain,
    ( ~ subset(sK1,singleton(sK0))
    | spl2_3 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f43,plain,
    ( spl2_3
  <=> subset(sK1,singleton(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

fof(f50,plain,
    ( ~ spl2_2
    | spl2_3 ),
    inference(avatar_contradiction_clause,[],[f49]) ).

fof(f49,plain,
    ( $false
    | ~ spl2_2
    | spl2_3 ),
    inference(subsumption_resolution,[],[f48,f31]) ).

fof(f31,plain,
    ! [X1] : subset(empty_set,singleton(X1)),
    inference(equality_resolution,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( subset(X0,singleton(X1))
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( subset(X0,singleton(X1))
        | ( singleton(X1) != X0
          & empty_set != X0 ) )
      & ( singleton(X1) = X0
        | empty_set = X0
        | ~ subset(X0,singleton(X1)) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
      ( ( subset(X1,singleton(X0))
        | ( singleton(X0) != X1
          & empty_set != X1 ) )
      & ( singleton(X0) = X1
        | empty_set = X1
        | ~ subset(X1,singleton(X0)) ) ),
    inference(flattening,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] :
      ( ( subset(X1,singleton(X0))
        | ( singleton(X0) != X1
          & empty_set != X1 ) )
      & ( singleton(X0) = X1
        | empty_set = X1
        | ~ subset(X1,singleton(X0)) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X1,X0] :
      ( subset(X1,singleton(X0))
    <=> ( singleton(X0) = X1
        | empty_set = X1 ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X0] :
      ( subset(X0,singleton(X1))
    <=> ( singleton(X1) = X0
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).

fof(f48,plain,
    ( ~ subset(empty_set,singleton(sK0))
    | ~ spl2_2
    | spl2_3 ),
    inference(forward_demodulation,[],[f45,f40]) ).

fof(f40,plain,
    ( empty_set = sK1
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f38]) ).

fof(f38,plain,
    ( spl2_2
  <=> empty_set = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

fof(f47,plain,
    ( ~ spl2_1
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f29,f43,f34]) ).

fof(f29,plain,
    ( ~ subset(sK1,singleton(sK0))
    | singleton(sK0) != sK1 ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ( ( ~ subset(sK1,singleton(sK0))
      | ( singleton(sK0) != sK1
        & empty_set != sK1 ) )
    & ( subset(sK1,singleton(sK0))
      | singleton(sK0) = sK1
      | empty_set = sK1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f20,f21]) ).

fof(f21,plain,
    ( ? [X0,X1] :
        ( ( ~ subset(X1,singleton(X0))
          | ( singleton(X0) != X1
            & empty_set != X1 ) )
        & ( subset(X1,singleton(X0))
          | singleton(X0) = X1
          | empty_set = X1 ) )
   => ( ( ~ subset(sK1,singleton(sK0))
        | ( singleton(sK0) != sK1
          & empty_set != sK1 ) )
      & ( subset(sK1,singleton(sK0))
        | singleton(sK0) = sK1
        | empty_set = sK1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1] :
      ( ( ~ subset(X1,singleton(X0))
        | ( singleton(X0) != X1
          & empty_set != X1 ) )
      & ( subset(X1,singleton(X0))
        | singleton(X0) = X1
        | empty_set = X1 ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ? [X1,X0] :
      ( ( ~ subset(X0,singleton(X1))
        | ( singleton(X1) != X0
          & empty_set != X0 ) )
      & ( subset(X0,singleton(X1))
        | singleton(X1) = X0
        | empty_set = X0 ) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ? [X1,X0] :
      ( ( ~ subset(X0,singleton(X1))
        | ( singleton(X1) != X0
          & empty_set != X0 ) )
      & ( subset(X0,singleton(X1))
        | singleton(X1) = X0
        | empty_set = X0 ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ? [X1,X0] :
      ( ( singleton(X1) = X0
        | empty_set = X0 )
    <~> subset(X0,singleton(X1)) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,singleton(X1))
      <=> ( singleton(X1) = X0
          | empty_set = X0 ) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0,X1] :
      ( subset(X0,singleton(X1))
    <=> ( singleton(X1) = X0
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).

fof(f46,plain,
    ( ~ spl2_2
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f28,f43,f38]) ).

fof(f28,plain,
    ( ~ subset(sK1,singleton(sK0))
    | empty_set != sK1 ),
    inference(cnf_transformation,[],[f22]) ).

fof(f41,plain,
    ( spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f32,f38,f34]) ).

fof(f32,plain,
    ( empty_set = sK1
    | singleton(sK0) = sK1 ),
    inference(subsumption_resolution,[],[f27,f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ~ subset(X0,singleton(X1))
      | singleton(X1) = X0
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f27,plain,
    ( empty_set = sK1
    | singleton(sK0) = sK1
    | subset(sK1,singleton(sK0)) ),
    inference(cnf_transformation,[],[f22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU160+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n011.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 14:40:25 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.45  % (12103)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.46  % (12103)First to succeed.
% 0.19/0.47  % (12103)Refutation found. Thanks to Tanya!
% 0.19/0.47  % SZS status Theorem for theBenchmark
% 0.19/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47  % (12103)------------------------------
% 0.19/0.47  % (12103)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47  % (12103)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47  % (12103)Termination reason: Refutation
% 0.19/0.47  
% 0.19/0.47  % (12103)Memory used [KB]: 5884
% 0.19/0.47  % (12103)Time elapsed: 0.004 s
% 0.19/0.47  % (12103)Instructions burned: 2 (million)
% 0.19/0.47  % (12103)------------------------------
% 0.19/0.47  % (12103)------------------------------
% 0.19/0.47  % (12096)Success in time 0.117 s
%------------------------------------------------------------------------------