%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU122+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 : n023.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 18:26:45 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   22 (   9 unt;   0 def)
%            Number of atoms       :   51 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   56 (  27   ~;  14   |;  10   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   37 (  32   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f52,plain,
    $false,
    inference(unit_resulting_resolution,[],[f40,f50,f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( in(sK1(X0,X1),X0)
          & ~ in(sK1(X0,X1),X1) ) )
      & ( ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f25,f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( in(X2,X0)
          & ~ in(X2,X1) )
     => ( in(sK1(X0,X1),X0)
        & ~ in(sK1(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) ) )
      & ( ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) ) )
      & ( ! [X2] :
            ( ~ in(X2,X0)
            | in(X2,X1) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( ~ in(X2,X0)
          | in(X2,X1) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f50,plain,
    ! [X0] : ~ in(X0,empty_set),
    inference(resolution,[],[f41,f44]) ).

fof(f44,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0] :
      ( ~ empty(X0)
      | ~ in(X1,X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
      ~ ( in(X1,X0)
        & empty(X0) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X1,X0] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

fof(f40,plain,
    ~ subset(empty_set,sK2),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ~ subset(empty_set,sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f18,f28]) ).

fof(f28,plain,
    ( ? [X0] : ~ subset(empty_set,X0)
   => ~ subset(empty_set,sK2) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0] : ~ subset(empty_set,X0),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X0] : subset(empty_set,X0),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X0] : subset(empty_set,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU122+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
% 0.14/0.34  % Computer : n023.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 15:01:05 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.50  % (6234)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.20/0.50  % (6226)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.20/0.50  % (6234)First to succeed.
% 0.20/0.51  % (6219)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.51  % (6226)Refutation not found, incomplete strategy% (6226)------------------------------
% 0.20/0.51  % (6226)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (6226)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (6226)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51  
% 0.20/0.51  % (6226)Memory used [KB]: 5884
% 0.20/0.51  % (6226)Time elapsed: 0.111 s
% 0.20/0.51  % (6226)Instructions burned: 2 (million)
% 0.20/0.51  % (6226)------------------------------
% 0.20/0.51  % (6226)------------------------------
% 0.20/0.51  % (6235)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.20/0.52  % (6234)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (6234)------------------------------
% 0.20/0.52  % (6234)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (6234)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (6234)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (6234)Memory used [KB]: 5884
% 0.20/0.52  % (6234)Time elapsed: 0.102 s
% 0.20/0.52  % (6234)Instructions burned: 1 (million)
% 0.20/0.52  % (6234)------------------------------
% 0.20/0.52  % (6234)------------------------------
% 0.20/0.52  % (6205)Success in time 0.161 s
%------------------------------------------------------------------------------