%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET705+4 : TPTP v8.1.0. Released v2.2.0.
% 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 18:21:56 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   23 (   8 unt;   0 def)
%            Number of atoms       :   58 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   60 (  25   ~;  18   |;  10   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   40 (  35   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f37,plain,
    $false,
    inference(resolution,[],[f36,f31]) ).

fof(f31,plain,
    ~ subset(sK1,sK1),
    inference(resolution,[],[f29,f28]) ).

fof(f28,plain,
    ~ member(sK1,power_set(sK1)),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ~ member(sK1,power_set(sK1)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f15,f21]) ).

fof(f21,plain,
    ( ? [X0] : ~ member(X0,power_set(X0))
   => ~ member(sK1,power_set(sK1)) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ? [X0] : ~ member(X0,power_set(X0)),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0] : member(X0,power_set(X0)),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0] : member(X0,power_set(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI48) ).

fof(f29,plain,
    ! [X0,X1] :
      ( member(X1,power_set(X0))
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ~ member(X1,power_set(X0)) )
      & ( member(X1,power_set(X0))
        | ~ subset(X1,X0) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,plain,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        | ~ member(X0,power_set(X1)) )
      & ( member(X0,power_set(X1))
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> member(X0,power_set(X1)) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X2,X0] :
      ( subset(X2,X0)
    <=> member(X2,power_set(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).

fof(f36,plain,
    ! [X2] : subset(X2,X2),
    inference(duplicate_literal_removal,[],[f35]) ).

fof(f35,plain,
    ! [X2] :
      ( subset(X2,X2)
      | subset(X2,X2) ),
    inference(resolution,[],[f27,f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ member(sK0(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ( member(sK0(X0,X1),X1)
          & ~ member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X0) )
        | ~ subset(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X1)
          & ~ member(X2,X0) )
     => ( member(sK0(X0,X1),X1)
        & ~ member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( member(X2,X1)
            & ~ member(X2,X0) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X0) )
        | ~ subset(X1,X0) ) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( member(X2,X0)
            & ~ member(X2,X1) ) )
      & ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( ~ member(X2,X0)
          | member(X2,X1) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f27,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET705+4 : TPTP v8.1.0. Released v2.2.0.
% 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
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 14:48:35 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.49  % (30921)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.49  % (30921)First to succeed.
% 0.20/0.50  % (30939)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.50  % (30919)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.50  % (30921)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (30921)------------------------------
% 0.20/0.50  % (30921)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (30921)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (30921)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (30921)Memory used [KB]: 5884
% 0.20/0.50  % (30921)Time elapsed: 0.085 s
% 0.20/0.50  % (30921)Instructions burned: 1 (million)
% 0.20/0.50  % (30921)------------------------------
% 0.20/0.50  % (30921)------------------------------
% 0.20/0.50  % (30916)Success in time 0.149 s
%------------------------------------------------------------------------------