%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET573+3 : 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 : n002.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 18:21:28 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   25 (   6 unt;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   70 (  22   ~;  15   |;  25   &)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   50 (  33   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f37,plain,
    $false,
    inference(subsumption_resolution,[],[f36,f29]) ).

fof(f29,plain,
    ~ intersect(sK0,sK1),
    inference(resolution,[],[f22,f24]) ).

fof(f24,plain,
    disjoint(sK0,sK1),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( member(sK2,sK0)
    & disjoint(sK0,sK1)
    & member(sK2,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14]) ).

fof(f14,plain,
    ( ? [X0,X1,X2] :
        ( member(X2,X0)
        & disjoint(X0,X1)
        & member(X2,X1) )
   => ( member(sK2,sK0)
      & disjoint(sK0,sK1)
      & member(sK2,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0,X1,X2] :
      ( member(X2,X0)
      & disjoint(X0,X1)
      & member(X2,X1) ),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ? [X1,X2,X0] :
      ( member(X0,X1)
      & disjoint(X1,X2)
      & member(X0,X2) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ? [X0,X1,X2] :
      ( member(X0,X2)
      & member(X0,X1)
      & disjoint(X1,X2) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( member(X0,X1)
          & disjoint(X1,X2) )
       => ~ member(X0,X2) ),
    inference(negated_conjecture,[],[f4]) ).

fof(f4,conjecture,
    ! [X0,X1,X2] :
      ( ( member(X0,X1)
        & disjoint(X1,X2) )
     => ~ member(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th12) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ disjoint(X1,X0)
      | ~ intersect(X1,X0) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ( ~ intersect(X1,X0)
        | ~ disjoint(X1,X0) )
      & ( disjoint(X1,X0)
        | intersect(X1,X0) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,plain,
    ! [X0,X1] :
      ( ~ intersect(X1,X0)
    <=> disjoint(X1,X0) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( disjoint(X0,X1)
    <=> ~ intersect(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).

fof(f36,plain,
    intersect(sK0,sK1),
    inference(resolution,[],[f31,f25]) ).

fof(f25,plain,
    member(sK2,sK0),
    inference(cnf_transformation,[],[f15]) ).

fof(f31,plain,
    ! [X0] :
      ( ~ member(sK2,X0)
      | intersect(X0,sK1) ),
    inference(resolution,[],[f28,f23]) ).

fof(f23,plain,
    member(sK2,sK1),
    inference(cnf_transformation,[],[f15]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | intersect(X0,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( intersect(X0,X1)
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X2,X0) ) )
      & ( ( member(sK3(X0,X1),X1)
          & member(sK3(X0,X1),X0) )
        | ~ intersect(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f17,f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X1)
          & member(X3,X0) )
     => ( member(sK3(X0,X1),X1)
        & member(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( intersect(X0,X1)
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X2,X0) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & member(X3,X0) )
        | ~ intersect(X0,X1) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ! [X1,X0] :
      ( ( intersect(X1,X0)
        | ! [X2] :
            ( ~ member(X2,X0)
            | ~ member(X2,X1) ) )
      & ( ? [X2] :
            ( member(X2,X0)
            & member(X2,X1) )
        | ~ intersect(X1,X0) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,plain,
    ! [X1,X0] :
      ( intersect(X1,X0)
    <=> ? [X2] :
          ( member(X2,X0)
          & member(X2,X1) ) ),
    inference(rectify,[],[f1]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SET573+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n002.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 14:12:44 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  % (32331)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.50  % (32314)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.50  % (32331)First to succeed.
% 0.20/0.50  % (32331)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  % (32331)------------------------------
% 0.20/0.50  % (32331)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (32331)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (32331)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (32331)Memory used [KB]: 5884
% 0.20/0.50  % (32331)Time elapsed: 0.094 s
% 0.20/0.50  % (32331)Instructions burned: 2 (million)
% 0.20/0.50  % (32331)------------------------------
% 0.20/0.50  % (32331)------------------------------
% 0.20/0.50  % (32303)Success in time 0.145 s
%------------------------------------------------------------------------------