%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n017.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 18:22:45 EDT 2022

% Result   : Theorem 0.20s 0.55s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   41 (   3 unt;   0 def)
%            Number of atoms       :  102 (  25 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  107 (  46   ~;  41   |;   6   &)
%                                         (  13 <=>;   0  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   58 (  55   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f93,plain,
    $false,
    inference(avatar_sat_refutation,[],[f43,f44,f70,f92]) ).

fof(f92,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_contradiction_clause,[],[f91]) ).

fof(f91,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f78,f31]) ).

fof(f31,plain,
    ! [X2] : in(X2,singleton(X2)),
    inference(equality_resolution,[],[f30]) ).

fof(f30,plain,
    ! [X2,X1] :
      ( in(X2,singleton(X1))
      | X1 != X2 ),
    inference(equality_resolution,[],[f23]) ).

fof(f23,plain,
    ! [X2,X0,X1] :
      ( singleton(X1) != X0
      | in(X2,X0)
      | X1 != X2 ),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( X1 = X2
        <=> in(X2,X0) )
    <=> singleton(X1) = X0 ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f78,plain,
    ( ~ in(sK2,singleton(sK2))
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(unit_resulting_resolution,[],[f71,f28]) ).

fof(f28,plain,
    ! [X2,X3,X0] :
      ( ~ in(X3,set_difference(X0,X2))
      | ~ in(X3,X2) ),
    inference(equality_resolution,[],[f18]) ).

fof(f18,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(X3,X1)
      | ~ in(X3,X2)
      | set_difference(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X1,X2,X0] :
      ( set_difference(X0,X2) = X1
    <=> ! [X3] :
          ( ( in(X3,X0)
            & ~ in(X3,X2) )
        <=> in(X3,X1) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( ( in(X3,X0)
            & ~ in(X3,X1) )
        <=> in(X3,X2) )
    <=> set_difference(X0,X1) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(f71,plain,
    ( in(sK2,set_difference(sK3,singleton(sK2)))
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(forward_demodulation,[],[f37,f42]) ).

fof(f42,plain,
    ( sK2 = sK4
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f40]) ).

fof(f40,plain,
    ( spl5_2
  <=> sK2 = sK4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f37,plain,
    ( in(sK2,set_difference(sK3,singleton(sK4)))
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f36]) ).

fof(f36,plain,
    ( spl5_1
  <=> in(sK2,set_difference(sK3,singleton(sK4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f70,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_contradiction_clause,[],[f69]) ).

fof(f69,plain,
    ( $false
    | spl5_1
    | spl5_2 ),
    inference(subsumption_resolution,[],[f63,f33]) ).

fof(f33,plain,
    in(sK2,sK3),
    inference(subsumption_resolution,[],[f25,f27]) ).

fof(f27,plain,
    ! [X2,X3,X0] :
      ( ~ in(X3,set_difference(X0,X2))
      | in(X3,X0) ),
    inference(equality_resolution,[],[f19]) ).

fof(f19,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(X3,X1)
      | in(X3,X0)
      | set_difference(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f9]) ).

fof(f25,plain,
    ( in(sK2,set_difference(sK3,singleton(sK4)))
    | in(sK2,sK3) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ? [X2,X1,X0] :
      ( in(X2,set_difference(X1,singleton(X0)))
    <~> ( X0 != X2
        & in(X2,X1) ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,plain,
    ~ ! [X0,X1,X2] :
        ( in(X2,set_difference(X1,singleton(X0)))
      <=> ( X0 != X2
          & in(X2,X1) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,negated_conjecture,
    ~ ! [X2,X1,X0] :
        ( ( X0 != X2
          & in(X0,X1) )
      <=> in(X0,set_difference(X1,singleton(X2))) ),
    inference(negated_conjecture,[],[f6]) ).

fof(f6,conjecture,
    ! [X2,X1,X0] :
      ( ( X0 != X2
        & in(X0,X1) )
    <=> in(X0,set_difference(X1,singleton(X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).

fof(f63,plain,
    ( ~ in(sK2,sK3)
    | spl5_1
    | spl5_2 ),
    inference(unit_resulting_resolution,[],[f38,f50,f29]) ).

fof(f29,plain,
    ! [X2,X3,X0] :
      ( in(X3,set_difference(X0,X2))
      | in(X3,X2)
      | ~ in(X3,X0) ),
    inference(equality_resolution,[],[f17]) ).

fof(f17,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X1)
      | in(X3,X2)
      | ~ in(X3,X0)
      | set_difference(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f9]) ).

fof(f50,plain,
    ( ~ in(sK2,singleton(sK4))
    | spl5_2 ),
    inference(unit_resulting_resolution,[],[f41,f32]) ).

fof(f32,plain,
    ! [X2,X1] :
      ( ~ in(X2,singleton(X1))
      | X1 = X2 ),
    inference(equality_resolution,[],[f22]) ).

fof(f22,plain,
    ! [X2,X0,X1] :
      ( singleton(X1) != X0
      | ~ in(X2,X0)
      | X1 = X2 ),
    inference(cnf_transformation,[],[f10]) ).

fof(f41,plain,
    ( sK2 != sK4
    | spl5_2 ),
    inference(avatar_component_clause,[],[f40]) ).

fof(f38,plain,
    ( ~ in(sK2,set_difference(sK3,singleton(sK4)))
    | spl5_1 ),
    inference(avatar_component_clause,[],[f36]) ).

fof(f44,plain,
    ( spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f26,f40,f36]) ).

fof(f26,plain,
    ( sK2 != sK4
    | in(sK2,set_difference(sK3,singleton(sK4))) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f43,plain,
    ( ~ spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f34,f40,f36]) ).

fof(f34,plain,
    ( sK2 = sK4
    | ~ in(sK2,set_difference(sK3,singleton(sK4))) ),
    inference(subsumption_resolution,[],[f24,f27]) ).

fof(f24,plain,
    ( sK2 = sK4
    | ~ in(sK2,set_difference(sK3,singleton(sK4)))
    | ~ in(sK2,sK3) ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % 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 : n017.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 13:54:20 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.53  % (18627)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.53  % (18626)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.53  % (18628)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)
% 0.20/0.53  % (18628)First to succeed.
% 0.20/0.54  % (18643)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.54  % (18636)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54  % (18634)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.55  % (18625)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.55  % (18635)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.55  % (18628)Refutation found. Thanks to Tanya!
% 0.20/0.55  % SZS status Theorem for theBenchmark
% 0.20/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55  % (18628)------------------------------
% 0.20/0.55  % (18628)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (18628)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (18628)Termination reason: Refutation
% 0.20/0.55  
% 0.20/0.55  % (18628)Memory used [KB]: 5884
% 0.20/0.55  % (18628)Time elapsed: 0.111 s
% 0.20/0.55  % (18628)Instructions burned: 4 (million)
% 0.20/0.55  % (18628)------------------------------
% 0.20/0.55  % (18628)------------------------------
% 0.20/0.55  % (18619)Success in time 0.196 s
%------------------------------------------------------------------------------