TSTP Solution File: SET695+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET695+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 : n024.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 18:21:54 EDT 2022

% Result   : Theorem 0.18s 0.50s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   64 (   2 unt;   0 def)
%            Number of atoms       :  205 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  215 (  74   ~;  79   |;  41   &)
%                                         (  12 <=>;   7  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   87 (  66   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f210,plain,
    $false,
    inference(avatar_sat_refutation,[],[f50,f51,f104,f118,f120,f209]) ).

fof(f209,plain,
    ( ~ spl4_1
    | spl4_2 ),
    inference(avatar_contradiction_clause,[],[f208]) ).

fof(f208,plain,
    ( $false
    | ~ spl4_1
    | spl4_2 ),
    inference(subsumption_resolution,[],[f200,f139]) ).

fof(f139,plain,
    ( member(sK0(sK2,sK3),difference(sK1,sK2))
    | spl4_2 ),
    inference(unit_resulting_resolution,[],[f123,f131,f32]) ).

fof(f32,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | member(X2,difference(X1,X0))
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ( ( member(X2,X1)
          & ~ member(X2,X0) )
        | ~ member(X2,difference(X1,X0)) )
      & ( member(X2,difference(X1,X0))
        | ~ member(X2,X1)
        | member(X2,X0) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X0,X2,X1] :
      ( ( ( member(X1,X2)
          & ~ member(X1,X0) )
        | ~ member(X1,difference(X2,X0)) )
      & ( member(X1,difference(X2,X0))
        | ~ member(X1,X2)
        | member(X1,X0) ) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ! [X0,X2,X1] :
      ( ( ( member(X1,X2)
          & ~ member(X1,X0) )
        | ~ member(X1,difference(X2,X0)) )
      & ( member(X1,difference(X2,X0))
        | ~ member(X1,X2)
        | member(X1,X0) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X2,X1] :
      ( ( member(X1,X2)
        & ~ member(X1,X0) )
    <=> member(X1,difference(X2,X0)) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X3] :
      ( member(X1,difference(X3,X0))
    <=> ( member(X1,X3)
        & ~ member(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).

fof(f131,plain,
    ( member(sK0(sK2,sK3),sK1)
    | spl4_2 ),
    inference(unit_resulting_resolution,[],[f124,f53]) ).

fof(f53,plain,
    ! [X0] :
      ( member(X0,sK1)
      | ~ member(X0,sK3) ),
    inference(resolution,[],[f41,f37]) ).

fof(f37,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X0)
      | member(X2,X0)
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( ~ member(sK0(X0,X1),X0)
          & member(sK0(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ member(X3,X0)
          & member(X3,X1) )
     => ( ~ member(sK0(X0,X1),X0)
        & member(sK0(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( ~ member(X3,X0)
            & member(X3,X1) ) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X0)
          | ~ member(X2,X1) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f16]) ).

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

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

fof(f41,plain,
    subset(sK3,sK1),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ( subset(sK3,sK1)
    & subset(sK2,sK1)
    & ( ~ subset(sK3,sK2)
      | ~ subset(difference(sK1,sK2),difference(sK1,sK3)) )
    & ( subset(sK3,sK2)
      | subset(difference(sK1,sK2),difference(sK1,sK3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f29,f30]) ).

fof(f30,plain,
    ( ? [X0,X1,X2] :
        ( subset(X2,X0)
        & subset(X1,X0)
        & ( ~ subset(X2,X1)
          | ~ subset(difference(X0,X1),difference(X0,X2)) )
        & ( subset(X2,X1)
          | subset(difference(X0,X1),difference(X0,X2)) ) )
   => ( subset(sK3,sK1)
      & subset(sK2,sK1)
      & ( ~ subset(sK3,sK2)
        | ~ subset(difference(sK1,sK2),difference(sK1,sK3)) )
      & ( subset(sK3,sK2)
        | subset(difference(sK1,sK2),difference(sK1,sK3)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ? [X0,X1,X2] :
      ( subset(X2,X0)
      & subset(X1,X0)
      & ( ~ subset(X2,X1)
        | ~ subset(difference(X0,X1),difference(X0,X2)) )
      & ( subset(X2,X1)
        | subset(difference(X0,X1),difference(X0,X2)) ) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ? [X2,X0,X1] :
      ( subset(X1,X2)
      & subset(X0,X2)
      & ( ~ subset(X1,X0)
        | ~ subset(difference(X2,X0),difference(X2,X1)) )
      & ( subset(X1,X0)
        | subset(difference(X2,X0),difference(X2,X1)) ) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ? [X2,X0,X1] :
      ( subset(X1,X2)
      & subset(X0,X2)
      & ( ~ subset(X1,X0)
        | ~ subset(difference(X2,X0),difference(X2,X1)) )
      & ( subset(X1,X0)
        | subset(difference(X2,X0),difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f19,plain,
    ? [X2,X0,X1] :
      ( subset(X1,X2)
      & subset(X0,X2)
      & ( subset(difference(X2,X0),difference(X2,X1))
      <~> subset(X1,X0) ) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ? [X0,X2,X1] :
      ( ( subset(difference(X2,X0),difference(X2,X1))
      <~> subset(X1,X0) )
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X0,X2,X1] :
        ( ( subset(X1,X2)
          & subset(X0,X2) )
       => ( subset(X1,X0)
        <=> subset(difference(X2,X0),difference(X2,X1)) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X1,X0,X3] :
        ( ( subset(X1,X3)
          & subset(X0,X3) )
       => ( subset(difference(X3,X1),difference(X3,X0))
        <=> subset(X0,X1) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X1,X0,X3] :
      ( ( subset(X1,X3)
        & subset(X0,X3) )
     => ( subset(difference(X3,X1),difference(X3,X0))
      <=> subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI24) ).

fof(f124,plain,
    ( member(sK0(sK2,sK3),sK3)
    | spl4_2 ),
    inference(resolution,[],[f49,f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f49,plain,
    ( ~ subset(sK3,sK2)
    | spl4_2 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f47,plain,
    ( spl4_2
  <=> subset(sK3,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f123,plain,
    ( ~ member(sK0(sK2,sK3),sK2)
    | spl4_2 ),
    inference(resolution,[],[f49,f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ~ member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f200,plain,
    ( ~ member(sK0(sK2,sK3),difference(sK1,sK2))
    | ~ spl4_1
    | spl4_2 ),
    inference(resolution,[],[f138,f125]) ).

fof(f125,plain,
    ( ! [X0] :
        ( member(X0,difference(sK1,sK3))
        | ~ member(X0,difference(sK1,sK2)) )
    | ~ spl4_1 ),
    inference(resolution,[],[f44,f37]) ).

fof(f44,plain,
    ( subset(difference(sK1,sK2),difference(sK1,sK3))
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f43,plain,
    ( spl4_1
  <=> subset(difference(sK1,sK2),difference(sK1,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f138,plain,
    ( ! [X2] : ~ member(sK0(sK2,sK3),difference(X2,sK3))
    | spl4_2 ),
    inference(resolution,[],[f124,f33]) ).

fof(f33,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,difference(X1,X0))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f120,plain,
    ( ~ spl4_4
    | spl4_1
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f105,f47,f43,f101]) ).

fof(f101,plain,
    ( spl4_4
  <=> member(sK0(difference(sK1,sK3),difference(sK1,sK2)),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f105,plain,
    ( ~ member(sK0(difference(sK1,sK3),difference(sK1,sK2)),sK3)
    | spl4_1
    | ~ spl4_2 ),
    inference(unit_resulting_resolution,[],[f58,f69]) ).

fof(f69,plain,
    ( ! [X4,X5] :
        ( ~ member(X4,difference(X5,sK2))
        | ~ member(X4,sK3) )
    | ~ spl4_2 ),
    inference(resolution,[],[f54,f33]) ).

fof(f54,plain,
    ( ! [X0] :
        ( member(X0,sK2)
        | ~ member(X0,sK3) )
    | ~ spl4_2 ),
    inference(resolution,[],[f48,f37]) ).

fof(f48,plain,
    ( subset(sK3,sK2)
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f58,plain,
    ( member(sK0(difference(sK1,sK3),difference(sK1,sK2)),difference(sK1,sK2))
    | spl4_1 ),
    inference(resolution,[],[f45,f35]) ).

fof(f45,plain,
    ( ~ subset(difference(sK1,sK2),difference(sK1,sK3))
    | spl4_1 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f118,plain,
    ( spl4_1
    | spl4_3 ),
    inference(avatar_contradiction_clause,[],[f117]) ).

fof(f117,plain,
    ( $false
    | spl4_1
    | spl4_3 ),
    inference(subsumption_resolution,[],[f106,f99]) ).

fof(f99,plain,
    ( ~ member(sK0(difference(sK1,sK3),difference(sK1,sK2)),sK1)
    | spl4_3 ),
    inference(avatar_component_clause,[],[f97]) ).

fof(f97,plain,
    ( spl4_3
  <=> member(sK0(difference(sK1,sK3),difference(sK1,sK2)),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f106,plain,
    ( member(sK0(difference(sK1,sK3),difference(sK1,sK2)),sK1)
    | spl4_1 ),
    inference(unit_resulting_resolution,[],[f58,f34]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,difference(X1,X0))
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f104,plain,
    ( ~ spl4_3
    | spl4_4
    | spl4_1 ),
    inference(avatar_split_clause,[],[f92,f43,f101,f97]) ).

fof(f92,plain,
    ( member(sK0(difference(sK1,sK3),difference(sK1,sK2)),sK3)
    | ~ member(sK0(difference(sK1,sK3),difference(sK1,sK2)),sK1)
    | spl4_1 ),
    inference(resolution,[],[f57,f32]) ).

fof(f57,plain,
    ( ~ member(sK0(difference(sK1,sK3),difference(sK1,sK2)),difference(sK1,sK3))
    | spl4_1 ),
    inference(resolution,[],[f45,f36]) ).

fof(f51,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f38,f47,f43]) ).

fof(f38,plain,
    ( subset(sK3,sK2)
    | subset(difference(sK1,sK2),difference(sK1,sK3)) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f50,plain,
    ( ~ spl4_1
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f39,f47,f43]) ).

fof(f39,plain,
    ( ~ subset(sK3,sK2)
    | ~ subset(difference(sK1,sK2),difference(sK1,sK3)) ),
    inference(cnf_transformation,[],[f31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SET695+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 14:27:04 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.44  % (11786)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)
% 0.18/0.46  % (11786)Refutation not found, incomplete strategy% (11786)------------------------------
% 0.18/0.46  % (11786)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.46  % (11786)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.47  % (11786)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.47  
% 0.18/0.47  % (11786)Memory used [KB]: 1407
% 0.18/0.47  % (11786)Time elapsed: 0.062 s
% 0.18/0.47  % (11786)Instructions burned: 1 (million)
% 0.18/0.47  % (11786)------------------------------
% 0.18/0.47  % (11786)------------------------------
% 0.18/0.47  % (11781)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.48  % (11781)Instruction limit reached!
% 0.18/0.48  % (11781)------------------------------
% 0.18/0.48  % (11781)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.48  % (11781)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.48  % (11781)Termination reason: Unknown
% 0.18/0.48  % (11781)Termination phase: Saturation
% 0.18/0.48  
% 0.18/0.48  % (11781)Memory used [KB]: 5884
% 0.18/0.48  % (11781)Time elapsed: 0.071 s
% 0.18/0.48  % (11781)Instructions burned: 2 (million)
% 0.18/0.48  % (11781)------------------------------
% 0.18/0.48  % (11781)------------------------------
% 0.18/0.48  % (11770)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)
% 0.18/0.50  % (11768)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)
% 0.18/0.50  % (11770)First to succeed.
% 0.18/0.50  % (11770)Refutation found. Thanks to Tanya!
% 0.18/0.50  % SZS status Theorem for theBenchmark
% 0.18/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50  % (11770)------------------------------
% 0.18/0.50  % (11770)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (11770)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (11770)Termination reason: Refutation
% 0.18/0.50  
% 0.18/0.50  % (11770)Memory used [KB]: 6012
% 0.18/0.50  % (11770)Time elapsed: 0.093 s
% 0.18/0.50  % (11770)Instructions burned: 5 (million)
% 0.18/0.50  % (11770)------------------------------
% 0.18/0.50  % (11770)------------------------------
% 0.18/0.50  % (11762)Success in time 0.162 s
%------------------------------------------------------------------------------