TSTP Solution File: SWC001+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC001+1 : TPTP v8.1.0. Released v2.4.0.
% 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 : n008.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 18:38:08 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   47 (   6 unt;   0 def)
%            Number of atoms       :  352 (  32 equ)
%            Maximal formula atoms :   36 (   7 avg)
%            Number of connectives :  447 ( 142   ~; 139   |; 142   &)
%                                         (   4 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   74 (  31   !;  43   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f267,plain,
    $false,
    inference(avatar_sat_refutation,[],[f242,f247,f248,f249,f262,f266]) ).

fof(f266,plain,
    ( ~ spl16_1
    | spl16_2
    | ~ spl16_4 ),
    inference(avatar_contradiction_clause,[],[f265]) ).

fof(f265,plain,
    ( $false
    | ~ spl16_1
    | spl16_2
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f264,f237]) ).

fof(f237,plain,
    ( ~ memberP(sK5,sK6)
    | spl16_2 ),
    inference(avatar_component_clause,[],[f235]) ).

fof(f235,plain,
    ( spl16_2
  <=> memberP(sK5,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).

fof(f264,plain,
    ( memberP(sK5,sK6)
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f263,f246]) ).

fof(f246,plain,
    ( ssItem(sK6)
    | ~ spl16_4 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f244,plain,
    ( spl16_4
  <=> ssItem(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).

fof(f263,plain,
    ( ~ ssItem(sK6)
    | memberP(sK5,sK6)
    | ~ spl16_1 ),
    inference(resolution,[],[f217,f232]) ).

fof(f232,plain,
    ( memberP(sK2,sK6)
    | ~ spl16_1 ),
    inference(avatar_component_clause,[],[f231]) ).

fof(f231,plain,
    ( spl16_1
  <=> memberP(sK2,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).

fof(f217,plain,
    ! [X4] :
      ( ~ memberP(sK2,X4)
      | ~ ssItem(X4)
      | memberP(sK5,X4) ),
    inference(definition_unfolding,[],[f181,f183]) ).

fof(f183,plain,
    sK4 = sK2,
    inference(cnf_transformation,[],[f137]) ).

fof(f137,plain,
    ( ssList(sK3)
    & duplicatefreeP(sK4)
    & sK3 = sK5
    & sK4 = sK2
    & ! [X4] :
        ( ~ ssItem(X4)
        | ( ( ~ memberP(sK5,X4)
            | memberP(sK4,X4) )
          & ( ~ memberP(sK4,X4)
            | memberP(sK5,X4) ) ) )
    & ssList(sK5)
    & ( ( ( ~ memberP(sK2,sK6)
          | ~ memberP(sK3,sK6) )
        & ( memberP(sK2,sK6)
          | memberP(sK3,sK6) )
        & ssItem(sK6) )
      | ~ duplicatefreeP(sK2) )
    & ssList(sK4)
    & ssList(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f131,f136,f135,f134,f133,f132]) ).

fof(f132,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ? [X3] :
                    ( duplicatefreeP(X2)
                    & X1 = X3
                    & X0 = X2
                    & ! [X4] :
                        ( ~ ssItem(X4)
                        | ( ( ~ memberP(X3,X4)
                            | memberP(X2,X4) )
                          & ( ~ memberP(X2,X4)
                            | memberP(X3,X4) ) ) )
                    & ssList(X3)
                    & ( ? [X5] :
                          ( ( ~ memberP(X0,X5)
                            | ~ memberP(X1,X5) )
                          & ( memberP(X0,X5)
                            | memberP(X1,X5) )
                          & ssItem(X5) )
                      | ~ duplicatefreeP(X0) ) )
                & ssList(X2) ) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( duplicatefreeP(X2)
                  & X1 = X3
                  & sK2 = X2
                  & ! [X4] :
                      ( ~ ssItem(X4)
                      | ( ( ~ memberP(X3,X4)
                          | memberP(X2,X4) )
                        & ( ~ memberP(X2,X4)
                          | memberP(X3,X4) ) ) )
                  & ssList(X3)
                  & ( ? [X5] :
                        ( ( ~ memberP(sK2,X5)
                          | ~ memberP(X1,X5) )
                        & ( memberP(sK2,X5)
                          | memberP(X1,X5) )
                        & ssItem(X5) )
                    | ~ duplicatefreeP(sK2) ) )
              & ssList(X2) ) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f133,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ? [X3] :
                ( duplicatefreeP(X2)
                & X1 = X3
                & sK2 = X2
                & ! [X4] :
                    ( ~ ssItem(X4)
                    | ( ( ~ memberP(X3,X4)
                        | memberP(X2,X4) )
                      & ( ~ memberP(X2,X4)
                        | memberP(X3,X4) ) ) )
                & ssList(X3)
                & ( ? [X5] :
                      ( ( ~ memberP(sK2,X5)
                        | ~ memberP(X1,X5) )
                      & ( memberP(sK2,X5)
                        | memberP(X1,X5) )
                      & ssItem(X5) )
                  | ~ duplicatefreeP(sK2) ) )
            & ssList(X2) ) )
   => ( ssList(sK3)
      & ? [X2] :
          ( ? [X3] :
              ( duplicatefreeP(X2)
              & sK3 = X3
              & sK2 = X2
              & ! [X4] :
                  ( ~ ssItem(X4)
                  | ( ( ~ memberP(X3,X4)
                      | memberP(X2,X4) )
                    & ( ~ memberP(X2,X4)
                      | memberP(X3,X4) ) ) )
              & ssList(X3)
              & ( ? [X5] :
                    ( ( ~ memberP(sK2,X5)
                      | ~ memberP(sK3,X5) )
                    & ( memberP(sK2,X5)
                      | memberP(sK3,X5) )
                    & ssItem(X5) )
                | ~ duplicatefreeP(sK2) ) )
          & ssList(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f134,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( duplicatefreeP(X2)
            & sK3 = X3
            & sK2 = X2
            & ! [X4] :
                ( ~ ssItem(X4)
                | ( ( ~ memberP(X3,X4)
                    | memberP(X2,X4) )
                  & ( ~ memberP(X2,X4)
                    | memberP(X3,X4) ) ) )
            & ssList(X3)
            & ( ? [X5] :
                  ( ( ~ memberP(sK2,X5)
                    | ~ memberP(sK3,X5) )
                  & ( memberP(sK2,X5)
                    | memberP(sK3,X5) )
                  & ssItem(X5) )
              | ~ duplicatefreeP(sK2) ) )
        & ssList(X2) )
   => ( ? [X3] :
          ( duplicatefreeP(sK4)
          & sK3 = X3
          & sK4 = sK2
          & ! [X4] :
              ( ~ ssItem(X4)
              | ( ( ~ memberP(X3,X4)
                  | memberP(sK4,X4) )
                & ( ~ memberP(sK4,X4)
                  | memberP(X3,X4) ) ) )
          & ssList(X3)
          & ( ? [X5] :
                ( ( ~ memberP(sK2,X5)
                  | ~ memberP(sK3,X5) )
                & ( memberP(sK2,X5)
                  | memberP(sK3,X5) )
                & ssItem(X5) )
            | ~ duplicatefreeP(sK2) ) )
      & ssList(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( ? [X3] :
        ( duplicatefreeP(sK4)
        & sK3 = X3
        & sK4 = sK2
        & ! [X4] :
            ( ~ ssItem(X4)
            | ( ( ~ memberP(X3,X4)
                | memberP(sK4,X4) )
              & ( ~ memberP(sK4,X4)
                | memberP(X3,X4) ) ) )
        & ssList(X3)
        & ( ? [X5] :
              ( ( ~ memberP(sK2,X5)
                | ~ memberP(sK3,X5) )
              & ( memberP(sK2,X5)
                | memberP(sK3,X5) )
              & ssItem(X5) )
          | ~ duplicatefreeP(sK2) ) )
   => ( duplicatefreeP(sK4)
      & sK3 = sK5
      & sK4 = sK2
      & ! [X4] :
          ( ~ ssItem(X4)
          | ( ( ~ memberP(sK5,X4)
              | memberP(sK4,X4) )
            & ( ~ memberP(sK4,X4)
              | memberP(sK5,X4) ) ) )
      & ssList(sK5)
      & ( ? [X5] :
            ( ( ~ memberP(sK2,X5)
              | ~ memberP(sK3,X5) )
            & ( memberP(sK2,X5)
              | memberP(sK3,X5) )
            & ssItem(X5) )
        | ~ duplicatefreeP(sK2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ( ? [X5] :
        ( ( ~ memberP(sK2,X5)
          | ~ memberP(sK3,X5) )
        & ( memberP(sK2,X5)
          | memberP(sK3,X5) )
        & ssItem(X5) )
   => ( ( ~ memberP(sK2,sK6)
        | ~ memberP(sK3,sK6) )
      & ( memberP(sK2,sK6)
        | memberP(sK3,sK6) )
      & ssItem(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f131,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( duplicatefreeP(X2)
                  & X1 = X3
                  & X0 = X2
                  & ! [X4] :
                      ( ~ ssItem(X4)
                      | ( ( ~ memberP(X3,X4)
                          | memberP(X2,X4) )
                        & ( ~ memberP(X2,X4)
                          | memberP(X3,X4) ) ) )
                  & ssList(X3)
                  & ( ? [X5] :
                        ( ( ~ memberP(X0,X5)
                          | ~ memberP(X1,X5) )
                        & ( memberP(X0,X5)
                          | memberP(X1,X5) )
                        & ssItem(X5) )
                    | ~ duplicatefreeP(X0) ) )
              & ssList(X2) ) )
      & ssList(X0) ),
    inference(rectify,[],[f112]) ).

fof(f112,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( duplicatefreeP(X2)
                  & X1 = X3
                  & X0 = X2
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ( ( ~ memberP(X3,X5)
                          | memberP(X2,X5) )
                        & ( ~ memberP(X2,X5)
                          | memberP(X3,X5) ) ) )
                  & ssList(X3)
                  & ( ? [X4] :
                        ( ( ~ memberP(X0,X4)
                          | ~ memberP(X1,X4) )
                        & ( memberP(X0,X4)
                          | memberP(X1,X4) )
                        & ssItem(X4) )
                    | ~ duplicatefreeP(X0) ) )
              & ssList(X2) ) )
      & ssList(X0) ),
    inference(flattening,[],[f111]) ).

fof(f111,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & duplicatefreeP(X2)
                  & X0 = X2
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ( ( ~ memberP(X3,X5)
                          | memberP(X2,X5) )
                        & ( ~ memberP(X2,X5)
                          | memberP(X3,X5) ) ) )
                  & ( ~ duplicatefreeP(X0)
                    | ? [X4] :
                        ( ( ~ memberP(X0,X4)
                          | ~ memberP(X1,X4) )
                        & ( memberP(X0,X4)
                          | memberP(X1,X4) )
                        & ssItem(X4) ) )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( X1 != X3
                      | ~ duplicatefreeP(X2)
                      | X0 != X2
                      | ? [X5] :
                          ( ssItem(X5)
                          & ( ( ~ memberP(X3,X5)
                              & memberP(X2,X5) )
                            | ( memberP(X3,X5)
                              & ~ memberP(X2,X5) ) ) )
                      | ( duplicatefreeP(X0)
                        & ! [X4] :
                            ( ssItem(X4)
                           => ( ( memberP(X1,X4)
                                & memberP(X0,X4) )
                              | ( ~ memberP(X1,X4)
                                & ~ memberP(X0,X4) ) ) ) ) ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( X0 != X2
                      | ( ! [X5] :
                            ( ssItem(X5)
                           => ( ( memberP(X1,X5)
                                & memberP(X0,X5) )
                              | ( ~ memberP(X0,X5)
                                & ~ memberP(X1,X5) ) ) )
                        & duplicatefreeP(X0) )
                      | ? [X4] :
                          ( ssItem(X4)
                          & ( ( memberP(X2,X4)
                              & ~ memberP(X3,X4) )
                            | ( ~ memberP(X2,X4)
                              & memberP(X3,X4) ) ) )
                      | ~ duplicatefreeP(X2)
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( X0 != X2
                    | ( ! [X5] :
                          ( ssItem(X5)
                         => ( ( memberP(X1,X5)
                              & memberP(X0,X5) )
                            | ( ~ memberP(X0,X5)
                              & ~ memberP(X1,X5) ) ) )
                      & duplicatefreeP(X0) )
                    | ? [X4] :
                        ( ssItem(X4)
                        & ( ( memberP(X2,X4)
                            & ~ memberP(X3,X4) )
                          | ( ~ memberP(X2,X4)
                            & memberP(X3,X4) ) ) )
                    | ~ duplicatefreeP(X2)
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f181,plain,
    ! [X4] :
      ( ~ ssItem(X4)
      | ~ memberP(sK4,X4)
      | memberP(sK5,X4) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f262,plain,
    ( spl16_1
    | ~ spl16_2
    | ~ spl16_4 ),
    inference(avatar_contradiction_clause,[],[f261]) ).

fof(f261,plain,
    ( $false
    | spl16_1
    | ~ spl16_2
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f260,f233]) ).

fof(f233,plain,
    ( ~ memberP(sK2,sK6)
    | spl16_1 ),
    inference(avatar_component_clause,[],[f231]) ).

fof(f260,plain,
    ( memberP(sK2,sK6)
    | ~ spl16_2
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f259,f246]) ).

fof(f259,plain,
    ( ~ ssItem(sK6)
    | memberP(sK2,sK6)
    | ~ spl16_2 ),
    inference(resolution,[],[f216,f236]) ).

fof(f236,plain,
    ( memberP(sK5,sK6)
    | ~ spl16_2 ),
    inference(avatar_component_clause,[],[f235]) ).

fof(f216,plain,
    ! [X4] :
      ( ~ memberP(sK5,X4)
      | memberP(sK2,X4)
      | ~ ssItem(X4) ),
    inference(definition_unfolding,[],[f182,f183]) ).

fof(f182,plain,
    ! [X4] :
      ( ~ ssItem(X4)
      | ~ memberP(sK5,X4)
      | memberP(sK4,X4) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f249,plain,
    ( ~ spl16_3
    | spl16_2
    | spl16_1 ),
    inference(avatar_split_clause,[],[f219,f231,f235,f239]) ).

fof(f239,plain,
    ( spl16_3
  <=> duplicatefreeP(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).

fof(f219,plain,
    ( memberP(sK2,sK6)
    | memberP(sK5,sK6)
    | ~ duplicatefreeP(sK2) ),
    inference(definition_unfolding,[],[f178,f184]) ).

fof(f184,plain,
    sK3 = sK5,
    inference(cnf_transformation,[],[f137]) ).

fof(f178,plain,
    ( memberP(sK2,sK6)
    | memberP(sK3,sK6)
    | ~ duplicatefreeP(sK2) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f248,plain,
    spl16_3,
    inference(avatar_split_clause,[],[f215,f239]) ).

fof(f215,plain,
    duplicatefreeP(sK2),
    inference(definition_unfolding,[],[f185,f183]) ).

fof(f185,plain,
    duplicatefreeP(sK4),
    inference(cnf_transformation,[],[f137]) ).

fof(f247,plain,
    ( spl16_4
    | ~ spl16_3 ),
    inference(avatar_split_clause,[],[f177,f239,f244]) ).

fof(f177,plain,
    ( ~ duplicatefreeP(sK2)
    | ssItem(sK6) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f242,plain,
    ( ~ spl16_1
    | ~ spl16_2
    | ~ spl16_3 ),
    inference(avatar_split_clause,[],[f218,f239,f235,f231]) ).

fof(f218,plain,
    ( ~ duplicatefreeP(sK2)
    | ~ memberP(sK5,sK6)
    | ~ memberP(sK2,sK6) ),
    inference(definition_unfolding,[],[f179,f184]) ).

fof(f179,plain,
    ( ~ memberP(sK2,sK6)
    | ~ memberP(sK3,sK6)
    | ~ duplicatefreeP(sK2) ),
    inference(cnf_transformation,[],[f137]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC001+1 : TPTP v8.1.0. Released v2.4.0.
% 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
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 17:54:40 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.48  % (13750)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)
% 0.19/0.49  % (13750)First to succeed.
% 0.19/0.49  % (13750)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (13750)------------------------------
% 0.19/0.49  % (13750)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (13750)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (13750)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (13750)Memory used [KB]: 6140
% 0.19/0.49  % (13750)Time elapsed: 0.084 s
% 0.19/0.49  % (13750)Instructions burned: 5 (million)
% 0.19/0.49  % (13750)------------------------------
% 0.19/0.49  % (13750)------------------------------
% 0.19/0.49  % (13740)Success in time 0.146 s
%------------------------------------------------------------------------------