TSTP Solution File: SWC095+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC095+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 : 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 18:38:46 EDT 2022

% Result   : Theorem 0.18s 0.49s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   29 (  11 unt;   0 def)
%            Number of atoms       :  266 ( 109 equ)
%            Maximal formula atoms :   32 (   9 avg)
%            Number of connectives :  332 (  95   ~;  76   |; 139   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :  129 (  57   !;  72   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f184,plain,
    $false,
    inference(subsumption_resolution,[],[f183,f150]) ).

fof(f150,plain,
    ssList(sK7),
    inference(cnf_transformation,[],[f131]) ).

fof(f131,plain,
    ( ssList(sK2)
    & ssList(sK3)
    & ssList(sK4)
    & ssList(sK5)
    & ! [X4] :
        ( ! [X5] :
            ( ~ ssList(X5)
            | ! [X6] :
                ( app(app(X4,X5),X6) != sK2
                | ~ ssList(X6)
                | app(X4,X6) != sK3 ) )
        | ~ ssList(X4) )
    & sK5 = sK3
    & sK4 = sK2
    & ssList(sK6)
    & ssList(sK7)
    & app(sK6,sK8) = sK5
    & app(app(sK6,sK7),sK8) = sK4
    & ssList(sK8) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f123,f130,f129,f128,f127,f126,f125,f124]) ).

fof(f124,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( ssList(X3)
                    & ! [X4] :
                        ( ! [X5] :
                            ( ~ ssList(X5)
                            | ! [X6] :
                                ( app(app(X4,X5),X6) != X0
                                | ~ ssList(X6)
                                | app(X4,X6) != X1 ) )
                        | ~ ssList(X4) )
                    & X1 = X3
                    & X0 = X2
                    & ? [X7] :
                        ( ssList(X7)
                        & ? [X8] :
                            ( ssList(X8)
                            & ? [X9] :
                                ( app(X7,X9) = X3
                                & app(app(X7,X8),X9) = X2
                                & ssList(X9) ) ) ) ) ) ) )
   => ( ssList(sK2)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ! [X4] :
                      ( ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( app(app(X4,X5),X6) != sK2
                              | ~ ssList(X6)
                              | app(X4,X6) != X1 ) )
                      | ~ ssList(X4) )
                  & X1 = X3
                  & sK2 = X2
                  & ? [X7] :
                      ( ssList(X7)
                      & ? [X8] :
                          ( ssList(X8)
                          & ? [X9] :
                              ( app(X7,X9) = X3
                              & app(app(X7,X8),X9) = X2
                              & ssList(X9) ) ) ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssList(X3)
                & ! [X4] :
                    ( ! [X5] :
                        ( ~ ssList(X5)
                        | ! [X6] :
                            ( app(app(X4,X5),X6) != sK2
                            | ~ ssList(X6)
                            | app(X4,X6) != X1 ) )
                    | ~ ssList(X4) )
                & X1 = X3
                & sK2 = X2
                & ? [X7] :
                    ( ssList(X7)
                    & ? [X8] :
                        ( ssList(X8)
                        & ? [X9] :
                            ( app(X7,X9) = X3
                            & app(app(X7,X8),X9) = X2
                            & ssList(X9) ) ) ) ) ) )
   => ( ssList(sK3)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ! [X4] :
                  ( ! [X5] :
                      ( ~ ssList(X5)
                      | ! [X6] :
                          ( app(app(X4,X5),X6) != sK2
                          | ~ ssList(X6)
                          | app(X4,X6) != sK3 ) )
                  | ~ ssList(X4) )
              & sK3 = X3
              & sK2 = X2
              & ? [X7] :
                  ( ssList(X7)
                  & ? [X8] :
                      ( ssList(X8)
                      & ? [X9] :
                          ( app(X7,X9) = X3
                          & app(app(X7,X8),X9) = X2
                          & ssList(X9) ) ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f126,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( ssList(X3)
            & ! [X4] :
                ( ! [X5] :
                    ( ~ ssList(X5)
                    | ! [X6] :
                        ( app(app(X4,X5),X6) != sK2
                        | ~ ssList(X6)
                        | app(X4,X6) != sK3 ) )
                | ~ ssList(X4) )
            & sK3 = X3
            & sK2 = X2
            & ? [X7] :
                ( ssList(X7)
                & ? [X8] :
                    ( ssList(X8)
                    & ? [X9] :
                        ( app(X7,X9) = X3
                        & app(app(X7,X8),X9) = X2
                        & ssList(X9) ) ) ) ) )
   => ( ssList(sK4)
      & ? [X3] :
          ( ssList(X3)
          & ! [X4] :
              ( ! [X5] :
                  ( ~ ssList(X5)
                  | ! [X6] :
                      ( app(app(X4,X5),X6) != sK2
                      | ~ ssList(X6)
                      | app(X4,X6) != sK3 ) )
              | ~ ssList(X4) )
          & sK3 = X3
          & sK4 = sK2
          & ? [X7] :
              ( ssList(X7)
              & ? [X8] :
                  ( ssList(X8)
                  & ? [X9] :
                      ( app(X7,X9) = X3
                      & app(app(X7,X8),X9) = sK4
                      & ssList(X9) ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f127,plain,
    ( ? [X3] :
        ( ssList(X3)
        & ! [X4] :
            ( ! [X5] :
                ( ~ ssList(X5)
                | ! [X6] :
                    ( app(app(X4,X5),X6) != sK2
                    | ~ ssList(X6)
                    | app(X4,X6) != sK3 ) )
            | ~ ssList(X4) )
        & sK3 = X3
        & sK4 = sK2
        & ? [X7] :
            ( ssList(X7)
            & ? [X8] :
                ( ssList(X8)
                & ? [X9] :
                    ( app(X7,X9) = X3
                    & app(app(X7,X8),X9) = sK4
                    & ssList(X9) ) ) ) )
   => ( ssList(sK5)
      & ! [X4] :
          ( ! [X5] :
              ( ~ ssList(X5)
              | ! [X6] :
                  ( app(app(X4,X5),X6) != sK2
                  | ~ ssList(X6)
                  | app(X4,X6) != sK3 ) )
          | ~ ssList(X4) )
      & sK5 = sK3
      & sK4 = sK2
      & ? [X7] :
          ( ssList(X7)
          & ? [X8] :
              ( ssList(X8)
              & ? [X9] :
                  ( app(X7,X9) = sK5
                  & app(app(X7,X8),X9) = sK4
                  & ssList(X9) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f128,plain,
    ( ? [X7] :
        ( ssList(X7)
        & ? [X8] :
            ( ssList(X8)
            & ? [X9] :
                ( app(X7,X9) = sK5
                & app(app(X7,X8),X9) = sK4
                & ssList(X9) ) ) )
   => ( ssList(sK6)
      & ? [X8] :
          ( ssList(X8)
          & ? [X9] :
              ( sK5 = app(sK6,X9)
              & sK4 = app(app(sK6,X8),X9)
              & ssList(X9) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f129,plain,
    ( ? [X8] :
        ( ssList(X8)
        & ? [X9] :
            ( sK5 = app(sK6,X9)
            & sK4 = app(app(sK6,X8),X9)
            & ssList(X9) ) )
   => ( ssList(sK7)
      & ? [X9] :
          ( sK5 = app(sK6,X9)
          & sK4 = app(app(sK6,sK7),X9)
          & ssList(X9) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f130,plain,
    ( ? [X9] :
        ( sK5 = app(sK6,X9)
        & sK4 = app(app(sK6,sK7),X9)
        & ssList(X9) )
   => ( app(sK6,sK8) = sK5
      & app(app(sK6,sK7),sK8) = sK4
      & ssList(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f123,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ! [X4] :
                      ( ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( app(app(X4,X5),X6) != X0
                              | ~ ssList(X6)
                              | app(X4,X6) != X1 ) )
                      | ~ ssList(X4) )
                  & X1 = X3
                  & X0 = X2
                  & ? [X7] :
                      ( ssList(X7)
                      & ? [X8] :
                          ( ssList(X8)
                          & ? [X9] :
                              ( app(X7,X9) = X3
                              & app(app(X7,X8),X9) = X2
                              & ssList(X9) ) ) ) ) ) ) ),
    inference(rectify,[],[f108]) ).

fof(f108,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ! [X7] :
                      ( ! [X8] :
                          ( ~ ssList(X8)
                          | ! [X9] :
                              ( app(app(X7,X8),X9) != X0
                              | ~ ssList(X9)
                              | app(X7,X9) != X1 ) )
                      | ~ ssList(X7) )
                  & X1 = X3
                  & X0 = X2
                  & ? [X4] :
                      ( ssList(X4)
                      & ? [X5] :
                          ( ssList(X5)
                          & ? [X6] :
                              ( app(X4,X6) = X3
                              & app(app(X4,X5),X6) = X2
                              & ssList(X6) ) ) ) ) ) ) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ? [X7] :
                        ( ssList(X7)
                        & ? [X8] :
                            ( ssList(X8)
                            & ? [X9] :
                                ( app(X7,X9) = X1
                                & app(app(X7,X8),X9) = X0
                                & ssList(X9) ) ) )
                    | ~ ssList(X3)
                    | ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ! [X6] :
                                ( app(X4,X6) != X3
                                | app(app(X4,X5),X6) != X2
                                | ~ ssList(X6) ) ) )
                    | X1 != X3
                    | X0 != X2 ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( X0 != X2
                    | ! [X7] :
                        ( ssList(X7)
                       => ! [X8] :
                            ( ssList(X8)
                           => ! [X9] :
                                ( ~ ssList(X9)
                                | app(app(X7,X8),X9) != X2
                                | app(X7,X9) != X3 ) ) )
                    | ~ ssList(X3)
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( app(app(X4,X5),X6) = X0
                                & app(X4,X6) = X1
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssList(X4) )
                    | X1 != X3 ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( X0 != X2
                  | ! [X7] :
                      ( ssList(X7)
                     => ! [X8] :
                          ( ssList(X8)
                         => ! [X9] :
                              ( ~ ssList(X9)
                              | app(app(X7,X8),X9) != X2
                              | app(X7,X9) != X3 ) ) )
                  | ~ ssList(X3)
                  | ? [X4] :
                      ( ? [X5] :
                          ( ? [X6] :
                              ( app(app(X4,X5),X6) = X0
                              & app(X4,X6) = X1
                              & ssList(X6) )
                          & ssList(X5) )
                      & ssList(X4) )
                  | X1 != X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f183,plain,
    ~ ssList(sK7),
    inference(subsumption_resolution,[],[f182,f172]) ).

fof(f172,plain,
    app(sK6,sK8) = sK3,
    inference(definition_unfolding,[],[f149,f153]) ).

fof(f153,plain,
    sK5 = sK3,
    inference(cnf_transformation,[],[f131]) ).

fof(f149,plain,
    app(sK6,sK8) = sK5,
    inference(cnf_transformation,[],[f131]) ).

fof(f182,plain,
    ( app(sK6,sK8) != sK3
    | ~ ssList(sK7) ),
    inference(subsumption_resolution,[],[f181,f151]) ).

fof(f151,plain,
    ssList(sK6),
    inference(cnf_transformation,[],[f131]) ).

fof(f181,plain,
    ( ~ ssList(sK6)
    | app(sK6,sK8) != sK3
    | ~ ssList(sK7) ),
    inference(subsumption_resolution,[],[f180,f147]) ).

fof(f147,plain,
    ssList(sK8),
    inference(cnf_transformation,[],[f131]) ).

fof(f180,plain,
    ( ~ ssList(sK8)
    | ~ ssList(sK6)
    | app(sK6,sK8) != sK3
    | ~ ssList(sK7) ),
    inference(trivial_inequality_removal,[],[f179]) ).

fof(f179,plain,
    ( sK2 != sK2
    | ~ ssList(sK6)
    | app(sK6,sK8) != sK3
    | ~ ssList(sK7)
    | ~ ssList(sK8) ),
    inference(superposition,[],[f154,f173]) ).

fof(f173,plain,
    app(app(sK6,sK7),sK8) = sK2,
    inference(definition_unfolding,[],[f148,f152]) ).

fof(f152,plain,
    sK4 = sK2,
    inference(cnf_transformation,[],[f131]) ).

fof(f148,plain,
    app(app(sK6,sK7),sK8) = sK4,
    inference(cnf_transformation,[],[f131]) ).

fof(f154,plain,
    ! [X6,X4,X5] :
      ( app(app(X4,X5),X6) != sK2
      | app(X4,X6) != sK3
      | ~ ssList(X5)
      | ~ ssList(X6)
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f131]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC095+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
% 0.12/0.32  % Computer : n023.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Tue Aug 30 18:35:05 EDT 2022
% 0.12/0.32  % CPUTime    : 
% 0.18/0.47  % (28032)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)
% 0.18/0.48  % (28032)First to succeed.
% 0.18/0.48  % (28054)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.48  % (28051)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)
% 0.18/0.48  % (28030)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)
% 0.18/0.49  % (28032)Refutation found. Thanks to Tanya!
% 0.18/0.49  % SZS status Theorem for theBenchmark
% 0.18/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49  % (28032)------------------------------
% 0.18/0.49  % (28032)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49  % (28032)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.49  % (28032)Termination reason: Refutation
% 0.18/0.49  
% 0.18/0.49  % (28032)Memory used [KB]: 6140
% 0.18/0.49  % (28032)Time elapsed: 0.096 s
% 0.18/0.49  % (28032)Instructions burned: 4 (million)
% 0.18/0.49  % (28032)------------------------------
% 0.18/0.49  % (28032)------------------------------
% 0.18/0.49  % (28027)Success in time 0.153 s
%------------------------------------------------------------------------------