TSTP Solution File: SWC040+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC040+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 : n007.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 18:38:22 EDT 2022

% Result   : Theorem 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   20 (   7 unt;   0 def)
%            Number of atoms       :  208 ( 122 equ)
%            Maximal formula atoms :   30 (  10 avg)
%            Number of connectives :  238 (  50   ~;  36   |; 134   &)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   60 (  12   !;  48   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f206,plain,
    $false,
    inference(subsumption_resolution,[],[f202,f185]) ).

fof(f185,plain,
    sK0 != sK1,
    inference(definition_unfolding,[],[f148,f147]) ).

fof(f147,plain,
    nil = sK1,
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ( ssList(sK0)
    & ( ~ neq(sK3,nil)
      | ( ssItem(sK4)
        & sK2 = app(cons(sK4,nil),sK5)
        & app(sK5,cons(sK4,nil)) = sK3
        & ssList(sK5) ) )
    & ( nil != sK3
      | nil = sK2 )
    & nil != sK0
    & nil = sK1
    & ssList(sK3)
    & sK3 = sK1
    & sK2 = sK0
    & ssList(sK2)
    & ssList(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f107,f126,f125,f124,f123,f122,f121]) ).

fof(f121,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ neq(X3,nil)
                      | ? [X4] :
                          ( ssItem(X4)
                          & ? [X5] :
                              ( app(cons(X4,nil),X5) = X2
                              & app(X5,cons(X4,nil)) = X3
                              & ssList(X5) ) ) )
                    & ( nil != X3
                      | nil = X2 )
                    & nil != X0
                    & nil = X1
                    & ssList(X3)
                    & X1 = X3
                    & X0 = X2 )
                & ssList(X2) )
            & ssList(X1) ) )
   => ( ssList(sK0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ssItem(X4)
                        & ? [X5] :
                            ( app(cons(X4,nil),X5) = X2
                            & app(X5,cons(X4,nil)) = X3
                            & ssList(X5) ) ) )
                  & ( nil != X3
                    | nil = X2 )
                  & nil != sK0
                  & nil = X1
                  & ssList(X3)
                  & X1 = X3
                  & sK0 = X2 )
              & ssList(X2) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f122,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ neq(X3,nil)
                  | ? [X4] :
                      ( ssItem(X4)
                      & ? [X5] :
                          ( app(cons(X4,nil),X5) = X2
                          & app(X5,cons(X4,nil)) = X3
                          & ssList(X5) ) ) )
                & ( nil != X3
                  | nil = X2 )
                & nil != sK0
                & nil = X1
                & ssList(X3)
                & X1 = X3
                & sK0 = X2 )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ neq(X3,nil)
                | ? [X4] :
                    ( ssItem(X4)
                    & ? [X5] :
                        ( app(cons(X4,nil),X5) = X2
                        & app(X5,cons(X4,nil)) = X3
                        & ssList(X5) ) ) )
              & ( nil != X3
                | nil = X2 )
              & nil != sK0
              & nil = sK1
              & ssList(X3)
              & sK1 = X3
              & sK0 = X2 )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f123,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ neq(X3,nil)
              | ? [X4] :
                  ( ssItem(X4)
                  & ? [X5] :
                      ( app(cons(X4,nil),X5) = X2
                      & app(X5,cons(X4,nil)) = X3
                      & ssList(X5) ) ) )
            & ( nil != X3
              | nil = X2 )
            & nil != sK0
            & nil = sK1
            & ssList(X3)
            & sK1 = X3
            & sK0 = X2 )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ neq(X3,nil)
            | ? [X4] :
                ( ssItem(X4)
                & ? [X5] :
                    ( app(cons(X4,nil),X5) = sK2
                    & app(X5,cons(X4,nil)) = X3
                    & ssList(X5) ) ) )
          & ( nil != X3
            | nil = sK2 )
          & nil != sK0
          & nil = sK1
          & ssList(X3)
          & sK1 = X3
          & sK2 = sK0 )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ( ? [X3] :
        ( ( ~ neq(X3,nil)
          | ? [X4] :
              ( ssItem(X4)
              & ? [X5] :
                  ( app(cons(X4,nil),X5) = sK2
                  & app(X5,cons(X4,nil)) = X3
                  & ssList(X5) ) ) )
        & ( nil != X3
          | nil = sK2 )
        & nil != sK0
        & nil = sK1
        & ssList(X3)
        & sK1 = X3
        & sK2 = sK0 )
   => ( ( ~ neq(sK3,nil)
        | ? [X4] :
            ( ssItem(X4)
            & ? [X5] :
                ( app(cons(X4,nil),X5) = sK2
                & app(X5,cons(X4,nil)) = sK3
                & ssList(X5) ) ) )
      & ( nil != sK3
        | nil = sK2 )
      & nil != sK0
      & nil = sK1
      & ssList(sK3)
      & sK3 = sK1
      & sK2 = sK0 ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ( ? [X4] :
        ( ssItem(X4)
        & ? [X5] :
            ( app(cons(X4,nil),X5) = sK2
            & app(X5,cons(X4,nil)) = sK3
            & ssList(X5) ) )
   => ( ssItem(sK4)
      & ? [X5] :
          ( sK2 = app(cons(sK4,nil),X5)
          & app(X5,cons(sK4,nil)) = sK3
          & ssList(X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f126,plain,
    ( ? [X5] :
        ( sK2 = app(cons(sK4,nil),X5)
        & app(X5,cons(sK4,nil)) = sK3
        & ssList(X5) )
   => ( sK2 = app(cons(sK4,nil),sK5)
      & app(sK5,cons(sK4,nil)) = sK3
      & ssList(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ssItem(X4)
                        & ? [X5] :
                            ( app(cons(X4,nil),X5) = X2
                            & app(X5,cons(X4,nil)) = X3
                            & ssList(X5) ) ) )
                  & ( nil != X3
                    | nil = X2 )
                  & nil != X0
                  & nil = X1
                  & ssList(X3)
                  & X1 = X3
                  & X0 = X2 )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(flattening,[],[f106]) ).

fof(f106,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & nil = X1
                  & X1 = X3
                  & ( nil != X3
                    | nil = X2 )
                  & ( ? [X4] :
                        ( ? [X5] :
                            ( app(X5,cons(X4,nil)) = X3
                            & app(cons(X4,nil),X5) = X2
                            & ssList(X5) )
                        & ssItem(X4) )
                    | ~ neq(X3,nil) )
                  & nil != X0
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( X0 != X2
                      | nil != X1
                      | X1 != X3
                      | ( nil = X3
                        & nil != X2 )
                      | ( ! [X4] :
                            ( ssItem(X4)
                           => ! [X5] :
                                ( ssList(X5)
                               => ( app(X5,cons(X4,nil)) != X3
                                  | app(cons(X4,nil),X5) != X2 ) ) )
                        & neq(X3,nil) )
                      | nil = X0 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( X0 != X2
                    | nil != X1
                    | X1 != X3
                    | ( nil = X3
                      & nil != X2 )
                    | ( ! [X4] :
                          ( ssItem(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( app(X5,cons(X4,nil)) != X3
                                | app(cons(X4,nil),X5) != X2 ) ) )
                      & neq(X3,nil) )
                    | nil = X0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f148,plain,
    nil != sK0,
    inference(cnf_transformation,[],[f127]) ).

fof(f202,plain,
    sK0 = sK1,
    inference(trivial_inequality_removal,[],[f184]) ).

fof(f184,plain,
    ( sK0 = sK1
    | sK1 != sK1 ),
    inference(definition_unfolding,[],[f149,f147,f145,f147,f144]) ).

fof(f144,plain,
    sK2 = sK0,
    inference(cnf_transformation,[],[f127]) ).

fof(f145,plain,
    sK3 = sK1,
    inference(cnf_transformation,[],[f127]) ).

fof(f149,plain,
    ( nil != sK3
    | nil = sK2 ),
    inference(cnf_transformation,[],[f127]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : SWC040+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12  % 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 : n007.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 17:57:46 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.47  % (18063)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.19/0.47  % (18041)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)
% 0.19/0.47  % (18064)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.47  % (18041)First to succeed.
% 0.19/0.47  % (18041)Refutation found. Thanks to Tanya!
% 0.19/0.47  % SZS status Theorem for theBenchmark
% 0.19/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47  % (18041)------------------------------
% 0.19/0.47  % (18041)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47  % (18041)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47  % (18041)Termination reason: Refutation
% 0.19/0.47  
% 0.19/0.47  % (18041)Memory used [KB]: 1535
% 0.19/0.47  % (18041)Time elapsed: 0.100 s
% 0.19/0.47  % (18041)Instructions burned: 3 (million)
% 0.19/0.47  % (18041)------------------------------
% 0.19/0.47  % (18041)------------------------------
% 0.19/0.47  % (18035)Success in time 0.131 s
%------------------------------------------------------------------------------