TSTP Solution File: SWC255+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC255+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 : n025.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 18:39:55 EDT 2022

% Result   : Theorem 1.77s 0.59s
% Output   : Refutation 1.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   20 (   6 unt;   0 def)
%            Number of atoms       :  147 (  28 equ)
%            Maximal formula atoms :   22 (   7 avg)
%            Number of connectives :  165 (  38   ~;  26   |;  89   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   32 (   8   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f176,plain,
    $false,
    inference(subsumption_resolution,[],[f175,f174]) ).

fof(f174,plain,
    ~ singletonP(sK0),
    inference(subsumption_resolution,[],[f132,f171]) ).

fof(f171,plain,
    neq(sK3,nil),
    inference(duplicate_literal_removal,[],[f163]) ).

fof(f163,plain,
    ( neq(sK3,nil)
    | neq(sK3,nil) ),
    inference(definition_unfolding,[],[f133,f138,f138]) ).

fof(f138,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ( ssList(sK0)
    & ssList(sK2)
    & sK1 = sK3
    & ssList(sK3)
    & ( ( singletonP(sK2)
        & neq(sK1,nil)
        & ~ singletonP(sK0) )
      | ( ~ neq(sK3,nil)
        & neq(sK1,nil) ) )
    & sK2 = sK0
    & ssList(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f107,f114,f113,f112,f111]) ).

fof(f111,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( X1 = X3
                    & ssList(X3)
                    & ( ( singletonP(X2)
                        & neq(X1,nil)
                        & ~ singletonP(X0) )
                      | ( ~ neq(X3,nil)
                        & neq(X1,nil) ) )
                    & X0 = X2 ) )
            & ssList(X1) ) )
   => ( ssList(sK0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ssList(X3)
                  & ( ( singletonP(X2)
                      & neq(X1,nil)
                      & ~ singletonP(sK0) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) )
                  & sK0 = X2 ) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f112,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( X1 = X3
                & ssList(X3)
                & ( ( singletonP(X2)
                    & neq(X1,nil)
                    & ~ singletonP(sK0) )
                  | ( ~ neq(X3,nil)
                    & neq(X1,nil) ) )
                & sK0 = X2 ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( sK1 = X3
              & ssList(X3)
              & ( ( singletonP(X2)
                  & neq(sK1,nil)
                  & ~ singletonP(sK0) )
                | ( ~ neq(X3,nil)
                  & neq(sK1,nil) ) )
              & sK0 = X2 ) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f113,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( sK1 = X3
            & ssList(X3)
            & ( ( singletonP(X2)
                & neq(sK1,nil)
                & ~ singletonP(sK0) )
              | ( ~ neq(X3,nil)
                & neq(sK1,nil) ) )
            & sK0 = X2 ) )
   => ( ssList(sK2)
      & ? [X3] :
          ( sK1 = X3
          & ssList(X3)
          & ( ( singletonP(sK2)
              & neq(sK1,nil)
              & ~ singletonP(sK0) )
            | ( ~ neq(X3,nil)
              & neq(sK1,nil) ) )
          & sK2 = sK0 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ( ? [X3] :
        ( sK1 = X3
        & ssList(X3)
        & ( ( singletonP(sK2)
            & neq(sK1,nil)
            & ~ singletonP(sK0) )
          | ( ~ neq(X3,nil)
            & neq(sK1,nil) ) )
        & sK2 = sK0 )
   => ( sK1 = sK3
      & ssList(sK3)
      & ( ( singletonP(sK2)
          & neq(sK1,nil)
          & ~ singletonP(sK0) )
        | ( ~ neq(sK3,nil)
          & neq(sK1,nil) ) )
      & sK2 = sK0 ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ssList(X3)
                  & ( ( singletonP(X2)
                      & neq(X1,nil)
                      & ~ singletonP(X0) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) )
                  & X0 = X2 ) )
          & ssList(X1) ) ),
    inference(flattening,[],[f106]) ).

fof(f106,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & X1 = X3
                  & ( ( singletonP(X2)
                      & neq(X1,nil)
                      & ~ singletonP(X0) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) )
                  & 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
                      | X1 != X3
                      | ( ( ~ neq(X1,nil)
                          | neq(X3,nil) )
                        & ( ~ singletonP(X2)
                          | singletonP(X0)
                          | ~ neq(X1,nil) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f133,plain,
    ( neq(sK1,nil)
    | neq(sK1,nil) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f132,plain,
    ( ~ neq(sK3,nil)
    | ~ singletonP(sK0) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f175,plain,
    singletonP(sK0),
    inference(subsumption_resolution,[],[f160,f171]) ).

fof(f160,plain,
    ( ~ neq(sK3,nil)
    | singletonP(sK0) ),
    inference(definition_unfolding,[],[f136,f130]) ).

fof(f130,plain,
    sK2 = sK0,
    inference(cnf_transformation,[],[f115]) ).

fof(f136,plain,
    ( singletonP(sK2)
    | ~ neq(sK3,nil) ),
    inference(cnf_transformation,[],[f115]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SWC255+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n025.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 18:48:15 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 1.43/0.58  % (32177)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)
% 1.43/0.58  % (32177)First to succeed.
% 1.43/0.58  % (32173)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.77/0.59  % (32177)Refutation found. Thanks to Tanya!
% 1.77/0.59  % SZS status Theorem for theBenchmark
% 1.77/0.59  % SZS output start Proof for theBenchmark
% See solution above
% 1.77/0.59  % (32177)------------------------------
% 1.77/0.59  % (32177)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.77/0.59  % (32177)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.77/0.59  % (32177)Termination reason: Refutation
% 1.77/0.59  
% 1.77/0.59  % (32177)Memory used [KB]: 1535
% 1.77/0.59  % (32177)Time elapsed: 0.132 s
% 1.77/0.59  % (32177)Instructions burned: 3 (million)
% 1.77/0.59  % (32177)------------------------------
% 1.77/0.59  % (32177)------------------------------
% 1.77/0.59  % (32171)Success in time 0.232 s
%------------------------------------------------------------------------------