TSTP Solution File: SWC206+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC206+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 : n013.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 18:39:36 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   42 (  17 unt;   0 def)
%            Number of atoms       :  255 (  69 equ)
%            Maximal formula atoms :   30 (   6 avg)
%            Number of connectives :  287 (  74   ~;  59   |; 132   &)
%                                         (   4 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   57 (  22   !;  35   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f286,plain,
    $false,
    inference(subsumption_resolution,[],[f282,f229]) ).

fof(f229,plain,
    ~ neq(nil,nil),
    inference(backward_demodulation,[],[f169,f228]) ).

fof(f228,plain,
    nil = sK2,
    inference(subsumption_resolution,[],[f227,f158]) ).

fof(f158,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f227,plain,
    ( nil = sK2
    | ~ ssList(nil) ),
    inference(subsumption_resolution,[],[f225,f160]) ).

fof(f160,plain,
    ssList(sK2),
    inference(cnf_transformation,[],[f138]) ).

fof(f138,plain,
    ( ssList(sK3)
    & sK4 = sK2
    & sK3 = sK5
    & ~ neq(sK2,nil)
    & neq(sK3,nil)
    & ( nil = sK4
      | nil != sK5 )
    & ( ( ssList(sK6)
        & neq(sK6,nil)
        & segmentP(sK5,sK6)
        & segmentP(sK4,sK6) )
      | ~ neq(sK5,nil) )
    & ssList(sK5)
    & ssList(sK4)
    & ssList(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f105,f137,f136,f135,f134,f133]) ).

fof(f133,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ? [X3] :
                    ( X0 = X2
                    & X1 = X3
                    & ~ neq(X0,nil)
                    & neq(X1,nil)
                    & ( nil = X2
                      | nil != X3 )
                    & ( ? [X4] :
                          ( ssList(X4)
                          & neq(X4,nil)
                          & segmentP(X3,X4)
                          & segmentP(X2,X4) )
                      | ~ neq(X3,nil) )
                    & ssList(X3) )
                & ssList(X2) ) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( sK2 = X2
                  & X1 = X3
                  & ~ neq(sK2,nil)
                  & neq(X1,nil)
                  & ( nil = X2
                    | nil != X3 )
                  & ( ? [X4] :
                        ( ssList(X4)
                        & neq(X4,nil)
                        & segmentP(X3,X4)
                        & segmentP(X2,X4) )
                    | ~ neq(X3,nil) )
                  & ssList(X3) )
              & ssList(X2) ) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f134,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ? [X3] :
                ( sK2 = X2
                & X1 = X3
                & ~ neq(sK2,nil)
                & neq(X1,nil)
                & ( nil = X2
                  | nil != X3 )
                & ( ? [X4] :
                      ( ssList(X4)
                      & neq(X4,nil)
                      & segmentP(X3,X4)
                      & segmentP(X2,X4) )
                  | ~ neq(X3,nil) )
                & ssList(X3) )
            & ssList(X2) ) )
   => ( ssList(sK3)
      & ? [X2] :
          ( ? [X3] :
              ( sK2 = X2
              & sK3 = X3
              & ~ neq(sK2,nil)
              & neq(sK3,nil)
              & ( nil = X2
                | nil != X3 )
              & ( ? [X4] :
                    ( ssList(X4)
                    & neq(X4,nil)
                    & segmentP(X3,X4)
                    & segmentP(X2,X4) )
                | ~ neq(X3,nil) )
              & ssList(X3) )
          & ssList(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( sK2 = X2
            & sK3 = X3
            & ~ neq(sK2,nil)
            & neq(sK3,nil)
            & ( nil = X2
              | nil != X3 )
            & ( ? [X4] :
                  ( ssList(X4)
                  & neq(X4,nil)
                  & segmentP(X3,X4)
                  & segmentP(X2,X4) )
              | ~ neq(X3,nil) )
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( sK4 = sK2
          & sK3 = X3
          & ~ neq(sK2,nil)
          & neq(sK3,nil)
          & ( nil = sK4
            | nil != X3 )
          & ( ? [X4] :
                ( ssList(X4)
                & neq(X4,nil)
                & segmentP(X3,X4)
                & segmentP(sK4,X4) )
            | ~ neq(X3,nil) )
          & ssList(X3) )
      & ssList(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ( ? [X3] :
        ( sK4 = sK2
        & sK3 = X3
        & ~ neq(sK2,nil)
        & neq(sK3,nil)
        & ( nil = sK4
          | nil != X3 )
        & ( ? [X4] :
              ( ssList(X4)
              & neq(X4,nil)
              & segmentP(X3,X4)
              & segmentP(sK4,X4) )
          | ~ neq(X3,nil) )
        & ssList(X3) )
   => ( sK4 = sK2
      & sK3 = sK5
      & ~ neq(sK2,nil)
      & neq(sK3,nil)
      & ( nil = sK4
        | nil != sK5 )
      & ( ? [X4] :
            ( ssList(X4)
            & neq(X4,nil)
            & segmentP(sK5,X4)
            & segmentP(sK4,X4) )
        | ~ neq(sK5,nil) )
      & ssList(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f137,plain,
    ( ? [X4] :
        ( ssList(X4)
        & neq(X4,nil)
        & segmentP(sK5,X4)
        & segmentP(sK4,X4) )
   => ( ssList(sK6)
      & neq(sK6,nil)
      & segmentP(sK5,sK6)
      & segmentP(sK4,sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f105,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & X1 = X3
                  & ~ neq(X0,nil)
                  & neq(X1,nil)
                  & ( nil = X2
                    | nil != X3 )
                  & ( ? [X4] :
                        ( ssList(X4)
                        & neq(X4,nil)
                        & segmentP(X3,X4)
                        & segmentP(X2,X4) )
                    | ~ neq(X3,nil) )
                  & ssList(X3) )
              & ssList(X2) ) )
      & ssList(X0) ),
    inference(flattening,[],[f104]) ).

fof(f104,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & neq(X1,nil)
                  & ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( segmentP(X2,X4)
                        & segmentP(X3,X4)
                        & neq(X4,nil)
                        & ssList(X4) ) )
                  & X1 = X3
                  & ~ neq(X0,nil)
                  & ( nil = X2
                    | nil != X3 )
                  & 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
                      | ~ neq(X1,nil)
                      | ( neq(X3,nil)
                        & ! [X4] :
                            ( ssList(X4)
                           => ( ~ segmentP(X2,X4)
                              | ~ segmentP(X3,X4)
                              | ~ neq(X4,nil) ) ) )
                      | X1 != X3
                      | neq(X0,nil)
                      | ( nil = X3
                        & nil != X2 ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f225,plain,
    ( ~ ssList(sK2)
    | ~ ssList(nil)
    | nil = sK2 ),
    inference(resolution,[],[f169,f175]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f139]) ).

fof(f139,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( X0 != X1
          <=> neq(X0,X1) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( X0 != X1
          <=> neq(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f169,plain,
    ~ neq(sK2,nil),
    inference(cnf_transformation,[],[f138]) ).

fof(f282,plain,
    neq(nil,nil),
    inference(backward_demodulation,[],[f260,f271]) ).

fof(f271,plain,
    nil = sK6,
    inference(subsumption_resolution,[],[f263,f235]) ).

fof(f235,plain,
    ssList(sK6),
    inference(subsumption_resolution,[],[f166,f204]) ).

fof(f204,plain,
    neq(sK5,nil),
    inference(definition_unfolding,[],[f168,f170]) ).

fof(f170,plain,
    sK3 = sK5,
    inference(cnf_transformation,[],[f138]) ).

fof(f168,plain,
    neq(sK3,nil),
    inference(cnf_transformation,[],[f138]) ).

fof(f166,plain,
    ( ssList(sK6)
    | ~ neq(sK5,nil) ),
    inference(cnf_transformation,[],[f138]) ).

fof(f263,plain,
    ( nil = sK6
    | ~ ssList(sK6) ),
    inference(resolution,[],[f262,f199]) ).

fof(f199,plain,
    ! [X0] :
      ( ~ segmentP(nil,X0)
      | ~ ssList(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f151]) ).

fof(f151,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) ) ),
    inference(nnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).

fof(f262,plain,
    segmentP(nil,sK6),
    inference(forward_demodulation,[],[f261,f228]) ).

fof(f261,plain,
    segmentP(sK2,sK6),
    inference(subsumption_resolution,[],[f206,f204]) ).

fof(f206,plain,
    ( ~ neq(sK5,nil)
    | segmentP(sK2,sK6) ),
    inference(definition_unfolding,[],[f163,f171]) ).

fof(f171,plain,
    sK4 = sK2,
    inference(cnf_transformation,[],[f138]) ).

fof(f163,plain,
    ( segmentP(sK4,sK6)
    | ~ neq(sK5,nil) ),
    inference(cnf_transformation,[],[f138]) ).

fof(f260,plain,
    neq(sK6,nil),
    inference(subsumption_resolution,[],[f165,f204]) ).

fof(f165,plain,
    ( ~ neq(sK5,nil)
    | neq(sK6,nil) ),
    inference(cnf_transformation,[],[f138]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC206+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 18:30:46 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (7750)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)
% 0.19/0.49  % (7758)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (7754)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.51  % (7750)First to succeed.
% 0.19/0.51  % (7759)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.51  % (7759)Instruction limit reached!
% 0.19/0.51  % (7759)------------------------------
% 0.19/0.51  % (7759)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (7750)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Theorem for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (7750)------------------------------
% 0.19/0.52  % (7750)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (7750)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (7750)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (7750)Memory used [KB]: 1663
% 0.19/0.52  % (7750)Time elapsed: 0.112 s
% 0.19/0.52  % (7750)Instructions burned: 5 (million)
% 0.19/0.52  % (7750)------------------------------
% 0.19/0.52  % (7750)------------------------------
% 0.19/0.52  % (7744)Success in time 0.17 s
%------------------------------------------------------------------------------