TSTP Solution File: SWC086+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC086+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n016.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 : Thu Aug 31 20:56:26 EDT 2023

% Result   : Theorem 0.20s 0.42s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   68 (  11 unt;   0 def)
%            Number of atoms       :  318 (  64 equ)
%            Maximal formula atoms :   30 (   4 avg)
%            Number of connectives :  384 ( 134   ~; 127   |; 106   &)
%                                         (   4 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   49 (;  23   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f675,plain,
    $false,
    inference(avatar_sat_refutation,[],[f580,f585,f590,f591,f620,f652,f674]) ).

fof(f674,plain,
    ( ~ spl51_1
    | spl51_2
    | ~ spl51_3 ),
    inference(avatar_contradiction_clause,[],[f673]) ).

fof(f673,plain,
    ( $false
    | ~ spl51_1
    | spl51_2
    | ~ spl51_3 ),
    inference(subsumption_resolution,[],[f668,f356]) ).

fof(f356,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/tmp/tmp.q76Q9OiE2V/Vampire---4.8_22110',ax17) ).

fof(f668,plain,
    ( ~ ssList(nil)
    | ~ spl51_1
    | spl51_2
    | ~ spl51_3 ),
    inference(resolution,[],[f661,f409]) ).

fof(f409,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f143,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.q76Q9OiE2V/Vampire---4.8_22110',ax55) ).

fof(f661,plain,
    ( ~ segmentP(nil,nil)
    | ~ spl51_1
    | spl51_2
    | ~ spl51_3 ),
    inference(forward_demodulation,[],[f660,f635]) ).

fof(f635,plain,
    ( nil = sK1
    | ~ spl51_3 ),
    inference(superposition,[],[f584,f340]) ).

fof(f340,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f227]) ).

fof(f227,plain,
    ( ( ( segmentP(sK3,sK2)
        & neq(sK2,nil) )
      | ( nil = sK2
        & nil = sK3 ) )
    & ! [X4] :
        ( ~ segmentP(sK0,X4)
        | ~ segmentP(sK1,X4)
        | ~ neq(X4,nil)
        | ~ ssList(X4) )
    & neq(sK1,nil)
    & sK0 = sK2
    & sK1 = sK3
    & ssList(sK3)
    & ssList(sK2)
    & ssList(sK1)
    & ssList(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f99,f226,f225,f224,f223]) ).

fof(f223,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( segmentP(X3,X2)
                        & neq(X2,nil) )
                      | ( nil = X2
                        & nil = X3 ) )
                    & ! [X4] :
                        ( ~ segmentP(X0,X4)
                        | ~ segmentP(X1,X4)
                        | ~ neq(X4,nil)
                        | ~ ssList(X4) )
                    & neq(X1,nil)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( segmentP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ! [X4] :
                      ( ~ segmentP(sK0,X4)
                      | ~ segmentP(X1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & neq(X1,nil)
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f224,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( segmentP(X3,X2)
                    & neq(X2,nil) )
                  | ( nil = X2
                    & nil = X3 ) )
                & ! [X4] :
                    ( ~ segmentP(sK0,X4)
                    | ~ segmentP(X1,X4)
                    | ~ neq(X4,nil)
                    | ~ ssList(X4) )
                & neq(X1,nil)
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( segmentP(X3,X2)
                  & neq(X2,nil) )
                | ( nil = X2
                  & nil = X3 ) )
              & ! [X4] :
                  ( ~ segmentP(sK0,X4)
                  | ~ segmentP(sK1,X4)
                  | ~ neq(X4,nil)
                  | ~ ssList(X4) )
              & neq(sK1,nil)
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f225,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( segmentP(X3,X2)
                & neq(X2,nil) )
              | ( nil = X2
                & nil = X3 ) )
            & ! [X4] :
                ( ~ segmentP(sK0,X4)
                | ~ segmentP(sK1,X4)
                | ~ neq(X4,nil)
                | ~ ssList(X4) )
            & neq(sK1,nil)
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( segmentP(X3,sK2)
              & neq(sK2,nil) )
            | ( nil = sK2
              & nil = X3 ) )
          & ! [X4] :
              ( ~ segmentP(sK0,X4)
              | ~ segmentP(sK1,X4)
              | ~ neq(X4,nil)
              | ~ ssList(X4) )
          & neq(sK1,nil)
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f226,plain,
    ( ? [X3] :
        ( ( ( segmentP(X3,sK2)
            & neq(sK2,nil) )
          | ( nil = sK2
            & nil = X3 ) )
        & ! [X4] :
            ( ~ segmentP(sK0,X4)
            | ~ segmentP(sK1,X4)
            | ~ neq(X4,nil)
            | ~ ssList(X4) )
        & neq(sK1,nil)
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ( ( segmentP(sK3,sK2)
          & neq(sK2,nil) )
        | ( nil = sK2
          & nil = sK3 ) )
      & ! [X4] :
          ( ~ segmentP(sK0,X4)
          | ~ segmentP(sK1,X4)
          | ~ neq(X4,nil)
          | ~ ssList(X4) )
      & neq(sK1,nil)
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( segmentP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ! [X4] :
                      ( ~ segmentP(X0,X4)
                      | ~ segmentP(X1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( segmentP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ! [X4] :
                      ( ~ segmentP(X0,X4)
                      | ~ segmentP(X1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = 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)
                   => ( ( ( ~ segmentP(X3,X2)
                          | ~ neq(X2,nil) )
                        & ( nil != X2
                          | nil != X3 ) )
                      | ? [X4] :
                          ( segmentP(X0,X4)
                          & segmentP(X1,X4)
                          & neq(X4,nil)
                          & ssList(X4) )
                      | ~ neq(X1,nil)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( ~ segmentP(X3,X2)
                        | ~ neq(X2,nil) )
                      & ( nil != X2
                        | nil != X3 ) )
                    | ? [X4] :
                        ( segmentP(X0,X4)
                        & segmentP(X1,X4)
                        & neq(X4,nil)
                        & ssList(X4) )
                    | ~ neq(X1,nil)
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.q76Q9OiE2V/Vampire---4.8_22110',co1) ).

fof(f584,plain,
    ( nil = sK3
    | ~ spl51_3 ),
    inference(avatar_component_clause,[],[f582]) ).

fof(f582,plain,
    ( spl51_3
  <=> nil = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_3])]) ).

fof(f660,plain,
    ( ~ segmentP(sK1,nil)
    | ~ spl51_1
    | spl51_2 ),
    inference(forward_demodulation,[],[f659,f340]) ).

fof(f659,plain,
    ( ~ segmentP(sK3,nil)
    | ~ spl51_1
    | spl51_2 ),
    inference(forward_demodulation,[],[f658,f633]) ).

fof(f633,plain,
    ( nil = sK0
    | ~ spl51_1 ),
    inference(superposition,[],[f575,f341]) ).

fof(f341,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f227]) ).

fof(f575,plain,
    ( nil = sK2
    | ~ spl51_1 ),
    inference(avatar_component_clause,[],[f573]) ).

fof(f573,plain,
    ( spl51_1
  <=> nil = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_1])]) ).

fof(f658,plain,
    ( ~ segmentP(sK3,sK0)
    | spl51_2 ),
    inference(forward_demodulation,[],[f578,f341]) ).

fof(f578,plain,
    ( ~ segmentP(sK3,sK2)
    | spl51_2 ),
    inference(avatar_component_clause,[],[f577]) ).

fof(f577,plain,
    ( spl51_2
  <=> segmentP(sK3,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_2])]) ).

fof(f652,plain,
    ( ~ spl51_1
    | ~ spl51_2
    | ~ spl51_3 ),
    inference(avatar_contradiction_clause,[],[f651]) ).

fof(f651,plain,
    ( $false
    | ~ spl51_1
    | ~ spl51_2
    | ~ spl51_3 ),
    inference(subsumption_resolution,[],[f650,f644]) ).

fof(f644,plain,
    ( segmentP(nil,nil)
    | ~ spl51_1
    | ~ spl51_2
    | ~ spl51_3 ),
    inference(forward_demodulation,[],[f641,f635]) ).

fof(f641,plain,
    ( segmentP(sK1,nil)
    | ~ spl51_1
    | ~ spl51_2 ),
    inference(superposition,[],[f596,f633]) ).

fof(f596,plain,
    ( segmentP(sK1,sK0)
    | ~ spl51_2 ),
    inference(forward_demodulation,[],[f595,f340]) ).

fof(f595,plain,
    ( segmentP(sK3,sK0)
    | ~ spl51_2 ),
    inference(forward_demodulation,[],[f579,f341]) ).

fof(f579,plain,
    ( segmentP(sK3,sK2)
    | ~ spl51_2 ),
    inference(avatar_component_clause,[],[f577]) ).

fof(f650,plain,
    ( ~ segmentP(nil,nil)
    | ~ spl51_1
    | ~ spl51_3 ),
    inference(forward_demodulation,[],[f649,f633]) ).

fof(f649,plain,
    ( ~ segmentP(sK0,nil)
    | ~ spl51_3 ),
    inference(forward_demodulation,[],[f648,f635]) ).

fof(f648,plain,
    ~ segmentP(sK0,sK1),
    inference(subsumption_resolution,[],[f647,f592]) ).

fof(f592,plain,
    ssList(sK1),
    inference(forward_demodulation,[],[f339,f340]) ).

fof(f339,plain,
    ssList(sK3),
    inference(cnf_transformation,[],[f227]) ).

fof(f647,plain,
    ( ~ segmentP(sK0,sK1)
    | ~ ssList(sK1) ),
    inference(subsumption_resolution,[],[f615,f342]) ).

fof(f342,plain,
    neq(sK1,nil),
    inference(cnf_transformation,[],[f227]) ).

fof(f615,plain,
    ( ~ segmentP(sK0,sK1)
    | ~ neq(sK1,nil)
    | ~ ssList(sK1) ),
    inference(duplicate_literal_removal,[],[f613]) ).

fof(f613,plain,
    ( ~ segmentP(sK0,sK1)
    | ~ neq(sK1,nil)
    | ~ ssList(sK1)
    | ~ ssList(sK1) ),
    inference(resolution,[],[f343,f409]) ).

fof(f343,plain,
    ! [X4] :
      ( ~ segmentP(sK1,X4)
      | ~ segmentP(sK0,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f227]) ).

fof(f620,plain,
    ( ~ spl51_2
    | ~ spl51_4 ),
    inference(avatar_contradiction_clause,[],[f619]) ).

fof(f619,plain,
    ( $false
    | ~ spl51_2
    | ~ spl51_4 ),
    inference(subsumption_resolution,[],[f618,f593]) ).

fof(f593,plain,
    ssList(sK0),
    inference(forward_demodulation,[],[f338,f341]) ).

fof(f338,plain,
    ssList(sK2),
    inference(cnf_transformation,[],[f227]) ).

fof(f618,plain,
    ( ~ ssList(sK0)
    | ~ spl51_2
    | ~ spl51_4 ),
    inference(resolution,[],[f617,f409]) ).

fof(f617,plain,
    ( ~ segmentP(sK0,sK0)
    | ~ spl51_2
    | ~ spl51_4 ),
    inference(subsumption_resolution,[],[f616,f593]) ).

fof(f616,plain,
    ( ~ segmentP(sK0,sK0)
    | ~ ssList(sK0)
    | ~ spl51_2
    | ~ spl51_4 ),
    inference(subsumption_resolution,[],[f612,f594]) ).

fof(f594,plain,
    ( neq(sK0,nil)
    | ~ spl51_4 ),
    inference(forward_demodulation,[],[f589,f341]) ).

fof(f589,plain,
    ( neq(sK2,nil)
    | ~ spl51_4 ),
    inference(avatar_component_clause,[],[f587]) ).

fof(f587,plain,
    ( spl51_4
  <=> neq(sK2,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_4])]) ).

fof(f612,plain,
    ( ~ segmentP(sK0,sK0)
    | ~ neq(sK0,nil)
    | ~ ssList(sK0)
    | ~ spl51_2 ),
    inference(resolution,[],[f343,f596]) ).

fof(f591,plain,
    ( spl51_3
    | spl51_4 ),
    inference(avatar_split_clause,[],[f344,f587,f582]) ).

fof(f344,plain,
    ( neq(sK2,nil)
    | nil = sK3 ),
    inference(cnf_transformation,[],[f227]) ).

fof(f590,plain,
    ( spl51_1
    | spl51_4 ),
    inference(avatar_split_clause,[],[f345,f587,f573]) ).

fof(f345,plain,
    ( neq(sK2,nil)
    | nil = sK2 ),
    inference(cnf_transformation,[],[f227]) ).

fof(f585,plain,
    ( spl51_3
    | spl51_2 ),
    inference(avatar_split_clause,[],[f346,f577,f582]) ).

fof(f346,plain,
    ( segmentP(sK3,sK2)
    | nil = sK3 ),
    inference(cnf_transformation,[],[f227]) ).

fof(f580,plain,
    ( spl51_1
    | spl51_2 ),
    inference(avatar_split_clause,[],[f347,f577,f573]) ).

fof(f347,plain,
    ( segmentP(sK3,sK2)
    | nil = sK2 ),
    inference(cnf_transformation,[],[f227]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13  % Problem    : SWC086+1 : TPTP v8.1.2. Released v2.4.0.
% 0.09/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 28 16:36:14 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.35  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.q76Q9OiE2V/Vampire---4.8_22110
% 0.14/0.36  % (22218)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41  % (22225)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.20/0.41  % (22223)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.20/0.41  % (22220)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.20/0.41  % (22224)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.20/0.41  % (22221)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.20/0.41  % (22219)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.20/0.42  % (22222)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.20/0.42  % (22225)First to succeed.
% 0.20/0.42  % (22225)Refutation found. Thanks to Tanya!
% 0.20/0.42  % SZS status Theorem for Vampire---4
% 0.20/0.42  % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.42  % (22225)------------------------------
% 0.20/0.42  % (22225)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.42  % (22225)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.42  % (22225)Termination reason: Refutation
% 0.20/0.42  
% 0.20/0.42  % (22225)Memory used [KB]: 6012
% 0.20/0.42  % (22225)Time elapsed: 0.009 s
% 0.20/0.42  % (22225)------------------------------
% 0.20/0.42  % (22225)------------------------------
% 0.20/0.42  % (22218)Success in time 0.061 s
% 0.20/0.43  % Vampire---4.8 exiting
%------------------------------------------------------------------------------