TSTP Solution File: SWC050+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC050+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 : n003.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 20:55:56 EDT 2023

% Result   : Theorem 0.21s 0.44s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   51 (   5 unt;   0 def)
%            Number of atoms       :  335 (  30 equ)
%            Maximal formula atoms :   34 (   6 avg)
%            Number of connectives :  421 ( 137   ~; 119   |; 138   &)
%                                         (   7 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   8 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   67 (;  29   !;  38   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f668,plain,
    $false,
    inference(avatar_sat_refutation,[],[f589,f594,f599,f604,f608,f619,f624,f665]) ).

fof(f665,plain,
    ( ~ spl52_1
    | ~ spl52_3
    | ~ spl52_4
    | ~ spl52_5
    | ~ spl52_6 ),
    inference(avatar_contradiction_clause,[],[f664]) ).

fof(f664,plain,
    ( $false
    | ~ spl52_1
    | ~ spl52_3
    | ~ spl52_4
    | ~ spl52_5
    | ~ spl52_6 ),
    inference(subsumption_resolution,[],[f663,f627]) ).

fof(f627,plain,
    ( rearsegP(sK0,sK4)
    | ~ spl52_1 ),
    inference(forward_demodulation,[],[f584,f343]) ).

fof(f343,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f229]) ).

fof(f229,plain,
    ( ( ( ~ neq(sK3,nil)
        & neq(sK1,nil) )
      | ( rearsegP(sK2,sK4)
        & rearsegP(sK3,sK4)
        & neq(sK4,nil)
        & ssList(sK4)
        & ! [X5] :
            ( ~ rearsegP(sK0,X5)
            | ~ rearsegP(sK1,X5)
            | ~ neq(X5,nil)
            | ~ ssList(X5) )
        & 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,sK4])],[f100,f228,f227,f226,f225,f224]) ).

fof(f224,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | ( ? [X4] :
                            ( rearsegP(X2,X4)
                            & rearsegP(X3,X4)
                            & neq(X4,nil)
                            & ssList(X4) )
                        & ! [X5] :
                            ( ~ rearsegP(X0,X5)
                            | ~ rearsegP(X1,X5)
                            | ~ neq(X5,nil)
                            | ~ ssList(X5) )
                        & neq(X1,nil) ) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( rearsegP(X2,X4)
                          & rearsegP(X3,X4)
                          & neq(X4,nil)
                          & ssList(X4) )
                      & ! [X5] :
                          ( ~ rearsegP(sK0,X5)
                          | ~ rearsegP(X1,X5)
                          | ~ neq(X5,nil)
                          | ~ ssList(X5) )
                      & neq(X1,nil) ) )
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f225,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | ( ? [X4] :
                        ( rearsegP(X2,X4)
                        & rearsegP(X3,X4)
                        & neq(X4,nil)
                        & ssList(X4) )
                    & ! [X5] :
                        ( ~ rearsegP(sK0,X5)
                        | ~ rearsegP(X1,X5)
                        | ~ neq(X5,nil)
                        | ~ ssList(X5) )
                    & neq(X1,nil) ) )
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ neq(X3,nil)
                  & neq(sK1,nil) )
                | ( ? [X4] :
                      ( rearsegP(X2,X4)
                      & rearsegP(X3,X4)
                      & neq(X4,nil)
                      & ssList(X4) )
                  & ! [X5] :
                      ( ~ rearsegP(sK0,X5)
                      | ~ rearsegP(sK1,X5)
                      | ~ neq(X5,nil)
                      | ~ ssList(X5) )
                  & neq(sK1,nil) ) )
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f226,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ neq(X3,nil)
                & neq(sK1,nil) )
              | ( ? [X4] :
                    ( rearsegP(X2,X4)
                    & rearsegP(X3,X4)
                    & neq(X4,nil)
                    & ssList(X4) )
                & ! [X5] :
                    ( ~ rearsegP(sK0,X5)
                    | ~ rearsegP(sK1,X5)
                    | ~ neq(X5,nil)
                    | ~ ssList(X5) )
                & neq(sK1,nil) ) )
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ neq(X3,nil)
              & neq(sK1,nil) )
            | ( ? [X4] :
                  ( rearsegP(sK2,X4)
                  & rearsegP(X3,X4)
                  & neq(X4,nil)
                  & ssList(X4) )
              & ! [X5] :
                  ( ~ rearsegP(sK0,X5)
                  | ~ rearsegP(sK1,X5)
                  | ~ neq(X5,nil)
                  | ~ ssList(X5) )
              & neq(sK1,nil) ) )
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f227,plain,
    ( ? [X3] :
        ( ( ( ~ neq(X3,nil)
            & neq(sK1,nil) )
          | ( ? [X4] :
                ( rearsegP(sK2,X4)
                & rearsegP(X3,X4)
                & neq(X4,nil)
                & ssList(X4) )
            & ! [X5] :
                ( ~ rearsegP(sK0,X5)
                | ~ rearsegP(sK1,X5)
                | ~ neq(X5,nil)
                | ~ ssList(X5) )
            & neq(sK1,nil) ) )
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ( ( ~ neq(sK3,nil)
          & neq(sK1,nil) )
        | ( ? [X4] :
              ( rearsegP(sK2,X4)
              & rearsegP(sK3,X4)
              & neq(X4,nil)
              & ssList(X4) )
          & ! [X5] :
              ( ~ rearsegP(sK0,X5)
              | ~ rearsegP(sK1,X5)
              | ~ neq(X5,nil)
              | ~ ssList(X5) )
          & neq(sK1,nil) ) )
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f228,plain,
    ( ? [X4] :
        ( rearsegP(sK2,X4)
        & rearsegP(sK3,X4)
        & neq(X4,nil)
        & ssList(X4) )
   => ( rearsegP(sK2,sK4)
      & rearsegP(sK3,sK4)
      & neq(sK4,nil)
      & ssList(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( rearsegP(X2,X4)
                          & rearsegP(X3,X4)
                          & neq(X4,nil)
                          & ssList(X4) )
                      & ! [X5] :
                          ( ~ rearsegP(X0,X5)
                          | ~ rearsegP(X1,X5)
                          | ~ neq(X5,nil)
                          | ~ ssList(X5) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( rearsegP(X2,X4)
                          & rearsegP(X3,X4)
                          & neq(X4,nil)
                          & ssList(X4) )
                      & ! [X5] :
                          ( ~ rearsegP(X0,X5)
                          | ~ rearsegP(X1,X5)
                          | ~ neq(X5,nil)
                          | ~ ssList(X5) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ! [X4] :
                              ( ssList(X4)
                             => ( ~ rearsegP(X2,X4)
                                | ~ rearsegP(X3,X4)
                                | ~ neq(X4,nil) ) )
                          | ? [X5] :
                              ( rearsegP(X0,X5)
                              & rearsegP(X1,X5)
                              & neq(X5,nil)
                              & ssList(X5) )
                          | ~ neq(X1,nil) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ! [X5] :
                              ( ssList(X5)
                             => ( ~ rearsegP(X2,X5)
                                | ~ rearsegP(X3,X5)
                                | ~ neq(X5,nil) ) )
                          | ? [X4] :
                              ( rearsegP(X0,X4)
                              & rearsegP(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)
                 => ( ( ( neq(X3,nil)
                        | ~ neq(X1,nil) )
                      & ( ! [X5] :
                            ( ssList(X5)
                           => ( ~ rearsegP(X2,X5)
                              | ~ rearsegP(X3,X5)
                              | ~ neq(X5,nil) ) )
                        | ? [X4] :
                            ( rearsegP(X0,X4)
                            & rearsegP(X1,X4)
                            & neq(X4,nil)
                            & ssList(X4) )
                        | ~ neq(X1,nil) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.kymD3AfwnK/Vampire---4.8_9925',co1) ).

fof(f584,plain,
    ( rearsegP(sK2,sK4)
    | ~ spl52_1 ),
    inference(avatar_component_clause,[],[f582]) ).

fof(f582,plain,
    ( spl52_1
  <=> rearsegP(sK2,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_1])]) ).

fof(f663,plain,
    ( ~ rearsegP(sK0,sK4)
    | ~ spl52_3
    | ~ spl52_4
    | ~ spl52_5
    | ~ spl52_6 ),
    inference(subsumption_resolution,[],[f662,f598]) ).

fof(f598,plain,
    ( neq(sK4,nil)
    | ~ spl52_4 ),
    inference(avatar_component_clause,[],[f596]) ).

fof(f596,plain,
    ( spl52_4
  <=> neq(sK4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_4])]) ).

fof(f662,plain,
    ( ~ neq(sK4,nil)
    | ~ rearsegP(sK0,sK4)
    | ~ spl52_3
    | ~ spl52_5
    | ~ spl52_6 ),
    inference(subsumption_resolution,[],[f658,f603]) ).

fof(f603,plain,
    ( ssList(sK4)
    | ~ spl52_5 ),
    inference(avatar_component_clause,[],[f601]) ).

fof(f601,plain,
    ( spl52_5
  <=> ssList(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_5])]) ).

fof(f658,plain,
    ( ~ ssList(sK4)
    | ~ neq(sK4,nil)
    | ~ rearsegP(sK0,sK4)
    | ~ spl52_3
    | ~ spl52_6 ),
    inference(resolution,[],[f607,f625]) ).

fof(f625,plain,
    ( rearsegP(sK1,sK4)
    | ~ spl52_3 ),
    inference(forward_demodulation,[],[f593,f342]) ).

fof(f342,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f229]) ).

fof(f593,plain,
    ( rearsegP(sK3,sK4)
    | ~ spl52_3 ),
    inference(avatar_component_clause,[],[f591]) ).

fof(f591,plain,
    ( spl52_3
  <=> rearsegP(sK3,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_3])]) ).

fof(f607,plain,
    ( ! [X5] :
        ( ~ rearsegP(sK1,X5)
        | ~ ssList(X5)
        | ~ neq(X5,nil)
        | ~ rearsegP(sK0,X5) )
    | ~ spl52_6 ),
    inference(avatar_component_clause,[],[f606]) ).

fof(f606,plain,
    ( spl52_6
  <=> ! [X5] :
        ( ~ rearsegP(sK0,X5)
        | ~ ssList(X5)
        | ~ neq(X5,nil)
        | ~ rearsegP(sK1,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_6])]) ).

fof(f624,plain,
    ( spl52_2
    | ~ spl52_7 ),
    inference(avatar_contradiction_clause,[],[f623]) ).

fof(f623,plain,
    ( $false
    | spl52_2
    | ~ spl52_7 ),
    inference(subsumption_resolution,[],[f622,f612]) ).

fof(f612,plain,
    ( neq(sK1,nil)
    | ~ spl52_7 ),
    inference(avatar_component_clause,[],[f610]) ).

fof(f610,plain,
    ( spl52_7
  <=> neq(sK1,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_7])]) ).

fof(f622,plain,
    ( ~ neq(sK1,nil)
    | spl52_2 ),
    inference(forward_demodulation,[],[f588,f342]) ).

fof(f588,plain,
    ( ~ neq(sK3,nil)
    | spl52_2 ),
    inference(avatar_component_clause,[],[f586]) ).

fof(f586,plain,
    ( spl52_2
  <=> neq(sK3,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_2])]) ).

fof(f619,plain,
    spl52_7,
    inference(avatar_split_clause,[],[f580,f610]) ).

fof(f580,plain,
    neq(sK1,nil),
    inference(duplicate_literal_removal,[],[f344]) ).

fof(f344,plain,
    ( neq(sK1,nil)
    | neq(sK1,nil) ),
    inference(cnf_transformation,[],[f229]) ).

fof(f608,plain,
    ( spl52_6
    | ~ spl52_2 ),
    inference(avatar_split_clause,[],[f351,f586,f606]) ).

fof(f351,plain,
    ! [X5] :
      ( ~ neq(sK3,nil)
      | ~ rearsegP(sK0,X5)
      | ~ rearsegP(sK1,X5)
      | ~ neq(X5,nil)
      | ~ ssList(X5) ),
    inference(cnf_transformation,[],[f229]) ).

fof(f604,plain,
    ( spl52_5
    | ~ spl52_2 ),
    inference(avatar_split_clause,[],[f352,f586,f601]) ).

fof(f352,plain,
    ( ~ neq(sK3,nil)
    | ssList(sK4) ),
    inference(cnf_transformation,[],[f229]) ).

fof(f599,plain,
    ( spl52_4
    | ~ spl52_2 ),
    inference(avatar_split_clause,[],[f353,f586,f596]) ).

fof(f353,plain,
    ( ~ neq(sK3,nil)
    | neq(sK4,nil) ),
    inference(cnf_transformation,[],[f229]) ).

fof(f594,plain,
    ( spl52_3
    | ~ spl52_2 ),
    inference(avatar_split_clause,[],[f354,f586,f591]) ).

fof(f354,plain,
    ( ~ neq(sK3,nil)
    | rearsegP(sK3,sK4) ),
    inference(cnf_transformation,[],[f229]) ).

fof(f589,plain,
    ( spl52_1
    | ~ spl52_2 ),
    inference(avatar_split_clause,[],[f355,f586,f582]) ).

fof(f355,plain,
    ( ~ neq(sK3,nil)
    | rearsegP(sK2,sK4) ),
    inference(cnf_transformation,[],[f229]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SWC050+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon Aug 28 17:48:10 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.kymD3AfwnK/Vampire---4.8_9925
% 0.21/0.37  % (10032)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43  % (10037)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)
% 0.21/0.43  % (10035)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)
% 0.21/0.43  % (10039)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.21/0.43  % (10034)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.21/0.43  % (10036)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.21/0.43  % (10038)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)
% 0.21/0.43  % (10039)First to succeed.
% 0.21/0.44  % (10039)Refutation found. Thanks to Tanya!
% 0.21/0.44  % SZS status Theorem for Vampire---4
% 0.21/0.44  % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.44  % (10039)------------------------------
% 0.21/0.44  % (10039)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.44  % (10039)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.44  % (10039)Termination reason: Refutation
% 0.21/0.44  
% 0.21/0.44  % (10039)Memory used [KB]: 6012
% 0.21/0.44  % (10039)Time elapsed: 0.010 s
% 0.21/0.44  % (10039)------------------------------
% 0.21/0.44  % (10039)------------------------------
% 0.21/0.44  % (10032)Success in time 0.072 s
% 0.21/0.44  % Vampire---4.8 exiting
%------------------------------------------------------------------------------