TSTP Solution File: SWC257+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC257+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 : n009.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 20:57:55 EDT 2023

% Result   : Theorem 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   42 (   8 unt;   0 def)
%            Number of atoms       :  289 (  99 equ)
%            Maximal formula atoms :   32 (   6 avg)
%            Number of connectives :  357 ( 110   ~; 105   |; 124   &)
%                                         (   5 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   4 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   65 (;  33   !;  32   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f744,plain,
    $false,
    inference(avatar_sat_refutation,[],[f592,f597,f615,f687]) ).

fof(f687,plain,
    ( ~ spl52_4
    | ~ spl52_5 ),
    inference(avatar_contradiction_clause,[],[f686]) ).

fof(f686,plain,
    ( $false
    | ~ spl52_4
    | ~ spl52_5 ),
    inference(subsumption_resolution,[],[f685,f596]) ).

fof(f596,plain,
    ( ssItem(sK4)
    | ~ spl52_5 ),
    inference(avatar_component_clause,[],[f594]) ).

fof(f594,plain,
    ( spl52_5
  <=> ssItem(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_5])]) ).

fof(f685,plain,
    ( ~ ssItem(sK4)
    | ~ spl52_4 ),
    inference(subsumption_resolution,[],[f684,f359]) ).

fof(f359,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/tmp/tmp.n8WezrfEU9/Vampire---4.8_19093',ax17) ).

fof(f684,plain,
    ( ~ ssList(nil)
    | ~ ssItem(sK4)
    | ~ spl52_4 ),
    inference(subsumption_resolution,[],[f635,f342]) ).

fof(f342,plain,
    ~ totalorderedP(sK0),
    inference(cnf_transformation,[],[f227]) ).

fof(f227,plain,
    ( ( ( nil = sK2
        & nil = sK3 )
      | ( ! [X5] :
            ( ~ leq(sK4,X5)
            | ~ memberP(sK3,X5)
            | sK4 = X5
            | ~ ssItem(X5) )
        & memberP(sK3,sK4)
        & sK2 = cons(sK4,nil)
        & ssItem(sK4) ) )
    & ~ totalorderedP(sK0)
    & sK0 = sK2
    & sK1 = sK3
    & ssList(sK3)
    & ssList(sK2)
    & ssList(sK1)
    & ssList(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f98,f226,f225,f224,f223,f222]) ).

fof(f222,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X2
                        & nil = X3 )
                      | ? [X4] :
                          ( ! [X5] :
                              ( ~ leq(X4,X5)
                              | ~ memberP(X3,X5)
                              | X4 = X5
                              | ~ ssItem(X5) )
                          & memberP(X3,X4)
                          & cons(X4,nil) = X2
                          & ssItem(X4) ) )
                    & ~ totalorderedP(X0)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ! [X5] :
                            ( ~ leq(X4,X5)
                            | ~ memberP(X3,X5)
                            | X4 = X5
                            | ~ ssItem(X5) )
                        & memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ~ totalorderedP(sK0)
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f223,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X2
                    & nil = X3 )
                  | ? [X4] :
                      ( ! [X5] :
                          ( ~ leq(X4,X5)
                          | ~ memberP(X3,X5)
                          | X4 = X5
                          | ~ ssItem(X5) )
                      & memberP(X3,X4)
                      & cons(X4,nil) = X2
                      & ssItem(X4) ) )
                & ~ totalorderedP(sK0)
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil = X2
                  & nil = X3 )
                | ? [X4] :
                    ( ! [X5] :
                        ( ~ leq(X4,X5)
                        | ~ memberP(X3,X5)
                        | X4 = X5
                        | ~ ssItem(X5) )
                    & memberP(X3,X4)
                    & cons(X4,nil) = X2
                    & ssItem(X4) ) )
              & ~ totalorderedP(sK0)
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f224,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = X2
                & nil = X3 )
              | ? [X4] :
                  ( ! [X5] :
                      ( ~ leq(X4,X5)
                      | ~ memberP(X3,X5)
                      | X4 = X5
                      | ~ ssItem(X5) )
                  & memberP(X3,X4)
                  & cons(X4,nil) = X2
                  & ssItem(X4) ) )
            & ~ totalorderedP(sK0)
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK2
              & nil = X3 )
            | ? [X4] :
                ( ! [X5] :
                    ( ~ leq(X4,X5)
                    | ~ memberP(X3,X5)
                    | X4 = X5
                    | ~ ssItem(X5) )
                & memberP(X3,X4)
                & cons(X4,nil) = sK2
                & ssItem(X4) ) )
          & ~ totalorderedP(sK0)
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f225,plain,
    ( ? [X3] :
        ( ( ( nil = sK2
            & nil = X3 )
          | ? [X4] :
              ( ! [X5] :
                  ( ~ leq(X4,X5)
                  | ~ memberP(X3,X5)
                  | X4 = X5
                  | ~ ssItem(X5) )
              & memberP(X3,X4)
              & cons(X4,nil) = sK2
              & ssItem(X4) ) )
        & ~ totalorderedP(sK0)
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ( ( nil = sK2
          & nil = sK3 )
        | ? [X4] :
            ( ! [X5] :
                ( ~ leq(X4,X5)
                | ~ memberP(sK3,X5)
                | X4 = X5
                | ~ ssItem(X5) )
            & memberP(sK3,X4)
            & cons(X4,nil) = sK2
            & ssItem(X4) ) )
      & ~ totalorderedP(sK0)
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f226,plain,
    ( ? [X4] :
        ( ! [X5] :
            ( ~ leq(X4,X5)
            | ~ memberP(sK3,X5)
            | X4 = X5
            | ~ ssItem(X5) )
        & memberP(sK3,X4)
        & cons(X4,nil) = sK2
        & ssItem(X4) )
   => ( ! [X5] :
          ( ~ leq(sK4,X5)
          | ~ memberP(sK3,X5)
          | sK4 = X5
          | ~ ssItem(X5) )
      & memberP(sK3,sK4)
      & sK2 = cons(sK4,nil)
      & ssItem(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ! [X5] :
                            ( ~ leq(X4,X5)
                            | ~ memberP(X3,X5)
                            | X4 = X5
                            | ~ ssItem(X5) )
                        & memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ~ totalorderedP(X0)
                  & 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] :
                    ( ( ( nil != X2
                        | nil != X3 )
                      & ! [X4] :
                          ( ? [X5] :
                              ( leq(X4,X5)
                              & memberP(X3,X5)
                              & X4 != X5
                              & ssItem(X5) )
                          | ~ memberP(X3,X4)
                          | cons(X4,nil) != X2
                          | ~ ssItem(X4) ) )
                    | totalorderedP(X0)
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ( ( nil != X2
                      | nil != X3 )
                    & ! [X4] :
                        ( ? [X5] :
                            ( leq(X4,X5)
                            & memberP(X3,X5)
                            & X4 != X5
                            & ssItem(X5) )
                        | ~ memberP(X3,X4)
                        | cons(X4,nil) != X2
                        | ~ ssItem(X4) ) )
                  | totalorderedP(X0)
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.n8WezrfEU9/Vampire---4.8_19093',co1) ).

fof(f635,plain,
    ( totalorderedP(sK0)
    | ~ ssList(nil)
    | ~ ssItem(sK4)
    | ~ spl52_4 ),
    inference(superposition,[],[f547,f616]) ).

fof(f616,plain,
    ( sK0 = cons(sK4,nil)
    | ~ spl52_4 ),
    inference(forward_demodulation,[],[f591,f341]) ).

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

fof(f591,plain,
    ( sK2 = cons(sK4,nil)
    | ~ spl52_4 ),
    inference(avatar_component_clause,[],[f589]) ).

fof(f589,plain,
    ( spl52_4
  <=> sK2 = cons(sK4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_4])]) ).

fof(f547,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssList(nil)
      | ~ ssItem(X0) ),
    inference(equality_resolution,[],[f404]) ).

fof(f404,plain,
    ! [X0,X1] :
      ( totalorderedP(cons(X0,X1))
      | nil != X1
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f240]) ).

fof(f240,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( totalorderedP(cons(X0,X1))
              | ( ( ~ leq(X0,hd(X1))
                  | ~ totalorderedP(X1)
                  | nil = X1 )
                & nil != X1 ) )
            & ( ( leq(X0,hd(X1))
                & totalorderedP(X1)
                & nil != X1 )
              | nil = X1
              | ~ totalorderedP(cons(X0,X1)) ) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f239]) ).

fof(f239,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( totalorderedP(cons(X0,X1))
              | ( ( ~ leq(X0,hd(X1))
                  | ~ totalorderedP(X1)
                  | nil = X1 )
                & nil != X1 ) )
            & ( ( leq(X0,hd(X1))
                & totalorderedP(X1)
                & nil != X1 )
              | nil = X1
              | ~ totalorderedP(cons(X0,X1)) ) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f137]) ).

fof(f137,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( totalorderedP(cons(X0,X1))
          <=> ( ( leq(X0,hd(X1))
                & totalorderedP(X1)
                & nil != X1 )
              | nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f67,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( totalorderedP(cons(X0,X1))
          <=> ( ( leq(X0,hd(X1))
                & totalorderedP(X1)
                & nil != X1 )
              | nil = X1 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.n8WezrfEU9/Vampire---4.8_19093',ax67) ).

fof(f615,plain,
    ~ spl52_2,
    inference(avatar_contradiction_clause,[],[f614]) ).

fof(f614,plain,
    ( $false
    | ~ spl52_2 ),
    inference(subsumption_resolution,[],[f613,f358]) ).

fof(f358,plain,
    totalorderedP(nil),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,axiom,
    totalorderedP(nil),
    file('/export/starexec/sandbox/tmp/tmp.n8WezrfEU9/Vampire---4.8_19093',ax66) ).

fof(f613,plain,
    ( ~ totalorderedP(nil)
    | ~ spl52_2 ),
    inference(superposition,[],[f342,f608]) ).

fof(f608,plain,
    ( nil = sK0
    | ~ spl52_2 ),
    inference(superposition,[],[f581,f341]) ).

fof(f581,plain,
    ( nil = sK2
    | ~ spl52_2 ),
    inference(avatar_component_clause,[],[f579]) ).

fof(f579,plain,
    ( spl52_2
  <=> nil = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_2])]) ).

fof(f597,plain,
    ( spl52_5
    | spl52_2 ),
    inference(avatar_split_clause,[],[f347,f579,f594]) ).

fof(f347,plain,
    ( nil = sK2
    | ssItem(sK4) ),
    inference(cnf_transformation,[],[f227]) ).

fof(f592,plain,
    ( spl52_4
    | spl52_2 ),
    inference(avatar_split_clause,[],[f348,f579,f589]) ).

fof(f348,plain,
    ( nil = sK2
    | sK2 = cons(sK4,nil) ),
    inference(cnf_transformation,[],[f227]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SWC257+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.13  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 16:31:20 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.34  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.n8WezrfEU9/Vampire---4.8_19093
% 0.12/0.35  % (19200)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.41  % (19207)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.12/0.41  % (19205)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)
% 0.12/0.41  % (19203)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)
% 0.12/0.41  % (19206)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)
% 0.12/0.41  % (19201)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)
% 0.12/0.41  % (19202)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.12/0.41  % (19204)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.19/0.41  % (19207)First to succeed.
% 0.19/0.42  % (19207)Refutation found. Thanks to Tanya!
% 0.19/0.42  % SZS status Theorem for Vampire---4
% 0.19/0.42  % SZS output start Proof for Vampire---4
% See solution above
% 0.19/0.42  % (19207)------------------------------
% 0.19/0.42  % (19207)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.19/0.42  % (19207)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.19/0.42  % (19207)Termination reason: Refutation
% 0.19/0.42  
% 0.19/0.42  % (19207)Memory used [KB]: 6012
% 0.19/0.42  % (19207)Time elapsed: 0.011 s
% 0.19/0.42  % (19207)------------------------------
% 0.19/0.42  % (19207)------------------------------
% 0.19/0.42  % (19200)Success in time 0.067 s
% 0.19/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------