TSTP Solution File: SWC417+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC417+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -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 : Wed May  1 04:02:01 EDT 2024

% Result   : Theorem 0.55s 0.75s
% Output   : Refutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   76 (  10 unt;   0 def)
%            Number of atoms       :  419 ( 128 equ)
%            Maximal formula atoms :   36 (   5 avg)
%            Number of connectives :  522 ( 179   ~; 159   |; 145   &)
%                                         (  11 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   16 (  14 usr;  12 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :  135 (  78   !;  57   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f708,plain,
    $false,
    inference(avatar_sat_refutation,[],[f600,f605,f610,f615,f619,f625,f630,f663,f665,f677,f694,f707]) ).

fof(f707,plain,
    ( ~ spl53_14
    | spl53_13 ),
    inference(avatar_split_clause,[],[f706,f660,f669]) ).

fof(f669,plain,
    ( spl53_14
  <=> ssList(sK49) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_14])]) ).

fof(f660,plain,
    ( spl53_13
  <=> sK49 = app(sK49,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_13])]) ).

fof(f706,plain,
    ( ~ ssList(sK49)
    | spl53_13 ),
    inference(trivial_inequality_removal,[],[f705]) ).

fof(f705,plain,
    ( sK49 != sK49
    | ~ ssList(sK49)
    | spl53_13 ),
    inference(superposition,[],[f662,f515]) ).

fof(f515,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f202]) ).

fof(f202,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox/tmp/tmp.Ywhidtw87B/Vampire---4.8_14460',ax84) ).

fof(f662,plain,
    ( sK49 != app(sK49,nil)
    | spl53_13 ),
    inference(avatar_component_clause,[],[f660]) ).

fof(f694,plain,
    ( ~ spl53_10
    | ~ spl53_5
    | spl53_12 ),
    inference(avatar_split_clause,[],[f689,f656,f612,f646]) ).

fof(f646,plain,
    ( spl53_10
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_10])]) ).

fof(f612,plain,
    ( spl53_5
  <=> ssItem(sK51) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_5])]) ).

fof(f656,plain,
    ( spl53_12
  <=> ssList(cons(sK51,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_12])]) ).

fof(f689,plain,
    ( ~ ssItem(sK51)
    | ~ ssList(nil)
    | spl53_12 ),
    inference(resolution,[],[f421,f658]) ).

fof(f658,plain,
    ( ~ ssList(cons(sK51,nil))
    | spl53_12 ),
    inference(avatar_component_clause,[],[f656]) ).

fof(f421,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Ywhidtw87B/Vampire---4.8_14460',ax16) ).

fof(f677,plain,
    spl53_14,
    inference(avatar_contradiction_clause,[],[f676]) ).

fof(f676,plain,
    ( $false
    | spl53_14 ),
    inference(resolution,[],[f671,f531]) ).

fof(f531,plain,
    ssList(sK49),
    inference(cnf_transformation,[],[f338]) ).

fof(f338,plain,
    ( ( ( ~ neq(sK50,nil)
        & neq(sK48,nil) )
      | ( sK49 = app(sK52,cons(sK51,nil))
        & sK50 = app(cons(sK51,nil),sK52)
        & ssList(sK52)
        & ssItem(sK51)
        & ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( app(app(X8,cons(X6,nil)),X7) != sK47
                    | app(app(X7,cons(X6,nil)),X8) != sK48
                    | ~ ssList(X8) )
                | ~ ssList(X7) )
            | ~ ssItem(X6) )
        & neq(sK48,nil) ) )
    & sK47 = sK49
    & sK48 = sK50
    & ssList(sK50)
    & ssList(sK49)
    & ssList(sK48)
    & ssList(sK47) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48,sK49,sK50,sK51,sK52])],[f223,f337,f336,f335,f334,f333,f332]) ).

fof(f332,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | ( ? [X4] :
                            ( ? [X5] :
                                ( app(X5,cons(X4,nil)) = X2
                                & app(cons(X4,nil),X5) = X3
                                & ssList(X5) )
                            & ssItem(X4) )
                        & ! [X6] :
                            ( ! [X7] :
                                ( ! [X8] :
                                    ( app(app(X8,cons(X6,nil)),X7) != X0
                                    | app(app(X7,cons(X6,nil)),X8) != X1
                                    | ~ ssList(X8) )
                                | ~ ssList(X7) )
                            | ~ ssItem(X6) )
                        & 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] :
                          ( ? [X5] :
                              ( app(X5,cons(X4,nil)) = X2
                              & app(cons(X4,nil),X5) = X3
                              & ssList(X5) )
                          & ssItem(X4) )
                      & ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( app(app(X8,cons(X6,nil)),X7) != sK47
                                  | app(app(X7,cons(X6,nil)),X8) != X1
                                  | ~ ssList(X8) )
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & neq(X1,nil) ) )
                  & sK47 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK47) ) ),
    introduced(choice_axiom,[]) ).

fof(f333,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | ( ? [X4] :
                        ( ? [X5] :
                            ( app(X5,cons(X4,nil)) = X2
                            & app(cons(X4,nil),X5) = X3
                            & ssList(X5) )
                        & ssItem(X4) )
                    & ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( app(app(X8,cons(X6,nil)),X7) != sK47
                                | app(app(X7,cons(X6,nil)),X8) != X1
                                | ~ ssList(X8) )
                            | ~ ssList(X7) )
                        | ~ ssItem(X6) )
                    & neq(X1,nil) ) )
                & sK47 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ neq(X3,nil)
                  & neq(sK48,nil) )
                | ( ? [X4] :
                      ( ? [X5] :
                          ( app(X5,cons(X4,nil)) = X2
                          & app(cons(X4,nil),X5) = X3
                          & ssList(X5) )
                      & ssItem(X4) )
                  & ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( app(app(X8,cons(X6,nil)),X7) != sK47
                              | app(app(X7,cons(X6,nil)),X8) != sK48
                              | ~ ssList(X8) )
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & neq(sK48,nil) ) )
              & sK47 = X2
              & sK48 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK48) ) ),
    introduced(choice_axiom,[]) ).

fof(f334,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ neq(X3,nil)
                & neq(sK48,nil) )
              | ( ? [X4] :
                    ( ? [X5] :
                        ( app(X5,cons(X4,nil)) = X2
                        & app(cons(X4,nil),X5) = X3
                        & ssList(X5) )
                    & ssItem(X4) )
                & ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( app(app(X8,cons(X6,nil)),X7) != sK47
                            | app(app(X7,cons(X6,nil)),X8) != sK48
                            | ~ ssList(X8) )
                        | ~ ssList(X7) )
                    | ~ ssItem(X6) )
                & neq(sK48,nil) ) )
            & sK47 = X2
            & sK48 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ neq(X3,nil)
              & neq(sK48,nil) )
            | ( ? [X4] :
                  ( ? [X5] :
                      ( app(X5,cons(X4,nil)) = sK49
                      & app(cons(X4,nil),X5) = X3
                      & ssList(X5) )
                  & ssItem(X4) )
              & ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( app(app(X8,cons(X6,nil)),X7) != sK47
                          | app(app(X7,cons(X6,nil)),X8) != sK48
                          | ~ ssList(X8) )
                      | ~ ssList(X7) )
                  | ~ ssItem(X6) )
              & neq(sK48,nil) ) )
          & sK47 = sK49
          & sK48 = X3
          & ssList(X3) )
      & ssList(sK49) ) ),
    introduced(choice_axiom,[]) ).

fof(f335,plain,
    ( ? [X3] :
        ( ( ( ~ neq(X3,nil)
            & neq(sK48,nil) )
          | ( ? [X4] :
                ( ? [X5] :
                    ( app(X5,cons(X4,nil)) = sK49
                    & app(cons(X4,nil),X5) = X3
                    & ssList(X5) )
                & ssItem(X4) )
            & ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( app(app(X8,cons(X6,nil)),X7) != sK47
                        | app(app(X7,cons(X6,nil)),X8) != sK48
                        | ~ ssList(X8) )
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            & neq(sK48,nil) ) )
        & sK47 = sK49
        & sK48 = X3
        & ssList(X3) )
   => ( ( ( ~ neq(sK50,nil)
          & neq(sK48,nil) )
        | ( ? [X4] :
              ( ? [X5] :
                  ( app(X5,cons(X4,nil)) = sK49
                  & app(cons(X4,nil),X5) = sK50
                  & ssList(X5) )
              & ssItem(X4) )
          & ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( app(app(X8,cons(X6,nil)),X7) != sK47
                      | app(app(X7,cons(X6,nil)),X8) != sK48
                      | ~ ssList(X8) )
                  | ~ ssList(X7) )
              | ~ ssItem(X6) )
          & neq(sK48,nil) ) )
      & sK47 = sK49
      & sK48 = sK50
      & ssList(sK50) ) ),
    introduced(choice_axiom,[]) ).

fof(f336,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( app(X5,cons(X4,nil)) = sK49
            & app(cons(X4,nil),X5) = sK50
            & ssList(X5) )
        & ssItem(X4) )
   => ( ? [X5] :
          ( sK49 = app(X5,cons(sK51,nil))
          & sK50 = app(cons(sK51,nil),X5)
          & ssList(X5) )
      & ssItem(sK51) ) ),
    introduced(choice_axiom,[]) ).

fof(f337,plain,
    ( ? [X5] :
        ( sK49 = app(X5,cons(sK51,nil))
        & sK50 = app(cons(sK51,nil),X5)
        & ssList(X5) )
   => ( sK49 = app(sK52,cons(sK51,nil))
      & sK50 = app(cons(sK51,nil),sK52)
      & ssList(sK52) ) ),
    introduced(choice_axiom,[]) ).

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( ? [X5] :
                              ( app(X5,cons(X4,nil)) = X2
                              & app(cons(X4,nil),X5) = X3
                              & ssList(X5) )
                          & ssItem(X4) )
                      & ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( app(app(X8,cons(X6,nil)),X7) != X0
                                  | app(app(X7,cons(X6,nil)),X8) != X1
                                  | ~ ssList(X8) )
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( ? [X5] :
                              ( app(X5,cons(X4,nil)) = X2
                              & app(cons(X4,nil),X5) = X3
                              & ssList(X5) )
                          & ssItem(X4) )
                      & ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( app(app(X8,cons(X6,nil)),X7) != X0
                                  | app(app(X7,cons(X6,nil)),X8) != X1
                                  | ~ ssList(X8) )
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & 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] :
                              ( ssItem(X4)
                             => ! [X5] :
                                  ( ssList(X5)
                                 => ( app(X5,cons(X4,nil)) != X2
                                    | app(cons(X4,nil),X5) != X3 ) ) )
                          | ? [X6] :
                              ( ? [X7] :
                                  ( ? [X8] :
                                      ( app(app(X8,cons(X6,nil)),X7) = X0
                                      & app(app(X7,cons(X6,nil)),X8) = X1
                                      & ssList(X8) )
                                  & ssList(X7) )
                              & ssItem(X6) )
                          | ~ 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) )
                        & ( ! [X7] :
                              ( ssItem(X7)
                             => ! [X8] :
                                  ( ssList(X8)
                                 => ( app(X8,cons(X7,nil)) != X2
                                    | app(cons(X7,nil),X8) != X3 ) ) )
                          | ? [X4] :
                              ( ? [X5] :
                                  ( ? [X6] :
                                      ( app(app(X6,cons(X4,nil)),X5) = X0
                                      & app(app(X5,cons(X4,nil)),X6) = X1
                                      & ssList(X6) )
                                  & ssList(X5) )
                              & ssItem(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) )
                      & ( ! [X7] :
                            ( ssItem(X7)
                           => ! [X8] :
                                ( ssList(X8)
                               => ( app(X8,cons(X7,nil)) != X2
                                  | app(cons(X7,nil),X8) != X3 ) ) )
                        | ? [X4] :
                            ( ? [X5] :
                                ( ? [X6] :
                                    ( app(app(X6,cons(X4,nil)),X5) = X0
                                    & app(app(X5,cons(X4,nil)),X6) = X1
                                    & ssList(X6) )
                                & ssList(X5) )
                            & ssItem(X4) )
                        | ~ neq(X1,nil) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Ywhidtw87B/Vampire---4.8_14460',co1) ).

fof(f671,plain,
    ( ~ ssList(sK49)
    | spl53_14 ),
    inference(avatar_component_clause,[],[f669]) ).

fof(f665,plain,
    spl53_10,
    inference(avatar_contradiction_clause,[],[f664]) ).

fof(f664,plain,
    ( $false
    | spl53_10 ),
    inference(resolution,[],[f648,f422]) ).

fof(f422,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/tmp/tmp.Ywhidtw87B/Vampire---4.8_14460',ax17) ).

fof(f648,plain,
    ( ~ ssList(nil)
    | spl53_10 ),
    inference(avatar_component_clause,[],[f646]) ).

fof(f663,plain,
    ( ~ spl53_12
    | ~ spl53_10
    | ~ spl53_13
    | ~ spl53_3
    | ~ spl53_7 ),
    inference(avatar_split_clause,[],[f654,f628,f602,f660,f646,f656]) ).

fof(f602,plain,
    ( spl53_3
  <=> sK50 = app(cons(sK51,nil),sK52) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_3])]) ).

fof(f628,plain,
    ( spl53_7
  <=> ! [X0] :
        ( sK49 != app(sK49,X0)
        | sK50 != app(app(X0,cons(sK51,nil)),sK52)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_7])]) ).

fof(f654,plain,
    ( sK49 != app(sK49,nil)
    | ~ ssList(nil)
    | ~ ssList(cons(sK51,nil))
    | ~ spl53_3
    | ~ spl53_7 ),
    inference(trivial_inequality_removal,[],[f653]) ).

fof(f653,plain,
    ( sK50 != sK50
    | sK49 != app(sK49,nil)
    | ~ ssList(nil)
    | ~ ssList(cons(sK51,nil))
    | ~ spl53_3
    | ~ spl53_7 ),
    inference(forward_demodulation,[],[f644,f604]) ).

fof(f604,plain,
    ( sK50 = app(cons(sK51,nil),sK52)
    | ~ spl53_3 ),
    inference(avatar_component_clause,[],[f602]) ).

fof(f644,plain,
    ( sK50 != app(cons(sK51,nil),sK52)
    | sK49 != app(sK49,nil)
    | ~ ssList(nil)
    | ~ ssList(cons(sK51,nil))
    | ~ spl53_7 ),
    inference(superposition,[],[f629,f436]) ).

fof(f436,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f135,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox/tmp/tmp.Ywhidtw87B/Vampire---4.8_14460',ax28) ).

fof(f629,plain,
    ( ! [X0] :
        ( sK50 != app(app(X0,cons(sK51,nil)),sK52)
        | sK49 != app(sK49,X0)
        | ~ ssList(X0) )
    | ~ spl53_7 ),
    inference(avatar_component_clause,[],[f628]) ).

fof(f630,plain,
    ( ~ spl53_4
    | ~ spl53_5
    | spl53_7
    | ~ spl53_1
    | ~ spl53_6 ),
    inference(avatar_split_clause,[],[f626,f617,f593,f628,f612,f607]) ).

fof(f607,plain,
    ( spl53_4
  <=> ssList(sK52) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_4])]) ).

fof(f593,plain,
    ( spl53_1
  <=> sK49 = app(sK52,cons(sK51,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_1])]) ).

fof(f617,plain,
    ( spl53_6
  <=> ! [X6,X7,X8] :
        ( app(app(X8,cons(X6,nil)),X7) != sK49
        | ~ ssItem(X6)
        | ~ ssList(X7)
        | ~ ssList(X8)
        | app(app(X7,cons(X6,nil)),X8) != sK50 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_6])]) ).

fof(f626,plain,
    ( ! [X0] :
        ( sK49 != app(sK49,X0)
        | ~ ssItem(sK51)
        | ~ ssList(X0)
        | ~ ssList(sK52)
        | sK50 != app(app(X0,cons(sK51,nil)),sK52) )
    | ~ spl53_1
    | ~ spl53_6 ),
    inference(superposition,[],[f618,f595]) ).

fof(f595,plain,
    ( sK49 = app(sK52,cons(sK51,nil))
    | ~ spl53_1 ),
    inference(avatar_component_clause,[],[f593]) ).

fof(f618,plain,
    ( ! [X8,X6,X7] :
        ( app(app(X8,cons(X6,nil)),X7) != sK49
        | ~ ssItem(X6)
        | ~ ssList(X7)
        | ~ ssList(X8)
        | app(app(X7,cons(X6,nil)),X8) != sK50 )
    | ~ spl53_6 ),
    inference(avatar_component_clause,[],[f617]) ).

fof(f625,plain,
    spl53_2,
    inference(avatar_split_clause,[],[f584,f597]) ).

fof(f597,plain,
    ( spl53_2
  <=> neq(sK50,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_2])]) ).

fof(f584,plain,
    neq(sK50,nil),
    inference(duplicate_literal_removal,[],[f554]) ).

fof(f554,plain,
    ( neq(sK50,nil)
    | neq(sK50,nil) ),
    inference(definition_unfolding,[],[f535,f533,f533]) ).

fof(f533,plain,
    sK48 = sK50,
    inference(cnf_transformation,[],[f338]) ).

fof(f535,plain,
    ( neq(sK48,nil)
    | neq(sK48,nil) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f619,plain,
    ( spl53_6
    | ~ spl53_2 ),
    inference(avatar_split_clause,[],[f547,f597,f617]) ).

fof(f547,plain,
    ! [X8,X6,X7] :
      ( ~ neq(sK50,nil)
      | app(app(X8,cons(X6,nil)),X7) != sK49
      | app(app(X7,cons(X6,nil)),X8) != sK50
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6) ),
    inference(definition_unfolding,[],[f542,f534,f533]) ).

fof(f534,plain,
    sK47 = sK49,
    inference(cnf_transformation,[],[f338]) ).

fof(f542,plain,
    ! [X8,X6,X7] :
      ( ~ neq(sK50,nil)
      | app(app(X8,cons(X6,nil)),X7) != sK47
      | app(app(X7,cons(X6,nil)),X8) != sK48
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f615,plain,
    ( spl53_5
    | ~ spl53_2 ),
    inference(avatar_split_clause,[],[f543,f597,f612]) ).

fof(f543,plain,
    ( ~ neq(sK50,nil)
    | ssItem(sK51) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f610,plain,
    ( spl53_4
    | ~ spl53_2 ),
    inference(avatar_split_clause,[],[f544,f597,f607]) ).

fof(f544,plain,
    ( ~ neq(sK50,nil)
    | ssList(sK52) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f605,plain,
    ( spl53_3
    | ~ spl53_2 ),
    inference(avatar_split_clause,[],[f545,f597,f602]) ).

fof(f545,plain,
    ( ~ neq(sK50,nil)
    | sK50 = app(cons(sK51,nil),sK52) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f600,plain,
    ( spl53_1
    | ~ spl53_2 ),
    inference(avatar_split_clause,[],[f546,f597,f593]) ).

fof(f546,plain,
    ( ~ neq(sK50,nil)
    | sK49 = app(sK52,cons(sK51,nil)) ),
    inference(cnf_transformation,[],[f338]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SWC417+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35  % Computer : n009.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Apr 30 18:14:56 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.35  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.Ywhidtw87B/Vampire---4.8_14460
% 0.55/0.74  % (14718)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.55/0.74  % (14719)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.55/0.74  % (14712)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.55/0.74  % (14714)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.55/0.74  % (14716)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.55/0.74  % (14713)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.55/0.74  % (14715)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.55/0.74  % (14717)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.55/0.74  % (14719)Refutation not found, incomplete strategy% (14719)------------------------------
% 0.55/0.74  % (14719)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.55/0.74  % (14719)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.74  
% 0.55/0.74  % (14719)Memory used [KB]: 1146
% 0.55/0.74  % (14719)Time elapsed: 0.004 s
% 0.55/0.74  % (14719)Instructions burned: 4 (million)
% 0.55/0.74  % (14719)------------------------------
% 0.55/0.74  % (14719)------------------------------
% 0.55/0.74  % (14717)Refutation not found, incomplete strategy% (14717)------------------------------
% 0.55/0.74  % (14717)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.55/0.74  % (14717)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.74  
% 0.55/0.74  % (14717)Memory used [KB]: 1143
% 0.55/0.74  % (14717)Time elapsed: 0.004 s
% 0.55/0.74  % (14717)Instructions burned: 4 (million)
% 0.55/0.74  % (14717)------------------------------
% 0.55/0.74  % (14717)------------------------------
% 0.55/0.74  % (14720)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.55/0.75  % (14721)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.55/0.75  % (14713)First to succeed.
% 0.55/0.75  % (14713)Refutation found. Thanks to Tanya!
% 0.55/0.75  % SZS status Theorem for Vampire---4
% 0.55/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.55/0.75  % (14713)------------------------------
% 0.55/0.75  % (14713)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.55/0.75  % (14713)Termination reason: Refutation
% 0.55/0.75  
% 0.55/0.75  % (14713)Memory used [KB]: 1472
% 0.55/0.75  % (14713)Time elapsed: 0.014 s
% 0.55/0.75  % (14713)Instructions burned: 23 (million)
% 0.55/0.75  % (14713)------------------------------
% 0.55/0.75  % (14713)------------------------------
% 0.55/0.75  % (14708)Success in time 0.385 s
% 0.55/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------