TSTP Solution File: SWC237+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC237+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 : n002.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 04:00:47 EDT 2024

% Result   : Theorem 0.61s 0.78s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   85 (  10 unt;   0 def)
%            Number of atoms       :  672 ( 190 equ)
%            Maximal formula atoms :   56 (   7 avg)
%            Number of connectives :  966 ( 379   ~; 347   |; 209   &)
%                                         (   7 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   15 (  13 usr;   8 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :  256 ( 185   !;  71   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f837,plain,
    $false,
    inference(avatar_sat_refutation,[],[f596,f609,f625,f627,f675,f716,f720,f836]) ).

fof(f836,plain,
    ( ~ spl53_11
    | spl53_2
    | ~ spl53_22
    | ~ spl53_23 ),
    inference(avatar_split_clause,[],[f835,f718,f714,f592,f645]) ).

fof(f645,plain,
    ( spl53_11
  <=> ssList(sK49) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_11])]) ).

fof(f592,plain,
    ( spl53_2
  <=> nil = sK49 ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_2])]) ).

fof(f714,plain,
    ( spl53_22
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | memberP(nil,sK52(X0,nil,X1))
        | ~ ssList(X1)
        | sK49 != app(cons(X0,nil),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_22])]) ).

fof(f718,plain,
    ( spl53_23
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ssItem(sK52(X0,nil,X1))
        | ~ ssList(X1)
        | sK49 != app(cons(X0,nil),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_23])]) ).

fof(f835,plain,
    ( nil = sK49
    | ~ ssList(sK49)
    | ~ spl53_22
    | ~ spl53_23 ),
    inference(equality_resolution,[],[f834]) ).

fof(f834,plain,
    ( ! [X0] :
        ( sK49 != X0
        | nil = X0
        | ~ ssList(X0) )
    | ~ spl53_22
    | ~ spl53_23 ),
    inference(duplicate_literal_removal,[],[f833]) ).

fof(f833,plain,
    ( ! [X0] :
        ( sK49 != X0
        | nil = X0
        | ~ ssList(X0)
        | nil = X0
        | ~ ssList(X0) )
    | ~ spl53_22
    | ~ spl53_23 ),
    inference(resolution,[],[f832,f426]) ).

fof(f426,plain,
    ! [X0] :
      ( ssItem(sK44(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f307]) ).

fof(f307,plain,
    ! [X0] :
      ( ( cons(sK44(X0),sK43(X0)) = X0
        & ssItem(sK44(X0))
        & ssList(sK43(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44])],[f125,f306,f305]) ).

fof(f305,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
     => ( ? [X2] :
            ( cons(X2,sK43(X0)) = X0
            & ssItem(X2) )
        & ssList(sK43(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f306,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,sK43(X0)) = X0
          & ssItem(X2) )
     => ( cons(sK44(X0),sK43(X0)) = X0
        & ssItem(sK44(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f124]) ).

fof(f124,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( ? [X1] :
            ( ? [X2] :
                ( cons(X2,X1) = X0
                & ssItem(X2) )
            & ssList(X1) )
        | nil = X0 ) ),
    file('/export/starexec/sandbox/tmp/tmp.bFd6E1DUhW/Vampire---4.8_17229',ax20) ).

fof(f832,plain,
    ( ! [X0] :
        ( ~ ssItem(sK44(X0))
        | sK49 != X0
        | nil = X0
        | ~ ssList(X0) )
    | ~ spl53_22
    | ~ spl53_23 ),
    inference(duplicate_literal_removal,[],[f831]) ).

fof(f831,plain,
    ( ! [X0] :
        ( ~ ssItem(sK44(X0))
        | sK49 != X0
        | nil = X0
        | ~ ssList(X0)
        | nil = X0
        | ~ ssList(X0) )
    | ~ spl53_22
    | ~ spl53_23 ),
    inference(resolution,[],[f829,f425]) ).

fof(f425,plain,
    ! [X0] :
      ( ssList(sK43(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f307]) ).

fof(f829,plain,
    ( ! [X0] :
        ( ~ ssList(sK43(X0))
        | ~ ssItem(sK44(X0))
        | sK49 != X0
        | nil = X0
        | ~ ssList(X0) )
    | ~ spl53_22
    | ~ spl53_23 ),
    inference(superposition,[],[f828,f427]) ).

fof(f427,plain,
    ! [X0] :
      ( cons(sK44(X0),sK43(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f307]) ).

fof(f828,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) != sK49
        | ~ ssItem(X0)
        | ~ ssList(X1) )
    | ~ spl53_22
    | ~ spl53_23 ),
    inference(duplicate_literal_removal,[],[f825]) ).

fof(f825,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) != sK49
        | ~ ssItem(X0)
        | cons(X0,X1) != sK49
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | ~ ssList(X1) )
    | ~ spl53_22
    | ~ spl53_23 ),
    inference(superposition,[],[f823,f509]) ).

fof(f509,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f199]) ).

fof(f199,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.bFd6E1DUhW/Vampire---4.8_17229',ax81) ).

fof(f823,plain,
    ( ! [X0,X1] :
        ( app(cons(X1,nil),X0) != sK49
        | ~ ssItem(X1)
        | cons(X1,X0) != sK49
        | ~ ssList(X0) )
    | ~ spl53_22
    | ~ spl53_23 ),
    inference(duplicate_literal_removal,[],[f820]) ).

fof(f820,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssItem(X1)
        | cons(X1,X0) != sK49
        | ~ ssItem(X1)
        | ~ ssList(X0)
        | app(cons(X1,nil),X0) != sK49 )
    | ~ spl53_22
    | ~ spl53_23 ),
    inference(resolution,[],[f819,f719]) ).

fof(f719,plain,
    ( ! [X0,X1] :
        ( ssItem(sK52(X0,nil,X1))
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | sK49 != app(cons(X0,nil),X1) )
    | ~ spl53_23 ),
    inference(avatar_component_clause,[],[f718]) ).

fof(f819,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(sK52(X0,nil,X1))
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | cons(X0,X1) != sK49 )
    | ~ spl53_22 ),
    inference(duplicate_literal_removal,[],[f801]) ).

fof(f801,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) != sK49
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | ~ ssItem(sK52(X0,nil,X1))
        | ~ ssItem(X0)
        | ~ ssList(X1) )
    | ~ spl53_22 ),
    inference(superposition,[],[f724,f509]) ).

fof(f724,plain,
    ( ! [X0,X1] :
        ( sK49 != app(cons(X0,nil),X1)
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | ~ ssItem(sK52(X0,nil,X1)) )
    | ~ spl53_22 ),
    inference(resolution,[],[f715,f451]) ).

fof(f451,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.bFd6E1DUhW/Vampire---4.8_17229',ax38) ).

fof(f715,plain,
    ( ! [X0,X1] :
        ( memberP(nil,sK52(X0,nil,X1))
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | sK49 != app(cons(X0,nil),X1) )
    | ~ spl53_22 ),
    inference(avatar_component_clause,[],[f714]) ).

fof(f720,plain,
    ( ~ spl53_3
    | spl53_23
    | ~ spl53_8 ),
    inference(avatar_split_clause,[],[f696,f623,f718,f603]) ).

fof(f603,plain,
    ( spl53_3
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_3])]) ).

fof(f623,plain,
    ( spl53_8
  <=> ! [X0,X1] :
        ( sK49 != app(cons(X0,nil),X1)
        | ~ ssList(cons(X0,nil))
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ssItem(sK52(X0,nil,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_8])]) ).

fof(f696,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(nil)
        | sK49 != app(cons(X0,nil),X1)
        | ~ ssList(X1)
        | ssItem(sK52(X0,nil,X1)) )
    | ~ spl53_8 ),
    inference(duplicate_literal_removal,[],[f695]) ).

fof(f695,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(nil)
        | sK49 != app(cons(X0,nil),X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ssItem(sK52(X0,nil,X1)) )
    | ~ spl53_8 ),
    inference(resolution,[],[f420,f624]) ).

fof(f624,plain,
    ( ! [X0,X1] :
        ( ~ ssList(cons(X0,nil))
        | sK49 != app(cons(X0,nil),X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ssItem(sK52(X0,nil,X1)) )
    | ~ spl53_8 ),
    inference(avatar_component_clause,[],[f623]) ).

fof(f420,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.bFd6E1DUhW/Vampire---4.8_17229',ax16) ).

fof(f716,plain,
    ( ~ spl53_3
    | spl53_22
    | ~ spl53_4 ),
    inference(avatar_split_clause,[],[f697,f607,f714,f603]) ).

fof(f607,plain,
    ( spl53_4
  <=> ! [X0,X1] :
        ( sK49 != app(cons(X0,nil),X1)
        | ~ ssList(cons(X0,nil))
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | memberP(nil,sK52(X0,nil,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_4])]) ).

fof(f697,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(nil)
        | sK49 != app(cons(X0,nil),X1)
        | ~ ssList(X1)
        | memberP(nil,sK52(X0,nil,X1)) )
    | ~ spl53_4 ),
    inference(duplicate_literal_removal,[],[f694]) ).

fof(f694,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(nil)
        | sK49 != app(cons(X0,nil),X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | memberP(nil,sK52(X0,nil,X1)) )
    | ~ spl53_4 ),
    inference(resolution,[],[f420,f608]) ).

fof(f608,plain,
    ( ! [X0,X1] :
        ( ~ ssList(cons(X0,nil))
        | sK49 != app(cons(X0,nil),X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | memberP(nil,sK52(X0,nil,X1)) )
    | ~ spl53_4 ),
    inference(avatar_component_clause,[],[f607]) ).

fof(f675,plain,
    spl53_11,
    inference(avatar_contradiction_clause,[],[f674]) ).

fof(f674,plain,
    ( $false
    | spl53_11 ),
    inference(resolution,[],[f647,f530]) ).

fof(f530,plain,
    ssList(sK49),
    inference(cnf_transformation,[],[f337]) ).

fof(f337,plain,
    ( ( nil != sK49
      | nil = sK50 )
    & ! [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ~ lt(X7,X5)
                    | app(X8,cons(X7,nil)) != sK49
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | app(cons(X5,nil),X6) != sK51
            | ~ ssList(X6) )
        | ~ ssItem(X5) )
    & strictorderedP(sK49)
    & sK50 = app(sK49,sK51)
    & ssList(sK51)
    & ! [X9] :
        ( ! [X10] :
            ( ! [X11] :
                ( ( ~ lt(X9,sK52(X9,X10,X11))
                  & leq(X9,sK52(X9,X10,X11))
                  & memberP(X11,sK52(X9,X10,X11))
                  & memberP(X10,sK52(X9,X10,X11))
                  & ssItem(sK52(X9,X10,X11)) )
                | app(app(X10,cons(X9,nil)),X11) != sK47
                | ~ ssList(X11) )
            | ~ ssList(X10) )
        | ~ ssItem(X9) )
    & nil != sK47
    & 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])],[f222,f336,f335,f334,f333,f332,f331]) ).

fof(f331,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( nil != X2
                      | nil = X3 )
                    & ? [X4] :
                        ( ! [X5] :
                            ( ! [X6] :
                                ( ! [X7] :
                                    ( ! [X8] :
                                        ( ~ lt(X7,X5)
                                        | app(X8,cons(X7,nil)) != X2
                                        | ~ ssList(X8) )
                                    | ~ ssItem(X7) )
                                | app(cons(X5,nil),X6) != X4
                                | ~ ssList(X6) )
                            | ~ ssItem(X5) )
                        & strictorderedP(X2)
                        & app(X2,X4) = X3
                        & ssList(X4) )
                    & ! [X9] :
                        ( ! [X10] :
                            ( ! [X11] :
                                ( ? [X12] :
                                    ( ~ lt(X9,X12)
                                    & leq(X9,X12)
                                    & memberP(X11,X12)
                                    & memberP(X10,X12)
                                    & ssItem(X12) )
                                | app(app(X10,cons(X9,nil)),X11) != X0
                                | ~ ssList(X11) )
                            | ~ ssList(X10) )
                        | ~ ssItem(X9) )
                    & nil != X0
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ~ lt(X7,X5)
                                      | app(X8,cons(X7,nil)) != X2
                                      | ~ ssList(X8) )
                                  | ~ ssItem(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & strictorderedP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & ! [X9] :
                      ( ! [X10] :
                          ( ! [X11] :
                              ( ? [X12] :
                                  ( ~ lt(X9,X12)
                                  & leq(X9,X12)
                                  & memberP(X11,X12)
                                  & memberP(X10,X12)
                                  & ssItem(X12) )
                              | app(app(X10,cons(X9,nil)),X11) != sK47
                              | ~ ssList(X11) )
                          | ~ ssList(X10) )
                      | ~ ssItem(X9) )
                  & nil != sK47
                  & sK47 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK47) ) ),
    introduced(choice_axiom,[]) ).

fof(f332,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( nil != X2
                  | nil = X3 )
                & ? [X4] :
                    ( ! [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ! [X8] :
                                    ( ~ lt(X7,X5)
                                    | app(X8,cons(X7,nil)) != X2
                                    | ~ ssList(X8) )
                                | ~ ssItem(X7) )
                            | app(cons(X5,nil),X6) != X4
                            | ~ ssList(X6) )
                        | ~ ssItem(X5) )
                    & strictorderedP(X2)
                    & app(X2,X4) = X3
                    & ssList(X4) )
                & ! [X9] :
                    ( ! [X10] :
                        ( ! [X11] :
                            ( ? [X12] :
                                ( ~ lt(X9,X12)
                                & leq(X9,X12)
                                & memberP(X11,X12)
                                & memberP(X10,X12)
                                & ssItem(X12) )
                            | app(app(X10,cons(X9,nil)),X11) != sK47
                            | ~ ssList(X11) )
                        | ~ ssList(X10) )
                    | ~ ssItem(X9) )
                & nil != sK47
                & sK47 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( nil != X2
                | nil = X3 )
              & ? [X4] :
                  ( ! [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ~ lt(X7,X5)
                                  | app(X8,cons(X7,nil)) != X2
                                  | ~ ssList(X8) )
                              | ~ ssItem(X7) )
                          | app(cons(X5,nil),X6) != X4
                          | ~ ssList(X6) )
                      | ~ ssItem(X5) )
                  & strictorderedP(X2)
                  & app(X2,X4) = X3
                  & ssList(X4) )
              & ! [X9] :
                  ( ! [X10] :
                      ( ! [X11] :
                          ( ? [X12] :
                              ( ~ lt(X9,X12)
                              & leq(X9,X12)
                              & memberP(X11,X12)
                              & memberP(X10,X12)
                              & ssItem(X12) )
                          | app(app(X10,cons(X9,nil)),X11) != sK47
                          | ~ ssList(X11) )
                      | ~ ssList(X10) )
                  | ~ ssItem(X9) )
              & nil != sK47
              & sK47 = X2
              & sK48 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK48) ) ),
    introduced(choice_axiom,[]) ).

fof(f333,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( nil != X2
              | nil = X3 )
            & ? [X4] :
                ( ! [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( ~ lt(X7,X5)
                                | app(X8,cons(X7,nil)) != X2
                                | ~ ssList(X8) )
                            | ~ ssItem(X7) )
                        | app(cons(X5,nil),X6) != X4
                        | ~ ssList(X6) )
                    | ~ ssItem(X5) )
                & strictorderedP(X2)
                & app(X2,X4) = X3
                & ssList(X4) )
            & ! [X9] :
                ( ! [X10] :
                    ( ! [X11] :
                        ( ? [X12] :
                            ( ~ lt(X9,X12)
                            & leq(X9,X12)
                            & memberP(X11,X12)
                            & memberP(X10,X12)
                            & ssItem(X12) )
                        | app(app(X10,cons(X9,nil)),X11) != sK47
                        | ~ ssList(X11) )
                    | ~ ssList(X10) )
                | ~ ssItem(X9) )
            & nil != sK47
            & sK47 = X2
            & sK48 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( nil != sK49
            | nil = X3 )
          & ? [X4] :
              ( ! [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ~ lt(X7,X5)
                              | app(X8,cons(X7,nil)) != sK49
                              | ~ ssList(X8) )
                          | ~ ssItem(X7) )
                      | app(cons(X5,nil),X6) != X4
                      | ~ ssList(X6) )
                  | ~ ssItem(X5) )
              & strictorderedP(sK49)
              & app(sK49,X4) = X3
              & ssList(X4) )
          & ! [X9] :
              ( ! [X10] :
                  ( ! [X11] :
                      ( ? [X12] :
                          ( ~ lt(X9,X12)
                          & leq(X9,X12)
                          & memberP(X11,X12)
                          & memberP(X10,X12)
                          & ssItem(X12) )
                      | app(app(X10,cons(X9,nil)),X11) != sK47
                      | ~ ssList(X11) )
                  | ~ ssList(X10) )
              | ~ ssItem(X9) )
          & nil != sK47
          & sK47 = sK49
          & sK48 = X3
          & ssList(X3) )
      & ssList(sK49) ) ),
    introduced(choice_axiom,[]) ).

fof(f334,plain,
    ( ? [X3] :
        ( ( nil != sK49
          | nil = X3 )
        & ? [X4] :
            ( ! [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ~ lt(X7,X5)
                            | app(X8,cons(X7,nil)) != sK49
                            | ~ ssList(X8) )
                        | ~ ssItem(X7) )
                    | app(cons(X5,nil),X6) != X4
                    | ~ ssList(X6) )
                | ~ ssItem(X5) )
            & strictorderedP(sK49)
            & app(sK49,X4) = X3
            & ssList(X4) )
        & ! [X9] :
            ( ! [X10] :
                ( ! [X11] :
                    ( ? [X12] :
                        ( ~ lt(X9,X12)
                        & leq(X9,X12)
                        & memberP(X11,X12)
                        & memberP(X10,X12)
                        & ssItem(X12) )
                    | app(app(X10,cons(X9,nil)),X11) != sK47
                    | ~ ssList(X11) )
                | ~ ssList(X10) )
            | ~ ssItem(X9) )
        & nil != sK47
        & sK47 = sK49
        & sK48 = X3
        & ssList(X3) )
   => ( ( nil != sK49
        | nil = sK50 )
      & ? [X4] :
          ( ! [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ~ lt(X7,X5)
                          | app(X8,cons(X7,nil)) != sK49
                          | ~ ssList(X8) )
                      | ~ ssItem(X7) )
                  | app(cons(X5,nil),X6) != X4
                  | ~ ssList(X6) )
              | ~ ssItem(X5) )
          & strictorderedP(sK49)
          & app(sK49,X4) = sK50
          & ssList(X4) )
      & ! [X9] :
          ( ! [X10] :
              ( ! [X11] :
                  ( ? [X12] :
                      ( ~ lt(X9,X12)
                      & leq(X9,X12)
                      & memberP(X11,X12)
                      & memberP(X10,X12)
                      & ssItem(X12) )
                  | app(app(X10,cons(X9,nil)),X11) != sK47
                  | ~ ssList(X11) )
              | ~ ssList(X10) )
          | ~ ssItem(X9) )
      & nil != sK47
      & sK47 = sK49
      & sK48 = sK50
      & ssList(sK50) ) ),
    introduced(choice_axiom,[]) ).

fof(f335,plain,
    ( ? [X4] :
        ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ~ lt(X7,X5)
                        | app(X8,cons(X7,nil)) != sK49
                        | ~ ssList(X8) )
                    | ~ ssItem(X7) )
                | app(cons(X5,nil),X6) != X4
                | ~ ssList(X6) )
            | ~ ssItem(X5) )
        & strictorderedP(sK49)
        & app(sK49,X4) = sK50
        & ssList(X4) )
   => ( ! [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ~ lt(X7,X5)
                      | app(X8,cons(X7,nil)) != sK49
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | app(cons(X5,nil),X6) != sK51
              | ~ ssList(X6) )
          | ~ ssItem(X5) )
      & strictorderedP(sK49)
      & sK50 = app(sK49,sK51)
      & ssList(sK51) ) ),
    introduced(choice_axiom,[]) ).

fof(f336,plain,
    ! [X9,X10,X11] :
      ( ? [X12] :
          ( ~ lt(X9,X12)
          & leq(X9,X12)
          & memberP(X11,X12)
          & memberP(X10,X12)
          & ssItem(X12) )
     => ( ~ lt(X9,sK52(X9,X10,X11))
        & leq(X9,sK52(X9,X10,X11))
        & memberP(X11,sK52(X9,X10,X11))
        & memberP(X10,sK52(X9,X10,X11))
        & ssItem(sK52(X9,X10,X11)) ) ),
    introduced(choice_axiom,[]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ~ lt(X7,X5)
                                      | app(X8,cons(X7,nil)) != X2
                                      | ~ ssList(X8) )
                                  | ~ ssItem(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & strictorderedP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & ! [X9] :
                      ( ! [X10] :
                          ( ! [X11] :
                              ( ? [X12] :
                                  ( ~ lt(X9,X12)
                                  & leq(X9,X12)
                                  & memberP(X11,X12)
                                  & memberP(X10,X12)
                                  & ssItem(X12) )
                              | app(app(X10,cons(X9,nil)),X11) != X0
                              | ~ ssList(X11) )
                          | ~ ssList(X10) )
                      | ~ ssItem(X9) )
                  & nil != X0
                  & 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] :
                    ( ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ? [X7] :
                                    ( ? [X8] :
                                        ( lt(X7,X5)
                                        & app(X8,cons(X7,nil)) = X2
                                        & ssList(X8) )
                                    & ssItem(X7) )
                                & app(cons(X5,nil),X6) = X4
                                & ssList(X6) )
                            & ssItem(X5) )
                        | ~ strictorderedP(X2)
                        | app(X2,X4) != X3
                        | ~ ssList(X4) )
                    | ? [X9] :
                        ( ? [X10] :
                            ( ? [X11] :
                                ( ! [X12] :
                                    ( lt(X9,X12)
                                    | ~ leq(X9,X12)
                                    | ~ memberP(X11,X12)
                                    | ~ memberP(X10,X12)
                                    | ~ ssItem(X12) )
                                & app(app(X10,cons(X9,nil)),X11) = X0
                                & ssList(X11) )
                            & ssList(X10) )
                        & ssItem(X9) )
                    | nil = X0
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( nil = X2
                      & nil != X3 )
                    | ! [X8] :
                        ( ? [X9] :
                            ( ? [X10] :
                                ( ? [X11] :
                                    ( ? [X12] :
                                        ( lt(X11,X9)
                                        & app(X12,cons(X11,nil)) = X2
                                        & ssList(X12) )
                                    & ssItem(X11) )
                                & app(cons(X9,nil),X10) = X8
                                & ssList(X10) )
                            & ssItem(X9) )
                        | ~ strictorderedP(X2)
                        | app(X2,X8) != X3
                        | ~ ssList(X8) )
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ! [X7] :
                                    ( lt(X4,X7)
                                    | ~ leq(X4,X7)
                                    | ~ memberP(X6,X7)
                                    | ~ memberP(X5,X7)
                                    | ~ ssItem(X7) )
                                & app(app(X5,cons(X4,nil)),X6) = X0
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) )
                    | nil = 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 )
                  | ! [X8] :
                      ( ? [X9] :
                          ( ? [X10] :
                              ( ? [X11] :
                                  ( ? [X12] :
                                      ( lt(X11,X9)
                                      & app(X12,cons(X11,nil)) = X2
                                      & ssList(X12) )
                                  & ssItem(X11) )
                              & app(cons(X9,nil),X10) = X8
                              & ssList(X10) )
                          & ssItem(X9) )
                      | ~ strictorderedP(X2)
                      | app(X2,X8) != X3
                      | ~ ssList(X8) )
                  | ? [X4] :
                      ( ? [X5] :
                          ( ? [X6] :
                              ( ! [X7] :
                                  ( lt(X4,X7)
                                  | ~ leq(X4,X7)
                                  | ~ memberP(X6,X7)
                                  | ~ memberP(X5,X7)
                                  | ~ ssItem(X7) )
                              & app(app(X5,cons(X4,nil)),X6) = X0
                              & ssList(X6) )
                          & ssList(X5) )
                      & ssItem(X4) )
                  | nil = X0
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.bFd6E1DUhW/Vampire---4.8_17229',co1) ).

fof(f647,plain,
    ( ~ ssList(sK49)
    | spl53_11 ),
    inference(avatar_component_clause,[],[f645]) ).

fof(f627,plain,
    spl53_3,
    inference(avatar_contradiction_clause,[],[f626]) ).

fof(f626,plain,
    ( $false
    | spl53_3 ),
    inference(resolution,[],[f605,f421]) ).

fof(f421,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/tmp/tmp.bFd6E1DUhW/Vampire---4.8_17229',ax17) ).

fof(f605,plain,
    ( ~ ssList(nil)
    | spl53_3 ),
    inference(avatar_component_clause,[],[f603]) ).

fof(f625,plain,
    ( ~ spl53_3
    | spl53_8 ),
    inference(avatar_split_clause,[],[f601,f623,f603]) ).

fof(f601,plain,
    ! [X0,X1] :
      ( sK49 != app(cons(X0,nil),X1)
      | ssItem(sK52(X0,nil,X1))
      | ~ ssList(X1)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil)) ),
    inference(superposition,[],[f549,f435]) ).

fof(f435,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.bFd6E1DUhW/Vampire---4.8_17229',ax28) ).

fof(f549,plain,
    ! [X10,X11,X9] :
      ( app(app(X10,cons(X9,nil)),X11) != sK49
      | ssItem(sK52(X9,X10,X11))
      | ~ ssList(X11)
      | ~ ssList(X10)
      | ~ ssItem(X9) ),
    inference(definition_unfolding,[],[f535,f533]) ).

fof(f533,plain,
    sK47 = sK49,
    inference(cnf_transformation,[],[f337]) ).

fof(f535,plain,
    ! [X10,X11,X9] :
      ( ssItem(sK52(X9,X10,X11))
      | app(app(X10,cons(X9,nil)),X11) != sK47
      | ~ ssList(X11)
      | ~ ssList(X10)
      | ~ ssItem(X9) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f609,plain,
    ( ~ spl53_3
    | spl53_4 ),
    inference(avatar_split_clause,[],[f597,f607,f603]) ).

fof(f597,plain,
    ! [X0,X1] :
      ( sK49 != app(cons(X0,nil),X1)
      | memberP(nil,sK52(X0,nil,X1))
      | ~ ssList(X1)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil)) ),
    inference(superposition,[],[f548,f435]) ).

fof(f548,plain,
    ! [X10,X11,X9] :
      ( app(app(X10,cons(X9,nil)),X11) != sK49
      | memberP(X10,sK52(X9,X10,X11))
      | ~ ssList(X11)
      | ~ ssList(X10)
      | ~ ssItem(X9) ),
    inference(definition_unfolding,[],[f536,f533]) ).

fof(f536,plain,
    ! [X10,X11,X9] :
      ( memberP(X10,sK52(X9,X10,X11))
      | app(app(X10,cons(X9,nil)),X11) != sK47
      | ~ ssList(X11)
      | ~ ssList(X10)
      | ~ ssItem(X9) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f596,plain,
    ~ spl53_2,
    inference(avatar_split_clause,[],[f550,f592]) ).

fof(f550,plain,
    nil != sK49,
    inference(definition_unfolding,[],[f534,f533]) ).

fof(f534,plain,
    nil != sK47,
    inference(cnf_transformation,[],[f337]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWC237+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15  % 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
% 0.16/0.37  % Computer : n002.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Tue Apr 30 18:34:55 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  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.bFd6E1DUhW/Vampire---4.8_17229
% 0.61/0.76  % (17489)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)
% 0.61/0.76  % (17484)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)
% 0.61/0.76  % (17486)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)
% 0.61/0.76  % (17485)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.61/0.76  % (17483)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)
% 0.61/0.76  % (17490)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)
% 0.61/0.76  % (17487)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)
% 0.61/0.77  % (17488)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)
% 0.61/0.78  % (17484)First to succeed.
% 0.61/0.78  % (17486)Instruction limit reached!
% 0.61/0.78  % (17486)------------------------------
% 0.61/0.78  % (17486)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.78  % (17486)Termination reason: Unknown
% 0.61/0.78  % (17486)Termination phase: Saturation
% 0.61/0.78  
% 0.61/0.78  % (17486)Memory used [KB]: 1737
% 0.61/0.78  % (17486)Time elapsed: 0.020 s
% 0.61/0.78  % (17486)Instructions burned: 34 (million)
% 0.61/0.78  % (17486)------------------------------
% 0.61/0.78  % (17486)------------------------------
% 0.61/0.78  % (17487)Instruction limit reached!
% 0.61/0.78  % (17487)------------------------------
% 0.61/0.78  % (17487)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.78  % (17487)Termination reason: Unknown
% 0.61/0.78  % (17487)Termination phase: Saturation
% 0.61/0.78  
% 0.61/0.78  % (17487)Memory used [KB]: 1922
% 0.61/0.78  % (17487)Time elapsed: 0.019 s
% 0.61/0.78  % (17487)Instructions burned: 34 (million)
% 0.61/0.78  % (17487)------------------------------
% 0.61/0.78  % (17487)------------------------------
% 0.61/0.78  % (17484)Refutation found. Thanks to Tanya!
% 0.61/0.78  % SZS status Theorem for Vampire---4
% 0.61/0.78  % SZS output start Proof for Vampire---4
% See solution above
% 0.61/0.78  % (17484)------------------------------
% 0.61/0.78  % (17484)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.78  % (17484)Termination reason: Refutation
% 0.61/0.78  
% 0.61/0.78  % (17484)Memory used [KB]: 1493
% 0.61/0.78  % (17484)Time elapsed: 0.021 s
% 0.61/0.78  % (17484)Instructions burned: 32 (million)
% 0.61/0.78  % (17484)------------------------------
% 0.61/0.78  % (17484)------------------------------
% 0.61/0.78  % (17479)Success in time 0.394 s
% 0.61/0.78  % Vampire---4.8 exiting
%------------------------------------------------------------------------------