TSTP Solution File: SWC198+1 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC198+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n028.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 : Fri May  3 03:11:33 EDT 2024

% Result   : Theorem 29.15s 4.74s
% Output   : CNFRefutation 29.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   73 (  12 unt;   0 def)
%            Number of atoms       :  457 ( 150 equ)
%            Maximal formula atoms :   38 (   6 avg)
%            Number of connectives :  572 ( 188   ~; 177   |; 171   &)
%                                         (   2 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :  157 (   0 sgn  76   !;  58   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ? [X0] :
      ( ? [X1] :
          ( X0 != X1
          & ssItem(X1) )
      & ssItem(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f37,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( memberP(cons(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | X0 = X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

fof(f87,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( ( geq(X1,X0)
              & geq(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).

fof(f89,axiom,
    ! [X0] :
      ( ssItem(X0)
     => geq(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( nil != X2
                        | nil != X3 )
                      & ! [X6] :
                          ( ssItem(X6)
                         => ( ? [X7] :
                                ( leq(X6,X7)
                                & memberP(X3,X7)
                                & X6 != X7
                                & ssItem(X7) )
                            | ~ memberP(X3,X6)
                            | cons(X6,nil) != X2 ) ) )
                    | ? [X4] :
                        ( ! [X5] :
                            ( ssItem(X5)
                           => ( X4 = X5
                              | ~ memberP(X0,X5) ) )
                        & ssItem(X4) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( nil != X2
                          | nil != X3 )
                        & ! [X6] :
                            ( ssItem(X6)
                           => ( ? [X7] :
                                  ( leq(X6,X7)
                                  & memberP(X3,X7)
                                  & X6 != X7
                                  & ssItem(X7) )
                              | ~ memberP(X3,X6)
                              | cons(X6,nil) != X2 ) ) )
                      | ? [X4] :
                          ( ! [X5] :
                              ( ssItem(X5)
                             => ( X4 = X5
                                | ~ memberP(X0,X5) ) )
                          & ssItem(X4) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( nil != X2
                          | nil != X3 )
                        & ! [X4] :
                            ( ssItem(X4)
                           => ( ? [X5] :
                                  ( leq(X4,X5)
                                  & memberP(X3,X5)
                                  & X4 != X5
                                  & ssItem(X5) )
                              | ~ memberP(X3,X4)
                              | cons(X4,nil) != X2 ) ) )
                      | ? [X6] :
                          ( ! [X7] :
                              ( ssItem(X7)
                             => ( X6 = X7
                                | ~ memberP(X0,X7) ) )
                          & ssItem(X6) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f148,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( memberP(cons(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | X0 = X1 ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f37]) ).

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

fof(f207,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ geq(X1,X0)
          | ~ geq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f87]) ).

fof(f208,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ geq(X1,X0)
          | ~ geq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f207]) ).

fof(f211,plain,
    ! [X0] :
      ( geq(X0,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f89]) ).

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) ) )
                  & ! [X6] :
                      ( ? [X7] :
                          ( X6 != X7
                          & memberP(X0,X7)
                          & ssItem(X7) )
                      | ~ ssItem(X6) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f223,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) ) )
                  & ! [X6] :
                      ( ? [X7] :
                          ( X6 != X7
                          & memberP(X0,X7)
                          & ssItem(X7) )
                      | ~ ssItem(X6) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f234,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( X0 != X1
            & ssItem(X1) )
        & ssItem(X0) )
   => ( ? [X1] :
          ( sK6 != X1
          & ssItem(X1) )
      & ssItem(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f235,plain,
    ( ? [X1] :
        ( sK6 != X1
        & ssItem(X1) )
   => ( sK6 != sK7
      & ssItem(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f236,plain,
    ( sK6 != sK7
    & ssItem(sK7)
    & ssItem(sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f2,f235,f234]) ).

fof(f325,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(cons(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & X0 != X1 ) )
                & ( memberP(X2,X0)
                  | X0 = X1
                  | ~ memberP(cons(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f148]) ).

fof(f326,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(cons(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & X0 != X1 ) )
                & ( memberP(X2,X0)
                  | X0 = X1
                  | ~ memberP(cons(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f325]) ).

fof(f344,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) ) )
                    & ! [X6] :
                        ( ? [X7] :
                            ( X6 != X7
                            & memberP(X0,X7)
                            & ssItem(X7) )
                        | ~ ssItem(X6) )
                    & 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) ) )
                  & ! [X6] :
                      ( ? [X7] :
                          ( X6 != X7
                          & memberP(sK53,X7)
                          & ssItem(X7) )
                      | ~ ssItem(X6) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,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) ) )
                & ! [X6] :
                    ( ? [X7] :
                        ( X6 != X7
                        & memberP(sK53,X7)
                        & ssItem(X7) )
                    | ~ ssItem(X6) )
                & sK53 = 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) ) )
              & ! [X6] :
                  ( ? [X7] :
                      ( X6 != X7
                      & memberP(sK53,X7)
                      & ssItem(X7) )
                  | ~ ssItem(X6) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,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) ) )
            & ! [X6] :
                ( ? [X7] :
                    ( X6 != X7
                    & memberP(sK53,X7)
                    & ssItem(X7) )
                | ~ ssItem(X6) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK55
              & nil = X3 )
            | ? [X4] :
                ( ! [X5] :
                    ( ~ leq(X4,X5)
                    | ~ memberP(X3,X5)
                    | X4 = X5
                    | ~ ssItem(X5) )
                & memberP(X3,X4)
                & cons(X4,nil) = sK55
                & ssItem(X4) ) )
          & ! [X6] :
              ( ? [X7] :
                  ( X6 != X7
                  & memberP(sK53,X7)
                  & ssItem(X7) )
              | ~ ssItem(X6) )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X3] :
        ( ( ( nil = sK55
            & nil = X3 )
          | ? [X4] :
              ( ! [X5] :
                  ( ~ leq(X4,X5)
                  | ~ memberP(X3,X5)
                  | X4 = X5
                  | ~ ssItem(X5) )
              & memberP(X3,X4)
              & cons(X4,nil) = sK55
              & ssItem(X4) ) )
        & ! [X6] :
            ( ? [X7] :
                ( X6 != X7
                & memberP(sK53,X7)
                & ssItem(X7) )
            | ~ ssItem(X6) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ( nil = sK55
          & nil = sK56 )
        | ? [X4] :
            ( ! [X5] :
                ( ~ leq(X4,X5)
                | ~ memberP(sK56,X5)
                | X4 = X5
                | ~ ssItem(X5) )
            & memberP(sK56,X4)
            & cons(X4,nil) = sK55
            & ssItem(X4) ) )
      & ! [X6] :
          ( ? [X7] :
              ( X6 != X7
              & memberP(sK53,X7)
              & ssItem(X7) )
          | ~ ssItem(X6) )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X4] :
        ( ! [X5] :
            ( ~ leq(X4,X5)
            | ~ memberP(sK56,X5)
            | X4 = X5
            | ~ ssItem(X5) )
        & memberP(sK56,X4)
        & cons(X4,nil) = sK55
        & ssItem(X4) )
   => ( ! [X5] :
          ( ~ leq(sK57,X5)
          | ~ memberP(sK56,X5)
          | sK57 = X5
          | ~ ssItem(X5) )
      & memberP(sK56,sK57)
      & sK55 = cons(sK57,nil)
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ! [X6] :
      ( ? [X7] :
          ( X6 != X7
          & memberP(sK53,X7)
          & ssItem(X7) )
     => ( sK58(X6) != X6
        & memberP(sK53,sK58(X6))
        & ssItem(sK58(X6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ( ( ( nil = sK55
        & nil = sK56 )
      | ( ! [X5] :
            ( ~ leq(sK57,X5)
            | ~ memberP(sK56,X5)
            | sK57 = X5
            | ~ ssItem(X5) )
        & memberP(sK56,sK57)
        & sK55 = cons(sK57,nil)
        & ssItem(sK57) ) )
    & ! [X6] :
        ( ( sK58(X6) != X6
          & memberP(sK53,sK58(X6))
          & ssItem(sK58(X6)) )
        | ~ ssItem(X6) )
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58])],[f223,f349,f348,f347,f346,f345,f344]) ).

fof(f354,plain,
    ssItem(sK7),
    inference(cnf_transformation,[],[f236]) ).

fof(f443,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f470,plain,
    ! [X2,X0,X1] :
      ( memberP(X2,X0)
      | X0 = X1
      | ~ memberP(cons(X1,X2),X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f326]) ).

fof(f473,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f539,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ geq(X1,X0)
      | ~ geq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f208]) ).

fof(f541,plain,
    ! [X0] :
      ( geq(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f211]) ).

fof(f555,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f350]) ).

fof(f556,plain,
    ! [X6] :
      ( ssItem(sK58(X6))
      | ~ ssItem(X6) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f557,plain,
    ! [X6] :
      ( memberP(sK53,sK58(X6))
      | ~ ssItem(X6) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f558,plain,
    ! [X6] :
      ( sK58(X6) != X6
      | ~ ssItem(X6) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f563,plain,
    ( nil = sK55
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f564,plain,
    ( nil = sK55
    | sK55 = cons(sK57,nil) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f567,plain,
    ! [X6] :
      ( memberP(sK55,sK58(X6))
      | ~ ssItem(X6) ),
    inference(definition_unfolding,[],[f557,f555]) ).

cnf(c_52,plain,
    ssItem(sK7),
    inference(cnf_transformation,[],[f354]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f443]) ).

cnf(c_170,plain,
    ( ~ memberP(cons(X0,X1),X2)
    | ~ ssItem(X0)
    | ~ ssItem(X2)
    | ~ ssList(X1)
    | X0 = X2
    | memberP(X1,X2) ),
    inference(cnf_transformation,[],[f470]) ).

cnf(c_171,negated_conjecture,
    ( ~ memberP(nil,X0)
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f473]) ).

cnf(c_235,plain,
    ( ~ geq(X0,X1)
    | ~ geq(X1,X0)
    | ~ ssItem(X0)
    | ~ ssItem(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f539]) ).

cnf(c_237,plain,
    ( ~ ssItem(X0)
    | geq(X0,X0) ),
    inference(cnf_transformation,[],[f541]) ).

cnf(c_248,negated_conjecture,
    ( cons(sK57,nil) = sK55
    | nil = sK55 ),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_249,negated_conjecture,
    ( nil = sK55
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f563]) ).

cnf(c_254,negated_conjecture,
    ( sK58(X0) != X0
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f558]) ).

cnf(c_255,negated_conjecture,
    ( ~ ssItem(X0)
    | memberP(sK55,sK58(X0)) ),
    inference(cnf_transformation,[],[f567]) ).

cnf(c_256,negated_conjecture,
    ( ~ ssItem(X0)
    | ssItem(sK58(X0)) ),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_553,plain,
    ( X0 != X1
    | X2 != X3
    | ~ memberP(X1,X3)
    | memberP(X0,X2) ),
    theory(equality) ).

cnf(c_687,plain,
    ( ~ ssItem(sK7)
    | ssItem(sK58(sK7)) ),
    inference(instantiation,[status(thm)],[c_256]) ).

cnf(c_688,plain,
    ( ~ ssItem(sK7)
    | memberP(sK55,sK58(sK7)) ),
    inference(instantiation,[status(thm)],[c_255]) ).

cnf(c_895,plain,
    ( ~ ssItem(sK58(sK7))
    | geq(sK58(sK7),sK58(sK7)) ),
    inference(instantiation,[status(thm)],[c_237]) ).

cnf(c_911,plain,
    ( ~ memberP(nil,sK58(sK7))
    | ~ ssItem(sK58(sK7)) ),
    inference(instantiation,[status(thm)],[c_171]) ).

cnf(c_1014,plain,
    ( X0 != sK55
    | X1 != sK58(sK7)
    | ~ memberP(sK55,sK58(sK7))
    | memberP(X0,X1) ),
    inference(instantiation,[status(thm)],[c_553]) ).

cnf(c_3440,plain,
    ( ~ geq(sK58(sK7),sK58(sK7))
    | ~ ssItem(sK58(sK7))
    | sK58(sK7) = sK58(sK7) ),
    inference(instantiation,[status(thm)],[c_235]) ).

cnf(c_6468,plain,
    ( sK58(sK7) != sK58(sK7)
    | X0 != sK55
    | ~ memberP(sK55,sK58(sK7))
    | memberP(X0,sK58(sK7)) ),
    inference(instantiation,[status(thm)],[c_1014]) ).

cnf(c_6470,plain,
    ( sK58(sK7) != sK58(sK7)
    | nil != sK55
    | ~ memberP(sK55,sK58(sK7))
    | memberP(nil,sK58(sK7)) ),
    inference(instantiation,[status(thm)],[c_6468]) ).

cnf(c_11818,negated_conjecture,
    cons(sK57,nil) = sK55,
    inference(global_subsumption_just,[status(thm)],[c_248,c_52,c_248,c_688,c_687,c_911,c_895,c_3440,c_6470]) ).

cnf(c_21623,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | ~ ssItem(sK57)
    | ~ ssList(nil)
    | X0 = sK57
    | memberP(nil,X0) ),
    inference(superposition,[status(thm)],[c_11818,c_170]) ).

cnf(c_24995,negated_conjecture,
    ssItem(sK57),
    inference(global_subsumption_just,[status(thm)],[c_249,c_52,c_249,c_688,c_687,c_911,c_895,c_3440,c_6470]) ).

cnf(c_25003,negated_conjecture,
    cons(sK57,nil) = sK55,
    inference(global_subsumption_just,[status(thm)],[c_248,c_52,c_248,c_688,c_687,c_911,c_895,c_3440,c_6470]) ).

cnf(c_28095,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | ~ ssItem(sK57)
    | ~ ssList(nil)
    | X0 = sK57
    | memberP(nil,X0) ),
    inference(superposition,[status(thm)],[c_25003,c_170]) ).

cnf(c_30959,plain,
    ( X0 = sK57
    | ~ ssItem(X0)
    | ~ memberP(sK55,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_28095,c_141,c_52,c_249,c_171,c_688,c_687,c_911,c_895,c_3440,c_6470,c_21623]) ).

cnf(c_30960,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | X0 = sK57 ),
    inference(renaming,[status(thm)],[c_30959]) ).

cnf(c_30962,plain,
    ( ~ ssItem(sK58(X0))
    | ~ ssItem(X0)
    | sK58(X0) = sK57 ),
    inference(superposition,[status(thm)],[c_255,c_30960]) ).

cnf(c_30965,plain,
    ( ~ ssItem(X0)
    | sK58(X0) = sK57 ),
    inference(global_subsumption_just,[status(thm)],[c_30962,c_256,c_30962]) ).

cnf(c_30988,plain,
    sK58(sK57) = sK57,
    inference(superposition,[status(thm)],[c_24995,c_30965]) ).

cnf(c_30993,plain,
    ~ ssItem(sK57),
    inference(superposition,[status(thm)],[c_30988,c_254]) ).

cnf(c_31024,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_30993,c_6470,c_3440,c_895,c_911,c_687,c_688,c_249,c_52]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC198+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May  2 23:57:48 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  Running first-order theorem proving
% 0.20/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 29.15/4.74  % SZS status Started for theBenchmark.p
% 29.15/4.74  % SZS status Theorem for theBenchmark.p
% 29.15/4.74  
% 29.15/4.74  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 29.15/4.74  
% 29.15/4.74  ------  iProver source info
% 29.15/4.74  
% 29.15/4.74  git: date: 2024-05-02 19:28:25 +0000
% 29.15/4.74  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 29.15/4.74  git: non_committed_changes: false
% 29.15/4.74  
% 29.15/4.74  ------ Parsing...
% 29.15/4.74  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 29.15/4.74  
% 29.15/4.74  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e 
% 29.15/4.74  
% 29.15/4.74  ------ Preprocessing...
% 29.15/4.74  
% 29.15/4.74  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 29.15/4.74  ------ Proving...
% 29.15/4.74  ------ Problem Properties 
% 29.15/4.74  
% 29.15/4.74  
% 29.15/4.74  clauses                                 206
% 29.15/4.74  conjectures                             25
% 29.15/4.74  EPR                                     70
% 29.15/4.74  Horn                                    128
% 29.15/4.74  unary                                   18
% 29.15/4.74  binary                                  57
% 29.15/4.74  lits                                    681
% 29.15/4.74  lits eq                                 93
% 29.15/4.74  fd_pure                                 0
% 29.15/4.74  fd_pseudo                               0
% 29.15/4.74  fd_cond                                 23
% 29.15/4.74  fd_pseudo_cond                          16
% 29.15/4.74  AC symbols                              0
% 29.15/4.74  
% 29.15/4.74  ------ Input Options Time Limit: Unbounded
% 29.15/4.74  
% 29.15/4.74  
% 29.15/4.74  ------ 
% 29.15/4.74  Current options:
% 29.15/4.74  ------ 
% 29.15/4.74  
% 29.15/4.74  
% 29.15/4.74  
% 29.15/4.74  
% 29.15/4.74  ------ Proving...
% 29.15/4.74  
% 29.15/4.74  
% 29.15/4.74  % SZS status Theorem for theBenchmark.p
% 29.15/4.74  
% 29.15/4.74  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 29.15/4.75  
% 29.15/4.75  
%------------------------------------------------------------------------------