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FindProof---0.1.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : SWC002+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 03:05:03 PM UTC 2026

% Result   : Theorem 24.08s 3.48s
% Output   : Proof 24.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   79 (  15 unt;   0 def)
%            Number of atoms       :  350 ( 112 equ)
%            Maximal formula atoms :   27 (   4 avg)
%            Number of connectives :  483 ( 212   ~; 203   |;  52   &)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-3 aty)
%            Number of variables   :   81 (   0 sgn  24   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f95,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( ( ( neq(X,nil)
                        | ~ neq(V,nil) )
                      & ( ! [X3] :
                            ( ssItem(X3)
                           => ! [X4] :
                                ( ssList(X4)
                               => ! [X5] :
                                    ( ssList(X5)
                                   => ( ? [X6] :
                                          ( geq(X6,X3)
                                          & memberP(X,X6)
                                          & X3 != X6
                                          & ssItem(X6) )
                                      | app(X4,X5) != W
                                      | app(app(X4,cons(X3,nil)),X5) != X ) ) ) )
                        | ? [Y] :
                            ( ? [Z] :
                                ( ? [X1] :
                                    ( ! [X2] :
                                        ( ssItem(X2)
                                       => ( Y = X2
                                          | ~ geq(X2,Y)
                                          | ~ memberP(V,X2) ) )
                                    & app(Z,X1) = U
                                    & app(app(Z,cons(Y,nil)),X1) = V
                                    & ssList(X1) )
                                & ssList(Z) )
                            & ssItem(Y) )
                        | ~ neq(V,nil) ) )
                    | U != W
                    | V != X ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f95_neg,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( ( neq(X,nil)
                          | ~ neq(V,nil) )
                        & ( ! [X3] :
                              ( ssItem(X3)
                             => ! [X4] :
                                  ( ssList(X4)
                                 => ! [X5] :
                                      ( ssList(X5)
                                     => ( ? [X6] :
                                            ( geq(X6,X3)
                                            & memberP(X,X6)
                                            & X3 != X6
                                            & ssItem(X6) )
                                        | app(X4,X5) != W
                                        | app(app(X4,cons(X3,nil)),X5) != X ) ) ) )
                          | ? [Y] :
                              ( ? [Z] :
                                  ( ? [X1] :
                                      ( ! [X2] :
                                          ( ssItem(X2)
                                         => ( Y = X2
                                            | ~ geq(X2,Y)
                                            | ~ memberP(V,X2) ) )
                                      & app(Z,X1) = U
                                      & app(app(Z,cons(Y,nil)),X1) = V
                                      & ssList(X1) )
                                  & ssList(Z) )
                              & ssItem(Y) )
                          | ~ neq(V,nil) ) )
                      | U != W
                      | V != X ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f95]) ).

fof(f95_nnf,plain,
    ? [U] :
      ( ? [V] :
          ( ? [W] :
              ( ? [X] :
                  ( ( ( ~ neq(X,nil)
                      & neq(V,nil) )
                    | ( ? [X3] :
                          ( ? [X4] :
                              ( ? [X5] :
                                  ( ! [X6] :
                                      ( ~ geq(X6,X3)
                                      | ~ memberP(X,X6)
                                      | X3 = X6
                                      | ~ ssItem(X6) )
                                  & app(X4,X5) = W
                                  & app(app(X4,cons(X3,nil)),X5) = X
                                  & ssList(X5) )
                              & ssList(X4) )
                          & ssItem(X3) )
                      & ! [Y] :
                          ( ! [Z] :
                              ( ! [X1] :
                                  ( ? [X2] :
                                      ( Y != X2
                                      & geq(X2,Y)
                                      & memberP(V,X2)
                                      & ssItem(X2) )
                                  | app(Z,X1) != U
                                  | app(app(Z,cons(Y,nil)),X1) != V
                                  | ~ ssList(X1) )
                              | ~ ssList(Z) )
                          | ~ ssItem(Y) )
                      & neq(V,nil) ) )
                  & U = W
                  & V = X
                  & ssList(X) )
              & ssList(W) )
          & ssList(V) )
      & ssList(U) ),
    inference(nnf_transformation,[status(thm)],[f95_neg]) ).

fof(f95_sk,plain,
    ! [Y,Z,X1,X6] :
      ( ( ( ~ neq(sk50,nil)
          & neq(sk48,nil) )
        | ( ( ~ geq(X6,sk52)
            | ~ memberP(sk50,X6)
            | sk52 = X6
            | ~ ssItem(X6) )
          & app(sk53,sk54) = sk49
          & app(app(sk53,cons(sk52,nil)),sk54) = sk50
          & ssList(sk54)
          & ssList(sk53)
          & ssItem(sk52)
          & ( ( Y != sk51(Y,Z,X1)
              & geq(sk51(Y,Z,X1),Y)
              & memberP(sk48,sk51(Y,Z,X1))
              & ssItem(sk51(Y,Z,X1)) )
            | app(Z,X1) != sk47
            | app(app(Z,cons(Y,nil)),X1) != sk48
            | ~ ssList(X1)
            | ~ ssList(Z)
            | ~ ssItem(Y) )
          & 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,sk53,sk54])],[f95_nnf]) ).

cnf(c194,plain,
    sk48 = sk50,
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(c207,plain,
    ( ~ neq(sk50,nil)
    | ssItem(sk52) ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p225,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk52) ),
    inference(superposition,[status(thm)],[c194,c207]) ).

cnf(c196,plain,
    ( neq(sk48,nil)
    | neq(sk48,nil) ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p234,plain,
    neq(sk48,nil),
    inference(factoring,[status(thm)],[c196]) ).

cnf(p484,plain,
    ssItem(sk52),
    inference(resolution,[status(thm)],[p225,p234]) ).

cnf(c213,plain,
    ( ~ neq(sk50,nil)
    | app(app(sk53,cons(sk52,nil)),sk54) = sk50 ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p224,plain,
    ( ~ neq(sk48,nil)
    | app(app(sk53,cons(sk52,nil)),sk54) = sk50 ),
    inference(superposition,[status(thm)],[c194,c213]) ).

cnf(p238,plain,
    app(app(sk53,cons(sk52,nil)),sk54) = sk50,
    inference(resolution,[status(thm)],[p224,p234]) ).

cnf(p239,plain,
    sk50 = sk48,
    inference(superposition,[status(thm)],[c194,p238]) ).

cnf(c203,plain,
    ( ~ neq(sk50,nil)
    | geq(sk51(X4,X5,X6),X4)
    | app(X5,X6) != sk47
    | app(app(X5,cons(X4,nil)),X6) != sk48
    | ~ ssList(X6)
    | ~ ssList(X5)
    | ~ ssItem(X4) ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p242,plain,
    ( ~ neq(sk48,nil)
    | geq(sk51(X0,X1,X2),X0)
    | app(X1,X2) != sk47
    | app(app(X1,cons(X0,nil)),X2) != sk48
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X0) ),
    inference(demodulation,[status(thm)],[p239,c203]) ).

cnf(p489,plain,
    ( ~ neq(sk48,nil)
    | geq(sk51(sk52,X0,X1),sk52)
    | app(X0,X1) != sk47
    | app(app(X0,cons(sk52,nil)),X1) != sk48
    | ~ ssList(X1)
    | ~ ssList(X0) ),
    inference(resolution,[status(thm)],[p484,p242]) ).

cnf(c209,plain,
    ( ~ neq(sk50,nil)
    | ssList(sk53) ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p220,plain,
    ( ~ neq(sk48,nil)
    | ssList(sk53) ),
    inference(superposition,[status(thm)],[c194,c209]) ).

cnf(c208,plain,
    ( neq(sk48,nil)
    | ssList(sk53) ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p228,plain,
    ( ssList(sk53)
    | ssList(sk53) ),
    inference(resolution,[status(thm)],[p220,c208]) ).

cnf(p230,plain,
    ssList(sk53),
    inference(factoring,[status(thm)],[p228]) ).

cnf(p605,plain,
    ( ~ neq(sk48,nil)
    | geq(sk51(sk52,sk53,X0),sk52)
    | app(sk53,X0) != sk47
    | app(app(sk53,cons(sk52,nil)),X0) != sk48
    | ~ ssList(X0) ),
    inference(resolution,[status(thm)],[p489,p230]) ).

cnf(c211,plain,
    ( ~ neq(sk50,nil)
    | ssList(sk54) ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p221,plain,
    ( ~ neq(sk48,nil)
    | ssList(sk54) ),
    inference(superposition,[status(thm)],[c194,c211]) ).

cnf(c210,plain,
    ( neq(sk48,nil)
    | ssList(sk54) ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p232,plain,
    ( ssList(sk54)
    | ssList(sk54) ),
    inference(resolution,[status(thm)],[p221,c210]) ).

cnf(p233,plain,
    ssList(sk54),
    inference(factoring,[status(thm)],[p232]) ).

cnf(p621,plain,
    ( ~ neq(sk48,nil)
    | geq(sk51(sk52,sk53,sk54),sk52)
    | sk47 != sk47
    | sk48 != sk48 ),
    inference(resolution,[status(thm)],[p605,p233]) ).

cnf(p623,plain,
    ( ~ neq(sk48,nil)
    | geq(sk51(sk52,sk53,sk54),sk52)
    | sk47 != sk47 ),
    inference(equality_resolution,[status(thm)],[p621]) ).

cnf(p625,plain,
    ( ~ neq(sk48,nil)
    | geq(sk51(sk52,sk53,sk54),sk52) ),
    inference(equality_resolution,[status(thm)],[p623]) ).

cnf(p626,plain,
    geq(sk51(sk52,sk53,sk54),sk52),
    inference(resolution,[status(thm)],[p625,p234]) ).

cnf(c201,plain,
    ( ~ neq(sk50,nil)
    | memberP(sk48,sk51(X4,X5,X6))
    | app(X5,X6) != sk47
    | app(app(X5,cons(X4,nil)),X6) != sk48
    | ~ ssList(X6)
    | ~ ssList(X5)
    | ~ ssItem(X4) ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p241,plain,
    ( ~ neq(sk48,nil)
    | memberP(sk48,sk51(X0,X1,X2))
    | app(X1,X2) != sk47
    | app(app(X1,cons(X0,nil)),X2) != sk48
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X0) ),
    inference(demodulation,[status(thm)],[p239,c201]) ).

cnf(p487,plain,
    ( ~ neq(sk48,nil)
    | memberP(sk48,sk51(sk52,X0,X1))
    | app(X0,X1) != sk47
    | app(app(X0,cons(sk52,nil)),X1) != sk48
    | ~ ssList(X1)
    | ~ ssList(X0) ),
    inference(resolution,[status(thm)],[p484,p241]) ).

cnf(p575,plain,
    ( ~ neq(sk48,nil)
    | memberP(sk48,sk51(sk52,sk53,X0))
    | app(sk53,X0) != sk47
    | app(app(sk53,cons(sk52,nil)),X0) != sk48
    | ~ ssList(X0) ),
    inference(resolution,[status(thm)],[p487,p230]) ).

cnf(p588,plain,
    ( ~ neq(sk48,nil)
    | memberP(sk48,sk51(sk52,sk53,sk54))
    | sk47 != sk47
    | sk48 != sk48 ),
    inference(resolution,[status(thm)],[p575,p233]) ).

cnf(p590,plain,
    ( ~ neq(sk48,nil)
    | memberP(sk48,sk51(sk52,sk53,sk54))
    | sk47 != sk47 ),
    inference(equality_resolution,[status(thm)],[p588]) ).

cnf(p592,plain,
    ( ~ neq(sk48,nil)
    | memberP(sk48,sk51(sk52,sk53,sk54)) ),
    inference(equality_resolution,[status(thm)],[p590]) ).

cnf(p593,plain,
    memberP(sk48,sk51(sk52,sk53,sk54)),
    inference(resolution,[status(thm)],[p592,p234]) ).

cnf(c199,plain,
    ( ~ neq(sk50,nil)
    | ssItem(sk51(X4,X5,X6))
    | app(X5,X6) != sk47
    | app(app(X5,cons(X4,nil)),X6) != sk48
    | ~ ssList(X6)
    | ~ ssList(X5)
    | ~ ssItem(X4) ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p240,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(X0,X1,X2))
    | app(X1,X2) != sk47
    | app(app(X1,cons(X0,nil)),X2) != sk48
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X0) ),
    inference(demodulation,[status(thm)],[p239,c199]) ).

cnf(p486,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(sk52,X0,X1))
    | app(X0,X1) != sk47
    | app(app(X0,cons(sk52,nil)),X1) != sk48
    | ~ ssList(X1)
    | ~ ssList(X0) ),
    inference(resolution,[status(thm)],[p484,p240]) ).

cnf(p537,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(sk52,sk53,X0))
    | app(sk53,X0) != sk47
    | app(app(sk53,cons(sk52,nil)),X0) != sk48
    | ~ ssList(X0) ),
    inference(resolution,[status(thm)],[p486,p230]) ).

cnf(p550,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(sk52,sk53,sk54))
    | sk47 != sk47
    | sk48 != sk48 ),
    inference(resolution,[status(thm)],[p537,p233]) ).

cnf(p552,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(sk52,sk53,sk54))
    | sk47 != sk47 ),
    inference(equality_resolution,[status(thm)],[p550]) ).

cnf(p554,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(sk52,sk53,sk54)) ),
    inference(equality_resolution,[status(thm)],[p552]) ).

cnf(p555,plain,
    ssItem(sk51(sk52,sk53,sk54)),
    inference(resolution,[status(thm)],[p554,p234]) ).

cnf(c217,plain,
    ( ~ neq(sk50,nil)
    | ~ geq(X11,sk52)
    | ~ memberP(sk50,X11)
    | sk52 = X11
    | ~ ssItem(X11) ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p244,plain,
    ( ~ neq(sk48,nil)
    | ~ geq(X0,sk52)
    | ~ memberP(sk48,X0)
    | sk52 = X0
    | ~ ssItem(X0) ),
    inference(demodulation,[status(thm)],[p239,c217]) ).

cnf(p556,plain,
    ( ~ neq(sk48,nil)
    | ~ geq(sk51(sk52,sk53,sk54),sk52)
    | ~ memberP(sk48,sk51(sk52,sk53,sk54))
    | sk52 = sk51(sk52,sk53,sk54) ),
    inference(resolution,[status(thm)],[p555,p244]) ).

cnf(p594,plain,
    ( ~ neq(sk48,nil)
    | ~ geq(sk51(sk52,sk53,sk54),sk52)
    | sk52 = sk51(sk52,sk53,sk54) ),
    inference(resolution,[status(thm)],[p593,p556]) ).

cnf(p627,plain,
    ( ~ neq(sk48,nil)
    | sk52 = sk51(sk52,sk53,sk54) ),
    inference(resolution,[status(thm)],[p626,p594]) ).

cnf(p628,plain,
    sk52 = sk51(sk52,sk53,sk54),
    inference(resolution,[status(thm)],[p627,p234]) ).

cnf(p558,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(sk51(sk52,sk53,sk54),X0,X1))
    | app(X0,X1) != sk47
    | app(app(X0,cons(sk51(sk52,sk53,sk54),nil)),X1) != sk48
    | ~ ssList(X1)
    | ~ ssList(X0) ),
    inference(resolution,[status(thm)],[p555,p240]) ).

cnf(p663,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(sk51(sk52,sk53,sk54),sk53,X0))
    | app(sk53,X0) != sk47
    | app(app(sk53,cons(sk51(sk52,sk53,sk54),nil)),X0) != sk48
    | ~ ssList(X0) ),
    inference(resolution,[status(thm)],[p558,p230]) ).

cnf(p684,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(sk51(sk52,sk53,sk54),sk53,sk54))
    | sk47 != sk47
    | app(app(sk53,cons(sk51(sk52,sk53,sk54),nil)),sk54) != sk48 ),
    inference(resolution,[status(thm)],[p663,p233]) ).

cnf(p686,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(sk51(sk52,sk53,sk54),sk53,sk54))
    | app(app(sk53,cons(sk51(sk52,sk53,sk54),nil)),sk54) != sk48 ),
    inference(equality_resolution,[status(thm)],[p684]) ).

cnf(p687,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(sk51(sk52,sk53,sk54),sk53,sk54))
    | sk48 != sk48 ),
    inference(superposition,[status(thm)],[p628,p686]) ).

cnf(p688,plain,
    ( ~ neq(sk48,nil)
    | ssItem(sk51(sk51(sk52,sk53,sk54),sk53,sk54)) ),
    inference(equality_resolution,[status(thm)],[p687]) ).

cnf(p689,plain,
    ssItem(sk51(sk51(sk52,sk53,sk54),sk53,sk54)),
    inference(resolution,[status(thm)],[p688,p234]) ).

cnf(p690,plain,
    ( ~ neq(sk48,nil)
    | ~ geq(sk51(sk51(sk52,sk53,sk54),sk53,sk54),sk52)
    | ~ memberP(sk48,sk51(sk51(sk52,sk53,sk54),sk53,sk54))
    | sk52 = sk51(sk51(sk52,sk53,sk54),sk53,sk54) ),
    inference(resolution,[status(thm)],[p689,p244]) ).

cnf(p702,plain,
    ( ~ neq(sk48,nil)
    | ~ geq(sk51(sk51(sk52,sk53,sk54),sk53,sk54),sk52)
    | ~ memberP(sk48,sk51(sk52,sk53,sk54))
    | sk52 = sk51(sk51(sk52,sk53,sk54),sk53,sk54) ),
    inference(superposition,[status(thm)],[p628,p690]) ).

cnf(p703,plain,
    ( ~ neq(sk48,nil)
    | ~ geq(sk51(sk51(sk52,sk53,sk54),sk53,sk54),sk52)
    | sk52 = sk51(sk51(sk52,sk53,sk54),sk53,sk54) ),
    inference(resolution,[status(thm)],[p702,p593]) ).

cnf(p704,plain,
    ( ~ neq(sk48,nil)
    | ~ geq(sk51(sk52,sk53,sk54),sk52)
    | sk52 = sk51(sk51(sk52,sk53,sk54),sk53,sk54) ),
    inference(superposition,[status(thm)],[p628,p703]) ).

cnf(p705,plain,
    ( ~ neq(sk48,nil)
    | sk52 = sk51(sk51(sk52,sk53,sk54),sk53,sk54) ),
    inference(resolution,[status(thm)],[p704,p626]) ).

cnf(p706,plain,
    sk52 = sk51(sk51(sk52,sk53,sk54),sk53,sk54),
    inference(resolution,[status(thm)],[p705,p234]) ).

cnf(c205,plain,
    ( ~ neq(sk50,nil)
    | X4 != sk51(X4,X5,X6)
    | app(X5,X6) != sk47
    | app(app(X5,cons(X4,nil)),X6) != sk48
    | ~ ssList(X6)
    | ~ ssList(X5)
    | ~ ssItem(X4) ),
    inference(cnf_transformation,[status(esa)],[f95_sk]) ).

cnf(p243,plain,
    ( ~ neq(sk48,nil)
    | X0 != sk51(X0,X1,X2)
    | app(X1,X2) != sk47
    | app(app(X1,cons(X0,nil)),X2) != sk48
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X0) ),
    inference(demodulation,[status(thm)],[p239,c205]) ).

cnf(p563,plain,
    ( ~ neq(sk48,nil)
    | sk51(sk52,sk53,sk54) != sk51(sk51(sk52,sk53,sk54),X0,X1)
    | app(X0,X1) != sk47
    | app(app(X0,cons(sk51(sk52,sk53,sk54),nil)),X1) != sk48
    | ~ ssList(X1)
    | ~ ssList(X0) ),
    inference(resolution,[status(thm)],[p555,p243]) ).

cnf(p859,plain,
    ( ~ neq(sk48,nil)
    | sk51(sk52,sk53,sk54) != sk51(sk51(sk52,sk53,sk54),sk53,X0)
    | app(sk53,X0) != sk47
    | app(app(sk53,cons(sk51(sk52,sk53,sk54),nil)),X0) != sk48
    | ~ ssList(X0) ),
    inference(resolution,[status(thm)],[p563,p230]) ).

cnf(p880,plain,
    ( ~ neq(sk48,nil)
    | sk51(sk52,sk53,sk54) != sk51(sk51(sk52,sk53,sk54),sk53,sk54)
    | sk47 != sk47
    | app(app(sk53,cons(sk51(sk52,sk53,sk54),nil)),sk54) != sk48 ),
    inference(resolution,[status(thm)],[p859,p233]) ).

cnf(p882,plain,
    ( ~ neq(sk48,nil)
    | sk51(sk52,sk53,sk54) != sk51(sk51(sk52,sk53,sk54),sk53,sk54)
    | app(app(sk53,cons(sk51(sk52,sk53,sk54),nil)),sk54) != sk48 ),
    inference(equality_resolution,[status(thm)],[p880]) ).

cnf(p883,plain,
    ( ~ neq(sk48,nil)
    | sk51(sk52,sk53,sk54) != sk51(sk51(sk52,sk53,sk54),sk53,sk54)
    | sk48 != sk48 ),
    inference(superposition,[status(thm)],[p628,p882]) ).

cnf(p884,plain,
    ( ~ neq(sk48,nil)
    | sk51(sk52,sk53,sk54) != sk51(sk51(sk52,sk53,sk54),sk53,sk54) ),
    inference(equality_resolution,[status(thm)],[p883]) ).

cnf(p887,plain,
    ( ~ neq(sk48,nil)
    | sk51(sk52,sk53,sk54) != sk52 ),
    inference(superposition,[status(thm)],[p706,p884]) ).

cnf(p888,plain,
    ( ~ neq(sk48,nil)
    | sk52 != sk52 ),
    inference(superposition,[status(thm)],[p628,p887]) ).

cnf(p889,plain,
    ~ neq(sk48,nil),
    inference(equality_resolution,[status(thm)],[p888]) ).

cnf(p890,plain,
    $false,
    inference(resolution,[status(thm)],[p889,p234]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC002+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35  % Computer : n013.cluster.edu
% 0.08/0.35  % Model    : x86_64 x86_64
% 0.08/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35  % Memory   : 8046.5625MB
% 0.08/0.35  % OS       : Linux 6.8.0-71-generic
% 0.08/0.35  % CPULimit : 300
% 0.08/0.35  % WCLimit  : 300
% 0.08/0.35  % DateTime : Thu Sep 24 15:51:10 UTC 2026
% 0.12/0.35  % CPUTime  : 
% 0.12/0.35  Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.08/3.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.08/3.48  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------