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Drodi---4.1.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : SWC343+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n020.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 : Thu Sep 24 02:40:51 PM UTC 2026

% Result   : Theorem 0.12s 0.40s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   62 (  13 unt;   1 def)
%            Number of atoms       :  364 ( 134 equ)
%            Maximal formula atoms :   30 (   5 avg)
%            Number of connectives :  509 ( 207   ~; 180   |; 103   &)
%                                         (   1 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   8 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :  178 ( 138   !;  40   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f96,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( ( ( nil = V
                        | nil != U )
                      & ? [X4] :
                          ( strictorderedP(U)
                          & ! [X5] :
                              ( ssItem(X5)
                             => ! [X6] :
                                  ( ssList(X6)
                                 => ( ! [X7] :
                                        ( ssItem(X7)
                                       => ! [X8] :
                                            ( ssList(X8)
                                           => ( ~ lt(X7,X5)
                                              | app(X8,cons(X7,nil)) != U ) ) )
                                    | app(cons(X5,nil),X6) != X4 ) ) )
                          & app(U,X4) = V
                          & ssList(X4) ) )
                    | ( nil = W
                      & nil != X )
                    | ! [Y] :
                        ( ssList(Y)
                       => ( ? [Z] :
                              ( ? [X1] :
                                  ( ? [X2] :
                                      ( ? [X3] :
                                          ( lt(X2,Z)
                                          & app(X3,cons(X2,nil)) = W
                                          & ssList(X3) )
                                      & ssItem(X2) )
                                  & app(cons(Z,nil),X1) = Y
                                  & ssList(X1) )
                              & ssItem(Z) )
                          | ~ strictorderedP(W)
                          | app(W,Y) != X ) )
                    | U != W
                    | V != X ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f97,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( ( nil = V
                          | nil != U )
                        & ? [X4] :
                            ( strictorderedP(U)
                            & ! [X5] :
                                ( ssItem(X5)
                               => ! [X6] :
                                    ( ssList(X6)
                                   => ( ! [X7] :
                                          ( ssItem(X7)
                                         => ! [X8] :
                                              ( ssList(X8)
                                             => ( ~ lt(X7,X5)
                                                | app(X8,cons(X7,nil)) != U ) ) )
                                      | app(cons(X5,nil),X6) != X4 ) ) )
                            & app(U,X4) = V
                            & ssList(X4) ) )
                      | ( nil = W
                        & nil != X )
                      | ! [Y] :
                          ( ssList(Y)
                         => ( ? [Z] :
                                ( ? [X1] :
                                    ( ? [X2] :
                                        ( ? [X3] :
                                            ( lt(X2,Z)
                                            & app(X3,cons(X2,nil)) = W
                                            & ssList(X3) )
                                        & ssItem(X2) )
                                    & app(cons(Z,nil),X1) = Y
                                    & ssList(X1) )
                                & ssItem(Z) )
                            | ~ strictorderedP(W)
                            | app(W,Y) != X ) )
                      | U != W
                      | V != X ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f415,plain,
    ? [U] :
      ( ? [V] :
          ( ? [W] :
              ( ? [X] :
                  ( ( ( nil != V
                      & nil = U )
                    | ! [X4] :
                        ( ~ strictorderedP(U)
                        | ? [X5] :
                            ( ? [X6] :
                                ( ? [X7] :
                                    ( ? [X8] :
                                        ( lt(X7,X5)
                                        & app(X8,cons(X7,nil)) = U
                                        & ssList(X8) )
                                    & ssItem(X7) )
                                & app(cons(X5,nil),X6) = X4
                                & ssList(X6) )
                            & ssItem(X5) )
                        | app(U,X4) != V
                        | ~ ssList(X4) ) )
                  & ( nil != W
                    | nil = X )
                  & ? [Y] :
                      ( ! [Z] :
                          ( ! [X1] :
                              ( ! [X2] :
                                  ( ! [X3] :
                                      ( ~ lt(X2,Z)
                                      | app(X3,cons(X2,nil)) != W
                                      | ~ ssList(X3) )
                                  | ~ ssItem(X2) )
                              | app(cons(Z,nil),X1) != Y
                              | ~ ssList(X1) )
                          | ~ ssItem(Z) )
                      & strictorderedP(W)
                      & app(W,Y) = X
                      & ssList(Y) )
                  & U = W
                  & V = X
                  & ssList(X) )
              & ssList(W) )
          & ssList(V) )
      & ssList(U) ),
    inference(pre_NNF_transformation,[status(thm)],[f97]) ).

fof(f416,definition,
    ! [U,X4,X5] :
      ( sP0_prd(X5,X4,U)
    <=> ( ? [X6] :
            ( ? [X7] :
                ( ? [X8] :
                    ( lt(X7,X5)
                    & app(X8,cons(X7,nil)) = U
                    & ssList(X8) )
                & ssItem(X7) )
            & app(cons(X5,nil),X6) = X4
            & ssList(X6) )
        & ssItem(X5) ) ),
    introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).

fof(f417,plain,
    ? [U] :
      ( ? [V] :
          ( ? [W] :
              ( ? [X] :
                  ( ( ( nil != V
                      & nil = U )
                    | ! [X4] :
                        ( ~ strictorderedP(U)
                        | ? [X5] : sP0_prd(X5,X4,U)
                        | app(U,X4) != V
                        | ~ ssList(X4) ) )
                  & ( nil != W
                    | nil = X )
                  & ? [Y] :
                      ( ! [Z] :
                          ( ! [X1] :
                              ( ! [X2] :
                                  ( ! [X3] :
                                      ( ~ lt(X2,Z)
                                      | app(X3,cons(X2,nil)) != W
                                      | ~ ssList(X3) )
                                  | ~ ssItem(X2) )
                              | app(cons(Z,nil),X1) != Y
                              | ~ ssList(X1) )
                          | ~ ssItem(Z) )
                      & strictorderedP(W)
                      & app(W,Y) = X
                      & ssList(Y) )
                  & U = W
                  & V = X
                  & ssList(X) )
              & ssList(W) )
          & ssList(V) )
      & ssList(U) ),
    inference(formula_renaming,[status(thm)],[f415,f416]) ).

fof(f418,plain,
    ? [U] :
      ( ? [V] :
          ( ? [W] :
              ( ? [X] :
                  ( ( ( nil != V
                      & nil = U )
                    | ~ strictorderedP(U)
                    | ! [X4] :
                        ( ? [X5] : sP0_prd(X5,X4,U)
                        | app(U,X4) != V
                        | ~ ssList(X4) ) )
                  & ( nil != W
                    | nil = X )
                  & ? [Y] :
                      ( ! [Z] :
                          ( ! [X2] :
                              ( ~ lt(X2,Z)
                              | ! [X3] :
                                  ( app(X3,cons(X2,nil)) != W
                                  | ~ ssList(X3) )
                              | ~ ssItem(X2) )
                          | ! [X1] :
                              ( app(cons(Z,nil),X1) != Y
                              | ~ ssList(X1) )
                          | ~ ssItem(Z) )
                      & strictorderedP(W)
                      & app(W,Y) = X
                      & ssList(Y) )
                  & U = W
                  & V = X
                  & ssList(X) )
              & ssList(W) )
          & ssList(V) )
      & ssList(U) ),
    inference(miniscoping,[status(thm)],[f417]) ).

fof(f419,plain,
    ( ( ( nil != sK48_skl
        & nil = sK47_skl )
      | ~ strictorderedP(sK47_skl)
      | ! [X4] :
          ( sP0_prd(sK52_skl(X4),X4,sK47_skl)
          | app(sK47_skl,X4) != sK48_skl
          | ~ ssList(X4) ) )
    & ( nil != sK49_skl
      | nil = sK50_skl )
    & ! [Z] :
        ( ! [X2] :
            ( ~ lt(X2,Z)
            | ! [X3] :
                ( app(X3,cons(X2,nil)) != sK49_skl
                | ~ ssList(X3) )
            | ~ ssItem(X2) )
        | ! [X1] :
            ( app(cons(Z,nil),X1) != sK51_skl
            | ~ ssList(X1) )
        | ~ ssItem(Z) )
    & strictorderedP(sK49_skl)
    & app(sK49_skl,sK51_skl) = sK50_skl
    & ssList(sK51_skl)
    & sK47_skl = sK49_skl
    & sK48_skl = sK50_skl
    & ssList(sK50_skl)
    & ssList(sK49_skl)
    & ssList(sK48_skl)
    & ssList(sK47_skl) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(X5,sK52_skl(X4))],[f418]) ).

fof(f424,plain,
    sK48_skl = sK50_skl,
    inference(cnf_transformation,[status(thm)],[f419]) ).

fof(f425,plain,
    sK47_skl = sK49_skl,
    inference(cnf_transformation,[status(thm)],[f419]) ).

fof(f426,plain,
    ssList(sK51_skl),
    inference(cnf_transformation,[status(thm)],[f419]) ).

fof(f427,plain,
    app(sK49_skl,sK51_skl) = sK50_skl,
    inference(cnf_transformation,[status(thm)],[f419]) ).

fof(f428,plain,
    strictorderedP(sK49_skl),
    inference(cnf_transformation,[status(thm)],[f419]) ).

fof(f429,plain,
    ! [X0,X1,X2,X3] :
      ( ~ lt(X2,X0)
      | app(X3,cons(X2,nil)) != sK49_skl
      | ~ ssList(X3)
      | ~ ssItem(X2)
      | app(cons(X0,nil),X1) != sK51_skl
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[status(thm)],[f419]) ).

fof(f430,plain,
    ( nil != sK49_skl
    | nil = sK50_skl ),
    inference(cnf_transformation,[status(thm)],[f419]) ).

fof(f431,plain,
    ! [X0] :
      ( nil = sK47_skl
      | ~ strictorderedP(sK47_skl)
      | sP0_prd(sK52_skl(X0),X0,sK47_skl)
      | app(sK47_skl,X0) != sK48_skl
      | ~ ssList(X0) ),
    inference(cnf_transformation,[status(thm)],[f419]) ).

fof(f432,plain,
    ! [X0] :
      ( nil != sK48_skl
      | ~ strictorderedP(sK47_skl)
      | sP0_prd(sK52_skl(X0),X0,sK47_skl)
      | app(sK47_skl,X0) != sK48_skl
      | ~ ssList(X0) ),
    inference(cnf_transformation,[status(thm)],[f419]) ).

fof(f433,plain,
    ! [U,X4,X5] :
      ( ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ~ lt(X7,X5)
                    | app(X8,cons(X7,nil)) != U
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | app(cons(X5,nil),X6) != X4
            | ~ ssList(X6) )
        | ~ ssItem(X5)
        | sP0_prd(X5,X4,U) )
      & ( ( ? [X6] :
              ( ? [X7] :
                  ( ? [X8] :
                      ( lt(X7,X5)
                      & app(X8,cons(X7,nil)) = U
                      & ssList(X8) )
                  & ssItem(X7) )
              & app(cons(X5,nil),X6) = X4
              & ssList(X6) )
          & ssItem(X5) )
        | ~ sP0_prd(X5,X4,U) ) ),
    inference(NNF_transformation,[status(thm)],[f416]) ).

fof(f434,plain,
    ( ! [U,X4,X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ~ lt(X7,X5)
                    | app(X8,cons(X7,nil)) != U
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | app(cons(X5,nil),X6) != X4
            | ~ ssList(X6) )
        | ~ ssItem(X5)
        | sP0_prd(X5,X4,U) )
    & ! [U,X4,X5] :
        ( ( ? [X6] :
              ( ? [X7] :
                  ( ? [X8] :
                      ( lt(X7,X5)
                      & app(X8,cons(X7,nil)) = U
                      & ssList(X8) )
                  & ssItem(X7) )
              & app(cons(X5,nil),X6) = X4
              & ssList(X6) )
          & ssItem(X5) )
        | ~ sP0_prd(X5,X4,U) ) ),
    inference(miniscoping,[status(thm)],[f433]) ).

fof(f435,plain,
    ( ! [U,X4,X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ~ lt(X7,X5)
                    | app(X8,cons(X7,nil)) != U
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | app(cons(X5,nil),X6) != X4
            | ~ ssList(X6) )
        | ~ ssItem(X5)
        | sP0_prd(X5,X4,U) )
    & ! [U,X4,X5] :
        ( ( lt(sK54_skl(X5,X4,U),X5)
          & app(sK55_skl(X5,X4,U),cons(sK54_skl(X5,X4,U),nil)) = U
          & ssList(sK55_skl(X5,X4,U))
          & ssItem(sK54_skl(X5,X4,U))
          & app(cons(X5,nil),sK53_skl(X5,X4,U)) = X4
          & ssList(sK53_skl(X5,X4,U))
          & ssItem(X5) )
        | ~ sP0_prd(X5,X4,U) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl,sK54_skl,sK55_skl]),skolemize(X6,sK53_skl(X5,X4,U)),skolemize(X7,sK54_skl(X5,X4,U)),skolemize(X8,sK55_skl(X5,X4,U))],[f434]) ).

fof(f436,plain,
    ! [X0,X1,X2] :
      ( ssItem(X0)
      | ~ sP0_prd(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f435]) ).

fof(f437,plain,
    ! [X0,X1,X2] :
      ( ssList(sK53_skl(X0,X1,X2))
      | ~ sP0_prd(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f435]) ).

fof(f438,plain,
    ! [X0,X1,X2] :
      ( app(cons(X0,nil),sK53_skl(X0,X1,X2)) = X1
      | ~ sP0_prd(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f435]) ).

fof(f439,plain,
    ! [X0,X1,X2] :
      ( ssItem(sK54_skl(X0,X1,X2))
      | ~ sP0_prd(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f435]) ).

fof(f440,plain,
    ! [X0,X1,X2] :
      ( ssList(sK55_skl(X0,X1,X2))
      | ~ sP0_prd(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f435]) ).

fof(f441,plain,
    ! [X0,X1,X2] :
      ( app(sK55_skl(X0,X1,X2),cons(sK54_skl(X0,X1,X2),nil)) = X2
      | ~ sP0_prd(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f435]) ).

fof(f442,plain,
    ! [X0,X1,X2] :
      ( lt(sK54_skl(X0,X1,X2),X0)
      | ~ sP0_prd(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f435]) ).

fof(f477,plain,
    strictorderedP(sK47_skl),
    inference(forward_demodulation,[status(thm)],[f425,f428]) ).

fof(f479,plain,
    app(sK47_skl,sK51_skl) = sK50_skl,
    inference(forward_demodulation,[status(thm)],[f425,f427]) ).

fof(f480,plain,
    app(sK47_skl,sK51_skl) = sK48_skl,
    inference(forward_demodulation,[status(thm)],[f424,f479]) ).

fof(f481,plain,
    ( nil != sK49_skl
    | nil = sK48_skl ),
    inference(forward_demodulation,[status(thm)],[f424,f430]) ).

fof(f482,plain,
    ( nil != sK47_skl
    | nil = sK48_skl ),
    inference(forward_demodulation,[status(thm)],[f425,f481]) ).

fof(f483,plain,
    ! [X0,X1,X2,X3] :
      ( ~ lt(X2,X0)
      | app(X3,cons(X2,nil)) != sK47_skl
      | ~ ssList(X3)
      | ~ ssItem(X2)
      | app(cons(X0,nil),X1) != sK51_skl
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(forward_demodulation,[status(thm)],[f425,f429]) ).

fof(f487,plain,
    ! [X0] :
      ( nil = sK47_skl
      | sP0_prd(sK52_skl(X0),X0,sK47_skl)
      | app(sK47_skl,X0) != sK48_skl
      | ~ ssList(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f431,f477]) ).

fof(f514,plain,
    ! [X0,X1,X2,X3] :
      ( ~ lt(X2,X0)
      | app(X3,cons(X2,nil)) != sK47_skl
      | ~ ssList(X3)
      | ~ ssItem(X2)
      | ~ ssList(sK53_skl(X0,sK51_skl,X1))
      | ~ ssItem(X0)
      | ~ sP0_prd(X0,sK51_skl,X1) ),
    inference(resolution,[status(thm)],[f438,f483]) ).

fof(f515,plain,
    ! [X0,X1,X2,X3] :
      ( ~ lt(X2,X0)
      | app(X3,cons(X2,nil)) != sK47_skl
      | ~ ssList(X3)
      | ~ ssItem(X2)
      | ~ ssList(sK53_skl(X0,sK51_skl,X1))
      | ~ sP0_prd(X0,sK51_skl,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f514,f436]) ).

fof(f521,plain,
    ! [X0] :
      ( nil != sK48_skl
      | sP0_prd(sK52_skl(X0),X0,sK47_skl)
      | app(sK47_skl,X0) != sK48_skl
      | ~ ssList(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f432,f477]) ).

fof(f710,plain,
    ! [X0,X1,X2,X3] :
      ( ~ lt(X2,X0)
      | app(X3,cons(X2,nil)) != sK47_skl
      | ~ ssList(X3)
      | ~ ssItem(X2)
      | ~ sP0_prd(X0,sK51_skl,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f515,f437]) ).

fof(f712,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sP0_prd(X2,X3,sK47_skl)
      | ~ lt(sK54_skl(X2,X3,sK47_skl),X0)
      | ~ ssList(sK55_skl(X2,X3,sK47_skl))
      | ~ ssItem(sK54_skl(X2,X3,sK47_skl))
      | ~ sP0_prd(X0,sK51_skl,X1) ),
    inference(resolution,[status(thm)],[f710,f441]) ).

fof(f714,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sP0_prd(X2,X3,sK47_skl)
      | ~ lt(sK54_skl(X2,X3,sK47_skl),X0)
      | ~ ssList(sK55_skl(X2,X3,sK47_skl))
      | ~ sP0_prd(X0,sK51_skl,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f712,f439]) ).

fof(f790,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sP0_prd(X2,X3,sK47_skl)
      | ~ lt(sK54_skl(X2,X3,sK47_skl),X0)
      | ~ sP0_prd(X0,sK51_skl,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f714,f440]) ).

fof(f792,plain,
    ! [X0,X1,X2] :
      ( ~ sP0_prd(X0,X2,sK47_skl)
      | ~ sP0_prd(X0,X2,sK47_skl)
      | ~ sP0_prd(X0,sK51_skl,X1) ),
    inference(resolution,[status(thm)],[f790,f442]) ).

fof(f796,plain,
    ! [X0,X1,X2] :
      ( ~ sP0_prd(X0,X2,sK47_skl)
      | ~ sP0_prd(X0,sK51_skl,X1) ),
    inference(duplicate_literals_removal,[status(thm)],[f792]) ).

fof(f802,plain,
    ! [X0] :
      ( nil != sK48_skl
      | app(sK47_skl,sK51_skl) != sK48_skl
      | ~ ssList(sK51_skl)
      | ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
    inference(resolution,[status(thm)],[f796,f521]) ).

fof(f803,plain,
    ! [X0] :
      ( nil = sK47_skl
      | app(sK47_skl,sK51_skl) != sK48_skl
      | ~ ssList(sK51_skl)
      | ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
    inference(resolution,[status(thm)],[f796,f487]) ).

fof(f804,plain,
    ! [X0] :
      ( nil != sK48_skl
      | sK48_skl != sK48_skl
      | ~ ssList(sK51_skl)
      | ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
    inference(forward_demodulation,[status(thm)],[f480,f802]) ).

fof(f805,plain,
    ! [X0] :
      ( nil != sK48_skl
      | ~ ssList(sK51_skl)
      | ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
    inference(trivial_equality_resolution,[status(thm)],[f804]) ).

fof(f806,plain,
    ! [X0] :
      ( nil != sK48_skl
      | ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
    inference(forward_subsumption_resolution,[status(thm)],[f805,f426]) ).

fof(f807,plain,
    ! [X0] :
      ( nil = sK47_skl
      | sK48_skl != sK48_skl
      | ~ ssList(sK51_skl)
      | ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
    inference(forward_demodulation,[status(thm)],[f480,f803]) ).

fof(f808,plain,
    ! [X0] :
      ( nil = sK47_skl
      | ~ ssList(sK51_skl)
      | ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
    inference(trivial_equality_resolution,[status(thm)],[f807]) ).

fof(f809,plain,
    ! [X0] :
      ( nil = sK47_skl
      | ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
    inference(forward_subsumption_resolution,[status(thm)],[f808,f426]) ).

fof(f810,plain,
    ( nil != sK48_skl
    | app(sK47_skl,sK51_skl) != sK48_skl
    | ~ ssList(sK51_skl)
    | nil != sK48_skl ),
    inference(resolution,[status(thm)],[f806,f521]) ).

fof(f812,plain,
    ( nil != sK48_skl
    | sK48_skl != sK48_skl
    | ~ ssList(sK51_skl)
    | nil != sK48_skl ),
    inference(forward_demodulation,[status(thm)],[f480,f810]) ).

fof(f813,plain,
    ( sK48_skl != sK48_skl
    | ~ ssList(sK51_skl)
    | nil != sK48_skl ),
    inference(duplicate_literals_removal,[status(thm)],[f812]) ).

fof(f814,plain,
    ( ~ ssList(sK51_skl)
    | nil != sK48_skl ),
    inference(trivial_equality_resolution,[status(thm)],[f813]) ).

fof(f815,plain,
    nil != sK48_skl,
    inference(forward_subsumption_resolution,[status(thm)],[f814,f426]) ).

fof(f818,plain,
    nil != sK47_skl,
    inference(backward_subsumption_resolution,[status(thm)],[f482,f815]) ).

fof(f821,plain,
    ! [X0] :
      ( sP0_prd(sK52_skl(X0),X0,sK47_skl)
      | app(sK47_skl,X0) != sK48_skl
      | ~ ssList(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[f487,f818]) ).

fof(f822,plain,
    ! [X0] : ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl),
    inference(forward_subsumption_resolution,[status(thm)],[f809,f818]) ).

fof(f823,plain,
    ( app(sK47_skl,sK51_skl) != sK48_skl
    | ~ ssList(sK51_skl) ),
    inference(resolution,[status(thm)],[f821,f822]) ).

fof(f827,plain,
    ( sK48_skl != sK48_skl
    | ~ ssList(sK51_skl) ),
    inference(forward_demodulation,[status(thm)],[f480,f823]) ).

fof(f828,plain,
    ~ ssList(sK51_skl),
    inference(trivial_equality_resolution,[status(thm)],[f827]) ).

fof(f829,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f828,f426]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC343+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35  % Computer : n020.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 : Mon Sep 21 08:18:17 UTC 2026
% 0.08/0.35  % CPUTime  : 
% 0.08/0.37  % Drodi V4.1.1
% 0.12/0.40  % Refutation found
% 0.12/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44  % Elapsed time: 0.076417 seconds
% 0.12/0.44  % CPU time: 0.266905 seconds
% 0.12/0.44  % Total memory used: 112.760 MB
% 0.12/0.44  % Net memory used: 112.486 MB
%------------------------------------------------------------------------------