TSTP Solution File: SWC181+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWC181+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n007.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 : Tue Apr 30 20:44:51 EDT 2024

% Result   : Theorem 19.49s 2.83s
% Output   : CNFRefutation 19.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   89 (  12 unt;   0 def)
%            Number of atoms       :  423 (  78 equ)
%            Maximal formula atoms :   27 (   4 avg)
%            Number of connectives :  535 ( 201   ~; 195   |;  93   &)
%                                         (  16 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   19 (  17 usr;  13 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;   7 con; 0-2 aty)
%            Number of variables   :  152 ( 114   !;  38   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f12,axiom,
    ! [U] :
      ( ssList(U)
     => ( strictorderedP(U)
      <=> ! [V] :
            ( ssItem(V)
           => ! [W] :
                ( ssItem(W)
               => ! [X] :
                    ( ssList(X)
                   => ! [Y] :
                        ( ssList(Y)
                       => ! [Z] :
                            ( ssList(Z)
                           => ( app(app(X,cons(V,Y)),cons(W,Z)) = U
                             => lt(V,W) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [U] :
      ( ssList(U)
     => ( duplicatefreeP(U)
      <=> ! [V] :
            ( ssItem(V)
           => ! [W] :
                ( ssItem(W)
               => ! [X] :
                    ( ssList(X)
                   => ! [Y] :
                        ( ssList(Y)
                       => ! [Z] :
                            ( ssList(Z)
                           => ( app(app(X,cons(V,Y)),cons(W,Z)) = U
                             => V != W ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f26,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ssList(app(U,V)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    ! [U] :
      ( ssList(U)
     => app(nil,U) = U ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f90,axiom,
    ! [U] :
      ( ssItem(U)
     => ~ lt(U,U) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f96,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( V != X
                    | U != W
                    | ! [Y] :
                        ( ssList(Y)
                       => ! [Z] :
                            ( ssList(Z)
                           => ( app(app(Y,W),Z) != X
                              | ~ strictorderedP(W)
                              | ? [X1] :
                                  ( ssItem(X1)
                                  & ? [X2] :
                                      ( ssList(X2)
                                      & app(X2,cons(X1,nil)) = Y
                                      & ? [X3] :
                                          ( ssItem(X3)
                                          & ? [X4] :
                                              ( ssList(X4)
                                              & app(cons(X3,nil),X4) = W
                                              & lt(X1,X3) ) ) ) )
                              | ? [X5] :
                                  ( ssItem(X5)
                                  & ? [X6] :
                                      ( ssList(X6)
                                      & app(cons(X5,nil),X6) = Z
                                      & ? [X7] :
                                          ( ssItem(X7)
                                          & ? [X8] :
                                              ( ssList(X8)
                                              & app(X8,cons(X7,nil)) = W
                                              & lt(X7,X5) ) ) ) ) ) ) )
                    | duplicatefreeP(U)
                    | ( nil != X
                      & nil = W ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f185,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( strictorderedP(U)
      <=> ! [V] :
            ( ~ ssItem(V)
            | ! [W] :
                ( ~ ssItem(W)
                | ! [X] :
                    ( ~ ssList(X)
                    | ! [Y] :
                        ( ~ ssList(Y)
                        | ! [Z] :
                            ( ~ ssList(Z)
                            | app(app(X,cons(V,Y)),cons(W,Z)) != U
                            | lt(V,W) ) ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f186,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ strictorderedP(U)
          | ! [V] :
              ( ~ ssItem(V)
              | ! [W] :
                  ( ~ ssItem(W)
                  | ! [X] :
                      ( ~ ssList(X)
                      | ! [Y] :
                          ( ~ ssList(Y)
                          | ! [Z] :
                              ( ~ ssList(Z)
                              | app(app(X,cons(V,Y)),cons(W,Z)) != U
                              | lt(V,W) ) ) ) ) ) )
        & ( strictorderedP(U)
          | ? [V] :
              ( ssItem(V)
              & ? [W] :
                  ( ssItem(W)
                  & ? [X] :
                      ( ssList(X)
                      & ? [Y] :
                          ( ssList(Y)
                          & ? [Z] :
                              ( ssList(Z)
                              & app(app(X,cons(V,Y)),cons(W,Z)) = U
                              & ~ lt(V,W) ) ) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f185]) ).

fof(f187,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ strictorderedP(U)
          | ! [V] :
              ( ~ ssItem(V)
              | ! [W] :
                  ( ~ ssItem(W)
                  | ! [X] :
                      ( ~ ssList(X)
                      | ! [Y] :
                          ( ~ ssList(Y)
                          | ! [Z] :
                              ( ~ ssList(Z)
                              | app(app(X,cons(V,Y)),cons(W,Z)) != U
                              | lt(V,W) ) ) ) ) ) )
        & ( strictorderedP(U)
          | ( ssItem(sk0_29(U))
            & ssItem(sk0_30(U))
            & ssList(sk0_31(U))
            & ssList(sk0_32(U))
            & ssList(sk0_33(U))
            & app(app(sk0_31(U),cons(sk0_29(U),sk0_32(U))),cons(sk0_30(U),sk0_33(U))) = U
            & ~ lt(sk0_29(U),sk0_30(U)) ) ) ) ),
    inference(skolemization,[status(esa)],[f186]) ).

fof(f188,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ ssList(X0)
      | ~ strictorderedP(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X2)
      | ~ ssList(X3)
      | ~ ssList(X4)
      | ~ ssList(X5)
      | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
      | lt(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f187]) ).

fof(f196,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( duplicatefreeP(U)
      <=> ! [V] :
            ( ~ ssItem(V)
            | ! [W] :
                ( ~ ssItem(W)
                | ! [X] :
                    ( ~ ssList(X)
                    | ! [Y] :
                        ( ~ ssList(Y)
                        | ! [Z] :
                            ( ~ ssList(Z)
                            | app(app(X,cons(V,Y)),cons(W,Z)) != U
                            | V != W ) ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f197,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ duplicatefreeP(U)
          | ! [V] :
              ( ~ ssItem(V)
              | ! [W] :
                  ( ~ ssItem(W)
                  | ! [X] :
                      ( ~ ssList(X)
                      | ! [Y] :
                          ( ~ ssList(Y)
                          | ! [Z] :
                              ( ~ ssList(Z)
                              | app(app(X,cons(V,Y)),cons(W,Z)) != U
                              | V != W ) ) ) ) ) )
        & ( duplicatefreeP(U)
          | ? [V] :
              ( ssItem(V)
              & ? [W] :
                  ( ssItem(W)
                  & ? [X] :
                      ( ssList(X)
                      & ? [Y] :
                          ( ssList(Y)
                          & ? [Z] :
                              ( ssList(Z)
                              & app(app(X,cons(V,Y)),cons(W,Z)) = U
                              & V = W ) ) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f196]) ).

fof(f198,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ duplicatefreeP(U)
          | ! [V] :
              ( ~ ssItem(V)
              | ! [W] :
                  ( ~ ssItem(W)
                  | ! [X] :
                      ( ~ ssList(X)
                      | ! [Y] :
                          ( ~ ssList(Y)
                          | ! [Z] :
                              ( ~ ssList(Z)
                              | app(app(X,cons(V,Y)),cons(W,Z)) != U
                              | V != W ) ) ) ) ) )
        & ( duplicatefreeP(U)
          | ( ssItem(sk0_34(U))
            & ssItem(sk0_35(U))
            & ssList(sk0_36(U))
            & ssList(sk0_37(U))
            & ssList(sk0_38(U))
            & app(app(sk0_36(U),cons(sk0_34(U),sk0_37(U))),cons(sk0_35(U),sk0_38(U))) = U
            & sk0_34(U) = sk0_35(U) ) ) ) ),
    inference(skolemization,[status(esa)],[f197]) ).

fof(f200,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | duplicatefreeP(X0)
      | ssItem(sk0_34(X0)) ),
    inference(cnf_transformation,[status(esa)],[f198]) ).

fof(f202,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | duplicatefreeP(X0)
      | ssList(sk0_36(X0)) ),
    inference(cnf_transformation,[status(esa)],[f198]) ).

fof(f203,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | duplicatefreeP(X0)
      | ssList(sk0_37(X0)) ),
    inference(cnf_transformation,[status(esa)],[f198]) ).

fof(f204,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | duplicatefreeP(X0)
      | ssList(sk0_38(X0)) ),
    inference(cnf_transformation,[status(esa)],[f198]) ).

fof(f205,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | duplicatefreeP(X0)
      | app(app(sk0_36(X0),cons(sk0_34(X0),sk0_37(X0))),cons(sk0_35(X0),sk0_38(X0))) = X0 ),
    inference(cnf_transformation,[status(esa)],[f198]) ).

fof(f206,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | duplicatefreeP(X0)
      | sk0_34(X0) = sk0_35(X0) ),
    inference(cnf_transformation,[status(esa)],[f198]) ).

fof(f223,plain,
    ssList(nil),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f244,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ssList(app(U,V)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f26]) ).

fof(f245,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f244]) ).

fof(f248,plain,
    ! [U] :
      ( ~ ssList(U)
      | app(nil,U) = U ),
    inference(pre_NNF_transformation,[status(esa)],[f28]) ).

fof(f249,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[status(esa)],[f248]) ).

fof(f400,plain,
    ! [U] :
      ( ~ ssItem(U)
      | ~ lt(U,U) ),
    inference(pre_NNF_transformation,[status(esa)],[f90]) ).

fof(f401,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ lt(X0,X0) ),
    inference(cnf_transformation,[status(esa)],[f400]) ).

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

fof(f416,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ? [Y] :
                      ( ssList(Y)
                      & ? [Z] :
                          ( ssList(Z)
                          & app(app(Y,W),Z) = X
                          & strictorderedP(W)
                          & ! [X1] :
                              ( ~ ssItem(X1)
                              | ! [X2] :
                                  ( ~ ssList(X2)
                                  | app(X2,cons(X1,nil)) != Y )
                              | ! [X3] :
                                  ( ~ ssItem(X3)
                                  | ! [X4] :
                                      ( ~ ssList(X4)
                                      | app(cons(X3,nil),X4) != W )
                                  | ~ lt(X1,X3) ) )
                          & ! [X5] :
                              ( ~ ssItem(X5)
                              | ! [X6] :
                                  ( ~ ssList(X6)
                                  | app(cons(X5,nil),X6) != Z )
                              | ! [X7] :
                                  ( ~ ssItem(X7)
                                  | ! [X8] :
                                      ( ~ ssList(X8)
                                      | app(X8,cons(X7,nil)) != W )
                                  | ~ lt(X7,X5) ) ) ) )
                  & ~ duplicatefreeP(U)
                  & ( nil = X
                    | nil != W ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f415]) ).

fof(f417,plain,
    ( ssList(sk0_47)
    & ssList(sk0_48)
    & ssList(sk0_49)
    & ssList(sk0_50)
    & sk0_48 = sk0_50
    & sk0_47 = sk0_49
    & ssList(sk0_51)
    & ssList(sk0_52)
    & app(app(sk0_51,sk0_49),sk0_52) = sk0_50
    & strictorderedP(sk0_49)
    & ! [X1] :
        ( ~ ssItem(X1)
        | ! [X2] :
            ( ~ ssList(X2)
            | app(X2,cons(X1,nil)) != sk0_51 )
        | ! [X3] :
            ( ~ ssItem(X3)
            | ! [X4] :
                ( ~ ssList(X4)
                | app(cons(X3,nil),X4) != sk0_49 )
            | ~ lt(X1,X3) ) )
    & ! [X5] :
        ( ~ ssItem(X5)
        | ! [X6] :
            ( ~ ssList(X6)
            | app(cons(X5,nil),X6) != sk0_52 )
        | ! [X7] :
            ( ~ ssItem(X7)
            | ! [X8] :
                ( ~ ssList(X8)
                | app(X8,cons(X7,nil)) != sk0_49 )
            | ~ lt(X7,X5) ) )
    & ~ duplicatefreeP(sk0_47)
    & ( nil = sk0_50
      | nil != sk0_49 ) ),
    inference(skolemization,[status(esa)],[f416]) ).

fof(f418,plain,
    ssList(sk0_47),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f423,plain,
    sk0_47 = sk0_49,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f427,plain,
    strictorderedP(sk0_49),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f430,plain,
    ~ duplicatefreeP(sk0_47),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f450,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X4)
      | lt(X1,X3) ),
    inference(destructive_equality_resolution,[status(esa)],[f188]) ).

fof(f471,plain,
    strictorderedP(sk0_47),
    inference(forward_demodulation,[status(thm)],[f423,f427]) ).

fof(f476,plain,
    app(nil,sk0_47) = sk0_47,
    inference(resolution,[status(thm)],[f249,f418]) ).

fof(f528,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssList(app(X0,sk0_47)) ),
    inference(resolution,[status(thm)],[f245,f418]) ).

fof(f576,plain,
    ( spl0_2
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f578,plain,
    ( ~ ssList(nil)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f576]) ).

fof(f584,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f578,f223]) ).

fof(f585,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f584]) ).

fof(f625,plain,
    ( spl0_5
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f628,plain,
    ( ~ ssList(nil)
    | ssList(sk0_47) ),
    inference(paramodulation,[status(thm)],[f476,f528]) ).

fof(f629,plain,
    ( ~ spl0_2
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f628,f576,f625]) ).

fof(f1724,plain,
    ( spl0_25
  <=> ssItem(sk0_34(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f1725,plain,
    ( ssItem(sk0_34(sk0_47))
    | ~ spl0_25 ),
    inference(component_clause,[status(thm)],[f1724]) ).

fof(f1727,plain,
    ( ~ ssList(sk0_47)
    | ssItem(sk0_34(sk0_47)) ),
    inference(resolution,[status(thm)],[f200,f430]) ).

fof(f1728,plain,
    ( ~ spl0_5
    | spl0_25 ),
    inference(split_clause,[status(thm)],[f1727,f625,f1724]) ).

fof(f1738,plain,
    ( spl0_27
  <=> ssList(sk0_36(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f1741,plain,
    ( ~ ssList(sk0_47)
    | ssList(sk0_36(sk0_47)) ),
    inference(resolution,[status(thm)],[f202,f430]) ).

fof(f1742,plain,
    ( ~ spl0_5
    | spl0_27 ),
    inference(split_clause,[status(thm)],[f1741,f625,f1738]) ).

fof(f1745,plain,
    ( spl0_28
  <=> ssList(sk0_37(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f1748,plain,
    ( ~ ssList(sk0_47)
    | ssList(sk0_37(sk0_47)) ),
    inference(resolution,[status(thm)],[f203,f430]) ).

fof(f1749,plain,
    ( ~ spl0_5
    | spl0_28 ),
    inference(split_clause,[status(thm)],[f1748,f625,f1745]) ).

fof(f1840,plain,
    ( ~ lt(sk0_34(sk0_47),sk0_34(sk0_47))
    | ~ spl0_25 ),
    inference(resolution,[status(thm)],[f1725,f401]) ).

fof(f3300,plain,
    ( spl0_151
  <=> ssList(sk0_38(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f3303,plain,
    ( ~ ssList(sk0_47)
    | ssList(sk0_38(sk0_47)) ),
    inference(resolution,[status(thm)],[f204,f430]) ).

fof(f3304,plain,
    ( ~ spl0_5
    | spl0_151 ),
    inference(split_clause,[status(thm)],[f3303,f625,f3300]) ).

fof(f4326,plain,
    ( spl0_219
  <=> sk0_34(sk0_47) = sk0_35(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f4327,plain,
    ( sk0_34(sk0_47) = sk0_35(sk0_47)
    | ~ spl0_219 ),
    inference(component_clause,[status(thm)],[f4326]) ).

fof(f4329,plain,
    ( ~ ssList(sk0_47)
    | sk0_34(sk0_47) = sk0_35(sk0_47) ),
    inference(resolution,[status(thm)],[f206,f430]) ).

fof(f4330,plain,
    ( ~ spl0_5
    | spl0_219 ),
    inference(split_clause,[status(thm)],[f4329,f625,f4326]) ).

fof(f11309,plain,
    ( spl0_489
  <=> app(app(sk0_36(sk0_47),cons(sk0_34(sk0_47),sk0_37(sk0_47))),cons(sk0_35(sk0_47),sk0_38(sk0_47))) = sk0_47 ),
    introduced(split_symbol_definition) ).

fof(f11310,plain,
    ( app(app(sk0_36(sk0_47),cons(sk0_34(sk0_47),sk0_37(sk0_47))),cons(sk0_35(sk0_47),sk0_38(sk0_47))) = sk0_47
    | ~ spl0_489 ),
    inference(component_clause,[status(thm)],[f11309]) ).

fof(f11312,plain,
    ( ~ ssList(sk0_47)
    | app(app(sk0_36(sk0_47),cons(sk0_34(sk0_47),sk0_37(sk0_47))),cons(sk0_35(sk0_47),sk0_38(sk0_47))) = sk0_47 ),
    inference(resolution,[status(thm)],[f205,f430]) ).

fof(f11313,plain,
    ( ~ spl0_5
    | spl0_489 ),
    inference(split_clause,[status(thm)],[f11312,f625,f11309]) ).

fof(f11496,plain,
    ( spl0_493
  <=> lt(sk0_34(sk0_47),sk0_34(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f11497,plain,
    ( lt(sk0_34(sk0_47),sk0_34(sk0_47))
    | ~ spl0_493 ),
    inference(component_clause,[status(thm)],[f11496]) ).

fof(f11514,plain,
    ( spl0_497
  <=> duplicatefreeP(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f11515,plain,
    ( duplicatefreeP(sk0_47)
    | ~ spl0_497 ),
    inference(component_clause,[status(thm)],[f11514]) ).

fof(f11519,plain,
    ( spl0_498
  <=> strictorderedP(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f11521,plain,
    ( ~ strictorderedP(sk0_47)
    | spl0_498 ),
    inference(component_clause,[status(thm)],[f11519]) ).

fof(f11589,plain,
    ( $false
    | spl0_498 ),
    inference(forward_subsumption_resolution,[status(thm)],[f11521,f471]) ).

fof(f11590,plain,
    spl0_498,
    inference(contradiction_clause,[status(thm)],[f11589]) ).

fof(f11683,plain,
    ( app(app(sk0_36(sk0_47),cons(sk0_34(sk0_47),sk0_37(sk0_47))),cons(sk0_34(sk0_47),sk0_38(sk0_47))) = sk0_47
    | ~ spl0_219
    | ~ spl0_489 ),
    inference(forward_demodulation,[status(thm)],[f4327,f11310]) ).

fof(f13271,plain,
    ( $false
    | ~ spl0_25
    | ~ spl0_493 ),
    inference(forward_subsumption_resolution,[status(thm)],[f11497,f1840]) ).

fof(f13272,plain,
    ( ~ spl0_25
    | ~ spl0_493 ),
    inference(contradiction_clause,[status(thm)],[f13271]) ).

fof(f16361,plain,
    ( $false
    | ~ spl0_497 ),
    inference(forward_subsumption_resolution,[status(thm)],[f11515,f430]) ).

fof(f16362,plain,
    ~ spl0_497,
    inference(contradiction_clause,[status(thm)],[f16361]) ).

fof(f17019,plain,
    ( spl0_948
  <=> ssList(app(app(sk0_36(sk0_47),cons(sk0_34(sk0_47),sk0_37(sk0_47))),cons(sk0_34(sk0_47),sk0_38(sk0_47)))) ),
    introduced(split_symbol_definition) ).

fof(f17021,plain,
    ( ~ ssList(app(app(sk0_36(sk0_47),cons(sk0_34(sk0_47),sk0_37(sk0_47))),cons(sk0_34(sk0_47),sk0_38(sk0_47))))
    | spl0_948 ),
    inference(component_clause,[status(thm)],[f17019]) ).

fof(f17024,plain,
    ( ~ ssList(app(app(sk0_36(sk0_47),cons(sk0_34(sk0_47),sk0_37(sk0_47))),cons(sk0_34(sk0_47),sk0_38(sk0_47))))
    | ~ strictorderedP(sk0_47)
    | ~ ssItem(sk0_34(sk0_47))
    | ~ ssItem(sk0_34(sk0_47))
    | ~ ssList(sk0_36(sk0_47))
    | ~ ssList(sk0_37(sk0_47))
    | ~ ssList(sk0_38(sk0_47))
    | lt(sk0_34(sk0_47),sk0_34(sk0_47))
    | ~ spl0_219
    | ~ spl0_489 ),
    inference(paramodulation,[status(thm)],[f11683,f450]) ).

fof(f17025,plain,
    ( ~ spl0_948
    | ~ spl0_498
    | ~ spl0_25
    | ~ spl0_27
    | ~ spl0_28
    | ~ spl0_151
    | spl0_493
    | ~ spl0_219
    | ~ spl0_489 ),
    inference(split_clause,[status(thm)],[f17024,f17019,f11519,f1724,f1738,f1745,f3300,f11496,f4326,f11309]) ).

fof(f17108,plain,
    ( ~ ssList(sk0_47)
    | ~ spl0_219
    | ~ spl0_489
    | spl0_948 ),
    inference(forward_demodulation,[status(thm)],[f11683,f17021]) ).

fof(f17109,plain,
    ( $false
    | ~ spl0_219
    | ~ spl0_489
    | spl0_948 ),
    inference(forward_subsumption_resolution,[status(thm)],[f17108,f418]) ).

fof(f17110,plain,
    ( ~ spl0_219
    | ~ spl0_489
    | spl0_948 ),
    inference(contradiction_clause,[status(thm)],[f17109]) ).

fof(f17111,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f585,f629,f1728,f1742,f1749,f3304,f4330,f11313,f11590,f13272,f16362,f17025,f17110]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWC181+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 23:52:02 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 19.49/2.83  % Refutation found
% 19.49/2.83  % SZS status Theorem for theBenchmark: Theorem is valid
% 19.49/2.83  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.49/2.88  % Elapsed time: 2.513436 seconds
% 19.49/2.88  % CPU time: 19.785298 seconds
% 19.49/2.88  % Total memory used: 209.190 MB
% 19.49/2.88  % Net memory used: 203.098 MB
%------------------------------------------------------------------------------