TSTP Solution File: SWC272+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWC272+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n032.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 20:45:09 EDT 2024

% Result   : Theorem 59.55s 7.82s
% Output   : CNFRefutation 59.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   39
% Syntax   : Number of formulae    :  189 (  47 unt;   0 def)
%            Number of atoms       :  591 ( 120 equ)
%            Maximal formula atoms :   19 (   3 avg)
%            Number of connectives :  676 ( 274   ~; 247   |;  89   &)
%                                         (  34 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   35 (  33 usr;  27 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;   8 con; 0-2 aty)
%            Number of variables   :  172 ( 139   !;  33   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ? [U] :
      ( ssItem(U)
      & ? [V] :
          ( ssItem(V)
          & U != V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( frontsegP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & app(V,W) = U ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [U] :
      ( ssList(U)
     => ( totalorderedP(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
                             => leq(V,W) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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/sandbox/benchmark/theBenchmark.p') ).

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

fof(f18,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => cons(V,U) != U ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => nil != cons(V,U) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f42,axiom,
    ! [U] :
      ( ssList(U)
     => frontsegP(U,U) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f69,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f93,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssItem(V)
         => ( lt(U,V)
          <=> ( U != V
              & leq(U,V) ) ) ) ),
    file('/export/starexec/sandbox/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)
                      | app(W,Y) != X
                      | ~ strictorderedP(W)
                      | ? [Z] :
                          ( ssItem(Z)
                          & ? [X1] :
                              ( ssList(X1)
                              & app(cons(Z,nil),X1) = Y
                              & ? [X2] :
                                  ( ssItem(X2)
                                  & ? [X3] :
                                      ( ssList(X3)
                                      & app(X3,cons(X2,nil)) = W
                                      & lt(X2,Z) ) ) ) ) )
                  | totalorderedP(U)
                  | ( nil != X
                    & nil = W ) ) ) ) ),
    file('/export/starexec/sandbox/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)
                        | app(W,Y) != X
                        | ~ strictorderedP(W)
                        | ? [Z] :
                            ( ssItem(Z)
                            & ? [X1] :
                                ( ssList(X1)
                                & app(cons(Z,nil),X1) = Y
                                & ? [X2] :
                                    ( ssItem(X2)
                                    & ? [X3] :
                                        ( ssList(X3)
                                        & app(X3,cons(X2,nil)) = W
                                        & lt(X2,Z) ) ) ) ) )
                    | totalorderedP(U)
                    | ( nil != X
                      & nil = W ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f102,plain,
    ( ssItem(sk0_0)
    & ssItem(sk0_1)
    & sk0_0 != sk0_1 ),
    inference(skolemization,[status(esa)],[f2]) ).

fof(f103,plain,
    ssItem(sk0_0),
    inference(cnf_transformation,[status(esa)],[f102]) ).

fof(f104,plain,
    ssItem(sk0_1),
    inference(cnf_transformation,[status(esa)],[f102]) ).

fof(f105,plain,
    sk0_0 != sk0_1,
    inference(cnf_transformation,[status(esa)],[f102]) ).

fof(f119,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( frontsegP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & app(V,W) = U ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f120,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( ~ frontsegP(U,V)
              | ? [W] :
                  ( ssList(W)
                  & app(V,W) = U ) )
            & ( frontsegP(U,V)
              | ! [W] :
                  ( ~ ssList(W)
                  | app(V,W) != U ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f119]) ).

fof(f121,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( ~ frontsegP(U,V)
              | ( ssList(sk0_5(V,U))
                & app(V,sk0_5(V,U)) = U ) )
            & ( frontsegP(U,V)
              | ! [W] :
                  ( ~ ssList(W)
                  | app(V,W) != U ) ) ) ) ),
    inference(skolemization,[status(esa)],[f120]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ frontsegP(X0,X1)
      | app(X1,sk0_5(X1,X0)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f121]) ).

fof(f174,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( totalorderedP(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
                            | leq(V,W) ) ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f11]) ).

fof(f175,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ totalorderedP(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
                              | leq(V,W) ) ) ) ) ) )
        & ( totalorderedP(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
                              & ~ leq(V,W) ) ) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f174]) ).

fof(f176,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ totalorderedP(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
                              | leq(V,W) ) ) ) ) ) )
        & ( totalorderedP(U)
          | ( ssItem(sk0_24(U))
            & ssItem(sk0_25(U))
            & ssList(sk0_26(U))
            & ssList(sk0_27(U))
            & ssList(sk0_28(U))
            & app(app(sk0_26(U),cons(sk0_24(U),sk0_27(U))),cons(sk0_25(U),sk0_28(U))) = U
            & ~ leq(sk0_24(U),sk0_25(U)) ) ) ) ),
    inference(skolemization,[status(esa)],[f175]) ).

fof(f178,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderedP(X0)
      | ssItem(sk0_24(X0)) ),
    inference(cnf_transformation,[status(esa)],[f176]) ).

fof(f179,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderedP(X0)
      | ssItem(sk0_25(X0)) ),
    inference(cnf_transformation,[status(esa)],[f176]) ).

fof(f180,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderedP(X0)
      | ssList(sk0_26(X0)) ),
    inference(cnf_transformation,[status(esa)],[f176]) ).

fof(f181,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderedP(X0)
      | ssList(sk0_27(X0)) ),
    inference(cnf_transformation,[status(esa)],[f176]) ).

fof(f182,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderedP(X0)
      | ssList(sk0_28(X0)) ),
    inference(cnf_transformation,[status(esa)],[f176]) ).

fof(f183,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderedP(X0)
      | app(app(sk0_26(X0),cons(sk0_24(X0),sk0_27(X0))),cons(sk0_25(X0),sk0_28(X0))) = X0 ),
    inference(cnf_transformation,[status(esa)],[f176]) ).

fof(f184,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderedP(X0)
      | ~ leq(sk0_24(X0),sk0_25(X0)) ),
    inference(cnf_transformation,[status(esa)],[f176]) ).

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

fof(f224,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssItem(V)
          | cons(V,U) != U ) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f225,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | cons(X1,X0) != X0 ),
    inference(cnf_transformation,[status(esa)],[f224]) ).

fof(f234,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssItem(V)
          | nil != cons(V,U) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f21]) ).

fof(f235,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | nil != cons(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f234]) ).

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(f285,plain,
    ! [U] :
      ( ~ ssList(U)
      | frontsegP(U,U) ),
    inference(pre_NNF_transformation,[status(esa)],[f42]) ).

fof(f286,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | frontsegP(X0,X0) ),
    inference(cnf_transformation,[status(esa)],[f285]) ).

fof(f349,plain,
    strictorderedP(nil),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f406,plain,
    ! [U] :
      ( ~ ssItem(U)
      | ! [V] :
          ( ~ ssItem(V)
          | ( lt(U,V)
          <=> ( U != V
              & leq(U,V) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f93]) ).

fof(f407,plain,
    ! [U] :
      ( ~ ssItem(U)
      | ! [V] :
          ( ~ ssItem(V)
          | ( ( ~ lt(U,V)
              | ( U != V
                & leq(U,V) ) )
            & ( lt(U,V)
              | U = V
              | ~ leq(U,V) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f406]) ).

fof(f409,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ lt(X0,X1)
      | leq(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f407]) ).

fof(f415,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ? [Y] :
                      ( ssList(Y)
                      & app(W,Y) = X
                      & strictorderedP(W)
                      & ! [Z] :
                          ( ~ ssItem(Z)
                          | ! [X1] :
                              ( ~ ssList(X1)
                              | app(cons(Z,nil),X1) != Y
                              | ! [X2] :
                                  ( ~ ssItem(X2)
                                  | ! [X3] :
                                      ( ~ ssList(X3)
                                      | app(X3,cons(X2,nil)) != W
                                      | ~ lt(X2,Z) ) ) ) ) )
                  & ~ totalorderedP(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)
                      & app(W,Y) = X
                      & strictorderedP(W)
                      & ! [Z] :
                          ( ~ ssItem(Z)
                          | ! [X1] :
                              ( ~ ssList(X1)
                              | app(cons(Z,nil),X1) != Y )
                          | ! [X2] :
                              ( ~ ssItem(X2)
                              | ! [X3] :
                                  ( ~ ssList(X3)
                                  | app(X3,cons(X2,nil)) != W )
                              | ~ lt(X2,Z) ) ) )
                  & ~ totalorderedP(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)
    & app(sk0_49,sk0_51) = sk0_50
    & strictorderedP(sk0_49)
    & ! [Z] :
        ( ~ ssItem(Z)
        | ! [X1] :
            ( ~ ssList(X1)
            | app(cons(Z,nil),X1) != sk0_51 )
        | ! [X2] :
            ( ~ ssItem(X2)
            | ! [X3] :
                ( ~ ssList(X3)
                | app(X3,cons(X2,nil)) != sk0_49 )
            | ~ lt(X2,Z) ) )
    & ~ totalorderedP(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(f419,plain,
    ssList(sk0_48),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f422,plain,
    sk0_48 = sk0_50,
    inference(cnf_transformation,[status(esa)],[f417]) ).

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

fof(f424,plain,
    ssList(sk0_51),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f425,plain,
    app(sk0_49,sk0_51) = sk0_50,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f426,plain,
    strictorderedP(sk0_49),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f428,plain,
    ~ totalorderedP(sk0_47),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f448,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(f469,plain,
    strictorderedP(sk0_47),
    inference(forward_demodulation,[status(thm)],[f423,f426]) ).

fof(f470,plain,
    app(sk0_47,sk0_51) = sk0_50,
    inference(forward_demodulation,[status(thm)],[f423,f425]) ).

fof(f471,plain,
    app(sk0_47,sk0_51) = sk0_48,
    inference(forward_demodulation,[status(thm)],[f422,f470]) ).

fof(f472,plain,
    app(nil,sk0_51) = sk0_51,
    inference(resolution,[status(thm)],[f249,f424]) ).

fof(f488,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | cons(sk0_1,X0) != X0 ),
    inference(resolution,[status(thm)],[f225,f104]) ).

fof(f489,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | cons(sk0_0,X0) != X0 ),
    inference(resolution,[status(thm)],[f225,f103]) ).

fof(f492,plain,
    cons(sk0_1,nil) != nil,
    inference(resolution,[status(thm)],[f488,f223]) ).

fof(f497,plain,
    cons(sk0_0,nil) != nil,
    inference(resolution,[status(thm)],[f489,f223]) ).

fof(f500,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil != cons(sk0_1,X0) ),
    inference(resolution,[status(thm)],[f235,f104]) ).

fof(f501,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil != cons(sk0_0,X0) ),
    inference(resolution,[status(thm)],[f235,f103]) ).

fof(f503,plain,
    nil != cons(sk0_1,sk0_51),
    inference(resolution,[status(thm)],[f500,f424]) ).

fof(f505,plain,
    nil != cons(sk0_1,sk0_48),
    inference(resolution,[status(thm)],[f500,f419]) ).

fof(f506,plain,
    nil != cons(sk0_1,sk0_47),
    inference(resolution,[status(thm)],[f500,f418]) ).

fof(f508,plain,
    nil != cons(sk0_0,sk0_51),
    inference(resolution,[status(thm)],[f501,f424]) ).

fof(f510,plain,
    nil != cons(sk0_0,sk0_48),
    inference(resolution,[status(thm)],[f501,f419]) ).

fof(f511,plain,
    nil != cons(sk0_0,sk0_47),
    inference(resolution,[status(thm)],[f501,f418]) ).

fof(f517,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssList(app(X0,sk0_51)) ),
    inference(resolution,[status(thm)],[f245,f424]) ).

fof(f525,plain,
    ssList(app(sk0_48,sk0_51)),
    inference(resolution,[status(thm)],[f517,f419]) ).

fof(f1555,plain,
    ( spl0_11
  <=> strictorderedP(nil) ),
    introduced(split_symbol_definition) ).

fof(f1557,plain,
    ( ~ strictorderedP(nil)
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f1555]) ).

fof(f1780,plain,
    ( spl0_12
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f1782,plain,
    ( ~ ssList(sk0_47)
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f1780]) ).

fof(f1783,plain,
    ( spl0_13
  <=> ssItem(sk0_24(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f1786,plain,
    ( ~ ssList(sk0_47)
    | ssItem(sk0_24(sk0_47)) ),
    inference(resolution,[status(thm)],[f178,f428]) ).

fof(f1787,plain,
    ( ~ spl0_12
    | spl0_13 ),
    inference(split_clause,[status(thm)],[f1786,f1780,f1783]) ).

fof(f1788,plain,
    ( $false
    | spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1782,f418]) ).

fof(f1789,plain,
    spl0_12,
    inference(contradiction_clause,[status(thm)],[f1788]) ).

fof(f1794,plain,
    ( spl0_14
  <=> ssItem(sk0_25(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f1797,plain,
    ( ~ ssList(sk0_47)
    | ssItem(sk0_25(sk0_47)) ),
    inference(resolution,[status(thm)],[f179,f428]) ).

fof(f1798,plain,
    ( ~ spl0_12
    | spl0_14 ),
    inference(split_clause,[status(thm)],[f1797,f1780,f1794]) ).

fof(f1803,plain,
    ( spl0_15
  <=> ssList(sk0_26(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f1806,plain,
    ( ~ ssList(sk0_47)
    | ssList(sk0_26(sk0_47)) ),
    inference(resolution,[status(thm)],[f180,f428]) ).

fof(f1807,plain,
    ( ~ spl0_12
    | spl0_15 ),
    inference(split_clause,[status(thm)],[f1806,f1780,f1803]) ).

fof(f1812,plain,
    ( spl0_16
  <=> ssList(sk0_27(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f1815,plain,
    ( ~ ssList(sk0_47)
    | ssList(sk0_27(sk0_47)) ),
    inference(resolution,[status(thm)],[f181,f428]) ).

fof(f1816,plain,
    ( ~ spl0_12
    | spl0_16 ),
    inference(split_clause,[status(thm)],[f1815,f1780,f1812]) ).

fof(f1821,plain,
    ( spl0_17
  <=> ssList(sk0_28(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f1824,plain,
    ( ~ ssList(sk0_47)
    | ssList(sk0_28(sk0_47)) ),
    inference(resolution,[status(thm)],[f182,f428]) ).

fof(f1825,plain,
    ( ~ spl0_12
    | spl0_17 ),
    inference(split_clause,[status(thm)],[f1824,f1780,f1821]) ).

fof(f1851,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ ssList(X0)
      | app(X0,sk0_5(X0,X0)) = X0
      | ~ ssList(X0) ),
    inference(resolution,[status(thm)],[f123,f286]) ).

fof(f1852,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,sk0_5(X0,X0)) = X0 ),
    inference(duplicate_literals_removal,[status(esa)],[f1851]) ).

fof(f5357,plain,
    app(sk0_48,sk0_5(sk0_48,sk0_48)) = sk0_48,
    inference(resolution,[status(thm)],[f1852,f419]) ).

fof(f9669,plain,
    ( spl0_404
  <=> sk0_0 = sk0_1 ),
    introduced(split_symbol_definition) ).

fof(f9670,plain,
    ( sk0_0 = sk0_1
    | ~ spl0_404 ),
    inference(component_clause,[status(thm)],[f9669]) ).

fof(f10133,plain,
    ( spl0_425
  <=> ssList(app(sk0_48,sk0_5(sk0_48,sk0_48))) ),
    introduced(split_symbol_definition) ).

fof(f10135,plain,
    ( ~ ssList(app(sk0_48,sk0_5(sk0_48,sk0_48)))
    | spl0_425 ),
    inference(component_clause,[status(thm)],[f10133]) ).

fof(f10245,plain,
    ( spl0_445
  <=> app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47))) = sk0_47 ),
    introduced(split_symbol_definition) ).

fof(f10246,plain,
    ( app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47))) = sk0_47
    | ~ spl0_445 ),
    inference(component_clause,[status(thm)],[f10245]) ).

fof(f10248,plain,
    ( ~ ssList(sk0_47)
    | app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47))) = sk0_47 ),
    inference(resolution,[status(thm)],[f183,f428]) ).

fof(f10249,plain,
    ( ~ spl0_12
    | spl0_445 ),
    inference(split_clause,[status(thm)],[f10248,f1780,f10245]) ).

fof(f10265,plain,
    ( spl0_447
  <=> lt(sk0_24(sk0_47),sk0_25(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f10266,plain,
    ( lt(sk0_24(sk0_47),sk0_25(sk0_47))
    | ~ spl0_447 ),
    inference(component_clause,[status(thm)],[f10265]) ).

fof(f10276,plain,
    ( spl0_450
  <=> leq(sk0_24(sk0_47),sk0_25(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f10287,plain,
    ( spl0_453
  <=> strictorderedP(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f10289,plain,
    ( ~ strictorderedP(sk0_47)
    | spl0_453 ),
    inference(component_clause,[status(thm)],[f10287]) ).

fof(f10292,plain,
    ( spl0_454
  <=> totalorderedP(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f10293,plain,
    ( totalorderedP(sk0_47)
    | ~ spl0_454 ),
    inference(component_clause,[status(thm)],[f10292]) ).

fof(f10361,plain,
    ( $false
    | spl0_453 ),
    inference(forward_subsumption_resolution,[status(thm)],[f10289,f469]) ).

fof(f10362,plain,
    spl0_453,
    inference(contradiction_clause,[status(thm)],[f10361]) ).

fof(f10365,plain,
    ( ~ ssList(sk0_48)
    | spl0_425 ),
    inference(forward_demodulation,[status(thm)],[f5357,f10135]) ).

fof(f10366,plain,
    ( $false
    | spl0_425 ),
    inference(forward_subsumption_resolution,[status(thm)],[f10365,f419]) ).

fof(f10367,plain,
    spl0_425,
    inference(contradiction_clause,[status(thm)],[f10366]) ).

fof(f11615,plain,
    ( spl0_550
  <=> ssList(app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47)))) ),
    introduced(split_symbol_definition) ).

fof(f11617,plain,
    ( ~ ssList(app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47))))
    | spl0_550 ),
    inference(component_clause,[status(thm)],[f11615]) ).

fof(f11618,plain,
    ( ~ ssList(app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47))))
    | ~ strictorderedP(sk0_47)
    | ~ ssItem(sk0_24(sk0_47))
    | ~ ssItem(sk0_25(sk0_47))
    | ~ ssList(sk0_26(sk0_47))
    | ~ ssList(sk0_27(sk0_47))
    | ~ ssList(sk0_28(sk0_47))
    | lt(sk0_24(sk0_47),sk0_25(sk0_47))
    | ~ spl0_445 ),
    inference(paramodulation,[status(thm)],[f10246,f448]) ).

fof(f11619,plain,
    ( ~ spl0_550
    | ~ spl0_453
    | ~ spl0_13
    | ~ spl0_14
    | ~ spl0_15
    | ~ spl0_16
    | ~ spl0_17
    | spl0_447
    | ~ spl0_445 ),
    inference(split_clause,[status(thm)],[f11618,f11615,f10287,f1783,f1794,f1803,f1812,f1821,f10265,f10245]) ).

fof(f11672,plain,
    ( ~ ssList(sk0_47)
    | ~ spl0_445
    | spl0_550 ),
    inference(forward_demodulation,[status(thm)],[f10246,f11617]) ).

fof(f11673,plain,
    ( $false
    | ~ spl0_445
    | spl0_550 ),
    inference(forward_subsumption_resolution,[status(thm)],[f11672,f418]) ).

fof(f11674,plain,
    ( ~ spl0_445
    | spl0_550 ),
    inference(contradiction_clause,[status(thm)],[f11673]) ).

fof(f13758,plain,
    ( spl0_690
  <=> nil = cons(sk0_0,sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f13759,plain,
    ( nil = cons(sk0_0,sk0_48)
    | ~ spl0_690 ),
    inference(component_clause,[status(thm)],[f13758]) ).

fof(f13763,plain,
    ( $false
    | ~ spl0_690 ),
    inference(forward_subsumption_resolution,[status(thm)],[f13759,f510]) ).

fof(f13764,plain,
    ~ spl0_690,
    inference(contradiction_clause,[status(thm)],[f13763]) ).

fof(f13768,plain,
    ( spl0_692
  <=> nil = cons(sk0_0,sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f13769,plain,
    ( nil = cons(sk0_0,sk0_47)
    | ~ spl0_692 ),
    inference(component_clause,[status(thm)],[f13768]) ).

fof(f13773,plain,
    ( $false
    | ~ spl0_692 ),
    inference(forward_subsumption_resolution,[status(thm)],[f13769,f511]) ).

fof(f13774,plain,
    ~ spl0_692,
    inference(contradiction_clause,[status(thm)],[f13773]) ).

fof(f13778,plain,
    ( spl0_694
  <=> nil = cons(sk0_0,sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f13779,plain,
    ( nil = cons(sk0_0,sk0_51)
    | ~ spl0_694 ),
    inference(component_clause,[status(thm)],[f13778]) ).

fof(f13783,plain,
    ( $false
    | ~ spl0_694 ),
    inference(forward_subsumption_resolution,[status(thm)],[f13779,f508]) ).

fof(f13784,plain,
    ~ spl0_694,
    inference(contradiction_clause,[status(thm)],[f13783]) ).

fof(f13788,plain,
    ( spl0_696
  <=> nil = cons(sk0_0,nil) ),
    introduced(split_symbol_definition) ).

fof(f13789,plain,
    ( nil = cons(sk0_0,nil)
    | ~ spl0_696 ),
    inference(component_clause,[status(thm)],[f13788]) ).

fof(f13793,plain,
    ( $false
    | ~ spl0_696 ),
    inference(forward_subsumption_resolution,[status(thm)],[f13789,f497]) ).

fof(f13794,plain,
    ~ spl0_696,
    inference(contradiction_clause,[status(thm)],[f13793]) ).

fof(f13855,plain,
    ( spl0_698
  <=> nil = cons(sk0_1,sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f13856,plain,
    ( nil = cons(sk0_1,sk0_48)
    | ~ spl0_698 ),
    inference(component_clause,[status(thm)],[f13855]) ).

fof(f13860,plain,
    ( $false
    | ~ spl0_698 ),
    inference(forward_subsumption_resolution,[status(thm)],[f13856,f505]) ).

fof(f13861,plain,
    ~ spl0_698,
    inference(contradiction_clause,[status(thm)],[f13860]) ).

fof(f13865,plain,
    ( spl0_700
  <=> nil = cons(sk0_1,sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f13866,plain,
    ( nil = cons(sk0_1,sk0_47)
    | ~ spl0_700 ),
    inference(component_clause,[status(thm)],[f13865]) ).

fof(f13870,plain,
    ( $false
    | ~ spl0_700 ),
    inference(forward_subsumption_resolution,[status(thm)],[f13866,f506]) ).

fof(f13871,plain,
    ~ spl0_700,
    inference(contradiction_clause,[status(thm)],[f13870]) ).

fof(f13875,plain,
    ( spl0_702
  <=> nil = cons(sk0_1,sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f13876,plain,
    ( nil = cons(sk0_1,sk0_51)
    | ~ spl0_702 ),
    inference(component_clause,[status(thm)],[f13875]) ).

fof(f13880,plain,
    ( $false
    | ~ spl0_702 ),
    inference(forward_subsumption_resolution,[status(thm)],[f13876,f503]) ).

fof(f13881,plain,
    ~ spl0_702,
    inference(contradiction_clause,[status(thm)],[f13880]) ).

fof(f13885,plain,
    ( spl0_704
  <=> nil = cons(sk0_1,nil) ),
    introduced(split_symbol_definition) ).

fof(f13886,plain,
    ( nil = cons(sk0_1,nil)
    | ~ spl0_704 ),
    inference(component_clause,[status(thm)],[f13885]) ).

fof(f13890,plain,
    ( $false
    | ~ spl0_704 ),
    inference(forward_subsumption_resolution,[status(thm)],[f13886,f492]) ).

fof(f13891,plain,
    ~ spl0_704,
    inference(contradiction_clause,[status(thm)],[f13890]) ).

fof(f15079,plain,
    ( spl0_805
  <=> sk0_51 = app(nil,sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f15081,plain,
    ( sk0_51 != app(nil,sk0_51)
    | spl0_805 ),
    inference(component_clause,[status(thm)],[f15079]) ).

fof(f15085,plain,
    ( sk0_51 != sk0_51
    | spl0_805 ),
    inference(forward_demodulation,[status(thm)],[f472,f15081]) ).

fof(f15086,plain,
    ( $false
    | spl0_805 ),
    inference(trivial_equality_resolution,[status(esa)],[f15085]) ).

fof(f15087,plain,
    spl0_805,
    inference(contradiction_clause,[status(thm)],[f15086]) ).

fof(f15101,plain,
    ( spl0_808
  <=> sk0_48 = app(sk0_47,sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f15103,plain,
    ( sk0_48 != app(sk0_47,sk0_51)
    | spl0_808 ),
    inference(component_clause,[status(thm)],[f15101]) ).

fof(f15453,plain,
    ( sk0_48 != sk0_48
    | spl0_808 ),
    inference(forward_demodulation,[status(thm)],[f471,f15103]) ).

fof(f15454,plain,
    ( $false
    | spl0_808 ),
    inference(trivial_equality_resolution,[status(esa)],[f15453]) ).

fof(f15455,plain,
    spl0_808,
    inference(contradiction_clause,[status(thm)],[f15454]) ).

fof(f19990,plain,
    ( spl0_1088
  <=> ssList(app(sk0_48,sk0_51)) ),
    introduced(split_symbol_definition) ).

fof(f19992,plain,
    ( ~ ssList(app(sk0_48,sk0_51))
    | spl0_1088 ),
    inference(component_clause,[status(thm)],[f19990]) ).

fof(f21446,plain,
    ( $false
    | spl0_1088 ),
    inference(forward_subsumption_resolution,[status(thm)],[f19992,f525]) ).

fof(f21447,plain,
    spl0_1088,
    inference(contradiction_clause,[status(thm)],[f21446]) ).

fof(f23167,plain,
    ( $false
    | ~ spl0_404 ),
    inference(forward_subsumption_resolution,[status(thm)],[f9670,f105]) ).

fof(f23168,plain,
    ~ spl0_404,
    inference(contradiction_clause,[status(thm)],[f23167]) ).

fof(f23179,plain,
    ( $false
    | spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1557,f349]) ).

fof(f23180,plain,
    spl0_11,
    inference(contradiction_clause,[status(thm)],[f23179]) ).

fof(f28410,plain,
    ( ~ ssItem(sk0_24(sk0_47))
    | ~ ssItem(sk0_25(sk0_47))
    | leq(sk0_24(sk0_47),sk0_25(sk0_47))
    | ~ spl0_447 ),
    inference(resolution,[status(thm)],[f10266,f409]) ).

fof(f28411,plain,
    ( ~ spl0_13
    | ~ spl0_14
    | spl0_450
    | ~ spl0_447 ),
    inference(split_clause,[status(thm)],[f28410,f1783,f1794,f10276,f10265]) ).

fof(f28419,plain,
    ( $false
    | ~ spl0_454 ),
    inference(forward_subsumption_resolution,[status(thm)],[f10293,f428]) ).

fof(f28420,plain,
    ~ spl0_454,
    inference(contradiction_clause,[status(thm)],[f28419]) ).

fof(f30901,plain,
    ( ~ ssList(sk0_47)
    | ~ leq(sk0_24(sk0_47),sk0_25(sk0_47)) ),
    inference(resolution,[status(thm)],[f184,f428]) ).

fof(f30902,plain,
    ( ~ spl0_12
    | ~ spl0_450 ),
    inference(split_clause,[status(thm)],[f30901,f1780,f10276]) ).

fof(f30903,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f1787,f1789,f1798,f1807,f1816,f1825,f10249,f10362,f10367,f11619,f11674,f13764,f13774,f13784,f13794,f13861,f13871,f13881,f13891,f15087,f15455,f21447,f23168,f23180,f28411,f28420,f30902]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SWC272+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 300
% 0.09/0.28  % DateTime : Tue Apr 30 00:14:50 EDT 2024
% 0.09/0.29  % CPUTime  : 
% 0.13/0.30  % Drodi V3.6.0
% 59.55/7.82  % Refutation found
% 59.55/7.82  % SZS status Theorem for theBenchmark: Theorem is valid
% 59.55/7.82  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 59.87/7.88  % Elapsed time: 7.582230 seconds
% 59.87/7.88  % CPU time: 60.136064 seconds
% 59.87/7.88  % Total memory used: 345.049 MB
% 59.87/7.88  % Net memory used: 333.908 MB
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