TSTP Solution File: SWC344+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC344+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May  3 03:12:05 EDT 2024

% Result   : Theorem 24.89s 4.24s
% Output   : CNFRefutation 24.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  172 (  18 unt;   0 def)
%            Number of atoms       : 1336 ( 384 equ)
%            Maximal formula atoms :   58 (   7 avg)
%            Number of connectives : 1852 ( 688   ~; 727   |; 381   &)
%                                         (   0 <=>;  56  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   7 con; 0-2 aty)
%            Number of variables   :  610 (   0 sgn 293   !; 162   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( nil = X1
                        | nil != X0 )
                      & ? [X14] :
                          ( ? [X15] :
                              ( strictorderedP(X0)
                              & ! [X20] :
                                  ( ssItem(X20)
                                 => ! [X21] :
                                      ( ssList(X21)
                                     => ( ! [X22] :
                                            ( ssItem(X22)
                                           => ! [X23] :
                                                ( ssList(X23)
                                               => ( ~ lt(X22,X20)
                                                  | app(X23,cons(X22,nil)) != X0 ) ) )
                                        | app(cons(X20,nil),X21) != X15 ) ) )
                              & ! [X16] :
                                  ( ssItem(X16)
                                 => ! [X17] :
                                      ( ssList(X17)
                                     => ( ! [X18] :
                                            ( ssItem(X18)
                                           => ! [X19] :
                                                ( ssList(X19)
                                               => ( ~ lt(X16,X18)
                                                  | app(cons(X18,nil),X19) != X0 ) ) )
                                        | app(X17,cons(X16,nil)) != X14 ) ) )
                              & app(app(X14,X0),X15) = X1
                              & ssList(X15) )
                          & ssList(X14) ) )
                    | ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( ? [X10] :
                                  ( ? [X11] :
                                      ( ? [X12] :
                                          ( ? [X13] :
                                              ( lt(X12,X10)
                                              & app(X13,cons(X12,nil)) = X2
                                              & ssList(X13) )
                                          & ssItem(X12) )
                                      & app(cons(X10,nil),X11) = X5
                                      & ssList(X11) )
                                  & ssItem(X10) )
                              | ? [X6] :
                                  ( ? [X7] :
                                      ( ? [X8] :
                                          ( ? [X9] :
                                              ( lt(X6,X8)
                                              & app(cons(X8,nil),X9) = X2
                                              & ssList(X9) )
                                          & ssItem(X8) )
                                      & app(X7,cons(X6,nil)) = X4
                                      & ssList(X7) )
                                  & ssItem(X6) )
                              | ~ strictorderedP(X2)
                              | app(app(X4,X2),X5) != X3 ) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( nil = X1
                          | nil != X0 )
                        & ? [X14] :
                            ( ? [X15] :
                                ( strictorderedP(X0)
                                & ! [X20] :
                                    ( ssItem(X20)
                                   => ! [X21] :
                                        ( ssList(X21)
                                       => ( ! [X22] :
                                              ( ssItem(X22)
                                             => ! [X23] :
                                                  ( ssList(X23)
                                                 => ( ~ lt(X22,X20)
                                                    | app(X23,cons(X22,nil)) != X0 ) ) )
                                          | app(cons(X20,nil),X21) != X15 ) ) )
                                & ! [X16] :
                                    ( ssItem(X16)
                                   => ! [X17] :
                                        ( ssList(X17)
                                       => ( ! [X18] :
                                              ( ssItem(X18)
                                             => ! [X19] :
                                                  ( ssList(X19)
                                                 => ( ~ lt(X16,X18)
                                                    | app(cons(X18,nil),X19) != X0 ) ) )
                                          | app(X17,cons(X16,nil)) != X14 ) ) )
                                & app(app(X14,X0),X15) = X1
                                & ssList(X15) )
                            & ssList(X14) ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( ? [X10] :
                                    ( ? [X11] :
                                        ( ? [X12] :
                                            ( ? [X13] :
                                                ( lt(X12,X10)
                                                & app(X13,cons(X12,nil)) = X2
                                                & ssList(X13) )
                                            & ssItem(X12) )
                                        & app(cons(X10,nil),X11) = X5
                                        & ssList(X11) )
                                    & ssItem(X10) )
                                | ? [X6] :
                                    ( ? [X7] :
                                        ( ? [X8] :
                                            ( ? [X9] :
                                                ( lt(X6,X8)
                                                & app(cons(X8,nil),X9) = X2
                                                & ssList(X9) )
                                            & ssItem(X8) )
                                        & app(X7,cons(X6,nil)) = X4
                                        & ssList(X7) )
                                    & ssItem(X6) )
                                | ~ strictorderedP(X2)
                                | app(app(X4,X2),X5) != X3 ) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( nil = X1
                          | nil != X0 )
                        & ? [X4] :
                            ( ? [X5] :
                                ( strictorderedP(X0)
                                & ! [X6] :
                                    ( ssItem(X6)
                                   => ! [X7] :
                                        ( ssList(X7)
                                       => ( ! [X8] :
                                              ( ssItem(X8)
                                             => ! [X9] :
                                                  ( ssList(X9)
                                                 => ( ~ lt(X8,X6)
                                                    | app(X9,cons(X8,nil)) != X0 ) ) )
                                          | app(cons(X6,nil),X7) != X5 ) ) )
                                & ! [X10] :
                                    ( ssItem(X10)
                                   => ! [X11] :
                                        ( ssList(X11)
                                       => ( ! [X12] :
                                              ( ssItem(X12)
                                             => ! [X13] :
                                                  ( ssList(X13)
                                                 => ( ~ lt(X10,X12)
                                                    | app(cons(X12,nil),X13) != X0 ) ) )
                                          | app(X11,cons(X10,nil)) != X4 ) ) )
                                & app(app(X4,X0),X5) = X1
                                & ssList(X5) )
                            & ssList(X4) ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X14] :
                          ( ssList(X14)
                         => ! [X15] :
                              ( ssList(X15)
                             => ( ? [X16] :
                                    ( ? [X17] :
                                        ( ? [X18] :
                                            ( ? [X19] :
                                                ( lt(X18,X16)
                                                & app(X19,cons(X18,nil)) = X2
                                                & ssList(X19) )
                                            & ssItem(X18) )
                                        & app(cons(X16,nil),X17) = X15
                                        & ssList(X17) )
                                    & ssItem(X16) )
                                | ? [X20] :
                                    ( ? [X21] :
                                        ( ? [X22] :
                                            ( ? [X23] :
                                                ( lt(X20,X22)
                                                & app(cons(X22,nil),X23) = X2
                                                & ssList(X23) )
                                            & ssItem(X22) )
                                        & app(X21,cons(X20,nil)) = X14
                                        & ssList(X21) )
                                    & ssItem(X20) )
                                | ~ strictorderedP(X2)
                                | app(app(X14,X2),X15) != X3 ) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = X0 )
                    | ! [X4] :
                        ( ! [X5] :
                            ( ~ strictorderedP(X0)
                            | ? [X6] :
                                ( ? [X7] :
                                    ( ? [X8] :
                                        ( ? [X9] :
                                            ( lt(X8,X6)
                                            & app(X9,cons(X8,nil)) = X0
                                            & ssList(X9) )
                                        & ssItem(X8) )
                                    & app(cons(X6,nil),X7) = X5
                                    & ssList(X7) )
                                & ssItem(X6) )
                            | ? [X10] :
                                ( ? [X11] :
                                    ( ? [X12] :
                                        ( ? [X13] :
                                            ( lt(X10,X12)
                                            & app(cons(X12,nil),X13) = X0
                                            & ssList(X13) )
                                        & ssItem(X12) )
                                    & app(X11,cons(X10,nil)) = X4
                                    & ssList(X11) )
                                & ssItem(X10) )
                            | app(app(X4,X0),X5) != X1
                            | ~ ssList(X5) )
                        | ~ ssList(X4) ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X14] :
                      ( ? [X15] :
                          ( ! [X16] :
                              ( ! [X17] :
                                  ( ! [X18] :
                                      ( ! [X19] :
                                          ( ~ lt(X18,X16)
                                          | app(X19,cons(X18,nil)) != X2
                                          | ~ ssList(X19) )
                                      | ~ ssItem(X18) )
                                  | app(cons(X16,nil),X17) != X15
                                  | ~ ssList(X17) )
                              | ~ ssItem(X16) )
                          & ! [X20] :
                              ( ! [X21] :
                                  ( ! [X22] :
                                      ( ! [X23] :
                                          ( ~ lt(X20,X22)
                                          | app(cons(X22,nil),X23) != X2
                                          | ~ ssList(X23) )
                                      | ~ ssItem(X22) )
                                  | app(X21,cons(X20,nil)) != X14
                                  | ~ ssList(X21) )
                              | ~ ssItem(X20) )
                          & strictorderedP(X2)
                          & app(app(X14,X2),X15) = X3
                          & ssList(X15) )
                      & ssList(X14) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = X0 )
                    | ! [X4] :
                        ( ! [X5] :
                            ( ~ strictorderedP(X0)
                            | ? [X6] :
                                ( ? [X7] :
                                    ( ? [X8] :
                                        ( ? [X9] :
                                            ( lt(X8,X6)
                                            & app(X9,cons(X8,nil)) = X0
                                            & ssList(X9) )
                                        & ssItem(X8) )
                                    & app(cons(X6,nil),X7) = X5
                                    & ssList(X7) )
                                & ssItem(X6) )
                            | ? [X10] :
                                ( ? [X11] :
                                    ( ? [X12] :
                                        ( ? [X13] :
                                            ( lt(X10,X12)
                                            & app(cons(X12,nil),X13) = X0
                                            & ssList(X13) )
                                        & ssItem(X12) )
                                    & app(X11,cons(X10,nil)) = X4
                                    & ssList(X11) )
                                & ssItem(X10) )
                            | app(app(X4,X0),X5) != X1
                            | ~ ssList(X5) )
                        | ~ ssList(X4) ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X14] :
                      ( ? [X15] :
                          ( ! [X16] :
                              ( ! [X17] :
                                  ( ! [X18] :
                                      ( ! [X19] :
                                          ( ~ lt(X18,X16)
                                          | app(X19,cons(X18,nil)) != X2
                                          | ~ ssList(X19) )
                                      | ~ ssItem(X18) )
                                  | app(cons(X16,nil),X17) != X15
                                  | ~ ssList(X17) )
                              | ~ ssItem(X16) )
                          & ! [X20] :
                              ( ! [X21] :
                                  ( ! [X22] :
                                      ( ! [X23] :
                                          ( ~ lt(X20,X22)
                                          | app(cons(X22,nil),X23) != X2
                                          | ~ ssList(X23) )
                                      | ~ ssItem(X22) )
                                  | app(X21,cons(X20,nil)) != X14
                                  | ~ ssList(X21) )
                              | ~ ssItem(X20) )
                          & strictorderedP(X2)
                          & app(app(X14,X2),X15) = X3
                          & ssList(X15) )
                      & ssList(X14) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f233,plain,
    ! [X0,X4] :
      ( ? [X10] :
          ( ? [X11] :
              ( ? [X12] :
                  ( ? [X13] :
                      ( lt(X10,X12)
                      & app(cons(X12,nil),X13) = X0
                      & ssList(X13) )
                  & ssItem(X12) )
              & app(X11,cons(X10,nil)) = X4
              & ssList(X11) )
          & ssItem(X10) )
      | ~ sP6(X0,X4) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f234,plain,
    ! [X0,X1] :
      ( ! [X4] :
          ( ! [X5] :
              ( ~ strictorderedP(X0)
              | ? [X6] :
                  ( ? [X7] :
                      ( ? [X8] :
                          ( ? [X9] :
                              ( lt(X8,X6)
                              & app(X9,cons(X8,nil)) = X0
                              & ssList(X9) )
                          & ssItem(X8) )
                      & app(cons(X6,nil),X7) = X5
                      & ssList(X7) )
                  & ssItem(X6) )
              | sP6(X0,X4)
              | app(app(X4,X0),X5) != X1
              | ~ ssList(X5) )
          | ~ ssList(X4) )
      | ~ sP7(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f235,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = X0 )
                    | sP7(X0,X1) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X14] :
                      ( ? [X15] :
                          ( ! [X16] :
                              ( ! [X17] :
                                  ( ! [X18] :
                                      ( ! [X19] :
                                          ( ~ lt(X18,X16)
                                          | app(X19,cons(X18,nil)) != X2
                                          | ~ ssList(X19) )
                                      | ~ ssItem(X18) )
                                  | app(cons(X16,nil),X17) != X15
                                  | ~ ssList(X17) )
                              | ~ ssItem(X16) )
                          & ! [X20] :
                              ( ! [X21] :
                                  ( ! [X22] :
                                      ( ! [X23] :
                                          ( ~ lt(X20,X22)
                                          | app(cons(X22,nil),X23) != X2
                                          | ~ ssList(X23) )
                                      | ~ ssItem(X22) )
                                  | app(X21,cons(X20,nil)) != X14
                                  | ~ ssList(X21) )
                              | ~ ssItem(X20) )
                          & strictorderedP(X2)
                          & app(app(X14,X2),X15) = X3
                          & ssList(X15) )
                      & ssList(X14) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f223,f234,f233]) ).

fof(f347,plain,
    ! [X0,X1] :
      ( ! [X4] :
          ( ! [X5] :
              ( ~ strictorderedP(X0)
              | ? [X6] :
                  ( ? [X7] :
                      ( ? [X8] :
                          ( ? [X9] :
                              ( lt(X8,X6)
                              & app(X9,cons(X8,nil)) = X0
                              & ssList(X9) )
                          & ssItem(X8) )
                      & app(cons(X6,nil),X7) = X5
                      & ssList(X7) )
                  & ssItem(X6) )
              | sP6(X0,X4)
              | app(app(X4,X0),X5) != X1
              | ~ ssList(X5) )
          | ~ ssList(X4) )
      | ~ sP7(X0,X1) ),
    inference(nnf_transformation,[],[f234]) ).

fof(f348,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ! [X3] :
              ( ~ strictorderedP(X0)
              | ? [X4] :
                  ( ? [X5] :
                      ( ? [X6] :
                          ( ? [X7] :
                              ( lt(X6,X4)
                              & app(X7,cons(X6,nil)) = X0
                              & ssList(X7) )
                          & ssItem(X6) )
                      & app(cons(X4,nil),X5) = X3
                      & ssList(X5) )
                  & ssItem(X4) )
              | sP6(X0,X2)
              | app(app(X2,X0),X3) != X1
              | ~ ssList(X3) )
          | ~ ssList(X2) )
      | ~ sP7(X0,X1) ),
    inference(rectify,[],[f347]) ).

fof(f349,plain,
    ! [X0,X3] :
      ( ? [X4] :
          ( ? [X5] :
              ( ? [X6] :
                  ( ? [X7] :
                      ( lt(X6,X4)
                      & app(X7,cons(X6,nil)) = X0
                      & ssList(X7) )
                  & ssItem(X6) )
              & app(cons(X4,nil),X5) = X3
              & ssList(X5) )
          & ssItem(X4) )
     => ( ? [X5] :
            ( ? [X6] :
                ( ? [X7] :
                    ( lt(X6,sK55(X0,X3))
                    & app(X7,cons(X6,nil)) = X0
                    & ssList(X7) )
                & ssItem(X6) )
            & app(cons(sK55(X0,X3),nil),X5) = X3
            & ssList(X5) )
        & ssItem(sK55(X0,X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ! [X0,X3] :
      ( ? [X5] :
          ( ? [X6] :
              ( ? [X7] :
                  ( lt(X6,sK55(X0,X3))
                  & app(X7,cons(X6,nil)) = X0
                  & ssList(X7) )
              & ssItem(X6) )
          & app(cons(sK55(X0,X3),nil),X5) = X3
          & ssList(X5) )
     => ( ? [X6] :
            ( ? [X7] :
                ( lt(X6,sK55(X0,X3))
                & app(X7,cons(X6,nil)) = X0
                & ssList(X7) )
            & ssItem(X6) )
        & app(cons(sK55(X0,X3),nil),sK56(X0,X3)) = X3
        & ssList(sK56(X0,X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f351,plain,
    ! [X0,X3] :
      ( ? [X6] :
          ( ? [X7] :
              ( lt(X6,sK55(X0,X3))
              & app(X7,cons(X6,nil)) = X0
              & ssList(X7) )
          & ssItem(X6) )
     => ( ? [X7] :
            ( lt(sK57(X0,X3),sK55(X0,X3))
            & app(X7,cons(sK57(X0,X3),nil)) = X0
            & ssList(X7) )
        & ssItem(sK57(X0,X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f352,plain,
    ! [X0,X3] :
      ( ? [X7] :
          ( lt(sK57(X0,X3),sK55(X0,X3))
          & app(X7,cons(sK57(X0,X3),nil)) = X0
          & ssList(X7) )
     => ( lt(sK57(X0,X3),sK55(X0,X3))
        & app(sK58(X0,X3),cons(sK57(X0,X3),nil)) = X0
        & ssList(sK58(X0,X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f353,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ! [X3] :
              ( ~ strictorderedP(X0)
              | ( lt(sK57(X0,X3),sK55(X0,X3))
                & app(sK58(X0,X3),cons(sK57(X0,X3),nil)) = X0
                & ssList(sK58(X0,X3))
                & ssItem(sK57(X0,X3))
                & app(cons(sK55(X0,X3),nil),sK56(X0,X3)) = X3
                & ssList(sK56(X0,X3))
                & ssItem(sK55(X0,X3)) )
              | sP6(X0,X2)
              | app(app(X2,X0),X3) != X1
              | ~ ssList(X3) )
          | ~ ssList(X2) )
      | ~ sP7(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56,sK57,sK58])],[f348,f352,f351,f350,f349]) ).

fof(f354,plain,
    ! [X0,X4] :
      ( ? [X10] :
          ( ? [X11] :
              ( ? [X12] :
                  ( ? [X13] :
                      ( lt(X10,X12)
                      & app(cons(X12,nil),X13) = X0
                      & ssList(X13) )
                  & ssItem(X12) )
              & app(X11,cons(X10,nil)) = X4
              & ssList(X11) )
          & ssItem(X10) )
      | ~ sP6(X0,X4) ),
    inference(nnf_transformation,[],[f233]) ).

fof(f355,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( lt(X2,X4)
                      & app(cons(X4,nil),X5) = X0
                      & ssList(X5) )
                  & ssItem(X4) )
              & app(X3,cons(X2,nil)) = X1
              & ssList(X3) )
          & ssItem(X2) )
      | ~ sP6(X0,X1) ),
    inference(rectify,[],[f354]) ).

fof(f356,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( lt(X2,X4)
                      & app(cons(X4,nil),X5) = X0
                      & ssList(X5) )
                  & ssItem(X4) )
              & app(X3,cons(X2,nil)) = X1
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( lt(sK59(X0,X1),X4)
                    & app(cons(X4,nil),X5) = X0
                    & ssList(X5) )
                & ssItem(X4) )
            & app(X3,cons(sK59(X0,X1),nil)) = X1
            & ssList(X3) )
        & ssItem(sK59(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f357,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( lt(sK59(X0,X1),X4)
                  & app(cons(X4,nil),X5) = X0
                  & ssList(X5) )
              & ssItem(X4) )
          & app(X3,cons(sK59(X0,X1),nil)) = X1
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( lt(sK59(X0,X1),X4)
                & app(cons(X4,nil),X5) = X0
                & ssList(X5) )
            & ssItem(X4) )
        & app(sK60(X0,X1),cons(sK59(X0,X1),nil)) = X1
        & ssList(sK60(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f358,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( lt(sK59(X0,X1),X4)
              & app(cons(X4,nil),X5) = X0
              & ssList(X5) )
          & ssItem(X4) )
     => ( ? [X5] :
            ( lt(sK59(X0,X1),sK61(X0,X1))
            & app(cons(sK61(X0,X1),nil),X5) = X0
            & ssList(X5) )
        & ssItem(sK61(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f359,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( lt(sK59(X0,X1),sK61(X0,X1))
          & app(cons(sK61(X0,X1),nil),X5) = X0
          & ssList(X5) )
     => ( lt(sK59(X0,X1),sK61(X0,X1))
        & app(cons(sK61(X0,X1),nil),sK62(X0,X1)) = X0
        & ssList(sK62(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f360,plain,
    ! [X0,X1] :
      ( ( lt(sK59(X0,X1),sK61(X0,X1))
        & app(cons(sK61(X0,X1),nil),sK62(X0,X1)) = X0
        & ssList(sK62(X0,X1))
        & ssItem(sK61(X0,X1))
        & app(sK60(X0,X1),cons(sK59(X0,X1),nil)) = X1
        & ssList(sK60(X0,X1))
        & ssItem(sK59(X0,X1)) )
      | ~ sP6(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60,sK61,sK62])],[f355,f359,f358,f357,f356]) ).

fof(f361,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = X0 )
                    | sP7(X0,X1) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ lt(X8,X6)
                                          | app(X9,cons(X8,nil)) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(cons(X6,nil),X7) != X5
                                  | ~ ssList(X7) )
                              | ~ ssItem(X6) )
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ lt(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & strictorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ssList(X5) )
                      & ssList(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(rectify,[],[f235]) ).

fof(f362,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil != X1
                        & nil = X0 )
                      | sP7(X0,X1) )
                    & ( nil != X2
                      | nil = X3 )
                    & ? [X4] :
                        ( ? [X5] :
                            ( ! [X6] :
                                ( ! [X7] :
                                    ( ! [X8] :
                                        ( ! [X9] :
                                            ( ~ lt(X8,X6)
                                            | app(X9,cons(X8,nil)) != X2
                                            | ~ ssList(X9) )
                                        | ~ ssItem(X8) )
                                    | app(cons(X6,nil),X7) != X5
                                    | ~ ssList(X7) )
                                | ~ ssItem(X6) )
                            & ! [X10] :
                                ( ! [X11] :
                                    ( ! [X12] :
                                        ( ! [X13] :
                                            ( ~ lt(X10,X12)
                                            | app(cons(X12,nil),X13) != X2
                                            | ~ ssList(X13) )
                                        | ~ ssItem(X12) )
                                    | app(X11,cons(X10,nil)) != X4
                                    | ~ ssList(X11) )
                                | ~ ssItem(X10) )
                            & strictorderedP(X2)
                            & app(app(X4,X2),X5) = X3
                            & ssList(X5) )
                        & ssList(X4) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = sK63 )
                    | sP7(sK63,X1) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ lt(X8,X6)
                                          | app(X9,cons(X8,nil)) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(cons(X6,nil),X7) != X5
                                  | ~ ssList(X7) )
                              | ~ ssItem(X6) )
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ lt(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & strictorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ssList(X5) )
                      & ssList(X4) )
                  & sK63 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK63) ) ),
    introduced(choice_axiom,[]) ).

fof(f363,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil != X1
                    & nil = sK63 )
                  | sP7(sK63,X1) )
                & ( nil != X2
                  | nil = X3 )
                & ? [X4] :
                    ( ? [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ! [X8] :
                                    ( ! [X9] :
                                        ( ~ lt(X8,X6)
                                        | app(X9,cons(X8,nil)) != X2
                                        | ~ ssList(X9) )
                                    | ~ ssItem(X8) )
                                | app(cons(X6,nil),X7) != X5
                                | ~ ssList(X7) )
                            | ~ ssItem(X6) )
                        & ! [X10] :
                            ( ! [X11] :
                                ( ! [X12] :
                                    ( ! [X13] :
                                        ( ~ lt(X10,X12)
                                        | app(cons(X12,nil),X13) != X2
                                        | ~ ssList(X13) )
                                    | ~ ssItem(X12) )
                                | app(X11,cons(X10,nil)) != X4
                                | ~ ssList(X11) )
                            | ~ ssItem(X10) )
                        & strictorderedP(X2)
                        & app(app(X4,X2),X5) = X3
                        & ssList(X5) )
                    & ssList(X4) )
                & sK63 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil != sK64
                  & nil = sK63 )
                | sP7(sK63,sK64) )
              & ( nil != X2
                | nil = X3 )
              & ? [X4] :
                  ( ? [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ! [X9] :
                                      ( ~ lt(X8,X6)
                                      | app(X9,cons(X8,nil)) != X2
                                      | ~ ssList(X9) )
                                  | ~ ssItem(X8) )
                              | app(cons(X6,nil),X7) != X5
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & ! [X10] :
                          ( ! [X11] :
                              ( ! [X12] :
                                  ( ! [X13] :
                                      ( ~ lt(X10,X12)
                                      | app(cons(X12,nil),X13) != X2
                                      | ~ ssList(X13) )
                                  | ~ ssItem(X12) )
                              | app(X11,cons(X10,nil)) != X4
                              | ~ ssList(X11) )
                          | ~ ssItem(X10) )
                      & strictorderedP(X2)
                      & app(app(X4,X2),X5) = X3
                      & ssList(X5) )
                  & ssList(X4) )
              & sK63 = X2
              & sK64 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK64) ) ),
    introduced(choice_axiom,[]) ).

fof(f364,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil != sK64
                & nil = sK63 )
              | sP7(sK63,sK64) )
            & ( nil != X2
              | nil = X3 )
            & ? [X4] :
                ( ? [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( ! [X9] :
                                    ( ~ lt(X8,X6)
                                    | app(X9,cons(X8,nil)) != X2
                                    | ~ ssList(X9) )
                                | ~ ssItem(X8) )
                            | app(cons(X6,nil),X7) != X5
                            | ~ ssList(X7) )
                        | ~ ssItem(X6) )
                    & ! [X10] :
                        ( ! [X11] :
                            ( ! [X12] :
                                ( ! [X13] :
                                    ( ~ lt(X10,X12)
                                    | app(cons(X12,nil),X13) != X2
                                    | ~ ssList(X13) )
                                | ~ ssItem(X12) )
                            | app(X11,cons(X10,nil)) != X4
                            | ~ ssList(X11) )
                        | ~ ssItem(X10) )
                    & strictorderedP(X2)
                    & app(app(X4,X2),X5) = X3
                    & ssList(X5) )
                & ssList(X4) )
            & sK63 = X2
            & sK64 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil != sK64
              & nil = sK63 )
            | sP7(sK63,sK64) )
          & ( nil != sK65
            | nil = X3 )
          & ? [X4] :
              ( ? [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ! [X9] :
                                  ( ~ lt(X8,X6)
                                  | app(X9,cons(X8,nil)) != sK65
                                  | ~ ssList(X9) )
                              | ~ ssItem(X8) )
                          | app(cons(X6,nil),X7) != X5
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & ! [X10] :
                      ( ! [X11] :
                          ( ! [X12] :
                              ( ! [X13] :
                                  ( ~ lt(X10,X12)
                                  | app(cons(X12,nil),X13) != sK65
                                  | ~ ssList(X13) )
                              | ~ ssItem(X12) )
                          | app(X11,cons(X10,nil)) != X4
                          | ~ ssList(X11) )
                      | ~ ssItem(X10) )
                  & strictorderedP(sK65)
                  & app(app(X4,sK65),X5) = X3
                  & ssList(X5) )
              & ssList(X4) )
          & sK63 = sK65
          & sK64 = X3
          & ssList(X3) )
      & ssList(sK65) ) ),
    introduced(choice_axiom,[]) ).

fof(f365,plain,
    ( ? [X3] :
        ( ( ( nil != sK64
            & nil = sK63 )
          | sP7(sK63,sK64) )
        & ( nil != sK65
          | nil = X3 )
        & ? [X4] :
            ( ? [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ! [X9] :
                                ( ~ lt(X8,X6)
                                | app(X9,cons(X8,nil)) != sK65
                                | ~ ssList(X9) )
                            | ~ ssItem(X8) )
                        | app(cons(X6,nil),X7) != X5
                        | ~ ssList(X7) )
                    | ~ ssItem(X6) )
                & ! [X10] :
                    ( ! [X11] :
                        ( ! [X12] :
                            ( ! [X13] :
                                ( ~ lt(X10,X12)
                                | app(cons(X12,nil),X13) != sK65
                                | ~ ssList(X13) )
                            | ~ ssItem(X12) )
                        | app(X11,cons(X10,nil)) != X4
                        | ~ ssList(X11) )
                    | ~ ssItem(X10) )
                & strictorderedP(sK65)
                & app(app(X4,sK65),X5) = X3
                & ssList(X5) )
            & ssList(X4) )
        & sK63 = sK65
        & sK64 = X3
        & ssList(X3) )
   => ( ( ( nil != sK64
          & nil = sK63 )
        | sP7(sK63,sK64) )
      & ( nil != sK65
        | nil = sK66 )
      & ? [X4] :
          ( ? [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ! [X9] :
                              ( ~ lt(X8,X6)
                              | app(X9,cons(X8,nil)) != sK65
                              | ~ ssList(X9) )
                          | ~ ssItem(X8) )
                      | app(cons(X6,nil),X7) != X5
                      | ~ ssList(X7) )
                  | ~ ssItem(X6) )
              & ! [X10] :
                  ( ! [X11] :
                      ( ! [X12] :
                          ( ! [X13] :
                              ( ~ lt(X10,X12)
                              | app(cons(X12,nil),X13) != sK65
                              | ~ ssList(X13) )
                          | ~ ssItem(X12) )
                      | app(X11,cons(X10,nil)) != X4
                      | ~ ssList(X11) )
                  | ~ ssItem(X10) )
              & strictorderedP(sK65)
              & app(app(X4,sK65),X5) = sK66
              & ssList(X5) )
          & ssList(X4) )
      & sK63 = sK65
      & sK64 = sK66
      & ssList(sK66) ) ),
    introduced(choice_axiom,[]) ).

fof(f366,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ! [X9] :
                            ( ~ lt(X8,X6)
                            | app(X9,cons(X8,nil)) != sK65
                            | ~ ssList(X9) )
                        | ~ ssItem(X8) )
                    | app(cons(X6,nil),X7) != X5
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            & ! [X10] :
                ( ! [X11] :
                    ( ! [X12] :
                        ( ! [X13] :
                            ( ~ lt(X10,X12)
                            | app(cons(X12,nil),X13) != sK65
                            | ~ ssList(X13) )
                        | ~ ssItem(X12) )
                    | app(X11,cons(X10,nil)) != X4
                    | ~ ssList(X11) )
                | ~ ssItem(X10) )
            & strictorderedP(sK65)
            & app(app(X4,sK65),X5) = sK66
            & ssList(X5) )
        & ssList(X4) )
   => ( ? [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ~ lt(X8,X6)
                          | app(X9,cons(X8,nil)) != sK65
                          | ~ ssList(X9) )
                      | ~ ssItem(X8) )
                  | app(cons(X6,nil),X7) != X5
                  | ~ ssList(X7) )
              | ~ ssItem(X6) )
          & ! [X10] :
              ( ! [X11] :
                  ( ! [X12] :
                      ( ! [X13] :
                          ( ~ lt(X10,X12)
                          | app(cons(X12,nil),X13) != sK65
                          | ~ ssList(X13) )
                      | ~ ssItem(X12) )
                  | app(X11,cons(X10,nil)) != sK67
                  | ~ ssList(X11) )
              | ~ ssItem(X10) )
          & strictorderedP(sK65)
          & sK66 = app(app(sK67,sK65),X5)
          & ssList(X5) )
      & ssList(sK67) ) ),
    introduced(choice_axiom,[]) ).

fof(f367,plain,
    ( ? [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ~ lt(X8,X6)
                        | app(X9,cons(X8,nil)) != sK65
                        | ~ ssList(X9) )
                    | ~ ssItem(X8) )
                | app(cons(X6,nil),X7) != X5
                | ~ ssList(X7) )
            | ~ ssItem(X6) )
        & ! [X10] :
            ( ! [X11] :
                ( ! [X12] :
                    ( ! [X13] :
                        ( ~ lt(X10,X12)
                        | app(cons(X12,nil),X13) != sK65
                        | ~ ssList(X13) )
                    | ~ ssItem(X12) )
                | app(X11,cons(X10,nil)) != sK67
                | ~ ssList(X11) )
            | ~ ssItem(X10) )
        & strictorderedP(sK65)
        & sK66 = app(app(sK67,sK65),X5)
        & ssList(X5) )
   => ( ! [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( ! [X9] :
                      ( ~ lt(X8,X6)
                      | app(X9,cons(X8,nil)) != sK65
                      | ~ ssList(X9) )
                  | ~ ssItem(X8) )
              | app(cons(X6,nil),X7) != sK68
              | ~ ssList(X7) )
          | ~ ssItem(X6) )
      & ! [X10] :
          ( ! [X11] :
              ( ! [X12] :
                  ( ! [X13] :
                      ( ~ lt(X10,X12)
                      | app(cons(X12,nil),X13) != sK65
                      | ~ ssList(X13) )
                  | ~ ssItem(X12) )
              | app(X11,cons(X10,nil)) != sK67
              | ~ ssList(X11) )
          | ~ ssItem(X10) )
      & strictorderedP(sK65)
      & sK66 = app(app(sK67,sK65),sK68)
      & ssList(sK68) ) ),
    introduced(choice_axiom,[]) ).

fof(f368,plain,
    ( ( ( nil != sK64
        & nil = sK63 )
      | sP7(sK63,sK64) )
    & ( nil != sK65
      | nil = sK66 )
    & ! [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( ! [X9] :
                    ( ~ lt(X8,X6)
                    | app(X9,cons(X8,nil)) != sK65
                    | ~ ssList(X9) )
                | ~ ssItem(X8) )
            | app(cons(X6,nil),X7) != sK68
            | ~ ssList(X7) )
        | ~ ssItem(X6) )
    & ! [X10] :
        ( ! [X11] :
            ( ! [X12] :
                ( ! [X13] :
                    ( ~ lt(X10,X12)
                    | app(cons(X12,nil),X13) != sK65
                    | ~ ssList(X13) )
                | ~ ssItem(X12) )
            | app(X11,cons(X10,nil)) != sK67
            | ~ ssList(X11) )
        | ~ ssItem(X10) )
    & strictorderedP(sK65)
    & sK66 = app(app(sK67,sK65),sK68)
    & ssList(sK68)
    & ssList(sK67)
    & sK63 = sK65
    & sK64 = sK66
    & ssList(sK66)
    & ssList(sK65)
    & ssList(sK64)
    & ssList(sK63) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64,sK65,sK66,sK67,sK68])],[f361,f367,f366,f365,f364,f363,f362]) ).

fof(f568,plain,
    ! [X2,X3,X0,X1] :
      ( ~ strictorderedP(X0)
      | ssItem(sK55(X0,X3))
      | sP6(X0,X2)
      | app(app(X2,X0),X3) != X1
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f353]) ).

fof(f569,plain,
    ! [X2,X3,X0,X1] :
      ( ~ strictorderedP(X0)
      | ssList(sK56(X0,X3))
      | sP6(X0,X2)
      | app(app(X2,X0),X3) != X1
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f353]) ).

fof(f570,plain,
    ! [X2,X3,X0,X1] :
      ( ~ strictorderedP(X0)
      | app(cons(sK55(X0,X3),nil),sK56(X0,X3)) = X3
      | sP6(X0,X2)
      | app(app(X2,X0),X3) != X1
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f353]) ).

fof(f571,plain,
    ! [X2,X3,X0,X1] :
      ( ~ strictorderedP(X0)
      | ssItem(sK57(X0,X3))
      | sP6(X0,X2)
      | app(app(X2,X0),X3) != X1
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f353]) ).

fof(f572,plain,
    ! [X2,X3,X0,X1] :
      ( ~ strictorderedP(X0)
      | ssList(sK58(X0,X3))
      | sP6(X0,X2)
      | app(app(X2,X0),X3) != X1
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f353]) ).

fof(f573,plain,
    ! [X2,X3,X0,X1] :
      ( ~ strictorderedP(X0)
      | app(sK58(X0,X3),cons(sK57(X0,X3),nil)) = X0
      | sP6(X0,X2)
      | app(app(X2,X0),X3) != X1
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f353]) ).

fof(f574,plain,
    ! [X2,X3,X0,X1] :
      ( ~ strictorderedP(X0)
      | lt(sK57(X0,X3),sK55(X0,X3))
      | sP6(X0,X2)
      | app(app(X2,X0),X3) != X1
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f353]) ).

fof(f575,plain,
    ! [X0,X1] :
      ( ssItem(sK59(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f360]) ).

fof(f576,plain,
    ! [X0,X1] :
      ( ssList(sK60(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f360]) ).

fof(f577,plain,
    ! [X0,X1] :
      ( app(sK60(X0,X1),cons(sK59(X0,X1),nil)) = X1
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f360]) ).

fof(f578,plain,
    ! [X0,X1] :
      ( ssItem(sK61(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f360]) ).

fof(f579,plain,
    ! [X0,X1] :
      ( ssList(sK62(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f360]) ).

fof(f580,plain,
    ! [X0,X1] :
      ( app(cons(sK61(X0,X1),nil),sK62(X0,X1)) = X0
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f360]) ).

fof(f581,plain,
    ! [X0,X1] :
      ( lt(sK59(X0,X1),sK61(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f360]) ).

fof(f586,plain,
    sK64 = sK66,
    inference(cnf_transformation,[],[f368]) ).

fof(f587,plain,
    sK63 = sK65,
    inference(cnf_transformation,[],[f368]) ).

fof(f588,plain,
    ssList(sK67),
    inference(cnf_transformation,[],[f368]) ).

fof(f589,plain,
    ssList(sK68),
    inference(cnf_transformation,[],[f368]) ).

fof(f590,plain,
    sK66 = app(app(sK67,sK65),sK68),
    inference(cnf_transformation,[],[f368]) ).

fof(f591,plain,
    strictorderedP(sK65),
    inference(cnf_transformation,[],[f368]) ).

fof(f592,plain,
    ! [X10,X11,X12,X13] :
      ( ~ lt(X10,X12)
      | app(cons(X12,nil),X13) != sK65
      | ~ ssList(X13)
      | ~ ssItem(X12)
      | app(X11,cons(X10,nil)) != sK67
      | ~ ssList(X11)
      | ~ ssItem(X10) ),
    inference(cnf_transformation,[],[f368]) ).

fof(f593,plain,
    ! [X8,X6,X9,X7] :
      ( ~ lt(X8,X6)
      | app(X9,cons(X8,nil)) != sK65
      | ~ ssList(X9)
      | ~ ssItem(X8)
      | app(cons(X6,nil),X7) != sK68
      | ~ ssList(X7)
      | ~ ssItem(X6) ),
    inference(cnf_transformation,[],[f368]) ).

fof(f594,plain,
    ( nil != sK65
    | nil = sK66 ),
    inference(cnf_transformation,[],[f368]) ).

fof(f595,plain,
    ( nil = sK63
    | sP7(sK63,sK64) ),
    inference(cnf_transformation,[],[f368]) ).

fof(f596,plain,
    ( nil != sK64
    | sP7(sK63,sK64) ),
    inference(cnf_transformation,[],[f368]) ).

fof(f597,plain,
    ( nil != sK66
    | sP7(sK65,sK66) ),
    inference(definition_unfolding,[],[f596,f586,f587,f586]) ).

fof(f598,plain,
    ( nil = sK65
    | sP7(sK65,sK66) ),
    inference(definition_unfolding,[],[f595,f587,f587,f586]) ).

fof(f628,plain,
    ! [X2,X3,X0] :
      ( ~ strictorderedP(X0)
      | lt(sK57(X0,X3),sK55(X0,X3))
      | sP6(X0,X2)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,app(app(X2,X0),X3)) ),
    inference(equality_resolution,[],[f574]) ).

fof(f629,plain,
    ! [X2,X3,X0] :
      ( ~ strictorderedP(X0)
      | app(sK58(X0,X3),cons(sK57(X0,X3),nil)) = X0
      | sP6(X0,X2)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,app(app(X2,X0),X3)) ),
    inference(equality_resolution,[],[f573]) ).

fof(f630,plain,
    ! [X2,X3,X0] :
      ( ~ strictorderedP(X0)
      | ssList(sK58(X0,X3))
      | sP6(X0,X2)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,app(app(X2,X0),X3)) ),
    inference(equality_resolution,[],[f572]) ).

fof(f631,plain,
    ! [X2,X3,X0] :
      ( ~ strictorderedP(X0)
      | ssItem(sK57(X0,X3))
      | sP6(X0,X2)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,app(app(X2,X0),X3)) ),
    inference(equality_resolution,[],[f571]) ).

fof(f632,plain,
    ! [X2,X3,X0] :
      ( ~ strictorderedP(X0)
      | app(cons(sK55(X0,X3),nil),sK56(X0,X3)) = X3
      | sP6(X0,X2)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,app(app(X2,X0),X3)) ),
    inference(equality_resolution,[],[f570]) ).

fof(f633,plain,
    ! [X2,X3,X0] :
      ( ~ strictorderedP(X0)
      | ssList(sK56(X0,X3))
      | sP6(X0,X2)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,app(app(X2,X0),X3)) ),
    inference(equality_resolution,[],[f569]) ).

fof(f634,plain,
    ! [X2,X3,X0] :
      ( ~ strictorderedP(X0)
      | ssItem(sK55(X0,X3))
      | sP6(X0,X2)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ sP7(X0,app(app(X2,X0),X3)) ),
    inference(equality_resolution,[],[f568]) ).

cnf(c_246,plain,
    ( ~ sP7(X0,app(app(X1,X0),X2))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ strictorderedP(X0)
    | lt(sK57(X0,X2),sK55(X0,X2))
    | sP6(X0,X1) ),
    inference(cnf_transformation,[],[f628]) ).

cnf(c_247,plain,
    ( ~ sP7(X0,app(app(X1,X0),X2))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ strictorderedP(X0)
    | app(sK58(X0,X2),cons(sK57(X0,X2),nil)) = X0
    | sP6(X0,X1) ),
    inference(cnf_transformation,[],[f629]) ).

cnf(c_248,plain,
    ( ~ sP7(X0,app(app(X1,X0),X2))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ strictorderedP(X0)
    | ssList(sK58(X0,X2))
    | sP6(X0,X1) ),
    inference(cnf_transformation,[],[f630]) ).

cnf(c_249,plain,
    ( ~ sP7(X0,app(app(X1,X0),X2))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ strictorderedP(X0)
    | ssItem(sK57(X0,X2))
    | sP6(X0,X1) ),
    inference(cnf_transformation,[],[f631]) ).

cnf(c_250,plain,
    ( ~ sP7(X0,app(app(X1,X0),X2))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ strictorderedP(X0)
    | app(cons(sK55(X0,X2),nil),sK56(X0,X2)) = X2
    | sP6(X0,X1) ),
    inference(cnf_transformation,[],[f632]) ).

cnf(c_251,plain,
    ( ~ sP7(X0,app(app(X1,X0),X2))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ strictorderedP(X0)
    | ssList(sK56(X0,X2))
    | sP6(X0,X1) ),
    inference(cnf_transformation,[],[f633]) ).

cnf(c_252,plain,
    ( ~ sP7(X0,app(app(X1,X0),X2))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ strictorderedP(X0)
    | ssItem(sK55(X0,X2))
    | sP6(X0,X1) ),
    inference(cnf_transformation,[],[f634]) ).

cnf(c_253,plain,
    ( ~ sP6(X0,X1)
    | lt(sK59(X0,X1),sK61(X0,X1)) ),
    inference(cnf_transformation,[],[f581]) ).

cnf(c_254,plain,
    ( ~ sP6(X0,X1)
    | app(cons(sK61(X0,X1),nil),sK62(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f580]) ).

cnf(c_255,plain,
    ( ~ sP6(X0,X1)
    | ssList(sK62(X0,X1)) ),
    inference(cnf_transformation,[],[f579]) ).

cnf(c_256,plain,
    ( ~ sP6(X0,X1)
    | ssItem(sK61(X0,X1)) ),
    inference(cnf_transformation,[],[f578]) ).

cnf(c_257,plain,
    ( ~ sP6(X0,X1)
    | app(sK60(X0,X1),cons(sK59(X0,X1),nil)) = X1 ),
    inference(cnf_transformation,[],[f577]) ).

cnf(c_258,plain,
    ( ~ sP6(X0,X1)
    | ssList(sK60(X0,X1)) ),
    inference(cnf_transformation,[],[f576]) ).

cnf(c_259,plain,
    ( ~ sP6(X0,X1)
    | ssItem(sK59(X0,X1)) ),
    inference(cnf_transformation,[],[f575]) ).

cnf(c_260,negated_conjecture,
    ( nil != sK66
    | sP7(sK65,sK66) ),
    inference(cnf_transformation,[],[f597]) ).

cnf(c_261,negated_conjecture,
    ( nil = sK65
    | sP7(sK65,sK66) ),
    inference(cnf_transformation,[],[f598]) ).

cnf(c_262,negated_conjecture,
    ( nil != sK65
    | nil = sK66 ),
    inference(cnf_transformation,[],[f594]) ).

cnf(c_263,negated_conjecture,
    ( app(cons(X0,nil),X1) != sK68
    | app(X2,cons(X3,nil)) != sK65
    | ~ lt(X3,X0)
    | ~ ssItem(X0)
    | ~ ssItem(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cnf_transformation,[],[f593]) ).

cnf(c_264,negated_conjecture,
    ( app(cons(X0,nil),X1) != sK65
    | app(X2,cons(X3,nil)) != sK67
    | ~ lt(X3,X0)
    | ~ ssItem(X0)
    | ~ ssItem(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cnf_transformation,[],[f592]) ).

cnf(c_265,negated_conjecture,
    strictorderedP(sK65),
    inference(cnf_transformation,[],[f591]) ).

cnf(c_266,negated_conjecture,
    app(app(sK67,sK65),sK68) = sK66,
    inference(cnf_transformation,[],[f590]) ).

cnf(c_267,negated_conjecture,
    ssList(sK68),
    inference(cnf_transformation,[],[f589]) ).

cnf(c_268,negated_conjecture,
    ssList(sK67),
    inference(cnf_transformation,[],[f588]) ).

cnf(c_399,negated_conjecture,
    sP7(sK65,sK66),
    inference(global_subsumption_just,[status(thm)],[c_261,c_261,c_260,c_262]) ).

cnf(c_401,negated_conjecture,
    sP7(sK65,sK66),
    inference(global_subsumption_just,[status(thm)],[c_260,c_399]) ).

cnf(c_2116,plain,
    ( app(app(X0,X1),X2) != sK66
    | X1 != sK65
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ~ strictorderedP(X1)
    | ssItem(sK55(X1,X2))
    | sP6(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_252,c_401]) ).

cnf(c_2117,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ strictorderedP(sK65)
    | ssItem(sK55(sK65,X1))
    | sP6(sK65,X0) ),
    inference(unflattening,[status(thm)],[c_2116]) ).

cnf(c_2119,plain,
    ( ~ ssList(X1)
    | ~ ssList(X0)
    | app(app(X0,sK65),X1) != sK66
    | ssItem(sK55(sK65,X1))
    | sP6(sK65,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_2117,c_265,c_2117]) ).

cnf(c_2120,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ssItem(sK55(sK65,X1))
    | sP6(sK65,X0) ),
    inference(renaming,[status(thm)],[c_2119]) ).

cnf(c_2137,plain,
    ( app(app(X0,X1),X2) != sK66
    | X1 != sK65
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ~ strictorderedP(X1)
    | ssList(sK56(X1,X2))
    | sP6(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_251,c_401]) ).

cnf(c_2138,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ strictorderedP(sK65)
    | ssList(sK56(sK65,X1))
    | sP6(sK65,X0) ),
    inference(unflattening,[status(thm)],[c_2137]) ).

cnf(c_2140,plain,
    ( ~ ssList(X1)
    | ~ ssList(X0)
    | app(app(X0,sK65),X1) != sK66
    | ssList(sK56(sK65,X1))
    | sP6(sK65,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_2138,c_265,c_2138]) ).

cnf(c_2141,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(sK56(sK65,X1))
    | sP6(sK65,X0) ),
    inference(renaming,[status(thm)],[c_2140]) ).

cnf(c_2158,plain,
    ( app(app(X0,X1),X2) != sK66
    | X1 != sK65
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ~ strictorderedP(X1)
    | app(cons(sK55(X1,X2),nil),sK56(X1,X2)) = X2
    | sP6(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_250,c_401]) ).

cnf(c_2159,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ strictorderedP(sK65)
    | app(cons(sK55(sK65,X1),nil),sK56(sK65,X1)) = X1
    | sP6(sK65,X0) ),
    inference(unflattening,[status(thm)],[c_2158]) ).

cnf(c_2161,plain,
    ( ~ ssList(X1)
    | ~ ssList(X0)
    | app(app(X0,sK65),X1) != sK66
    | app(cons(sK55(sK65,X1),nil),sK56(sK65,X1)) = X1
    | sP6(sK65,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_2159,c_265,c_2159]) ).

cnf(c_2162,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | app(cons(sK55(sK65,X1),nil),sK56(sK65,X1)) = X1
    | sP6(sK65,X0) ),
    inference(renaming,[status(thm)],[c_2161]) ).

cnf(c_2179,plain,
    ( app(app(X0,X1),X2) != sK66
    | X1 != sK65
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ~ strictorderedP(X1)
    | ssItem(sK57(X1,X2))
    | sP6(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_249,c_401]) ).

cnf(c_2180,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ strictorderedP(sK65)
    | ssItem(sK57(sK65,X1))
    | sP6(sK65,X0) ),
    inference(unflattening,[status(thm)],[c_2179]) ).

cnf(c_2182,plain,
    ( ~ ssList(X1)
    | ~ ssList(X0)
    | app(app(X0,sK65),X1) != sK66
    | ssItem(sK57(sK65,X1))
    | sP6(sK65,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_2180,c_265,c_2180]) ).

cnf(c_2183,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ssItem(sK57(sK65,X1))
    | sP6(sK65,X0) ),
    inference(renaming,[status(thm)],[c_2182]) ).

cnf(c_2200,plain,
    ( app(app(X0,X1),X2) != sK66
    | X1 != sK65
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ~ strictorderedP(X1)
    | ssList(sK58(X1,X2))
    | sP6(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_248,c_401]) ).

cnf(c_2201,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ strictorderedP(sK65)
    | ssList(sK58(sK65,X1))
    | sP6(sK65,X0) ),
    inference(unflattening,[status(thm)],[c_2200]) ).

cnf(c_2203,plain,
    ( ~ ssList(X1)
    | ~ ssList(X0)
    | app(app(X0,sK65),X1) != sK66
    | ssList(sK58(sK65,X1))
    | sP6(sK65,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_2201,c_265,c_2201]) ).

cnf(c_2204,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(sK58(sK65,X1))
    | sP6(sK65,X0) ),
    inference(renaming,[status(thm)],[c_2203]) ).

cnf(c_2221,plain,
    ( app(app(X0,X1),X2) != sK66
    | X1 != sK65
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ~ strictorderedP(X1)
    | app(sK58(X1,X2),cons(sK57(X1,X2),nil)) = X1
    | sP6(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_247,c_401]) ).

cnf(c_2222,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ strictorderedP(sK65)
    | app(sK58(sK65,X1),cons(sK57(sK65,X1),nil)) = sK65
    | sP6(sK65,X0) ),
    inference(unflattening,[status(thm)],[c_2221]) ).

cnf(c_2224,plain,
    ( ~ ssList(X1)
    | ~ ssList(X0)
    | app(app(X0,sK65),X1) != sK66
    | app(sK58(sK65,X1),cons(sK57(sK65,X1),nil)) = sK65
    | sP6(sK65,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_2222,c_265,c_2222]) ).

cnf(c_2225,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | app(sK58(sK65,X1),cons(sK57(sK65,X1),nil)) = sK65
    | sP6(sK65,X0) ),
    inference(renaming,[status(thm)],[c_2224]) ).

cnf(c_2242,plain,
    ( app(app(X0,X1),X2) != sK66
    | X1 != sK65
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ~ strictorderedP(X1)
    | lt(sK57(X1,X2),sK55(X1,X2))
    | sP6(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_246,c_401]) ).

cnf(c_2243,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ strictorderedP(sK65)
    | lt(sK57(sK65,X1),sK55(sK65,X1))
    | sP6(sK65,X0) ),
    inference(unflattening,[status(thm)],[c_2242]) ).

cnf(c_2245,plain,
    ( ~ ssList(X1)
    | ~ ssList(X0)
    | app(app(X0,sK65),X1) != sK66
    | lt(sK57(sK65,X1),sK55(sK65,X1))
    | sP6(sK65,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_2243,c_265,c_2243]) ).

cnf(c_2246,plain,
    ( app(app(X0,sK65),X1) != sK66
    | ~ ssList(X0)
    | ~ ssList(X1)
    | lt(sK57(sK65,X1),sK55(sK65,X1))
    | sP6(sK65,X0) ),
    inference(renaming,[status(thm)],[c_2245]) ).

cnf(c_9019,plain,
    ( app(app(X0_13,sK65),X1_13) != sK66
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | lt(sK57(sK65,X1_13),sK55(sK65,X1_13))
    | sP6(sK65,X0_13) ),
    inference(subtyping,[status(esa)],[c_2246]) ).

cnf(c_9020,plain,
    ( app(app(X0_13,sK65),X1_13) != sK66
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | app(sK58(sK65,X1_13),cons(sK57(sK65,X1_13),nil)) = sK65
    | sP6(sK65,X0_13) ),
    inference(subtyping,[status(esa)],[c_2225]) ).

cnf(c_9021,plain,
    ( app(app(X0_13,sK65),X1_13) != sK66
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | ssList(sK58(sK65,X1_13))
    | sP6(sK65,X0_13) ),
    inference(subtyping,[status(esa)],[c_2204]) ).

cnf(c_9022,plain,
    ( app(app(X0_13,sK65),X1_13) != sK66
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | ssItem(sK57(sK65,X1_13))
    | sP6(sK65,X0_13) ),
    inference(subtyping,[status(esa)],[c_2183]) ).

cnf(c_9023,plain,
    ( app(app(X0_13,sK65),X1_13) != sK66
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | app(cons(sK55(sK65,X1_13),nil),sK56(sK65,X1_13)) = X1_13
    | sP6(sK65,X0_13) ),
    inference(subtyping,[status(esa)],[c_2162]) ).

cnf(c_9024,plain,
    ( app(app(X0_13,sK65),X1_13) != sK66
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | ssList(sK56(sK65,X1_13))
    | sP6(sK65,X0_13) ),
    inference(subtyping,[status(esa)],[c_2141]) ).

cnf(c_9025,plain,
    ( app(app(X0_13,sK65),X1_13) != sK66
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | ssItem(sK55(sK65,X1_13))
    | sP6(sK65,X0_13) ),
    inference(subtyping,[status(esa)],[c_2120]) ).

cnf(c_9042,negated_conjecture,
    app(app(sK67,sK65),sK68) = sK66,
    inference(subtyping,[status(esa)],[c_266]) ).

cnf(c_9044,negated_conjecture,
    ( app(cons(X0_14,nil),X0_13) != sK65
    | app(X1_13,cons(X1_14,nil)) != sK67
    | ~ lt(X1_14,X0_14)
    | ~ ssItem(X0_14)
    | ~ ssItem(X1_14)
    | ~ ssList(X0_13)
    | ~ ssList(X1_13) ),
    inference(subtyping,[status(esa)],[c_264]) ).

cnf(c_9045,negated_conjecture,
    ( app(cons(X0_14,nil),X0_13) != sK68
    | app(X1_13,cons(X1_14,nil)) != sK65
    | ~ lt(X1_14,X0_14)
    | ~ ssItem(X0_14)
    | ~ ssItem(X1_14)
    | ~ ssList(X0_13)
    | ~ ssList(X1_13) ),
    inference(subtyping,[status(esa)],[c_263]) ).

cnf(c_9047,plain,
    ( ~ sP6(X0_13,X1_13)
    | ssItem(sK59(X0_13,X1_13)) ),
    inference(subtyping,[status(esa)],[c_259]) ).

cnf(c_9048,plain,
    ( ~ sP6(X0_13,X1_13)
    | ssList(sK60(X0_13,X1_13)) ),
    inference(subtyping,[status(esa)],[c_258]) ).

cnf(c_9049,plain,
    ( ~ sP6(X0_13,X1_13)
    | app(sK60(X0_13,X1_13),cons(sK59(X0_13,X1_13),nil)) = X1_13 ),
    inference(subtyping,[status(esa)],[c_257]) ).

cnf(c_9050,plain,
    ( ~ sP6(X0_13,X1_13)
    | ssItem(sK61(X0_13,X1_13)) ),
    inference(subtyping,[status(esa)],[c_256]) ).

cnf(c_9051,plain,
    ( ~ sP6(X0_13,X1_13)
    | ssList(sK62(X0_13,X1_13)) ),
    inference(subtyping,[status(esa)],[c_255]) ).

cnf(c_9052,plain,
    ( ~ sP6(X0_13,X1_13)
    | app(cons(sK61(X0_13,X1_13),nil),sK62(X0_13,X1_13)) = X0_13 ),
    inference(subtyping,[status(esa)],[c_254]) ).

cnf(c_9053,plain,
    ( ~ sP6(X0_13,X1_13)
    | lt(sK59(X0_13,X1_13),sK61(X0_13,X1_13)) ),
    inference(subtyping,[status(esa)],[c_253]) ).

cnf(c_9231,plain,
    ( X0_13 != X1_13
    | ~ ssList(X1_13)
    | ssList(X0_13) ),
    theory(equality) ).

cnf(c_12450,plain,
    ( app(cons(sK61(X0_13,X1_13),nil),X2_13) != sK65
    | app(X3_13,cons(sK59(X0_13,X1_13),nil)) != sK67
    | ~ lt(sK59(X0_13,X1_13),sK61(X0_13,X1_13))
    | ~ ssItem(sK59(X0_13,X1_13))
    | ~ ssItem(sK61(X0_13,X1_13))
    | ~ ssList(X2_13)
    | ~ ssList(X3_13) ),
    inference(instantiation,[status(thm)],[c_9044]) ).

cnf(c_13460,plain,
    ( ~ sP6(sK65,sK67)
    | ssItem(sK61(sK65,sK67)) ),
    inference(instantiation,[status(thm)],[c_9050]) ).

cnf(c_14389,plain,
    ( ~ ssList(sK68)
    | ~ ssList(sK67)
    | ssList(sK58(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(superposition,[status(thm)],[c_9042,c_9021]) ).

cnf(c_14407,plain,
    ( ssList(sK58(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(global_subsumption_just,[status(thm)],[c_14389,c_268,c_267,c_14389]) ).

cnf(c_14409,plain,
    ( ~ ssList(sK68)
    | ~ ssList(sK67)
    | ssItem(sK57(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(superposition,[status(thm)],[c_9042,c_9022]) ).

cnf(c_14410,plain,
    ( ssItem(sK57(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(global_subsumption_just,[status(thm)],[c_14409,c_268,c_267,c_14409]) ).

cnf(c_14429,plain,
    ( ~ ssList(sK68)
    | ~ ssList(sK67)
    | ssList(sK56(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(superposition,[status(thm)],[c_9042,c_9024]) ).

cnf(c_14430,plain,
    ( ssList(sK56(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(global_subsumption_just,[status(thm)],[c_14429,c_268,c_267,c_14429]) ).

cnf(c_14437,plain,
    ( ~ ssList(sK68)
    | ~ ssList(sK67)
    | ssItem(sK55(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(superposition,[status(thm)],[c_9042,c_9025]) ).

cnf(c_14457,plain,
    ( ssItem(sK55(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(global_subsumption_just,[status(thm)],[c_14437,c_268,c_267,c_14437]) ).

cnf(c_14459,plain,
    ( ~ ssList(sK68)
    | ~ ssList(sK67)
    | lt(sK57(sK65,sK68),sK55(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(superposition,[status(thm)],[c_9042,c_9019]) ).

cnf(c_14460,plain,
    ( lt(sK57(sK65,sK68),sK55(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(global_subsumption_just,[status(thm)],[c_14459,c_268,c_267,c_14459]) ).

cnf(c_14481,plain,
    ( ~ ssList(sK68)
    | ~ ssList(sK67)
    | app(sK58(sK65,sK68),cons(sK57(sK65,sK68),nil)) = sK65
    | sP6(sK65,sK67) ),
    inference(superposition,[status(thm)],[c_9042,c_9020]) ).

cnf(c_14482,plain,
    ( app(sK58(sK65,sK68),cons(sK57(sK65,sK68),nil)) = sK65
    | sP6(sK65,sK67) ),
    inference(global_subsumption_just,[status(thm)],[c_14481,c_268,c_267,c_14481]) ).

cnf(c_14484,plain,
    ( ~ ssList(sK68)
    | ~ ssList(sK67)
    | app(cons(sK55(sK65,sK68),nil),sK56(sK65,sK68)) = sK68
    | sP6(sK65,sK67) ),
    inference(superposition,[status(thm)],[c_9042,c_9023]) ).

cnf(c_14504,plain,
    ( app(cons(sK55(sK65,sK68),nil),sK56(sK65,sK68)) = sK68
    | sP6(sK65,sK67) ),
    inference(global_subsumption_just,[status(thm)],[c_14484,c_268,c_267,c_14484]) ).

cnf(c_15817,plain,
    ( app(cons(sK61(sK65,sK67),nil),X0_13) != sK65
    | app(X1_13,cons(sK59(sK65,sK67),nil)) != sK67
    | ~ lt(sK59(sK65,sK67),sK61(sK65,sK67))
    | ~ ssItem(sK59(sK65,sK67))
    | ~ ssItem(sK61(sK65,sK67))
    | ~ ssList(X0_13)
    | ~ ssList(X1_13) ),
    inference(instantiation,[status(thm)],[c_12450]) ).

cnf(c_17648,plain,
    ( ~ ssList(sK68)
    | ~ ssList(sK67)
    | app(sK58(sK65,sK68),cons(sK57(sK65,sK68),nil)) = sK65
    | sP6(sK65,sK67) ),
    inference(resolution,[status(thm)],[c_9020,c_9042]) ).

cnf(c_17649,plain,
    ( app(sK58(sK65,sK68),cons(sK57(sK65,sK68),nil)) = sK65
    | sP6(sK65,sK67) ),
    inference(global_subsumption_just,[status(thm)],[c_17648,c_14482]) ).

cnf(c_17659,plain,
    ( app(cons(X0_14,nil),X0_13) != sK68
    | ~ lt(sK57(sK65,sK68),X0_14)
    | ~ ssItem(sK57(sK65,sK68))
    | ~ ssList(sK58(sK65,sK68))
    | ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | sP6(sK65,sK67) ),
    inference(resolution,[status(thm)],[c_17649,c_9045]) ).

cnf(c_17661,plain,
    ( ~ ssList(sK65)
    | ssList(app(sK58(sK65,sK68),cons(sK57(sK65,sK68),nil)))
    | sP6(sK65,sK67) ),
    inference(resolution,[status(thm)],[c_17649,c_9231]) ).

cnf(c_17697,plain,
    ( ~ ssList(sK68)
    | ~ ssList(sK67)
    | app(cons(sK55(sK65,sK68),nil),sK56(sK65,sK68)) = sK68
    | sP6(sK65,sK67) ),
    inference(resolution,[status(thm)],[c_9023,c_9042]) ).

cnf(c_17698,plain,
    ( app(cons(sK55(sK65,sK68),nil),sK56(sK65,sK68)) = sK68
    | sP6(sK65,sK67) ),
    inference(global_subsumption_just,[status(thm)],[c_17697,c_14504]) ).

cnf(c_17744,plain,
    ( app(cons(X0_14,nil),X0_13) != sK68
    | ~ lt(sK57(sK65,sK68),X0_14)
    | ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | sP6(sK65,sK67) ),
    inference(global_subsumption_just,[status(thm)],[c_17659,c_14407,c_14410,c_17659]) ).

cnf(c_17780,plain,
    ( ~ lt(sK57(sK65,sK68),sK55(sK65,sK68))
    | ~ ssItem(sK55(sK65,sK68))
    | ~ ssList(sK56(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(resolution,[status(thm)],[c_17744,c_17698]) ).

cnf(c_17781,plain,
    sP6(sK65,sK67),
    inference(global_subsumption_just,[status(thm)],[c_17661,c_14430,c_14457,c_14460,c_17780]) ).

cnf(c_21608,plain,
    ( ~ sP6(sK65,sK67)
    | ssItem(sK59(sK65,sK67)) ),
    inference(instantiation,[status(thm)],[c_9047]) ).

cnf(c_22007,plain,
    ( ~ sP6(sK65,sK67)
    | lt(sK59(sK65,sK67),sK61(sK65,sK67)) ),
    inference(instantiation,[status(thm)],[c_9053]) ).

cnf(c_23639,plain,
    ( ~ ssList(sK68)
    | ~ ssList(sK67)
    | ssList(sK58(sK65,sK68))
    | sP6(sK65,sK67) ),
    inference(superposition,[status(thm)],[c_9042,c_9021]) ).

cnf(c_23640,plain,
    sP6(sK65,sK67),
    inference(global_subsumption_just,[status(thm)],[c_23639,c_17781]) ).

cnf(c_26982,plain,
    app(sK60(sK65,sK67),cons(sK59(sK65,sK67),nil)) = sK67,
    inference(superposition,[status(thm)],[c_23640,c_9049]) ).

cnf(c_26983,plain,
    app(cons(sK61(sK65,sK67),nil),sK62(sK65,sK67)) = sK65,
    inference(superposition,[status(thm)],[c_23640,c_9052]) ).

cnf(c_30123,plain,
    ( app(cons(sK61(sK65,sK67),nil),sK62(sK65,sK67)) != sK65
    | app(X0_13,cons(sK59(sK65,sK67),nil)) != sK67
    | ~ lt(sK59(sK65,sK67),sK61(sK65,sK67))
    | ~ ssItem(sK59(sK65,sK67))
    | ~ ssItem(sK61(sK65,sK67))
    | ~ ssList(sK62(sK65,sK67))
    | ~ ssList(X0_13) ),
    inference(instantiation,[status(thm)],[c_15817]) ).

cnf(c_34665,plain,
    ( ~ sP6(sK65,sK67)
    | ssList(sK62(sK65,sK67)) ),
    inference(instantiation,[status(thm)],[c_9051]) ).

cnf(c_40582,plain,
    ( app(cons(sK61(sK65,sK67),nil),sK62(sK65,sK67)) != sK65
    | app(sK60(sK65,sK67),cons(sK59(sK65,sK67),nil)) != sK67
    | ~ lt(sK59(sK65,sK67),sK61(sK65,sK67))
    | ~ ssItem(sK59(sK65,sK67))
    | ~ ssItem(sK61(sK65,sK67))
    | ~ ssList(sK62(sK65,sK67))
    | ~ ssList(sK60(sK65,sK67)) ),
    inference(instantiation,[status(thm)],[c_30123]) ).

cnf(c_49060,plain,
    ( ~ sP6(sK65,sK67)
    | ssList(sK60(sK65,sK67)) ),
    inference(instantiation,[status(thm)],[c_9048]) ).

cnf(c_49061,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_49060,c_40582,c_34665,c_26983,c_26982,c_22007,c_21608,c_17781,c_13460]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC344+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n002.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May  2 23:46:12 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.89/4.24  % SZS status Started for theBenchmark.p
% 24.89/4.24  % SZS status Theorem for theBenchmark.p
% 24.89/4.24  
% 24.89/4.24  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 24.89/4.24  
% 24.89/4.24  ------  iProver source info
% 24.89/4.24  
% 24.89/4.24  git: date: 2024-05-02 19:28:25 +0000
% 24.89/4.24  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 24.89/4.24  git: non_committed_changes: false
% 24.89/4.24  
% 24.89/4.24  ------ Parsing...
% 24.89/4.24  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 24.89/4.24  
% 24.89/4.24  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e 
% 24.89/4.24  
% 24.89/4.24  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 24.89/4.24  
% 24.89/4.24  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 24.89/4.24  ------ Proving...
% 24.89/4.24  ------ Problem Properties 
% 24.89/4.24  
% 24.89/4.24  
% 24.89/4.24  clauses                                 203
% 24.89/4.24  conjectures                             9
% 24.89/4.24  EPR                                     55
% 24.89/4.24  Horn                                    128
% 24.89/4.24  unary                                   22
% 24.89/4.24  binary                                  48
% 24.89/4.24  lits                                    689
% 24.89/4.24  lits eq                                 96
% 24.89/4.24  fd_pure                                 0
% 24.89/4.24  fd_pseudo                               0
% 24.89/4.24  fd_cond                                 21
% 24.89/4.24  fd_pseudo_cond                          14
% 24.89/4.24  AC symbols                              0
% 24.89/4.24  
% 24.89/4.24  ------ Input Options Time Limit: Unbounded
% 24.89/4.24  
% 24.89/4.24  
% 24.89/4.24  ------ 
% 24.89/4.24  Current options:
% 24.89/4.24  ------ 
% 24.89/4.24  
% 24.89/4.24  
% 24.89/4.24  
% 24.89/4.24  
% 24.89/4.24  ------ Proving...
% 24.89/4.24  
% 24.89/4.24  
% 24.89/4.24  % SZS status Theorem for theBenchmark.p
% 24.89/4.24  
% 24.89/4.24  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.89/4.24  
% 24.89/4.24  
%------------------------------------------------------------------------------