TSTP Solution File: SWC181+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC181+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n021.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 03:11:30 EDT 2024

% Result   : Theorem 12.07s 2.64s
% Output   : CNFRefutation 12.07s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f600)

% Comments : 
%------------------------------------------------------------------------------
fof(f12,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( strictorderedP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => lt(X1,X2) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).

fof(f13,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => X1 != X2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( nil = X2
                      & nil != X3 )
                    | duplicatefreeP(X0)
                    | ! [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/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( nil = X2
                        & nil != X3 )
                      | duplicatefreeP(X0)
                      | ! [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 = X2
                        & nil != X3 )
                      | duplicatefreeP(X0)
                      | ! [X4] :
                          ( ssList(X4)
                         => ! [X5] :
                              ( ssList(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 ) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f113,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f114,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f113]) ).

fof(f115,plain,
    ! [X0] :
      ( ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f116,plain,
    ! [X0] :
      ( ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f115]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X2
                    | nil = X3 )
                  & ~ duplicatefreeP(X0)
                  & ? [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(ennf_transformation,[],[f98]) ).

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X2
                    | nil = X3 )
                  & ~ duplicatefreeP(X0)
                  & ? [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(flattening,[],[f222]) ).

fof(f294,plain,
    ! [X0] :
      ( ( ( strictorderedP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( ~ lt(X1,X2)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5) )
                          & ssList(X4) )
                      & ssList(X3) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X1] :
              ( ! [X2] :
                  ( ! [X3] :
                      ( ! [X4] :
                          ( ! [X5] :
                              ( lt(X1,X2)
                              | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                              | ~ ssList(X5) )
                          | ~ ssList(X4) )
                      | ~ ssList(X3) )
                  | ~ ssItem(X2) )
              | ~ ssItem(X1) )
          | ~ strictorderedP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f114]) ).

fof(f295,plain,
    ! [X0] :
      ( ( ( strictorderedP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( ~ lt(X1,X2)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5) )
                          & ssList(X4) )
                      & ssList(X3) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( lt(X6,X7)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ strictorderedP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f294]) ).

fof(f296,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ lt(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ~ lt(sK35(X0),X2)
                        & app(app(X3,cons(sK35(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK35(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f297,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ lt(sK35(X0),X2)
                      & app(app(X3,cons(sK35(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ lt(sK35(X0),sK36(X0))
                    & app(app(X3,cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK36(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f298,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ lt(sK35(X0),sK36(X0))
                  & app(app(X3,cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ lt(sK35(X0),sK36(X0))
                & app(app(sK37(X0),cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK37(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f299,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ lt(sK35(X0),sK36(X0))
              & app(app(sK37(X0),cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ lt(sK35(X0),sK36(X0))
            & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK38(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f300,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ lt(sK35(X0),sK36(X0))
          & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ lt(sK35(X0),sK36(X0))
        & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0
        & ssList(sK39(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f301,plain,
    ! [X0] :
      ( ( ( strictorderedP(X0)
          | ( ~ lt(sK35(X0),sK36(X0))
            & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0
            & ssList(sK39(X0))
            & ssList(sK38(X0))
            & ssList(sK37(X0))
            & ssItem(sK36(X0))
            & ssItem(sK35(X0)) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( lt(X6,X7)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ strictorderedP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36,sK37,sK38,sK39])],[f295,f300,f299,f298,f297,f296]) ).

fof(f302,plain,
    ! [X0] :
      ( ( ( duplicatefreeP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( X1 = X2
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5) )
                          & ssList(X4) )
                      & ssList(X3) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X1] :
              ( ! [X2] :
                  ( ! [X3] :
                      ( ! [X4] :
                          ( ! [X5] :
                              ( X1 != X2
                              | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                              | ~ ssList(X5) )
                          | ~ ssList(X4) )
                      | ~ ssList(X3) )
                  | ~ ssItem(X2) )
              | ~ ssItem(X1) )
          | ~ duplicatefreeP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f116]) ).

fof(f303,plain,
    ! [X0] :
      ( ( ( duplicatefreeP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( X1 = X2
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5) )
                          & ssList(X4) )
                      & ssList(X3) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( X6 != X7
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ duplicatefreeP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f302]) ).

fof(f304,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( X1 = X2
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( sK40(X0) = X2
                        & app(app(X3,cons(sK40(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK40(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f305,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( sK40(X0) = X2
                      & app(app(X3,cons(sK40(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( sK40(X0) = sK41(X0)
                    & app(app(X3,cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK41(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f306,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( sK40(X0) = sK41(X0)
                  & app(app(X3,cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( sK40(X0) = sK41(X0)
                & app(app(sK42(X0),cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK42(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f307,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( sK40(X0) = sK41(X0)
              & app(app(sK42(X0),cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( sK40(X0) = sK41(X0)
            & app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK43(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f308,plain,
    ! [X0] :
      ( ? [X5] :
          ( sK40(X0) = sK41(X0)
          & app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),X5)) = X0
          & ssList(X5) )
     => ( sK40(X0) = sK41(X0)
        & app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0
        & ssList(sK44(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f309,plain,
    ! [X0] :
      ( ( ( duplicatefreeP(X0)
          | ( sK40(X0) = sK41(X0)
            & app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0
            & ssList(sK44(X0))
            & ssList(sK43(X0))
            & ssList(sK42(X0))
            & ssItem(sK41(X0))
            & ssItem(sK40(X0)) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( X6 != X7
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ duplicatefreeP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42,sK43,sK44])],[f303,f308,f307,f306,f305,f304]) ).

fof(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( nil != X2
                      | nil = X3 )
                    & ~ duplicatefreeP(X0)
                    & ? [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 != X2
                    | nil = X3 )
                  & ~ duplicatefreeP(sK53)
                  & ? [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) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( nil != X2
                  | nil = X3 )
                & ~ duplicatefreeP(sK53)
                & ? [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) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( nil != X2
                | nil = X3 )
              & ~ duplicatefreeP(sK53)
              & ? [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) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( nil != X2
              | nil = X3 )
            & ~ duplicatefreeP(sK53)
            & ? [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) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( nil != sK55
            | nil = X3 )
          & ~ duplicatefreeP(sK53)
          & ? [X4] :
              ( ? [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ! [X9] :
                                  ( ~ lt(X8,X6)
                                  | app(X9,cons(X8,nil)) != sK55
                                  | ~ 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) != sK55
                                  | ~ ssList(X13) )
                              | ~ ssItem(X12) )
                          | app(X11,cons(X10,nil)) != X4
                          | ~ ssList(X11) )
                      | ~ ssItem(X10) )
                  & strictorderedP(sK55)
                  & app(app(X4,sK55),X5) = X3
                  & ssList(X5) )
              & ssList(X4) )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X3] :
        ( ( nil != sK55
          | nil = X3 )
        & ~ duplicatefreeP(sK53)
        & ? [X4] :
            ( ? [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ! [X9] :
                                ( ~ lt(X8,X6)
                                | app(X9,cons(X8,nil)) != sK55
                                | ~ 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) != sK55
                                | ~ ssList(X13) )
                            | ~ ssItem(X12) )
                        | app(X11,cons(X10,nil)) != X4
                        | ~ ssList(X11) )
                    | ~ ssItem(X10) )
                & strictorderedP(sK55)
                & app(app(X4,sK55),X5) = X3
                & ssList(X5) )
            & ssList(X4) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( nil != sK55
        | nil = sK56 )
      & ~ duplicatefreeP(sK53)
      & ? [X4] :
          ( ? [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ! [X9] :
                              ( ~ lt(X8,X6)
                              | app(X9,cons(X8,nil)) != sK55
                              | ~ 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) != sK55
                              | ~ ssList(X13) )
                          | ~ ssItem(X12) )
                      | app(X11,cons(X10,nil)) != X4
                      | ~ ssList(X11) )
                  | ~ ssItem(X10) )
              & strictorderedP(sK55)
              & app(app(X4,sK55),X5) = sK56
              & ssList(X5) )
          & ssList(X4) )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ! [X9] :
                            ( ~ lt(X8,X6)
                            | app(X9,cons(X8,nil)) != sK55
                            | ~ 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) != sK55
                            | ~ ssList(X13) )
                        | ~ ssItem(X12) )
                    | app(X11,cons(X10,nil)) != X4
                    | ~ ssList(X11) )
                | ~ ssItem(X10) )
            & strictorderedP(sK55)
            & app(app(X4,sK55),X5) = sK56
            & ssList(X5) )
        & ssList(X4) )
   => ( ? [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ~ lt(X8,X6)
                          | app(X9,cons(X8,nil)) != sK55
                          | ~ 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) != sK55
                          | ~ ssList(X13) )
                      | ~ ssItem(X12) )
                  | app(X11,cons(X10,nil)) != sK57
                  | ~ ssList(X11) )
              | ~ ssItem(X10) )
          & strictorderedP(sK55)
          & sK56 = app(app(sK57,sK55),X5)
          & ssList(X5) )
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ? [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ~ lt(X8,X6)
                        | app(X9,cons(X8,nil)) != sK55
                        | ~ 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) != sK55
                        | ~ ssList(X13) )
                    | ~ ssItem(X12) )
                | app(X11,cons(X10,nil)) != sK57
                | ~ ssList(X11) )
            | ~ ssItem(X10) )
        & strictorderedP(sK55)
        & sK56 = app(app(sK57,sK55),X5)
        & ssList(X5) )
   => ( ! [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( ! [X9] :
                      ( ~ lt(X8,X6)
                      | app(X9,cons(X8,nil)) != sK55
                      | ~ ssList(X9) )
                  | ~ ssItem(X8) )
              | app(cons(X6,nil),X7) != sK58
              | ~ ssList(X7) )
          | ~ ssItem(X6) )
      & ! [X10] :
          ( ! [X11] :
              ( ! [X12] :
                  ( ! [X13] :
                      ( ~ lt(X10,X12)
                      | app(cons(X12,nil),X13) != sK55
                      | ~ ssList(X13) )
                  | ~ ssItem(X12) )
              | app(X11,cons(X10,nil)) != sK57
              | ~ ssList(X11) )
          | ~ ssItem(X10) )
      & strictorderedP(sK55)
      & sK56 = app(app(sK57,sK55),sK58)
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ( ( nil != sK55
      | nil = sK56 )
    & ~ duplicatefreeP(sK53)
    & ! [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( ! [X9] :
                    ( ~ lt(X8,X6)
                    | app(X9,cons(X8,nil)) != sK55
                    | ~ ssList(X9) )
                | ~ ssItem(X8) )
            | app(cons(X6,nil),X7) != sK58
            | ~ ssList(X7) )
        | ~ ssItem(X6) )
    & ! [X10] :
        ( ! [X11] :
            ( ! [X12] :
                ( ! [X13] :
                    ( ~ lt(X10,X12)
                    | app(cons(X12,nil),X13) != sK55
                    | ~ ssList(X13) )
                | ~ ssItem(X12) )
            | app(X11,cons(X10,nil)) != sK57
            | ~ ssList(X11) )
        | ~ ssItem(X10) )
    & strictorderedP(sK55)
    & sK56 = app(app(sK57,sK55),sK58)
    & ssList(sK58)
    & ssList(sK57)
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58])],[f223,f349,f348,f347,f346,f345,f344]) ).

fof(f417,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( lt(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ strictorderedP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f301]) ).

fof(f426,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | ssItem(sK40(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f309]) ).

fof(f427,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | ssItem(sK41(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f309]) ).

fof(f428,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | ssList(sK42(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f309]) ).

fof(f429,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | ssList(sK43(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f309]) ).

fof(f430,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | ssList(sK44(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f309]) ).

fof(f431,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f309]) ).

fof(f432,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | sK40(X0) = sK41(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f309]) ).

fof(f550,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f350]) ).

fof(f555,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f350]) ).

fof(f559,plain,
    strictorderedP(sK55),
    inference(cnf_transformation,[],[f350]) ).

fof(f562,plain,
    ~ duplicatefreeP(sK53),
    inference(cnf_transformation,[],[f350]) ).

fof(f564,plain,
    ~ duplicatefreeP(sK55),
    inference(definition_unfolding,[],[f562,f555]) ).

fof(f566,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f550,f555]) ).

fof(f577,plain,
    ! [X10,X8,X6,X9,X7] :
      ( lt(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ strictorderedP(app(app(X8,cons(X6,X9)),cons(X7,X10)))
      | ~ ssList(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f417]) ).

cnf(c_122,plain,
    ( ~ 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(cnf_transformation,[],[f577]) ).

cnf(c_123,plain,
    ( ~ ssList(X0)
    | sK40(X0) = sK41(X0)
    | duplicatefreeP(X0) ),
    inference(cnf_transformation,[],[f432]) ).

cnf(c_124,plain,
    ( ~ ssList(X0)
    | app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0
    | duplicatefreeP(X0) ),
    inference(cnf_transformation,[],[f431]) ).

cnf(c_125,plain,
    ( ~ ssList(X0)
    | ssList(sK44(X0))
    | duplicatefreeP(X0) ),
    inference(cnf_transformation,[],[f430]) ).

cnf(c_126,plain,
    ( ~ ssList(X0)
    | ssList(sK43(X0))
    | duplicatefreeP(X0) ),
    inference(cnf_transformation,[],[f429]) ).

cnf(c_127,plain,
    ( ~ ssList(X0)
    | ssList(sK42(X0))
    | duplicatefreeP(X0) ),
    inference(cnf_transformation,[],[f428]) ).

cnf(c_128,plain,
    ( ~ ssList(X0)
    | ssItem(sK41(X0))
    | duplicatefreeP(X0) ),
    inference(cnf_transformation,[],[f427]) ).

cnf(c_129,plain,
    ( ~ ssList(X0)
    | ssItem(sK40(X0))
    | duplicatefreeP(X0) ),
    inference(cnf_transformation,[],[f426]) ).

cnf(c_243,plain,
    ( ~ lt(X0,X0)
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f600]) ).

cnf(c_247,negated_conjecture,
    ~ duplicatefreeP(sK55),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_250,negated_conjecture,
    strictorderedP(sK55),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_257,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_3667,plain,
    ( X0 != sK55
    | ~ ssList(X0)
    | ssItem(sK40(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_129,c_247]) ).

cnf(c_3668,plain,
    ( ~ ssList(sK55)
    | ssItem(sK40(sK55)) ),
    inference(unflattening,[status(thm)],[c_3667]) ).

cnf(c_3681,plain,
    ( X0 != sK55
    | ~ ssList(X0)
    | ssList(sK42(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_127,c_247]) ).

cnf(c_3682,plain,
    ( ~ ssList(sK55)
    | ssList(sK42(sK55)) ),
    inference(unflattening,[status(thm)],[c_3681]) ).

cnf(c_3688,plain,
    ( X0 != sK55
    | ~ ssList(X0)
    | ssList(sK43(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_126,c_247]) ).

cnf(c_3689,plain,
    ( ~ ssList(sK55)
    | ssList(sK43(sK55)) ),
    inference(unflattening,[status(thm)],[c_3688]) ).

cnf(c_3695,plain,
    ( X0 != sK55
    | ~ ssList(X0)
    | ssList(sK44(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_125,c_247]) ).

cnf(c_3696,plain,
    ( ~ ssList(sK55)
    | ssList(sK44(sK55)) ),
    inference(unflattening,[status(thm)],[c_3695]) ).

cnf(c_9052,negated_conjecture,
    ssList(sK55),
    inference(demodulation,[status(thm)],[c_257]) ).

cnf(c_9057,negated_conjecture,
    strictorderedP(sK55),
    inference(demodulation,[status(thm)],[c_250]) ).

cnf(c_9060,negated_conjecture,
    ~ duplicatefreeP(sK55),
    inference(demodulation,[status(thm)],[c_247]) ).

cnf(c_12581,plain,
    ( sK40(sK55) = sK41(sK55)
    | duplicatefreeP(sK55) ),
    inference(superposition,[status(thm)],[c_9052,c_123]) ).

cnf(c_12588,plain,
    sK40(sK55) = sK41(sK55),
    inference(forward_subsumption_resolution,[status(thm)],[c_12581,c_9060]) ).

cnf(c_12697,plain,
    ( ~ ssList(sK55)
    | ssItem(sK40(sK55))
    | duplicatefreeP(sK55) ),
    inference(superposition,[status(thm)],[c_12588,c_128]) ).

cnf(c_12698,plain,
    ssItem(sK40(sK55)),
    inference(forward_subsumption_resolution,[status(thm)],[c_12697,c_9060,c_9052]) ).

cnf(c_14987,plain,
    ( ~ lt(sK40(sK55),sK40(sK55))
    | ~ ssItem(sK40(sK55)) ),
    inference(instantiation,[status(thm)],[c_243]) ).

cnf(c_23513,plain,
    ( app(app(sK42(sK55),cons(sK40(sK55),sK43(sK55))),cons(sK41(sK55),sK44(sK55))) = sK55
    | duplicatefreeP(sK55) ),
    inference(superposition,[status(thm)],[c_9052,c_124]) ).

cnf(c_23525,plain,
    ( app(app(sK42(sK55),cons(sK40(sK55),sK43(sK55))),cons(sK40(sK55),sK44(sK55))) = sK55
    | duplicatefreeP(sK55) ),
    inference(light_normalisation,[status(thm)],[c_23513,c_12588]) ).

cnf(c_23526,plain,
    app(app(sK42(sK55),cons(sK40(sK55),sK43(sK55))),cons(sK40(sK55),sK44(sK55))) = sK55,
    inference(forward_subsumption_resolution,[status(thm)],[c_23525,c_9060]) ).

cnf(c_37114,plain,
    ( ~ strictorderedP(app(app(sK42(sK55),cons(sK40(sK55),sK43(sK55))),cons(sK40(sK55),sK44(sK55))))
    | ~ ssItem(sK40(sK55))
    | ~ ssList(sK42(sK55))
    | ~ ssList(sK43(sK55))
    | ~ ssList(sK44(sK55))
    | ~ ssList(sK55)
    | lt(sK40(sK55),sK40(sK55)) ),
    inference(superposition,[status(thm)],[c_23526,c_122]) ).

cnf(c_37212,plain,
    ( ~ ssItem(sK40(sK55))
    | ~ ssList(sK42(sK55))
    | ~ ssList(sK43(sK55))
    | ~ ssList(sK44(sK55))
    | ~ ssList(sK55)
    | ~ strictorderedP(sK55)
    | lt(sK40(sK55),sK40(sK55)) ),
    inference(light_normalisation,[status(thm)],[c_37114,c_23526]) ).

cnf(c_37213,plain,
    ( ~ ssList(sK42(sK55))
    | ~ ssList(sK43(sK55))
    | ~ ssList(sK44(sK55))
    | lt(sK40(sK55),sK40(sK55)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_37212,c_9057,c_9052,c_12698]) ).

cnf(c_37284,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_37213,c_14987,c_3696,c_3689,c_3682,c_3668,c_257]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWC181+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n021.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 23:25:28 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.16/0.43  Running first-order theorem proving
% 0.16/0.43  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.07/2.64  % SZS status Started for theBenchmark.p
% 12.07/2.64  % SZS status Theorem for theBenchmark.p
% 12.07/2.64  
% 12.07/2.64  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 12.07/2.64  
% 12.07/2.64  ------  iProver source info
% 12.07/2.64  
% 12.07/2.64  git: date: 2024-05-02 19:28:25 +0000
% 12.07/2.64  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 12.07/2.64  git: non_committed_changes: false
% 12.07/2.64  
% 12.07/2.64  ------ Parsing...
% 12.07/2.64  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 12.07/2.64  
% 12.07/2.64  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 12.07/2.64  
% 12.07/2.64  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 12.07/2.64  
% 12.07/2.64  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 12.07/2.64  ------ Proving...
% 12.07/2.64  ------ Problem Properties 
% 12.07/2.64  
% 12.07/2.64  
% 12.07/2.64  clauses                                 192
% 12.07/2.64  conjectures                             9
% 12.07/2.64  EPR                                     57
% 12.07/2.64  Horn                                    124
% 12.07/2.64  unary                                   26
% 12.07/2.64  binary                                  40
% 12.07/2.64  lits                                    642
% 12.07/2.64  lits eq                                 86
% 12.07/2.64  fd_pure                                 0
% 12.07/2.64  fd_pseudo                               0
% 12.07/2.64  fd_cond                                 21
% 12.07/2.64  fd_pseudo_cond                          14
% 12.07/2.64  AC symbols                              0
% 12.07/2.64  
% 12.07/2.64  ------ Schedule dynamic 5 is on 
% 12.07/2.64  
% 12.07/2.64  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 12.07/2.64  
% 12.07/2.64  
% 12.07/2.64  ------ 
% 12.07/2.64  Current options:
% 12.07/2.64  ------ 
% 12.07/2.64  
% 12.07/2.64  
% 12.07/2.64  
% 12.07/2.64  
% 12.07/2.64  ------ Proving...
% 12.07/2.64  
% 12.07/2.64  
% 12.07/2.64  % SZS status Theorem for theBenchmark.p
% 12.07/2.64  
% 12.07/2.64  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.07/2.65  
% 12.07/2.65  
%------------------------------------------------------------------------------