TSTP Solution File: SWC241+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC241+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n029.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 03:11:43 EDT 2024

% Result   : Theorem 6.86s 1.63s
% Output   : CNFRefutation 6.86s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f93,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( lt(X0,X1)
          <=> ( leq(X0,X1)
              & X0 != X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ( ! [X8] :
                        ( ssItem(X8)
                       => ! [X9] :
                            ( ssList(X9)
                           => ! [X10] :
                                ( ? [X11] :
                                    ( leq(X8,X11)
                                    & memberP(X10,X11)
                                    & memberP(X9,X11)
                                    & ~ leq(X11,X8)
                                    & ssItem(X11) )
                                | app(app(X9,cons(X8,nil)),X10) != X2
                                | ~ ssList(X10) ) ) )
                    & nil != X2 )
                  | ? [X4] :
                      ( ? [X5] :
                          ( ? [X6] :
                              ( ! [X7] :
                                  ( leq(X4,X7)
                                  | ~ lt(X4,X7)
                                  | ~ memberP(X6,X7)
                                  | ~ memberP(X5,X7)
                                  | ~ ssItem(X7) )
                              & app(app(X5,cons(X4,nil)),X6) = X0
                              & ssList(X6) )
                          & ssList(X5) )
                      & ssItem(X4) )
                  | nil = X0
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( ! [X8] :
                          ( ssItem(X8)
                         => ! [X9] :
                              ( ssList(X9)
                             => ! [X10] :
                                  ( ? [X11] :
                                      ( leq(X8,X11)
                                      & memberP(X10,X11)
                                      & memberP(X9,X11)
                                      & ~ leq(X11,X8)
                                      & ssItem(X11) )
                                  | app(app(X9,cons(X8,nil)),X10) != X2
                                  | ~ ssList(X10) ) ) )
                      & nil != X2 )
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ! [X7] :
                                    ( leq(X4,X7)
                                    | ~ lt(X4,X7)
                                    | ~ memberP(X6,X7)
                                    | ~ memberP(X5,X7)
                                    | ~ ssItem(X7) )
                                & app(app(X5,cons(X4,nil)),X6) = X0
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) )
                    | nil = X0
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( ! [X4] :
                          ( ssItem(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ! [X6] :
                                  ( ? [X7] :
                                      ( leq(X4,X7)
                                      & memberP(X6,X7)
                                      & memberP(X5,X7)
                                      & ~ leq(X7,X4)
                                      & ssItem(X7) )
                                  | app(app(X5,cons(X4,nil)),X6) != X2
                                  | ~ ssList(X6) ) ) )
                      & nil != X2 )
                    | ? [X8] :
                        ( ? [X9] :
                            ( ? [X10] :
                                ( ! [X11] :
                                    ( leq(X8,X11)
                                    | ~ lt(X8,X11)
                                    | ~ memberP(X10,X11)
                                    | ~ memberP(X9,X11)
                                    | ~ ssItem(X11) )
                                & app(app(X9,cons(X8,nil)),X10) = X0
                                & ssList(X10) )
                            & ssList(X9) )
                        & ssItem(X8) )
                    | nil = X0
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f217,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( lt(X0,X1)
          <=> ( leq(X0,X1)
              & X0 != X1 ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f93]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ! [X7] :
                                    ( ~ leq(X4,X7)
                                    | ~ memberP(X6,X7)
                                    | ~ memberP(X5,X7)
                                    | leq(X7,X4)
                                    | ~ ssItem(X7) )
                                & app(app(X5,cons(X4,nil)),X6) = X2
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) )
                    | nil = X2 )
                  & ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( ? [X11] :
                                  ( ~ leq(X8,X11)
                                  & lt(X8,X11)
                                  & memberP(X10,X11)
                                  & memberP(X9,X11)
                                  & ssItem(X11) )
                              | app(app(X9,cons(X8,nil)),X10) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssItem(X8) )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f341,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( lt(X0,X1)
              | ~ leq(X0,X1)
              | X0 = X1 )
            & ( ( leq(X0,X1)
                & X0 != X1 )
              | ~ lt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f217]) ).

fof(f342,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( lt(X0,X1)
              | ~ leq(X0,X1)
              | X0 = X1 )
            & ( ( leq(X0,X1)
                & X0 != X1 )
              | ~ lt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f341]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ? [X4] :
                          ( ? [X5] :
                              ( ? [X6] :
                                  ( ! [X7] :
                                      ( ~ leq(X4,X7)
                                      | ~ memberP(X6,X7)
                                      | ~ memberP(X5,X7)
                                      | leq(X7,X4)
                                      | ~ ssItem(X7) )
                                  & app(app(X5,cons(X4,nil)),X6) = X2
                                  & ssList(X6) )
                              & ssList(X5) )
                          & ssItem(X4) )
                      | nil = X2 )
                    & ! [X8] :
                        ( ! [X9] :
                            ( ! [X10] :
                                ( ? [X11] :
                                    ( ~ leq(X8,X11)
                                    & lt(X8,X11)
                                    & memberP(X10,X11)
                                    & memberP(X9,X11)
                                    & ssItem(X11) )
                                | app(app(X9,cons(X8,nil)),X10) != X0
                                | ~ ssList(X10) )
                            | ~ ssList(X9) )
                        | ~ ssItem(X8) )
                    & nil != X0
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ! [X7] :
                                    ( ~ leq(X4,X7)
                                    | ~ memberP(X6,X7)
                                    | ~ memberP(X5,X7)
                                    | leq(X7,X4)
                                    | ~ ssItem(X7) )
                                & app(app(X5,cons(X4,nil)),X6) = X2
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) )
                    | nil = X2 )
                  & ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( ? [X11] :
                                  ( ~ leq(X8,X11)
                                  & lt(X8,X11)
                                  & memberP(X10,X11)
                                  & memberP(X9,X11)
                                  & ssItem(X11) )
                              | app(app(X9,cons(X8,nil)),X10) != sK53
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssItem(X8) )
                  & nil != sK53
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ? [X4] :
                      ( ? [X5] :
                          ( ? [X6] :
                              ( ! [X7] :
                                  ( ~ leq(X4,X7)
                                  | ~ memberP(X6,X7)
                                  | ~ memberP(X5,X7)
                                  | leq(X7,X4)
                                  | ~ ssItem(X7) )
                              & app(app(X5,cons(X4,nil)),X6) = X2
                              & ssList(X6) )
                          & ssList(X5) )
                      & ssItem(X4) )
                  | nil = X2 )
                & ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( ? [X11] :
                                ( ~ leq(X8,X11)
                                & lt(X8,X11)
                                & memberP(X10,X11)
                                & memberP(X9,X11)
                                & ssItem(X11) )
                            | app(app(X9,cons(X8,nil)),X10) != sK53
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssItem(X8) )
                & nil != sK53
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ? [X4] :
                    ( ? [X5] :
                        ( ? [X6] :
                            ( ! [X7] :
                                ( ~ leq(X4,X7)
                                | ~ memberP(X6,X7)
                                | ~ memberP(X5,X7)
                                | leq(X7,X4)
                                | ~ ssItem(X7) )
                            & app(app(X5,cons(X4,nil)),X6) = X2
                            & ssList(X6) )
                        & ssList(X5) )
                    & ssItem(X4) )
                | nil = X2 )
              & ! [X8] :
                  ( ! [X9] :
                      ( ! [X10] :
                          ( ? [X11] :
                              ( ~ leq(X8,X11)
                              & lt(X8,X11)
                              & memberP(X10,X11)
                              & memberP(X9,X11)
                              & ssItem(X11) )
                          | app(app(X9,cons(X8,nil)),X10) != sK53
                          | ~ ssList(X10) )
                      | ~ ssList(X9) )
                  | ~ ssItem(X8) )
              & nil != sK53
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ? [X4] :
                  ( ? [X5] :
                      ( ? [X6] :
                          ( ! [X7] :
                              ( ~ leq(X4,X7)
                              | ~ memberP(X6,X7)
                              | ~ memberP(X5,X7)
                              | leq(X7,X4)
                              | ~ ssItem(X7) )
                          & app(app(X5,cons(X4,nil)),X6) = X2
                          & ssList(X6) )
                      & ssList(X5) )
                  & ssItem(X4) )
              | nil = X2 )
            & ! [X8] :
                ( ! [X9] :
                    ( ! [X10] :
                        ( ? [X11] :
                            ( ~ leq(X8,X11)
                            & lt(X8,X11)
                            & memberP(X10,X11)
                            & memberP(X9,X11)
                            & ssItem(X11) )
                        | app(app(X9,cons(X8,nil)),X10) != sK53
                        | ~ ssList(X10) )
                    | ~ ssList(X9) )
                | ~ ssItem(X8) )
            & nil != sK53
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ? [X4] :
                ( ? [X5] :
                    ( ? [X6] :
                        ( ! [X7] :
                            ( ~ leq(X4,X7)
                            | ~ memberP(X6,X7)
                            | ~ memberP(X5,X7)
                            | leq(X7,X4)
                            | ~ ssItem(X7) )
                        & app(app(X5,cons(X4,nil)),X6) = sK55
                        & ssList(X6) )
                    & ssList(X5) )
                & ssItem(X4) )
            | nil = sK55 )
          & ! [X8] :
              ( ! [X9] :
                  ( ! [X10] :
                      ( ? [X11] :
                          ( ~ leq(X8,X11)
                          & lt(X8,X11)
                          & memberP(X10,X11)
                          & memberP(X9,X11)
                          & ssItem(X11) )
                      | app(app(X9,cons(X8,nil)),X10) != sK53
                      | ~ ssList(X10) )
                  | ~ ssList(X9) )
              | ~ ssItem(X8) )
          & nil != sK53
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ( ? [X4] :
              ( ? [X5] :
                  ( ? [X6] :
                      ( ! [X7] :
                          ( ~ leq(X4,X7)
                          | ~ memberP(X6,X7)
                          | ~ memberP(X5,X7)
                          | leq(X7,X4)
                          | ~ ssItem(X7) )
                      & app(app(X5,cons(X4,nil)),X6) = sK55
                      & ssList(X6) )
                  & ssList(X5) )
              & ssItem(X4) )
          | nil = sK55 )
        & ! [X8] :
            ( ! [X9] :
                ( ! [X10] :
                    ( ? [X11] :
                        ( ~ leq(X8,X11)
                        & lt(X8,X11)
                        & memberP(X10,X11)
                        & memberP(X9,X11)
                        & ssItem(X11) )
                    | app(app(X9,cons(X8,nil)),X10) != sK53
                    | ~ ssList(X10) )
                | ~ ssList(X9) )
            | ~ ssItem(X8) )
        & nil != sK53
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ? [X4] :
            ( ? [X5] :
                ( ? [X6] :
                    ( ! [X7] :
                        ( ~ leq(X4,X7)
                        | ~ memberP(X6,X7)
                        | ~ memberP(X5,X7)
                        | leq(X7,X4)
                        | ~ ssItem(X7) )
                    & app(app(X5,cons(X4,nil)),X6) = sK55
                    & ssList(X6) )
                & ssList(X5) )
            & ssItem(X4) )
        | nil = sK55 )
      & ! [X8] :
          ( ! [X9] :
              ( ! [X10] :
                  ( ? [X11] :
                      ( ~ leq(X8,X11)
                      & lt(X8,X11)
                      & memberP(X10,X11)
                      & memberP(X9,X11)
                      & ssItem(X11) )
                  | app(app(X9,cons(X8,nil)),X10) != sK53
                  | ~ ssList(X10) )
              | ~ ssList(X9) )
          | ~ ssItem(X8) )
      & nil != sK53
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( ? [X6] :
                ( ! [X7] :
                    ( ~ leq(X4,X7)
                    | ~ memberP(X6,X7)
                    | ~ memberP(X5,X7)
                    | leq(X7,X4)
                    | ~ ssItem(X7) )
                & app(app(X5,cons(X4,nil)),X6) = sK55
                & ssList(X6) )
            & ssList(X5) )
        & ssItem(X4) )
   => ( ? [X5] :
          ( ? [X6] :
              ( ! [X7] :
                  ( ~ leq(sK57,X7)
                  | ~ memberP(X6,X7)
                  | ~ memberP(X5,X7)
                  | leq(X7,sK57)
                  | ~ ssItem(X7) )
              & sK55 = app(app(X5,cons(sK57,nil)),X6)
              & ssList(X6) )
          & ssList(X5) )
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X5] :
        ( ? [X6] :
            ( ! [X7] :
                ( ~ leq(sK57,X7)
                | ~ memberP(X6,X7)
                | ~ memberP(X5,X7)
                | leq(X7,sK57)
                | ~ ssItem(X7) )
            & sK55 = app(app(X5,cons(sK57,nil)),X6)
            & ssList(X6) )
        & ssList(X5) )
   => ( ? [X6] :
          ( ! [X7] :
              ( ~ leq(sK57,X7)
              | ~ memberP(X6,X7)
              | ~ memberP(sK58,X7)
              | leq(X7,sK57)
              | ~ ssItem(X7) )
          & sK55 = app(app(sK58,cons(sK57,nil)),X6)
          & ssList(X6) )
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ? [X6] :
        ( ! [X7] :
            ( ~ leq(sK57,X7)
            | ~ memberP(X6,X7)
            | ~ memberP(sK58,X7)
            | leq(X7,sK57)
            | ~ ssItem(X7) )
        & sK55 = app(app(sK58,cons(sK57,nil)),X6)
        & ssList(X6) )
   => ( ! [X7] :
          ( ~ leq(sK57,X7)
          | ~ memberP(sK59,X7)
          | ~ memberP(sK58,X7)
          | leq(X7,sK57)
          | ~ ssItem(X7) )
      & sK55 = app(app(sK58,cons(sK57,nil)),sK59)
      & ssList(sK59) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ! [X8,X9,X10] :
      ( ? [X11] :
          ( ~ leq(X8,X11)
          & lt(X8,X11)
          & memberP(X10,X11)
          & memberP(X9,X11)
          & ssItem(X11) )
     => ( ~ leq(X8,sK60(X8,X9,X10))
        & lt(X8,sK60(X8,X9,X10))
        & memberP(X10,sK60(X8,X9,X10))
        & memberP(X9,sK60(X8,X9,X10))
        & ssItem(sK60(X8,X9,X10)) ) ),
    introduced(choice_axiom,[]) ).

fof(f351,plain,
    ( ( ( ! [X7] :
            ( ~ leq(sK57,X7)
            | ~ memberP(sK59,X7)
            | ~ memberP(sK58,X7)
            | leq(X7,sK57)
            | ~ ssItem(X7) )
        & sK55 = app(app(sK58,cons(sK57,nil)),sK59)
        & ssList(sK59)
        & ssList(sK58)
        & ssItem(sK57) )
      | nil = sK55 )
    & ! [X8] :
        ( ! [X9] :
            ( ! [X10] :
                ( ( ~ leq(X8,sK60(X8,X9,X10))
                  & lt(X8,sK60(X8,X9,X10))
                  & memberP(X10,sK60(X8,X9,X10))
                  & memberP(X9,sK60(X8,X9,X10))
                  & ssItem(sK60(X8,X9,X10)) )
                | app(app(X9,cons(X8,nil)),X10) != sK53
                | ~ ssList(X10) )
            | ~ ssList(X9) )
        | ~ ssItem(X8) )
    & nil != sK53
    & 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,sK59,sK60])],[f222,f350,f349,f348,f347,f346,f345,f344,f343]) ).

fof(f547,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | ~ lt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f342]) ).

fof(f556,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f351]) ).

fof(f557,plain,
    nil != sK53,
    inference(cnf_transformation,[],[f351]) ).

fof(f558,plain,
    ! [X10,X8,X9] :
      ( ssItem(sK60(X8,X9,X10))
      | app(app(X9,cons(X8,nil)),X10) != sK53
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssItem(X8) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f561,plain,
    ! [X10,X8,X9] :
      ( lt(X8,sK60(X8,X9,X10))
      | app(app(X9,cons(X8,nil)),X10) != sK53
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssItem(X8) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f562,plain,
    ! [X10,X8,X9] :
      ( ~ leq(X8,sK60(X8,X9,X10))
      | app(app(X9,cons(X8,nil)),X10) != sK53
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssItem(X8) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f563,plain,
    ( ssItem(sK57)
    | nil = sK55 ),
    inference(cnf_transformation,[],[f351]) ).

fof(f564,plain,
    ( ssList(sK58)
    | nil = sK55 ),
    inference(cnf_transformation,[],[f351]) ).

fof(f565,plain,
    ( ssList(sK59)
    | nil = sK55 ),
    inference(cnf_transformation,[],[f351]) ).

fof(f566,plain,
    ( sK55 = app(app(sK58,cons(sK57,nil)),sK59)
    | nil = sK55 ),
    inference(cnf_transformation,[],[f351]) ).

fof(f568,plain,
    ! [X10,X8,X9] :
      ( ~ leq(X8,sK60(X8,X9,X10))
      | app(app(X9,cons(X8,nil)),X10) != sK55
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssItem(X8) ),
    inference(definition_unfolding,[],[f562,f556]) ).

fof(f569,plain,
    ! [X10,X8,X9] :
      ( lt(X8,sK60(X8,X9,X10))
      | app(app(X9,cons(X8,nil)),X10) != sK55
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssItem(X8) ),
    inference(definition_unfolding,[],[f561,f556]) ).

fof(f572,plain,
    ! [X10,X8,X9] :
      ( ssItem(sK60(X8,X9,X10))
      | app(app(X9,cons(X8,nil)),X10) != sK55
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssItem(X8) ),
    inference(definition_unfolding,[],[f558,f556]) ).

fof(f573,plain,
    nil != sK55,
    inference(definition_unfolding,[],[f557,f556]) ).

cnf(c_242,plain,
    ( ~ lt(X0,X1)
    | ~ ssItem(X0)
    | ~ ssItem(X1)
    | leq(X0,X1) ),
    inference(cnf_transformation,[],[f547]) ).

cnf(c_247,negated_conjecture,
    ( app(app(sK58,cons(sK57,nil)),sK59) = sK55
    | nil = sK55 ),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_248,negated_conjecture,
    ( nil = sK55
    | ssList(sK59) ),
    inference(cnf_transformation,[],[f565]) ).

cnf(c_249,negated_conjecture,
    ( nil = sK55
    | ssList(sK58) ),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_250,negated_conjecture,
    ( nil = sK55
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f563]) ).

cnf(c_251,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ leq(X1,sK60(X1,X0,X2))
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2) ),
    inference(cnf_transformation,[],[f568]) ).

cnf(c_252,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | lt(X1,sK60(X1,X0,X2)) ),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_255,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ssItem(sK60(X1,X0,X2)) ),
    inference(cnf_transformation,[],[f572]) ).

cnf(c_256,negated_conjecture,
    nil != sK55,
    inference(cnf_transformation,[],[f573]) ).

cnf(c_372,negated_conjecture,
    ssItem(sK57),
    inference(global_subsumption_just,[status(thm)],[c_250,c_256,c_250]) ).

cnf(c_374,negated_conjecture,
    ssList(sK58),
    inference(global_subsumption_just,[status(thm)],[c_249,c_256,c_249]) ).

cnf(c_376,negated_conjecture,
    ssList(sK59),
    inference(global_subsumption_just,[status(thm)],[c_248,c_256,c_248]) ).

cnf(c_390,negated_conjecture,
    app(app(sK58,cons(sK57,nil)),sK59) = sK55,
    inference(global_subsumption_just,[status(thm)],[c_247,c_256,c_247]) ).

cnf(c_9050,plain,
    cons(sK57,nil) = sP0_iProver_def,
    definition ).

cnf(c_9051,plain,
    app(sK58,sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_9052,plain,
    app(sP1_iProver_def,sK59) = sP2_iProver_def,
    definition ).

cnf(c_9054,negated_conjecture,
    sP2_iProver_def = sK55,
    inference(demodulation,[status(thm)],[c_390,c_9050,c_9051,c_9052]) ).

cnf(c_9055,negated_conjecture,
    ssList(sK59),
    inference(demodulation,[status(thm)],[c_376]) ).

cnf(c_9056,negated_conjecture,
    ssList(sK58),
    inference(demodulation,[status(thm)],[c_374]) ).

cnf(c_9057,negated_conjecture,
    ssItem(sK57),
    inference(demodulation,[status(thm)],[c_372]) ).

cnf(c_9061,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ssItem(sK60(X1,X0,X2)) ),
    inference(demodulation,[status(thm)],[c_255]) ).

cnf(c_9064,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | lt(X1,sK60(X1,X0,X2)) ),
    inference(demodulation,[status(thm)],[c_252]) ).

cnf(c_9065,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ leq(X1,sK60(X1,X0,X2))
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2) ),
    inference(demodulation,[status(thm)],[c_251]) ).

cnf(c_12008,plain,
    ( app(app(X0,cons(X1,nil)),X2) != sP2_iProver_def
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ssItem(sK60(X1,X0,X2)) ),
    inference(light_normalisation,[status(thm)],[c_9061,c_9054]) ).

cnf(c_12041,plain,
    ( app(app(X0,cons(X1,nil)),X2) != sP2_iProver_def
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | lt(X1,sK60(X1,X0,X2)) ),
    inference(light_normalisation,[status(thm)],[c_9064,c_9054]) ).

cnf(c_12052,plain,
    ( app(app(X0,cons(X1,nil)),X2) != sP2_iProver_def
    | ~ leq(X1,sK60(X1,X0,X2))
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2) ),
    inference(light_normalisation,[status(thm)],[c_9065,c_9054]) ).

cnf(c_12063,plain,
    ( app(app(X0,sP0_iProver_def),X1) != sP2_iProver_def
    | ~ leq(sK57,sK60(sK57,X0,X1))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssItem(sK57) ),
    inference(superposition,[status(thm)],[c_9050,c_12052]) ).

cnf(c_12064,plain,
    ( app(app(X0,sP0_iProver_def),X1) != sP2_iProver_def
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssItem(sK57)
    | lt(sK57,sK60(sK57,X0,X1)) ),
    inference(superposition,[status(thm)],[c_9050,c_12041]) ).

cnf(c_12067,plain,
    ( app(app(X0,sP0_iProver_def),X1) != sP2_iProver_def
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssItem(sK57)
    | ssItem(sK60(sK57,X0,X1)) ),
    inference(superposition,[status(thm)],[c_9050,c_12008]) ).

cnf(c_12068,plain,
    ( app(app(X0,sP0_iProver_def),X1) != sP2_iProver_def
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ssItem(sK60(sK57,X0,X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12067,c_9057]) ).

cnf(c_12083,plain,
    ( app(app(X0,sP0_iProver_def),X1) != sP2_iProver_def
    | ~ ssList(X0)
    | ~ ssList(X1)
    | lt(sK57,sK60(sK57,X0,X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12064,c_9057]) ).

cnf(c_12088,plain,
    ( app(app(X0,sP0_iProver_def),X1) != sP2_iProver_def
    | ~ leq(sK57,sK60(sK57,X0,X1))
    | ~ ssList(X0)
    | ~ ssList(X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12063,c_9057]) ).

cnf(c_12165,plain,
    ( app(sP1_iProver_def,X0) != sP2_iProver_def
    | ~ leq(sK57,sK60(sK57,sK58,X0))
    | ~ ssList(X0)
    | ~ ssList(sK58) ),
    inference(superposition,[status(thm)],[c_9051,c_12088]) ).

cnf(c_12166,plain,
    ( app(sP1_iProver_def,X0) != sP2_iProver_def
    | ~ ssList(X0)
    | ~ ssList(sK58)
    | lt(sK57,sK60(sK57,sK58,X0)) ),
    inference(superposition,[status(thm)],[c_9051,c_12083]) ).

cnf(c_12169,plain,
    ( app(sP1_iProver_def,X0) != sP2_iProver_def
    | ~ ssList(X0)
    | ~ ssList(sK58)
    | ssItem(sK60(sK57,sK58,X0)) ),
    inference(superposition,[status(thm)],[c_9051,c_12068]) ).

cnf(c_12170,plain,
    ( app(sP1_iProver_def,X0) != sP2_iProver_def
    | ~ ssList(X0)
    | ssItem(sK60(sK57,sK58,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12169,c_9056]) ).

cnf(c_12182,plain,
    ( app(sP1_iProver_def,X0) != sP2_iProver_def
    | ~ ssList(X0)
    | lt(sK57,sK60(sK57,sK58,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12166,c_9056]) ).

cnf(c_12186,plain,
    ( app(sP1_iProver_def,X0) != sP2_iProver_def
    | ~ leq(sK57,sK60(sK57,sK58,X0))
    | ~ ssList(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12165,c_9056]) ).

cnf(c_12269,plain,
    ( ~ leq(sK57,sK60(sK57,sK58,sK59))
    | ~ ssList(sK59) ),
    inference(superposition,[status(thm)],[c_9052,c_12186]) ).

cnf(c_12270,plain,
    ( ~ ssList(sK59)
    | lt(sK57,sK60(sK57,sK58,sK59)) ),
    inference(superposition,[status(thm)],[c_9052,c_12182]) ).

cnf(c_12273,plain,
    ( ~ ssList(sK59)
    | ssItem(sK60(sK57,sK58,sK59)) ),
    inference(superposition,[status(thm)],[c_9052,c_12170]) ).

cnf(c_12274,plain,
    ssItem(sK60(sK57,sK58,sK59)),
    inference(forward_subsumption_resolution,[status(thm)],[c_12273,c_9055]) ).

cnf(c_12277,plain,
    lt(sK57,sK60(sK57,sK58,sK59)),
    inference(forward_subsumption_resolution,[status(thm)],[c_12270,c_9055]) ).

cnf(c_12278,plain,
    ~ leq(sK57,sK60(sK57,sK58,sK59)),
    inference(forward_subsumption_resolution,[status(thm)],[c_12269,c_9055]) ).

cnf(c_15257,plain,
    ( ~ ssItem(sK60(sK57,sK58,sK59))
    | ~ ssItem(sK57)
    | leq(sK57,sK60(sK57,sK58,sK59)) ),
    inference(superposition,[status(thm)],[c_12277,c_242]) ).

cnf(c_15258,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_15257,c_12278,c_9057,c_12274]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SWC241+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n029.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 23:58:22 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.17/0.44  Running first-order theorem proving
% 0.17/0.44  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
% 6.86/1.63  % SZS status Started for theBenchmark.p
% 6.86/1.63  % SZS status Theorem for theBenchmark.p
% 6.86/1.63  
% 6.86/1.63  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 6.86/1.63  
% 6.86/1.63  ------  iProver source info
% 6.86/1.63  
% 6.86/1.63  git: date: 2024-05-02 19:28:25 +0000
% 6.86/1.63  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 6.86/1.63  git: non_committed_changes: false
% 6.86/1.63  
% 6.86/1.63  ------ Parsing...
% 6.86/1.63  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 6.86/1.63  
% 6.86/1.63  ------ 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 
% 6.86/1.63  
% 6.86/1.63  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 6.86/1.63  
% 6.86/1.63  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 6.86/1.63  ------ Proving...
% 6.86/1.63  ------ Problem Properties 
% 6.86/1.63  
% 6.86/1.63  
% 6.86/1.63  clauses                                 196
% 6.86/1.63  conjectures                             13
% 6.86/1.63  EPR                                     57
% 6.86/1.63  Horn                                    128
% 6.86/1.63  unary                                   26
% 6.86/1.63  binary                                  40
% 6.86/1.63  lits                                    658
% 6.86/1.63  lits eq                                 88
% 6.86/1.63  fd_pure                                 0
% 6.86/1.63  fd_pseudo                               0
% 6.86/1.63  fd_cond                                 21
% 6.86/1.63  fd_pseudo_cond                          14
% 6.86/1.63  AC symbols                              0
% 6.86/1.63  
% 6.86/1.63  ------ Schedule dynamic 5 is on 
% 6.86/1.63  
% 6.86/1.63  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.86/1.63  
% 6.86/1.63  
% 6.86/1.63  ------ 
% 6.86/1.63  Current options:
% 6.86/1.63  ------ 
% 6.86/1.63  
% 6.86/1.63  
% 6.86/1.63  
% 6.86/1.63  
% 6.86/1.63  ------ Proving...
% 6.86/1.63  
% 6.86/1.63  
% 6.86/1.63  % SZS status Theorem for theBenchmark.p
% 6.86/1.63  
% 6.86/1.63  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.86/1.63  
% 6.86/1.63  
%------------------------------------------------------------------------------