TSTP Solution File: SWC327+1 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC327+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 03:12:01 EDT 2024

% Result   : Theorem 0.46s 1.15s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( nil = X1
                        | nil != X0 )
                      & ? [X8] :
                          ( equalelemsP(X0)
                          & ! [X9] :
                              ( ssItem(X9)
                             => ! [X10] :
                                  ( ssList(X10)
                                 => ( ! [X11] :
                                        ( ssList(X11)
                                       => app(X11,cons(X9,nil)) != X0 )
                                    | app(cons(X9,nil),X10) != X8 ) ) )
                          & app(X0,X8) = X1
                          & ssList(X8) ) )
                    | ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( ssList(X4)
                       => ( ? [X5] :
                              ( ? [X6] :
                                  ( ? [X7] :
                                      ( app(X7,cons(X5,nil)) = X2
                                      & ssList(X7) )
                                  & app(cons(X5,nil),X6) = X4
                                  & ssList(X6) )
                              & ssItem(X5) )
                          | ~ equalelemsP(X2)
                          | app(X2,X4) != 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 )
                        & ? [X8] :
                            ( equalelemsP(X0)
                            & ! [X9] :
                                ( ssItem(X9)
                               => ! [X10] :
                                    ( ssList(X10)
                                   => ( ! [X11] :
                                          ( ssList(X11)
                                         => app(X11,cons(X9,nil)) != X0 )
                                      | app(cons(X9,nil),X10) != X8 ) ) )
                            & app(X0,X8) = X1
                            & ssList(X8) ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ( ? [X5] :
                                ( ? [X6] :
                                    ( ? [X7] :
                                        ( app(X7,cons(X5,nil)) = X2
                                        & ssList(X7) )
                                    & app(cons(X5,nil),X6) = X4
                                    & ssList(X6) )
                                & ssItem(X5) )
                            | ~ equalelemsP(X2)
                            | app(X2,X4) != 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] :
                            ( equalelemsP(X0)
                            & ! [X5] :
                                ( ssItem(X5)
                               => ! [X6] :
                                    ( ssList(X6)
                                   => ( ! [X7] :
                                          ( ssList(X7)
                                         => app(X7,cons(X5,nil)) != X0 )
                                      | app(cons(X5,nil),X6) != X4 ) ) )
                            & app(X0,X4) = X1
                            & ssList(X4) ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X8] :
                          ( ssList(X8)
                         => ( ? [X9] :
                                ( ? [X10] :
                                    ( ? [X11] :
                                        ( app(X11,cons(X9,nil)) = X2
                                        & ssList(X11) )
                                    & app(cons(X9,nil),X10) = X8
                                    & ssList(X10) )
                                & ssItem(X9) )
                            | ~ equalelemsP(X2)
                            | app(X2,X8) != X3 ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

fof(f233,plain,
    ! [X0,X1] :
      ( ! [X4] :
          ( ~ equalelemsP(X0)
          | ? [X5] :
              ( ? [X6] :
                  ( ? [X7] :
                      ( app(X7,cons(X5,nil)) = X0
                      & ssList(X7) )
                  & app(cons(X5,nil),X6) = X4
                  & ssList(X6) )
              & ssItem(X5) )
          | app(X0,X4) != X1
          | ~ ssList(X4) )
      | ~ sP6(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f234,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = X0 )
                    | sP6(X0,X1) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( ! [X11] :
                                  ( app(X11,cons(X9,nil)) != X2
                                  | ~ ssList(X11) )
                              | app(cons(X9,nil),X10) != X8
                              | ~ ssList(X10) )
                          | ~ ssItem(X9) )
                      & equalelemsP(X2)
                      & app(X2,X8) = X3
                      & ssList(X8) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f223,f233]) ).

fof(f346,plain,
    ! [X0,X1] :
      ( ! [X4] :
          ( ~ equalelemsP(X0)
          | ? [X5] :
              ( ? [X6] :
                  ( ? [X7] :
                      ( app(X7,cons(X5,nil)) = X0
                      & ssList(X7) )
                  & app(cons(X5,nil),X6) = X4
                  & ssList(X6) )
              & ssItem(X5) )
          | app(X0,X4) != X1
          | ~ ssList(X4) )
      | ~ sP6(X0,X1) ),
    inference(nnf_transformation,[],[f233]) ).

fof(f347,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ equalelemsP(X0)
          | ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( app(X5,cons(X3,nil)) = X0
                      & ssList(X5) )
                  & app(cons(X3,nil),X4) = X2
                  & ssList(X4) )
              & ssItem(X3) )
          | app(X0,X2) != X1
          | ~ ssList(X2) )
      | ~ sP6(X0,X1) ),
    inference(rectify,[],[f346]) ).

fof(f348,plain,
    ! [X0,X2] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( app(X5,cons(X3,nil)) = X0
                  & ssList(X5) )
              & app(cons(X3,nil),X4) = X2
              & ssList(X4) )
          & ssItem(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( app(X5,cons(sK54(X0,X2),nil)) = X0
                & ssList(X5) )
            & app(cons(sK54(X0,X2),nil),X4) = X2
            & ssList(X4) )
        & ssItem(sK54(X0,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ! [X0,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X5,cons(sK54(X0,X2),nil)) = X0
              & ssList(X5) )
          & app(cons(sK54(X0,X2),nil),X4) = X2
          & ssList(X4) )
     => ( ? [X5] :
            ( app(X5,cons(sK54(X0,X2),nil)) = X0
            & ssList(X5) )
        & app(cons(sK54(X0,X2),nil),sK55(X0,X2)) = X2
        & ssList(sK55(X0,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ! [X0,X2] :
      ( ? [X5] :
          ( app(X5,cons(sK54(X0,X2),nil)) = X0
          & ssList(X5) )
     => ( app(sK56(X0,X2),cons(sK54(X0,X2),nil)) = X0
        & ssList(sK56(X0,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f351,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ equalelemsP(X0)
          | ( app(sK56(X0,X2),cons(sK54(X0,X2),nil)) = X0
            & ssList(sK56(X0,X2))
            & app(cons(sK54(X0,X2),nil),sK55(X0,X2)) = X2
            & ssList(sK55(X0,X2))
            & ssItem(sK54(X0,X2)) )
          | app(X0,X2) != X1
          | ~ ssList(X2) )
      | ~ sP6(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55,sK56])],[f347,f350,f349,f348]) ).

fof(f352,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = X0 )
                    | sP6(X0,X1) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( app(X7,cons(X5,nil)) != X2
                                  | ~ ssList(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & equalelemsP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(rectify,[],[f234]) ).

fof(f353,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil != X1
                        & nil = X0 )
                      | sP6(X0,X1) )
                    & ( nil != X2
                      | nil = X3 )
                    & ? [X4] :
                        ( ! [X5] :
                            ( ! [X6] :
                                ( ! [X7] :
                                    ( app(X7,cons(X5,nil)) != X2
                                    | ~ ssList(X7) )
                                | app(cons(X5,nil),X6) != X4
                                | ~ ssList(X6) )
                            | ~ ssItem(X5) )
                        & equalelemsP(X2)
                        & app(X2,X4) = X3
                        & ssList(X4) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = sK57 )
                    | sP6(sK57,X1) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( app(X7,cons(X5,nil)) != X2
                                  | ~ ssList(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & equalelemsP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & sK57 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f354,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil != X1
                    & nil = sK57 )
                  | sP6(sK57,X1) )
                & ( nil != X2
                  | nil = X3 )
                & ? [X4] :
                    ( ! [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( app(X7,cons(X5,nil)) != X2
                                | ~ ssList(X7) )
                            | app(cons(X5,nil),X6) != X4
                            | ~ ssList(X6) )
                        | ~ ssItem(X5) )
                    & equalelemsP(X2)
                    & app(X2,X4) = X3
                    & ssList(X4) )
                & sK57 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil != sK58
                  & nil = sK57 )
                | sP6(sK57,sK58) )
              & ( nil != X2
                | nil = X3 )
              & ? [X4] :
                  ( ! [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( app(X7,cons(X5,nil)) != X2
                              | ~ ssList(X7) )
                          | app(cons(X5,nil),X6) != X4
                          | ~ ssList(X6) )
                      | ~ ssItem(X5) )
                  & equalelemsP(X2)
                  & app(X2,X4) = X3
                  & ssList(X4) )
              & sK57 = X2
              & sK58 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f355,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil != sK58
                & nil = sK57 )
              | sP6(sK57,sK58) )
            & ( nil != X2
              | nil = X3 )
            & ? [X4] :
                ( ! [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( app(X7,cons(X5,nil)) != X2
                            | ~ ssList(X7) )
                        | app(cons(X5,nil),X6) != X4
                        | ~ ssList(X6) )
                    | ~ ssItem(X5) )
                & equalelemsP(X2)
                & app(X2,X4) = X3
                & ssList(X4) )
            & sK57 = X2
            & sK58 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil != sK58
              & nil = sK57 )
            | sP6(sK57,sK58) )
          & ( nil != sK59
            | nil = X3 )
          & ? [X4] :
              ( ! [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( app(X7,cons(X5,nil)) != sK59
                          | ~ ssList(X7) )
                      | app(cons(X5,nil),X6) != X4
                      | ~ ssList(X6) )
                  | ~ ssItem(X5) )
              & equalelemsP(sK59)
              & app(sK59,X4) = X3
              & ssList(X4) )
          & sK57 = sK59
          & sK58 = X3
          & ssList(X3) )
      & ssList(sK59) ) ),
    introduced(choice_axiom,[]) ).

fof(f356,plain,
    ( ? [X3] :
        ( ( ( nil != sK58
            & nil = sK57 )
          | sP6(sK57,sK58) )
        & ( nil != sK59
          | nil = X3 )
        & ? [X4] :
            ( ! [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( app(X7,cons(X5,nil)) != sK59
                        | ~ ssList(X7) )
                    | app(cons(X5,nil),X6) != X4
                    | ~ ssList(X6) )
                | ~ ssItem(X5) )
            & equalelemsP(sK59)
            & app(sK59,X4) = X3
            & ssList(X4) )
        & sK57 = sK59
        & sK58 = X3
        & ssList(X3) )
   => ( ( ( nil != sK58
          & nil = sK57 )
        | sP6(sK57,sK58) )
      & ( nil != sK59
        | nil = sK60 )
      & ? [X4] :
          ( ! [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( app(X7,cons(X5,nil)) != sK59
                      | ~ ssList(X7) )
                  | app(cons(X5,nil),X6) != X4
                  | ~ ssList(X6) )
              | ~ ssItem(X5) )
          & equalelemsP(sK59)
          & app(sK59,X4) = sK60
          & ssList(X4) )
      & sK57 = sK59
      & sK58 = sK60
      & ssList(sK60) ) ),
    introduced(choice_axiom,[]) ).

fof(f357,plain,
    ( ? [X4] :
        ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( app(X7,cons(X5,nil)) != sK59
                    | ~ ssList(X7) )
                | app(cons(X5,nil),X6) != X4
                | ~ ssList(X6) )
            | ~ ssItem(X5) )
        & equalelemsP(sK59)
        & app(sK59,X4) = sK60
        & ssList(X4) )
   => ( ! [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( app(X7,cons(X5,nil)) != sK59
                  | ~ ssList(X7) )
              | app(cons(X5,nil),X6) != sK61
              | ~ ssList(X6) )
          | ~ ssItem(X5) )
      & equalelemsP(sK59)
      & sK60 = app(sK59,sK61)
      & ssList(sK61) ) ),
    introduced(choice_axiom,[]) ).

fof(f358,plain,
    ( ( ( nil != sK58
        & nil = sK57 )
      | sP6(sK57,sK58) )
    & ( nil != sK59
      | nil = sK60 )
    & ! [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( app(X7,cons(X5,nil)) != sK59
                | ~ ssList(X7) )
            | app(cons(X5,nil),X6) != sK61
            | ~ ssList(X6) )
        | ~ ssItem(X5) )
    & equalelemsP(sK59)
    & sK60 = app(sK59,sK61)
    & ssList(sK61)
    & sK57 = sK59
    & sK58 = sK60
    & ssList(sK60)
    & ssList(sK59)
    & ssList(sK58)
    & ssList(sK57) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60,sK61])],[f352,f357,f356,f355,f354,f353]) ).

fof(f558,plain,
    ! [X2,X0,X1] :
      ( ~ equalelemsP(X0)
      | ssItem(sK54(X0,X2))
      | app(X0,X2) != X1
      | ~ ssList(X2)
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f559,plain,
    ! [X2,X0,X1] :
      ( ~ equalelemsP(X0)
      | ssList(sK55(X0,X2))
      | app(X0,X2) != X1
      | ~ ssList(X2)
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f560,plain,
    ! [X2,X0,X1] :
      ( ~ equalelemsP(X0)
      | app(cons(sK54(X0,X2),nil),sK55(X0,X2)) = X2
      | app(X0,X2) != X1
      | ~ ssList(X2)
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f561,plain,
    ! [X2,X0,X1] :
      ( ~ equalelemsP(X0)
      | ssList(sK56(X0,X2))
      | app(X0,X2) != X1
      | ~ ssList(X2)
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f562,plain,
    ! [X2,X0,X1] :
      ( ~ equalelemsP(X0)
      | app(sK56(X0,X2),cons(sK54(X0,X2),nil)) = X0
      | app(X0,X2) != X1
      | ~ ssList(X2)
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f567,plain,
    sK58 = sK60,
    inference(cnf_transformation,[],[f358]) ).

fof(f568,plain,
    sK57 = sK59,
    inference(cnf_transformation,[],[f358]) ).

fof(f569,plain,
    ssList(sK61),
    inference(cnf_transformation,[],[f358]) ).

fof(f570,plain,
    sK60 = app(sK59,sK61),
    inference(cnf_transformation,[],[f358]) ).

fof(f571,plain,
    equalelemsP(sK59),
    inference(cnf_transformation,[],[f358]) ).

fof(f572,plain,
    ! [X6,X7,X5] :
      ( app(X7,cons(X5,nil)) != sK59
      | ~ ssList(X7)
      | app(cons(X5,nil),X6) != sK61
      | ~ ssList(X6)
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f358]) ).

fof(f573,plain,
    ( nil != sK59
    | nil = sK60 ),
    inference(cnf_transformation,[],[f358]) ).

fof(f574,plain,
    ( nil = sK57
    | sP6(sK57,sK58) ),
    inference(cnf_transformation,[],[f358]) ).

fof(f575,plain,
    ( nil != sK58
    | sP6(sK57,sK58) ),
    inference(cnf_transformation,[],[f358]) ).

fof(f576,plain,
    ( nil != sK60
    | sP6(sK59,sK60) ),
    inference(definition_unfolding,[],[f575,f567,f568,f567]) ).

fof(f577,plain,
    ( nil = sK59
    | sP6(sK59,sK60) ),
    inference(definition_unfolding,[],[f574,f568,f568,f567]) ).

fof(f607,plain,
    ! [X2,X0] :
      ( ~ equalelemsP(X0)
      | app(sK56(X0,X2),cons(sK54(X0,X2),nil)) = X0
      | ~ ssList(X2)
      | ~ sP6(X0,app(X0,X2)) ),
    inference(equality_resolution,[],[f562]) ).

fof(f608,plain,
    ! [X2,X0] :
      ( ~ equalelemsP(X0)
      | ssList(sK56(X0,X2))
      | ~ ssList(X2)
      | ~ sP6(X0,app(X0,X2)) ),
    inference(equality_resolution,[],[f561]) ).

fof(f609,plain,
    ! [X2,X0] :
      ( ~ equalelemsP(X0)
      | app(cons(sK54(X0,X2),nil),sK55(X0,X2)) = X2
      | ~ ssList(X2)
      | ~ sP6(X0,app(X0,X2)) ),
    inference(equality_resolution,[],[f560]) ).

fof(f610,plain,
    ! [X2,X0] :
      ( ~ equalelemsP(X0)
      | ssList(sK55(X0,X2))
      | ~ ssList(X2)
      | ~ sP6(X0,app(X0,X2)) ),
    inference(equality_resolution,[],[f559]) ).

fof(f611,plain,
    ! [X2,X0] :
      ( ~ equalelemsP(X0)
      | ssItem(sK54(X0,X2))
      | ~ ssList(X2)
      | ~ sP6(X0,app(X0,X2)) ),
    inference(equality_resolution,[],[f558]) ).

cnf(c_246,plain,
    ( ~ sP6(X0,app(X0,X1))
    | ~ ssList(X1)
    | ~ equalelemsP(X0)
    | app(sK56(X0,X1),cons(sK54(X0,X1),nil)) = X0 ),
    inference(cnf_transformation,[],[f607]) ).

cnf(c_247,plain,
    ( ~ sP6(X0,app(X0,X1))
    | ~ ssList(X1)
    | ~ equalelemsP(X0)
    | ssList(sK56(X0,X1)) ),
    inference(cnf_transformation,[],[f608]) ).

cnf(c_248,plain,
    ( ~ sP6(X0,app(X0,X1))
    | ~ ssList(X1)
    | ~ equalelemsP(X0)
    | app(cons(sK54(X0,X1),nil),sK55(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f609]) ).

cnf(c_249,plain,
    ( ~ sP6(X0,app(X0,X1))
    | ~ ssList(X1)
    | ~ equalelemsP(X0)
    | ssList(sK55(X0,X1)) ),
    inference(cnf_transformation,[],[f610]) ).

cnf(c_250,plain,
    ( ~ sP6(X0,app(X0,X1))
    | ~ ssList(X1)
    | ~ equalelemsP(X0)
    | ssItem(sK54(X0,X1)) ),
    inference(cnf_transformation,[],[f611]) ).

cnf(c_251,negated_conjecture,
    ( nil != sK60
    | sP6(sK59,sK60) ),
    inference(cnf_transformation,[],[f576]) ).

cnf(c_252,negated_conjecture,
    ( nil = sK59
    | sP6(sK59,sK60) ),
    inference(cnf_transformation,[],[f577]) ).

cnf(c_253,negated_conjecture,
    ( nil != sK59
    | nil = sK60 ),
    inference(cnf_transformation,[],[f573]) ).

cnf(c_254,negated_conjecture,
    ( app(cons(X0,nil),X1) != sK61
    | app(X2,cons(X0,nil)) != sK59
    | ~ ssItem(X0)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cnf_transformation,[],[f572]) ).

cnf(c_255,negated_conjecture,
    equalelemsP(sK59),
    inference(cnf_transformation,[],[f571]) ).

cnf(c_256,negated_conjecture,
    app(sK59,sK61) = sK60,
    inference(cnf_transformation,[],[f570]) ).

cnf(c_257,negated_conjecture,
    ssList(sK61),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_380,negated_conjecture,
    sP6(sK59,sK60),
    inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_251,c_253]) ).

cnf(c_382,negated_conjecture,
    sP6(sK59,sK60),
    inference(global_subsumption_just,[status(thm)],[c_251,c_380]) ).

cnf(c_3319,plain,
    ( app(X0,X1) != sK60
    | X0 != sK59
    | ~ ssList(X1)
    | ~ equalelemsP(X0)
    | ssItem(sK54(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_250,c_382]) ).

cnf(c_3320,plain,
    ( app(sK59,X0) != sK60
    | ~ ssList(X0)
    | ~ equalelemsP(sK59)
    | ssItem(sK54(sK59,X0)) ),
    inference(unflattening,[status(thm)],[c_3319]) ).

cnf(c_3322,plain,
    ( ~ ssList(X0)
    | app(sK59,X0) != sK60
    | ssItem(sK54(sK59,X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_3320,c_255,c_3320]) ).

cnf(c_3323,plain,
    ( app(sK59,X0) != sK60
    | ~ ssList(X0)
    | ssItem(sK54(sK59,X0)) ),
    inference(renaming,[status(thm)],[c_3322]) ).

cnf(c_3334,plain,
    ( app(X0,X1) != sK60
    | X0 != sK59
    | ~ ssList(X1)
    | ~ equalelemsP(X0)
    | ssList(sK55(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_249,c_382]) ).

cnf(c_3335,plain,
    ( app(sK59,X0) != sK60
    | ~ ssList(X0)
    | ~ equalelemsP(sK59)
    | ssList(sK55(sK59,X0)) ),
    inference(unflattening,[status(thm)],[c_3334]) ).

cnf(c_3337,plain,
    ( ~ ssList(X0)
    | app(sK59,X0) != sK60
    | ssList(sK55(sK59,X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_3335,c_255,c_3335]) ).

cnf(c_3338,plain,
    ( app(sK59,X0) != sK60
    | ~ ssList(X0)
    | ssList(sK55(sK59,X0)) ),
    inference(renaming,[status(thm)],[c_3337]) ).

cnf(c_3349,plain,
    ( app(X0,X1) != sK60
    | X0 != sK59
    | ~ ssList(X1)
    | ~ equalelemsP(X0)
    | app(cons(sK54(X0,X1),nil),sK55(X0,X1)) = X1 ),
    inference(resolution_lifted,[status(thm)],[c_248,c_382]) ).

cnf(c_3350,plain,
    ( app(sK59,X0) != sK60
    | ~ ssList(X0)
    | ~ equalelemsP(sK59)
    | app(cons(sK54(sK59,X0),nil),sK55(sK59,X0)) = X0 ),
    inference(unflattening,[status(thm)],[c_3349]) ).

cnf(c_3352,plain,
    ( ~ ssList(X0)
    | app(sK59,X0) != sK60
    | app(cons(sK54(sK59,X0),nil),sK55(sK59,X0)) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_3350,c_255,c_3350]) ).

cnf(c_3353,plain,
    ( app(sK59,X0) != sK60
    | ~ ssList(X0)
    | app(cons(sK54(sK59,X0),nil),sK55(sK59,X0)) = X0 ),
    inference(renaming,[status(thm)],[c_3352]) ).

cnf(c_3364,plain,
    ( app(X0,X1) != sK60
    | X0 != sK59
    | ~ ssList(X1)
    | ~ equalelemsP(X0)
    | ssList(sK56(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_247,c_382]) ).

cnf(c_3365,plain,
    ( app(sK59,X0) != sK60
    | ~ ssList(X0)
    | ~ equalelemsP(sK59)
    | ssList(sK56(sK59,X0)) ),
    inference(unflattening,[status(thm)],[c_3364]) ).

cnf(c_3367,plain,
    ( ~ ssList(X0)
    | app(sK59,X0) != sK60
    | ssList(sK56(sK59,X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_3365,c_255,c_3365]) ).

cnf(c_3368,plain,
    ( app(sK59,X0) != sK60
    | ~ ssList(X0)
    | ssList(sK56(sK59,X0)) ),
    inference(renaming,[status(thm)],[c_3367]) ).

cnf(c_3379,plain,
    ( app(X0,X1) != sK60
    | X0 != sK59
    | ~ ssList(X1)
    | ~ equalelemsP(X0)
    | app(sK56(X0,X1),cons(sK54(X0,X1),nil)) = X0 ),
    inference(resolution_lifted,[status(thm)],[c_246,c_382]) ).

cnf(c_3380,plain,
    ( app(sK59,X0) != sK60
    | ~ ssList(X0)
    | ~ equalelemsP(sK59)
    | app(sK56(sK59,X0),cons(sK54(sK59,X0),nil)) = sK59 ),
    inference(unflattening,[status(thm)],[c_3379]) ).

cnf(c_3382,plain,
    ( ~ ssList(X0)
    | app(sK59,X0) != sK60
    | app(sK56(sK59,X0),cons(sK54(sK59,X0),nil)) = sK59 ),
    inference(global_subsumption_just,[status(thm)],[c_3380,c_255,c_3380]) ).

cnf(c_3383,plain,
    ( app(sK59,X0) != sK60
    | ~ ssList(X0)
    | app(sK56(sK59,X0),cons(sK54(sK59,X0),nil)) = sK59 ),
    inference(renaming,[status(thm)],[c_3382]) ).

cnf(c_9148,plain,
    app(sK59,sK61) = sP0_iProver_def,
    definition ).

cnf(c_9151,negated_conjecture,
    ssList(sK61),
    inference(demodulation,[status(thm)],[c_257]) ).

cnf(c_9152,negated_conjecture,
    sP0_iProver_def = sK60,
    inference(demodulation,[status(thm)],[c_256,c_9148]) ).

cnf(c_9154,negated_conjecture,
    ( app(cons(X0,nil),X1) != sK61
    | app(X2,cons(X0,nil)) != sK59
    | ~ ssItem(X0)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(demodulation,[status(thm)],[c_254]) ).

cnf(c_12083,plain,
    ( app(sK59,X0) != sP0_iProver_def
    | ~ ssList(X0)
    | ssItem(sK54(sK59,X0)) ),
    inference(light_normalisation,[status(thm)],[c_3323,c_9152]) ).

cnf(c_12090,plain,
    ( app(sK59,X0) != sP0_iProver_def
    | ~ ssList(X0)
    | ssList(sK55(sK59,X0)) ),
    inference(light_normalisation,[status(thm)],[c_3338,c_9152]) ).

cnf(c_12097,plain,
    ( app(sK59,X0) != sP0_iProver_def
    | ~ ssList(X0)
    | ssList(sK56(sK59,X0)) ),
    inference(light_normalisation,[status(thm)],[c_3368,c_9152]) ).

cnf(c_12104,plain,
    ( app(sK59,X0) != sP0_iProver_def
    | ~ ssList(X0)
    | app(cons(sK54(sK59,X0),nil),sK55(sK59,X0)) = X0 ),
    inference(light_normalisation,[status(thm)],[c_3353,c_9152]) ).

cnf(c_12111,plain,
    ( app(sK59,X0) != sP0_iProver_def
    | ~ ssList(X0)
    | app(sK56(sK59,X0),cons(sK54(sK59,X0),nil)) = sK59 ),
    inference(light_normalisation,[status(thm)],[c_3383,c_9152]) ).

cnf(c_12118,plain,
    ( ~ ssList(sK61)
    | app(sK56(sK59,sK61),cons(sK54(sK59,sK61),nil)) = sK59 ),
    inference(superposition,[status(thm)],[c_9148,c_12111]) ).

cnf(c_12119,plain,
    ( ~ ssList(sK61)
    | app(cons(sK54(sK59,sK61),nil),sK55(sK59,sK61)) = sK61 ),
    inference(superposition,[status(thm)],[c_9148,c_12104]) ).

cnf(c_12120,plain,
    ( ~ ssList(sK61)
    | ssList(sK56(sK59,sK61)) ),
    inference(superposition,[status(thm)],[c_9148,c_12097]) ).

cnf(c_12121,plain,
    ( ~ ssList(sK61)
    | ssList(sK55(sK59,sK61)) ),
    inference(superposition,[status(thm)],[c_9148,c_12090]) ).

cnf(c_12122,plain,
    ( ~ ssList(sK61)
    | ssItem(sK54(sK59,sK61)) ),
    inference(superposition,[status(thm)],[c_9148,c_12083]) ).

cnf(c_12123,plain,
    ssItem(sK54(sK59,sK61)),
    inference(forward_subsumption_resolution,[status(thm)],[c_12122,c_9151]) ).

cnf(c_12124,plain,
    ssList(sK55(sK59,sK61)),
    inference(forward_subsumption_resolution,[status(thm)],[c_12121,c_9151]) ).

cnf(c_12125,plain,
    ssList(sK56(sK59,sK61)),
    inference(forward_subsumption_resolution,[status(thm)],[c_12120,c_9151]) ).

cnf(c_12126,plain,
    app(cons(sK54(sK59,sK61),nil),sK55(sK59,sK61)) = sK61,
    inference(forward_subsumption_resolution,[status(thm)],[c_12119,c_9151]) ).

cnf(c_12127,plain,
    app(sK56(sK59,sK61),cons(sK54(sK59,sK61),nil)) = sK59,
    inference(forward_subsumption_resolution,[status(thm)],[c_12118,c_9151]) ).

cnf(c_12136,plain,
    ( app(X0,cons(sK54(sK59,sK61),nil)) != sK59
    | ~ ssItem(sK54(sK59,sK61))
    | ~ ssList(sK55(sK59,sK61))
    | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12126,c_9154]) ).

cnf(c_12137,plain,
    ( app(X0,cons(sK54(sK59,sK61),nil)) != sK59
    | ~ ssList(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12136,c_12124,c_12123]) ).

cnf(c_12145,plain,
    ~ ssList(sK56(sK59,sK61)),
    inference(superposition,[status(thm)],[c_12127,c_12137]) ).

cnf(c_12146,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_12145,c_12125]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWC327+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n002.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May  2 23:41:57 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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
% 0.46/1.15  % SZS status Started for theBenchmark.p
% 0.46/1.15  % SZS status Theorem for theBenchmark.p
% 0.46/1.15  
% 0.46/1.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.46/1.15  
% 0.46/1.15  ------  iProver source info
% 0.46/1.15  
% 0.46/1.15  git: date: 2024-05-02 19:28:25 +0000
% 0.46/1.15  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.46/1.15  git: non_committed_changes: false
% 0.46/1.15  
% 0.46/1.15  ------ Parsing...
% 0.46/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.46/1.15  
% 0.46/1.15  ------ 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 
% 0.46/1.15  
% 0.46/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.46/1.15  
% 0.46/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.46/1.15  ------ Proving...
% 0.46/1.15  ------ Problem Properties 
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  clauses                                 193
% 0.46/1.15  conjectures                             7
% 0.46/1.15  EPR                                     55
% 0.46/1.15  Horn                                    125
% 0.46/1.15  unary                                   22
% 0.46/1.15  binary                                  41
% 0.46/1.15  lits                                    646
% 0.46/1.15  lits eq                                 91
% 0.46/1.15  fd_pure                                 0
% 0.46/1.15  fd_pseudo                               0
% 0.46/1.15  fd_cond                                 21
% 0.46/1.15  fd_pseudo_cond                          14
% 0.46/1.15  AC symbols                              0
% 0.46/1.15  
% 0.46/1.15  ------ Schedule dynamic 5 is on 
% 0.46/1.15  
% 0.46/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  ------ 
% 0.46/1.15  Current options:
% 0.46/1.15  ------ 
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  ------ Proving...
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  % SZS status Theorem for theBenchmark.p
% 0.46/1.15  
% 0.46/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.15  
% 0.46/1.16  
%------------------------------------------------------------------------------