TSTP Solution File: SWC399+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC399+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.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 03:12:21 EDT 2024

% Result   : Theorem 4.29s 1.16s
% Output   : CNFRefutation 4.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   56 (  20 unt;   0 def)
%            Number of atoms       :  507 ( 141 equ)
%            Maximal formula atoms :   50 (   9 avg)
%            Number of connectives :  722 ( 271   ~; 234   |; 191   &)
%                                         (   2 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :  218 (   0 sgn 129   !;  70   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

fof(f36,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( memberP(app(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | memberP(X1,X0) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ( nil = X2
                    & nil != X3 )
                  | ! [X12] :
                      ( memberP(X1,X12)
                      | ~ memberP(X0,X12)
                      | ~ ssItem(X12) )
                  | ! [X4] :
                      ( ssList(X4)
                     => ! [X5] :
                          ( ? [X9] :
                              ( ? [X10] :
                                  ( ? [X11] :
                                      ( app(X11,cons(X9,nil)) = X2
                                      & ssList(X11) )
                                  & app(cons(X9,nil),X10) = X5
                                  & ssList(X10) )
                              & ssItem(X9) )
                          | ? [X6] :
                              ( ? [X7] :
                                  ( ? [X8] :
                                      ( app(cons(X6,nil),X8) = X2
                                      & ssList(X8) )
                                  & app(X7,cons(X6,nil)) = X4
                                  & ssList(X7) )
                              & ssItem(X6) )
                          | ~ equalelemsP(X2)
                          | app(app(X4,X2),X5) != X3
                          | ~ ssList(X5) ) )
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( nil = X2
                      & nil != X3 )
                    | ! [X12] :
                        ( memberP(X1,X12)
                        | ~ memberP(X0,X12)
                        | ~ ssItem(X12) )
                    | ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ? [X9] :
                                ( ? [X10] :
                                    ( ? [X11] :
                                        ( app(X11,cons(X9,nil)) = X2
                                        & ssList(X11) )
                                    & app(cons(X9,nil),X10) = X5
                                    & ssList(X10) )
                                & ssItem(X9) )
                            | ? [X6] :
                                ( ? [X7] :
                                    ( ? [X8] :
                                        ( app(cons(X6,nil),X8) = X2
                                        & ssList(X8) )
                                    & app(X7,cons(X6,nil)) = X4
                                    & ssList(X7) )
                                & ssItem(X6) )
                            | ~ equalelemsP(X2)
                            | app(app(X4,X2),X5) != X3
                            | ~ ssList(X5) ) )
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( memberP(X1,X4)
                        | ~ memberP(X0,X4)
                        | ~ ssItem(X4) )
                    | ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ? [X7] :
                                ( ? [X8] :
                                    ( ? [X9] :
                                        ( app(X9,cons(X7,nil)) = X2
                                        & ssList(X9) )
                                    & app(cons(X7,nil),X8) = X6
                                    & ssList(X8) )
                                & ssItem(X7) )
                            | ? [X10] :
                                ( ? [X11] :
                                    ( ? [X12] :
                                        ( app(cons(X10,nil),X12) = X2
                                        & ssList(X12) )
                                    & app(X11,cons(X10,nil)) = X5
                                    & ssList(X11) )
                                & ssItem(X10) )
                            | ~ equalelemsP(X2)
                            | app(app(X5,X2),X6) != X3
                            | ~ ssList(X6) ) )
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f133,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(app(X0,X1))
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f147,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( memberP(app(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | memberP(X1,X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ~ memberP(X1,X4)
                      & memberP(X0,X4)
                      & ssItem(X4) )
                  & ? [X5] :
                      ( ? [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ! [X9] :
                                      ( app(X9,cons(X7,nil)) != X2
                                      | ~ ssList(X9) )
                                  | app(cons(X7,nil),X8) != X6
                                  | ~ ssList(X8) )
                              | ~ ssItem(X7) )
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( app(cons(X10,nil),X12) != X2
                                      | ~ ssList(X12) )
                                  | app(X11,cons(X10,nil)) != X5
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & equalelemsP(X2)
                          & app(app(X5,X2),X6) = X3
                          & ssList(X6) )
                      & ssList(X5) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f322,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & ~ memberP(X1,X0) ) )
                & ( memberP(X2,X0)
                  | memberP(X1,X0)
                  | ~ memberP(app(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f147]) ).

fof(f323,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & ~ memberP(X1,X0) ) )
                & ( memberP(X2,X0)
                  | memberP(X1,X0)
                  | ~ memberP(app(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f322]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( nil != X2
                      | nil = X3 )
                    & ? [X4] :
                        ( ~ memberP(X1,X4)
                        & memberP(X0,X4)
                        & ssItem(X4) )
                    & ? [X5] :
                        ( ? [X6] :
                            ( ! [X7] :
                                ( ! [X8] :
                                    ( ! [X9] :
                                        ( app(X9,cons(X7,nil)) != X2
                                        | ~ ssList(X9) )
                                    | app(cons(X7,nil),X8) != X6
                                    | ~ ssList(X8) )
                                | ~ ssItem(X7) )
                            & ! [X10] :
                                ( ! [X11] :
                                    ( ! [X12] :
                                        ( app(cons(X10,nil),X12) != X2
                                        | ~ ssList(X12) )
                                    | app(X11,cons(X10,nil)) != X5
                                    | ~ ssList(X11) )
                                | ~ ssItem(X10) )
                            & equalelemsP(X2)
                            & app(app(X5,X2),X6) = X3
                            & ssList(X6) )
                        & ssList(X5) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ~ memberP(X1,X4)
                      & memberP(sK53,X4)
                      & ssItem(X4) )
                  & ? [X5] :
                      ( ? [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ! [X9] :
                                      ( app(X9,cons(X7,nil)) != X2
                                      | ~ ssList(X9) )
                                  | app(cons(X7,nil),X8) != X6
                                  | ~ ssList(X8) )
                              | ~ ssItem(X7) )
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( app(cons(X10,nil),X12) != X2
                                      | ~ ssList(X12) )
                                  | app(X11,cons(X10,nil)) != X5
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & equalelemsP(X2)
                          & app(app(X5,X2),X6) = X3
                          & ssList(X6) )
                      & ssList(X5) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( nil != X2
                  | nil = X3 )
                & ? [X4] :
                    ( ~ memberP(X1,X4)
                    & memberP(sK53,X4)
                    & ssItem(X4) )
                & ? [X5] :
                    ( ? [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( ! [X9] :
                                    ( app(X9,cons(X7,nil)) != X2
                                    | ~ ssList(X9) )
                                | app(cons(X7,nil),X8) != X6
                                | ~ ssList(X8) )
                            | ~ ssItem(X7) )
                        & ! [X10] :
                            ( ! [X11] :
                                ( ! [X12] :
                                    ( app(cons(X10,nil),X12) != X2
                                    | ~ ssList(X12) )
                                | app(X11,cons(X10,nil)) != X5
                                | ~ ssList(X11) )
                            | ~ ssItem(X10) )
                        & equalelemsP(X2)
                        & app(app(X5,X2),X6) = X3
                        & ssList(X6) )
                    & ssList(X5) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( nil != X2
                | nil = X3 )
              & ? [X4] :
                  ( ~ memberP(sK54,X4)
                  & memberP(sK53,X4)
                  & ssItem(X4) )
              & ? [X5] :
                  ( ? [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ! [X9] :
                                  ( app(X9,cons(X7,nil)) != X2
                                  | ~ ssList(X9) )
                              | app(cons(X7,nil),X8) != X6
                              | ~ ssList(X8) )
                          | ~ ssItem(X7) )
                      & ! [X10] :
                          ( ! [X11] :
                              ( ! [X12] :
                                  ( app(cons(X10,nil),X12) != X2
                                  | ~ ssList(X12) )
                              | app(X11,cons(X10,nil)) != X5
                              | ~ ssList(X11) )
                          | ~ ssItem(X10) )
                      & equalelemsP(X2)
                      & app(app(X5,X2),X6) = X3
                      & ssList(X6) )
                  & ssList(X5) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( nil != X2
              | nil = X3 )
            & ? [X4] :
                ( ~ memberP(sK54,X4)
                & memberP(sK53,X4)
                & ssItem(X4) )
            & ? [X5] :
                ( ? [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ! [X9] :
                                ( app(X9,cons(X7,nil)) != X2
                                | ~ ssList(X9) )
                            | app(cons(X7,nil),X8) != X6
                            | ~ ssList(X8) )
                        | ~ ssItem(X7) )
                    & ! [X10] :
                        ( ! [X11] :
                            ( ! [X12] :
                                ( app(cons(X10,nil),X12) != X2
                                | ~ ssList(X12) )
                            | app(X11,cons(X10,nil)) != X5
                            | ~ ssList(X11) )
                        | ~ ssItem(X10) )
                    & equalelemsP(X2)
                    & app(app(X5,X2),X6) = X3
                    & ssList(X6) )
                & ssList(X5) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( nil != sK55
            | nil = X3 )
          & ? [X4] :
              ( ~ memberP(sK54,X4)
              & memberP(sK53,X4)
              & ssItem(X4) )
          & ? [X5] :
              ( ? [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ! [X9] :
                              ( app(X9,cons(X7,nil)) != sK55
                              | ~ ssList(X9) )
                          | app(cons(X7,nil),X8) != X6
                          | ~ ssList(X8) )
                      | ~ ssItem(X7) )
                  & ! [X10] :
                      ( ! [X11] :
                          ( ! [X12] :
                              ( app(cons(X10,nil),X12) != sK55
                              | ~ ssList(X12) )
                          | app(X11,cons(X10,nil)) != X5
                          | ~ ssList(X11) )
                      | ~ ssItem(X10) )
                  & equalelemsP(sK55)
                  & app(app(X5,sK55),X6) = X3
                  & ssList(X6) )
              & ssList(X5) )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ( nil != sK55
          | nil = X3 )
        & ? [X4] :
            ( ~ memberP(sK54,X4)
            & memberP(sK53,X4)
            & ssItem(X4) )
        & ? [X5] :
            ( ? [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ! [X9] :
                            ( app(X9,cons(X7,nil)) != sK55
                            | ~ ssList(X9) )
                        | app(cons(X7,nil),X8) != X6
                        | ~ ssList(X8) )
                    | ~ ssItem(X7) )
                & ! [X10] :
                    ( ! [X11] :
                        ( ! [X12] :
                            ( app(cons(X10,nil),X12) != sK55
                            | ~ ssList(X12) )
                        | app(X11,cons(X10,nil)) != X5
                        | ~ ssList(X11) )
                    | ~ ssItem(X10) )
                & equalelemsP(sK55)
                & app(app(X5,sK55),X6) = X3
                & ssList(X6) )
            & ssList(X5) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( nil != sK55
        | nil = sK56 )
      & ? [X4] :
          ( ~ memberP(sK54,X4)
          & memberP(sK53,X4)
          & ssItem(X4) )
      & ? [X5] :
          ( ? [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( app(X9,cons(X7,nil)) != sK55
                          | ~ ssList(X9) )
                      | app(cons(X7,nil),X8) != X6
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              & ! [X10] :
                  ( ! [X11] :
                      ( ! [X12] :
                          ( app(cons(X10,nil),X12) != sK55
                          | ~ ssList(X12) )
                      | app(X11,cons(X10,nil)) != X5
                      | ~ ssList(X11) )
                  | ~ ssItem(X10) )
              & equalelemsP(sK55)
              & app(app(X5,sK55),X6) = sK56
              & ssList(X6) )
          & ssList(X5) )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X4] :
        ( ~ memberP(sK54,X4)
        & memberP(sK53,X4)
        & ssItem(X4) )
   => ( ~ memberP(sK54,sK57)
      & memberP(sK53,sK57)
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X5] :
        ( ? [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( app(X9,cons(X7,nil)) != sK55
                        | ~ ssList(X9) )
                    | app(cons(X7,nil),X8) != X6
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            & ! [X10] :
                ( ! [X11] :
                    ( ! [X12] :
                        ( app(cons(X10,nil),X12) != sK55
                        | ~ ssList(X12) )
                    | app(X11,cons(X10,nil)) != X5
                    | ~ ssList(X11) )
                | ~ ssItem(X10) )
            & equalelemsP(sK55)
            & app(app(X5,sK55),X6) = sK56
            & ssList(X6) )
        & ssList(X5) )
   => ( ? [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( ! [X9] :
                      ( app(X9,cons(X7,nil)) != sK55
                      | ~ ssList(X9) )
                  | app(cons(X7,nil),X8) != X6
                  | ~ ssList(X8) )
              | ~ ssItem(X7) )
          & ! [X10] :
              ( ! [X11] :
                  ( ! [X12] :
                      ( app(cons(X10,nil),X12) != sK55
                      | ~ ssList(X12) )
                  | app(X11,cons(X10,nil)) != sK58
                  | ~ ssList(X11) )
              | ~ ssItem(X10) )
          & equalelemsP(sK55)
          & sK56 = app(app(sK58,sK55),X6)
          & ssList(X6) )
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ? [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( ! [X9] :
                    ( app(X9,cons(X7,nil)) != sK55
                    | ~ ssList(X9) )
                | app(cons(X7,nil),X8) != X6
                | ~ ssList(X8) )
            | ~ ssItem(X7) )
        & ! [X10] :
            ( ! [X11] :
                ( ! [X12] :
                    ( app(cons(X10,nil),X12) != sK55
                    | ~ ssList(X12) )
                | app(X11,cons(X10,nil)) != sK58
                | ~ ssList(X11) )
            | ~ ssItem(X10) )
        & equalelemsP(sK55)
        & sK56 = app(app(sK58,sK55),X6)
        & ssList(X6) )
   => ( ! [X7] :
          ( ! [X8] :
              ( ! [X9] :
                  ( app(X9,cons(X7,nil)) != sK55
                  | ~ ssList(X9) )
              | app(cons(X7,nil),X8) != sK59
              | ~ ssList(X8) )
          | ~ ssItem(X7) )
      & ! [X10] :
          ( ! [X11] :
              ( ! [X12] :
                  ( app(cons(X10,nil),X12) != sK55
                  | ~ ssList(X12) )
              | app(X11,cons(X10,nil)) != sK58
              | ~ ssList(X11) )
          | ~ ssItem(X10) )
      & equalelemsP(sK55)
      & sK56 = app(app(sK58,sK55),sK59)
      & ssList(sK59) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ( ( nil != sK55
      | nil = sK56 )
    & ~ memberP(sK54,sK57)
    & memberP(sK53,sK57)
    & ssItem(sK57)
    & ! [X7] :
        ( ! [X8] :
            ( ! [X9] :
                ( app(X9,cons(X7,nil)) != sK55
                | ~ ssList(X9) )
            | app(cons(X7,nil),X8) != sK59
            | ~ ssList(X8) )
        | ~ ssItem(X7) )
    & ! [X10] :
        ( ! [X11] :
            ( ! [X12] :
                ( app(cons(X10,nil),X12) != sK55
                | ~ ssList(X12) )
            | app(X11,cons(X10,nil)) != sK58
            | ~ ssList(X11) )
        | ~ ssItem(X10) )
    & equalelemsP(sK55)
    & sK56 = app(app(sK58,sK55),sK59)
    & ssList(sK59)
    & ssList(sK58)
    & 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])],[f222,f349,f348,f347,f346,f345,f344,f343]) ).

fof(f455,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f468,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X1,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f323]) ).

fof(f469,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f323]) ).

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

fof(f554,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f350]) ).

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

fof(f556,plain,
    ssList(sK58),
    inference(cnf_transformation,[],[f350]) ).

fof(f557,plain,
    ssList(sK59),
    inference(cnf_transformation,[],[f350]) ).

fof(f558,plain,
    sK56 = app(app(sK58,sK55),sK59),
    inference(cnf_transformation,[],[f350]) ).

fof(f562,plain,
    ssItem(sK57),
    inference(cnf_transformation,[],[f350]) ).

fof(f563,plain,
    memberP(sK53,sK57),
    inference(cnf_transformation,[],[f350]) ).

fof(f564,plain,
    ~ memberP(sK54,sK57),
    inference(cnf_transformation,[],[f350]) ).

fof(f566,plain,
    ~ memberP(sK56,sK57),
    inference(definition_unfolding,[],[f564,f554]) ).

fof(f567,plain,
    memberP(sK55,sK57),
    inference(definition_unfolding,[],[f563,f555]) ).

fof(f569,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f550,f555]) ).

cnf(c_153,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f455]) ).

cnf(c_165,plain,
    ( ~ memberP(X0,X1)
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X2,X0),X1) ),
    inference(cnf_transformation,[],[f469]) ).

cnf(c_166,plain,
    ( ~ memberP(X0,X1)
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X0,X2),X1) ),
    inference(cnf_transformation,[],[f468]) ).

cnf(c_247,negated_conjecture,
    ~ memberP(sK56,sK57),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_248,negated_conjecture,
    memberP(sK55,sK57),
    inference(cnf_transformation,[],[f567]) ).

cnf(c_249,negated_conjecture,
    ssItem(sK57),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_253,negated_conjecture,
    app(app(sK58,sK55),sK59) = sK56,
    inference(cnf_transformation,[],[f558]) ).

cnf(c_254,negated_conjecture,
    ssList(sK59),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_255,negated_conjecture,
    ssList(sK58),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_259,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_11947,plain,
    ( ~ memberP(app(sK58,sK55),X0)
    | ~ ssList(app(sK58,sK55))
    | ~ ssItem(X0)
    | ~ ssList(sK59)
    | memberP(sK56,X0) ),
    inference(superposition,[status(thm)],[c_253,c_166]) ).

cnf(c_12391,plain,
    ( ~ memberP(app(sK58,sK55),X0)
    | ~ ssList(app(sK58,sK55))
    | ~ ssItem(X0)
    | ~ ssList(sK59)
    | memberP(sK56,X0) ),
    inference(superposition,[status(thm)],[c_253,c_166]) ).

cnf(c_12420,plain,
    ( ~ ssItem(X0)
    | ~ ssList(app(sK58,sK55))
    | ~ memberP(app(sK58,sK55),X0)
    | memberP(sK56,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_11947,c_254,c_11947]) ).

cnf(c_12421,plain,
    ( ~ memberP(app(sK58,sK55),X0)
    | ~ ssList(app(sK58,sK55))
    | ~ ssItem(X0)
    | memberP(sK56,X0) ),
    inference(renaming,[status(thm)],[c_12420]) ).

cnf(c_12431,plain,
    ( ~ ssList(app(sK58,sK55))
    | ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | ~ ssList(sK55)
    | ~ ssList(sK58)
    | memberP(sK56,X0) ),
    inference(superposition,[status(thm)],[c_165,c_12421]) ).

cnf(c_13235,plain,
    ( ~ ssItem(X0)
    | ~ ssList(app(sK58,sK55))
    | ~ memberP(app(sK58,sK55),X0)
    | memberP(sK56,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_12391,c_254,c_11947]) ).

cnf(c_13236,plain,
    ( ~ memberP(app(sK58,sK55),X0)
    | ~ ssList(app(sK58,sK55))
    | ~ ssItem(X0)
    | memberP(sK56,X0) ),
    inference(renaming,[status(thm)],[c_13235]) ).

cnf(c_13245,plain,
    ( ~ ssList(app(sK58,sK55))
    | ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | ~ ssList(sK55)
    | ~ ssList(sK58)
    | memberP(sK56,X0) ),
    inference(superposition,[status(thm)],[c_165,c_13236]) ).

cnf(c_13763,plain,
    ( ~ ssList(app(sK58,sK55))
    | ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | memberP(sK56,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_12431,c_259,c_255,c_12431]) ).

cnf(c_13774,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | ~ ssList(sK55)
    | ~ ssList(sK58)
    | memberP(sK56,X0) ),
    inference(superposition,[status(thm)],[c_153,c_13763]) ).

cnf(c_15201,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | memberP(sK56,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_13245,c_259,c_255,c_13774]) ).

cnf(c_15210,plain,
    ( ~ ssItem(sK57)
    | memberP(sK56,sK57) ),
    inference(superposition,[status(thm)],[c_248,c_15201]) ).

cnf(c_15211,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_15210,c_247,c_249]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SWC399+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n031.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 : Fri May  3 00:03:31 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.19/0.48  Running first-order theorem proving
% 0.19/0.48  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
% 4.29/1.16  % SZS status Started for theBenchmark.p
% 4.29/1.16  % SZS status Theorem for theBenchmark.p
% 4.29/1.16  
% 4.29/1.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.29/1.16  
% 4.29/1.16  ------  iProver source info
% 4.29/1.16  
% 4.29/1.16  git: date: 2024-05-02 19:28:25 +0000
% 4.29/1.16  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.29/1.16  git: non_committed_changes: false
% 4.29/1.16  
% 4.29/1.16  ------ Parsing...
% 4.29/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.29/1.16  
% 4.29/1.16  ------ 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 
% 4.29/1.16  
% 4.29/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.29/1.16  
% 4.29/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.29/1.16  ------ Proving...
% 4.29/1.16  ------ Problem Properties 
% 4.29/1.16  
% 4.29/1.16  
% 4.29/1.16  clauses                                 192
% 4.29/1.16  conjectures                             12
% 4.29/1.16  EPR                                     58
% 4.29/1.16  Horn                                    124
% 4.29/1.16  unary                                   25
% 4.29/1.16  binary                                  41
% 4.29/1.16  lits                                    639
% 4.29/1.16  lits eq                                 85
% 4.29/1.16  fd_pure                                 0
% 4.29/1.16  fd_pseudo                               0
% 4.29/1.16  fd_cond                                 21
% 4.29/1.16  fd_pseudo_cond                          14
% 4.29/1.16  AC symbols                              0
% 4.29/1.16  
% 4.29/1.16  ------ Input Options Time Limit: Unbounded
% 4.29/1.16  
% 4.29/1.16  
% 4.29/1.16  ------ 
% 4.29/1.16  Current options:
% 4.29/1.16  ------ 
% 4.29/1.16  
% 4.29/1.16  
% 4.29/1.16  
% 4.29/1.16  
% 4.29/1.16  ------ Proving...
% 4.29/1.16  
% 4.29/1.16  
% 4.29/1.16  % SZS status Theorem for theBenchmark.p
% 4.29/1.16  
% 4.29/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.29/1.16  
% 4.29/1.16  
%------------------------------------------------------------------------------