TSTP Solution File: SWC306+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC306+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 03:11:56 EDT 2024

% Result   : Theorem 24.94s 4.24s
% Output   : CNFRefutation 24.94s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f606)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

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(f37,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( memberP(cons(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | X0 = X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

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

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

fof(f100,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f120,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

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(f148,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( memberP(cons(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | X0 = X1 ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

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

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ? [X5] :
                      ( ? [X6] :
                          ( ? [X7] :
                              ( ? [X8] :
                                  ( ? [X9] :
                                      ( lt(X6,X5)
                                      & app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = X0
                                      & ssList(X9) )
                                  & ssList(X8) )
                              & ssList(X7) )
                          & ssItem(X6) )
                      & ssItem(X5) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f237,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(X2,cons(X1,X3)) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f100]) ).

fof(f238,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(X4,cons(X1,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f237]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X4,cons(X1,X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(sK8(X0,X1),cons(X1,X5)) = X0
            & ssList(X5) )
        & ssList(sK8(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f240,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(sK8(X0,X1),cons(X1,X5)) = X0
          & ssList(X5) )
     => ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
        & ssList(sK9(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f241,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
                & ssList(sK9(X0,X1))
                & ssList(sK8(X0,X1)) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f238,f240,f239]) ).

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(nnf_transformation,[],[f147]) ).

fof(f324,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,[],[f323]) ).

fof(f325,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(cons(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & X0 != X1 ) )
                & ( memberP(X2,X0)
                  | X0 = X1
                  | ~ memberP(cons(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f148]) ).

fof(f326,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(cons(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & X0 != X1 ) )
                & ( memberP(X2,X0)
                  | X0 = X1
                  | ~ memberP(cons(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f325]) ).

fof(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X2
                        & nil = X3 )
                      | ? [X4] :
                          ( memberP(X3,X4)
                          & cons(X4,nil) = X2
                          & ssItem(X4) ) )
                    & ? [X5] :
                        ( ? [X6] :
                            ( ? [X7] :
                                ( ? [X8] :
                                    ( ? [X9] :
                                        ( lt(X6,X5)
                                        & app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = X0
                                        & ssList(X9) )
                                    & ssList(X8) )
                                & ssList(X7) )
                            & ssItem(X6) )
                        & ssItem(X5) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ? [X5] :
                      ( ? [X6] :
                          ( ? [X7] :
                              ( ? [X8] :
                                  ( ? [X9] :
                                      ( lt(X6,X5)
                                      & app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = sK53
                                      & ssList(X9) )
                                  & ssList(X8) )
                              & ssList(X7) )
                          & ssItem(X6) )
                      & ssItem(X5) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X2
                    & nil = X3 )
                  | ? [X4] :
                      ( memberP(X3,X4)
                      & cons(X4,nil) = X2
                      & ssItem(X4) ) )
                & ? [X5] :
                    ( ? [X6] :
                        ( ? [X7] :
                            ( ? [X8] :
                                ( ? [X9] :
                                    ( lt(X6,X5)
                                    & app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = sK53
                                    & ssList(X9) )
                                & ssList(X8) )
                            & ssList(X7) )
                        & ssItem(X6) )
                    & ssItem(X5) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil = X2
                  & nil = X3 )
                | ? [X4] :
                    ( memberP(X3,X4)
                    & cons(X4,nil) = X2
                    & ssItem(X4) ) )
              & ? [X5] :
                  ( ? [X6] :
                      ( ? [X7] :
                          ( ? [X8] :
                              ( ? [X9] :
                                  ( lt(X6,X5)
                                  & app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = sK53
                                  & ssList(X9) )
                              & ssList(X8) )
                          & ssList(X7) )
                      & ssItem(X6) )
                  & ssItem(X5) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = X2
                & nil = X3 )
              | ? [X4] :
                  ( memberP(X3,X4)
                  & cons(X4,nil) = X2
                  & ssItem(X4) ) )
            & ? [X5] :
                ( ? [X6] :
                    ( ? [X7] :
                        ( ? [X8] :
                            ( ? [X9] :
                                ( lt(X6,X5)
                                & app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = sK53
                                & ssList(X9) )
                            & ssList(X8) )
                        & ssList(X7) )
                    & ssItem(X6) )
                & ssItem(X5) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK55
              & nil = X3 )
            | ? [X4] :
                ( memberP(X3,X4)
                & cons(X4,nil) = sK55
                & ssItem(X4) ) )
          & ? [X5] :
              ( ? [X6] :
                  ( ? [X7] :
                      ( ? [X8] :
                          ( ? [X9] :
                              ( lt(X6,X5)
                              & app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = sK53
                              & ssList(X9) )
                          & ssList(X8) )
                      & ssList(X7) )
                  & ssItem(X6) )
              & ssItem(X5) )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X3] :
        ( ( ( nil = sK55
            & nil = X3 )
          | ? [X4] :
              ( memberP(X3,X4)
              & cons(X4,nil) = sK55
              & ssItem(X4) ) )
        & ? [X5] :
            ( ? [X6] :
                ( ? [X7] :
                    ( ? [X8] :
                        ( ? [X9] :
                            ( lt(X6,X5)
                            & app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = sK53
                            & ssList(X9) )
                        & ssList(X8) )
                    & ssList(X7) )
                & ssItem(X6) )
            & ssItem(X5) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ( nil = sK55
          & nil = sK56 )
        | ? [X4] :
            ( memberP(sK56,X4)
            & cons(X4,nil) = sK55
            & ssItem(X4) ) )
      & ? [X5] :
          ( ? [X6] :
              ( ? [X7] :
                  ( ? [X8] :
                      ( ? [X9] :
                          ( lt(X6,X5)
                          & app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = sK53
                          & ssList(X9) )
                      & ssList(X8) )
                  & ssList(X7) )
              & ssItem(X6) )
          & ssItem(X5) )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X4] :
        ( memberP(sK56,X4)
        & cons(X4,nil) = sK55
        & ssItem(X4) )
   => ( memberP(sK56,sK57)
      & sK55 = cons(sK57,nil)
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ? [X5] :
        ( ? [X6] :
            ( ? [X7] :
                ( ? [X8] :
                    ( ? [X9] :
                        ( lt(X6,X5)
                        & app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = sK53
                        & ssList(X9) )
                    & ssList(X8) )
                & ssList(X7) )
            & ssItem(X6) )
        & ssItem(X5) )
   => ( ? [X6] :
          ( ? [X7] :
              ( ? [X8] :
                  ( ? [X9] :
                      ( lt(X6,sK58)
                      & sK53 = app(app(app(app(X7,cons(sK58,nil)),X8),cons(X6,nil)),X9)
                      & ssList(X9) )
                  & ssList(X8) )
              & ssList(X7) )
          & ssItem(X6) )
      & ssItem(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ( ? [X6] :
        ( ? [X7] :
            ( ? [X8] :
                ( ? [X9] :
                    ( lt(X6,sK58)
                    & sK53 = app(app(app(app(X7,cons(sK58,nil)),X8),cons(X6,nil)),X9)
                    & ssList(X9) )
                & ssList(X8) )
            & ssList(X7) )
        & ssItem(X6) )
   => ( ? [X7] :
          ( ? [X8] :
              ( ? [X9] :
                  ( lt(sK59,sK58)
                  & sK53 = app(app(app(app(X7,cons(sK58,nil)),X8),cons(sK59,nil)),X9)
                  & ssList(X9) )
              & ssList(X8) )
          & ssList(X7) )
      & ssItem(sK59) ) ),
    introduced(choice_axiom,[]) ).

fof(f351,plain,
    ( ? [X7] :
        ( ? [X8] :
            ( ? [X9] :
                ( lt(sK59,sK58)
                & sK53 = app(app(app(app(X7,cons(sK58,nil)),X8),cons(sK59,nil)),X9)
                & ssList(X9) )
            & ssList(X8) )
        & ssList(X7) )
   => ( ? [X8] :
          ( ? [X9] :
              ( lt(sK59,sK58)
              & sK53 = app(app(app(app(sK60,cons(sK58,nil)),X8),cons(sK59,nil)),X9)
              & ssList(X9) )
          & ssList(X8) )
      & ssList(sK60) ) ),
    introduced(choice_axiom,[]) ).

fof(f352,plain,
    ( ? [X8] :
        ( ? [X9] :
            ( lt(sK59,sK58)
            & sK53 = app(app(app(app(sK60,cons(sK58,nil)),X8),cons(sK59,nil)),X9)
            & ssList(X9) )
        & ssList(X8) )
   => ( ? [X9] :
          ( lt(sK59,sK58)
          & sK53 = app(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)),X9)
          & ssList(X9) )
      & ssList(sK61) ) ),
    introduced(choice_axiom,[]) ).

fof(f353,plain,
    ( ? [X9] :
        ( lt(sK59,sK58)
        & sK53 = app(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)),X9)
        & ssList(X9) )
   => ( lt(sK59,sK58)
      & sK53 = app(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)),sK62)
      & ssList(sK62) ) ),
    introduced(choice_axiom,[]) ).

fof(f354,plain,
    ( ( ( nil = sK55
        & nil = sK56 )
      | ( memberP(sK56,sK57)
        & sK55 = cons(sK57,nil)
        & ssItem(sK57) ) )
    & lt(sK59,sK58)
    & sK53 = app(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)),sK62)
    & ssList(sK62)
    & ssList(sK61)
    & ssList(sK60)
    & ssItem(sK59)
    & ssItem(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,sK60,sK61,sK62])],[f223,f353,f352,f351,f350,f349,f348,f347,f346,f345,f344]) ).

fof(f363,plain,
    ! [X2,X3,X0,X1] :
      ( memberP(X0,X1)
      | app(X2,cons(X1,X3)) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f241]) ).

fof(f446,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f447,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f459,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f472,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X1,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f324]) ).

fof(f473,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f324]) ).

fof(f474,plain,
    ! [X2,X0,X1] :
      ( memberP(X2,X0)
      | X0 = X1
      | ~ memberP(cons(X1,X2),X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f326]) ).

fof(f477,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f559,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f354]) ).

fof(f560,plain,
    ssItem(sK58),
    inference(cnf_transformation,[],[f354]) ).

fof(f561,plain,
    ssItem(sK59),
    inference(cnf_transformation,[],[f354]) ).

fof(f562,plain,
    ssList(sK60),
    inference(cnf_transformation,[],[f354]) ).

fof(f563,plain,
    ssList(sK61),
    inference(cnf_transformation,[],[f354]) ).

fof(f564,plain,
    ssList(sK62),
    inference(cnf_transformation,[],[f354]) ).

fof(f565,plain,
    sK53 = app(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)),sK62),
    inference(cnf_transformation,[],[f354]) ).

fof(f566,plain,
    lt(sK59,sK58),
    inference(cnf_transformation,[],[f354]) ).

fof(f567,plain,
    ( nil = sK56
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f354]) ).

fof(f568,plain,
    ( nil = sK56
    | sK55 = cons(sK57,nil) ),
    inference(cnf_transformation,[],[f354]) ).

fof(f570,plain,
    ( nil = sK55
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f354]) ).

fof(f572,plain,
    ( nil = sK55
    | memberP(sK56,sK57) ),
    inference(cnf_transformation,[],[f354]) ).

fof(f573,plain,
    sK55 = app(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)),sK62),
    inference(definition_unfolding,[],[f565,f559]) ).

fof(f577,plain,
    ! [X2,X3,X1] :
      ( memberP(app(X2,cons(X1,X3)),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(app(X2,cons(X1,X3))) ),
    inference(equality_resolution,[],[f363]) ).

cnf(c_54,plain,
    ( ~ ssList(app(X0,cons(X1,X2)))
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X0,cons(X1,X2)),X1) ),
    inference(cnf_transformation,[],[f577]) ).

cnf(c_140,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | ssList(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f446]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f447]) ).

cnf(c_153,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f459]) ).

cnf(c_165,plain,
    ( ~ memberP(X0,X1)
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X2,X0),X1) ),
    inference(cnf_transformation,[],[f473]) ).

cnf(c_166,plain,
    ( ~ memberP(X0,X1)
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X0,X2),X1) ),
    inference(cnf_transformation,[],[f472]) ).

cnf(c_169,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | memberP(cons(X0,X1),X0) ),
    inference(cnf_transformation,[],[f606]) ).

cnf(c_170,plain,
    ( ~ memberP(cons(X0,X1),X2)
    | ~ ssItem(X0)
    | ~ ssItem(X2)
    | ~ ssList(X1)
    | X0 = X2
    | memberP(X1,X2) ),
    inference(cnf_transformation,[],[f474]) ).

cnf(c_171,plain,
    ( ~ memberP(nil,X0)
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f477]) ).

cnf(c_243,plain,
    ( ~ lt(X0,X0)
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f609]) ).

cnf(c_246,negated_conjecture,
    ( nil = sK55
    | memberP(sK56,sK57) ),
    inference(cnf_transformation,[],[f572]) ).

cnf(c_248,negated_conjecture,
    ( nil = sK55
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f570]) ).

cnf(c_250,negated_conjecture,
    ( cons(sK57,nil) = sK55
    | nil = sK56 ),
    inference(cnf_transformation,[],[f568]) ).

cnf(c_251,negated_conjecture,
    ( nil = sK56
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f567]) ).

cnf(c_252,negated_conjecture,
    lt(sK59,sK58),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_253,negated_conjecture,
    app(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)),sK62) = sK55,
    inference(cnf_transformation,[],[f573]) ).

cnf(c_254,negated_conjecture,
    ssList(sK62),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_255,negated_conjecture,
    ssList(sK61),
    inference(cnf_transformation,[],[f563]) ).

cnf(c_256,negated_conjecture,
    ssList(sK60),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_257,negated_conjecture,
    ssItem(sK59),
    inference(cnf_transformation,[],[f561]) ).

cnf(c_258,negated_conjecture,
    ssItem(sK58),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_7653,negated_conjecture,
    ssItem(sK58),
    inference(subtyping,[status(esa)],[c_258]) ).

cnf(c_7654,negated_conjecture,
    ssItem(sK59),
    inference(subtyping,[status(esa)],[c_257]) ).

cnf(c_7655,negated_conjecture,
    ssList(sK60),
    inference(subtyping,[status(esa)],[c_256]) ).

cnf(c_7656,negated_conjecture,
    ssList(sK61),
    inference(subtyping,[status(esa)],[c_255]) ).

cnf(c_7657,negated_conjecture,
    ssList(sK62),
    inference(subtyping,[status(esa)],[c_254]) ).

cnf(c_7658,negated_conjecture,
    app(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)),sK62) = sK55,
    inference(subtyping,[status(esa)],[c_253]) ).

cnf(c_7659,negated_conjecture,
    lt(sK59,sK58),
    inference(subtyping,[status(esa)],[c_252]) ).

cnf(c_7660,negated_conjecture,
    ( nil = sK56
    | ssItem(sK57) ),
    inference(subtyping,[status(esa)],[c_251]) ).

cnf(c_7661,negated_conjecture,
    ( cons(sK57,nil) = sK55
    | nil = sK56 ),
    inference(subtyping,[status(esa)],[c_250]) ).

cnf(c_7663,negated_conjecture,
    ( nil = sK55
    | ssItem(sK57) ),
    inference(subtyping,[status(esa)],[c_248]) ).

cnf(c_7665,negated_conjecture,
    ( nil = sK55
    | memberP(sK56,sK57) ),
    inference(subtyping,[status(esa)],[c_246]) ).

cnf(c_7671,plain,
    ( ~ lt(X0_14,X0_14)
    | ~ ssItem(X0_14) ),
    inference(subtyping,[status(esa)],[c_243]) ).

cnf(c_7726,plain,
    ( ~ memberP(nil,X0_14)
    | ~ ssItem(X0_14) ),
    inference(subtyping,[status(esa)],[c_171]) ).

cnf(c_7727,plain,
    ( ~ memberP(cons(X0_14,X0_13),X1_14)
    | ~ ssItem(X0_14)
    | ~ ssItem(X1_14)
    | ~ ssList(X0_13)
    | X0_14 = X1_14
    | memberP(X0_13,X1_14) ),
    inference(subtyping,[status(esa)],[c_170]) ).

cnf(c_7728,plain,
    ( ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | memberP(cons(X0_14,X0_13),X0_14) ),
    inference(subtyping,[status(esa)],[c_169]) ).

cnf(c_7731,plain,
    ( ~ memberP(X0_13,X0_14)
    | ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | memberP(app(X0_13,X1_13),X0_14) ),
    inference(subtyping,[status(esa)],[c_166]) ).

cnf(c_7732,plain,
    ( ~ memberP(X0_13,X0_14)
    | ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | memberP(app(X1_13,X0_13),X0_14) ),
    inference(subtyping,[status(esa)],[c_165]) ).

cnf(c_7744,plain,
    ( ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | ssList(app(X0_13,X1_13)) ),
    inference(subtyping,[status(esa)],[c_153]) ).

cnf(c_7756,plain,
    ssList(nil),
    inference(subtyping,[status(esa)],[c_141]) ).

cnf(c_7757,plain,
    ( ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | ssList(cons(X0_14,X0_13)) ),
    inference(subtyping,[status(esa)],[c_140]) ).

cnf(c_7830,plain,
    ( ~ ssList(app(X0_13,cons(X0_14,X1_13)))
    | ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | memberP(app(X0_13,cons(X0_14,X1_13)),X0_14) ),
    inference(subtyping,[status(esa)],[c_54]) ).

cnf(c_18450,plain,
    ( ~ memberP(sK55,X0_14)
    | ~ ssItem(X0_14)
    | ~ ssItem(sK57)
    | ~ ssList(nil)
    | X0_14 = sK57
    | nil = sK56
    | memberP(nil,X0_14) ),
    inference(superposition,[status(thm)],[c_7661,c_7727]) ).

cnf(c_18451,plain,
    ( ~ memberP(sK55,X0_14)
    | ~ ssItem(X0_14)
    | ~ ssItem(sK57)
    | X0_14 = sK57
    | nil = sK56
    | memberP(nil,X0_14) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_18450,c_7756]) ).

cnf(c_18468,plain,
    ( ~ memberP(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)),X0_14)
    | ~ ssList(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)))
    | ~ ssItem(X0_14)
    | ~ ssList(sK62)
    | memberP(sK55,X0_14) ),
    inference(superposition,[status(thm)],[c_7658,c_7731]) ).

cnf(c_18470,plain,
    ( ~ memberP(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)),X0_14)
    | ~ ssList(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)))
    | ~ ssItem(X0_14)
    | memberP(sK55,X0_14) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_18468,c_7657]) ).

cnf(c_18925,plain,
    ( ~ ssList(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)))
    | ~ ssList(app(app(sK60,cons(sK58,nil)),sK61))
    | ~ memberP(cons(sK59,nil),X0_14)
    | ~ ssList(cons(sK59,nil))
    | ~ ssItem(X0_14)
    | memberP(sK55,X0_14) ),
    inference(superposition,[status(thm)],[c_7732,c_18470]) ).

cnf(c_18926,plain,
    ( ~ ssList(app(app(app(sK60,cons(sK58,nil)),sK61),cons(sK59,nil)))
    | ~ memberP(app(app(sK60,cons(sK58,nil)),sK61),X0_14)
    | ~ ssList(app(app(sK60,cons(sK58,nil)),sK61))
    | ~ ssList(cons(sK59,nil))
    | ~ ssItem(X0_14)
    | memberP(sK55,X0_14) ),
    inference(superposition,[status(thm)],[c_7731,c_18470]) ).

cnf(c_19633,plain,
    ( ~ ssList(app(app(sK60,cons(sK58,nil)),sK61))
    | ~ memberP(cons(sK59,nil),X0_14)
    | ~ ssList(cons(sK59,nil))
    | ~ ssItem(X0_14)
    | memberP(sK55,X0_14) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_18925,c_7744]) ).

cnf(c_19634,plain,
    ( ~ ssList(app(sK60,cons(sK58,nil)))
    | ~ memberP(cons(sK59,nil),X0_14)
    | ~ ssList(cons(sK59,nil))
    | ~ ssItem(X0_14)
    | ~ ssList(sK61)
    | memberP(sK55,X0_14) ),
    inference(superposition,[status(thm)],[c_7744,c_19633]) ).

cnf(c_19635,plain,
    ( ~ ssList(app(sK60,cons(sK58,nil)))
    | ~ memberP(cons(sK59,nil),X0_14)
    | ~ ssList(cons(sK59,nil))
    | ~ ssItem(X0_14)
    | memberP(sK55,X0_14) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19634,c_7656]) ).

cnf(c_19642,plain,
    ( ~ memberP(app(app(sK60,cons(sK58,nil)),sK61),X0_14)
    | ~ ssList(app(app(sK60,cons(sK58,nil)),sK61))
    | ~ ssList(cons(sK59,nil))
    | ~ ssItem(X0_14)
    | memberP(sK55,X0_14) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_18926,c_7744]) ).

cnf(c_19644,plain,
    ( ~ ssList(app(app(sK60,cons(sK58,nil)),sK61))
    | ~ memberP(app(sK60,cons(sK58,nil)),X0_14)
    | ~ ssList(app(sK60,cons(sK58,nil)))
    | ~ ssList(cons(sK59,nil))
    | ~ ssItem(X0_14)
    | ~ ssList(sK61)
    | memberP(sK55,X0_14) ),
    inference(superposition,[status(thm)],[c_7731,c_19642]) ).

cnf(c_19647,plain,
    ( ~ ssList(app(app(sK60,cons(sK58,nil)),sK61))
    | ~ memberP(app(sK60,cons(sK58,nil)),X0_14)
    | ~ ssList(app(sK60,cons(sK58,nil)))
    | ~ ssList(cons(sK59,nil))
    | ~ ssItem(X0_14)
    | memberP(sK55,X0_14) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19644,c_7656]) ).

cnf(c_19922,plain,
    ( ~ memberP(sK55,X0_14)
    | ~ ssItem(X0_14)
    | X0_14 = sK57
    | nil = sK56 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_18451,c_7726,c_7660]) ).

cnf(c_20351,plain,
    ( ~ memberP(cons(sK59,nil),X0_14)
    | ~ ssList(cons(sK59,nil))
    | ~ ssList(cons(sK58,nil))
    | ~ ssItem(X0_14)
    | ~ ssList(sK60)
    | memberP(sK55,X0_14) ),
    inference(superposition,[status(thm)],[c_7744,c_19635]) ).

cnf(c_20352,plain,
    ( ~ memberP(cons(sK59,nil),X0_14)
    | ~ ssList(cons(sK59,nil))
    | ~ ssList(cons(sK58,nil))
    | ~ ssItem(X0_14)
    | memberP(sK55,X0_14) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20351,c_7655]) ).

cnf(c_20794,plain,
    ( ~ memberP(app(sK60,cons(sK58,nil)),X0_14)
    | ~ ssList(app(sK60,cons(sK58,nil)))
    | ~ ssList(cons(sK59,nil))
    | ~ ssItem(X0_14)
    | ~ ssList(sK61)
    | memberP(sK55,X0_14) ),
    inference(superposition,[status(thm)],[c_7744,c_19647]) ).

cnf(c_20795,plain,
    ( ~ memberP(app(sK60,cons(sK58,nil)),X0_14)
    | ~ ssList(app(sK60,cons(sK58,nil)))
    | ~ ssList(cons(sK59,nil))
    | ~ ssItem(X0_14)
    | memberP(sK55,X0_14) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20794,c_7656]) ).

cnf(c_21588,plain,
    ( ~ ssList(cons(sK59,nil))
    | ~ ssList(cons(sK58,nil))
    | ~ ssItem(sK59)
    | ~ ssList(nil)
    | memberP(sK55,sK59) ),
    inference(superposition,[status(thm)],[c_7728,c_20352]) ).

cnf(c_21589,plain,
    ( ~ ssList(cons(sK59,nil))
    | ~ ssList(cons(sK58,nil))
    | memberP(sK55,sK59) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_21588,c_7756,c_7654]) ).

cnf(c_21920,plain,
    ( ~ ssList(app(sK60,cons(sK58,nil)))
    | ~ ssList(cons(sK59,nil))
    | ~ ssItem(sK58)
    | ~ ssList(nil)
    | ~ ssList(sK60)
    | memberP(sK55,sK58) ),
    inference(superposition,[status(thm)],[c_7830,c_20795]) ).

cnf(c_21922,plain,
    ( ~ ssList(app(sK60,cons(sK58,nil)))
    | ~ ssList(cons(sK59,nil))
    | memberP(sK55,sK58) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_21920,c_7655,c_7756,c_7653]) ).

cnf(c_22583,plain,
    ( ~ ssList(cons(sK58,nil))
    | ~ ssItem(sK59)
    | ~ ssList(nil)
    | memberP(sK55,sK59) ),
    inference(superposition,[status(thm)],[c_7757,c_21589]) ).

cnf(c_22584,plain,
    ( ~ ssList(cons(sK58,nil))
    | memberP(sK55,sK59) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22583,c_7756,c_7654]) ).

cnf(c_22861,plain,
    ( ~ ssList(cons(sK59,nil))
    | ~ ssList(cons(sK58,nil))
    | ~ ssList(sK60)
    | memberP(sK55,sK58) ),
    inference(superposition,[status(thm)],[c_7744,c_21922]) ).

cnf(c_22862,plain,
    ( ~ ssList(cons(sK59,nil))
    | ~ ssList(cons(sK58,nil))
    | memberP(sK55,sK58) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22861,c_7655]) ).

cnf(c_25178,plain,
    ( ~ ssItem(sK58)
    | ~ ssList(nil)
    | memberP(sK55,sK59) ),
    inference(superposition,[status(thm)],[c_7757,c_22584]) ).

cnf(c_25179,plain,
    memberP(sK55,sK59),
    inference(forward_subsumption_resolution,[status(thm)],[c_25178,c_7756,c_7653]) ).

cnf(c_25217,plain,
    ( ~ ssItem(sK59)
    | nil = sK56
    | sK57 = sK59 ),
    inference(superposition,[status(thm)],[c_25179,c_19922]) ).

cnf(c_25218,plain,
    ( nil = sK56
    | sK57 = sK59 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_25217,c_7654]) ).

cnf(c_27528,plain,
    ( ~ ssList(cons(sK58,nil))
    | ~ ssItem(sK59)
    | ~ ssList(nil)
    | memberP(sK55,sK58) ),
    inference(superposition,[status(thm)],[c_7757,c_22862]) ).

cnf(c_27529,plain,
    ( ~ ssList(cons(sK58,nil))
    | memberP(sK55,sK58) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_27528,c_7756,c_7654]) ).

cnf(c_27768,plain,
    ( ~ ssItem(sK58)
    | ~ ssList(nil)
    | memberP(sK55,sK58) ),
    inference(superposition,[status(thm)],[c_7757,c_27529]) ).

cnf(c_27769,plain,
    memberP(sK55,sK58),
    inference(forward_subsumption_resolution,[status(thm)],[c_27768,c_7756,c_7653]) ).

cnf(c_28434,plain,
    ( ~ ssItem(sK58)
    | nil = sK56
    | sK57 = sK58 ),
    inference(superposition,[status(thm)],[c_27769,c_19922]) ).

cnf(c_28435,plain,
    ( nil = sK56
    | sK57 = sK58 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28434,c_7653]) ).

cnf(c_28498,plain,
    ( nil = sK56
    | sK59 = sK58 ),
    inference(superposition,[status(thm)],[c_28435,c_25218]) ).

cnf(c_28849,plain,
    ( nil = sK56
    | lt(sK58,sK58) ),
    inference(superposition,[status(thm)],[c_28498,c_7659]) ).

cnf(c_29565,plain,
    ( ~ ssItem(sK58)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_28849,c_7671]) ).

cnf(c_29567,plain,
    nil = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_29565,c_7653]) ).

cnf(c_29602,plain,
    ( nil = sK55
    | memberP(nil,sK57) ),
    inference(superposition,[status(thm)],[c_29567,c_7665]) ).

cnf(c_29609,plain,
    ( ~ ssItem(sK57)
    | nil = sK55 ),
    inference(superposition,[status(thm)],[c_29602,c_7726]) ).

cnf(c_29683,plain,
    nil = sK55,
    inference(forward_subsumption_resolution,[status(thm)],[c_29609,c_7663]) ).

cnf(c_29685,plain,
    memberP(nil,sK58),
    inference(superposition,[status(thm)],[c_29683,c_27769]) ).

cnf(c_29726,plain,
    ~ ssItem(sK58),
    inference(superposition,[status(thm)],[c_29685,c_7726]) ).

cnf(c_29764,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_29726,c_7653]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWC306+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n029.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 23:45:22 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.94/4.24  % SZS status Started for theBenchmark.p
% 24.94/4.24  % SZS status Theorem for theBenchmark.p
% 24.94/4.24  
% 24.94/4.24  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 24.94/4.24  
% 24.94/4.24  ------  iProver source info
% 24.94/4.24  
% 24.94/4.24  git: date: 2024-05-02 19:28:25 +0000
% 24.94/4.24  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 24.94/4.24  git: non_committed_changes: false
% 24.94/4.24  
% 24.94/4.24  ------ Parsing...
% 24.94/4.24  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 24.94/4.24  
% 24.94/4.24  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 24.94/4.24  
% 24.94/4.24  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 24.94/4.24  
% 24.94/4.24  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 24.94/4.24  ------ Proving...
% 24.94/4.24  ------ Problem Properties 
% 24.94/4.24  
% 24.94/4.24  
% 24.94/4.24  clauses                                 195
% 24.94/4.24  conjectures                             15
% 24.94/4.24  EPR                                     61
% 24.94/4.24  Horn                                    121
% 24.94/4.24  unary                                   25
% 24.94/4.24  binary                                  46
% 24.94/4.24  lits                                    639
% 24.94/4.24  lits eq                                 87
% 24.94/4.24  fd_pure                                 0
% 24.94/4.24  fd_pseudo                               0
% 24.94/4.24  fd_cond                                 21
% 24.94/4.24  fd_pseudo_cond                          14
% 24.94/4.24  AC symbols                              0
% 24.94/4.24  
% 24.94/4.24  ------ Input Options Time Limit: Unbounded
% 24.94/4.24  
% 24.94/4.24  
% 24.94/4.24  ------ 
% 24.94/4.24  Current options:
% 24.94/4.24  ------ 
% 24.94/4.24  
% 24.94/4.24  
% 24.94/4.24  
% 24.94/4.24  
% 24.94/4.24  ------ Proving...
% 24.94/4.24  
% 24.94/4.24  
% 24.94/4.24  % SZS status Theorem for theBenchmark.p
% 24.94/4.24  
% 24.94/4.24  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.94/4.24  
% 24.94/4.25  
%------------------------------------------------------------------------------