TSTP Solution File: SWC409+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWC409+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n003.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 : Thu Aug 31 20:43:12 EDT 2023

% Result   : Timeout 299.66s 38.90s
% Output   : None 
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f597)

% 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/sandbox/benchmark/theBenchmark.p',ax3) ).

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

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

fof(f29,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( ( leq(X1,X0)
              & leq(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).

fof(f31,axiom,
    ! [X0] :
      ( ssItem(X0)
     => leq(X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).

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/sandbox/benchmark/theBenchmark.p',ax36) ).

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

fof(f75,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( hd(X0) = X1
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).

fof(f76,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( tl(X0) = X1
            & ssList(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).

fof(f91,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ( ( lt(X1,X2)
                  & leq(X0,X1) )
               => lt(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax91) ).

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

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

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

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( nil = X3
                        & nil != X2 )
                      | ! [X4] :
                          ( ssItem(X4)
                         => ( memberP(X0,X4)
                            | ~ memberP(X1,X4) ) )
                      | ? [X5] :
                          ( ? [X6] :
                              ( app(cons(X5,nil),X6) = X3
                              & app(X6,cons(X5,nil)) != X2
                              & ssList(X6) )
                          & ssItem(X5) )
                      | 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(f136,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ leq(X1,X0)
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f137,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ leq(X1,X0)
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f136]) ).

fof(f140,plain,
    ! [X0] :
      ( leq(X0,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f31]) ).

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

fof(f187,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f188,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f187]) ).

fof(f189,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f76]) ).

fof(f190,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f189]) ).

fof(f193,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f194,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f193]) ).

fof(f199,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f213,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f91]) ).

fof(f214,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f213]) ).

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

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

fof(f224,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( ~ leq(X2,X1)
                          | ~ leq(X1,X2)
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

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(f260,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( leq(X2,X1)
                            & leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( ~ leq(X2,X1)
                            | ~ leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f224]) ).

fof(f261,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( leq(X2,X1)
                            & leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( ~ leq(X7,X6)
                            | ~ leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f260]) ).

fof(f262,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( leq(X2,X1)
                          & leq(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( leq(X2,sK15(X0))
                        & leq(sK15(X0),X2)
                        & app(app(X3,cons(sK15(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK15(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f263,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( leq(X2,sK15(X0))
                      & leq(sK15(X0),X2)
                      & app(app(X3,cons(sK15(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( leq(sK16(X0),sK15(X0))
                    & leq(sK15(X0),sK16(X0))
                    & app(app(X3,cons(sK15(X0),X4)),cons(sK16(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK16(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f264,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( leq(sK16(X0),sK15(X0))
                  & leq(sK15(X0),sK16(X0))
                  & app(app(X3,cons(sK15(X0),X4)),cons(sK16(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( leq(sK16(X0),sK15(X0))
                & leq(sK15(X0),sK16(X0))
                & app(app(sK17(X0),cons(sK15(X0),X4)),cons(sK16(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK17(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f265,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( leq(sK16(X0),sK15(X0))
              & leq(sK15(X0),sK16(X0))
              & app(app(sK17(X0),cons(sK15(X0),X4)),cons(sK16(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( leq(sK16(X0),sK15(X0))
            & leq(sK15(X0),sK16(X0))
            & app(app(sK17(X0),cons(sK15(X0),sK18(X0))),cons(sK16(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK18(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f266,plain,
    ! [X0] :
      ( ? [X5] :
          ( leq(sK16(X0),sK15(X0))
          & leq(sK15(X0),sK16(X0))
          & app(app(sK17(X0),cons(sK15(X0),sK18(X0))),cons(sK16(X0),X5)) = X0
          & ssList(X5) )
     => ( leq(sK16(X0),sK15(X0))
        & leq(sK15(X0),sK16(X0))
        & app(app(sK17(X0),cons(sK15(X0),sK18(X0))),cons(sK16(X0),sK19(X0))) = X0
        & ssList(sK19(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f267,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ( leq(sK16(X0),sK15(X0))
          & leq(sK15(X0),sK16(X0))
          & app(app(sK17(X0),cons(sK15(X0),sK18(X0))),cons(sK16(X0),sK19(X0))) = X0
          & ssList(sK19(X0))
          & ssList(sK18(X0))
          & ssList(sK17(X0))
          & ssItem(sK16(X0))
          & ssItem(sK15(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( ~ leq(X7,X6)
                            | ~ leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18,sK19])],[f261,f266,f265,f264,f263,f262]) ).

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(f336,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
     => ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f337,plain,
    ! [X0] :
      ( ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f188,f336]) ).

fof(f338,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
     => ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f339,plain,
    ! [X0] :
      ( ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f190,f338]) ).

fof(f342,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( lt(X0,X1)
              | ~ leq(X0,X1)
              | X0 = X1 )
            & ( ( leq(X0,X1)
                & X0 != X1 )
              | ~ lt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f217]) ).

fof(f343,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( lt(X0,X1)
              | ~ leq(X0,X1)
              | X0 = X1 )
            & ( ( leq(X0,X1)
                & X0 != X1 )
              | ~ lt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f342]) ).

fof(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( nil != X3
                      | nil = X2 )
                    & ? [X4] :
                        ( ~ memberP(X0,X4)
                        & memberP(X1,X4)
                        & ssItem(X4) )
                    & ! [X5] :
                        ( ! [X6] :
                            ( app(cons(X5,nil),X6) != X3
                            | app(X6,cons(X5,nil)) = X2
                            | ~ ssList(X6) )
                        | ~ ssItem(X5) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X3
                    | nil = X2 )
                  & ? [X4] :
                      ( ~ memberP(sK53,X4)
                      & memberP(X1,X4)
                      & ssItem(X4) )
                  & ! [X5] :
                      ( ! [X6] :
                          ( app(cons(X5,nil),X6) != X3
                          | app(X6,cons(X5,nil)) = X2
                          | ~ ssList(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 != X3
                  | nil = X2 )
                & ? [X4] :
                    ( ~ memberP(sK53,X4)
                    & memberP(X1,X4)
                    & ssItem(X4) )
                & ! [X5] :
                    ( ! [X6] :
                        ( app(cons(X5,nil),X6) != X3
                        | app(X6,cons(X5,nil)) = X2
                        | ~ ssList(X6) )
                    | ~ ssItem(X5) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( nil != X3
                | nil = X2 )
              & ? [X4] :
                  ( ~ memberP(sK53,X4)
                  & memberP(sK54,X4)
                  & ssItem(X4) )
              & ! [X5] :
                  ( ! [X6] :
                      ( app(cons(X5,nil),X6) != X3
                      | app(X6,cons(X5,nil)) = X2
                      | ~ ssList(X6) )
                  | ~ ssItem(X5) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f348,plain,
    ( ? [X4] :
        ( ~ memberP(sK53,X4)
        & memberP(sK54,X4)
        & ssItem(X4) )
   => ( ~ memberP(sK53,sK57)
      & memberP(sK54,sK57)
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ( nil != sK56
      | nil = sK55 )
    & ~ memberP(sK53,sK57)
    & memberP(sK54,sK57)
    & ssItem(sK57)
    & ! [X5] :
        ( ! [X6] :
            ( app(cons(X5,nil),X6) != sK56
            | app(X6,cons(X5,nil)) = sK55
            | ~ ssList(X6) )
        | ~ ssItem(X5) )
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f223,f348,f347,f346,f345,f344]) ).

fof(f357,plain,
    ! [X0,X1] :
      ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
      | ~ memberP(X0,X1)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f241]) ).

fof(f374,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( ~ leq(X7,X6)
      | ~ leq(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f267]) ).

fof(f441,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f442,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f457,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ leq(X1,X0)
      | ~ leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f459,plain,
    ! [X0] :
      ( leq(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f140]) ).

fof(f466,plain,
    ! [X2,X0,X1] :
      ( memberP(X2,X0)
      | memberP(X1,X0)
      | ~ memberP(app(X1,X2),X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f324]) ).

fof(f467,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X1,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f324]) ).

fof(f468,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f324]) ).

fof(f472,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f522,plain,
    ! [X0] :
      ( ssItem(sK51(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f523,plain,
    ! [X0] :
      ( hd(X0) = sK51(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f524,plain,
    ! [X0] :
      ( ssList(sK52(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f525,plain,
    ! [X0] :
      ( tl(X0) = sK52(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f527,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f530,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f199]) ).

fof(f542,plain,
    ! [X2,X0,X1] :
      ( lt(X0,X2)
      | ~ lt(X1,X2)
      | ~ leq(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f214]) ).

fof(f546,plain,
    ! [X0,X1] :
      ( lt(X0,X1)
      | ~ leq(X0,X1)
      | X0 = X1
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f343]) ).

fof(f550,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f349]) ).

fof(f553,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f349]) ).

fof(f554,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f349]) ).

fof(f555,plain,
    ! [X6,X5] :
      ( app(cons(X5,nil),X6) != sK56
      | app(X6,cons(X5,nil)) = sK55
      | ~ ssList(X6)
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f556,plain,
    ssItem(sK57),
    inference(cnf_transformation,[],[f349]) ).

fof(f557,plain,
    memberP(sK54,sK57),
    inference(cnf_transformation,[],[f349]) ).

fof(f558,plain,
    ~ memberP(sK53,sK57),
    inference(cnf_transformation,[],[f349]) ).

fof(f559,plain,
    ( nil != sK56
    | nil = sK55 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f560,plain,
    ~ memberP(sK55,sK57),
    inference(definition_unfolding,[],[f558,f554]) ).

fof(f561,plain,
    memberP(sK56,sK57),
    inference(definition_unfolding,[],[f557,f553]) ).

fof(f562,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f550,f553]) ).

fof(f570,plain,
    ! [X10,X8,X6,X9,X7] :
      ( ~ leq(X7,X6)
      | ~ leq(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP0(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f374]) ).

cnf(c_55,plain,
    ( ~ memberP(X0,X1)
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0 ),
    inference(cnf_transformation,[],[f357]) ).

cnf(c_81,plain,
    ( ~ sP0(app(app(X0,cons(X1,X2)),cons(X3,X4)))
    | ~ leq(X1,X3)
    | ~ leq(X3,X1)
    | ~ ssItem(X1)
    | ~ ssItem(X3)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f570]) ).

cnf(c_140,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | ssList(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f441]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f442]) ).

cnf(c_156,plain,
    ( ~ leq(X0,X1)
    | ~ leq(X1,X0)
    | ~ ssItem(X0)
    | ~ ssItem(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f457]) ).

cnf(c_158,plain,
    ( ~ ssItem(X0)
    | leq(X0,X0) ),
    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,[],[f468]) ).

cnf(c_166,plain,
    ( ~ memberP(X0,X1)
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X0,X2),X1) ),
    inference(cnf_transformation,[],[f467]) ).

cnf(c_167,plain,
    ( ~ memberP(app(X0,X1),X2)
    | ~ ssItem(X2)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | memberP(X0,X2)
    | memberP(X1,X2) ),
    inference(cnf_transformation,[],[f466]) ).

cnf(c_171,plain,
    ( ~ memberP(nil,X0)
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f472]) ).

cnf(c_219,plain,
    ( ~ ssList(X0)
    | hd(X0) = sK51(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f523]) ).

cnf(c_220,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssItem(sK51(X0)) ),
    inference(cnf_transformation,[],[f522]) ).

cnf(c_221,plain,
    ( ~ ssList(X0)
    | tl(X0) = sK52(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f525]) ).

cnf(c_222,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssList(sK52(X0)) ),
    inference(cnf_transformation,[],[f524]) ).

cnf(c_224,plain,
    ( ~ ssList(X0)
    | cons(hd(X0),tl(X0)) = X0
    | X0 = nil ),
    inference(cnf_transformation,[],[f527]) ).

cnf(c_227,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | app(cons(X0,nil),X1) = cons(X0,X1) ),
    inference(cnf_transformation,[],[f530]) ).

cnf(c_239,plain,
    ( ~ leq(X0,X1)
    | ~ lt(X1,X2)
    | ~ ssItem(X0)
    | ~ ssItem(X1)
    | ~ ssItem(X2)
    | lt(X0,X2) ),
    inference(cnf_transformation,[],[f542]) ).

cnf(c_241,plain,
    ( ~ leq(X0,X1)
    | ~ ssItem(X0)
    | ~ ssItem(X1)
    | X0 = X1
    | lt(X0,X1) ),
    inference(cnf_transformation,[],[f546]) ).

cnf(c_243,plain,
    ( ~ lt(X0,X0)
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f597]) ).

cnf(c_246,negated_conjecture,
    ( nil != sK56
    | nil = sK55 ),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_247,negated_conjecture,
    ~ memberP(sK55,sK57),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_248,negated_conjecture,
    memberP(sK56,sK57),
    inference(cnf_transformation,[],[f561]) ).

cnf(c_249,negated_conjecture,
    ssItem(sK57),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_250,negated_conjecture,
    ( app(cons(X0,nil),X1) != sK56
    | ~ ssItem(X0)
    | ~ ssList(X1)
    | app(X1,cons(X0,nil)) = sK55 ),
    inference(cnf_transformation,[],[f555]) ).

cnf(c_253,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_8829,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_8835,plain,
    ( X0 != X1
    | X2 != X3
    | ~ memberP(X1,X3)
    | memberP(X0,X2) ),
    theory(equality) ).

cnf(c_13034,plain,
    ( ~ memberP(nil,sK57)
    | ~ ssItem(sK57) ),
    inference(instantiation,[status(thm)],[c_171]) ).

cnf(c_13256,plain,
    ( ~ ssItem(sK57)
    | leq(sK57,sK57) ),
    inference(instantiation,[status(thm)],[c_158]) ).

cnf(c_13262,plain,
    ( ~ lt(sK57,sK57)
    | ~ ssItem(sK57) ),
    inference(instantiation,[status(thm)],[c_243]) ).

cnf(c_13768,plain,
    ( hd(sK56) = sK51(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_253,c_219]) ).

cnf(c_14031,plain,
    ( X0 != sK56
    | X1 != sK57
    | ~ memberP(sK56,sK57)
    | memberP(X0,X1) ),
    inference(instantiation,[status(thm)],[c_8835]) ).

cnf(c_14170,plain,
    ( ~ lt(X0,X1)
    | ~ leq(sK57,X0)
    | ~ ssItem(X0)
    | ~ ssItem(X1)
    | ~ ssItem(sK57)
    | lt(sK57,X1) ),
    inference(instantiation,[status(thm)],[c_239]) ).

cnf(c_14206,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssItem(hd(sK56)) ),
    inference(superposition,[status(thm)],[c_13768,c_220]) ).

cnf(c_14207,plain,
    ( nil = sK56
    | ssItem(hd(sK56)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14206,c_253]) ).

cnf(c_16530,plain,
    ( X0 != sK56
    | sK57 != sK57
    | ~ memberP(sK56,sK57)
    | memberP(X0,sK57) ),
    inference(instantiation,[status(thm)],[c_14031]) ).

cnf(c_16531,plain,
    sK57 = sK57,
    inference(instantiation,[status(thm)],[c_8829]) ).

cnf(c_16532,plain,
    ( nil != sK56
    | sK57 != sK57
    | ~ memberP(sK56,sK57)
    | memberP(nil,sK57) ),
    inference(instantiation,[status(thm)],[c_16530]) ).

cnf(c_31411,plain,
    ( ~ leq(X0,sK57)
    | ~ leq(sK57,X0)
    | ~ ssItem(X0)
    | ~ ssItem(sK57)
    | sK57 = X0 ),
    inference(instantiation,[status(thm)],[c_156]) ).

cnf(c_40080,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(X0)
    | ssList(cons(hd(sK56),X0)) ),
    inference(instantiation,[status(thm)],[c_140]) ).

cnf(c_40081,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(nil)
    | ssList(cons(hd(sK56),nil)) ),
    inference(instantiation,[status(thm)],[c_40080]) ).

cnf(c_72300,plain,
    ( ~ leq(sK57,X0)
    | ~ lt(X0,sK57)
    | ~ ssItem(X0)
    | ~ ssItem(sK57)
    | lt(sK57,sK57) ),
    inference(instantiation,[status(thm)],[c_14170]) ).

cnf(c_93359,negated_conjecture,
    nil != sK56,
    inference(global_subsumption_just,[status(thm)],[c_246,c_249,c_248,c_13034,c_16532,c_16531]) ).

cnf(c_319883,plain,
    ( X0 != sK56
    | X1 != sK57
    | memberP(X0,X1) ),
    inference(resolution,[status(thm)],[c_8835,c_248]) ).

cnf(c_319927,plain,
    ( X0 != sK57
    | memberP(sK56,X0) ),
    inference(resolution,[status(thm)],[c_319883,c_8829]) ).

cnf(c_320299,plain,
    ( ~ leq(X0,sK57)
    | ~ ssItem(X0)
    | ~ ssItem(sK57)
    | memberP(sK56,X0)
    | lt(X0,sK57) ),
    inference(resolution,[status(thm)],[c_319927,c_241]) ).

cnf(c_322669,plain,
    ( ~ ssItem(X0)
    | ~ leq(X0,sK57)
    | memberP(sK56,X0)
    | lt(X0,sK57) ),
    inference(global_subsumption_just,[status(thm)],[c_320299,c_249,c_320299]) ).

cnf(c_322670,plain,
    ( ~ leq(X0,sK57)
    | ~ ssItem(X0)
    | memberP(sK56,X0)
    | lt(X0,sK57) ),
    inference(renaming,[status(thm)],[c_322669]) ).

cnf(c_397504,plain,
    ( sK55 != X0
    | sK57 != X1
    | ~ memberP(X0,X1)
    | memberP(sK55,sK57) ),
    inference(instantiation,[status(thm)],[c_8835]) ).

cnf(c_414748,plain,
    ( sK55 != sK55
    | sK57 != X0
    | ~ memberP(sK55,X0)
    | memberP(sK55,sK57) ),
    inference(instantiation,[status(thm)],[c_397504]) ).

cnf(c_414749,plain,
    sK55 = sK55,
    inference(instantiation,[status(thm)],[c_8829]) ).

cnf(c_644879,plain,
    ( ~ ssItem(sK57)
    | ~ ssList(sK56)
    | app(sK8(sK56,sK57),cons(sK57,sK9(sK56,sK57))) = sK56 ),
    inference(superposition,[status(thm)],[c_248,c_55]) ).

cnf(c_644880,plain,
    app(sK8(sK56,sK57),cons(sK57,sK9(sK56,sK57))) = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_644879,c_253,c_249]) ).

cnf(c_650714,plain,
    ( hd(sK56) = sK51(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_253,c_219]) ).

cnf(c_650718,plain,
    hd(sK56) = sK51(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_650714,c_93359]) ).

cnf(c_650840,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssItem(hd(sK56)) ),
    inference(superposition,[status(thm)],[c_650718,c_220]) ).

cnf(c_650841,plain,
    ssItem(hd(sK56)),
    inference(forward_subsumption_resolution,[status(thm)],[c_650840,c_93359,c_253]) ).

cnf(c_650904,plain,
    ( tl(sK56) = sK52(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_253,c_221]) ).

cnf(c_650908,plain,
    tl(sK56) = sK52(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_650904,c_93359]) ).

cnf(c_651216,plain,
    ( cons(hd(sK56),tl(sK56)) = sK56
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_253,c_224]) ).

cnf(c_651220,plain,
    cons(hd(sK56),tl(sK56)) = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_651216,c_93359]) ).

cnf(c_651466,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssList(tl(sK56)) ),
    inference(superposition,[status(thm)],[c_650908,c_222]) ).

cnf(c_651467,plain,
    ssList(tl(sK56)),
    inference(forward_subsumption_resolution,[status(thm)],[c_651466,c_93359,c_253]) ).

cnf(c_651839,plain,
    ( ~ ssList(X0)
    | app(cons(hd(sK56),nil),X0) = cons(hd(sK56),X0) ),
    inference(superposition,[status(thm)],[c_650841,c_227]) ).

cnf(c_654180,plain,
    ( ~ sP0(app(sK56,cons(X0,X1)))
    | ~ ssList(sK8(sK56,sK57))
    | ~ ssList(sK9(sK56,sK57))
    | ~ leq(X0,sK57)
    | ~ leq(sK57,X0)
    | ~ ssItem(X0)
    | ~ ssList(X1)
    | ~ ssItem(sK57) ),
    inference(superposition,[status(thm)],[c_644880,c_81]) ).

cnf(c_654263,plain,
    ( ~ sP0(app(sK56,cons(X0,X1)))
    | ~ ssList(sK8(sK56,sK57))
    | ~ ssList(sK9(sK56,sK57))
    | ~ leq(X0,sK57)
    | ~ leq(sK57,X0)
    | ~ ssItem(X0)
    | ~ ssList(X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_654180,c_249]) ).

cnf(c_841275,plain,
    app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)),
    inference(superposition,[status(thm)],[c_651467,c_651839]) ).

cnf(c_841278,plain,
    app(cons(hd(sK56),nil),tl(sK56)) = sK56,
    inference(light_normalisation,[status(thm)],[c_841275,c_651220]) ).

cnf(c_882933,plain,
    ( ~ ssList(cons(hd(sK56),nil))
    | ~ memberP(sK56,X0)
    | ~ ssList(tl(sK56))
    | ~ ssItem(X0)
    | memberP(cons(hd(sK56),nil),X0)
    | memberP(tl(sK56),X0) ),
    inference(superposition,[status(thm)],[c_841278,c_167]) ).

cnf(c_882944,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
    inference(superposition,[status(thm)],[c_841278,c_250]) ).

cnf(c_882951,plain,
    app(tl(sK56),cons(hd(sK56),nil)) = sK55,
    inference(forward_subsumption_resolution,[status(thm)],[c_882944,c_651467,c_650841]) ).

cnf(c_882974,plain,
    ( ~ ssList(cons(hd(sK56),nil))
    | ~ memberP(sK56,X0)
    | ~ ssItem(X0)
    | memberP(cons(hd(sK56),nil),X0)
    | memberP(tl(sK56),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_882933,c_651467]) ).

cnf(c_940795,plain,
    ( ~ memberP(cons(hd(sK56),nil),X0)
    | ~ ssList(cons(hd(sK56),nil))
    | ~ ssList(tl(sK56))
    | ~ ssItem(X0)
    | memberP(sK55,X0) ),
    inference(superposition,[status(thm)],[c_882951,c_165]) ).

cnf(c_940798,plain,
    ( ~ ssList(cons(hd(sK56),nil))
    | ~ memberP(tl(sK56),X0)
    | ~ ssList(tl(sK56))
    | ~ ssItem(X0)
    | memberP(sK55,X0) ),
    inference(superposition,[status(thm)],[c_882951,c_166]) ).

cnf(c_940824,plain,
    ( ~ ssList(cons(hd(sK56),nil))
    | ~ memberP(tl(sK56),X0)
    | ~ ssItem(X0)
    | memberP(sK55,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_940798,c_651467]) ).

cnf(c_940851,plain,
    ( ~ memberP(cons(hd(sK56),nil),X0)
    | ~ ssList(cons(hd(sK56),nil))
    | ~ ssItem(X0)
    | memberP(sK55,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_940795,c_651467]) ).

cnf(c_942571,plain,
    ( ~ ssItem(X0)
    | ~ leq(sK57,X0)
    | ~ leq(X0,sK57) ),
    inference(global_subsumption_just,[status(thm)],[c_654263,c_249,c_141,c_248,c_247,c_13034,c_13262,c_14207,c_16532,c_16531,c_31411,c_40081,c_72300,c_322670,c_414748,c_414749,c_882974,c_940824,c_940851]) ).

cnf(c_942572,plain,
    ( ~ leq(X0,sK57)
    | ~ leq(sK57,X0)
    | ~ ssItem(X0) ),
    inference(renaming,[status(thm)],[c_942571]) ).

cnf(c_942580,plain,
    ( ~ leq(sK57,sK57)
    | ~ ssItem(sK57) ),
    inference(superposition,[status(thm)],[c_158,c_942572]) ).

cnf(c_942581,plain,
    ~ leq(sK57,sK57),
    inference(forward_subsumption_resolution,[status(thm)],[c_942580,c_249]) ).

cnf(c_942582,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_942581,c_13256,c_249]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC409+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Aug 28 17:19:55 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 299.66/38.90  % SZS status Started for theBenchmark.p
% 299.66/38.90  % SZS status Theorem for theBenchmark.p
% 299.66/38.90  
% 299.66/38.90  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 299.66/38.90  
% 299.66/38.90  ------  iProver source info
% 299.66/38.90  
% 299.66/38.90  git: date: 2023-05-31 18:12:56 +0000
% 299.66/38.90  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 299.66/38.90  git: non_committed_changes: false
% 299.66/38.90  git: last_make_outside_of_git: false
% 299.66/38.90  
% 299.66/38.90  ------ Parsing...
% 299.66/38.90  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 299.66/38.90  
% 299.66/38.90  ------ 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 
% 299.66/38.90  
% 299.66/38.90  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 299.66/38.90  
% 299.66/38.90  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 299.66/38.90  ------ Proving...
% 299.66/38.90  ------ Problem Properties 
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  clauses                                 187
% 299.66/38.90  conjectures                             7
% 299.66/38.90  EPR                                     55
% 299.66/38.90  Horn                                    119
% 299.66/38.90  unary                                   21
% 299.66/38.90  binary                                  41
% 299.66/38.90  lits                                    629
% 299.66/38.90  lits eq                                 82
% 299.66/38.90  fd_pure                                 0
% 299.66/38.90  fd_pseudo                               0
% 299.66/38.90  fd_cond                                 21
% 299.66/38.90  fd_pseudo_cond                          14
% 299.66/38.90  AC symbols                              0
% 299.66/38.90  
% 299.66/38.90  ------ Schedule dynamic 5 is on 
% 299.66/38.90  
% 299.66/38.90  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  ------ 
% 299.66/38.90  Current options:
% 299.66/38.90  ------ 
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  ------ Proving...
% 299.66/38.90  Proof_search_loop: time out after: 10571 full_loop iterations
% 299.66/38.90  
% 299.66/38.90  ------ Input Options"--res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  ------ 
% 299.66/38.90  Current options:
% 299.66/38.90  ------ 
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  ------ Proving...
% 299.66/38.90  Proof_search_loop: time out after: 12261 full_loop iterations
% 299.66/38.90  
% 299.66/38.90  ------ Option_1: Negative Selections Time Limit: 35.
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  ------ 
% 299.66/38.90  Current options:
% 299.66/38.90  ------ 
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  ------ Proving...
% 299.66/38.90  
% 299.66/38.90  
% 299.66/38.90  % SZS status Theorem for theBenchmark.p
% 299.66/38.90  
% 299.66/38.90  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 299.66/38.90  
% 299.66/38.92  
%------------------------------------------------------------------------------