TSTP Solution File: SWC237+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC237+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n017.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 03:11:42 EDT 2024

% Result   : Theorem 147.10s 20.32s
% Output   : CNFRefutation 147.10s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f605)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

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(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

fof(f24,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssList(tl(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).

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

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

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

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).

fof(f76,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( tl(X0) = X1
            & ssList(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).

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

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

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

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f5]) ).

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

fof(f127,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f128,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f127]) ).

fof(f130,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f131,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f130]) ).

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

fof(f135,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

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

fof(f177,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

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

fof(f245,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( app(X1,X2) = X0
                  & ssList(X2) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f102]) ).

fof(f246,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X3] :
                  ( app(X1,X3) = X0
                  & ssList(X3) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f245]) ).

fof(f247,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X1,X3) = X0
          & ssList(X3) )
     => ( app(X1,sK11(X0,X1)) = X0
        & ssList(sK11(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f248,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(X1,sK11(X0,X1)) = X0
                & ssList(sK11(X0,X1)) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f246,f247]) ).

fof(f330,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f177]) ).

fof(f337,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
     => ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f338,plain,
    ! [X0] :
      ( ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f190,f337]) ).

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

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

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

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

fof(f347,plain,
    ( ? [X4] :
        ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ~ lt(X7,X5)
                        | app(X8,cons(X7,nil)) != sK55
                        | ~ ssList(X8) )
                    | ~ ssItem(X7) )
                | app(cons(X5,nil),X6) != X4
                | ~ ssList(X6) )
            | ~ ssItem(X5) )
        & strictorderedP(sK55)
        & app(sK55,X4) = sK56
        & ssList(X4) )
   => ( ! [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ~ lt(X7,X5)
                      | app(X8,cons(X7,nil)) != sK55
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | app(cons(X5,nil),X6) != sK57
              | ~ ssList(X6) )
          | ~ ssItem(X5) )
      & strictorderedP(sK55)
      & sK56 = app(sK55,sK57)
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ! [X9,X10,X11] :
      ( ? [X12] :
          ( ~ lt(X9,X12)
          & leq(X9,X12)
          & memberP(X11,X12)
          & memberP(X10,X12)
          & ssItem(X12) )
     => ( ~ lt(X9,sK58(X9,X10,X11))
        & leq(X9,sK58(X9,X10,X11))
        & memberP(X11,sK58(X9,X10,X11))
        & memberP(X10,sK58(X9,X10,X11))
        & ssItem(sK58(X9,X10,X11)) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ( nil != sK55
      | nil = sK56 )
    & ! [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ~ lt(X7,X5)
                    | app(X8,cons(X7,nil)) != sK55
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | app(cons(X5,nil),X6) != sK57
            | ~ ssList(X6) )
        | ~ ssItem(X5) )
    & strictorderedP(sK55)
    & sK56 = app(sK55,sK57)
    & ssList(sK57)
    & ! [X9] :
        ( ! [X10] :
            ( ! [X11] :
                ( ( ~ lt(X9,sK58(X9,X10,X11))
                  & leq(X9,sK58(X9,X10,X11))
                  & memberP(X11,sK58(X9,X10,X11))
                  & memberP(X10,sK58(X9,X10,X11))
                  & ssItem(sK58(X9,X10,X11)) )
                | app(app(X10,cons(X9,nil)),X11) != sK53
                | ~ ssList(X11) )
            | ~ ssList(X10) )
        | ~ ssItem(X9) )
    & nil != sK53
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58])],[f222,f348,f347,f346,f345,f344,f343]) ).

fof(f362,plain,
    ! [X0,X1] :
      ( ssList(sK11(X0,X1))
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f248]) ).

fof(f363,plain,
    ! [X0,X1] :
      ( app(X1,sK11(X0,X1)) = X0
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f248]) ).

fof(f364,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X1)
      | app(X1,X2) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f248]) ).

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(f450,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f128]) ).

fof(f452,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f454,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f456,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f135]) ).

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

fof(f496,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f497,plain,
    ! [X0] :
      ( segmentP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f524,plain,
    ! [X0] :
      ( ssList(sK52(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f525,plain,
    ! [X0] :
      ( tl(X0) = sK52(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f338]) ).

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

fof(f549,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f349]) ).

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

fof(f555,plain,
    nil != sK53,
    inference(cnf_transformation,[],[f349]) ).

fof(f556,plain,
    ! [X10,X11,X9] :
      ( ssItem(sK58(X9,X10,X11))
      | app(app(X10,cons(X9,nil)),X11) != sK53
      | ~ ssList(X11)
      | ~ ssList(X10)
      | ~ ssItem(X9) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f557,plain,
    ! [X10,X11,X9] :
      ( memberP(X10,sK58(X9,X10,X11))
      | app(app(X10,cons(X9,nil)),X11) != sK53
      | ~ ssList(X11)
      | ~ ssList(X10)
      | ~ ssItem(X9) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f569,plain,
    ! [X10,X11,X9] :
      ( memberP(X10,sK58(X9,X10,X11))
      | app(app(X10,cons(X9,nil)),X11) != sK55
      | ~ ssList(X11)
      | ~ ssList(X10)
      | ~ ssItem(X9) ),
    inference(definition_unfolding,[],[f557,f554]) ).

fof(f570,plain,
    ! [X10,X11,X9] :
      ( ssItem(sK58(X9,X10,X11))
      | app(app(X10,cons(X9,nil)),X11) != sK55
      | ~ ssList(X11)
      | ~ ssList(X10)
      | ~ ssItem(X9) ),
    inference(definition_unfolding,[],[f556,f554]) ).

fof(f571,plain,
    nil != sK55,
    inference(definition_unfolding,[],[f555,f554]) ).

fof(f573,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f549,f554]) ).

fof(f577,plain,
    ! [X2,X1] :
      ( frontsegP(app(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X1,X2)) ),
    inference(equality_resolution,[],[f364]) ).

fof(f593,plain,
    ( segmentP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f497]) ).

cnf(c_61,plain,
    ( ~ ssList(app(X0,X1))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(cnf_transformation,[],[f577]) ).

cnf(c_62,plain,
    ( ~ frontsegP(X0,X1)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | app(X1,sK11(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f363]) ).

cnf(c_63,plain,
    ( ~ frontsegP(X0,X1)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(sK11(X0,X1)) ),
    inference(cnf_transformation,[],[f362]) ).

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_149,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssItem(hd(X0)) ),
    inference(cnf_transformation,[],[f450]) ).

cnf(c_151,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssList(tl(X0)) ),
    inference(cnf_transformation,[],[f452]) ).

cnf(c_153,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f454]) ).

cnf(c_155,plain,
    ( ~ ssList(X0)
    | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f456]) ).

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

cnf(c_177,plain,
    ( ~ frontsegP(X0,X1)
    | ~ ssItem(X2)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(cons(X2,X0),cons(X2,X1)) ),
    inference(cnf_transformation,[],[f605]) ).

cnf(c_195,plain,
    ( ~ ssList(nil)
    | segmentP(nil,nil) ),
    inference(cnf_transformation,[],[f593]) ).

cnf(c_196,plain,
    ( ~ segmentP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f496]) ).

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_254,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(X0,sK58(X1,X0,X2)) ),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_255,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ssItem(sK58(X1,X0,X2)) ),
    inference(cnf_transformation,[],[f570]) ).

cnf(c_256,negated_conjecture,
    nil != sK55,
    inference(cnf_transformation,[],[f571]) ).

cnf(c_260,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f573]) ).

cnf(c_310,plain,
    ( ~ segmentP(nil,nil)
    | ~ ssList(nil)
    | nil = nil ),
    inference(instantiation,[status(thm)],[c_196]) ).

cnf(c_595,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).

cnf(c_6824,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_6826,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_6833,plain,
    ( X0 != X1
    | X2 != X3
    | ~ frontsegP(X1,X3)
    | frontsegP(X0,X2) ),
    theory(equality) ).

cnf(c_10155,plain,
    ( nil != X0
    | sK55 != X0
    | nil = sK55 ),
    inference(instantiation,[status(thm)],[c_6826]) ).

cnf(c_10156,plain,
    ( nil != nil
    | sK55 != nil
    | nil = sK55 ),
    inference(instantiation,[status(thm)],[c_10155]) ).

cnf(c_10258,plain,
    ( ~ ssList(sK55)
    | cons(hd(sK55),tl(sK55)) = sK55
    | sK55 = nil ),
    inference(instantiation,[status(thm)],[c_224]) ).

cnf(c_10260,plain,
    ( ~ ssList(sK55)
    | tl(sK55) = sK52(sK55)
    | sK55 = nil ),
    inference(instantiation,[status(thm)],[c_221]) ).

cnf(c_10267,plain,
    ( ~ ssList(sK55)
    | sK55 = nil
    | ssList(tl(sK55)) ),
    inference(instantiation,[status(thm)],[c_151]) ).

cnf(c_10268,plain,
    ( ~ ssList(sK55)
    | sK55 = nil
    | ssItem(hd(sK55)) ),
    inference(instantiation,[status(thm)],[c_149]) ).

cnf(c_11293,plain,
    ( ~ ssItem(hd(sK55))
    | ~ ssList(X0)
    | ssList(cons(hd(sK55),X0)) ),
    inference(instantiation,[status(thm)],[c_140]) ).

cnf(c_11300,plain,
    ( ~ ssItem(hd(sK55))
    | ~ ssList(nil)
    | ssList(cons(hd(sK55),nil)) ),
    inference(instantiation,[status(thm)],[c_11293]) ).

cnf(c_11633,plain,
    sK55 = sK55,
    inference(instantiation,[status(thm)],[c_6824]) ).

cnf(c_16271,plain,
    ( ~ ssList(cons(X0,X1))
    | ~ ssList(X2)
    | ssList(app(X2,cons(X0,X1))) ),
    inference(instantiation,[status(thm)],[c_153]) ).

cnf(c_20234,plain,
    ( ~ ssList(cons(hd(sK55),X0))
    | ~ ssList(X1)
    | ssList(app(X1,cons(hd(sK55),X0))) ),
    inference(instantiation,[status(thm)],[c_16271]) ).

cnf(c_20235,plain,
    ( ~ ssList(cons(hd(sK55),nil))
    | ~ ssList(nil)
    | ssList(app(nil,cons(hd(sK55),nil))) ),
    inference(instantiation,[status(thm)],[c_20234]) ).

cnf(c_21425,plain,
    ( tl(sK55) = sK52(sK55)
    | nil = sK55 ),
    inference(superposition,[status(thm)],[c_260,c_221]) ).

cnf(c_21718,plain,
    tl(sK55) = sK52(sK55),
    inference(global_subsumption_just,[status(thm)],[c_21425,c_260,c_141,c_256,c_195,c_310,c_10156,c_10260]) ).

cnf(c_21720,plain,
    ( ~ ssList(sK55)
    | nil = sK55
    | ssList(tl(sK55)) ),
    inference(superposition,[status(thm)],[c_21718,c_222]) ).

cnf(c_21801,plain,
    ssList(tl(sK55)),
    inference(global_subsumption_just,[status(thm)],[c_21720,c_260,c_141,c_256,c_195,c_310,c_10156,c_10267]) ).

cnf(c_21810,plain,
    app(nil,tl(sK55)) = tl(sK55),
    inference(superposition,[status(thm)],[c_21801,c_155]) ).

cnf(c_21920,plain,
    ( cons(hd(sK55),tl(sK55)) = sK55
    | nil = sK55 ),
    inference(superposition,[status(thm)],[c_260,c_224]) ).

cnf(c_22003,plain,
    ( ~ ssList(tl(sK55))
    | ~ ssList(nil)
    | frontsegP(tl(sK55),nil) ),
    inference(superposition,[status(thm)],[c_21810,c_595]) ).

cnf(c_22267,plain,
    cons(hd(sK55),tl(sK55)) = sK55,
    inference(global_subsumption_just,[status(thm)],[c_21920,c_260,c_141,c_256,c_195,c_310,c_10156,c_10258]) ).

cnf(c_24779,plain,
    ( ~ frontsegP(tl(sK55),X0)
    | ~ ssItem(hd(sK55))
    | ~ ssList(tl(sK55))
    | ~ ssList(X0)
    | frontsegP(sK55,cons(hd(sK55),X0)) ),
    inference(superposition,[status(thm)],[c_22267,c_177]) ).

cnf(c_24801,plain,
    ( ~ frontsegP(tl(sK55),nil)
    | ~ ssItem(hd(sK55))
    | ~ ssList(tl(sK55))
    | ~ ssList(nil)
    | frontsegP(sK55,cons(hd(sK55),nil)) ),
    inference(instantiation,[status(thm)],[c_24779]) ).

cnf(c_25465,plain,
    ( ~ ssList(cons(X0,X1))
    | app(nil,cons(X0,X1)) = cons(X0,X1) ),
    inference(instantiation,[status(thm)],[c_155]) ).

cnf(c_64396,plain,
    ( ~ ssList(cons(hd(sK55),X0))
    | app(nil,cons(hd(sK55),X0)) = cons(hd(sK55),X0) ),
    inference(instantiation,[status(thm)],[c_25465]) ).

cnf(c_64397,plain,
    ( ~ ssList(cons(hd(sK55),nil))
    | app(nil,cons(hd(sK55),nil)) = cons(hd(sK55),nil) ),
    inference(instantiation,[status(thm)],[c_64396]) ).

cnf(c_73887,plain,
    ( app(app(X0,cons(hd(sK55),nil)),X1) != sK55
    | ~ ssItem(hd(sK55))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | memberP(X0,sK58(hd(sK55),X0,X1)) ),
    inference(instantiation,[status(thm)],[c_254]) ).

cnf(c_73891,plain,
    ( app(app(X0,cons(hd(sK55),nil)),X1) != sK55
    | ~ ssItem(hd(sK55))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ssItem(sK58(hd(sK55),X0,X1)) ),
    inference(instantiation,[status(thm)],[c_255]) ).

cnf(c_75983,plain,
    ( ~ frontsegP(sK55,app(X0,cons(X1,nil)))
    | ~ ssList(app(X0,cons(X1,nil)))
    | ~ ssList(sK55)
    | app(app(X0,cons(X1,nil)),sK11(sK55,app(X0,cons(X1,nil)))) = sK55 ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_77536,plain,
    ( app(X0,cons(X1,nil)) != X2
    | sK55 != X3
    | ~ frontsegP(X3,X2)
    | frontsegP(sK55,app(X0,cons(X1,nil))) ),
    inference(instantiation,[status(thm)],[c_6833]) ).

cnf(c_78669,plain,
    ( ~ frontsegP(sK55,app(X0,cons(X1,nil)))
    | ~ ssList(app(X0,cons(X1,nil)))
    | ~ ssList(sK55)
    | ssList(sK11(sK55,app(X0,cons(X1,nil)))) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_83684,plain,
    ( app(X0,cons(X1,nil)) != X2
    | sK55 != sK55
    | ~ frontsegP(sK55,X2)
    | frontsegP(sK55,app(X0,cons(X1,nil))) ),
    inference(instantiation,[status(thm)],[c_77536]) ).

cnf(c_151816,plain,
    ( ~ frontsegP(sK55,app(X0,cons(hd(sK55),nil)))
    | ~ ssList(app(X0,cons(hd(sK55),nil)))
    | ~ ssList(sK55)
    | app(app(X0,cons(hd(sK55),nil)),sK11(sK55,app(X0,cons(hd(sK55),nil)))) = sK55 ),
    inference(instantiation,[status(thm)],[c_75983]) ).

cnf(c_151818,plain,
    ( app(app(X0,cons(hd(sK55),nil)),sK11(sK55,app(X0,cons(hd(sK55),nil)))) != sK55
    | ~ ssList(sK11(sK55,app(X0,cons(hd(sK55),nil))))
    | ~ ssItem(hd(sK55))
    | ~ ssList(X0)
    | memberP(X0,sK58(hd(sK55),X0,sK11(sK55,app(X0,cons(hd(sK55),nil))))) ),
    inference(instantiation,[status(thm)],[c_73887]) ).

cnf(c_151819,plain,
    ( app(app(X0,cons(hd(sK55),nil)),sK11(sK55,app(X0,cons(hd(sK55),nil)))) != sK55
    | ~ ssList(sK11(sK55,app(X0,cons(hd(sK55),nil))))
    | ~ ssItem(hd(sK55))
    | ~ ssList(X0)
    | ssItem(sK58(hd(sK55),X0,sK11(sK55,app(X0,cons(hd(sK55),nil))))) ),
    inference(instantiation,[status(thm)],[c_73891]) ).

cnf(c_151821,plain,
    ( ~ frontsegP(sK55,app(nil,cons(hd(sK55),nil)))
    | ~ ssList(app(nil,cons(hd(sK55),nil)))
    | ~ ssList(sK55)
    | app(app(nil,cons(hd(sK55),nil)),sK11(sK55,app(nil,cons(hd(sK55),nil)))) = sK55 ),
    inference(instantiation,[status(thm)],[c_151816]) ).

cnf(c_151823,plain,
    ( app(app(nil,cons(hd(sK55),nil)),sK11(sK55,app(nil,cons(hd(sK55),nil)))) != sK55
    | ~ ssList(sK11(sK55,app(nil,cons(hd(sK55),nil))))
    | ~ ssItem(hd(sK55))
    | ~ ssList(nil)
    | ssItem(sK58(hd(sK55),nil,sK11(sK55,app(nil,cons(hd(sK55),nil))))) ),
    inference(instantiation,[status(thm)],[c_151819]) ).

cnf(c_151824,plain,
    ( app(app(nil,cons(hd(sK55),nil)),sK11(sK55,app(nil,cons(hd(sK55),nil)))) != sK55
    | ~ ssList(sK11(sK55,app(nil,cons(hd(sK55),nil))))
    | ~ ssItem(hd(sK55))
    | ~ ssList(nil)
    | memberP(nil,sK58(hd(sK55),nil,sK11(sK55,app(nil,cons(hd(sK55),nil))))) ),
    inference(instantiation,[status(thm)],[c_151818]) ).

cnf(c_159242,plain,
    ( ~ frontsegP(sK55,app(X0,cons(hd(sK55),nil)))
    | ~ ssList(app(X0,cons(hd(sK55),nil)))
    | ~ ssList(sK55)
    | ssList(sK11(sK55,app(X0,cons(hd(sK55),nil)))) ),
    inference(instantiation,[status(thm)],[c_78669]) ).

cnf(c_159243,plain,
    ( ~ frontsegP(sK55,app(nil,cons(hd(sK55),nil)))
    | ~ ssList(app(nil,cons(hd(sK55),nil)))
    | ~ ssList(sK55)
    | ssList(sK11(sK55,app(nil,cons(hd(sK55),nil)))) ),
    inference(instantiation,[status(thm)],[c_159242]) ).

cnf(c_163790,plain,
    ( app(X0,cons(hd(sK55),nil)) != X1
    | sK55 != sK55
    | ~ frontsegP(sK55,X1)
    | frontsegP(sK55,app(X0,cons(hd(sK55),nil))) ),
    inference(instantiation,[status(thm)],[c_83684]) ).

cnf(c_170993,plain,
    ( app(nil,cons(hd(sK55),nil)) != cons(hd(sK55),nil)
    | sK55 != sK55
    | ~ frontsegP(sK55,cons(hd(sK55),nil))
    | frontsegP(sK55,app(nil,cons(hd(sK55),nil))) ),
    inference(instantiation,[status(thm)],[c_163790]) ).

cnf(c_180179,plain,
    ( ~ memberP(nil,sK58(hd(sK55),nil,sK11(sK55,app(nil,cons(hd(sK55),nil)))))
    | ~ ssItem(sK58(hd(sK55),nil,sK11(sK55,app(nil,cons(hd(sK55),nil))))) ),
    inference(instantiation,[status(thm)],[c_171]) ).

cnf(c_180180,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_180179,c_170993,c_159243,c_151824,c_151823,c_151821,c_64397,c_24801,c_22003,c_20235,c_11633,c_11300,c_10267,c_10268,c_10156,c_310,c_195,c_256,c_141,c_260]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SWC237+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n017.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 22:52:36 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 147.10/20.32  % SZS status Started for theBenchmark.p
% 147.10/20.32  % SZS status Theorem for theBenchmark.p
% 147.10/20.32  
% 147.10/20.32  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 147.10/20.32  
% 147.10/20.32  ------  iProver source info
% 147.10/20.32  
% 147.10/20.32  git: date: 2024-05-02 19:28:25 +0000
% 147.10/20.32  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 147.10/20.32  git: non_committed_changes: false
% 147.10/20.32  
% 147.10/20.32  ------ Parsing...
% 147.10/20.32  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 147.10/20.32  
% 147.10/20.32  ------ 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 
% 147.10/20.32  
% 147.10/20.32  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 147.10/20.32  
% 147.10/20.32  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 147.10/20.32  ------ Proving...
% 147.10/20.32  ------ Problem Properties 
% 147.10/20.32  
% 147.10/20.32  
% 147.10/20.32  clauses                                 192
% 147.10/20.32  conjectures                             12
% 147.10/20.32  EPR                                     54
% 147.10/20.32  Horn                                    124
% 147.10/20.32  unary                                   22
% 147.10/20.32  binary                                  40
% 147.10/20.32  lits                                    656
% 147.10/20.32  lits eq                                 87
% 147.10/20.32  fd_pure                                 0
% 147.10/20.32  fd_pseudo                               0
% 147.10/20.32  fd_cond                                 21
% 147.10/20.32  fd_pseudo_cond                          14
% 147.10/20.32  AC symbols                              0
% 147.10/20.32  
% 147.10/20.32  ------ Input Options Time Limit: Unbounded
% 147.10/20.32  
% 147.10/20.32  
% 147.10/20.32  ------ 
% 147.10/20.32  Current options:
% 147.10/20.32  ------ 
% 147.10/20.32  
% 147.10/20.32  
% 147.10/20.32  
% 147.10/20.32  
% 147.10/20.32  ------ Proving...
% 147.10/20.32  
% 147.10/20.32  
% 147.10/20.32  % SZS status Theorem for theBenchmark.p
% 147.10/20.32  
% 147.10/20.32  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 147.10/20.32  
% 147.10/20.33  
%------------------------------------------------------------------------------