TSTP Solution File: SWC109+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC109+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n022.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 03:11:16 EDT 2024

% Result   : Theorem 8.30s 1.64s
% Output   : CNFRefutation 8.30s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f609)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

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

fof(f18,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) != X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).

fof(f53,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( ( segmentP(X1,X2)
                  & segmentP(X0,X1) )
               => segmentP(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).

fof(f54,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ( segmentP(X1,X0)
              & segmentP(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).

fof(f57,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).

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

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

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

fof(f104,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f121,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) != X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f169,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( segmentP(X0,X2)
              | ~ segmentP(X1,X2)
              | ~ segmentP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f170,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( segmentP(X0,X2)
              | ~ segmentP(X1,X2)
              | ~ segmentP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f169]) ).

fof(f171,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ segmentP(X1,X0)
          | ~ segmentP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f54]) ).

fof(f172,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ segmentP(X1,X0)
          | ~ segmentP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f171]) ).

fof(f176,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f57]) ).

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

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

fof(f232,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( ? [X6] :
                  ( ! [X7] :
                      ( ~ lt(X7,X4)
                      | ~ memberP(X6,X7)
                      | ~ ssItem(X7) )
                  & ! [X8] :
                      ( ~ lt(X4,X8)
                      | ~ memberP(X5,X8)
                      | ~ ssItem(X8) )
                  & app(app(X5,X2),X6) = X3
                  & cons(X4,nil) = X2
                  & ssList(X6) )
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP6(X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f233,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ( ~ segmentP(X1,X0)
                        | ~ neq(X0,nil) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | sP6(X3,X2) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f222,f232]) ).

fof(f255,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(app(X2,X1),X3) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f104]) ).

fof(f256,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(app(X4,X1),X5) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f255]) ).

fof(f257,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK14(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK14(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK14(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0
        & ssList(sK15(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f259,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0
                & ssList(sK15(X0,X1))
                & ssList(sK14(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f256,f258,f257]) ).

fof(f318,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f119]) ).

fof(f332,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f177]) ).

fof(f345,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( ? [X6] :
                  ( ! [X7] :
                      ( ~ lt(X7,X4)
                      | ~ memberP(X6,X7)
                      | ~ ssItem(X7) )
                  & ! [X8] :
                      ( ~ lt(X4,X8)
                      | ~ memberP(X5,X8)
                      | ~ ssItem(X8) )
                  & app(app(X5,X2),X6) = X3
                  & cons(X4,nil) = X2
                  & ssList(X6) )
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP6(X3,X2) ),
    inference(nnf_transformation,[],[f232]) ).

fof(f346,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ! [X5] :
                      ( ~ lt(X5,X2)
                      | ~ memberP(X4,X5)
                      | ~ ssItem(X5) )
                  & ! [X6] :
                      ( ~ lt(X2,X6)
                      | ~ memberP(X3,X6)
                      | ~ ssItem(X6) )
                  & app(app(X3,X1),X4) = X0
                  & cons(X2,nil) = X1
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
      | ~ sP6(X0,X1) ),
    inference(rectify,[],[f345]) ).

fof(f347,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ! [X5] :
                      ( ~ lt(X5,X2)
                      | ~ memberP(X4,X5)
                      | ~ ssItem(X5) )
                  & ! [X6] :
                      ( ~ lt(X2,X6)
                      | ~ memberP(X3,X6)
                      | ~ ssItem(X6) )
                  & app(app(X3,X1),X4) = X0
                  & cons(X2,nil) = X1
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ! [X5] :
                    ( ~ lt(X5,sK54(X0,X1))
                    | ~ memberP(X4,X5)
                    | ~ ssItem(X5) )
                & ! [X6] :
                    ( ~ lt(sK54(X0,X1),X6)
                    | ~ memberP(X3,X6)
                    | ~ ssItem(X6) )
                & app(app(X3,X1),X4) = X0
                & cons(sK54(X0,X1),nil) = X1
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK54(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ? [X4] :
              ( ! [X5] :
                  ( ~ lt(X5,sK54(X0,X1))
                  | ~ memberP(X4,X5)
                  | ~ ssItem(X5) )
              & ! [X6] :
                  ( ~ lt(sK54(X0,X1),X6)
                  | ~ memberP(X3,X6)
                  | ~ ssItem(X6) )
              & app(app(X3,X1),X4) = X0
              & cons(sK54(X0,X1),nil) = X1
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ! [X5] :
                ( ~ lt(X5,sK54(X0,X1))
                | ~ memberP(X4,X5)
                | ~ ssItem(X5) )
            & ! [X6] :
                ( ~ lt(sK54(X0,X1),X6)
                | ~ memberP(sK55(X0,X1),X6)
                | ~ ssItem(X6) )
            & app(app(sK55(X0,X1),X1),X4) = X0
            & cons(sK54(X0,X1),nil) = X1
            & ssList(X4) )
        & ssList(sK55(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ! [X5] :
              ( ~ lt(X5,sK54(X0,X1))
              | ~ memberP(X4,X5)
              | ~ ssItem(X5) )
          & ! [X6] :
              ( ~ lt(sK54(X0,X1),X6)
              | ~ memberP(sK55(X0,X1),X6)
              | ~ ssItem(X6) )
          & app(app(sK55(X0,X1),X1),X4) = X0
          & cons(sK54(X0,X1),nil) = X1
          & ssList(X4) )
     => ( ! [X5] :
            ( ~ lt(X5,sK54(X0,X1))
            | ~ memberP(sK56(X0,X1),X5)
            | ~ ssItem(X5) )
        & ! [X6] :
            ( ~ lt(sK54(X0,X1),X6)
            | ~ memberP(sK55(X0,X1),X6)
            | ~ ssItem(X6) )
        & app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
        & cons(sK54(X0,X1),nil) = X1
        & ssList(sK56(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ! [X0,X1] :
      ( ( ! [X5] :
            ( ~ lt(X5,sK54(X0,X1))
            | ~ memberP(sK56(X0,X1),X5)
            | ~ ssItem(X5) )
        & ! [X6] :
            ( ~ lt(sK54(X0,X1),X6)
            | ~ memberP(sK55(X0,X1),X6)
            | ~ ssItem(X6) )
        & app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
        & cons(sK54(X0,X1),nil) = X1
        & ssList(sK56(X0,X1))
        & ssList(sK55(X0,X1))
        & ssItem(sK54(X0,X1)) )
      | ~ sP6(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55,sK56])],[f346,f349,f348,f347]) ).

fof(f351,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ( ~ segmentP(X1,X0)
                          | ~ neq(X0,nil) )
                        & neq(X1,nil) )
                      | ( nil != X0
                        & nil = X1 ) )
                    & ( ( nil = X2
                        & nil = X3 )
                      | sP6(X3,X2) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ( ~ segmentP(X1,sK57)
                        | ~ neq(sK57,nil) )
                      & neq(X1,nil) )
                    | ( nil != sK57
                      & nil = X1 ) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | sP6(X3,X2) )
                  & sK57 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f352,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ( ~ segmentP(X1,sK57)
                      | ~ neq(sK57,nil) )
                    & neq(X1,nil) )
                  | ( nil != sK57
                    & nil = X1 ) )
                & ( ( nil = X2
                    & nil = X3 )
                  | sP6(X3,X2) )
                & sK57 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ( ~ segmentP(sK58,sK57)
                    | ~ neq(sK57,nil) )
                  & neq(sK58,nil) )
                | ( nil != sK57
                  & nil = sK58 ) )
              & ( ( nil = X2
                  & nil = X3 )
                | sP6(X3,X2) )
              & sK57 = X2
              & sK58 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f353,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ( ~ segmentP(sK58,sK57)
                  | ~ neq(sK57,nil) )
                & neq(sK58,nil) )
              | ( nil != sK57
                & nil = sK58 ) )
            & ( ( nil = X2
                & nil = X3 )
              | sP6(X3,X2) )
            & sK57 = X2
            & sK58 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ( ~ segmentP(sK58,sK57)
                | ~ neq(sK57,nil) )
              & neq(sK58,nil) )
            | ( nil != sK57
              & nil = sK58 ) )
          & ( ( nil = sK59
              & nil = X3 )
            | sP6(X3,sK59) )
          & sK57 = sK59
          & sK58 = X3
          & ssList(X3) )
      & ssList(sK59) ) ),
    introduced(choice_axiom,[]) ).

fof(f354,plain,
    ( ? [X3] :
        ( ( ( ( ~ segmentP(sK58,sK57)
              | ~ neq(sK57,nil) )
            & neq(sK58,nil) )
          | ( nil != sK57
            & nil = sK58 ) )
        & ( ( nil = sK59
            & nil = X3 )
          | sP6(X3,sK59) )
        & sK57 = sK59
        & sK58 = X3
        & ssList(X3) )
   => ( ( ( ( ~ segmentP(sK58,sK57)
            | ~ neq(sK57,nil) )
          & neq(sK58,nil) )
        | ( nil != sK57
          & nil = sK58 ) )
      & ( ( nil = sK59
          & nil = sK60 )
        | sP6(sK60,sK59) )
      & sK57 = sK59
      & sK58 = sK60
      & ssList(sK60) ) ),
    introduced(choice_axiom,[]) ).

fof(f355,plain,
    ( ( ( ( ~ segmentP(sK58,sK57)
          | ~ neq(sK57,nil) )
        & neq(sK58,nil) )
      | ( nil != sK57
        & nil = sK58 ) )
    & ( ( nil = sK59
        & nil = sK60 )
      | sP6(sK60,sK59) )
    & sK57 = sK59
    & sK58 = sK60
    & ssList(sK60)
    & ssList(sK59)
    & ssList(sK58)
    & ssList(sK57) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60])],[f233,f354,f353,f352,f351]) ).

fof(f377,plain,
    ! [X2,X3,X0,X1] :
      ( segmentP(X0,X1)
      | app(app(X2,X1),X3) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f259]) ).

fof(f446,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f318]) ).

fof(f448,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f449,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f497,plain,
    ! [X2,X0,X1] :
      ( segmentP(X0,X2)
      | ~ segmentP(X1,X2)
      | ~ segmentP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f170]) ).

fof(f498,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ segmentP(X1,X0)
      | ~ segmentP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f172]) ).

fof(f501,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f176]) ).

fof(f502,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f332]) ).

fof(f503,plain,
    ! [X0] :
      ( segmentP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f332]) ).

fof(f555,plain,
    ! [X0,X1] :
      ( ssItem(sK54(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f556,plain,
    ! [X0,X1] :
      ( ssList(sK55(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f557,plain,
    ! [X0,X1] :
      ( ssList(sK56(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f558,plain,
    ! [X0,X1] :
      ( cons(sK54(X0,X1),nil) = X1
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f559,plain,
    ! [X0,X1] :
      ( app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f562,plain,
    ssList(sK57),
    inference(cnf_transformation,[],[f355]) ).

fof(f563,plain,
    ssList(sK58),
    inference(cnf_transformation,[],[f355]) ).

fof(f566,plain,
    sK58 = sK60,
    inference(cnf_transformation,[],[f355]) ).

fof(f567,plain,
    sK57 = sK59,
    inference(cnf_transformation,[],[f355]) ).

fof(f568,plain,
    ( nil = sK60
    | sP6(sK60,sK59) ),
    inference(cnf_transformation,[],[f355]) ).

fof(f569,plain,
    ( nil = sK59
    | sP6(sK60,sK59) ),
    inference(cnf_transformation,[],[f355]) ).

fof(f570,plain,
    ( neq(sK58,nil)
    | nil = sK58 ),
    inference(cnf_transformation,[],[f355]) ).

fof(f571,plain,
    ( neq(sK58,nil)
    | nil != sK57 ),
    inference(cnf_transformation,[],[f355]) ).

fof(f572,plain,
    ( ~ segmentP(sK58,sK57)
    | ~ neq(sK57,nil)
    | nil = sK58 ),
    inference(cnf_transformation,[],[f355]) ).

fof(f575,plain,
    ( ~ segmentP(sK60,sK59)
    | ~ neq(sK59,nil)
    | nil = sK60 ),
    inference(definition_unfolding,[],[f572,f566,f567,f567,f566]) ).

fof(f576,plain,
    ( neq(sK60,nil)
    | nil != sK59 ),
    inference(definition_unfolding,[],[f571,f566,f567]) ).

fof(f577,plain,
    ( neq(sK60,nil)
    | nil = sK60 ),
    inference(definition_unfolding,[],[f570,f566,f566]) ).

fof(f578,plain,
    ssList(sK60),
    inference(definition_unfolding,[],[f563,f566]) ).

fof(f579,plain,
    ssList(sK59),
    inference(definition_unfolding,[],[f562,f567]) ).

fof(f585,plain,
    ! [X2,X3,X1] :
      ( segmentP(app(app(X2,X1),X3),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(app(X2,X1),X3)) ),
    inference(equality_resolution,[],[f377]) ).

fof(f599,plain,
    ( segmentP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f503]) ).

cnf(c_67,plain,
    ( ~ ssList(app(app(X0,X1),X2))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | segmentP(app(app(X0,X1),X2),X1) ),
    inference(cnf_transformation,[],[f585]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f446]) ).

cnf(c_139,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f609]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f448]) ).

cnf(c_142,plain,
    ( cons(X0,X1) != X1
    | ~ ssItem(X0)
    | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f449]) ).

cnf(c_190,plain,
    ( ~ segmentP(X0,X1)
    | ~ segmentP(X1,X2)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | segmentP(X0,X2) ),
    inference(cnf_transformation,[],[f497]) ).

cnf(c_191,plain,
    ( ~ segmentP(X0,X1)
    | ~ segmentP(X1,X0)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f498]) ).

cnf(c_194,plain,
    ( ~ ssList(X0)
    | segmentP(X0,nil) ),
    inference(cnf_transformation,[],[f501]) ).

cnf(c_195,plain,
    ( ~ ssList(nil)
    | segmentP(nil,nil) ),
    inference(cnf_transformation,[],[f599]) ).

cnf(c_196,plain,
    ( ~ segmentP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f502]) ).

cnf(c_248,plain,
    ( ~ sP6(X0,X1)
    | app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_249,plain,
    ( ~ sP6(X0,X1)
    | cons(sK54(X0,X1),nil) = X1 ),
    inference(cnf_transformation,[],[f558]) ).

cnf(c_250,plain,
    ( ~ sP6(X0,X1)
    | ssList(sK56(X0,X1)) ),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_251,plain,
    ( ~ sP6(X0,X1)
    | ssList(sK55(X0,X1)) ),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_252,plain,
    ( ~ sP6(X0,X1)
    | ssItem(sK54(X0,X1)) ),
    inference(cnf_transformation,[],[f555]) ).

cnf(c_254,negated_conjecture,
    ( ~ neq(sK59,nil)
    | ~ segmentP(sK60,sK59)
    | nil = sK60 ),
    inference(cnf_transformation,[],[f575]) ).

cnf(c_255,negated_conjecture,
    ( nil != sK59
    | neq(sK60,nil) ),
    inference(cnf_transformation,[],[f576]) ).

cnf(c_256,negated_conjecture,
    ( nil = sK60
    | neq(sK60,nil) ),
    inference(cnf_transformation,[],[f577]) ).

cnf(c_257,negated_conjecture,
    ( nil = sK59
    | sP6(sK60,sK59) ),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_258,negated_conjecture,
    ( nil = sK60
    | sP6(sK60,sK59) ),
    inference(cnf_transformation,[],[f568]) ).

cnf(c_261,negated_conjecture,
    ssList(sK60),
    inference(cnf_transformation,[],[f578]) ).

cnf(c_262,negated_conjecture,
    ssList(sK59),
    inference(cnf_transformation,[],[f579]) ).

cnf(c_315,plain,
    ( ~ segmentP(nil,nil)
    | ~ ssList(nil)
    | nil = nil ),
    inference(instantiation,[status(thm)],[c_196]) ).

cnf(c_420,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(prop_impl_just,[status(thm)],[c_139]) ).

cnf(c_512,plain,
    ( ~ sP6(X0,X1)
    | app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0 ),
    inference(prop_impl_just,[status(thm)],[c_248]) ).

cnf(c_514,plain,
    ( ~ sP6(X0,X1)
    | cons(sK54(X0,X1),nil) = X1 ),
    inference(prop_impl_just,[status(thm)],[c_249]) ).

cnf(c_516,plain,
    ( ~ sP6(X0,X1)
    | ssList(sK56(X0,X1)) ),
    inference(prop_impl_just,[status(thm)],[c_250]) ).

cnf(c_518,plain,
    ( ~ sP6(X0,X1)
    | ssList(sK55(X0,X1)) ),
    inference(prop_impl_just,[status(thm)],[c_251]) ).

cnf(c_520,plain,
    ( ~ sP6(X0,X1)
    | ssItem(sK54(X0,X1)) ),
    inference(prop_impl_just,[status(thm)],[c_252]) ).

cnf(c_522,plain,
    ( nil != sK59
    | neq(sK60,nil) ),
    inference(prop_impl_just,[status(thm)],[c_255]) ).

cnf(c_572,plain,
    ( nil = sK60
    | neq(sK60,nil) ),
    inference(prop_impl_just,[status(thm)],[c_256]) ).

cnf(c_574,plain,
    ( nil = sK60
    | sP6(sK60,sK59) ),
    inference(prop_impl_just,[status(thm)],[c_258]) ).

cnf(c_580,plain,
    ( sP6(sK60,sK59)
    | neq(sK60,nil) ),
    inference(prop_impl_just,[status(thm)],[c_257,c_255]) ).

cnf(c_581,plain,
    ( neq(sK60,nil)
    | sP6(sK60,sK59) ),
    inference(renaming,[status(thm)],[c_580]) ).

cnf(c_832,plain,
    ( X0 != sK60
    | X1 != sK59
    | ssItem(sK54(X0,X1))
    | neq(sK60,nil) ),
    inference(resolution_lifted,[status(thm)],[c_520,c_581]) ).

cnf(c_833,plain,
    ( ssItem(sK54(sK60,sK59))
    | neq(sK60,nil) ),
    inference(unflattening,[status(thm)],[c_832]) ).

cnf(c_840,plain,
    ( X0 != sK60
    | X1 != sK59
    | nil = sK60
    | ssItem(sK54(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_520,c_574]) ).

cnf(c_841,plain,
    ( nil = sK60
    | ssItem(sK54(sK60,sK59)) ),
    inference(unflattening,[status(thm)],[c_840]) ).

cnf(c_856,plain,
    ( X0 != sK60
    | X1 != sK59
    | ssList(sK55(X0,X1))
    | neq(sK60,nil) ),
    inference(resolution_lifted,[status(thm)],[c_518,c_581]) ).

cnf(c_857,plain,
    ( ssList(sK55(sK60,sK59))
    | neq(sK60,nil) ),
    inference(unflattening,[status(thm)],[c_856]) ).

cnf(c_864,plain,
    ( X0 != sK60
    | X1 != sK59
    | nil = sK60
    | ssList(sK55(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_518,c_574]) ).

cnf(c_865,plain,
    ( nil = sK60
    | ssList(sK55(sK60,sK59)) ),
    inference(unflattening,[status(thm)],[c_864]) ).

cnf(c_880,plain,
    ( X0 != sK60
    | X1 != sK59
    | ssList(sK56(X0,X1))
    | neq(sK60,nil) ),
    inference(resolution_lifted,[status(thm)],[c_516,c_581]) ).

cnf(c_881,plain,
    ( ssList(sK56(sK60,sK59))
    | neq(sK60,nil) ),
    inference(unflattening,[status(thm)],[c_880]) ).

cnf(c_888,plain,
    ( X0 != sK60
    | X1 != sK59
    | nil = sK60
    | ssList(sK56(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_516,c_574]) ).

cnf(c_889,plain,
    ( nil = sK60
    | ssList(sK56(sK60,sK59)) ),
    inference(unflattening,[status(thm)],[c_888]) ).

cnf(c_904,plain,
    ( X0 != sK60
    | X1 != sK59
    | cons(sK54(X0,X1),nil) = X1
    | neq(sK60,nil) ),
    inference(resolution_lifted,[status(thm)],[c_514,c_581]) ).

cnf(c_905,plain,
    ( cons(sK54(sK60,sK59),nil) = sK59
    | neq(sK60,nil) ),
    inference(unflattening,[status(thm)],[c_904]) ).

cnf(c_912,plain,
    ( X0 != sK60
    | X1 != sK59
    | cons(sK54(X0,X1),nil) = X1
    | nil = sK60 ),
    inference(resolution_lifted,[status(thm)],[c_514,c_574]) ).

cnf(c_913,plain,
    ( cons(sK54(sK60,sK59),nil) = sK59
    | nil = sK60 ),
    inference(unflattening,[status(thm)],[c_912]) ).

cnf(c_928,plain,
    ( X0 != sK60
    | X1 != sK59
    | app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
    | neq(sK60,nil) ),
    inference(resolution_lifted,[status(thm)],[c_512,c_581]) ).

cnf(c_929,plain,
    ( app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60
    | neq(sK60,nil) ),
    inference(unflattening,[status(thm)],[c_928]) ).

cnf(c_936,plain,
    ( X0 != sK60
    | X1 != sK59
    | app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
    | nil = sK60 ),
    inference(resolution_lifted,[status(thm)],[c_512,c_574]) ).

cnf(c_937,plain,
    ( app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60
    | nil = sK60 ),
    inference(unflattening,[status(thm)],[c_936]) ).

cnf(c_2657,plain,
    ( X0 != sK59
    | X1 != nil
    | ~ segmentP(sK60,sK59)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | nil = sK60 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_254]) ).

cnf(c_2658,plain,
    ( ~ segmentP(sK60,sK59)
    | ~ ssList(nil)
    | ~ ssList(sK59)
    | nil = sK60
    | sK59 = nil ),
    inference(unflattening,[status(thm)],[c_2657]) ).

cnf(c_2659,plain,
    ( ~ segmentP(sK60,sK59)
    | nil = sK60
    | sK59 = nil ),
    inference(global_subsumption_just,[status(thm)],[c_2658,c_262,c_141,c_2658]) ).

cnf(c_2721,plain,
    ( X0 != nil
    | X0 != sK60
    | ~ ssList(X0)
    | app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60 ),
    inference(resolution_lifted,[status(thm)],[c_420,c_929]) ).

cnf(c_2722,plain,
    ( nil != sK60
    | ~ ssList(nil)
    | app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60 ),
    inference(unflattening,[status(thm)],[c_2721]) ).

cnf(c_2723,plain,
    app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60,
    inference(global_subsumption_just,[status(thm)],[c_2722,c_141,c_937,c_2722]) ).

cnf(c_2728,plain,
    ( X0 != nil
    | X0 != sK60
    | ~ ssList(X0)
    | cons(sK54(sK60,sK59),nil) = sK59 ),
    inference(resolution_lifted,[status(thm)],[c_420,c_905]) ).

cnf(c_2729,plain,
    ( nil != sK60
    | ~ ssList(nil)
    | cons(sK54(sK60,sK59),nil) = sK59 ),
    inference(unflattening,[status(thm)],[c_2728]) ).

cnf(c_2730,plain,
    cons(sK54(sK60,sK59),nil) = sK59,
    inference(global_subsumption_just,[status(thm)],[c_2729,c_141,c_913,c_2729]) ).

cnf(c_2735,plain,
    ( X0 != nil
    | X0 != sK60
    | ~ ssList(X0)
    | ssList(sK56(sK60,sK59)) ),
    inference(resolution_lifted,[status(thm)],[c_420,c_881]) ).

cnf(c_2736,plain,
    ( nil != sK60
    | ~ ssList(nil)
    | ssList(sK56(sK60,sK59)) ),
    inference(unflattening,[status(thm)],[c_2735]) ).

cnf(c_2737,plain,
    ssList(sK56(sK60,sK59)),
    inference(global_subsumption_just,[status(thm)],[c_2736,c_141,c_889,c_2736]) ).

cnf(c_2742,plain,
    ( X0 != nil
    | X0 != sK60
    | ~ ssList(X0)
    | ssList(sK55(sK60,sK59)) ),
    inference(resolution_lifted,[status(thm)],[c_420,c_857]) ).

cnf(c_2743,plain,
    ( nil != sK60
    | ~ ssList(nil)
    | ssList(sK55(sK60,sK59)) ),
    inference(unflattening,[status(thm)],[c_2742]) ).

cnf(c_2744,plain,
    ssList(sK55(sK60,sK59)),
    inference(global_subsumption_just,[status(thm)],[c_2743,c_141,c_865,c_2743]) ).

cnf(c_2749,plain,
    ( X0 != nil
    | X0 != sK60
    | ~ ssList(X0)
    | ssItem(sK54(sK60,sK59)) ),
    inference(resolution_lifted,[status(thm)],[c_420,c_833]) ).

cnf(c_2750,plain,
    ( nil != sK60
    | ~ ssList(nil)
    | ssItem(sK54(sK60,sK59)) ),
    inference(unflattening,[status(thm)],[c_2749]) ).

cnf(c_2751,plain,
    ssItem(sK54(sK60,sK59)),
    inference(global_subsumption_just,[status(thm)],[c_2750,c_141,c_841,c_2750]) ).

cnf(c_2758,plain,
    ( X0 != nil
    | X0 != sK60
    | nil != sK59
    | ~ ssList(X0) ),
    inference(resolution_lifted,[status(thm)],[c_420,c_522]) ).

cnf(c_2759,plain,
    ( nil != sK60
    | nil != sK59
    | ~ ssList(nil) ),
    inference(unflattening,[status(thm)],[c_2758]) ).

cnf(c_2760,plain,
    ( nil != sK59
    | nil != sK60 ),
    inference(global_subsumption_just,[status(thm)],[c_2759,c_141,c_2759]) ).

cnf(c_2761,plain,
    ( nil != sK60
    | nil != sK59 ),
    inference(renaming,[status(thm)],[c_2760]) ).

cnf(c_2799,plain,
    ( nil != nil
    | sK60 != sK59
    | ~ segmentP(sK60,sK59)
    | nil = sK60 ),
    inference(resolution_lifted,[status(thm)],[c_254,c_572]) ).

cnf(c_2800,plain,
    ( sK60 != sK59
    | ~ segmentP(sK60,sK59)
    | nil = sK60 ),
    inference(global_subsumption_just,[status(thm)],[c_2799,c_141,c_195,c_315,c_2799]) ).

cnf(c_2955,plain,
    ( nil != sK59
    | nil != sK60 ),
    inference(prop_impl_just,[status(thm)],[c_2761]) ).

cnf(c_2956,plain,
    ( nil != sK60
    | nil != sK59 ),
    inference(renaming,[status(thm)],[c_2955]) ).

cnf(c_4585,plain,
    ( sK60 != sK59
    | ~ segmentP(sK60,sK59)
    | nil = sK60 ),
    inference(subtyping,[status(esa)],[c_2800]) ).

cnf(c_4586,plain,
    ( nil != sK60
    | nil != sK59 ),
    inference(subtyping,[status(esa)],[c_2956]) ).

cnf(c_4590,plain,
    cons(sK54(sK60,sK59),nil) = sK59,
    inference(subtyping,[status(esa)],[c_2730]) ).

cnf(c_4591,plain,
    app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60,
    inference(subtyping,[status(esa)],[c_2723]) ).

cnf(c_4595,plain,
    ( ~ segmentP(sK60,sK59)
    | nil = sK60
    | sK59 = nil ),
    inference(subtyping,[status(esa)],[c_2659]) ).

cnf(c_4649,plain,
    ( ~ ssList(X0_13)
    | segmentP(X0_13,nil) ),
    inference(subtyping,[status(esa)],[c_194]) ).

cnf(c_4652,plain,
    ( ~ segmentP(X0_13,X1_13)
    | ~ segmentP(X1_13,X0_13)
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | X0_13 = X1_13 ),
    inference(subtyping,[status(esa)],[c_191]) ).

cnf(c_4653,plain,
    ( ~ segmentP(X0_13,X1_13)
    | ~ segmentP(X1_13,X2_13)
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | ~ ssList(X2_13)
    | segmentP(X0_13,X2_13) ),
    inference(subtyping,[status(esa)],[c_190]) ).

cnf(c_4699,plain,
    ( cons(X0_14,X0_13) != X0_13
    | ~ ssItem(X0_14)
    | ~ ssList(X0_13) ),
    inference(subtyping,[status(esa)],[c_142]) ).

cnf(c_4763,plain,
    ( ~ ssList(app(app(X0_13,X1_13),X2_13))
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | ~ ssList(X2_13)
    | segmentP(app(app(X0_13,X1_13),X2_13),X1_13) ),
    inference(subtyping,[status(esa)],[c_67]) ).

cnf(c_4973,plain,
    X0_13 = X0_13,
    theory(equality) ).

cnf(c_4975,plain,
    ( X0_13 != X1_13
    | X2_13 != X1_13
    | X2_13 = X0_13 ),
    theory(equality) ).

cnf(c_5100,plain,
    nil = nil,
    inference(instantiation,[status(thm)],[c_4973]) ).

cnf(c_6279,plain,
    ( ~ segmentP(sK60,sK59)
    | ~ segmentP(sK59,sK60)
    | ~ ssList(sK60)
    | ~ ssList(sK59)
    | sK60 = sK59 ),
    inference(instantiation,[status(thm)],[c_4652]) ).

cnf(c_6426,plain,
    ( nil != X0_13
    | sK59 != X0_13
    | nil = sK59 ),
    inference(instantiation,[status(thm)],[c_4975]) ).

cnf(c_6427,plain,
    ( nil != nil
    | sK59 != nil
    | nil = sK59 ),
    inference(instantiation,[status(thm)],[c_6426]) ).

cnf(c_6431,plain,
    ( nil != sK59
    | ~ ssItem(sK54(sK60,sK59))
    | ~ ssList(nil) ),
    inference(superposition,[status(thm)],[c_4590,c_4699]) ).

cnf(c_8802,plain,
    ( ~ segmentP(X0_13,sK60)
    | ~ segmentP(sK59,X0_13)
    | ~ ssList(X0_13)
    | ~ ssList(sK60)
    | ~ ssList(sK59)
    | segmentP(sK59,sK60) ),
    inference(instantiation,[status(thm)],[c_4653]) ).

cnf(c_8805,plain,
    ( ~ segmentP(nil,sK60)
    | ~ segmentP(sK59,nil)
    | ~ ssList(nil)
    | ~ ssList(sK60)
    | ~ ssList(sK59)
    | segmentP(sK59,sK60) ),
    inference(instantiation,[status(thm)],[c_8802]) ).

cnf(c_9308,plain,
    ( ~ ssList(sK59)
    | segmentP(sK59,nil) ),
    inference(instantiation,[status(thm)],[c_4649]) ).

cnf(c_11014,plain,
    nil != sK59,
    inference(global_subsumption_just,[status(thm)],[c_4586,c_141,c_841,c_2750,c_6431]) ).

cnf(c_13755,plain,
    ( ~ ssList(app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)))
    | ~ ssList(sK56(sK60,sK59))
    | ~ ssList(sK55(sK60,sK59))
    | ~ ssList(sK59)
    | segmentP(sK60,sK59) ),
    inference(superposition,[status(thm)],[c_4591,c_4763]) ).

cnf(c_13785,plain,
    ( ~ ssList(sK56(sK60,sK59))
    | ~ ssList(sK55(sK60,sK59))
    | ~ ssList(sK60)
    | ~ ssList(sK59)
    | segmentP(sK60,sK59) ),
    inference(demodulation,[status(thm)],[c_13755,c_4591]) ).

cnf(c_16451,plain,
    nil = sK60,
    inference(global_subsumption_just,[status(thm)],[c_4585,c_262,c_261,c_141,c_2737,c_2744,c_2751,c_5100,c_4595,c_6427,c_6431,c_13785]) ).

cnf(c_16525,plain,
    sK60 != sK59,
    inference(demodulation,[status(thm)],[c_11014,c_16451]) ).

cnf(c_16626,plain,
    ( ~ ssList(X0_13)
    | segmentP(X0_13,sK60) ),
    inference(demodulation,[status(thm)],[c_4649,c_16451]) ).

cnf(c_17622,plain,
    ( ~ ssList(nil)
    | segmentP(nil,sK60) ),
    inference(instantiation,[status(thm)],[c_16626]) ).

cnf(c_17623,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_17622,c_16525,c_13785,c_9308,c_8805,c_6279,c_2744,c_2737,c_141,c_261,c_262]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SWC109+1 : TPTP v8.1.2. Released v2.4.0.
% 0.09/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n022.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 23:20:57 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.16/0.44  Running first-order theorem proving
% 0.16/0.44  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
% 8.30/1.64  % SZS status Started for theBenchmark.p
% 8.30/1.64  % SZS status Theorem for theBenchmark.p
% 8.30/1.64  
% 8.30/1.64  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 8.30/1.64  
% 8.30/1.64  ------  iProver source info
% 8.30/1.64  
% 8.30/1.64  git: date: 2024-05-02 19:28:25 +0000
% 8.30/1.64  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 8.30/1.64  git: non_committed_changes: false
% 8.30/1.64  
% 8.30/1.64  ------ Parsing...
% 8.30/1.64  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 8.30/1.64  
% 8.30/1.64  ------ Preprocessing... sup_sim: 0  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 0  pe_s  pe_e 
% 8.30/1.64  
% 8.30/1.64  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  scvd_s sp: 0 0s scvd_e  snvd_s sp: 0 0s snvd_e 
% 8.30/1.64  
% 8.30/1.64  ------ Preprocessing...
% 8.30/1.64  ------ Proving...
% 8.30/1.64  ------ Problem Properties 
% 8.30/1.64  
% 8.30/1.64  
% 8.30/1.64  clauses                                 194
% 8.30/1.64  conjectures                             2
% 8.30/1.64  EPR                                     56
% 8.30/1.64  Horn                                    125
% 8.30/1.64  unary                                   23
% 8.30/1.64  binary                                  41
% 8.30/1.64  lits                                    645
% 8.30/1.64  lits eq                                 90
% 8.30/1.64  fd_pure                                 0
% 8.30/1.64  fd_pseudo                               0
% 8.30/1.64  fd_cond                                 21
% 8.30/1.64  fd_pseudo_cond                          14
% 8.30/1.64  AC symbols                              0
% 8.30/1.64  
% 8.30/1.64  ------ Input Options Time Limit: Unbounded
% 8.30/1.64  
% 8.30/1.64  
% 8.30/1.64  ------ 
% 8.30/1.64  Current options:
% 8.30/1.64  ------ 
% 8.30/1.64  
% 8.30/1.64  
% 8.30/1.64  
% 8.30/1.64  
% 8.30/1.64  ------ Proving...
% 8.30/1.64  
% 8.30/1.64  
% 8.30/1.64  % SZS status Theorem for theBenchmark.p
% 8.30/1.64  
% 8.30/1.64  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.30/1.64  
% 8.30/1.64  
%------------------------------------------------------------------------------