TSTP Solution File: SWC397+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWC397+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n027.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 20:43:07 EDT 2023

% Result   : Theorem 23.88s 4.22s
% Output   : CNFRefutation 23.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  176 (  30 unt;   0 def)
%            Number of atoms       :  789 ( 235 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  980 ( 367   ~; 371   |; 177   &)
%                                         (  12 <=>;  53  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :  276 (   0 sgn; 135   !;  64   ?)

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

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

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

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

fof(f27,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssItem(X2)
             => cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).

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

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

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

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

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).

fof(f83,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).

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

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

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( neq(X3,nil)
                        & ! [X4] :
                            ( ssItem(X4)
                           => ! [X5] :
                                ( ssList(X5)
                               => ( app(X5,cons(X4,nil)) != X3
                                  | app(cons(X4,nil),X5) != X2 ) ) ) )
                      | ( nil = X3
                        & nil != X2 )
                      | ! [X6] :
                          ( ssItem(X6)
                         => ( memberP(X1,X6)
                            | ~ memberP(X0,X6) ) )
                      | X0 != X2
                      | X1 != 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(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

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

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

fof(f134,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
              | ~ ssItem(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f27]) ).

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

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

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

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

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

fof(f201,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f202,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

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

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

fof(f246,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(f247,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,[],[f246]) ).

fof(f248,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X1,X3) = X0
          & ssList(X3) )
     => ( app(X1,sK11(X0,X1)) = X0
        & ssList(sK11(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f249,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])],[f247,f248]) ).

fof(f317,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f119]) ).

fof(f323,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & ~ memberP(X1,X0) ) )
                & ( memberP(X2,X0)
                  | memberP(X1,X0)
                  | ~ memberP(app(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f147]) ).

fof(f324,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & ~ memberP(X1,X0) ) )
                & ( memberP(X2,X0)
                  | memberP(X1,X0)
                  | ~ memberP(app(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f323]) ).

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

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

fof(f331,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f177]) ).

fof(f340,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f201]) ).

fof(f341,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f340]) ).

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

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

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

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

fof(f348,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( app(X5,cons(X4,nil)) = sK56
            & app(cons(X4,nil),X5) = sK55
            & ssList(X5) )
        & ssItem(X4) )
   => ( ? [X5] :
          ( sK56 = app(X5,cons(sK57,nil))
          & sK55 = app(cons(sK57,nil),X5)
          & ssList(X5) )
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ? [X5] :
        ( sK56 = app(X5,cons(sK57,nil))
        & sK55 = app(cons(sK57,nil),X5)
        & ssList(X5) )
   => ( sK56 = app(sK58,cons(sK57,nil))
      & sK55 = app(cons(sK57,nil),sK58)
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ( ? [X6] :
        ( ~ memberP(sK54,X6)
        & memberP(sK53,X6)
        & ssItem(X6) )
   => ( ~ memberP(sK54,sK59)
      & memberP(sK53,sK59)
      & ssItem(sK59) ) ),
    introduced(choice_axiom,[]) ).

fof(f351,plain,
    ( ( ~ neq(sK56,nil)
      | ( sK56 = app(sK58,cons(sK57,nil))
        & sK55 = app(cons(sK57,nil),sK58)
        & ssList(sK58)
        & ssItem(sK57) ) )
    & ( nil != sK56
      | nil = sK55 )
    & ~ memberP(sK54,sK59)
    & memberP(sK53,sK59)
    & ssItem(sK59)
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59])],[f223,f350,f349,f348,f347,f346,f345,f344]) ).

fof(f365,plain,
    ! [X0,X1] :
      ( app(X1,sK11(X0,X1)) = X0
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f249]) ).

fof(f366,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X1)
      | app(X1,X2) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f249]) ).

fof(f442,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f317]) ).

fof(f443,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f444,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f456,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f457,plain,
    ! [X2,X0,X1] :
      ( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f468,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(f469,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X1,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f324]) ).

fof(f470,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f324]) ).

fof(f471,plain,
    ! [X2,X0,X1] :
      ( memberP(X2,X0)
      | X0 = X1
      | ~ memberP(cons(X1,X2),X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f326]) ).

fof(f474,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f498,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f499,plain,
    ! [X0] :
      ( segmentP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f532,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f199]) ).

fof(f534,plain,
    ! [X0,X1] :
      ( nil = X1
      | nil != app(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f341]) ).

fof(f537,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f202]) ).

fof(f551,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f351]) ).

fof(f552,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f351]) ).

fof(f555,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f351]) ).

fof(f556,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f351]) ).

fof(f557,plain,
    ssItem(sK59),
    inference(cnf_transformation,[],[f351]) ).

fof(f558,plain,
    memberP(sK53,sK59),
    inference(cnf_transformation,[],[f351]) ).

fof(f559,plain,
    ~ memberP(sK54,sK59),
    inference(cnf_transformation,[],[f351]) ).

fof(f560,plain,
    ( nil != sK56
    | nil = sK55 ),
    inference(cnf_transformation,[],[f351]) ).

fof(f561,plain,
    ( ~ neq(sK56,nil)
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f562,plain,
    ( ~ neq(sK56,nil)
    | ssList(sK58) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f563,plain,
    ( ~ neq(sK56,nil)
    | sK55 = app(cons(sK57,nil),sK58) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f564,plain,
    ( ~ neq(sK56,nil)
    | sK56 = app(sK58,cons(sK57,nil)) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f565,plain,
    ~ memberP(sK56,sK59),
    inference(definition_unfolding,[],[f559,f555]) ).

fof(f566,plain,
    memberP(sK55,sK59),
    inference(definition_unfolding,[],[f558,f556]) ).

fof(f567,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f552,f555]) ).

fof(f568,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f551,f556]) ).

fof(f572,plain,
    ! [X2,X1] :
      ( frontsegP(app(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X1,X2)) ),
    inference(equality_resolution,[],[f366]) ).

fof(f588,plain,
    ( segmentP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f499]) ).

cnf(c_61,plain,
    ( ~ ssList(app(X0,X1))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(cnf_transformation,[],[f572]) ).

cnf(c_62,plain,
    ( ~ frontsegP(X0,X1)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | app(X1,sK11(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f365]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f442]) ).

cnf(c_140,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | ssList(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f443]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f444]) ).

cnf(c_153,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f456]) ).

cnf(c_154,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | cons(X0,app(X2,X1)) = app(cons(X0,X2),X1) ),
    inference(cnf_transformation,[],[f457]) ).

cnf(c_165,plain,
    ( ~ memberP(X0,X1)
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X2,X0),X1) ),
    inference(cnf_transformation,[],[f470]) ).

cnf(c_166,plain,
    ( ~ memberP(X0,X1)
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X0,X2),X1) ),
    inference(cnf_transformation,[],[f469]) ).

cnf(c_167,plain,
    ( ~ memberP(app(X0,X1),X2)
    | ~ ssItem(X2)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | memberP(X0,X2)
    | memberP(X1,X2) ),
    inference(cnf_transformation,[],[f468]) ).

cnf(c_170,plain,
    ( ~ memberP(cons(X0,X1),X2)
    | ~ ssItem(X0)
    | ~ ssItem(X2)
    | ~ ssList(X1)
    | X0 = X2
    | memberP(X1,X2) ),
    inference(cnf_transformation,[],[f471]) ).

cnf(c_171,plain,
    ( ~ memberP(nil,X0)
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f474]) ).

cnf(c_195,plain,
    ( ~ ssList(nil)
    | segmentP(nil,nil) ),
    inference(cnf_transformation,[],[f588]) ).

cnf(c_196,plain,
    ( ~ segmentP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f498]) ).

cnf(c_227,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | app(cons(X0,nil),X1) = cons(X0,X1) ),
    inference(cnf_transformation,[],[f532]) ).

cnf(c_231,plain,
    ( app(X0,X1) != nil
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X1 = nil ),
    inference(cnf_transformation,[],[f534]) ).

cnf(c_232,plain,
    ( ~ ssList(X0)
    | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f537]) ).

cnf(c_246,negated_conjecture,
    ( ~ neq(sK56,nil)
    | app(sK58,cons(sK57,nil)) = sK56 ),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_247,negated_conjecture,
    ( ~ neq(sK56,nil)
    | app(cons(sK57,nil),sK58) = sK55 ),
    inference(cnf_transformation,[],[f563]) ).

cnf(c_248,negated_conjecture,
    ( ~ neq(sK56,nil)
    | ssList(sK58) ),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_249,negated_conjecture,
    ( ~ neq(sK56,nil)
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f561]) ).

cnf(c_250,negated_conjecture,
    ( nil != sK56
    | nil = sK55 ),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_251,negated_conjecture,
    ~ memberP(sK56,sK59),
    inference(cnf_transformation,[],[f565]) ).

cnf(c_252,negated_conjecture,
    memberP(sK55,sK59),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_253,negated_conjecture,
    ssItem(sK59),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_256,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f567]) ).

cnf(c_257,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f568]) ).

cnf(c_307,plain,
    ( ~ segmentP(nil,nil)
    | ~ ssList(nil)
    | nil = nil ),
    inference(instantiation,[status(thm)],[c_196]) ).

cnf(c_379,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).

cnf(c_3243,plain,
    ( X0 != sK56
    | X1 != nil
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | ssItem(sK57) ),
    inference(resolution_lifted,[status(thm)],[c_138,c_249]) ).

cnf(c_3244,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK56)
    | sK56 = nil
    | ssItem(sK57) ),
    inference(unflattening,[status(thm)],[c_3243]) ).

cnf(c_3245,plain,
    ( sK56 = nil
    | ssItem(sK57) ),
    inference(global_subsumption_just,[status(thm)],[c_3244,c_256,c_141,c_3244]) ).

cnf(c_3253,plain,
    ( X0 != sK56
    | X1 != nil
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | ssList(sK58) ),
    inference(resolution_lifted,[status(thm)],[c_138,c_248]) ).

cnf(c_3254,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK56)
    | sK56 = nil
    | ssList(sK58) ),
    inference(unflattening,[status(thm)],[c_3253]) ).

cnf(c_3255,plain,
    ( sK56 = nil
    | ssList(sK58) ),
    inference(global_subsumption_just,[status(thm)],[c_3254,c_256,c_141,c_3254]) ).

cnf(c_3263,plain,
    ( X0 != sK56
    | X1 != nil
    | ~ ssList(X0)
    | ~ ssList(X1)
    | app(cons(sK57,nil),sK58) = sK55
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_247]) ).

cnf(c_3264,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK56)
    | app(cons(sK57,nil),sK58) = sK55
    | sK56 = nil ),
    inference(unflattening,[status(thm)],[c_3263]) ).

cnf(c_3265,plain,
    ( app(cons(sK57,nil),sK58) = sK55
    | sK56 = nil ),
    inference(global_subsumption_just,[status(thm)],[c_3264,c_256,c_141,c_3264]) ).

cnf(c_3273,plain,
    ( X0 != sK56
    | X1 != nil
    | ~ ssList(X0)
    | ~ ssList(X1)
    | app(sK58,cons(sK57,nil)) = sK56
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_246]) ).

cnf(c_3274,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK56)
    | app(sK58,cons(sK57,nil)) = sK56
    | sK56 = nil ),
    inference(unflattening,[status(thm)],[c_3273]) ).

cnf(c_3275,plain,
    ( app(sK58,cons(sK57,nil)) = sK56
    | sK56 = nil ),
    inference(global_subsumption_just,[status(thm)],[c_3274,c_256,c_141,c_3274]) ).

cnf(c_8920,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_8922,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_8926,plain,
    ( X0 != X1
    | X2 != X3
    | ~ memberP(X1,X3)
    | memberP(X0,X2) ),
    theory(equality) ).

cnf(c_12571,plain,
    app(sK55,nil) = sK55,
    inference(superposition,[status(thm)],[c_257,c_232]) ).

cnf(c_13511,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK55)
    | frontsegP(sK55,sK55) ),
    inference(superposition,[status(thm)],[c_12571,c_379]) ).

cnf(c_13516,plain,
    frontsegP(sK55,sK55),
    inference(forward_subsumption_resolution,[status(thm)],[c_13511,c_257,c_141]) ).

cnf(c_13564,plain,
    ( ~ memberP(nil,sK59)
    | ~ ssItem(sK59) ),
    inference(instantiation,[status(thm)],[c_171]) ).

cnf(c_14072,plain,
    ( ~ ssList(X0)
    | ~ ssItem(sK57)
    | ssList(cons(sK57,X0)) ),
    inference(instantiation,[status(thm)],[c_140]) ).

cnf(c_14073,plain,
    ( ~ ssItem(sK57)
    | ~ ssList(nil)
    | ssList(cons(sK57,nil)) ),
    inference(instantiation,[status(thm)],[c_14072]) ).

cnf(c_14074,plain,
    ( ~ ssList(X0)
    | ~ ssItem(sK59)
    | ssList(cons(sK59,X0)) ),
    inference(instantiation,[status(thm)],[c_140]) ).

cnf(c_14075,plain,
    ( ~ ssItem(sK59)
    | ~ ssList(nil)
    | ssList(cons(sK59,nil)) ),
    inference(instantiation,[status(thm)],[c_14074]) ).

cnf(c_14712,plain,
    ( X0 != sK55
    | X1 != sK59
    | ~ memberP(sK55,sK59)
    | memberP(X0,X1) ),
    inference(instantiation,[status(thm)],[c_8926]) ).

cnf(c_16913,plain,
    ( ~ ssList(X0)
    | app(cons(sK59,nil),X0) = cons(sK59,X0) ),
    inference(superposition,[status(thm)],[c_253,c_227]) ).

cnf(c_17351,plain,
    ( X0 != sK55
    | sK59 != sK59
    | ~ memberP(sK55,sK59)
    | memberP(X0,sK59) ),
    inference(instantiation,[status(thm)],[c_14712]) ).

cnf(c_17352,plain,
    sK59 = sK59,
    inference(instantiation,[status(thm)],[c_8920]) ).

cnf(c_17353,plain,
    ( nil != sK55
    | sK59 != sK59
    | ~ memberP(sK55,sK59)
    | memberP(nil,sK59) ),
    inference(instantiation,[status(thm)],[c_17351]) ).

cnf(c_17635,plain,
    app(cons(sK59,nil),sK56) = cons(sK59,sK56),
    inference(superposition,[status(thm)],[c_256,c_16913]) ).

cnf(c_18339,plain,
    ( ~ ssList(cons(sK59,nil))
    | ~ ssList(sK56)
    | ssList(cons(sK59,sK56)) ),
    inference(superposition,[status(thm)],[c_17635,c_153]) ).

cnf(c_18340,plain,
    ( ~ ssList(cons(sK59,nil))
    | ssList(cons(sK59,sK56)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_18339,c_256]) ).

cnf(c_18357,plain,
    ssList(cons(sK59,sK56)),
    inference(global_subsumption_just,[status(thm)],[c_18340,c_253,c_141,c_14075,c_18340]) ).

cnf(c_18527,plain,
    ( ~ ssList(sK55)
    | app(sK55,sK11(sK55,sK55)) = sK55 ),
    inference(superposition,[status(thm)],[c_13516,c_62]) ).

cnf(c_18529,plain,
    app(sK55,sK11(sK55,sK55)) = sK55,
    inference(forward_subsumption_resolution,[status(thm)],[c_18527,c_257]) ).

cnf(c_18744,plain,
    ( ~ memberP(cons(sK57,nil),X0)
    | ~ ssList(cons(sK57,nil))
    | ~ ssItem(X0)
    | ~ ssList(sK58)
    | nil = sK56
    | memberP(sK56,X0) ),
    inference(superposition,[status(thm)],[c_3275,c_165]) ).

cnf(c_18773,plain,
    ( ~ ssList(cons(sK59,nil))
    | ~ memberP(sK56,X0)
    | ~ ssItem(X0)
    | ~ ssList(sK56)
    | memberP(cons(sK59,sK56),X0) ),
    inference(superposition,[status(thm)],[c_17635,c_165]) ).

cnf(c_18784,plain,
    ( ~ ssList(cons(sK59,nil))
    | ~ memberP(sK56,X0)
    | ~ ssItem(X0)
    | memberP(cons(sK59,sK56),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_18773,c_256]) ).

cnf(c_18922,plain,
    ( nil != sK55
    | ~ ssList(sK11(sK55,sK55))
    | ~ ssList(sK55)
    | sK11(sK55,sK55) = nil ),
    inference(superposition,[status(thm)],[c_18529,c_231]) ).

cnf(c_18931,plain,
    ( nil != sK55
    | ~ ssList(sK11(sK55,sK55))
    | sK11(sK55,sK55) = nil ),
    inference(forward_subsumption_resolution,[status(thm)],[c_18922,c_257]) ).

cnf(c_19147,plain,
    ( ~ ssList(cons(sK57,nil))
    | ~ memberP(sK58,X0)
    | ~ ssItem(X0)
    | ~ ssList(sK58)
    | nil = sK56
    | memberP(sK56,X0) ),
    inference(superposition,[status(thm)],[c_3275,c_166]) ).

cnf(c_21510,plain,
    nil != sK55,
    inference(global_subsumption_just,[status(thm)],[c_18931,c_253,c_252,c_13564,c_17353,c_17352]) ).

cnf(c_21516,plain,
    nil != sK56,
    inference(backward_subsumption_resolution,[status(thm)],[c_250,c_21510]) ).

cnf(c_23275,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | cons(sK59,app(X1,X0)) = app(cons(sK59,X1),X0) ),
    inference(superposition,[status(thm)],[c_253,c_154]) ).

cnf(c_23533,plain,
    ( ~ ssList(cons(sK57,nil))
    | ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | ~ ssList(sK58)
    | nil = sK56
    | memberP(cons(sK57,nil),X0)
    | memberP(sK58,X0) ),
    inference(superposition,[status(thm)],[c_3265,c_167]) ).

cnf(c_23611,plain,
    ( ~ ssList(cons(sK57,nil))
    | ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | ~ ssList(sK58)
    | memberP(cons(sK57,nil),X0)
    | memberP(sK58,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23533,c_21516]) ).

cnf(c_24934,plain,
    ( ~ ssList(X0)
    | cons(sK59,app(X0,sK55)) = app(cons(sK59,X0),sK55) ),
    inference(superposition,[status(thm)],[c_257,c_23275]) ).

cnf(c_27657,plain,
    ( nil != X0
    | sK56 != X0
    | nil = sK56 ),
    inference(instantiation,[status(thm)],[c_8922]) ).

cnf(c_27658,plain,
    ( nil != nil
    | sK56 != nil
    | nil = sK56 ),
    inference(instantiation,[status(thm)],[c_27657]) ).

cnf(c_31106,plain,
    cons(sK59,app(sK56,sK55)) = app(cons(sK59,sK56),sK55),
    inference(superposition,[status(thm)],[c_256,c_24934]) ).

cnf(c_31307,plain,
    ( ~ memberP(cons(sK59,app(sK56,sK55)),X0)
    | ~ ssList(cons(sK59,sK56))
    | ~ ssItem(X0)
    | ~ ssList(sK55)
    | memberP(cons(sK59,sK56),X0)
    | memberP(sK55,X0) ),
    inference(superposition,[status(thm)],[c_31106,c_167]) ).

cnf(c_31316,plain,
    ( ~ ssList(cons(sK59,sK56))
    | ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | ~ ssList(sK55)
    | memberP(cons(sK59,app(sK56,sK55)),X0) ),
    inference(superposition,[status(thm)],[c_31106,c_165]) ).

cnf(c_31326,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | memberP(cons(sK59,app(sK56,sK55)),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31316,c_257,c_18357]) ).

cnf(c_31347,plain,
    ( ~ memberP(cons(sK59,app(sK56,sK55)),X0)
    | ~ ssItem(X0)
    | memberP(cons(sK59,sK56),X0)
    | memberP(sK55,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31307,c_257,c_18357]) ).

cnf(c_50146,plain,
    ( memberP(cons(sK59,sK56),X0)
    | ~ ssItem(X0)
    | ~ memberP(cons(sK59,app(sK56,sK55)),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_31347,c_253,c_141,c_252,c_195,c_250,c_307,c_3245,c_3255,c_13564,c_14073,c_14075,c_17353,c_17352,c_18784,c_18744,c_19147,c_23611,c_27658,c_31347]) ).

cnf(c_50147,plain,
    ( ~ memberP(cons(sK59,app(sK56,sK55)),X0)
    | ~ ssItem(X0)
    | memberP(cons(sK59,sK56),X0) ),
    inference(renaming,[status(thm)],[c_50146]) ).

cnf(c_50158,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | memberP(cons(sK59,sK56),X0) ),
    inference(superposition,[status(thm)],[c_31326,c_50147]) ).

cnf(c_84829,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | ~ ssItem(sK59)
    | ~ ssList(sK56)
    | X0 = sK59
    | memberP(sK56,X0) ),
    inference(superposition,[status(thm)],[c_50158,c_170]) ).

cnf(c_84836,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | X0 = sK59
    | memberP(sK56,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_84829,c_256,c_253]) ).

cnf(c_84881,plain,
    ( ~ ssItem(X0)
    | ~ memberP(sK55,X0)
    | memberP(sK56,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_84836,c_253,c_141,c_252,c_195,c_250,c_307,c_3245,c_3255,c_13564,c_14073,c_17353,c_17352,c_18744,c_19147,c_23611,c_27658]) ).

cnf(c_84882,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | memberP(sK56,X0) ),
    inference(renaming,[status(thm)],[c_84881]) ).

cnf(c_84890,plain,
    ( ~ ssItem(sK59)
    | memberP(sK56,sK59) ),
    inference(superposition,[status(thm)],[c_252,c_84882]) ).

cnf(c_84893,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_84890,c_251,c_253]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem  : SWC397+1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.16  % Command  : run_iprover %s %d THM
% 0.16/0.37  % Computer : n027.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon Aug 28 16:48:38 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.22/0.49  Running first-order theorem proving
% 0.22/0.49  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.88/4.22  % SZS status Started for theBenchmark.p
% 23.88/4.22  % SZS status Theorem for theBenchmark.p
% 23.88/4.22  
% 23.88/4.22  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 23.88/4.22  
% 23.88/4.22  ------  iProver source info
% 23.88/4.22  
% 23.88/4.22  git: date: 2023-05-31 18:12:56 +0000
% 23.88/4.22  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 23.88/4.22  git: non_committed_changes: false
% 23.88/4.22  git: last_make_outside_of_git: false
% 23.88/4.22  
% 23.88/4.22  ------ Parsing...
% 23.88/4.22  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 23.88/4.22  
% 23.88/4.22  ------ 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: 5 0s  sf_e  pe_s  pe_e 
% 23.88/4.22  
% 23.88/4.22  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 23.88/4.22  
% 23.88/4.22  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 23.88/4.22  ------ Proving...
% 23.88/4.22  ------ Problem Properties 
% 23.88/4.22  
% 23.88/4.22  
% 23.88/4.22  clauses                                 190
% 23.88/4.22  conjectures                             6
% 23.88/4.22  EPR                                     57
% 23.88/4.22  Horn                                    118
% 23.88/4.22  unary                                   21
% 23.88/4.22  binary                                  45
% 23.88/4.22  lits                                    633
% 23.88/4.22  lits eq                                 86
% 23.88/4.22  fd_pure                                 0
% 23.88/4.22  fd_pseudo                               0
% 23.88/4.22  fd_cond                                 21
% 23.88/4.22  fd_pseudo_cond                          14
% 23.88/4.22  AC symbols                              0
% 23.88/4.22  
% 23.88/4.22  ------ Schedule dynamic 5 is on 
% 23.88/4.22  
% 23.88/4.22  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 23.88/4.22  
% 23.88/4.22  
% 23.88/4.22  ------ 
% 23.88/4.22  Current options:
% 23.88/4.22  ------ 
% 23.88/4.22  
% 23.88/4.22  
% 23.88/4.22  
% 23.88/4.22  
% 23.88/4.22  ------ Proving...
% 23.88/4.22  
% 23.88/4.22  
% 23.88/4.22  % SZS status Theorem for theBenchmark.p
% 23.88/4.22  
% 23.88/4.22  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 23.88/4.22  
% 23.88/4.23  
%------------------------------------------------------------------------------