TSTP Solution File: SWC070+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC070+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.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 : Tue May 21 04:43:07 EDT 2024

% Result   : Theorem 2.35s 0.67s
% Output   : Refutation 2.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :  209
% Syntax   : Number of formulae    : 1021 (  44 unt;   0 def)
%            Number of atoms       : 4350 ( 700 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives : 5444 (2115   ~;2239   |; 726   &)
%                                         ( 133 <=>; 231  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  101 (  99 usr;  63 prp; 0-2 aty)
%            Number of functors    :   54 (  54 usr;   7 con; 0-2 aty)
%            Number of variables   : 1433 (1122   !; 311   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7365,plain,
    $false,
    inference(avatar_sat_refutation,[],[f651,f774,f795,f1069,f1100,f1409,f1413,f1428,f1432,f1512,f1516,f1531,f1535,f1645,f1649,f1742,f1746,f2086,f2206,f2210,f2263,f2267,f2559,f2568,f3008,f3013,f3343,f3348,f3401,f3406,f3459,f3492,f3548,f3720,f3949,f3972,f4197,f4201,f4561,f4565,f5369,f5637,f5641,f5654,f5881,f5885,f5994,f6038,f6041,f6045,f6054,f6057,f6084,f6128,f6131,f6135,f6144,f6147,f7132,f7341,f7343,f7364]) ).

fof(f7364,plain,
    ( spl69_1
    | ~ spl69_2 ),
    inference(avatar_contradiction_clause,[],[f7363]) ).

fof(f7363,plain,
    ( $false
    | spl69_1
    | ~ spl69_2 ),
    inference(subsumption_resolution,[],[f7362,f394]) ).

fof(f394,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f7362,plain,
    ( ~ ssList(nil)
    | spl69_1
    | ~ spl69_2 ),
    inference(resolution,[],[f7358,f631]) ).

fof(f631,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f624]) ).

fof(f624,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f573]) ).

fof(f573,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f355]) ).

fof(f355,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f198]) ).

fof(f198,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

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

fof(f7358,plain,
    ( neq(nil,nil)
    | spl69_1
    | ~ spl69_2 ),
    inference(forward_demodulation,[],[f654,f649]) ).

fof(f649,plain,
    ( nil = sK18
    | ~ spl69_2 ),
    inference(avatar_component_clause,[],[f648]) ).

fof(f648,plain,
    ( spl69_2
  <=> nil = sK18 ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_2])]) ).

fof(f654,plain,
    ( neq(sK18,nil)
    | spl69_1 ),
    inference(subsumption_resolution,[],[f653,f646]) ).

fof(f646,plain,
    ( nil != sK19
    | spl69_1 ),
    inference(avatar_component_clause,[],[f644]) ).

fof(f644,plain,
    ( spl69_1
  <=> nil = sK19 ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_1])]) ).

fof(f653,plain,
    ( nil = sK19
    | neq(sK18,nil) ),
    inference(forward_demodulation,[],[f652,f378]) ).

fof(f378,plain,
    sK19 = sK21,
    inference(cnf_transformation,[],[f254]) ).

fof(f254,plain,
    ( ( ( frontsegP(sK21,sK20)
        & neq(sK20,nil) )
      | ( nil = sK20
        & nil = sK21 ) )
    & ( nil != sK18
      | nil != sK19 )
    & ! [X4] :
        ( ~ segmentP(sK18,X4)
        | ~ segmentP(sK19,X4)
        | ~ neq(X4,nil)
        | ~ ssList(X4) )
    & sK18 = sK20
    & sK19 = sK21
    & ssList(sK21)
    & ssList(sK20)
    & ssList(sK19)
    & ssList(sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f99,f253,f252,f251,f250]) ).

fof(f250,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( frontsegP(X3,X2)
                        & neq(X2,nil) )
                      | ( nil = X2
                        & nil = X3 ) )
                    & ( nil != X0
                      | nil != X1 )
                    & ! [X4] :
                        ( ~ segmentP(X0,X4)
                        | ~ segmentP(X1,X4)
                        | ~ neq(X4,nil)
                        | ~ ssList(X4) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( frontsegP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ( nil != sK18
                    | nil != X1 )
                  & ! [X4] :
                      ( ~ segmentP(sK18,X4)
                      | ~ segmentP(X1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & sK18 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f251,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( frontsegP(X3,X2)
                    & neq(X2,nil) )
                  | ( nil = X2
                    & nil = X3 ) )
                & ( nil != sK18
                  | nil != X1 )
                & ! [X4] :
                    ( ~ segmentP(sK18,X4)
                    | ~ segmentP(X1,X4)
                    | ~ neq(X4,nil)
                    | ~ ssList(X4) )
                & sK18 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( frontsegP(X3,X2)
                  & neq(X2,nil) )
                | ( nil = X2
                  & nil = X3 ) )
              & ( nil != sK18
                | nil != sK19 )
              & ! [X4] :
                  ( ~ segmentP(sK18,X4)
                  | ~ segmentP(sK19,X4)
                  | ~ neq(X4,nil)
                  | ~ ssList(X4) )
              & sK18 = X2
              & sK19 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( frontsegP(X3,X2)
                & neq(X2,nil) )
              | ( nil = X2
                & nil = X3 ) )
            & ( nil != sK18
              | nil != sK19 )
            & ! [X4] :
                ( ~ segmentP(sK18,X4)
                | ~ segmentP(sK19,X4)
                | ~ neq(X4,nil)
                | ~ ssList(X4) )
            & sK18 = X2
            & sK19 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( frontsegP(X3,sK20)
              & neq(sK20,nil) )
            | ( nil = sK20
              & nil = X3 ) )
          & ( nil != sK18
            | nil != sK19 )
          & ! [X4] :
              ( ~ segmentP(sK18,X4)
              | ~ segmentP(sK19,X4)
              | ~ neq(X4,nil)
              | ~ ssList(X4) )
          & sK18 = sK20
          & sK19 = X3
          & ssList(X3) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ( ? [X3] :
        ( ( ( frontsegP(X3,sK20)
            & neq(sK20,nil) )
          | ( nil = sK20
            & nil = X3 ) )
        & ( nil != sK18
          | nil != sK19 )
        & ! [X4] :
            ( ~ segmentP(sK18,X4)
            | ~ segmentP(sK19,X4)
            | ~ neq(X4,nil)
            | ~ ssList(X4) )
        & sK18 = sK20
        & sK19 = X3
        & ssList(X3) )
   => ( ( ( frontsegP(sK21,sK20)
          & neq(sK20,nil) )
        | ( nil = sK20
          & nil = sK21 ) )
      & ( nil != sK18
        | nil != sK19 )
      & ! [X4] :
          ( ~ segmentP(sK18,X4)
          | ~ segmentP(sK19,X4)
          | ~ neq(X4,nil)
          | ~ ssList(X4) )
      & sK18 = sK20
      & sK19 = sK21
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( frontsegP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ( nil != X0
                    | nil != X1 )
                  & ! [X4] :
                      ( ~ segmentP(X0,X4)
                      | ~ segmentP(X1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( frontsegP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ( nil != X0
                    | nil != X1 )
                  & ! [X4] :
                      ( ~ segmentP(X0,X4)
                      | ~ segmentP(X1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( ~ frontsegP(X3,X2)
                          | ~ neq(X2,nil) )
                        & ( nil != X2
                          | nil != X3 ) )
                      | ( nil = X0
                        & nil = X1 )
                      | ? [X4] :
                          ( segmentP(X0,X4)
                          & segmentP(X1,X4)
                          & neq(X4,nil)
                          & ssList(X4) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( ~ frontsegP(X3,X2)
                        | ~ neq(X2,nil) )
                      & ( nil != X2
                        | nil != X3 ) )
                    | ( nil = X0
                      & nil = X1 )
                    | ? [X4] :
                        ( segmentP(X0,X4)
                        & segmentP(X1,X4)
                        & neq(X4,nil)
                        & ssList(X4) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f652,plain,
    ( neq(sK18,nil)
    | nil = sK21 ),
    inference(forward_demodulation,[],[f382,f379]) ).

fof(f379,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f254]) ).

fof(f382,plain,
    ( neq(sK20,nil)
    | nil = sK21 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f7343,plain,
    ( spl69_1
    | ~ spl69_2
    | ~ spl69_21
    | ~ spl69_29
    | spl69_44 ),
    inference(avatar_contradiction_clause,[],[f7342]) ).

fof(f7342,plain,
    ( $false
    | spl69_1
    | ~ spl69_2
    | ~ spl69_21
    | ~ spl69_29
    | spl69_44 ),
    inference(subsumption_resolution,[],[f7297,f3206]) ).

fof(f3206,plain,
    ( rearsegP(sK19,nil)
    | spl69_1
    | ~ spl69_29 ),
    inference(subsumption_resolution,[],[f3205,f3002]) ).

fof(f3002,plain,
    ( ssList(sK66(sK19,sK18))
    | ~ spl69_29 ),
    inference(avatar_component_clause,[],[f3001]) ).

fof(f3001,plain,
    ( spl69_29
  <=> ssList(sK66(sK19,sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_29])]) ).

fof(f3205,plain,
    ( rearsegP(sK19,nil)
    | ~ ssList(sK66(sK19,sK18))
    | spl69_1
    | ~ spl69_29 ),
    inference(subsumption_resolution,[],[f3203,f394]) ).

fof(f3203,plain,
    ( rearsegP(sK19,nil)
    | ~ ssList(nil)
    | ~ ssList(sK66(sK19,sK18))
    | spl69_1
    | ~ spl69_29 ),
    inference(resolution,[],[f3172,f450]) ).

fof(f450,plain,
    ! [X0] :
      ( rearsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ! [X0] :
      ( rearsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,axiom,
    ! [X0] :
      ( ssList(X0)
     => rearsegP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).

fof(f3172,plain,
    ( ! [X0] :
        ( ~ rearsegP(sK66(sK19,sK18),X0)
        | rearsegP(sK19,X0)
        | ~ ssList(X0) )
    | spl69_1
    | ~ spl69_29 ),
    inference(subsumption_resolution,[],[f3171,f3002]) ).

fof(f3171,plain,
    ( ! [X0] :
        ( rearsegP(sK19,X0)
        | ~ rearsegP(sK66(sK19,sK18),X0)
        | ~ ssList(X0)
        | ~ ssList(sK66(sK19,sK18)) )
    | spl69_1 ),
    inference(subsumption_resolution,[],[f3127,f374]) ).

fof(f374,plain,
    ssList(sK18),
    inference(cnf_transformation,[],[f254]) ).

fof(f3127,plain,
    ( ! [X0] :
        ( rearsegP(sK19,X0)
        | ~ rearsegP(sK66(sK19,sK18),X0)
        | ~ ssList(sK18)
        | ~ ssList(X0)
        | ~ ssList(sK66(sK19,sK18)) )
    | spl69_1 ),
    inference(superposition,[],[f592,f2989]) ).

fof(f2989,plain,
    ( sK19 = app(sK18,sK66(sK19,sK18))
    | spl69_1 ),
    inference(subsumption_resolution,[],[f2988,f375]) ).

fof(f375,plain,
    ssList(sK19),
    inference(cnf_transformation,[],[f254]) ).

fof(f2988,plain,
    ( sK19 = app(sK18,sK66(sK19,sK18))
    | ~ ssList(sK19)
    | spl69_1 ),
    inference(subsumption_resolution,[],[f2972,f374]) ).

fof(f2972,plain,
    ( sK19 = app(sK18,sK66(sK19,sK18))
    | ~ ssList(sK18)
    | ~ ssList(sK19)
    | spl69_1 ),
    inference(resolution,[],[f583,f659]) ).

fof(f659,plain,
    ( frontsegP(sK19,sK18)
    | spl69_1 ),
    inference(subsumption_resolution,[],[f658,f646]) ).

fof(f658,plain,
    ( nil = sK19
    | frontsegP(sK19,sK18) ),
    inference(forward_demodulation,[],[f657,f378]) ).

fof(f657,plain,
    ( frontsegP(sK19,sK18)
    | nil = sK21 ),
    inference(forward_demodulation,[],[f656,f378]) ).

fof(f656,plain,
    ( frontsegP(sK21,sK18)
    | nil = sK21 ),
    inference(forward_demodulation,[],[f384,f379]) ).

fof(f384,plain,
    ( frontsegP(sK21,sK20)
    | nil = sK21 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f583,plain,
    ! [X0,X1] :
      ( ~ frontsegP(X0,X1)
      | app(X1,sK66(X0,X1)) = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f368]) ).

fof(f368,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(X1,sK66(X0,X1)) = X0
                & ssList(sK66(X0,X1)) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f366,f367]) ).

fof(f367,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X1,X3) = X0
          & ssList(X3) )
     => ( app(X1,sK66(X0,X1)) = X0
        & ssList(sK66(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f366,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,[],[f365]) ).

fof(f365,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,[],[f201]) ).

fof(f201,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f5]) ).

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(f592,plain,
    ! [X2,X0,X1] :
      ( rearsegP(app(X2,X0),X1)
      | ~ rearsegP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f208]) ).

fof(f208,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( rearsegP(app(X2,X0),X1)
              | ~ rearsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f207]) ).

fof(f207,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( rearsegP(app(X2,X0),X1)
              | ~ rearsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( rearsegP(X0,X1)
               => rearsegP(app(X2,X0),X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).

fof(f7297,plain,
    ( ~ rearsegP(sK19,nil)
    | ~ spl69_2
    | ~ spl69_21
    | spl69_44 ),
    inference(superposition,[],[f3954,f649]) ).

fof(f3954,plain,
    ( ~ rearsegP(sK19,sK18)
    | ~ spl69_21
    | spl69_44 ),
    inference(subsumption_resolution,[],[f3952,f374]) ).

fof(f3952,plain,
    ( ~ rearsegP(sK19,sK18)
    | ~ ssList(sK18)
    | ~ spl69_21
    | spl69_44 ),
    inference(resolution,[],[f3947,f3168]) ).

fof(f3168,plain,
    ( ! [X0] :
        ( rearsegP(cons(sK67,sK19),X0)
        | ~ rearsegP(sK19,X0)
        | ~ ssList(X0) )
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f3167,f375]) ).

fof(f3167,plain,
    ( ! [X0] :
        ( rearsegP(cons(sK67,sK19),X0)
        | ~ rearsegP(sK19,X0)
        | ~ ssList(X0)
        | ~ ssList(sK19) )
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f3123,f2200]) ).

fof(f2200,plain,
    ( ssList(cons(sK67,nil))
    | ~ spl69_21 ),
    inference(avatar_component_clause,[],[f2199]) ).

fof(f2199,plain,
    ( spl69_21
  <=> ssList(cons(sK67,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_21])]) ).

fof(f3123,plain,
    ! [X0] :
      ( rearsegP(cons(sK67,sK19),X0)
      | ~ rearsegP(sK19,X0)
      | ~ ssList(cons(sK67,nil))
      | ~ ssList(X0)
      | ~ ssList(sK19) ),
    inference(superposition,[],[f592,f2709]) ).

fof(f2709,plain,
    cons(sK67,sK19) = app(cons(sK67,nil),sK19),
    inference(resolution,[],[f1901,f600]) ).

fof(f600,plain,
    ssItem(sK67),
    inference(cnf_transformation,[],[f373]) ).

fof(f373,plain,
    ( sK67 != sK68
    & ssItem(sK68)
    & ssItem(sK67) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f2,f372,f371]) ).

fof(f371,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( X0 != X1
            & ssItem(X1) )
        & ssItem(X0) )
   => ( ? [X1] :
          ( sK67 != X1
          & ssItem(X1) )
      & ssItem(sK67) ) ),
    introduced(choice_axiom,[]) ).

fof(f372,plain,
    ( ? [X1] :
        ( sK67 != X1
        & ssItem(X1) )
   => ( sK67 != sK68
      & ssItem(sK68) ) ),
    introduced(choice_axiom,[]) ).

fof(f2,axiom,
    ? [X0] :
      ( ? [X1] :
          ( X0 != X1
          & ssItem(X1) )
      & ssItem(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

fof(f1901,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | cons(X0,sK19) = app(cons(X0,nil),sK19) ),
    inference(resolution,[],[f561,f375]) ).

fof(f561,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | cons(X1,X0) = app(cons(X1,nil),X0) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f183,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

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(f3947,plain,
    ( ~ rearsegP(cons(sK67,sK19),sK18)
    | spl69_44 ),
    inference(avatar_component_clause,[],[f3946]) ).

fof(f3946,plain,
    ( spl69_44
  <=> rearsegP(cons(sK67,sK19),sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_44])]) ).

fof(f7341,plain,
    ( ~ spl69_2
    | ~ spl69_21
    | spl69_44 ),
    inference(avatar_contradiction_clause,[],[f7340]) ).

fof(f7340,plain,
    ( $false
    | ~ spl69_2
    | ~ spl69_21
    | spl69_44 ),
    inference(subsumption_resolution,[],[f7296,f637]) ).

fof(f637,plain,
    rearsegP(nil,nil),
    inference(global_subsumption,[],[f385,f384,f383,f382,f381,f380,f379,f378,f377,f376,f375,f374,f386,f387,f388,f389,f390,f391,f392,f393,f394,f395,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f412,f636,f414,f413,f416,f415,f419,f418,f635,f420,f421,f422,f423,f424,f427,f634,f425,f633,f429,f428,f432,f431,f437,f607,f435,f434,f438,f440,f439,f445,f609,f443,f442,f446,f449,f448,f447,f450,f451,f452,f453,f454,f455,f456,f457,f460,f459,f458,f461,f462,f463,f465,f464,f467,f466,f611,f469,f468,f471,f479,f478,f477,f476,f475,f474,f612,f480,f481,f490,f489,f488,f487,f486,f485,f484,f632,f491,f492,f502,f501,f500,f499,f498,f497,f496,f495,f615,f503,f504,f514,f513,f512,f511,f510,f509,f508,f507,f616,f515,f516,f526,f525,f524,f523,f522,f521,f520,f519,f617,f527,f529,f528,f537,f536,f535,f534,f533,f532,f531,f618,f538,f540,f539,f548,f547,f546,f545,f544,f543,f542,f619,f549,f620]) ).

fof(f620,plain,
    ( rearsegP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f551]) ).

fof(f551,plain,
    ! [X0] :
      ( rearsegP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f347,plain,
    ! [X0] :
      ( ( ( rearsegP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ rearsegP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f175]) ).

fof(f175,plain,
    ! [X0] :
      ( ( rearsegP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( rearsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).

fof(f549,plain,
    ! [X0] :
      ( sP17(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f249]) ).

fof(f249,plain,
    ! [X0] :
      ( sP17(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f174,f248,f247]) ).

fof(f247,plain,
    ! [X0] :
      ( sP16(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( lt(X1,X2)
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).

fof(f248,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> sP16(X0) )
      | ~ sP17(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).

fof(f174,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f173]) ).

fof(f173,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( strictorderedP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => lt(X1,X2) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).

fof(f619,plain,
    ! [X10,X8,X6,X9,X7] :
      ( lt(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP16(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f541]) ).

fof(f541,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( lt(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP16(X0) ),
    inference(cnf_transformation,[],[f346]) ).

fof(f346,plain,
    ! [X0] :
      ( ( sP16(X0)
        | ( ~ lt(sK56(X0),sK57(X0))
          & app(app(sK58(X0),cons(sK56(X0),sK59(X0))),cons(sK57(X0),sK60(X0))) = X0
          & ssList(sK60(X0))
          & ssList(sK59(X0))
          & ssList(sK58(X0))
          & ssItem(sK57(X0))
          & ssItem(sK56(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( lt(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP16(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57,sK58,sK59,sK60])],[f340,f345,f344,f343,f342,f341]) ).

fof(f341,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ lt(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ~ lt(sK56(X0),X2)
                        & app(app(X3,cons(sK56(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK56(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f342,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ lt(sK56(X0),X2)
                      & app(app(X3,cons(sK56(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ lt(sK56(X0),sK57(X0))
                    & app(app(X3,cons(sK56(X0),X4)),cons(sK57(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK57(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f343,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ lt(sK56(X0),sK57(X0))
                  & app(app(X3,cons(sK56(X0),X4)),cons(sK57(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ lt(sK56(X0),sK57(X0))
                & app(app(sK58(X0),cons(sK56(X0),X4)),cons(sK57(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK58(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ lt(sK56(X0),sK57(X0))
              & app(app(sK58(X0),cons(sK56(X0),X4)),cons(sK57(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ lt(sK56(X0),sK57(X0))
            & app(app(sK58(X0),cons(sK56(X0),sK59(X0))),cons(sK57(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK59(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ lt(sK56(X0),sK57(X0))
          & app(app(sK58(X0),cons(sK56(X0),sK59(X0))),cons(sK57(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ lt(sK56(X0),sK57(X0))
        & app(app(sK58(X0),cons(sK56(X0),sK59(X0))),cons(sK57(X0),sK60(X0))) = X0
        & ssList(sK60(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f340,plain,
    ! [X0] :
      ( ( sP16(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ lt(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( lt(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP16(X0) ) ),
    inference(rectify,[],[f339]) ).

fof(f339,plain,
    ! [X0] :
      ( ( sP16(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ lt(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP16(X0) ) ),
    inference(nnf_transformation,[],[f247]) ).

fof(f542,plain,
    ! [X0] :
      ( ssItem(sK56(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f346]) ).

fof(f543,plain,
    ! [X0] :
      ( ssItem(sK57(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f346]) ).

fof(f544,plain,
    ! [X0] :
      ( ssList(sK58(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f346]) ).

fof(f545,plain,
    ! [X0] :
      ( ssList(sK59(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f346]) ).

fof(f546,plain,
    ! [X0] :
      ( ssList(sK60(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f346]) ).

fof(f547,plain,
    ! [X0] :
      ( sP16(X0)
      | app(app(sK58(X0),cons(sK56(X0),sK59(X0))),cons(sK57(X0),sK60(X0))) = X0 ),
    inference(cnf_transformation,[],[f346]) ).

fof(f548,plain,
    ! [X0] :
      ( ~ lt(sK56(X0),sK57(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f346]) ).

fof(f539,plain,
    ! [X0] :
      ( ~ sP17(X0)
      | ~ strictorderedP(X0)
      | sP16(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f338,plain,
    ! [X0] :
      ( ( ( strictorderedP(X0)
          | ~ sP16(X0) )
        & ( sP16(X0)
          | ~ strictorderedP(X0) ) )
      | ~ sP17(X0) ),
    inference(nnf_transformation,[],[f248]) ).

fof(f540,plain,
    ! [X0] :
      ( ~ sP17(X0)
      | ~ sP16(X0)
      | strictorderedP(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f538,plain,
    ! [X0] :
      ( sP15(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f246]) ).

fof(f246,plain,
    ! [X0] :
      ( sP15(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f172,f245,f244]) ).

fof(f244,plain,
    ! [X0] :
      ( sP14(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( leq(X1,X2)
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

fof(f245,plain,
    ! [X0] :
      ( ( totalorderedP(X0)
      <=> sP14(X0) )
      | ~ sP15(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).

fof(f172,plain,
    ! [X0] :
      ( ( totalorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f171]) ).

fof(f171,plain,
    ! [X0] :
      ( ( totalorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( totalorderedP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => leq(X1,X2) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).

fof(f618,plain,
    ! [X10,X8,X6,X9,X7] :
      ( leq(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP14(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f530]) ).

fof(f530,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( leq(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP14(X0) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f337,plain,
    ! [X0] :
      ( ( sP14(X0)
        | ( ~ leq(sK51(X0),sK52(X0))
          & app(app(sK53(X0),cons(sK51(X0),sK54(X0))),cons(sK52(X0),sK55(X0))) = X0
          & ssList(sK55(X0))
          & ssList(sK54(X0))
          & ssList(sK53(X0))
          & ssItem(sK52(X0))
          & ssItem(sK51(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP14(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK51,sK52,sK53,sK54,sK55])],[f331,f336,f335,f334,f333,f332]) ).

fof(f332,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ leq(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ~ leq(sK51(X0),X2)
                        & app(app(X3,cons(sK51(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK51(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f333,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ leq(sK51(X0),X2)
                      & app(app(X3,cons(sK51(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ leq(sK51(X0),sK52(X0))
                    & app(app(X3,cons(sK51(X0),X4)),cons(sK52(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK52(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f334,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ leq(sK51(X0),sK52(X0))
                  & app(app(X3,cons(sK51(X0),X4)),cons(sK52(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ leq(sK51(X0),sK52(X0))
                & app(app(sK53(X0),cons(sK51(X0),X4)),cons(sK52(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK53(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f335,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ leq(sK51(X0),sK52(X0))
              & app(app(sK53(X0),cons(sK51(X0),X4)),cons(sK52(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ leq(sK51(X0),sK52(X0))
            & app(app(sK53(X0),cons(sK51(X0),sK54(X0))),cons(sK52(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK54(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f336,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ leq(sK51(X0),sK52(X0))
          & app(app(sK53(X0),cons(sK51(X0),sK54(X0))),cons(sK52(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ leq(sK51(X0),sK52(X0))
        & app(app(sK53(X0),cons(sK51(X0),sK54(X0))),cons(sK52(X0),sK55(X0))) = X0
        & ssList(sK55(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f331,plain,
    ! [X0] :
      ( ( sP14(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP14(X0) ) ),
    inference(rectify,[],[f330]) ).

fof(f330,plain,
    ! [X0] :
      ( ( sP14(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP14(X0) ) ),
    inference(nnf_transformation,[],[f244]) ).

fof(f531,plain,
    ! [X0] :
      ( ssItem(sK51(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f532,plain,
    ! [X0] :
      ( ssItem(sK52(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f533,plain,
    ! [X0] :
      ( ssList(sK53(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f534,plain,
    ! [X0] :
      ( ssList(sK54(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f535,plain,
    ! [X0] :
      ( ssList(sK55(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f536,plain,
    ! [X0] :
      ( sP14(X0)
      | app(app(sK53(X0),cons(sK51(X0),sK54(X0))),cons(sK52(X0),sK55(X0))) = X0 ),
    inference(cnf_transformation,[],[f337]) ).

fof(f537,plain,
    ! [X0] :
      ( ~ leq(sK51(X0),sK52(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f528,plain,
    ! [X0] :
      ( ~ sP15(X0)
      | ~ totalorderedP(X0)
      | sP14(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f329,plain,
    ! [X0] :
      ( ( ( totalorderedP(X0)
          | ~ sP14(X0) )
        & ( sP14(X0)
          | ~ totalorderedP(X0) ) )
      | ~ sP15(X0) ),
    inference(nnf_transformation,[],[f245]) ).

fof(f529,plain,
    ! [X0] :
      ( ~ sP15(X0)
      | ~ sP14(X0)
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f527,plain,
    ! [X0] :
      ( sP13(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f243]) ).

fof(f243,plain,
    ! [X0] :
      ( sP13(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f170,f242,f241]) ).

fof(f241,plain,
    ! [X0] :
      ( sP12(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( ~ leq(X2,X1)
                          | ~ leq(X1,X2)
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

fof(f242,plain,
    ! [X0] :
      ( ( cyclefreeP(X0)
      <=> sP12(X0) )
      | ~ sP13(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

fof(f170,plain,
    ! [X0] :
      ( ( cyclefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( ~ leq(X2,X1)
                            | ~ leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f169]) ).

fof(f169,plain,
    ! [X0] :
      ( ( cyclefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( ~ leq(X2,X1)
                            | ~ leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( cyclefreeP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => ~ ( leq(X2,X1)
                                  & leq(X1,X2) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).

fof(f617,plain,
    ! [X10,X8,X6,X9,X7] :
      ( ~ leq(X7,X6)
      | ~ leq(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP12(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f518]) ).

fof(f518,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( ~ leq(X7,X6)
      | ~ leq(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP12(X0) ),
    inference(cnf_transformation,[],[f328]) ).

fof(f328,plain,
    ! [X0] :
      ( ( sP12(X0)
        | ( leq(sK47(X0),sK46(X0))
          & leq(sK46(X0),sK47(X0))
          & app(app(sK48(X0),cons(sK46(X0),sK49(X0))),cons(sK47(X0),sK50(X0))) = X0
          & ssList(sK50(X0))
          & ssList(sK49(X0))
          & ssList(sK48(X0))
          & ssItem(sK47(X0))
          & ssItem(sK46(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( ~ leq(X7,X6)
                            | ~ leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP12(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47,sK48,sK49,sK50])],[f322,f327,f326,f325,f324,f323]) ).

fof(f323,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( leq(X2,X1)
                          & leq(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( leq(X2,sK46(X0))
                        & leq(sK46(X0),X2)
                        & app(app(X3,cons(sK46(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK46(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f324,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( leq(X2,sK46(X0))
                      & leq(sK46(X0),X2)
                      & app(app(X3,cons(sK46(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( leq(sK47(X0),sK46(X0))
                    & leq(sK46(X0),sK47(X0))
                    & app(app(X3,cons(sK46(X0),X4)),cons(sK47(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK47(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f325,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( leq(sK47(X0),sK46(X0))
                  & leq(sK46(X0),sK47(X0))
                  & app(app(X3,cons(sK46(X0),X4)),cons(sK47(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( leq(sK47(X0),sK46(X0))
                & leq(sK46(X0),sK47(X0))
                & app(app(sK48(X0),cons(sK46(X0),X4)),cons(sK47(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK48(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f326,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( leq(sK47(X0),sK46(X0))
              & leq(sK46(X0),sK47(X0))
              & app(app(sK48(X0),cons(sK46(X0),X4)),cons(sK47(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( leq(sK47(X0),sK46(X0))
            & leq(sK46(X0),sK47(X0))
            & app(app(sK48(X0),cons(sK46(X0),sK49(X0))),cons(sK47(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK49(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f327,plain,
    ! [X0] :
      ( ? [X5] :
          ( leq(sK47(X0),sK46(X0))
          & leq(sK46(X0),sK47(X0))
          & app(app(sK48(X0),cons(sK46(X0),sK49(X0))),cons(sK47(X0),X5)) = X0
          & ssList(X5) )
     => ( leq(sK47(X0),sK46(X0))
        & leq(sK46(X0),sK47(X0))
        & app(app(sK48(X0),cons(sK46(X0),sK49(X0))),cons(sK47(X0),sK50(X0))) = X0
        & ssList(sK50(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f322,plain,
    ! [X0] :
      ( ( sP12(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( leq(X2,X1)
                            & leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( ~ leq(X7,X6)
                            | ~ leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP12(X0) ) ),
    inference(rectify,[],[f321]) ).

fof(f321,plain,
    ! [X0] :
      ( ( sP12(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( leq(X2,X1)
                            & leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( ~ leq(X2,X1)
                            | ~ leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP12(X0) ) ),
    inference(nnf_transformation,[],[f241]) ).

fof(f519,plain,
    ! [X0] :
      ( ssItem(sK46(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f328]) ).

fof(f520,plain,
    ! [X0] :
      ( ssItem(sK47(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f328]) ).

fof(f521,plain,
    ! [X0] :
      ( ssList(sK48(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f328]) ).

fof(f522,plain,
    ! [X0] :
      ( ssList(sK49(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f328]) ).

fof(f523,plain,
    ! [X0] :
      ( ssList(sK50(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f328]) ).

fof(f524,plain,
    ! [X0] :
      ( sP12(X0)
      | app(app(sK48(X0),cons(sK46(X0),sK49(X0))),cons(sK47(X0),sK50(X0))) = X0 ),
    inference(cnf_transformation,[],[f328]) ).

fof(f525,plain,
    ! [X0] :
      ( leq(sK46(X0),sK47(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f328]) ).

fof(f526,plain,
    ! [X0] :
      ( leq(sK47(X0),sK46(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f328]) ).

fof(f516,plain,
    ! [X0] :
      ( ~ sP13(X0)
      | ~ cyclefreeP(X0)
      | sP12(X0) ),
    inference(cnf_transformation,[],[f320]) ).

fof(f320,plain,
    ! [X0] :
      ( ( ( cyclefreeP(X0)
          | ~ sP12(X0) )
        & ( sP12(X0)
          | ~ cyclefreeP(X0) ) )
      | ~ sP13(X0) ),
    inference(nnf_transformation,[],[f242]) ).

fof(f515,plain,
    ! [X0] :
      ( sP11(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f240]) ).

fof(f240,plain,
    ! [X0] :
      ( sP11(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f168,f239,f238]) ).

fof(f238,plain,
    ! [X0] :
      ( sP10(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( lt(X2,X1)
                          | lt(X1,X2)
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

fof(f239,plain,
    ! [X0] :
      ( ( strictorderP(X0)
      <=> sP10(X0) )
      | ~ sP11(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

fof(f168,plain,
    ! [X0] :
      ( ( strictorderP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X2,X1)
                            | lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f167]) ).

fof(f167,plain,
    ! [X0] :
      ( ( strictorderP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X2,X1)
                            | lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( strictorderP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => ( lt(X2,X1)
                                | lt(X1,X2) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).

fof(f616,plain,
    ! [X10,X8,X6,X9,X7] :
      ( lt(X7,X6)
      | lt(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP10(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f506]) ).

fof(f506,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( lt(X7,X6)
      | lt(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP10(X0) ),
    inference(cnf_transformation,[],[f319]) ).

fof(f319,plain,
    ! [X0] :
      ( ( sP10(X0)
        | ( ~ lt(sK42(X0),sK41(X0))
          & ~ lt(sK41(X0),sK42(X0))
          & app(app(sK43(X0),cons(sK41(X0),sK44(X0))),cons(sK42(X0),sK45(X0))) = X0
          & ssList(sK45(X0))
          & ssList(sK44(X0))
          & ssList(sK43(X0))
          & ssItem(sK42(X0))
          & ssItem(sK41(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( lt(X7,X6)
                            | lt(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP10(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42,sK43,sK44,sK45])],[f313,f318,f317,f316,f315,f314]) ).

fof(f314,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ lt(X2,X1)
                          & ~ lt(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ~ lt(X2,sK41(X0))
                        & ~ lt(sK41(X0),X2)
                        & app(app(X3,cons(sK41(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK41(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f315,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ lt(X2,sK41(X0))
                      & ~ lt(sK41(X0),X2)
                      & app(app(X3,cons(sK41(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ lt(sK42(X0),sK41(X0))
                    & ~ lt(sK41(X0),sK42(X0))
                    & app(app(X3,cons(sK41(X0),X4)),cons(sK42(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK42(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f316,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ lt(sK42(X0),sK41(X0))
                  & ~ lt(sK41(X0),sK42(X0))
                  & app(app(X3,cons(sK41(X0),X4)),cons(sK42(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ lt(sK42(X0),sK41(X0))
                & ~ lt(sK41(X0),sK42(X0))
                & app(app(sK43(X0),cons(sK41(X0),X4)),cons(sK42(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK43(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f317,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ lt(sK42(X0),sK41(X0))
              & ~ lt(sK41(X0),sK42(X0))
              & app(app(sK43(X0),cons(sK41(X0),X4)),cons(sK42(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ lt(sK42(X0),sK41(X0))
            & ~ lt(sK41(X0),sK42(X0))
            & app(app(sK43(X0),cons(sK41(X0),sK44(X0))),cons(sK42(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK44(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f318,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ lt(sK42(X0),sK41(X0))
          & ~ lt(sK41(X0),sK42(X0))
          & app(app(sK43(X0),cons(sK41(X0),sK44(X0))),cons(sK42(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ lt(sK42(X0),sK41(X0))
        & ~ lt(sK41(X0),sK42(X0))
        & app(app(sK43(X0),cons(sK41(X0),sK44(X0))),cons(sK42(X0),sK45(X0))) = X0
        & ssList(sK45(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f313,plain,
    ! [X0] :
      ( ( sP10(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ lt(X2,X1)
                            & ~ lt(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( lt(X7,X6)
                            | lt(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP10(X0) ) ),
    inference(rectify,[],[f312]) ).

fof(f312,plain,
    ! [X0] :
      ( ( sP10(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ lt(X2,X1)
                            & ~ lt(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X2,X1)
                            | lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP10(X0) ) ),
    inference(nnf_transformation,[],[f238]) ).

fof(f507,plain,
    ! [X0] :
      ( ssItem(sK41(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f319]) ).

fof(f508,plain,
    ! [X0] :
      ( ssItem(sK42(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f319]) ).

fof(f509,plain,
    ! [X0] :
      ( ssList(sK43(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f319]) ).

fof(f510,plain,
    ! [X0] :
      ( ssList(sK44(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f319]) ).

fof(f511,plain,
    ! [X0] :
      ( ssList(sK45(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f319]) ).

fof(f512,plain,
    ! [X0] :
      ( sP10(X0)
      | app(app(sK43(X0),cons(sK41(X0),sK44(X0))),cons(sK42(X0),sK45(X0))) = X0 ),
    inference(cnf_transformation,[],[f319]) ).

fof(f513,plain,
    ! [X0] :
      ( ~ lt(sK41(X0),sK42(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f319]) ).

fof(f514,plain,
    ! [X0] :
      ( ~ lt(sK42(X0),sK41(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f319]) ).

fof(f504,plain,
    ! [X0] :
      ( ~ sP11(X0)
      | ~ strictorderP(X0)
      | sP10(X0) ),
    inference(cnf_transformation,[],[f311]) ).

fof(f311,plain,
    ! [X0] :
      ( ( ( strictorderP(X0)
          | ~ sP10(X0) )
        & ( sP10(X0)
          | ~ strictorderP(X0) ) )
      | ~ sP11(X0) ),
    inference(nnf_transformation,[],[f239]) ).

fof(f503,plain,
    ! [X0] :
      ( sP9(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f237]) ).

fof(f237,plain,
    ! [X0] :
      ( sP9(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f166,f236,f235]) ).

fof(f235,plain,
    ! [X0] :
      ( sP8(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( leq(X2,X1)
                          | leq(X1,X2)
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f236,plain,
    ! [X0] :
      ( ( totalorderP(X0)
      <=> sP8(X0) )
      | ~ sP9(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

fof(f166,plain,
    ! [X0] :
      ( ( totalorderP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X2,X1)
                            | leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f165]) ).

fof(f165,plain,
    ! [X0] :
      ( ( totalorderP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X2,X1)
                            | leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( totalorderP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => ( leq(X2,X1)
                                | leq(X1,X2) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).

fof(f615,plain,
    ! [X10,X8,X6,X9,X7] :
      ( leq(X7,X6)
      | leq(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP8(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f494]) ).

fof(f494,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( leq(X7,X6)
      | leq(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f310]) ).

fof(f310,plain,
    ! [X0] :
      ( ( sP8(X0)
        | ( ~ leq(sK37(X0),sK36(X0))
          & ~ leq(sK36(X0),sK37(X0))
          & app(app(sK38(X0),cons(sK36(X0),sK39(X0))),cons(sK37(X0),sK40(X0))) = X0
          & ssList(sK40(X0))
          & ssList(sK39(X0))
          & ssList(sK38(X0))
          & ssItem(sK37(X0))
          & ssItem(sK36(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( leq(X7,X6)
                            | leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP8(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37,sK38,sK39,sK40])],[f304,f309,f308,f307,f306,f305]) ).

fof(f305,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ leq(X2,X1)
                          & ~ leq(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ~ leq(X2,sK36(X0))
                        & ~ leq(sK36(X0),X2)
                        & app(app(X3,cons(sK36(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK36(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f306,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ leq(X2,sK36(X0))
                      & ~ leq(sK36(X0),X2)
                      & app(app(X3,cons(sK36(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ leq(sK37(X0),sK36(X0))
                    & ~ leq(sK36(X0),sK37(X0))
                    & app(app(X3,cons(sK36(X0),X4)),cons(sK37(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK37(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f307,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ leq(sK37(X0),sK36(X0))
                  & ~ leq(sK36(X0),sK37(X0))
                  & app(app(X3,cons(sK36(X0),X4)),cons(sK37(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ leq(sK37(X0),sK36(X0))
                & ~ leq(sK36(X0),sK37(X0))
                & app(app(sK38(X0),cons(sK36(X0),X4)),cons(sK37(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK38(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f308,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ leq(sK37(X0),sK36(X0))
              & ~ leq(sK36(X0),sK37(X0))
              & app(app(sK38(X0),cons(sK36(X0),X4)),cons(sK37(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ leq(sK37(X0),sK36(X0))
            & ~ leq(sK36(X0),sK37(X0))
            & app(app(sK38(X0),cons(sK36(X0),sK39(X0))),cons(sK37(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK39(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f309,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ leq(sK37(X0),sK36(X0))
          & ~ leq(sK36(X0),sK37(X0))
          & app(app(sK38(X0),cons(sK36(X0),sK39(X0))),cons(sK37(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ leq(sK37(X0),sK36(X0))
        & ~ leq(sK36(X0),sK37(X0))
        & app(app(sK38(X0),cons(sK36(X0),sK39(X0))),cons(sK37(X0),sK40(X0))) = X0
        & ssList(sK40(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f304,plain,
    ! [X0] :
      ( ( sP8(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ leq(X2,X1)
                            & ~ leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( leq(X7,X6)
                            | leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP8(X0) ) ),
    inference(rectify,[],[f303]) ).

fof(f303,plain,
    ! [X0] :
      ( ( sP8(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ leq(X2,X1)
                            & ~ leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X2,X1)
                            | leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP8(X0) ) ),
    inference(nnf_transformation,[],[f235]) ).

fof(f495,plain,
    ! [X0] :
      ( ssItem(sK36(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f310]) ).

fof(f496,plain,
    ! [X0] :
      ( ssItem(sK37(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f310]) ).

fof(f497,plain,
    ! [X0] :
      ( ssList(sK38(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f310]) ).

fof(f498,plain,
    ! [X0] :
      ( ssList(sK39(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f310]) ).

fof(f499,plain,
    ! [X0] :
      ( ssList(sK40(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f310]) ).

fof(f500,plain,
    ! [X0] :
      ( sP8(X0)
      | app(app(sK38(X0),cons(sK36(X0),sK39(X0))),cons(sK37(X0),sK40(X0))) = X0 ),
    inference(cnf_transformation,[],[f310]) ).

fof(f501,plain,
    ! [X0] :
      ( ~ leq(sK36(X0),sK37(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f310]) ).

fof(f502,plain,
    ! [X0] :
      ( ~ leq(sK37(X0),sK36(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f310]) ).

fof(f492,plain,
    ! [X0] :
      ( ~ sP9(X0)
      | ~ totalorderP(X0)
      | sP8(X0) ),
    inference(cnf_transformation,[],[f302]) ).

fof(f302,plain,
    ! [X0] :
      ( ( ( totalorderP(X0)
          | ~ sP8(X0) )
        & ( sP8(X0)
          | ~ totalorderP(X0) ) )
      | ~ sP9(X0) ),
    inference(nnf_transformation,[],[f236]) ).

fof(f491,plain,
    ! [X0] :
      ( sP7(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f234]) ).

fof(f234,plain,
    ! [X0] :
      ( sP7(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f164,f233,f232]) ).

fof(f232,plain,
    ! [X0] :
      ( sP6(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( X1 != X2
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f233,plain,
    ! [X0] :
      ( ( duplicatefreeP(X0)
      <=> sP6(X0) )
      | ~ sP7(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f164,plain,
    ! [X0] :
      ( ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f163]) ).

fof(f163,plain,
    ! [X0] :
      ( ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => X1 != X2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).

fof(f632,plain,
    ! [X10,X8,X9,X7] :
      ( ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10)))
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssList(X10) ),
    inference(duplicate_literal_removal,[],[f614]) ).

fof(f614,plain,
    ! [X10,X8,X9,X7] :
      ( ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X7)
      | ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f613]) ).

fof(f613,plain,
    ! [X10,X0,X8,X9,X7] :
      ( app(app(X8,cons(X7,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X7)
      | ~ sP6(X0) ),
    inference(equality_resolution,[],[f483]) ).

fof(f483,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( X6 != X7
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP6(X0) ),
    inference(cnf_transformation,[],[f301]) ).

fof(f301,plain,
    ! [X0] :
      ( ( sP6(X0)
        | ( sK31(X0) = sK32(X0)
          & app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),sK35(X0))) = X0
          & ssList(sK35(X0))
          & ssList(sK34(X0))
          & ssList(sK33(X0))
          & ssItem(sK32(X0))
          & ssItem(sK31(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( X6 != X7
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP6(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32,sK33,sK34,sK35])],[f295,f300,f299,f298,f297,f296]) ).

fof(f296,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( X1 = X2
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( sK31(X0) = X2
                        & app(app(X3,cons(sK31(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK31(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f297,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( sK31(X0) = X2
                      & app(app(X3,cons(sK31(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( sK31(X0) = sK32(X0)
                    & app(app(X3,cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK32(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f298,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( sK31(X0) = sK32(X0)
                  & app(app(X3,cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( sK31(X0) = sK32(X0)
                & app(app(sK33(X0),cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK33(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f299,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( sK31(X0) = sK32(X0)
              & app(app(sK33(X0),cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( sK31(X0) = sK32(X0)
            & app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK34(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f300,plain,
    ! [X0] :
      ( ? [X5] :
          ( sK31(X0) = sK32(X0)
          & app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),X5)) = X0
          & ssList(X5) )
     => ( sK31(X0) = sK32(X0)
        & app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),sK35(X0))) = X0
        & ssList(sK35(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f295,plain,
    ! [X0] :
      ( ( sP6(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( X1 = X2
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( X6 != X7
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP6(X0) ) ),
    inference(rectify,[],[f294]) ).

fof(f294,plain,
    ! [X0] :
      ( ( sP6(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( X1 = X2
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP6(X0) ) ),
    inference(nnf_transformation,[],[f232]) ).

fof(f484,plain,
    ! [X0] :
      ( ssItem(sK31(X0))
      | sP6(X0) ),
    inference(cnf_transformation,[],[f301]) ).

fof(f485,plain,
    ! [X0] :
      ( ssItem(sK32(X0))
      | sP6(X0) ),
    inference(cnf_transformation,[],[f301]) ).

fof(f486,plain,
    ! [X0] :
      ( ssList(sK33(X0))
      | sP6(X0) ),
    inference(cnf_transformation,[],[f301]) ).

fof(f487,plain,
    ! [X0] :
      ( ssList(sK34(X0))
      | sP6(X0) ),
    inference(cnf_transformation,[],[f301]) ).

fof(f488,plain,
    ! [X0] :
      ( ssList(sK35(X0))
      | sP6(X0) ),
    inference(cnf_transformation,[],[f301]) ).

fof(f489,plain,
    ! [X0] :
      ( sP6(X0)
      | app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),sK35(X0))) = X0 ),
    inference(cnf_transformation,[],[f301]) ).

fof(f490,plain,
    ! [X0] :
      ( sP6(X0)
      | sK31(X0) = sK32(X0) ),
    inference(cnf_transformation,[],[f301]) ).

fof(f481,plain,
    ! [X0] :
      ( ~ sP7(X0)
      | ~ duplicatefreeP(X0)
      | sP6(X0) ),
    inference(cnf_transformation,[],[f293]) ).

fof(f293,plain,
    ! [X0] :
      ( ( ( duplicatefreeP(X0)
          | ~ sP6(X0) )
        & ( sP6(X0)
          | ~ duplicatefreeP(X0) ) )
      | ~ sP7(X0) ),
    inference(nnf_transformation,[],[f233]) ).

fof(f480,plain,
    ! [X0] :
      ( sP5(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f231]) ).

fof(f231,plain,
    ! [X0] :
      ( sP5(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f162,f230,f229]) ).

fof(f229,plain,
    ! [X0] :
      ( sP4(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( X1 = X2
                      | app(X3,cons(X1,cons(X2,X4))) != X0
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f230,plain,
    ! [X0] :
      ( ( equalelemsP(X0)
      <=> sP4(X0) )
      | ~ sP5(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

fof(f162,plain,
    ! [X0] :
      ( ( equalelemsP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( X1 = X2
                        | app(X3,cons(X1,cons(X2,X4))) != X0
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f161]) ).

fof(f161,plain,
    ! [X0] :
      ( ( equalelemsP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( X1 = X2
                        | app(X3,cons(X1,cons(X2,X4))) != X0
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( equalelemsP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ( app(X3,cons(X1,cons(X2,X4))) = X0
                         => X1 = X2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).

fof(f612,plain,
    ! [X8,X6,X7,X5] :
      ( ~ sP4(app(X7,cons(X5,cons(X6,X8))))
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6)
      | ~ ssItem(X5)
      | X5 = X6 ),
    inference(equality_resolution,[],[f473]) ).

fof(f473,plain,
    ! [X0,X8,X6,X7,X5] :
      ( X5 = X6
      | app(X7,cons(X5,cons(X6,X8))) != X0
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6)
      | ~ ssItem(X5)
      | ~ sP4(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f292,plain,
    ! [X0] :
      ( ( sP4(X0)
        | ( sK27(X0) != sK28(X0)
          & app(sK29(X0),cons(sK27(X0),cons(sK28(X0),sK30(X0)))) = X0
          & ssList(sK30(X0))
          & ssList(sK29(X0))
          & ssItem(sK28(X0))
          & ssItem(sK27(X0)) ) )
      & ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( X5 = X6
                        | app(X7,cons(X5,cons(X6,X8))) != X0
                        | ~ ssList(X8) )
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            | ~ ssItem(X5) )
        | ~ sP4(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29,sK30])],[f287,f291,f290,f289,f288]) ).

fof(f288,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( X1 != X2
                      & app(X3,cons(X1,cons(X2,X4))) = X0
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( sK27(X0) != X2
                    & app(X3,cons(sK27(X0),cons(X2,X4))) = X0
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK27(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f289,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( sK27(X0) != X2
                  & app(X3,cons(sK27(X0),cons(X2,X4))) = X0
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( sK27(X0) != sK28(X0)
                & app(X3,cons(sK27(X0),cons(sK28(X0),X4))) = X0
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK28(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f290,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( sK27(X0) != sK28(X0)
              & app(X3,cons(sK27(X0),cons(sK28(X0),X4))) = X0
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( sK27(X0) != sK28(X0)
            & app(sK29(X0),cons(sK27(X0),cons(sK28(X0),X4))) = X0
            & ssList(X4) )
        & ssList(sK29(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f291,plain,
    ! [X0] :
      ( ? [X4] :
          ( sK27(X0) != sK28(X0)
          & app(sK29(X0),cons(sK27(X0),cons(sK28(X0),X4))) = X0
          & ssList(X4) )
     => ( sK27(X0) != sK28(X0)
        & app(sK29(X0),cons(sK27(X0),cons(sK28(X0),sK30(X0)))) = X0
        & ssList(sK30(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f287,plain,
    ! [X0] :
      ( ( sP4(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( X1 != X2
                        & app(X3,cons(X1,cons(X2,X4))) = X0
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( X5 = X6
                        | app(X7,cons(X5,cons(X6,X8))) != X0
                        | ~ ssList(X8) )
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            | ~ ssItem(X5) )
        | ~ sP4(X0) ) ),
    inference(rectify,[],[f286]) ).

fof(f286,plain,
    ! [X0] :
      ( ( sP4(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( X1 != X2
                        & app(X3,cons(X1,cons(X2,X4))) = X0
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( X1 = X2
                        | app(X3,cons(X1,cons(X2,X4))) != X0
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP4(X0) ) ),
    inference(nnf_transformation,[],[f229]) ).

fof(f474,plain,
    ! [X0] :
      ( ssItem(sK27(X0))
      | sP4(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f475,plain,
    ! [X0] :
      ( ssItem(sK28(X0))
      | sP4(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f476,plain,
    ! [X0] :
      ( ssList(sK29(X0))
      | sP4(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f477,plain,
    ! [X0] :
      ( ssList(sK30(X0))
      | sP4(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f478,plain,
    ! [X0] :
      ( sP4(X0)
      | app(sK29(X0),cons(sK27(X0),cons(sK28(X0),sK30(X0)))) = X0 ),
    inference(cnf_transformation,[],[f292]) ).

fof(f479,plain,
    ! [X0] :
      ( sK27(X0) != sK28(X0)
      | sP4(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f471,plain,
    ! [X0] :
      ( ~ sP5(X0)
      | ~ equalelemsP(X0)
      | sP4(X0) ),
    inference(cnf_transformation,[],[f285]) ).

fof(f285,plain,
    ! [X0] :
      ( ( ( equalelemsP(X0)
          | ~ sP4(X0) )
        & ( sP4(X0)
          | ~ equalelemsP(X0) ) )
      | ~ sP5(X0) ),
    inference(nnf_transformation,[],[f230]) ).

fof(f468,plain,
    ! [X0] :
      ( ssItem(sK26(X0))
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f284]) ).

fof(f284,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ( cons(sK26(X0),nil) = X0
            & ssItem(sK26(X0)) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f282,f283]) ).

fof(f283,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,nil) = X0
          & ssItem(X2) )
     => ( cons(sK26(X0),nil) = X0
        & ssItem(sK26(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f282,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f281]) ).

fof(f281,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X1] :
              ( cons(X1,nil) = X0
              & ssItem(X1) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f160]) ).

fof(f160,plain,
    ! [X0] :
      ( ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

fof(f469,plain,
    ! [X0] :
      ( ~ singletonP(X0)
      | cons(sK26(X0),nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f284]) ).

fof(f611,plain,
    ! [X1] :
      ( singletonP(cons(X1,nil))
      | ~ ssItem(X1)
      | ~ ssList(cons(X1,nil)) ),
    inference(equality_resolution,[],[f470]) ).

fof(f470,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | cons(X1,nil) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f284]) ).

fof(f466,plain,
    ! [X0] :
      ( ssList(sK25(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f280]) ).

fof(f280,plain,
    ! [X0] :
      ( ( tl(X0) = sK25(X0)
        & ssList(sK25(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f159,f279]) ).

fof(f279,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
     => ( tl(X0) = sK25(X0)
        & ssList(sK25(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f158]) ).

fof(f158,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f76]) ).

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

fof(f467,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | tl(X0) = sK25(X0) ),
    inference(cnf_transformation,[],[f280]) ).

fof(f464,plain,
    ! [X0] :
      ( ssItem(sK24(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f278]) ).

fof(f278,plain,
    ! [X0] :
      ( ( hd(X0) = sK24(X0)
        & ssItem(sK24(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f157,f277]) ).

fof(f277,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
     => ( hd(X0) = sK24(X0)
        & ssItem(sK24(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f157,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f156]) ).

fof(f156,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f75,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( hd(X0) = X1
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).

fof(f465,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | hd(X0) = sK24(X0) ),
    inference(cnf_transformation,[],[f278]) ).

fof(f463,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | cons(hd(X0),tl(X0)) = X0 ),
    inference(cnf_transformation,[],[f155]) ).

fof(f155,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f154]) ).

fof(f154,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

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

fof(f462,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f153,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f152]) ).

fof(f152,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f24]) ).

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

fof(f461,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f151]) ).

fof(f151,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

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

fof(f458,plain,
    ! [X0] :
      ( ssList(sK22(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f276]) ).

fof(f276,plain,
    ! [X0] :
      ( ( cons(sK23(X0),sK22(X0)) = X0
        & ssItem(sK23(X0))
        & ssList(sK22(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f149,f275,f274]) ).

fof(f274,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
     => ( ? [X2] :
            ( cons(X2,sK22(X0)) = X0
            & ssItem(X2) )
        & ssList(sK22(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f275,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,sK22(X0)) = X0
          & ssItem(X2) )
     => ( cons(sK23(X0),sK22(X0)) = X0
        & ssItem(sK23(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f149,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f148]) ).

fof(f148,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( ? [X1] :
            ( ? [X2] :
                ( cons(X2,X1) = X0
                & ssItem(X2) )
            & ssList(X1) )
        | nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).

fof(f459,plain,
    ! [X0] :
      ( ssItem(sK23(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f276]) ).

fof(f460,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | cons(sK23(X0),sK22(X0)) = X0 ),
    inference(cnf_transformation,[],[f276]) ).

fof(f457,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f147]) ).

fof(f147,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

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

fof(f456,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f146,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

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

fof(f455,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f145,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).

fof(f454,plain,
    ! [X0] :
      ( rearsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ! [X0] :
      ( rearsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,axiom,
    ! [X0] :
      ( ssList(X0)
     => rearsegP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).

fof(f453,plain,
    ! [X0] :
      ( frontsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f143,plain,
    ! [X0] :
      ( frontsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X0] :
      ( ssList(X0)
     => frontsegP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).

fof(f452,plain,
    ! [X0] :
      ( frontsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ! [X0] :
      ( frontsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0] :
      ( ssList(X0)
     => frontsegP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).

fof(f451,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f141]) ).

fof(f141,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f57]) ).

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

fof(f447,plain,
    ! [X2,X0,X1] :
      ( ~ memberP(app(X1,X2),X0)
      | memberP(X1,X0)
      | memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f273]) ).

fof(f273,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,[],[f272]) ).

fof(f272,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,[],[f139]) ).

fof(f139,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(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(f448,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X1,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f273]) ).

fof(f449,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f273]) ).

fof(f446,plain,
    ! [X0,X1] :
      ( sP3(X0,X1)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f228]) ).

fof(f228,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP3(X0,X1)
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(definition_folding,[],[f138,f227,f226]) ).

fof(f226,plain,
    ! [X1,X0] :
      ( sP2(X1,X0)
    <=> ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f227,plain,
    ! [X0,X1] :
      ( ( strictorderedP(cons(X0,X1))
      <=> sP2(X1,X0) )
      | ~ sP3(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f138,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( strictorderedP(cons(X0,X1))
          <=> ( ( lt(X0,hd(X1))
                & strictorderedP(X1)
                & nil != X1 )
              | nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f70]) ).

fof(f70,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( strictorderedP(cons(X0,X1))
          <=> ( ( lt(X0,hd(X1))
                & strictorderedP(X1)
                & nil != X1 )
              | nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax70) ).

fof(f442,plain,
    ! [X0,X1] :
      ( ~ sP2(X0,X1)
      | nil = X0
      | strictorderedP(X0) ),
    inference(cnf_transformation,[],[f271]) ).

fof(f271,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ( ( ~ lt(X1,hd(X0))
            | ~ strictorderedP(X0)
            | nil = X0 )
          & nil != X0 ) )
      & ( ( lt(X1,hd(X0))
          & strictorderedP(X0)
          & nil != X0 )
        | nil = X0
        | ~ sP2(X0,X1) ) ),
    inference(rectify,[],[f270]) ).

fof(f270,plain,
    ! [X1,X0] :
      ( ( sP2(X1,X0)
        | ( ( ~ lt(X0,hd(X1))
            | ~ strictorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP2(X1,X0) ) ),
    inference(flattening,[],[f269]) ).

fof(f269,plain,
    ! [X1,X0] :
      ( ( sP2(X1,X0)
        | ( ( ~ lt(X0,hd(X1))
            | ~ strictorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP2(X1,X0) ) ),
    inference(nnf_transformation,[],[f226]) ).

fof(f443,plain,
    ! [X0,X1] :
      ( lt(X1,hd(X0))
      | nil = X0
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f271]) ).

fof(f609,plain,
    ! [X1] : sP2(nil,X1),
    inference(equality_resolution,[],[f444]) ).

fof(f444,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | nil != X0 ),
    inference(cnf_transformation,[],[f271]) ).

fof(f445,plain,
    ! [X0,X1] :
      ( ~ lt(X1,hd(X0))
      | sP2(X0,X1)
      | ~ strictorderedP(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f271]) ).

fof(f439,plain,
    ! [X0,X1] :
      ( ~ strictorderedP(cons(X0,X1))
      | sP2(X1,X0)
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f268]) ).

fof(f268,plain,
    ! [X0,X1] :
      ( ( ( strictorderedP(cons(X0,X1))
          | ~ sP2(X1,X0) )
        & ( sP2(X1,X0)
          | ~ strictorderedP(cons(X0,X1)) ) )
      | ~ sP3(X0,X1) ),
    inference(nnf_transformation,[],[f227]) ).

fof(f440,plain,
    ! [X0,X1] :
      ( strictorderedP(cons(X0,X1))
      | ~ sP2(X1,X0)
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f268]) ).

fof(f438,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f225]) ).

fof(f225,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP1(X0,X1)
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(definition_folding,[],[f137,f224,f223]) ).

fof(f223,plain,
    ! [X1,X0] :
      ( sP0(X1,X0)
    <=> ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f224,plain,
    ! [X0,X1] :
      ( ( totalorderedP(cons(X0,X1))
      <=> sP0(X1,X0) )
      | ~ sP1(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f137,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( totalorderedP(cons(X0,X1))
          <=> ( ( leq(X0,hd(X1))
                & totalorderedP(X1)
                & nil != X1 )
              | nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f67,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( totalorderedP(cons(X0,X1))
          <=> ( ( leq(X0,hd(X1))
                & totalorderedP(X1)
                & nil != X1 )
              | nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax67) ).

fof(f434,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | nil = X0
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f267]) ).

fof(f267,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( ~ leq(X1,hd(X0))
            | ~ totalorderedP(X0)
            | nil = X0 )
          & nil != X0 ) )
      & ( ( leq(X1,hd(X0))
          & totalorderedP(X0)
          & nil != X0 )
        | nil = X0
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f266]) ).

fof(f266,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | ( ( ~ leq(X0,hd(X1))
            | ~ totalorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP0(X1,X0) ) ),
    inference(flattening,[],[f265]) ).

fof(f265,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | ( ( ~ leq(X0,hd(X1))
            | ~ totalorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP0(X1,X0) ) ),
    inference(nnf_transformation,[],[f223]) ).

fof(f435,plain,
    ! [X0,X1] :
      ( leq(X1,hd(X0))
      | nil = X0
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f267]) ).

fof(f607,plain,
    ! [X1] : sP0(nil,X1),
    inference(equality_resolution,[],[f436]) ).

fof(f436,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | nil != X0 ),
    inference(cnf_transformation,[],[f267]) ).

fof(f437,plain,
    ! [X0,X1] :
      ( ~ leq(X1,hd(X0))
      | sP0(X0,X1)
      | ~ totalorderedP(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f267]) ).

fof(f431,plain,
    ! [X0,X1] :
      ( ~ totalorderedP(cons(X0,X1))
      | sP0(X1,X0)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f264,plain,
    ! [X0,X1] :
      ( ( ( totalorderedP(cons(X0,X1))
          | ~ sP0(X1,X0) )
        & ( sP0(X1,X0)
          | ~ totalorderedP(cons(X0,X1)) ) )
      | ~ sP1(X0,X1) ),
    inference(nnf_transformation,[],[f224]) ).

fof(f432,plain,
    ! [X0,X1] :
      ( totalorderedP(cons(X0,X1))
      | ~ sP0(X1,X0)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f428,plain,
    ! [X2,X3,X0,X1] :
      ( ~ frontsegP(cons(X0,X2),cons(X1,X3))
      | X0 = X1
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f263]) ).

fof(f263,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
                      | ~ frontsegP(X2,X3)
                      | X0 != X1 )
                    & ( ( frontsegP(X2,X3)
                        & X0 = X1 )
                      | ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f262]) ).

fof(f262,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
                      | ~ frontsegP(X2,X3)
                      | X0 != X1 )
                    & ( ( frontsegP(X2,X3)
                        & X0 = X1 )
                      | ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f136]) ).

fof(f136,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( frontsegP(cons(X0,X2),cons(X1,X3))
                  <=> ( frontsegP(X2,X3)
                      & X0 = X1 ) )
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( frontsegP(cons(X0,X2),cons(X1,X3))
                  <=> ( frontsegP(X2,X3)
                      & X0 = X1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).

fof(f429,plain,
    ! [X2,X3,X0,X1] :
      ( ~ frontsegP(cons(X0,X2),cons(X1,X3))
      | frontsegP(X2,X3)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f263]) ).

fof(f633,plain,
    ! [X2,X3,X1] :
      ( frontsegP(cons(X1,X2),cons(X1,X3))
      | ~ frontsegP(X2,X3)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f606]) ).

fof(f606,plain,
    ! [X2,X3,X1] :
      ( frontsegP(cons(X1,X2),cons(X1,X3))
      | ~ frontsegP(X2,X3)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f430]) ).

fof(f430,plain,
    ! [X2,X3,X0,X1] :
      ( frontsegP(cons(X0,X2),cons(X1,X3))
      | ~ frontsegP(X2,X3)
      | X0 != X1
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f263]) ).

fof(f425,plain,
    ! [X2,X0,X1] :
      ( ~ memberP(cons(X1,X2),X0)
      | X0 = X1
      | memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f261]) ).

fof(f261,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,[],[f260]) ).

fof(f260,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,[],[f135]) ).

fof(f135,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(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(f634,plain,
    ! [X2,X1] :
      ( memberP(cons(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f605]) ).

fof(f605,plain,
    ! [X2,X1] :
      ( memberP(cons(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f426]) ).

fof(f426,plain,
    ! [X2,X0,X1] :
      ( memberP(cons(X1,X2),X0)
      | X0 != X1
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f261]) ).

fof(f427,plain,
    ! [X2,X0,X1] :
      ( memberP(cons(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f261]) ).

fof(f424,plain,
    ! [X2,X0,X1] :
      ( ~ lt(X1,X2)
      | lt(X0,X2)
      | ~ lt(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ lt(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f133]) ).

fof(f133,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ lt(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ( ( lt(X1,X2)
                  & lt(X0,X1) )
               => lt(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).

fof(f423,plain,
    ! [X2,X0,X1] :
      ( ~ lt(X1,X2)
      | lt(X0,X2)
      | ~ leq(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f132]) ).

fof(f132,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f131]) ).

fof(f131,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f91]) ).

fof(f91,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ( ( lt(X1,X2)
                  & leq(X0,X1) )
               => lt(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax91) ).

fof(f422,plain,
    ! [X2,X0,X1] :
      ( ~ leq(X1,X2)
      | leq(X0,X2)
      | ~ leq(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( leq(X0,X2)
              | ~ leq(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f129]) ).

fof(f129,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( leq(X0,X2)
              | ~ leq(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ( ( leq(X1,X2)
                  & leq(X0,X1) )
               => leq(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).

fof(f421,plain,
    ! [X2,X0,X1] :
      ( ~ geq(X1,X2)
      | geq(X0,X2)
      | ~ geq(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f128]) ).

fof(f128,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( geq(X0,X2)
              | ~ geq(X1,X2)
              | ~ geq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( geq(X0,X2)
              | ~ geq(X1,X2)
              | ~ geq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f88]) ).

fof(f88,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ( ( geq(X1,X2)
                  & geq(X0,X1) )
               => geq(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax88) ).

fof(f420,plain,
    ! [X2,X0,X1] :
      ( ~ gt(X1,X2)
      | gt(X0,X2)
      | ~ gt(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f126,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( gt(X0,X2)
              | ~ gt(X1,X2)
              | ~ gt(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f125]) ).

fof(f125,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( gt(X0,X2)
              | ~ gt(X1,X2)
              | ~ gt(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f95]) ).

fof(f95,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ( ( gt(X1,X2)
                  & gt(X0,X1) )
               => gt(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax95) ).

fof(f635,plain,
    ! [X1] :
      ( ~ lt(X1,X1)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f604]) ).

fof(f604,plain,
    ! [X1] :
      ( ~ lt(X1,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f417]) ).

fof(f417,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ lt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f259]) ).

fof(f259,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( lt(X0,X1)
              | ~ leq(X0,X1)
              | X0 = X1 )
            & ( ( leq(X0,X1)
                & X0 != X1 )
              | ~ lt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f258]) ).

fof(f258,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( lt(X0,X1)
              | ~ leq(X0,X1)
              | X0 = X1 )
            & ( ( leq(X0,X1)
                & X0 != X1 )
              | ~ lt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f124]) ).

fof(f124,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( lt(X0,X1)
          <=> ( leq(X0,X1)
              & X0 != X1 ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f93]) ).

fof(f93,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( lt(X0,X1)
          <=> ( leq(X0,X1)
              & X0 != X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93) ).

fof(f418,plain,
    ! [X0,X1] :
      ( ~ lt(X0,X1)
      | leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f259]) ).

fof(f419,plain,
    ! [X0,X1] :
      ( lt(X0,X1)
      | ~ leq(X0,X1)
      | X0 = X1
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f259]) ).

fof(f415,plain,
    ! [X0,X1] :
      ( ~ geq(X0,X1)
      | leq(X1,X0)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f257]) ).

fof(f257,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( geq(X0,X1)
              | ~ leq(X1,X0) )
            & ( leq(X1,X0)
              | ~ geq(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f123]) ).

fof(f123,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( geq(X0,X1)
          <=> leq(X1,X0) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( geq(X0,X1)
          <=> leq(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).

fof(f416,plain,
    ! [X0,X1] :
      ( geq(X0,X1)
      | ~ leq(X1,X0)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f257]) ).

fof(f413,plain,
    ! [X0,X1] :
      ( ~ gt(X0,X1)
      | lt(X1,X0)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f256]) ).

fof(f256,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( gt(X0,X1)
              | ~ lt(X1,X0) )
            & ( lt(X1,X0)
              | ~ gt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( gt(X0,X1)
          <=> lt(X1,X0) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( gt(X0,X1)
          <=> lt(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).

fof(f414,plain,
    ! [X0,X1] :
      ( gt(X0,X1)
      | ~ lt(X1,X0)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f256]) ).

fof(f636,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f603]) ).

fof(f603,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f411]) ).

fof(f411,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f255]) ).

fof(f255,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f121]) ).

fof(f121,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

fof(f412,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f255]) ).

fof(f410,plain,
    ! [X0,X1] :
      ( ~ leq(X1,X0)
      | X0 = X1
      | ~ leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ leq(X1,X0)
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f119]) ).

fof(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ leq(X1,X0)
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( ( leq(X1,X0)
              & leq(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).

fof(f409,plain,
    ! [X0,X1] :
      ( ~ geq(X1,X0)
      | X0 = X1
      | ~ geq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ geq(X1,X0)
          | ~ geq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f117]) ).

fof(f117,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ geq(X1,X0)
          | ~ geq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f87]) ).

fof(f87,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( ( geq(X1,X0)
              & geq(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).

fof(f408,plain,
    ! [X0,X1] :
      ( ~ lt(X1,X0)
      | ~ lt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ lt(X1,X0)
          | ~ lt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f115]) ).

fof(f115,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ lt(X1,X0)
          | ~ lt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( lt(X0,X1)
           => ~ lt(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).

fof(f407,plain,
    ! [X0,X1] :
      ( lt(X0,X1)
      | X0 = X1
      | ~ leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f114]) ).

fof(f114,plain,
    ! [X0] :
      ( ! [X1] :
          ( lt(X0,X1)
          | X0 = X1
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ! [X1] :
          ( lt(X0,X1)
          | X0 = X1
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f92]) ).

fof(f92,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( leq(X0,X1)
           => ( lt(X0,X1)
              | X0 = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax92) ).

fof(f406,plain,
    ! [X0,X1] :
      ( ~ gt(X1,X0)
      | ~ gt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ gt(X1,X0)
          | ~ gt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f111]) ).

fof(f111,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ gt(X1,X0)
          | ~ gt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f94]) ).

fof(f94,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( gt(X0,X1)
           => ~ gt(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94) ).

fof(f405,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f65,axiom,
    ! [X0] :
      ( ssItem(X0)
     => totalorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).

fof(f404,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f68,axiom,
    ! [X0] :
      ( ssItem(X0)
     => strictorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).

fof(f403,plain,
    ! [X0] :
      ( strictorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0] :
      ( strictorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f63]) ).

fof(f63,axiom,
    ! [X0] :
      ( ssItem(X0)
     => strictorderP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).

fof(f402,plain,
    ! [X0] :
      ( totalorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( totalorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f61]) ).

fof(f61,axiom,
    ! [X0] :
      ( ssItem(X0)
     => totalorderP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).

fof(f401,plain,
    ! [X0] :
      ( cyclefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( cyclefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,axiom,
    ! [X0] :
      ( ssItem(X0)
     => cyclefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).

fof(f400,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f71]) ).

fof(f71,axiom,
    ! [X0] :
      ( ssItem(X0)
     => duplicatefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).

fof(f399,plain,
    ! [X0] :
      ( equalelemsP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( equalelemsP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f73]) ).

fof(f73,axiom,
    ! [X0] :
      ( ssItem(X0)
     => equalelemsP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).

fof(f398,plain,
    ! [X0] :
      ( leq(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( leq(X0,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0] :
      ( ssItem(X0)
     => leq(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).

fof(f397,plain,
    ! [X0] :
      ( geq(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( geq(X0,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f89]) ).

fof(f89,axiom,
    ! [X0] :
      ( ssItem(X0)
     => geq(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).

fof(f396,plain,
    ! [X0] :
      ( ~ lt(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ~ lt(X0,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f90]) ).

fof(f90,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ lt(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).

fof(f395,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

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

fof(f393,plain,
    totalorderedP(nil),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,axiom,
    totalorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).

fof(f392,plain,
    strictorderedP(nil),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).

fof(f391,plain,
    totalorderP(nil),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,axiom,
    totalorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).

fof(f390,plain,
    strictorderP(nil),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,axiom,
    strictorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).

fof(f389,plain,
    cyclefreeP(nil),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    cyclefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).

fof(f388,plain,
    duplicatefreeP(nil),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,axiom,
    duplicatefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).

fof(f387,plain,
    equalelemsP(nil),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,axiom,
    equalelemsP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).

fof(f386,plain,
    ~ singletonP(nil),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ~ singletonP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).

fof(f376,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f254]) ).

fof(f377,plain,
    ssList(sK21),
    inference(cnf_transformation,[],[f254]) ).

fof(f380,plain,
    ! [X4] :
      ( ~ segmentP(sK19,X4)
      | ~ segmentP(sK18,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f381,plain,
    ( nil != sK18
    | nil != sK19 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f383,plain,
    ( neq(sK20,nil)
    | nil = sK20 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f385,plain,
    ( frontsegP(sK21,sK20)
    | nil = sK20 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f7296,plain,
    ( ~ rearsegP(nil,nil)
    | ~ spl69_2
    | ~ spl69_21
    | spl69_44 ),
    inference(superposition,[],[f3953,f649]) ).

fof(f3953,plain,
    ( ~ rearsegP(nil,sK18)
    | ~ spl69_21
    | spl69_44 ),
    inference(subsumption_resolution,[],[f3951,f374]) ).

fof(f3951,plain,
    ( ~ rearsegP(nil,sK18)
    | ~ ssList(sK18)
    | ~ spl69_21
    | spl69_44 ),
    inference(resolution,[],[f3947,f3140]) ).

fof(f3140,plain,
    ( ! [X0] :
        ( rearsegP(cons(sK67,sK19),X0)
        | ~ rearsegP(nil,X0)
        | ~ ssList(X0) )
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f3139,f394]) ).

fof(f3139,plain,
    ( ! [X0] :
        ( rearsegP(cons(sK67,sK19),X0)
        | ~ rearsegP(nil,X0)
        | ~ ssList(X0)
        | ~ ssList(nil) )
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f3104,f2725]) ).

fof(f2725,plain,
    ( ssList(cons(sK67,sK19))
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f2724,f2200]) ).

fof(f2724,plain,
    ( ssList(cons(sK67,sK19))
    | ~ ssList(cons(sK67,nil)) ),
    inference(subsumption_resolution,[],[f2715,f375]) ).

fof(f2715,plain,
    ( ssList(cons(sK67,sK19))
    | ~ ssList(sK19)
    | ~ ssList(cons(sK67,nil)) ),
    inference(superposition,[],[f566,f2709]) ).

fof(f566,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f185]) ).

fof(f185,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(app(X0,X1))
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

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

fof(f3104,plain,
    ( ! [X0] :
        ( rearsegP(cons(sK67,sK19),X0)
        | ~ rearsegP(nil,X0)
        | ~ ssList(cons(sK67,sK19))
        | ~ ssList(X0)
        | ~ ssList(nil) )
    | ~ spl69_21 ),
    inference(superposition,[],[f592,f2736]) ).

fof(f2736,plain,
    ( cons(sK67,sK19) = app(cons(sK67,sK19),nil)
    | ~ spl69_21 ),
    inference(resolution,[],[f2725,f456]) ).

fof(f7132,plain,
    ( spl69_1
    | spl69_2
    | ~ spl69_29 ),
    inference(avatar_contradiction_clause,[],[f7131]) ).

fof(f7131,plain,
    ( $false
    | spl69_1
    | spl69_2
    | ~ spl69_29 ),
    inference(subsumption_resolution,[],[f7130,f374]) ).

fof(f7130,plain,
    ( ~ ssList(sK18)
    | spl69_1
    | spl69_2
    | ~ spl69_29 ),
    inference(resolution,[],[f7125,f455]) ).

fof(f7125,plain,
    ( ~ segmentP(sK18,sK18)
    | spl69_1
    | spl69_2
    | ~ spl69_29 ),
    inference(subsumption_resolution,[],[f7124,f374]) ).

fof(f7124,plain,
    ( ~ segmentP(sK18,sK18)
    | ~ ssList(sK18)
    | spl69_1
    | spl69_2
    | ~ spl69_29 ),
    inference(subsumption_resolution,[],[f7120,f1082]) ).

fof(f1082,plain,
    ( neq(sK18,nil)
    | spl69_2 ),
    inference(subsumption_resolution,[],[f1081,f650]) ).

fof(f650,plain,
    ( nil != sK18
    | spl69_2 ),
    inference(avatar_component_clause,[],[f648]) ).

fof(f1081,plain,
    ( nil = sK18
    | neq(sK18,nil) ),
    inference(forward_demodulation,[],[f655,f379]) ).

fof(f655,plain,
    ( neq(sK18,nil)
    | nil = sK20 ),
    inference(forward_demodulation,[],[f383,f379]) ).

fof(f7120,plain,
    ( ~ segmentP(sK18,sK18)
    | ~ neq(sK18,nil)
    | ~ ssList(sK18)
    | spl69_1
    | ~ spl69_29 ),
    inference(resolution,[],[f7119,f380]) ).

fof(f7119,plain,
    ( segmentP(sK19,sK18)
    | spl69_1
    | ~ spl69_29 ),
    inference(subsumption_resolution,[],[f7118,f375]) ).

fof(f7118,plain,
    ( ~ ssList(sK19)
    | segmentP(sK19,sK18)
    | spl69_1
    | ~ spl69_29 ),
    inference(forward_demodulation,[],[f7117,f2989]) ).

fof(f7117,plain,
    ( segmentP(sK19,sK18)
    | ~ ssList(app(sK18,sK66(sK19,sK18)))
    | spl69_1
    | ~ spl69_29 ),
    inference(subsumption_resolution,[],[f7108,f3002]) ).

fof(f7108,plain,
    ( segmentP(sK19,sK18)
    | ~ ssList(app(sK18,sK66(sK19,sK18)))
    | ~ ssList(sK66(sK19,sK18))
    | spl69_1 ),
    inference(superposition,[],[f7034,f2989]) ).

fof(f7034,plain,
    ! [X0] :
      ( segmentP(app(sK18,X0),sK18)
      | ~ ssList(app(sK18,X0))
      | ~ ssList(X0) ),
    inference(forward_demodulation,[],[f7033,f703]) ).

fof(f703,plain,
    sK18 = app(nil,sK18),
    inference(resolution,[],[f457,f374]) ).

fof(f7033,plain,
    ! [X0] :
      ( segmentP(app(sK18,X0),sK18)
      | ~ ssList(X0)
      | ~ ssList(app(app(nil,sK18),X0)) ),
    inference(subsumption_resolution,[],[f7032,f374]) ).

fof(f7032,plain,
    ! [X0] :
      ( segmentP(app(sK18,X0),sK18)
      | ~ ssList(X0)
      | ~ ssList(sK18)
      | ~ ssList(app(app(nil,sK18),X0)) ),
    inference(subsumption_resolution,[],[f6927,f394]) ).

fof(f6927,plain,
    ! [X0] :
      ( segmentP(app(sK18,X0),sK18)
      | ~ ssList(X0)
      | ~ ssList(nil)
      | ~ ssList(sK18)
      | ~ ssList(app(app(nil,sK18),X0)) ),
    inference(superposition,[],[f626,f703]) ).

fof(f626,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,[],[f581]) ).

fof(f581,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,[],[f364]) ).

fof(f364,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK64(X0,X1),X1),sK65(X0,X1)) = X0
                & ssList(sK65(X0,X1))
                & ssList(sK64(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65])],[f361,f363,f362]) ).

fof(f362,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK64(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK64(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f363,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK64(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK64(X0,X1),X1),sK65(X0,X1)) = X0
        & ssList(sK65(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f361,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,[],[f360]) ).

fof(f360,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,[],[f200]) ).

fof(f200,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(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(f6147,plain,
    ~ spl69_61,
    inference(avatar_contradiction_clause,[],[f6146]) ).

fof(f6146,plain,
    ( $false
    | ~ spl69_61 ),
    inference(subsumption_resolution,[],[f6145,f394]) ).

fof(f6145,plain,
    ( ~ ssList(nil)
    | ~ spl69_61 ),
    inference(subsumption_resolution,[],[f6124,f601]) ).

fof(f601,plain,
    ssItem(sK68),
    inference(cnf_transformation,[],[f373]) ).

fof(f6124,plain,
    ( ~ ssItem(sK68)
    | ~ ssList(nil)
    | ~ spl69_61 ),
    inference(trivial_inequality_removal,[],[f6120]) ).

fof(f6120,plain,
    ( nil != nil
    | ~ ssItem(sK68)
    | ~ ssList(nil)
    | ~ spl69_61 ),
    inference(superposition,[],[f558,f6079]) ).

fof(f6079,plain,
    ( nil = cons(sK68,nil)
    | ~ spl69_61 ),
    inference(avatar_component_clause,[],[f6077]) ).

fof(f6077,plain,
    ( spl69_61
  <=> nil = cons(sK68,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_61])]) ).

fof(f558,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f180,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) != X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f18]) ).

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

fof(f6144,plain,
    ~ spl69_61,
    inference(avatar_contradiction_clause,[],[f6143]) ).

fof(f6143,plain,
    ( $false
    | ~ spl69_61 ),
    inference(subsumption_resolution,[],[f6142,f394]) ).

fof(f6142,plain,
    ( ~ ssList(nil)
    | ~ spl69_61 ),
    inference(subsumption_resolution,[],[f6125,f601]) ).

fof(f6125,plain,
    ( ~ ssItem(sK68)
    | ~ ssList(nil)
    | ~ spl69_61 ),
    inference(trivial_inequality_removal,[],[f6119]) ).

fof(f6119,plain,
    ( nil != nil
    | ~ ssItem(sK68)
    | ~ ssList(nil)
    | ~ spl69_61 ),
    inference(superposition,[],[f557,f6079]) ).

fof(f557,plain,
    ! [X0,X1] :
      ( nil != cons(X1,X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f179,plain,
    ! [X0] :
      ( ! [X1] :
          ( nil != cons(X1,X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => nil != cons(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

fof(f6135,plain,
    ( ~ spl69_23
    | ~ spl69_61 ),
    inference(avatar_contradiction_clause,[],[f6134]) ).

fof(f6134,plain,
    ( $false
    | ~ spl69_23
    | ~ spl69_61 ),
    inference(subsumption_resolution,[],[f6133,f2257]) ).

fof(f2257,plain,
    ( ssList(cons(sK68,nil))
    | ~ spl69_23 ),
    inference(avatar_component_clause,[],[f2256]) ).

fof(f2256,plain,
    ( spl69_23
  <=> ssList(cons(sK68,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_23])]) ).

fof(f6133,plain,
    ( ~ ssList(cons(sK68,nil))
    | ~ spl69_61 ),
    inference(subsumption_resolution,[],[f6132,f601]) ).

fof(f6132,plain,
    ( ~ ssItem(sK68)
    | ~ ssList(cons(sK68,nil))
    | ~ spl69_61 ),
    inference(subsumption_resolution,[],[f6107,f386]) ).

fof(f6107,plain,
    ( singletonP(nil)
    | ~ ssItem(sK68)
    | ~ ssList(cons(sK68,nil))
    | ~ spl69_61 ),
    inference(superposition,[],[f611,f6079]) ).

fof(f6131,plain,
    ( spl69_40
    | ~ spl69_61 ),
    inference(avatar_contradiction_clause,[],[f6130]) ).

fof(f6130,plain,
    ( $false
    | spl69_40
    | ~ spl69_61 ),
    inference(subsumption_resolution,[],[f6129,f3546]) ).

fof(f3546,plain,
    ( sK19 != cons(sK68,sK19)
    | spl69_40 ),
    inference(avatar_component_clause,[],[f3545]) ).

fof(f3545,plain,
    ( spl69_40
  <=> sK19 = cons(sK68,sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_40])]) ).

fof(f6129,plain,
    ( sK19 = cons(sK68,sK19)
    | ~ spl69_61 ),
    inference(forward_demodulation,[],[f6096,f704]) ).

fof(f704,plain,
    sK19 = app(nil,sK19),
    inference(resolution,[],[f457,f375]) ).

fof(f6096,plain,
    ( app(nil,sK19) = cons(sK68,sK19)
    | ~ spl69_61 ),
    inference(superposition,[],[f2710,f6079]) ).

fof(f2710,plain,
    cons(sK68,sK19) = app(cons(sK68,nil),sK19),
    inference(resolution,[],[f1901,f601]) ).

fof(f6128,plain,
    ( spl69_28
    | ~ spl69_61 ),
    inference(avatar_contradiction_clause,[],[f6127]) ).

fof(f6127,plain,
    ( $false
    | spl69_28
    | ~ spl69_61 ),
    inference(subsumption_resolution,[],[f6126,f2566]) ).

fof(f2566,plain,
    ( sK18 != cons(sK68,sK18)
    | spl69_28 ),
    inference(avatar_component_clause,[],[f2565]) ).

fof(f2565,plain,
    ( spl69_28
  <=> sK18 = cons(sK68,sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_28])]) ).

fof(f6126,plain,
    ( sK18 = cons(sK68,sK18)
    | ~ spl69_61 ),
    inference(forward_demodulation,[],[f6087,f703]) ).

fof(f6087,plain,
    ( app(nil,sK18) = cons(sK68,sK18)
    | ~ spl69_61 ),
    inference(superposition,[],[f2188,f6079]) ).

fof(f2188,plain,
    cons(sK68,sK18) = app(cons(sK68,nil),sK18),
    inference(resolution,[],[f1900,f601]) ).

fof(f1900,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | cons(X0,sK18) = app(cons(X0,nil),sK18) ),
    inference(resolution,[],[f561,f374]) ).

fof(f6084,plain,
    ( spl69_61
    | spl69_62
    | ~ spl69_23 ),
    inference(avatar_split_clause,[],[f2280,f2256,f6081,f6077]) ).

fof(f6081,plain,
    ( spl69_62
  <=> sK68 = sK24(cons(sK68,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_62])]) ).

fof(f2280,plain,
    ( sK68 = sK24(cons(sK68,nil))
    | nil = cons(sK68,nil)
    | ~ spl69_23 ),
    inference(forward_demodulation,[],[f2272,f1196]) ).

fof(f1196,plain,
    sK68 = hd(cons(sK68,nil)),
    inference(resolution,[],[f978,f601]) ).

fof(f978,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | hd(cons(X0,nil)) = X0 ),
    inference(resolution,[],[f560,f394]) ).

fof(f560,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | hd(cons(X1,X0)) = X1 ),
    inference(cnf_transformation,[],[f182]) ).

fof(f182,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(cons(X1,X0)) = X1
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => hd(cons(X1,X0)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).

fof(f2272,plain,
    ( nil = cons(sK68,nil)
    | hd(cons(sK68,nil)) = sK24(cons(sK68,nil))
    | ~ spl69_23 ),
    inference(resolution,[],[f2257,f465]) ).

fof(f6057,plain,
    ~ spl69_59,
    inference(avatar_contradiction_clause,[],[f6056]) ).

fof(f6056,plain,
    ( $false
    | ~ spl69_59 ),
    inference(subsumption_resolution,[],[f6055,f394]) ).

fof(f6055,plain,
    ( ~ ssList(nil)
    | ~ spl69_59 ),
    inference(subsumption_resolution,[],[f6034,f600]) ).

fof(f6034,plain,
    ( ~ ssItem(sK67)
    | ~ ssList(nil)
    | ~ spl69_59 ),
    inference(trivial_inequality_removal,[],[f6030]) ).

fof(f6030,plain,
    ( nil != nil
    | ~ ssItem(sK67)
    | ~ ssList(nil)
    | ~ spl69_59 ),
    inference(superposition,[],[f558,f5989]) ).

fof(f5989,plain,
    ( nil = cons(sK67,nil)
    | ~ spl69_59 ),
    inference(avatar_component_clause,[],[f5987]) ).

fof(f5987,plain,
    ( spl69_59
  <=> nil = cons(sK67,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_59])]) ).

fof(f6054,plain,
    ~ spl69_59,
    inference(avatar_contradiction_clause,[],[f6053]) ).

fof(f6053,plain,
    ( $false
    | ~ spl69_59 ),
    inference(subsumption_resolution,[],[f6052,f394]) ).

fof(f6052,plain,
    ( ~ ssList(nil)
    | ~ spl69_59 ),
    inference(subsumption_resolution,[],[f6035,f600]) ).

fof(f6035,plain,
    ( ~ ssItem(sK67)
    | ~ ssList(nil)
    | ~ spl69_59 ),
    inference(trivial_inequality_removal,[],[f6029]) ).

fof(f6029,plain,
    ( nil != nil
    | ~ ssItem(sK67)
    | ~ ssList(nil)
    | ~ spl69_59 ),
    inference(superposition,[],[f557,f5989]) ).

fof(f6045,plain,
    ( ~ spl69_21
    | ~ spl69_59 ),
    inference(avatar_contradiction_clause,[],[f6044]) ).

fof(f6044,plain,
    ( $false
    | ~ spl69_21
    | ~ spl69_59 ),
    inference(subsumption_resolution,[],[f6043,f2200]) ).

fof(f6043,plain,
    ( ~ ssList(cons(sK67,nil))
    | ~ spl69_59 ),
    inference(subsumption_resolution,[],[f6042,f600]) ).

fof(f6042,plain,
    ( ~ ssItem(sK67)
    | ~ ssList(cons(sK67,nil))
    | ~ spl69_59 ),
    inference(subsumption_resolution,[],[f6017,f386]) ).

fof(f6017,plain,
    ( singletonP(nil)
    | ~ ssItem(sK67)
    | ~ ssList(cons(sK67,nil))
    | ~ spl69_59 ),
    inference(superposition,[],[f611,f5989]) ).

fof(f6041,plain,
    ( spl69_38
    | ~ spl69_59 ),
    inference(avatar_contradiction_clause,[],[f6040]) ).

fof(f6040,plain,
    ( $false
    | spl69_38
    | ~ spl69_59 ),
    inference(subsumption_resolution,[],[f6039,f3490]) ).

fof(f3490,plain,
    ( sK19 != cons(sK67,sK19)
    | spl69_38 ),
    inference(avatar_component_clause,[],[f3489]) ).

fof(f3489,plain,
    ( spl69_38
  <=> sK19 = cons(sK67,sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_38])]) ).

fof(f6039,plain,
    ( sK19 = cons(sK67,sK19)
    | ~ spl69_59 ),
    inference(forward_demodulation,[],[f6006,f704]) ).

fof(f6006,plain,
    ( app(nil,sK19) = cons(sK67,sK19)
    | ~ spl69_59 ),
    inference(superposition,[],[f2709,f5989]) ).

fof(f6038,plain,
    ( spl69_26
    | ~ spl69_59 ),
    inference(avatar_contradiction_clause,[],[f6037]) ).

fof(f6037,plain,
    ( $false
    | spl69_26
    | ~ spl69_59 ),
    inference(subsumption_resolution,[],[f6036,f2557]) ).

fof(f2557,plain,
    ( sK18 != cons(sK67,sK18)
    | spl69_26 ),
    inference(avatar_component_clause,[],[f2556]) ).

fof(f2556,plain,
    ( spl69_26
  <=> sK18 = cons(sK67,sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_26])]) ).

fof(f6036,plain,
    ( sK18 = cons(sK67,sK18)
    | ~ spl69_59 ),
    inference(forward_demodulation,[],[f5997,f703]) ).

fof(f5997,plain,
    ( app(nil,sK18) = cons(sK67,sK18)
    | ~ spl69_59 ),
    inference(superposition,[],[f2187,f5989]) ).

fof(f2187,plain,
    cons(sK67,sK18) = app(cons(sK67,nil),sK18),
    inference(resolution,[],[f1900,f600]) ).

fof(f5994,plain,
    ( spl69_59
    | spl69_60
    | ~ spl69_21 ),
    inference(avatar_split_clause,[],[f2223,f2199,f5991,f5987]) ).

fof(f5991,plain,
    ( spl69_60
  <=> sK67 = sK24(cons(sK67,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_60])]) ).

fof(f2223,plain,
    ( sK67 = sK24(cons(sK67,nil))
    | nil = cons(sK67,nil)
    | ~ spl69_21 ),
    inference(forward_demodulation,[],[f2215,f1195]) ).

fof(f1195,plain,
    sK67 = hd(cons(sK67,nil)),
    inference(resolution,[],[f978,f600]) ).

fof(f2215,plain,
    ( nil = cons(sK67,nil)
    | hd(cons(sK67,nil)) = sK24(cons(sK67,nil))
    | ~ spl69_21 ),
    inference(resolution,[],[f2200,f465]) ).

fof(f5885,plain,
    ( spl69_1
    | ~ spl69_13
    | ~ spl69_49
    | ~ spl69_55
    | spl69_57 ),
    inference(avatar_contradiction_clause,[],[f5884]) ).

fof(f5884,plain,
    ( $false
    | spl69_1
    | ~ spl69_13
    | ~ spl69_49
    | ~ spl69_55
    | spl69_57 ),
    inference(subsumption_resolution,[],[f5883,f375]) ).

fof(f5883,plain,
    ( ~ ssList(sK19)
    | spl69_1
    | ~ spl69_13
    | ~ spl69_49
    | ~ spl69_55
    | spl69_57 ),
    inference(subsumption_resolution,[],[f5882,f5791]) ).

fof(f5791,plain,
    ( singletonP(sK19)
    | spl69_1
    | ~ spl69_13
    | ~ spl69_49
    | ~ spl69_55 ),
    inference(subsumption_resolution,[],[f5790,f4555]) ).

fof(f4555,plain,
    ( ssList(cons(hd(sK19),nil))
    | ~ spl69_49 ),
    inference(avatar_component_clause,[],[f4554]) ).

fof(f4554,plain,
    ( spl69_49
  <=> ssList(cons(hd(sK19),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_49])]) ).

fof(f5790,plain,
    ( singletonP(sK19)
    | ~ ssList(cons(hd(sK19),nil))
    | spl69_1
    | ~ spl69_13
    | ~ spl69_55 ),
    inference(subsumption_resolution,[],[f5766,f1525]) ).

fof(f1525,plain,
    ( ssItem(hd(sK19))
    | ~ spl69_13 ),
    inference(avatar_component_clause,[],[f1524]) ).

fof(f1524,plain,
    ( spl69_13
  <=> ssItem(hd(sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_13])]) ).

fof(f5766,plain,
    ( singletonP(sK19)
    | ~ ssItem(hd(sK19))
    | ~ ssList(cons(hd(sK19),nil))
    | spl69_1
    | ~ spl69_55 ),
    inference(superposition,[],[f611,f5739]) ).

fof(f5739,plain,
    ( sK19 = cons(hd(sK19),nil)
    | spl69_1
    | ~ spl69_55 ),
    inference(superposition,[],[f1477,f5649]) ).

fof(f5649,plain,
    ( nil = tl(sK19)
    | ~ spl69_55 ),
    inference(avatar_component_clause,[],[f5647]) ).

fof(f5647,plain,
    ( spl69_55
  <=> nil = tl(sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_55])]) ).

fof(f1477,plain,
    ( sK19 = cons(hd(sK19),tl(sK19))
    | spl69_1 ),
    inference(subsumption_resolution,[],[f1444,f646]) ).

fof(f1444,plain,
    ( nil = sK19
    | sK19 = cons(hd(sK19),tl(sK19)) ),
    inference(resolution,[],[f463,f375]) ).

fof(f5882,plain,
    ( ~ singletonP(sK19)
    | ~ ssList(sK19)
    | spl69_57 ),
    inference(resolution,[],[f5876,f468]) ).

fof(f5876,plain,
    ( ~ ssItem(sK26(sK19))
    | spl69_57 ),
    inference(avatar_component_clause,[],[f5874]) ).

fof(f5874,plain,
    ( spl69_57
  <=> ssItem(sK26(sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_57])]) ).

fof(f5881,plain,
    ( ~ spl69_57
    | spl69_58
    | spl69_1
    | ~ spl69_13
    | ~ spl69_49
    | ~ spl69_55 ),
    inference(avatar_split_clause,[],[f5860,f5647,f4554,f1524,f644,f5878,f5874]) ).

fof(f5878,plain,
    ( spl69_58
  <=> memberP(sK19,sK26(sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_58])]) ).

fof(f5860,plain,
    ( memberP(sK19,sK26(sK19))
    | ~ ssItem(sK26(sK19))
    | spl69_1
    | ~ spl69_13
    | ~ spl69_49
    | ~ spl69_55 ),
    inference(subsumption_resolution,[],[f5850,f394]) ).

fof(f5850,plain,
    ( memberP(sK19,sK26(sK19))
    | ~ ssList(nil)
    | ~ ssItem(sK26(sK19))
    | spl69_1
    | ~ spl69_13
    | ~ spl69_49
    | ~ spl69_55 ),
    inference(superposition,[],[f634,f5815]) ).

fof(f5815,plain,
    ( sK19 = cons(sK26(sK19),nil)
    | spl69_1
    | ~ spl69_13
    | ~ spl69_49
    | ~ spl69_55 ),
    inference(subsumption_resolution,[],[f5812,f375]) ).

fof(f5812,plain,
    ( sK19 = cons(sK26(sK19),nil)
    | ~ ssList(sK19)
    | spl69_1
    | ~ spl69_13
    | ~ spl69_49
    | ~ spl69_55 ),
    inference(resolution,[],[f5791,f469]) ).

fof(f5654,plain,
    ( spl69_55
    | spl69_56
    | spl69_1
    | ~ spl69_9
    | ~ spl69_13
    | ~ spl69_17 ),
    inference(avatar_split_clause,[],[f4166,f1735,f1524,f1421,f644,f5651,f5647]) ).

fof(f5651,plain,
    ( spl69_56
  <=> hd(tl(sK19)) = sK24(tl(sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_56])]) ).

fof(f1421,plain,
    ( spl69_9
  <=> ssItem(sK23(sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_9])]) ).

fof(f1735,plain,
    ( spl69_17
  <=> ssList(sK22(sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_17])]) ).

fof(f4166,plain,
    ( hd(tl(sK19)) = sK24(tl(sK19))
    | nil = tl(sK19)
    | spl69_1
    | ~ spl69_9
    | ~ spl69_13
    | ~ spl69_17 ),
    inference(forward_demodulation,[],[f4165,f2010]) ).

fof(f2010,plain,
    ( tl(sK19) = sK22(sK19)
    | spl69_1
    | ~ spl69_9
    | ~ spl69_13
    | ~ spl69_17 ),
    inference(forward_demodulation,[],[f1988,f1801]) ).

fof(f1801,plain,
    ( sK19 = cons(hd(sK19),sK22(sK19))
    | spl69_1
    | ~ spl69_9
    | ~ spl69_17 ),
    inference(superposition,[],[f1374,f1799]) ).

fof(f1799,plain,
    ( hd(sK19) = sK23(sK19)
    | spl69_1
    | ~ spl69_9
    | ~ spl69_17 ),
    inference(forward_demodulation,[],[f1779,f1374]) ).

fof(f1779,plain,
    ( sK23(sK19) = hd(cons(sK23(sK19),sK22(sK19)))
    | ~ spl69_9
    | ~ spl69_17 ),
    inference(resolution,[],[f1754,f1422]) ).

fof(f1422,plain,
    ( ssItem(sK23(sK19))
    | ~ spl69_9 ),
    inference(avatar_component_clause,[],[f1421]) ).

fof(f1754,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | hd(cons(X0,sK22(sK19))) = X0 )
    | ~ spl69_17 ),
    inference(resolution,[],[f1736,f560]) ).

fof(f1736,plain,
    ( ssList(sK22(sK19))
    | ~ spl69_17 ),
    inference(avatar_component_clause,[],[f1735]) ).

fof(f1374,plain,
    ( sK19 = cons(sK23(sK19),sK22(sK19))
    | spl69_1 ),
    inference(subsumption_resolution,[],[f1341,f646]) ).

fof(f1341,plain,
    ( nil = sK19
    | sK19 = cons(sK23(sK19),sK22(sK19)) ),
    inference(resolution,[],[f460,f375]) ).

fof(f1988,plain,
    ( sK22(sK19) = tl(cons(hd(sK19),sK22(sK19)))
    | ~ spl69_13
    | ~ spl69_17 ),
    inference(resolution,[],[f1753,f1525]) ).

fof(f1753,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | sK22(sK19) = tl(cons(X0,sK22(sK19))) )
    | ~ spl69_17 ),
    inference(resolution,[],[f1736,f559]) ).

fof(f559,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | tl(cons(X1,X0)) = X0 ),
    inference(cnf_transformation,[],[f181]) ).

fof(f181,plain,
    ! [X0] :
      ( ! [X1] :
          ( tl(cons(X1,X0)) = X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => tl(cons(X1,X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).

fof(f4165,plain,
    ( nil = tl(sK19)
    | hd(sK22(sK19)) = sK24(sK22(sK19))
    | spl69_1
    | ~ spl69_9
    | ~ spl69_13
    | ~ spl69_17 ),
    inference(forward_demodulation,[],[f1751,f2010]) ).

fof(f1751,plain,
    ( nil = sK22(sK19)
    | hd(sK22(sK19)) = sK24(sK22(sK19))
    | ~ spl69_17 ),
    inference(resolution,[],[f1736,f465]) ).

fof(f5641,plain,
    ( spl69_2
    | ~ spl69_11
    | ~ spl69_47
    | ~ spl69_51
    | spl69_53 ),
    inference(avatar_contradiction_clause,[],[f5640]) ).

fof(f5640,plain,
    ( $false
    | spl69_2
    | ~ spl69_11
    | ~ spl69_47
    | ~ spl69_51
    | spl69_53 ),
    inference(subsumption_resolution,[],[f5639,f374]) ).

fof(f5639,plain,
    ( ~ ssList(sK18)
    | spl69_2
    | ~ spl69_11
    | ~ spl69_47
    | ~ spl69_51
    | spl69_53 ),
    inference(subsumption_resolution,[],[f5638,f5418]) ).

fof(f5418,plain,
    ( singletonP(sK18)
    | spl69_2
    | ~ spl69_11
    | ~ spl69_47
    | ~ spl69_51 ),
    inference(subsumption_resolution,[],[f5417,f4191]) ).

fof(f4191,plain,
    ( ssList(cons(hd(sK18),nil))
    | ~ spl69_47 ),
    inference(avatar_component_clause,[],[f4190]) ).

fof(f4190,plain,
    ( spl69_47
  <=> ssList(cons(hd(sK18),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_47])]) ).

fof(f5417,plain,
    ( singletonP(sK18)
    | ~ ssList(cons(hd(sK18),nil))
    | spl69_2
    | ~ spl69_11
    | ~ spl69_51 ),
    inference(subsumption_resolution,[],[f5397,f1506]) ).

fof(f1506,plain,
    ( ssItem(hd(sK18))
    | ~ spl69_11 ),
    inference(avatar_component_clause,[],[f1505]) ).

fof(f1505,plain,
    ( spl69_11
  <=> ssItem(hd(sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_11])]) ).

fof(f5397,plain,
    ( singletonP(sK18)
    | ~ ssItem(hd(sK18))
    | ~ ssList(cons(hd(sK18),nil))
    | spl69_2
    | ~ spl69_51 ),
    inference(superposition,[],[f611,f5370]) ).

fof(f5370,plain,
    ( sK18 = cons(hd(sK18),nil)
    | spl69_2
    | ~ spl69_51 ),
    inference(superposition,[],[f1476,f5364]) ).

fof(f5364,plain,
    ( nil = tl(sK18)
    | ~ spl69_51 ),
    inference(avatar_component_clause,[],[f5362]) ).

fof(f5362,plain,
    ( spl69_51
  <=> nil = tl(sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_51])]) ).

fof(f1476,plain,
    ( sK18 = cons(hd(sK18),tl(sK18))
    | spl69_2 ),
    inference(subsumption_resolution,[],[f1443,f650]) ).

fof(f1443,plain,
    ( nil = sK18
    | sK18 = cons(hd(sK18),tl(sK18)) ),
    inference(resolution,[],[f463,f374]) ).

fof(f5638,plain,
    ( ~ singletonP(sK18)
    | ~ ssList(sK18)
    | spl69_53 ),
    inference(resolution,[],[f5632,f468]) ).

fof(f5632,plain,
    ( ~ ssItem(sK26(sK18))
    | spl69_53 ),
    inference(avatar_component_clause,[],[f5630]) ).

fof(f5630,plain,
    ( spl69_53
  <=> ssItem(sK26(sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_53])]) ).

fof(f5637,plain,
    ( ~ spl69_53
    | spl69_54
    | spl69_2
    | ~ spl69_11
    | ~ spl69_47
    | ~ spl69_51 ),
    inference(avatar_split_clause,[],[f5535,f5362,f4190,f1505,f648,f5634,f5630]) ).

fof(f5634,plain,
    ( spl69_54
  <=> memberP(sK18,sK26(sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_54])]) ).

fof(f5535,plain,
    ( memberP(sK18,sK26(sK18))
    | ~ ssItem(sK26(sK18))
    | spl69_2
    | ~ spl69_11
    | ~ spl69_47
    | ~ spl69_51 ),
    inference(subsumption_resolution,[],[f5529,f394]) ).

fof(f5529,plain,
    ( memberP(sK18,sK26(sK18))
    | ~ ssList(nil)
    | ~ ssItem(sK26(sK18))
    | spl69_2
    | ~ spl69_11
    | ~ spl69_47
    | ~ spl69_51 ),
    inference(superposition,[],[f634,f5500]) ).

fof(f5500,plain,
    ( sK18 = cons(sK26(sK18),nil)
    | spl69_2
    | ~ spl69_11
    | ~ spl69_47
    | ~ spl69_51 ),
    inference(subsumption_resolution,[],[f5497,f374]) ).

fof(f5497,plain,
    ( sK18 = cons(sK26(sK18),nil)
    | ~ ssList(sK18)
    | spl69_2
    | ~ spl69_11
    | ~ spl69_47
    | ~ spl69_51 ),
    inference(resolution,[],[f5418,f469]) ).

fof(f5369,plain,
    ( spl69_51
    | spl69_52
    | spl69_2
    | ~ spl69_7
    | ~ spl69_11
    | ~ spl69_15 ),
    inference(avatar_split_clause,[],[f4108,f1638,f1505,f1402,f648,f5366,f5362]) ).

fof(f5366,plain,
    ( spl69_52
  <=> hd(tl(sK18)) = sK24(tl(sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_52])]) ).

fof(f1402,plain,
    ( spl69_7
  <=> ssItem(sK23(sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_7])]) ).

fof(f1638,plain,
    ( spl69_15
  <=> ssList(sK22(sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_15])]) ).

fof(f4108,plain,
    ( hd(tl(sK18)) = sK24(tl(sK18))
    | nil = tl(sK18)
    | spl69_2
    | ~ spl69_7
    | ~ spl69_11
    | ~ spl69_15 ),
    inference(forward_demodulation,[],[f4107,f1858]) ).

fof(f1858,plain,
    ( tl(sK18) = sK22(sK18)
    | spl69_2
    | ~ spl69_7
    | ~ spl69_11
    | ~ spl69_15 ),
    inference(forward_demodulation,[],[f1835,f1692]) ).

fof(f1692,plain,
    ( sK18 = cons(hd(sK18),sK22(sK18))
    | spl69_2
    | ~ spl69_7
    | ~ spl69_15 ),
    inference(superposition,[],[f1373,f1690]) ).

fof(f1690,plain,
    ( hd(sK18) = sK23(sK18)
    | spl69_2
    | ~ spl69_7
    | ~ spl69_15 ),
    inference(forward_demodulation,[],[f1670,f1373]) ).

fof(f1670,plain,
    ( sK23(sK18) = hd(cons(sK23(sK18),sK22(sK18)))
    | ~ spl69_7
    | ~ spl69_15 ),
    inference(resolution,[],[f1657,f1403]) ).

fof(f1403,plain,
    ( ssItem(sK23(sK18))
    | ~ spl69_7 ),
    inference(avatar_component_clause,[],[f1402]) ).

fof(f1657,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | hd(cons(X0,sK22(sK18))) = X0 )
    | ~ spl69_15 ),
    inference(resolution,[],[f1639,f560]) ).

fof(f1639,plain,
    ( ssList(sK22(sK18))
    | ~ spl69_15 ),
    inference(avatar_component_clause,[],[f1638]) ).

fof(f1373,plain,
    ( sK18 = cons(sK23(sK18),sK22(sK18))
    | spl69_2 ),
    inference(subsumption_resolution,[],[f1340,f650]) ).

fof(f1340,plain,
    ( nil = sK18
    | sK18 = cons(sK23(sK18),sK22(sK18)) ),
    inference(resolution,[],[f460,f374]) ).

fof(f1835,plain,
    ( sK22(sK18) = tl(cons(hd(sK18),sK22(sK18)))
    | ~ spl69_11
    | ~ spl69_15 ),
    inference(resolution,[],[f1656,f1506]) ).

fof(f1656,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | sK22(sK18) = tl(cons(X0,sK22(sK18))) )
    | ~ spl69_15 ),
    inference(resolution,[],[f1639,f559]) ).

fof(f4107,plain,
    ( nil = tl(sK18)
    | hd(sK22(sK18)) = sK24(sK22(sK18))
    | spl69_2
    | ~ spl69_7
    | ~ spl69_11
    | ~ spl69_15 ),
    inference(forward_demodulation,[],[f1654,f1858]) ).

fof(f1654,plain,
    ( nil = sK22(sK18)
    | hd(sK22(sK18)) = sK24(sK22(sK18))
    | ~ spl69_15 ),
    inference(resolution,[],[f1639,f465]) ).

fof(f4565,plain,
    ( ~ spl69_13
    | spl69_49 ),
    inference(avatar_contradiction_clause,[],[f4564]) ).

fof(f4564,plain,
    ( $false
    | ~ spl69_13
    | spl69_49 ),
    inference(subsumption_resolution,[],[f4563,f394]) ).

fof(f4563,plain,
    ( ~ ssList(nil)
    | ~ spl69_13
    | spl69_49 ),
    inference(subsumption_resolution,[],[f4562,f1525]) ).

fof(f4562,plain,
    ( ~ ssItem(hd(sK19))
    | ~ ssList(nil)
    | spl69_49 ),
    inference(resolution,[],[f4556,f556]) ).

fof(f556,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f178,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

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

fof(f4556,plain,
    ( ~ ssList(cons(hd(sK19),nil))
    | spl69_49 ),
    inference(avatar_component_clause,[],[f4554]) ).

fof(f4561,plain,
    ( ~ spl69_49
    | spl69_50
    | ~ spl69_13 ),
    inference(avatar_split_clause,[],[f4254,f1524,f4558,f4554]) ).

fof(f4558,plain,
    ( spl69_50
  <=> ssList(cons(hd(sK19),sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_50])]) ).

fof(f4254,plain,
    ( ssList(cons(hd(sK19),sK18))
    | ~ ssList(cons(hd(sK19),nil))
    | ~ spl69_13 ),
    inference(subsumption_resolution,[],[f4245,f374]) ).

fof(f4245,plain,
    ( ssList(cons(hd(sK19),sK18))
    | ~ ssList(sK18)
    | ~ ssList(cons(hd(sK19),nil))
    | ~ spl69_13 ),
    inference(superposition,[],[f566,f2167]) ).

fof(f2167,plain,
    ( cons(hd(sK19),sK18) = app(cons(hd(sK19),nil),sK18)
    | ~ spl69_13 ),
    inference(resolution,[],[f1900,f1525]) ).

fof(f4201,plain,
    ( ~ spl69_11
    | spl69_47 ),
    inference(avatar_contradiction_clause,[],[f4200]) ).

fof(f4200,plain,
    ( $false
    | ~ spl69_11
    | spl69_47 ),
    inference(subsumption_resolution,[],[f4199,f394]) ).

fof(f4199,plain,
    ( ~ ssList(nil)
    | ~ spl69_11
    | spl69_47 ),
    inference(subsumption_resolution,[],[f4198,f1506]) ).

fof(f4198,plain,
    ( ~ ssItem(hd(sK18))
    | ~ ssList(nil)
    | spl69_47 ),
    inference(resolution,[],[f4192,f556]) ).

fof(f4192,plain,
    ( ~ ssList(cons(hd(sK18),nil))
    | spl69_47 ),
    inference(avatar_component_clause,[],[f4190]) ).

fof(f4197,plain,
    ( ~ spl69_47
    | spl69_48
    | ~ spl69_11 ),
    inference(avatar_split_clause,[],[f4180,f1505,f4194,f4190]) ).

fof(f4194,plain,
    ( spl69_48
  <=> ssList(cons(hd(sK18),sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_48])]) ).

fof(f4180,plain,
    ( ssList(cons(hd(sK18),sK18))
    | ~ ssList(cons(hd(sK18),nil))
    | ~ spl69_11 ),
    inference(subsumption_resolution,[],[f4171,f374]) ).

fof(f4171,plain,
    ( ssList(cons(hd(sK18),sK18))
    | ~ ssList(sK18)
    | ~ ssList(cons(hd(sK18),nil))
    | ~ spl69_11 ),
    inference(superposition,[],[f566,f2166]) ).

fof(f2166,plain,
    ( cons(hd(sK18),sK18) = app(cons(hd(sK18),nil),sK18)
    | ~ spl69_11 ),
    inference(resolution,[],[f1900,f1506]) ).

fof(f3972,plain,
    ( ~ spl69_45
    | spl69_46
    | ~ spl69_21
    | ~ spl69_22 ),
    inference(avatar_split_clause,[],[f3906,f2203,f2199,f3969,f3965]) ).

fof(f3965,plain,
    ( spl69_45
  <=> rearsegP(sK18,cons(sK67,sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_45])]) ).

fof(f3969,plain,
    ( spl69_46
  <=> rearsegP(cons(sK67,sK18),sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_46])]) ).

fof(f2203,plain,
    ( spl69_22
  <=> ssList(cons(sK67,sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_22])]) ).

fof(f3906,plain,
    ( rearsegP(cons(sK67,sK18),sK19)
    | ~ rearsegP(sK18,cons(sK67,sK19))
    | ~ spl69_21
    | ~ spl69_22 ),
    inference(subsumption_resolution,[],[f3905,f2725]) ).

fof(f3905,plain,
    ( rearsegP(cons(sK67,sK18),sK19)
    | ~ rearsegP(sK18,cons(sK67,sK19))
    | ~ ssList(cons(sK67,sK19))
    | ~ spl69_21
    | ~ spl69_22 ),
    inference(subsumption_resolution,[],[f3885,f2205]) ).

fof(f2205,plain,
    ( ssList(cons(sK67,sK18))
    | ~ spl69_22 ),
    inference(avatar_component_clause,[],[f2203]) ).

fof(f3885,plain,
    ( rearsegP(cons(sK67,sK18),sK19)
    | ~ ssList(cons(sK67,sK18))
    | ~ rearsegP(sK18,cons(sK67,sK19))
    | ~ ssList(cons(sK67,sK19))
    | ~ spl69_21 ),
    inference(resolution,[],[f3806,f3164]) ).

fof(f3164,plain,
    ( ! [X0] :
        ( rearsegP(cons(sK67,sK18),X0)
        | ~ rearsegP(sK18,X0)
        | ~ ssList(X0) )
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f3163,f374]) ).

fof(f3163,plain,
    ( ! [X0] :
        ( rearsegP(cons(sK67,sK18),X0)
        | ~ rearsegP(sK18,X0)
        | ~ ssList(X0)
        | ~ ssList(sK18) )
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f3120,f2200]) ).

fof(f3120,plain,
    ! [X0] :
      ( rearsegP(cons(sK67,sK18),X0)
      | ~ rearsegP(sK18,X0)
      | ~ ssList(cons(sK67,nil))
      | ~ ssList(X0)
      | ~ ssList(sK18) ),
    inference(superposition,[],[f592,f2187]) ).

fof(f3806,plain,
    ( ! [X0] :
        ( ~ rearsegP(X0,cons(sK67,sK19))
        | rearsegP(X0,sK19)
        | ~ ssList(X0) )
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f3805,f2725]) ).

fof(f3805,plain,
    ( ! [X0] :
        ( rearsegP(X0,sK19)
        | ~ rearsegP(X0,cons(sK67,sK19))
        | ~ ssList(cons(sK67,sK19))
        | ~ ssList(X0) )
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f3758,f375]) ).

fof(f3758,plain,
    ( ! [X0] :
        ( rearsegP(X0,sK19)
        | ~ rearsegP(X0,cons(sK67,sK19))
        | ~ ssList(sK19)
        | ~ ssList(cons(sK67,sK19))
        | ~ ssList(X0) )
    | ~ spl69_21 ),
    inference(resolution,[],[f596,f2733]) ).

fof(f2733,plain,
    ( rearsegP(cons(sK67,sK19),sK19)
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f2732,f375]) ).

fof(f2732,plain,
    ( rearsegP(cons(sK67,sK19),sK19)
    | ~ ssList(sK19)
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f2718,f2200]) ).

fof(f2718,plain,
    ( rearsegP(cons(sK67,sK19),sK19)
    | ~ ssList(cons(sK67,nil))
    | ~ ssList(sK19) ),
    inference(superposition,[],[f2226,f2709]) ).

fof(f2226,plain,
    ! [X2,X1] :
      ( rearsegP(app(X2,X1),X1)
      | ~ ssList(X2)
      | ~ ssList(X1) ),
    inference(subsumption_resolution,[],[f625,f566]) ).

fof(f625,plain,
    ! [X2,X1] :
      ( rearsegP(app(X2,X1),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X2,X1)) ),
    inference(equality_resolution,[],[f577]) ).

fof(f577,plain,
    ! [X2,X0,X1] :
      ( rearsegP(X0,X1)
      | app(X2,X1) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f359]) ).

fof(f359,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( rearsegP(X0,X1)
              | ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(sK63(X0,X1),X1) = X0
                & ssList(sK63(X0,X1)) )
              | ~ rearsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK63])],[f357,f358]) ).

fof(f358,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X3,X1) = X0
          & ssList(X3) )
     => ( app(sK63(X0,X1),X1) = X0
        & ssList(sK63(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f357,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( rearsegP(X0,X1)
              | ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X3] :
                  ( app(X3,X1) = X0
                  & ssList(X3) )
              | ~ rearsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f356]) ).

fof(f356,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( rearsegP(X0,X1)
              | ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( app(X2,X1) = X0
                  & ssList(X2) )
              | ~ rearsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f199]) ).

fof(f199,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( rearsegP(X0,X1)
          <=> ? [X2] :
                ( app(X2,X1) = X0
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( rearsegP(X0,X1)
          <=> ? [X2] :
                ( app(X2,X1) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).

fof(f596,plain,
    ! [X2,X0,X1] :
      ( ~ rearsegP(X1,X2)
      | rearsegP(X0,X2)
      | ~ rearsegP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f216]) ).

fof(f216,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( rearsegP(X0,X2)
              | ~ rearsegP(X1,X2)
              | ~ rearsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f215]) ).

fof(f215,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( rearsegP(X0,X2)
              | ~ rearsegP(X1,X2)
              | ~ rearsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f47,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( ( rearsegP(X1,X2)
                  & rearsegP(X0,X1) )
               => rearsegP(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).

fof(f3949,plain,
    ( ~ spl69_43
    | spl69_44
    | ~ spl69_21
    | ~ spl69_22 ),
    inference(avatar_split_clause,[],[f3848,f2203,f2199,f3946,f3942]) ).

fof(f3942,plain,
    ( spl69_43
  <=> rearsegP(sK19,cons(sK67,sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_43])]) ).

fof(f3848,plain,
    ( rearsegP(cons(sK67,sK19),sK18)
    | ~ rearsegP(sK19,cons(sK67,sK18))
    | ~ spl69_21
    | ~ spl69_22 ),
    inference(subsumption_resolution,[],[f3847,f2205]) ).

fof(f3847,plain,
    ( rearsegP(cons(sK67,sK19),sK18)
    | ~ rearsegP(sK19,cons(sK67,sK18))
    | ~ ssList(cons(sK67,sK18))
    | ~ spl69_21
    | ~ spl69_22 ),
    inference(subsumption_resolution,[],[f3831,f2725]) ).

fof(f3831,plain,
    ( rearsegP(cons(sK67,sK19),sK18)
    | ~ ssList(cons(sK67,sK19))
    | ~ rearsegP(sK19,cons(sK67,sK18))
    | ~ ssList(cons(sK67,sK18))
    | ~ spl69_21
    | ~ spl69_22 ),
    inference(resolution,[],[f3802,f3168]) ).

fof(f3802,plain,
    ( ! [X0] :
        ( ~ rearsegP(X0,cons(sK67,sK18))
        | rearsegP(X0,sK18)
        | ~ ssList(X0) )
    | ~ spl69_21
    | ~ spl69_22 ),
    inference(subsumption_resolution,[],[f3801,f2205]) ).

fof(f3801,plain,
    ( ! [X0] :
        ( rearsegP(X0,sK18)
        | ~ rearsegP(X0,cons(sK67,sK18))
        | ~ ssList(cons(sK67,sK18))
        | ~ ssList(X0) )
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f3756,f374]) ).

fof(f3756,plain,
    ( ! [X0] :
        ( rearsegP(X0,sK18)
        | ~ rearsegP(X0,cons(sK67,sK18))
        | ~ ssList(sK18)
        | ~ ssList(cons(sK67,sK18))
        | ~ ssList(X0) )
    | ~ spl69_21 ),
    inference(resolution,[],[f596,f2325]) ).

fof(f2325,plain,
    ( rearsegP(cons(sK67,sK18),sK18)
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f2324,f374]) ).

fof(f2324,plain,
    ( rearsegP(cons(sK67,sK18),sK18)
    | ~ ssList(sK18)
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f2316,f2200]) ).

fof(f2316,plain,
    ( rearsegP(cons(sK67,sK18),sK18)
    | ~ ssList(cons(sK67,nil))
    | ~ ssList(sK18) ),
    inference(superposition,[],[f2226,f2187]) ).

fof(f3720,plain,
    ( ~ spl69_41
    | spl69_42
    | ~ spl69_33
    | ~ spl69_34 ),
    inference(avatar_split_clause,[],[f3424,f3398,f3394,f3717,f3713]) ).

fof(f3713,plain,
    ( spl69_41
  <=> rearsegP(sK66(sK19,sK19),sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_41])]) ).

fof(f3717,plain,
    ( spl69_42
  <=> sK19 = sK66(sK19,sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_42])]) ).

fof(f3394,plain,
    ( spl69_33
  <=> ssList(sK66(sK19,sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_33])]) ).

fof(f3398,plain,
    ( spl69_34
  <=> rearsegP(sK19,sK66(sK19,sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_34])]) ).

fof(f3424,plain,
    ( sK19 = sK66(sK19,sK19)
    | ~ rearsegP(sK66(sK19,sK19),sK19)
    | ~ spl69_33
    | ~ spl69_34 ),
    inference(subsumption_resolution,[],[f3423,f3395]) ).

fof(f3395,plain,
    ( ssList(sK66(sK19,sK19))
    | ~ spl69_33 ),
    inference(avatar_component_clause,[],[f3394]) ).

fof(f3423,plain,
    ( sK19 = sK66(sK19,sK19)
    | ~ rearsegP(sK66(sK19,sK19),sK19)
    | ~ ssList(sK66(sK19,sK19))
    | ~ spl69_34 ),
    inference(subsumption_resolution,[],[f3420,f375]) ).

fof(f3420,plain,
    ( sK19 = sK66(sK19,sK19)
    | ~ rearsegP(sK66(sK19,sK19),sK19)
    | ~ ssList(sK19)
    | ~ ssList(sK66(sK19,sK19))
    | ~ spl69_34 ),
    inference(resolution,[],[f3400,f570]) ).

fof(f570,plain,
    ! [X0,X1] :
      ( ~ rearsegP(X1,X0)
      | X0 = X1
      | ~ rearsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f193]) ).

fof(f193,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ rearsegP(X1,X0)
          | ~ rearsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f192]) ).

fof(f192,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ rearsegP(X1,X0)
          | ~ rearsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ( rearsegP(X1,X0)
              & rearsegP(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).

fof(f3400,plain,
    ( rearsegP(sK19,sK66(sK19,sK19))
    | ~ spl69_34 ),
    inference(avatar_component_clause,[],[f3398]) ).

fof(f3548,plain,
    ( ~ spl69_39
    | spl69_40
    | ~ spl69_23 ),
    inference(avatar_split_clause,[],[f2857,f2256,f3545,f3541]) ).

fof(f3541,plain,
    ( spl69_39
  <=> rearsegP(sK19,cons(sK68,sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_39])]) ).

fof(f2857,plain,
    ( sK19 = cons(sK68,sK19)
    | ~ rearsegP(sK19,cons(sK68,sK19))
    | ~ spl69_23 ),
    inference(subsumption_resolution,[],[f2856,f375]) ).

fof(f2856,plain,
    ( sK19 = cons(sK68,sK19)
    | ~ rearsegP(sK19,cons(sK68,sK19))
    | ~ ssList(sK19)
    | ~ spl69_23 ),
    inference(subsumption_resolution,[],[f2855,f2824]) ).

fof(f2824,plain,
    ( ssList(cons(sK68,sK19))
    | ~ spl69_23 ),
    inference(subsumption_resolution,[],[f2823,f2257]) ).

fof(f2823,plain,
    ( ssList(cons(sK68,sK19))
    | ~ ssList(cons(sK68,nil)) ),
    inference(subsumption_resolution,[],[f2814,f375]) ).

fof(f2814,plain,
    ( ssList(cons(sK68,sK19))
    | ~ ssList(sK19)
    | ~ ssList(cons(sK68,nil)) ),
    inference(superposition,[],[f566,f2710]) ).

fof(f2855,plain,
    ( sK19 = cons(sK68,sK19)
    | ~ rearsegP(sK19,cons(sK68,sK19))
    | ~ ssList(cons(sK68,sK19))
    | ~ ssList(sK19)
    | ~ spl69_23 ),
    inference(resolution,[],[f2832,f570]) ).

fof(f2832,plain,
    ( rearsegP(cons(sK68,sK19),sK19)
    | ~ spl69_23 ),
    inference(subsumption_resolution,[],[f2831,f375]) ).

fof(f2831,plain,
    ( rearsegP(cons(sK68,sK19),sK19)
    | ~ ssList(sK19)
    | ~ spl69_23 ),
    inference(subsumption_resolution,[],[f2817,f2257]) ).

fof(f2817,plain,
    ( rearsegP(cons(sK68,sK19),sK19)
    | ~ ssList(cons(sK68,nil))
    | ~ ssList(sK19) ),
    inference(superposition,[],[f2226,f2710]) ).

fof(f3492,plain,
    ( ~ spl69_37
    | spl69_38
    | ~ spl69_21 ),
    inference(avatar_split_clause,[],[f2757,f2199,f3489,f3485]) ).

fof(f3485,plain,
    ( spl69_37
  <=> rearsegP(sK19,cons(sK67,sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_37])]) ).

fof(f2757,plain,
    ( sK19 = cons(sK67,sK19)
    | ~ rearsegP(sK19,cons(sK67,sK19))
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f2756,f375]) ).

fof(f2756,plain,
    ( sK19 = cons(sK67,sK19)
    | ~ rearsegP(sK19,cons(sK67,sK19))
    | ~ ssList(sK19)
    | ~ spl69_21 ),
    inference(subsumption_resolution,[],[f2755,f2725]) ).

fof(f2755,plain,
    ( sK19 = cons(sK67,sK19)
    | ~ rearsegP(sK19,cons(sK67,sK19))
    | ~ ssList(cons(sK67,sK19))
    | ~ ssList(sK19)
    | ~ spl69_21 ),
    inference(resolution,[],[f2733,f570]) ).

fof(f3459,plain,
    ( ~ spl69_35
    | spl69_36
    | ~ spl69_29
    | ~ spl69_30 ),
    inference(avatar_split_clause,[],[f3031,f3005,f3001,f3456,f3452]) ).

fof(f3452,plain,
    ( spl69_35
  <=> rearsegP(sK66(sK19,sK18),sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_35])]) ).

fof(f3456,plain,
    ( spl69_36
  <=> sK19 = sK66(sK19,sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_36])]) ).

fof(f3005,plain,
    ( spl69_30
  <=> rearsegP(sK19,sK66(sK19,sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_30])]) ).

fof(f3031,plain,
    ( sK19 = sK66(sK19,sK18)
    | ~ rearsegP(sK66(sK19,sK18),sK19)
    | ~ spl69_29
    | ~ spl69_30 ),
    inference(subsumption_resolution,[],[f3030,f3002]) ).

fof(f3030,plain,
    ( sK19 = sK66(sK19,sK18)
    | ~ rearsegP(sK66(sK19,sK18),sK19)
    | ~ ssList(sK66(sK19,sK18))
    | ~ spl69_30 ),
    inference(subsumption_resolution,[],[f3027,f375]) ).

fof(f3027,plain,
    ( sK19 = sK66(sK19,sK18)
    | ~ rearsegP(sK66(sK19,sK18),sK19)
    | ~ ssList(sK19)
    | ~ ssList(sK66(sK19,sK18))
    | ~ spl69_30 ),
    inference(resolution,[],[f3007,f570]) ).

fof(f3007,plain,
    ( rearsegP(sK19,sK66(sK19,sK18))
    | ~ spl69_30 ),
    inference(avatar_component_clause,[],[f3005]) ).

fof(f3406,plain,
    ( spl69_1
    | ~ spl69_29
    | ~ spl69_31
    | ~ spl69_32
    | spl69_33 ),
    inference(avatar_contradiction_clause,[],[f3405]) ).

fof(f3405,plain,
    ( $false
    | spl69_1
    | ~ spl69_29
    | ~ spl69_31
    | ~ spl69_32
    | spl69_33 ),
    inference(subsumption_resolution,[],[f3404,f375]) ).

fof(f3404,plain,
    ( ~ ssList(sK19)
    | spl69_1
    | ~ spl69_29
    | ~ spl69_31
    | ~ spl69_32
    | spl69_33 ),
    inference(subsumption_resolution,[],[f3403,f3369]) ).

fof(f3369,plain,
    ( frontsegP(sK19,sK19)
    | spl69_1
    | ~ spl69_29
    | ~ spl69_31
    | ~ spl69_32 ),
    inference(superposition,[],[f3342,f3361]) ).

fof(f3361,plain,
    ( sK19 = sK63(sK19,nil)
    | spl69_1
    | ~ spl69_29
    | ~ spl69_31 ),
    inference(forward_demodulation,[],[f3349,f3210]) ).

fof(f3210,plain,
    ( sK19 = app(sK63(sK19,nil),nil)
    | spl69_1
    | ~ spl69_29 ),
    inference(subsumption_resolution,[],[f3209,f375]) ).

fof(f3209,plain,
    ( sK19 = app(sK63(sK19,nil),nil)
    | ~ ssList(sK19)
    | spl69_1
    | ~ spl69_29 ),
    inference(subsumption_resolution,[],[f3207,f394]) ).

fof(f3207,plain,
    ( sK19 = app(sK63(sK19,nil),nil)
    | ~ ssList(nil)
    | ~ ssList(sK19)
    | spl69_1
    | ~ spl69_29 ),
    inference(resolution,[],[f3206,f576]) ).

fof(f576,plain,
    ! [X0,X1] :
      ( ~ rearsegP(X0,X1)
      | app(sK63(X0,X1),X1) = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f359]) ).

fof(f3349,plain,
    ( sK63(sK19,nil) = app(sK63(sK19,nil),nil)
    | ~ spl69_31 ),
    inference(resolution,[],[f3337,f456]) ).

fof(f3337,plain,
    ( ssList(sK63(sK19,nil))
    | ~ spl69_31 ),
    inference(avatar_component_clause,[],[f3336]) ).

fof(f3336,plain,
    ( spl69_31
  <=> ssList(sK63(sK19,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_31])]) ).

fof(f3342,plain,
    ( frontsegP(sK19,sK63(sK19,nil))
    | ~ spl69_32 ),
    inference(avatar_component_clause,[],[f3340]) ).

fof(f3340,plain,
    ( spl69_32
  <=> frontsegP(sK19,sK63(sK19,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_32])]) ).

fof(f3403,plain,
    ( ~ frontsegP(sK19,sK19)
    | ~ ssList(sK19)
    | spl69_33 ),
    inference(duplicate_literal_removal,[],[f3402]) ).

fof(f3402,plain,
    ( ~ frontsegP(sK19,sK19)
    | ~ ssList(sK19)
    | ~ ssList(sK19)
    | spl69_33 ),
    inference(resolution,[],[f3396,f582]) ).

fof(f582,plain,
    ! [X0,X1] :
      ( ssList(sK66(X0,X1))
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f368]) ).

fof(f3396,plain,
    ( ~ ssList(sK66(sK19,sK19))
    | spl69_33 ),
    inference(avatar_component_clause,[],[f3394]) ).

fof(f3401,plain,
    ( ~ spl69_33
    | spl69_34
    | spl69_1
    | ~ spl69_29
    | ~ spl69_31
    | ~ spl69_32 ),
    inference(avatar_split_clause,[],[f3391,f3340,f3336,f3001,f644,f3398,f3394]) ).

fof(f3391,plain,
    ( rearsegP(sK19,sK66(sK19,sK19))
    | ~ ssList(sK66(sK19,sK19))
    | spl69_1
    | ~ spl69_29
    | ~ spl69_31
    | ~ spl69_32 ),
    inference(subsumption_resolution,[],[f3387,f375]) ).

fof(f3387,plain,
    ( rearsegP(sK19,sK66(sK19,sK19))
    | ~ ssList(sK19)
    | ~ ssList(sK66(sK19,sK19))
    | spl69_1
    | ~ spl69_29
    | ~ spl69_31
    | ~ spl69_32 ),
    inference(superposition,[],[f2226,f3379]) ).

fof(f3379,plain,
    ( sK19 = app(sK19,sK66(sK19,sK19))
    | spl69_1
    | ~ spl69_29
    | ~ spl69_31
    | ~ spl69_32 ),
    inference(subsumption_resolution,[],[f3378,f375]) ).

fof(f3378,plain,
    ( sK19 = app(sK19,sK66(sK19,sK19))
    | ~ ssList(sK19)
    | spl69_1
    | ~ spl69_29
    | ~ spl69_31
    | ~ spl69_32 ),
    inference(duplicate_literal_removal,[],[f3375]) ).

fof(f3375,plain,
    ( sK19 = app(sK19,sK66(sK19,sK19))
    | ~ ssList(sK19)
    | ~ ssList(sK19)
    | spl69_1
    | ~ spl69_29
    | ~ spl69_31
    | ~ spl69_32 ),
    inference(resolution,[],[f3369,f583]) ).

fof(f3348,plain,
    ( spl69_1
    | ~ spl69_29
    | spl69_31 ),
    inference(avatar_contradiction_clause,[],[f3347]) ).

fof(f3347,plain,
    ( $false
    | spl69_1
    | ~ spl69_29
    | spl69_31 ),
    inference(subsumption_resolution,[],[f3346,f375]) ).

fof(f3346,plain,
    ( ~ ssList(sK19)
    | spl69_1
    | ~ spl69_29
    | spl69_31 ),
    inference(subsumption_resolution,[],[f3345,f394]) ).

fof(f3345,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK19)
    | spl69_1
    | ~ spl69_29
    | spl69_31 ),
    inference(subsumption_resolution,[],[f3344,f3206]) ).

fof(f3344,plain,
    ( ~ rearsegP(sK19,nil)
    | ~ ssList(nil)
    | ~ ssList(sK19)
    | spl69_31 ),
    inference(resolution,[],[f3338,f575]) ).

fof(f575,plain,
    ! [X0,X1] :
      ( ssList(sK63(X0,X1))
      | ~ rearsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f359]) ).

fof(f3338,plain,
    ( ~ ssList(sK63(sK19,nil))
    | spl69_31 ),
    inference(avatar_component_clause,[],[f3336]) ).

fof(f3343,plain,
    ( ~ spl69_31
    | spl69_32
    | spl69_1
    | ~ spl69_29 ),
    inference(avatar_split_clause,[],[f3220,f3001,f644,f3340,f3336]) ).

fof(f3220,plain,
    ( frontsegP(sK19,sK63(sK19,nil))
    | ~ ssList(sK63(sK19,nil))
    | spl69_1
    | ~ spl69_29 ),
    inference(subsumption_resolution,[],[f3218,f394]) ).

fof(f3218,plain,
    ( frontsegP(sK19,sK63(sK19,nil))
    | ~ ssList(nil)
    | ~ ssList(sK63(sK19,nil))
    | spl69_1
    | ~ spl69_29 ),
    inference(superposition,[],[f2356,f3210]) ).

fof(f2356,plain,
    ! [X2,X1] :
      ( frontsegP(app(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1) ),
    inference(subsumption_resolution,[],[f627,f566]) ).

fof(f627,plain,
    ! [X2,X1] :
      ( frontsegP(app(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X1,X2)) ),
    inference(equality_resolution,[],[f584]) ).

fof(f584,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X1)
      | app(X1,X2) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f368]) ).

fof(f3013,plain,
    ( spl69_1
    | spl69_29 ),
    inference(avatar_contradiction_clause,[],[f3012]) ).

fof(f3012,plain,
    ( $false
    | spl69_1
    | spl69_29 ),
    inference(subsumption_resolution,[],[f3011,f375]) ).

fof(f3011,plain,
    ( ~ ssList(sK19)
    | spl69_1
    | spl69_29 ),
    inference(subsumption_resolution,[],[f3010,f374]) ).

fof(f3010,plain,
    ( ~ ssList(sK18)
    | ~ ssList(sK19)
    | spl69_1
    | spl69_29 ),
    inference(subsumption_resolution,[],[f3009,f659]) ).

fof(f3009,plain,
    ( ~ frontsegP(sK19,sK18)
    | ~ ssList(sK18)
    | ~ ssList(sK19)
    | spl69_29 ),
    inference(resolution,[],[f3003,f582]) ).

fof(f3003,plain,
    ( ~ ssList(sK66(sK19,sK18))
    | spl69_29 ),
    inference(avatar_component_clause,[],[f3001]) ).

fof(f3008,plain,
    ( ~ spl69_29
    | spl69_30
    | spl69_1 ),
    inference(avatar_split_clause,[],[f2999,f644,f3005,f3001]) ).

fof(f2999,plain,
    ( rearsegP(sK19,sK66(sK19,sK18))
    | ~ ssList(sK66(sK19,sK18))
    | spl69_1 ),
    inference(subsumption_resolution,[],[f2995,f374]) ).

fof(f2995,plain,
    ( rearsegP(sK19,sK66(sK19,sK18))
    | ~ ssList(sK18)
    | ~ ssList(sK66(sK19,sK18))
    | spl69_1 ),
    inference(superposition,[],[f2226,f2989]) ).

fof(f2568,plain,
    ( ~ spl69_27
    | spl69_28
    | ~ spl69_23
    | ~ spl69_24 ),
    inference(avatar_split_clause,[],[f2333,f2260,f2256,f2565,f2561]) ).

fof(f2561,plain,
    ( spl69_27
  <=> rearsegP(sK18,cons(sK68,sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_27])]) ).

fof(f2260,plain,
    ( spl69_24
  <=> ssList(cons(sK68,sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_24])]) ).

fof(f2333,plain,
    ( sK18 = cons(sK68,sK18)
    | ~ rearsegP(sK18,cons(sK68,sK18))
    | ~ spl69_23
    | ~ spl69_24 ),
    inference(subsumption_resolution,[],[f2332,f374]) ).

fof(f2332,plain,
    ( sK18 = cons(sK68,sK18)
    | ~ rearsegP(sK18,cons(sK68,sK18))
    | ~ ssList(sK18)
    | ~ spl69_23
    | ~ spl69_24 ),
    inference(subsumption_resolution,[],[f2331,f2262]) ).

fof(f2262,plain,
    ( ssList(cons(sK68,sK18))
    | ~ spl69_24 ),
    inference(avatar_component_clause,[],[f2260]) ).

fof(f2331,plain,
    ( sK18 = cons(sK68,sK18)
    | ~ rearsegP(sK18,cons(sK68,sK18))
    | ~ ssList(cons(sK68,sK18))
    | ~ ssList(sK18)
    | ~ spl69_23 ),
    inference(resolution,[],[f2327,f570]) ).

fof(f2327,plain,
    ( rearsegP(cons(sK68,sK18),sK18)
    | ~ spl69_23 ),
    inference(subsumption_resolution,[],[f2326,f374]) ).

fof(f2326,plain,
    ( rearsegP(cons(sK68,sK18),sK18)
    | ~ ssList(sK18)
    | ~ spl69_23 ),
    inference(subsumption_resolution,[],[f2317,f2257]) ).

fof(f2317,plain,
    ( rearsegP(cons(sK68,sK18),sK18)
    | ~ ssList(cons(sK68,nil))
    | ~ ssList(sK18) ),
    inference(superposition,[],[f2226,f2188]) ).

fof(f2559,plain,
    ( ~ spl69_25
    | spl69_26
    | ~ spl69_21
    | ~ spl69_22 ),
    inference(avatar_split_clause,[],[f2330,f2203,f2199,f2556,f2552]) ).

fof(f2552,plain,
    ( spl69_25
  <=> rearsegP(sK18,cons(sK67,sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_25])]) ).

fof(f2330,plain,
    ( sK18 = cons(sK67,sK18)
    | ~ rearsegP(sK18,cons(sK67,sK18))
    | ~ spl69_21
    | ~ spl69_22 ),
    inference(subsumption_resolution,[],[f2329,f374]) ).

fof(f2329,plain,
    ( sK18 = cons(sK67,sK18)
    | ~ rearsegP(sK18,cons(sK67,sK18))
    | ~ ssList(sK18)
    | ~ spl69_21
    | ~ spl69_22 ),
    inference(subsumption_resolution,[],[f2328,f2205]) ).

fof(f2328,plain,
    ( sK18 = cons(sK67,sK18)
    | ~ rearsegP(sK18,cons(sK67,sK18))
    | ~ ssList(cons(sK67,sK18))
    | ~ ssList(sK18)
    | ~ spl69_21 ),
    inference(resolution,[],[f2325,f570]) ).

fof(f2267,plain,
    spl69_23,
    inference(avatar_contradiction_clause,[],[f2266]) ).

fof(f2266,plain,
    ( $false
    | spl69_23 ),
    inference(subsumption_resolution,[],[f2265,f394]) ).

fof(f2265,plain,
    ( ~ ssList(nil)
    | spl69_23 ),
    inference(subsumption_resolution,[],[f2264,f601]) ).

fof(f2264,plain,
    ( ~ ssItem(sK68)
    | ~ ssList(nil)
    | spl69_23 ),
    inference(resolution,[],[f2258,f556]) ).

fof(f2258,plain,
    ( ~ ssList(cons(sK68,nil))
    | spl69_23 ),
    inference(avatar_component_clause,[],[f2256]) ).

fof(f2263,plain,
    ( ~ spl69_23
    | spl69_24 ),
    inference(avatar_split_clause,[],[f2254,f2260,f2256]) ).

fof(f2254,plain,
    ( ssList(cons(sK68,sK18))
    | ~ ssList(cons(sK68,nil)) ),
    inference(subsumption_resolution,[],[f2250,f374]) ).

fof(f2250,plain,
    ( ssList(cons(sK68,sK18))
    | ~ ssList(sK18)
    | ~ ssList(cons(sK68,nil)) ),
    inference(superposition,[],[f566,f2188]) ).

fof(f2210,plain,
    spl69_21,
    inference(avatar_contradiction_clause,[],[f2209]) ).

fof(f2209,plain,
    ( $false
    | spl69_21 ),
    inference(subsumption_resolution,[],[f2208,f394]) ).

fof(f2208,plain,
    ( ~ ssList(nil)
    | spl69_21 ),
    inference(subsumption_resolution,[],[f2207,f600]) ).

fof(f2207,plain,
    ( ~ ssItem(sK67)
    | ~ ssList(nil)
    | spl69_21 ),
    inference(resolution,[],[f2201,f556]) ).

fof(f2201,plain,
    ( ~ ssList(cons(sK67,nil))
    | spl69_21 ),
    inference(avatar_component_clause,[],[f2199]) ).

fof(f2206,plain,
    ( ~ spl69_21
    | spl69_22 ),
    inference(avatar_split_clause,[],[f2197,f2203,f2199]) ).

fof(f2197,plain,
    ( ssList(cons(sK67,sK18))
    | ~ ssList(cons(sK67,nil)) ),
    inference(subsumption_resolution,[],[f2193,f374]) ).

fof(f2193,plain,
    ( ssList(cons(sK67,sK18))
    | ~ ssList(sK18)
    | ~ ssList(cons(sK67,nil)) ),
    inference(superposition,[],[f566,f2187]) ).

fof(f2086,plain,
    ( ~ spl69_19
    | spl69_20
    | spl69_1 ),
    inference(avatar_split_clause,[],[f2077,f644,f2083,f2079]) ).

fof(f2079,plain,
    ( spl69_19
  <=> frontsegP(sK18,sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_19])]) ).

fof(f2083,plain,
    ( spl69_20
  <=> sK18 = sK19 ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_20])]) ).

fof(f2077,plain,
    ( sK18 = sK19
    | ~ frontsegP(sK18,sK19)
    | spl69_1 ),
    inference(subsumption_resolution,[],[f2076,f374]) ).

fof(f2076,plain,
    ( sK18 = sK19
    | ~ frontsegP(sK18,sK19)
    | ~ ssList(sK18)
    | spl69_1 ),
    inference(subsumption_resolution,[],[f2072,f375]) ).

fof(f2072,plain,
    ( sK18 = sK19
    | ~ frontsegP(sK18,sK19)
    | ~ ssList(sK19)
    | ~ ssList(sK18)
    | spl69_1 ),
    inference(resolution,[],[f572,f659]) ).

fof(f572,plain,
    ! [X0,X1] :
      ( ~ frontsegP(X1,X0)
      | X0 = X1
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f197]) ).

fof(f197,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ frontsegP(X1,X0)
          | ~ frontsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f196]) ).

fof(f196,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ frontsegP(X1,X0)
          | ~ frontsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ( frontsegP(X1,X0)
              & frontsegP(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).

fof(f1746,plain,
    ( spl69_1
    | spl69_17 ),
    inference(avatar_contradiction_clause,[],[f1745]) ).

fof(f1745,plain,
    ( $false
    | spl69_1
    | spl69_17 ),
    inference(subsumption_resolution,[],[f1744,f375]) ).

fof(f1744,plain,
    ( ~ ssList(sK19)
    | spl69_1
    | spl69_17 ),
    inference(subsumption_resolution,[],[f1743,f646]) ).

fof(f1743,plain,
    ( nil = sK19
    | ~ ssList(sK19)
    | spl69_17 ),
    inference(resolution,[],[f1737,f458]) ).

fof(f1737,plain,
    ( ~ ssList(sK22(sK19))
    | spl69_17 ),
    inference(avatar_component_clause,[],[f1735]) ).

fof(f1742,plain,
    ( ~ spl69_17
    | spl69_18
    | spl69_1
    | ~ spl69_9 ),
    inference(avatar_split_clause,[],[f1733,f1421,f644,f1739,f1735]) ).

fof(f1739,plain,
    ( spl69_18
  <=> memberP(sK19,sK23(sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_18])]) ).

fof(f1733,plain,
    ( memberP(sK19,sK23(sK19))
    | ~ ssList(sK22(sK19))
    | spl69_1
    | ~ spl69_9 ),
    inference(subsumption_resolution,[],[f1398,f1422]) ).

fof(f1398,plain,
    ( memberP(sK19,sK23(sK19))
    | ~ ssList(sK22(sK19))
    | ~ ssItem(sK23(sK19))
    | spl69_1 ),
    inference(superposition,[],[f634,f1374]) ).

fof(f1649,plain,
    ( spl69_2
    | spl69_15 ),
    inference(avatar_contradiction_clause,[],[f1648]) ).

fof(f1648,plain,
    ( $false
    | spl69_2
    | spl69_15 ),
    inference(subsumption_resolution,[],[f1647,f374]) ).

fof(f1647,plain,
    ( ~ ssList(sK18)
    | spl69_2
    | spl69_15 ),
    inference(subsumption_resolution,[],[f1646,f650]) ).

fof(f1646,plain,
    ( nil = sK18
    | ~ ssList(sK18)
    | spl69_15 ),
    inference(resolution,[],[f1640,f458]) ).

fof(f1640,plain,
    ( ~ ssList(sK22(sK18))
    | spl69_15 ),
    inference(avatar_component_clause,[],[f1638]) ).

fof(f1645,plain,
    ( ~ spl69_15
    | spl69_16
    | spl69_2
    | ~ spl69_7 ),
    inference(avatar_split_clause,[],[f1636,f1402,f648,f1642,f1638]) ).

fof(f1642,plain,
    ( spl69_16
  <=> memberP(sK18,sK23(sK18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_16])]) ).

fof(f1636,plain,
    ( memberP(sK18,sK23(sK18))
    | ~ ssList(sK22(sK18))
    | spl69_2
    | ~ spl69_7 ),
    inference(subsumption_resolution,[],[f1388,f1403]) ).

fof(f1388,plain,
    ( memberP(sK18,sK23(sK18))
    | ~ ssList(sK22(sK18))
    | ~ ssItem(sK23(sK18))
    | spl69_2 ),
    inference(superposition,[],[f634,f1373]) ).

fof(f1535,plain,
    ( spl69_1
    | spl69_13 ),
    inference(avatar_contradiction_clause,[],[f1534]) ).

fof(f1534,plain,
    ( $false
    | spl69_1
    | spl69_13 ),
    inference(subsumption_resolution,[],[f1533,f375]) ).

fof(f1533,plain,
    ( ~ ssList(sK19)
    | spl69_1
    | spl69_13 ),
    inference(subsumption_resolution,[],[f1532,f646]) ).

fof(f1532,plain,
    ( nil = sK19
    | ~ ssList(sK19)
    | spl69_13 ),
    inference(resolution,[],[f1526,f461]) ).

fof(f1526,plain,
    ( ~ ssItem(hd(sK19))
    | spl69_13 ),
    inference(avatar_component_clause,[],[f1524]) ).

fof(f1531,plain,
    ( ~ spl69_13
    | ~ spl69_14
    | spl69_1 ),
    inference(avatar_split_clause,[],[f1503,f644,f1528,f1524]) ).

fof(f1528,plain,
    ( spl69_14
  <=> sK19 = tl(sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_14])]) ).

fof(f1503,plain,
    ( sK19 != tl(sK19)
    | ~ ssItem(hd(sK19))
    | spl69_1 ),
    inference(subsumption_resolution,[],[f1502,f375]) ).

fof(f1502,plain,
    ( sK19 != tl(sK19)
    | ~ ssItem(hd(sK19))
    | ~ ssList(sK19)
    | spl69_1 ),
    inference(inner_rewriting,[],[f1500]) ).

fof(f1500,plain,
    ( sK19 != tl(sK19)
    | ~ ssItem(hd(sK19))
    | ~ ssList(tl(sK19))
    | spl69_1 ),
    inference(superposition,[],[f558,f1477]) ).

fof(f1516,plain,
    ( spl69_2
    | spl69_11 ),
    inference(avatar_contradiction_clause,[],[f1515]) ).

fof(f1515,plain,
    ( $false
    | spl69_2
    | spl69_11 ),
    inference(subsumption_resolution,[],[f1514,f374]) ).

fof(f1514,plain,
    ( ~ ssList(sK18)
    | spl69_2
    | spl69_11 ),
    inference(subsumption_resolution,[],[f1513,f650]) ).

fof(f1513,plain,
    ( nil = sK18
    | ~ ssList(sK18)
    | spl69_11 ),
    inference(resolution,[],[f1507,f461]) ).

fof(f1507,plain,
    ( ~ ssItem(hd(sK18))
    | spl69_11 ),
    inference(avatar_component_clause,[],[f1505]) ).

fof(f1512,plain,
    ( ~ spl69_11
    | ~ spl69_12
    | spl69_2 ),
    inference(avatar_split_clause,[],[f1493,f648,f1509,f1505]) ).

fof(f1509,plain,
    ( spl69_12
  <=> sK18 = tl(sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_12])]) ).

fof(f1493,plain,
    ( sK18 != tl(sK18)
    | ~ ssItem(hd(sK18))
    | spl69_2 ),
    inference(subsumption_resolution,[],[f1492,f374]) ).

fof(f1492,plain,
    ( sK18 != tl(sK18)
    | ~ ssItem(hd(sK18))
    | ~ ssList(sK18)
    | spl69_2 ),
    inference(inner_rewriting,[],[f1490]) ).

fof(f1490,plain,
    ( sK18 != tl(sK18)
    | ~ ssItem(hd(sK18))
    | ~ ssList(tl(sK18))
    | spl69_2 ),
    inference(superposition,[],[f558,f1476]) ).

fof(f1432,plain,
    ( spl69_1
    | spl69_9 ),
    inference(avatar_contradiction_clause,[],[f1431]) ).

fof(f1431,plain,
    ( $false
    | spl69_1
    | spl69_9 ),
    inference(subsumption_resolution,[],[f1430,f375]) ).

fof(f1430,plain,
    ( ~ ssList(sK19)
    | spl69_1
    | spl69_9 ),
    inference(subsumption_resolution,[],[f1429,f646]) ).

fof(f1429,plain,
    ( nil = sK19
    | ~ ssList(sK19)
    | spl69_9 ),
    inference(resolution,[],[f1423,f459]) ).

fof(f1423,plain,
    ( ~ ssItem(sK23(sK19))
    | spl69_9 ),
    inference(avatar_component_clause,[],[f1421]) ).

fof(f1428,plain,
    ( ~ spl69_9
    | ~ spl69_10
    | spl69_1 ),
    inference(avatar_split_clause,[],[f1400,f644,f1425,f1421]) ).

fof(f1425,plain,
    ( spl69_10
  <=> sK19 = sK22(sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_10])]) ).

fof(f1400,plain,
    ( sK19 != sK22(sK19)
    | ~ ssItem(sK23(sK19))
    | spl69_1 ),
    inference(subsumption_resolution,[],[f1399,f375]) ).

fof(f1399,plain,
    ( sK19 != sK22(sK19)
    | ~ ssItem(sK23(sK19))
    | ~ ssList(sK19)
    | spl69_1 ),
    inference(inner_rewriting,[],[f1397]) ).

fof(f1397,plain,
    ( sK19 != sK22(sK19)
    | ~ ssItem(sK23(sK19))
    | ~ ssList(sK22(sK19))
    | spl69_1 ),
    inference(superposition,[],[f558,f1374]) ).

fof(f1413,plain,
    ( spl69_2
    | spl69_7 ),
    inference(avatar_contradiction_clause,[],[f1412]) ).

fof(f1412,plain,
    ( $false
    | spl69_2
    | spl69_7 ),
    inference(subsumption_resolution,[],[f1411,f374]) ).

fof(f1411,plain,
    ( ~ ssList(sK18)
    | spl69_2
    | spl69_7 ),
    inference(subsumption_resolution,[],[f1410,f650]) ).

fof(f1410,plain,
    ( nil = sK18
    | ~ ssList(sK18)
    | spl69_7 ),
    inference(resolution,[],[f1404,f459]) ).

fof(f1404,plain,
    ( ~ ssItem(sK23(sK18))
    | spl69_7 ),
    inference(avatar_component_clause,[],[f1402]) ).

fof(f1409,plain,
    ( ~ spl69_7
    | ~ spl69_8
    | spl69_2 ),
    inference(avatar_split_clause,[],[f1390,f648,f1406,f1402]) ).

fof(f1406,plain,
    ( spl69_8
  <=> sK18 = sK22(sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_8])]) ).

fof(f1390,plain,
    ( sK18 != sK22(sK18)
    | ~ ssItem(sK23(sK18))
    | spl69_2 ),
    inference(subsumption_resolution,[],[f1389,f374]) ).

fof(f1389,plain,
    ( sK18 != sK22(sK18)
    | ~ ssItem(sK23(sK18))
    | ~ ssList(sK18)
    | spl69_2 ),
    inference(inner_rewriting,[],[f1387]) ).

fof(f1387,plain,
    ( sK18 != sK22(sK18)
    | ~ ssItem(sK23(sK18))
    | ~ ssList(sK22(sK18))
    | spl69_2 ),
    inference(superposition,[],[f558,f1373]) ).

fof(f1100,plain,
    ( ~ spl69_1
    | spl69_2 ),
    inference(avatar_contradiction_clause,[],[f1099]) ).

fof(f1099,plain,
    ( $false
    | ~ spl69_1
    | spl69_2 ),
    inference(subsumption_resolution,[],[f1098,f374]) ).

fof(f1098,plain,
    ( ~ ssList(sK18)
    | ~ spl69_1
    | spl69_2 ),
    inference(subsumption_resolution,[],[f1097,f650]) ).

fof(f1097,plain,
    ( nil = sK18
    | ~ ssList(sK18)
    | ~ spl69_1
    | spl69_2 ),
    inference(resolution,[],[f1095,f554]) ).

fof(f554,plain,
    ! [X0] :
      ( ~ frontsegP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f349,plain,
    ! [X0] :
      ( ( ( frontsegP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ frontsegP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f177]) ).

fof(f177,plain,
    ! [X0] :
      ( ( frontsegP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( frontsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).

fof(f1095,plain,
    ( frontsegP(nil,sK18)
    | ~ spl69_1
    | spl69_2 ),
    inference(forward_demodulation,[],[f1079,f645]) ).

fof(f645,plain,
    ( nil = sK19
    | ~ spl69_1 ),
    inference(avatar_component_clause,[],[f644]) ).

fof(f1079,plain,
    ( frontsegP(sK19,sK18)
    | spl69_2 ),
    inference(subsumption_resolution,[],[f1078,f650]) ).

fof(f1078,plain,
    ( nil = sK18
    | frontsegP(sK19,sK18) ),
    inference(forward_demodulation,[],[f661,f379]) ).

fof(f661,plain,
    ( frontsegP(sK19,sK18)
    | nil = sK20 ),
    inference(forward_demodulation,[],[f660,f378]) ).

fof(f660,plain,
    ( frontsegP(sK21,sK18)
    | nil = sK20 ),
    inference(forward_demodulation,[],[f385,f379]) ).

fof(f1069,plain,
    ( spl69_1
    | spl69_3 ),
    inference(avatar_contradiction_clause,[],[f1068]) ).

fof(f1068,plain,
    ( $false
    | spl69_1
    | spl69_3 ),
    inference(subsumption_resolution,[],[f1067,f375]) ).

fof(f1067,plain,
    ( ~ ssList(sK19)
    | spl69_1
    | spl69_3 ),
    inference(subsumption_resolution,[],[f1066,f394]) ).

fof(f1066,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK19)
    | spl69_1
    | spl69_3 ),
    inference(subsumption_resolution,[],[f1063,f646]) ).

fof(f1063,plain,
    ( nil = sK19
    | ~ ssList(nil)
    | ~ ssList(sK19)
    | spl69_3 ),
    inference(resolution,[],[f574,f769]) ).

fof(f769,plain,
    ( ~ neq(sK19,nil)
    | spl69_3 ),
    inference(avatar_component_clause,[],[f767]) ).

fof(f767,plain,
    ( spl69_3
  <=> neq(sK19,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_3])]) ).

fof(f574,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f355]) ).

fof(f795,plain,
    ( ~ spl69_5
    | ~ spl69_6
    | spl69_1
    | spl69_3 ),
    inference(avatar_split_clause,[],[f786,f767,f644,f792,f788]) ).

fof(f788,plain,
    ( spl69_5
  <=> ssItem(sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_5])]) ).

fof(f792,plain,
    ( spl69_6
  <=> ssItem(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_6])]) ).

fof(f786,plain,
    ( ~ ssItem(nil)
    | ~ ssItem(sK19)
    | spl69_1
    | spl69_3 ),
    inference(subsumption_resolution,[],[f783,f646]) ).

fof(f783,plain,
    ( nil = sK19
    | ~ ssItem(nil)
    | ~ ssItem(sK19)
    | spl69_3 ),
    inference(resolution,[],[f412,f769]) ).

fof(f774,plain,
    ( ~ spl69_3
    | ~ spl69_4 ),
    inference(avatar_split_clause,[],[f765,f771,f767]) ).

fof(f771,plain,
    ( spl69_4
  <=> segmentP(sK18,sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_4])]) ).

fof(f765,plain,
    ( ~ segmentP(sK18,sK19)
    | ~ neq(sK19,nil) ),
    inference(subsumption_resolution,[],[f764,f375]) ).

fof(f764,plain,
    ( ~ segmentP(sK18,sK19)
    | ~ neq(sK19,nil)
    | ~ ssList(sK19) ),
    inference(duplicate_literal_removal,[],[f763]) ).

fof(f763,plain,
    ( ~ segmentP(sK18,sK19)
    | ~ neq(sK19,nil)
    | ~ ssList(sK19)
    | ~ ssList(sK19) ),
    inference(resolution,[],[f380,f455]) ).

fof(f651,plain,
    ( ~ spl69_1
    | ~ spl69_2 ),
    inference(avatar_split_clause,[],[f381,f648,f644]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem    : SWC070+1 : TPTP v8.2.0. Released v2.4.0.
% 0.03/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32  % Computer : n008.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Sun May 19 03:23:08 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  % (32635)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35  % (32644)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.35  % (32643)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.35  % (32642)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.35  % (32637)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35  % (32640)WARNING: value z3 for option sas not known
% 0.12/0.35  % (32640)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.18/0.36  % (32641)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.36  % (32636)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.38  TRYING [1]
% 0.18/0.38  TRYING [1]
% 0.18/0.38  TRYING [2]
% 0.18/0.38  TRYING [2]
% 0.18/0.39  TRYING [3]
% 0.18/0.39  TRYING [3]
% 0.18/0.42  TRYING [4]
% 0.18/0.44  TRYING [4]
% 0.18/0.54  TRYING [5]
% 1.55/0.56  TRYING [5]
% 2.35/0.66  % (32640)First to succeed.
% 2.35/0.67  % (32640)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-32635"
% 2.35/0.67  % (32640)Refutation found. Thanks to Tanya!
% 2.35/0.67  % SZS status Theorem for theBenchmark
% 2.35/0.67  % SZS output start Proof for theBenchmark
% See solution above
% 2.35/0.67  % (32640)------------------------------
% 2.35/0.67  % (32640)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.35/0.67  % (32640)Termination reason: Refutation
% 2.35/0.67  
% 2.35/0.67  % (32640)Memory used [KB]: 5901
% 2.35/0.67  % (32640)Time elapsed: 0.318 s
% 2.35/0.67  % (32640)Instructions burned: 712 (million)
% 2.35/0.67  % (32635)Success in time 0.335 s
%------------------------------------------------------------------------------