TSTP Solution File: SWC342+1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWC342+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 04:32:42 EDT 2024

% Result   : Theorem 149.83s 27.59s
% Output   : Refutation 150.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :  142
% Syntax   : Number of formulae    :  923 (  80 unt;  46 typ;   0 def)
%            Number of atoms       : 3189 ( 708 equ;   0 cnn)
%            Maximal formula atoms :   19 (   3 avg)
%            Number of connectives : 7418 (1026   ~;1133   |; 123   &;4548   @)
%                                         (  26 <=>; 562  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   49 (  49   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   49 (  46 usr;  10 con; 0-2 aty)
%            Number of variables   :  853 (   0   ^ 820   !;  33   ?; 853   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ssList_type,type,
    ssList: $i > $o ).

thf(ssItem_type,type,
    ssItem: $i > $o ).

thf(cons_type,type,
    cons: $i > $i > $i ).

thf(nil_type,type,
    nil: $i ).

thf(memberP_type,type,
    memberP: $i > $i > $o ).

thf(segmentP_type,type,
    segmentP: $i > $i > $o ).

thf(totalorderedP_type,type,
    totalorderedP: $i > $o ).

thf(strictorderedP_type,type,
    strictorderedP: $i > $o ).

thf(lt_type,type,
    lt: $i > $i > $o ).

thf(frontsegP_type,type,
    frontsegP: $i > $i > $o ).

thf(gt_type,type,
    gt: $i > $i > $o ).

thf(hd_type,type,
    hd: $i > $i ).

thf(cyclefreeP_type,type,
    cyclefreeP: $i > $o ).

thf(app_type,type,
    app: $i > $i > $i ).

thf(leq_type,type,
    leq: $i > $i > $o ).

thf(strictorderP_type,type,
    strictorderP: $i > $o ).

thf(duplicatefreeP_type,type,
    duplicatefreeP: $i > $o ).

thf(singletonP_type,type,
    singletonP: $i > $o ).

thf(neq_type,type,
    neq: $i > $i > $o ).

thf(tl_type,type,
    tl: $i > $i ).

thf(totalorderP_type,type,
    totalorderP: $i > $o ).

thf(rearsegP_type,type,
    rearsegP: $i > $i > $o ).

thf(equalelemsP_type,type,
    equalelemsP: $i > $o ).

thf(geq_type,type,
    geq: $i > $i > $o ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(sk5_type,type,
    sk5: $i ).

thf(sk6_type,type,
    sk6: $i > $i ).

thf(sk7_type,type,
    sk7: $i > $i ).

thf(sk8_type,type,
    sk8: $i > $i ).

thf(sk9_type,type,
    sk9: $i > $i ).

thf(sk10_type,type,
    sk10: $i > $i ).

thf(sk11_type,type,
    sk11: $i > $i ).

thf(sk12_type,type,
    sk12: $i > $i ).

thf(sk13_type,type,
    sk13: $i > $i ).

thf(sk14_type,type,
    sk14: $i > $i ).

thf(sk15_type,type,
    sk15: $i > $i ).

thf(sk16_type,type,
    sk16: $i > $i ).

thf(sk17_type,type,
    sk17: $i > $i ).

thf(sk18_type,type,
    sk18: $i > $i ).

thf(sk19_type,type,
    sk19: $i > $i ).

thf(sk20_type,type,
    sk20: $i > $i ).

thf(sk38_type,type,
    sk38: $i ).

thf(sk39_type,type,
    sk39: $i ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ! [D: $i] :
                  ( ( ssList @ D )
                 => ( ( B != D )
                    | ( A != C )
                    | ( ! [E: $i] :
                          ( ( ssItem @ E )
                         => ( ( ( cons @ E @ nil )
                             != C )
                            | ~ ( memberP @ D @ E ) ) )
                      & ( ( nil != D )
                        | ( nil != C ) ) )
                    | ( ( segmentP @ B @ A )
                      & ( totalorderedP @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ssList @ A )
       => ! [B: $i] :
            ( ( ssList @ B )
           => ! [C: $i] :
                ( ( ssList @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ( ( B != D )
                      | ( A != C )
                      | ( ! [E: $i] :
                            ( ( ssItem @ E )
                           => ( ( ( cons @ E @ nil )
                               != C )
                              | ~ ( memberP @ D @ E ) ) )
                        & ( ( nil != D )
                          | ( nil != C ) ) )
                      | ( ( segmentP @ B @ A )
                        & ( totalorderedP @ A ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(98,plain,
    ~ ! [A: $i] :
        ( ( ssList @ A )
       => ! [B: $i] :
            ( ( ssList @ B )
           => ! [C: $i] :
                ( ( ssList @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ( ( B != D )
                      | ( A != C )
                      | ( ! [E: $i] :
                            ( ( ssItem @ E )
                           => ( ( ( cons @ E @ nil )
                               != C )
                              | ~ ( memberP @ D @ E ) ) )
                        & ( ( nil != D )
                          | ( nil != C ) ) )
                      | ( ( segmentP @ B @ A )
                        & ( totalorderedP @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(105,plain,
    ssList @ sk2,
    inference(cnf,[status(esa)],[98]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( strictorderedP @ A )
      <=> ! [B: $i] :
            ( ( ssItem @ B )
           => ! [C: $i] :
                ( ( ssItem @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ! [E: $i] :
                        ( ( ssList @ E )
                       => ! [F: $i] :
                            ( ( ssList @ F )
                           => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                = A )
                             => ( lt @ B @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).

thf(219,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( ( strictorderedP @ A )
         => ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ( lt @ B @ C ) ) ) ) ) ) ) )
        & ( ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ( lt @ B @ C ) ) ) ) ) ) )
         => ( strictorderedP @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(224,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssList @ ( sk18 @ A ) )
      | ( strictorderedP @ A ) ),
    inference(cnf,[status(esa)],[219]) ).

thf(29627,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk18 @ A ) )
      | ( strictorderedP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,224]) ).

thf(29628,plain,
    ( ( ssList @ ( sk18 @ sk2 ) )
    | ( strictorderedP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[29627:[bind(A,$thf( sk2 ))]]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( rearsegP @ A @ nil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).

thf(291,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( rearsegP @ A @ nil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(292,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( rearsegP @ A @ nil ) ),
    inference(cnf,[status(esa)],[291]) ).

thf(29861,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk18 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29628,292]) ).

thf(29862,plain,
    ( ( strictorderedP @ sk2 )
    | ( rearsegP @ ( sk18 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[29861:[bind(A,$thf( sk18 @ sk2 ))]]) ).

thf(106,plain,
    ssList @ sk1,
    inference(cnf,[status(esa)],[98]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( cyclefreeP @ A )
      <=> ! [B: $i] :
            ( ( ssItem @ B )
           => ! [C: $i] :
                ( ( ssItem @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ! [E: $i] :
                        ( ( ssList @ E )
                       => ! [F: $i] :
                            ( ( ssList @ F )
                           => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                = A )
                             => ~ ( ( leq @ B @ C )
                                  & ( leq @ C @ B ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).

thf(157,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( ( cyclefreeP @ A )
         => ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ~ ( ( leq @ B @ C )
                                    & ( leq @ C @ B ) ) ) ) ) ) ) ) )
        & ( ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ~ ( ( leq @ B @ C )
                                    & ( leq @ C @ B ) ) ) ) ) ) ) )
         => ( cyclefreeP @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(164,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssItem @ ( sk6 @ A ) )
      | ( cyclefreeP @ A ) ),
    inference(cnf,[status(esa)],[157]) ).

thf(4096,plain,
    ! [A: $i] :
      ( ( ssItem @ ( sk6 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,164]) ).

thf(4097,plain,
    ( ( ssItem @ ( sk6 @ sk1 ) )
    | ( cyclefreeP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[4096:[bind(A,$thf( sk1 ))]]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ~ ( memberP @ nil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

thf(231,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ~ ( memberP @ nil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(232,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( memberP @ nil @ A ) ),
    inference(cnf,[status(esa)],[231]) ).

thf(4200,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ~ ( memberP @ nil @ A )
      | ( ( ssItem @ ( sk6 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4097,232]) ).

thf(4201,plain,
    ( ( cyclefreeP @ sk1 )
    | ~ ( memberP @ nil @ ( sk6 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[4200:[bind(A,$thf( sk6 @ sk1 ))]]) ).

thf(227,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssItem @ ( sk16 @ A ) )
      | ( strictorderedP @ A ) ),
    inference(cnf,[status(esa)],[219]) ).

thf(31503,plain,
    ! [A: $i] :
      ( ( ssItem @ ( sk16 @ A ) )
      | ( strictorderedP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,227]) ).

thf(31504,plain,
    ( ( ssItem @ ( sk16 @ sk2 ) )
    | ( strictorderedP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[31503:[bind(A,$thf( sk2 ))]]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( strictorderP @ A )
      <=> ! [B: $i] :
            ( ( ssItem @ B )
           => ! [C: $i] :
                ( ( ssItem @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ! [E: $i] :
                        ( ( ssList @ E )
                       => ! [F: $i] :
                            ( ( ssList @ F )
                           => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                = A )
                             => ( ( lt @ B @ C )
                                | ( lt @ C @ B ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).

thf(172,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( ( strictorderP @ A )
         => ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ( ( lt @ B @ C )
                                  | ( lt @ C @ B ) ) ) ) ) ) ) ) )
        & ( ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ( ( lt @ B @ C )
                                  | ( lt @ C @ B ) ) ) ) ) ) ) )
         => ( strictorderP @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(175,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssItem @ ( sk11 @ A ) )
      | ( strictorderP @ A ) ),
    inference(cnf,[status(esa)],[172]) ).

thf(7716,plain,
    ! [A: $i] :
      ( ( ssItem @ ( sk11 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,175]) ).

thf(7717,plain,
    ( ( ssItem @ ( sk11 @ sk1 ) )
    | ( strictorderP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[7716:[bind(A,$thf( sk1 ))]]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( strictorderedP @ ( cons @ A @ nil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).

thf(123,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( strictorderedP @ ( cons @ A @ nil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(124,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( strictorderedP @ ( cons @ A @ nil ) ) ),
    inference(cnf,[status(esa)],[123]) ).

thf(7889,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk11 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7717,124]) ).

thf(7890,plain,
    ( ( strictorderP @ sk1 )
    | ( strictorderedP @ ( cons @ ( sk11 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[7889:[bind(A,$thf( sk11 @ sk1 ))]]) ).

thf(4168,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk6 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4097,124]) ).

thf(4169,plain,
    ( ( cyclefreeP @ sk1 )
    | ( strictorderedP @ ( cons @ ( sk6 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[4168:[bind(A,$thf( sk6 @ sk1 ))]]) ).

thf(61,axiom,
    ? [A: $i] :
      ( ( ssItem @ A )
      & ? [B: $i] :
          ( ( ssItem @ B )
          & ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

thf(375,plain,
    ? [A: $i] :
      ( ( ssItem @ A )
      & ? [B: $i] :
          ( ( ssItem @ B )
          & ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(377,plain,
    ssItem @ sk39,
    inference(cnf,[status(esa)],[375]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( equalelemsP @ ( cons @ A @ nil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).

thf(293,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( equalelemsP @ ( cons @ A @ nil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(294,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( equalelemsP @ ( cons @ A @ nil ) ) ),
    inference(cnf,[status(esa)],[293]) ).

thf(2411,plain,
    ! [A: $i] :
      ( ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ sk39 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[377,294]) ).

thf(2412,plain,
    equalelemsP @ ( cons @ sk39 @ nil ),
    inference(pattern_uni,[status(thm)],[2411:[bind(A,$thf( sk39 ))]]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( totalorderP @ A )
      <=> ! [B: $i] :
            ( ( ssItem @ B )
           => ! [C: $i] :
                ( ( ssItem @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ! [E: $i] :
                        ( ( ssList @ E )
                       => ! [F: $i] :
                            ( ( ssList @ F )
                           => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                = A )
                             => ( ( leq @ B @ C )
                                | ( leq @ C @ B ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).

thf(249,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( ( totalorderP @ A )
         => ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ( ( leq @ B @ C )
                                  | ( leq @ C @ B ) ) ) ) ) ) ) ) )
        & ( ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ( ( leq @ B @ C )
                                  | ( leq @ C @ B ) ) ) ) ) ) ) )
         => ( totalorderP @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( frontsegP @ nil @ A )
      <=> ( nil = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).

thf(125,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( ( frontsegP @ nil @ A )
         => ( nil = A ) )
        & ( ( nil = A )
         => ( frontsegP @ nil @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(126,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ( nil = A ) ),
    inference(cnf,[status(esa)],[125]) ).

thf(128,plain,
    ! [A: $i] :
      ( ( nil = A )
      | ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A ) ),
    inference(lifteq,[status(thm)],[126]) ).

thf(376,plain,
    sk38 != sk39,
    inference(cnf,[status(esa)],[375]) ).

thf(379,plain,
    sk39 != sk38,
    inference(lifteq,[status(thm)],[376]) ).

thf(786,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ( sk38 != nil )
      | ( A != sk39 ) ),
    inference(paramod_ordered,[status(thm)],[128,379]) ).

thf(787,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( frontsegP @ nil @ sk39 )
    | ( sk38 != nil ) ),
    inference(pattern_uni,[status(thm)],[786:[bind(A,$thf( sk39 ))]]) ).

thf(2458,plain,
    ( ~ ( frontsegP @ nil @ sk39 )
    | ( sk38 != nil )
    | ( ( ssList @ sk39 )
     != ( ssList @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[106,787]) ).

thf(2499,plain,
    ( ~ ( frontsegP @ nil @ sk39 )
    | ( sk38 != nil )
    | ( sk39 != sk1 ) ),
    inference(simp,[status(thm)],[2458]) ).

thf(85,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( geq @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).

thf(468,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( geq @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ! [D: $i] :
                  ( ( ssList @ D )
                 => ( ( segmentP @ A @ B )
                   => ( segmentP @ ( app @ ( app @ C @ A ) @ D ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).

thf(233,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ! [D: $i] :
                  ( ( ssList @ D )
                 => ( ( segmentP @ A @ B )
                   => ( segmentP @ ( app @ ( app @ C @ A ) @ D ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(234,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ~ ( ssList @ D )
      | ~ ( segmentP @ A @ B )
      | ( segmentP @ ( app @ ( app @ C @ A ) @ D ) @ B ) ),
    inference(cnf,[status(esa)],[233]) ).

thf(159,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssList @ ( sk10 @ A ) )
      | ( cyclefreeP @ A ) ),
    inference(cnf,[status(esa)],[157]) ).

thf(2762,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk10 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,159]) ).

thf(2763,plain,
    ( ( ssList @ ( sk10 @ sk2 ) )
    | ( cyclefreeP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[2762:[bind(A,$thf( sk2 ))]]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( app @ A @ nil )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).

thf(185,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( app @ A @ nil )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(186,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( app @ A @ nil )
        = A ) ),
    inference(cnf,[status(esa)],[185]) ).

thf(187,plain,
    ! [A: $i] :
      ( ( ( app @ A @ nil )
        = A )
      | ~ ( ssList @ A ) ),
    inference(lifteq,[status(thm)],[186]) ).

thf(11997,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk10 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2763,187]) ).

thf(11998,plain,
    ( ( cyclefreeP @ sk2 )
    | ( ( app @ ( sk10 @ sk2 ) @ nil )
      = ( sk10 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[11997:[bind(A,$thf( sk10 @ sk2 ))]]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( neq @ A @ B )
          <=> ( A != B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

thf(208,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( ( neq @ A @ B )
             => ( A != B ) )
            & ( ( A != B )
             => ( neq @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(210,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( neq @ A @ B )
      | ( A != B ) ),
    inference(cnf,[status(esa)],[208]) ).

thf(212,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( neq @ A @ B ) ),
    inference(lifteq,[status(thm)],[210]) ).

thf(213,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( neq @ A @ A ) ),
    inference(simp,[status(thm)],[212]) ).

thf(643,plain,
    ! [A: $i] :
      ( ~ ( neq @ A @ A )
      | ( ( ssItem @ sk39 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[377,213]) ).

thf(644,plain,
    ~ ( neq @ sk39 @ sk39 ),
    inference(pattern_uni,[status(thm)],[643:[bind(A,$thf( sk39 ))]]) ).

thf(776,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ~ ( neq @ nil @ sk39 )
      | ( A != sk39 ) ),
    inference(paramod_ordered,[status(thm)],[128,644]) ).

thf(777,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( frontsegP @ nil @ sk39 )
    | ~ ( neq @ nil @ sk39 ) ),
    inference(pattern_uni,[status(thm)],[776:[bind(A,$thf( sk39 ))]]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( hd @ ( cons @ B @ A ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).

thf(136,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( hd @ ( cons @ B @ A ) )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(137,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssItem @ B )
      | ( ( hd @ ( cons @ B @ A ) )
        = B ) ),
    inference(cnf,[status(esa)],[136]) ).

thf(138,plain,
    ! [B: $i,A: $i] :
      ( ( ( hd @ ( cons @ B @ A ) )
        = B )
      | ~ ( ssList @ A )
      | ~ ( ssItem @ B ) ),
    inference(lifteq,[status(thm)],[137]) ).

thf(1189,plain,
    ! [A: $i] :
      ( ( rearsegP @ A @ nil )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,292]) ).

thf(1190,plain,
    rearsegP @ sk1 @ nil,
    inference(pattern_uni,[status(thm)],[1189:[bind(A,$thf( sk1 ))]]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( lt @ A @ B )
           => ~ ( lt @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).

thf(479,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( lt @ A @ B )
           => ~ ( lt @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(181,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssItem @ ( sk12 @ A ) )
      | ( strictorderP @ A ) ),
    inference(cnf,[status(esa)],[172]) ).

thf(10109,plain,
    ! [A: $i] :
      ( ( ssItem @ ( sk12 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,181]) ).

thf(10110,plain,
    ( ( ssItem @ ( sk12 @ sk2 ) )
    | ( strictorderP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[10109:[bind(A,$thf( sk2 ))]]) ).

thf(10266,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk12 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10110,124]) ).

thf(10267,plain,
    ( ( strictorderP @ sk2 )
    | ( strictorderedP @ ( cons @ ( sk12 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[10266:[bind(A,$thf( sk12 @ sk2 ))]]) ).

thf(90,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( rearsegP @ A @ B )
               => ( rearsegP @ ( app @ C @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).

thf(481,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( rearsegP @ A @ B )
               => ( rearsegP @ ( app @ C @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(111,plain,
    ( ( ssItem @ sk5 )
    | ( nil = sk4 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(118,plain,
    ( ( sk4 = nil )
    | ( ssItem @ sk5 ) ),
    inference(lifteq,[status(thm)],[111]) ).

thf(108,plain,
    sk2 = sk4,
    inference(cnf,[status(esa)],[98]) ).

thf(115,plain,
    sk4 = sk2,
    inference(lifteq,[status(thm)],[108]) ).

thf(527,plain,
    ( ( sk2 = nil )
    | ( ssItem @ sk5 ) ),
    inference(rewrite,[status(thm)],[118,115]) ).

thf(110,plain,
    ( ( ssItem @ sk5 )
    | ( nil = sk3 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(113,plain,
    ( ( sk3 = nil )
    | ( ssItem @ sk5 ) ),
    inference(lifteq,[status(thm)],[110]) ).

thf(107,plain,
    sk1 = sk3,
    inference(cnf,[status(esa)],[98]) ).

thf(114,plain,
    sk3 = sk1,
    inference(lifteq,[status(thm)],[107]) ).

thf(512,plain,
    ( ( sk1 = nil )
    | ( ssItem @ sk5 ) ),
    inference(rewrite,[status(thm)],[113,114]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( segmentP @ nil @ A )
      <=> ( nil = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).

thf(139,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( ( segmentP @ nil @ A )
         => ( nil = A ) )
        & ( ( nil = A )
         => ( segmentP @ nil @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(141,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( nil != A )
      | ( segmentP @ nil @ A ) ),
    inference(cnf,[status(esa)],[139]) ).

thf(143,plain,
    ! [A: $i] :
      ( ( nil != A )
      | ~ ( ssList @ A )
      | ( segmentP @ nil @ A ) ),
    inference(lifteq,[status(thm)],[141]) ).

thf(144,plain,
    ( ~ ( ssList @ nil )
    | ( segmentP @ nil @ nil ) ),
    inference(simp,[status(thm)],[143]) ).

thf(53,axiom,
    ssList @ nil,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

thf(334,plain,
    ssList @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(593,plain,
    ( ~ $true
    | ( segmentP @ nil @ nil ) ),
    inference(rewrite,[status(thm)],[144,334]) ).

thf(594,plain,
    segmentP @ nil @ nil,
    inference(simp,[status(thm)],[593]) ).

thf(8,axiom,
    totalorderedP @ nil,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).

thf(133,plain,
    totalorderedP @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(109,plain,
    ( ~ ( segmentP @ sk2 @ sk1 )
    | ~ ( totalorderedP @ sk1 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(519,plain,
    ( ~ ( segmentP @ sk2 @ sk1 )
    | ( ( totalorderedP @ sk1 )
     != ( totalorderedP @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[133,109]) ).

thf(520,plain,
    ( ~ ( segmentP @ sk2 @ sk1 )
    | ( sk1 != nil ) ),
    inference(simp,[status(thm)],[519]) ).

thf(596,plain,
    ( ( sk1 != nil )
    | ( ( segmentP @ sk2 @ sk1 )
     != ( segmentP @ nil @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[594,520]) ).

thf(598,plain,
    ( ( sk1 != nil )
    | ( sk2 != nil )
    | ( sk1 != nil ) ),
    inference(simp,[status(thm)],[596]) ).

thf(599,plain,
    ( ( sk1 != nil )
    | ( sk2 != nil ) ),
    inference(simp,[status(thm)],[598]) ).

thf(602,plain,
    ( ( ssItem @ sk5 )
    | ( sk2 != nil )
    | ( sk1 != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[512,599]) ).

thf(603,plain,
    ( ( ssItem @ sk5 )
    | ( sk2 != nil ) ),
    inference(pattern_uni,[status(thm)],[602:[]]) ).

thf(608,plain,
    ( ( ssItem @ sk5 )
    | ( sk2 != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[527,603]) ).

thf(609,plain,
    ssItem @ sk5,
    inference(pattern_uni,[status(thm)],[608:[]]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( totalorderedP @ ( cons @ A @ nil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).

thf(195,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( totalorderedP @ ( cons @ A @ nil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(196,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( totalorderedP @ ( cons @ A @ nil ) ) ),
    inference(cnf,[status(esa)],[195]) ).

thf(2199,plain,
    ! [A: $i] :
      ( ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ sk5 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[609,196]) ).

thf(2200,plain,
    totalorderedP @ ( cons @ sk5 @ nil ),
    inference(pattern_uni,[status(thm)],[2199:[bind(A,$thf( sk5 ))]]) ).

thf(101,plain,
    ( ( ( cons @ sk5 @ nil )
      = sk3 )
    | ( nil = sk4 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(112,plain,
    ( ( ( cons @ sk5 @ nil )
      = sk3 )
    | ( sk4 = nil ) ),
    inference(lifteq,[status(thm)],[101]) ).

thf(537,plain,
    ( ( ( cons @ sk5 @ nil )
      = sk1 )
    | ( sk2 = nil ) ),
    inference(rewrite,[status(thm)],[112,114,115]) ).

thf(104,plain,
    ( ( memberP @ sk4 @ sk5 )
    | ( nil = sk3 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(117,plain,
    ( ( sk3 = nil )
    | ( memberP @ sk4 @ sk5 ) ),
    inference(lifteq,[status(thm)],[104]) ).

thf(565,plain,
    ( ( sk1 = nil )
    | ( memberP @ sk2 @ sk5 ) ),
    inference(rewrite,[status(thm)],[117,114,115]) ).

thf(600,plain,
    ( ( memberP @ sk2 @ sk5 )
    | ( sk2 != nil )
    | ( sk1 != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[565,599]) ).

thf(601,plain,
    ( ( memberP @ sk2 @ sk5 )
    | ( sk2 != nil ) ),
    inference(pattern_uni,[status(thm)],[600:[]]) ).

thf(622,plain,
    ! [A: $i] :
      ( ~ ( memberP @ nil @ A )
      | ( ( ssItem @ sk5 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[609,232]) ).

thf(623,plain,
    ~ ( memberP @ nil @ sk5 ),
    inference(pattern_uni,[status(thm)],[622:[bind(A,$thf( sk5 ))]]) ).

thf(685,plain,
    ( ( sk2 != nil )
    | ( ( memberP @ sk2 @ sk5 )
     != ( memberP @ nil @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[601,623]) ).

thf(693,plain,
    ( ( sk2 != nil )
    | ( sk2 != nil )
    | ( sk5 != sk5 ) ),
    inference(simp,[status(thm)],[685]) ).

thf(697,plain,
    sk2 != nil,
    inference(simp,[status(thm)],[693]) ).

thf(700,plain,
    ( ( cons @ sk5 @ nil )
    = sk1 ),
    inference(simplifyReflect,[status(thm)],[537,697]) ).

thf(2250,plain,
    totalorderedP @ sk1,
    inference(rewrite,[status(thm)],[2200,700]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ssList @ ( cons @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).

thf(170,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ssList @ ( cons @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(10091,plain,
    ! [A: $i] :
      ( ( ssItem @ ( sk12 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,181]) ).

thf(10092,plain,
    ( ( ssItem @ ( sk12 @ sk1 ) )
    | ( strictorderP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[10091:[bind(A,$thf( sk1 ))]]) ).

thf(10233,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk12 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10092,294]) ).

thf(10234,plain,
    ( ( strictorderP @ sk1 )
    | ( equalelemsP @ ( cons @ ( sk12 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[10233:[bind(A,$thf( sk12 @ sk1 ))]]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ~ ( lt @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).

thf(217,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ~ ( lt @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(174,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssList @ ( sk13 @ A ) )
      | ( strictorderP @ A ) ),
    inference(cnf,[status(esa)],[172]) ).

thf(7150,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk13 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,174]) ).

thf(7151,plain,
    ( ( ssList @ ( sk13 @ sk2 ) )
    | ( strictorderP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[7150:[bind(A,$thf( sk2 ))]]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( segmentP @ A @ nil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).

thf(242,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( segmentP @ A @ nil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(243,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( segmentP @ A @ nil ) ),
    inference(cnf,[status(esa)],[242]) ).

thf(7376,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk13 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7151,243]) ).

thf(7377,plain,
    ( ( strictorderP @ sk2 )
    | ( segmentP @ ( sk13 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[7376:[bind(A,$thf( sk13 @ sk2 ))]]) ).

thf(160,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssList @ ( sk9 @ A ) )
      | ( cyclefreeP @ A ) ),
    inference(cnf,[status(esa)],[157]) ).

thf(3142,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk9 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,160]) ).

thf(3143,plain,
    ( ( ssList @ ( sk9 @ sk1 ) )
    | ( cyclefreeP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[3142:[bind(A,$thf( sk1 ))]]) ).

thf(3229,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk9 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3143,292]) ).

thf(3230,plain,
    ( ( cyclefreeP @ sk1 )
    | ( rearsegP @ ( sk9 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[3229:[bind(A,$thf( sk9 @ sk1 ))]]) ).

thf(166,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssItem @ ( sk7 @ A ) )
      | ( cyclefreeP @ A ) ),
    inference(cnf,[status(esa)],[157]) ).

thf(5003,plain,
    ! [A: $i] :
      ( ( ssItem @ ( sk7 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,166]) ).

thf(5004,plain,
    ( ( ssItem @ ( sk7 @ sk1 ) )
    | ( cyclefreeP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[5003:[bind(A,$thf( sk1 ))]]) ).

thf(5068,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk7 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5004,196]) ).

thf(5069,plain,
    ( ( cyclefreeP @ sk1 )
    | ( totalorderedP @ ( cons @ ( sk7 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[5068:[bind(A,$thf( sk7 @ sk1 ))]]) ).

thf(3,axiom,
    strictorderedP @ nil,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).

thf(120,plain,
    strictorderedP @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(177,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssList @ ( sk14 @ A ) )
      | ( strictorderP @ A ) ),
    inference(cnf,[status(esa)],[172]) ).

thf(8523,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk14 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,177]) ).

thf(8524,plain,
    ( ( ssList @ ( sk14 @ sk1 ) )
    | ( strictorderP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[8523:[bind(A,$thf( sk1 ))]]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( segmentP @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).

thf(193,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( segmentP @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(194,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( segmentP @ A @ A ) ),
    inference(cnf,[status(esa)],[193]) ).

thf(13810,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk14 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8524,194]) ).

thf(13811,plain,
    ( ( strictorderP @ sk1 )
    | ( segmentP @ ( sk14 @ sk1 ) @ ( sk14 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[13810:[bind(A,$thf( sk14 @ sk1 ))]]) ).

thf(27,axiom,
    duplicatefreeP @ nil,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).

thf(202,plain,
    duplicatefreeP @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(165,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssList @ ( sk8 @ A ) )
      | ( cyclefreeP @ A ) ),
    inference(cnf,[status(esa)],[157]) ).

thf(4492,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk8 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,165]) ).

thf(4493,plain,
    ( ( ssList @ ( sk8 @ sk2 ) )
    | ( cyclefreeP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[4492:[bind(A,$thf( sk2 ))]]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( app @ nil @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

thf(214,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( app @ nil @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(215,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( app @ nil @ A )
        = A ) ),
    inference(cnf,[status(esa)],[214]) ).

thf(216,plain,
    ! [A: $i] :
      ( ( ( app @ nil @ A )
        = A )
      | ~ ( ssList @ A ) ),
    inference(lifteq,[status(thm)],[215]) ).

thf(25259,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( ( app @ nil @ A )
        = A )
      | ( ( ssList @ ( sk8 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4493,216]) ).

thf(25260,plain,
    ( ( cyclefreeP @ sk2 )
    | ( ( app @ nil @ ( sk8 @ sk2 ) )
      = ( sk8 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[25259:[bind(A,$thf( sk8 @ sk2 ))]]) ).

thf(10197,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk12 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10092,196]) ).

thf(10198,plain,
    ( ( strictorderP @ sk1 )
    | ( totalorderedP @ ( cons @ ( sk12 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[10197:[bind(A,$thf( sk12 @ sk1 ))]]) ).

thf(127,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( nil != A )
      | ( frontsegP @ nil @ A ) ),
    inference(cnf,[status(esa)],[125]) ).

thf(129,plain,
    ! [A: $i] :
      ( ( nil != A )
      | ~ ( ssList @ A )
      | ( frontsegP @ nil @ A ) ),
    inference(lifteq,[status(thm)],[127]) ).

thf(130,plain,
    ( ~ ( ssList @ nil )
    | ( frontsegP @ nil @ nil ) ),
    inference(simp,[status(thm)],[129]) ).

thf(591,plain,
    ( ~ $true
    | ( frontsegP @ nil @ nil ) ),
    inference(rewrite,[status(thm)],[130,334]) ).

thf(592,plain,
    frontsegP @ nil @ nil,
    inference(simp,[status(thm)],[591]) ).

thf(778,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ~ ( neq @ sk39 @ nil )
      | ( A != sk39 ) ),
    inference(paramod_ordered,[status(thm)],[128,644]) ).

thf(779,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( frontsegP @ nil @ sk39 )
    | ~ ( neq @ sk39 @ nil ) ),
    inference(pattern_uni,[status(thm)],[778:[bind(A,$thf( sk39 ))]]) ).

thf(19041,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( neq @ sk39 @ nil )
    | ( ( frontsegP @ nil @ sk39 )
     != ( frontsegP @ nil @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[592,779]) ).

thf(19070,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( neq @ sk39 @ nil )
    | ( nil != nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[19041]) ).

thf(19101,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( neq @ sk39 @ nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[19070]) ).

thf(19115,plain,
    ( ~ ( neq @ sk39 @ nil )
    | ( sk39 != nil )
    | ( ( ssList @ sk39 )
     != ( ssList @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[334,19101]) ).

thf(19193,plain,
    ( ~ ( neq @ sk39 @ nil )
    | ( sk39 != nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[19115]) ).

thf(19213,plain,
    ( ~ ( neq @ sk39 @ nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[19193]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( cons @ B @ A )
           != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).

thf(269,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( cons @ B @ A )
           != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(7118,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk13 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,174]) ).

thf(7119,plain,
    ( ( ssList @ ( sk13 @ sk1 ) )
    | ( strictorderP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[7118:[bind(A,$thf( sk1 ))]]) ).

thf(13814,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk13 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7119,194]) ).

thf(13815,plain,
    ( ( strictorderP @ sk1 )
    | ( segmentP @ ( sk13 @ sk1 ) @ ( sk13 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[13814:[bind(A,$thf( sk13 @ sk1 ))]]) ).

thf(140,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( segmentP @ nil @ A )
      | ( nil = A ) ),
    inference(cnf,[status(esa)],[139]) ).

thf(142,plain,
    ! [A: $i] :
      ( ( nil = A )
      | ~ ( ssList @ A )
      | ~ ( segmentP @ nil @ A ) ),
    inference(lifteq,[status(thm)],[140]) ).

thf(796,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ~ ( memberP @ nil @ nil )
      | ( A != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[128,623]) ).

thf(797,plain,
    ( ~ ( ssList @ sk5 )
    | ~ ( frontsegP @ nil @ sk5 )
    | ~ ( memberP @ nil @ nil ) ),
    inference(pattern_uni,[status(thm)],[796:[bind(A,$thf( sk5 ))]]) ).

thf(220,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssList @ ( sk19 @ A ) )
      | ( strictorderedP @ A ) ),
    inference(cnf,[status(esa)],[219]) ).

thf(27500,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk19 @ A ) )
      | ( strictorderedP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,220]) ).

thf(27501,plain,
    ( ( ssList @ ( sk19 @ sk2 ) )
    | ( strictorderedP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[27500:[bind(A,$thf( sk2 ))]]) ).

thf(27720,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk19 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[27501,243]) ).

thf(27721,plain,
    ( ( strictorderedP @ sk2 )
    | ( segmentP @ ( sk19 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[27720:[bind(A,$thf( sk19 @ sk2 ))]]) ).

thf(31728,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ~ ( memberP @ nil @ A )
      | ( ( ssItem @ ( sk16 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[31504,232]) ).

thf(31729,plain,
    ( ( strictorderedP @ sk2 )
    | ~ ( memberP @ nil @ ( sk16 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[31728:[bind(A,$thf( sk16 @ sk2 ))]]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( frontsegP @ A @ B )
               => ( frontsegP @ ( app @ A @ C ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).

thf(152,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( frontsegP @ A @ B )
               => ( frontsegP @ ( app @ A @ C ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(153,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ~ ( frontsegP @ A @ B )
      | ( frontsegP @ ( app @ A @ C ) @ B ) ),
    inference(cnf,[status(esa)],[152]) ).

thf(4468,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk8 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,165]) ).

thf(4469,plain,
    ( ( ssList @ ( sk8 @ sk1 ) )
    | ( cyclefreeP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[4468:[bind(A,$thf( sk1 ))]]) ).

thf(4574,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk8 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4469,243]) ).

thf(4575,plain,
    ( ( cyclefreeP @ sk1 )
    | ( segmentP @ ( sk8 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[4574:[bind(A,$thf( sk8 @ sk1 ))]]) ).

thf(852,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ( ssItem @ nil )
      | ( A != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[128,609]) ).

thf(853,plain,
    ( ~ ( ssList @ sk5 )
    | ~ ( frontsegP @ nil @ sk5 )
    | ( ssItem @ nil ) ),
    inference(pattern_uni,[status(thm)],[852:[bind(A,$thf( sk5 ))]]) ).

thf(7061,plain,
    ( ~ ( ssList @ sk5 )
    | ( ssItem @ nil )
    | ( ( frontsegP @ nil @ sk5 )
     != ( frontsegP @ nil @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[592,853]) ).

thf(7080,plain,
    ( ( ssItem @ nil )
    | ~ ( ssList @ sk5 )
    | ( nil != nil )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[7061]) ).

thf(7093,plain,
    ( ( ssItem @ nil )
    | ~ ( ssList @ sk5 )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[7080]) ).

thf(7565,plain,
    ( ( ssItem @ nil )
    | ( sk5 != nil )
    | ( ( ssList @ sk5 )
     != ( ssList @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[334,7093]) ).

thf(7621,plain,
    ( ( ssItem @ nil )
    | ( sk5 != nil )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[7565]) ).

thf(7637,plain,
    ( ( ssItem @ nil )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[7621]) ).

thf(7696,plain,
    ! [A: $i] :
      ( ( sk5 != nil )
      | ~ ( memberP @ nil @ A )
      | ( ( ssItem @ nil )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7637,232]) ).

thf(7697,plain,
    ( ( sk5 != nil )
    | ~ ( memberP @ nil @ nil ) ),
    inference(pattern_uni,[status(thm)],[7696:[bind(A,$thf( nil ))]]) ).

thf(3160,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk9 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,160]) ).

thf(3161,plain,
    ( ( ssList @ ( sk9 @ sk2 ) )
    | ( cyclefreeP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[3160:[bind(A,$thf( sk2 ))]]) ).

thf(3307,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk9 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3161,292]) ).

thf(3308,plain,
    ( ( cyclefreeP @ sk2 )
    | ( rearsegP @ ( sk9 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[3307:[bind(A,$thf( sk9 @ sk2 ))]]) ).

thf(12008,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk8 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4493,187]) ).

thf(12009,plain,
    ( ( cyclefreeP @ sk2 )
    | ( ( app @ ( sk8 @ sk2 ) @ nil )
      = ( sk8 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[12008:[bind(A,$thf( sk8 @ sk2 ))]]) ).

thf(222,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssItem @ ( sk17 @ A ) )
      | ( strictorderedP @ A ) ),
    inference(cnf,[status(esa)],[219]) ).

thf(29134,plain,
    ! [A: $i] :
      ( ( ssItem @ ( sk17 @ A ) )
      | ( strictorderedP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,222]) ).

thf(29135,plain,
    ( ( ssItem @ ( sk17 @ sk2 ) )
    | ( strictorderedP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[29134:[bind(A,$thf( sk2 ))]]) ).

thf(29355,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ~ ( memberP @ nil @ A )
      | ( ( ssItem @ ( sk17 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29135,232]) ).

thf(29356,plain,
    ( ( strictorderedP @ sk2 )
    | ~ ( memberP @ nil @ ( sk17 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[29355:[bind(A,$thf( sk17 @ sk2 ))]]) ).

thf(4664,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk8 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4493,292]) ).

thf(4665,plain,
    ( ( cyclefreeP @ sk2 )
    | ( rearsegP @ ( sk8 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[4664:[bind(A,$thf( sk8 @ sk2 ))]]) ).

thf(13799,plain,
    ! [A: $i] :
      ( ( segmentP @ A @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,194]) ).

thf(13800,plain,
    segmentP @ sk2 @ sk2,
    inference(pattern_uni,[status(thm)],[13799:[bind(A,$thf( sk2 ))]]) ).

thf(804,plain,
    ! [A: $i] :
      ( ( nil = A )
      | ~ ( frontsegP @ nil @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,128]) ).

thf(805,plain,
    ( ( sk1 = nil )
    | ~ ( frontsegP @ nil @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[804:[bind(A,$thf( sk1 ))]]) ).

thf(954,plain,
    ( ~ ( frontsegP @ nil @ sk1 )
    | ~ ( segmentP @ sk2 @ sk1 )
    | ( sk1 != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[805,520]) ).

thf(955,plain,
    ( ~ ( frontsegP @ nil @ sk1 )
    | ~ ( segmentP @ sk2 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[954:[]]) ).

thf(1005,plain,
    ( ~ ( frontsegP @ nil @ sk1 )
    | ~ ( segmentP @ sk2 @ nil )
    | ( sk1 != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[805,955]) ).

thf(1006,plain,
    ( ~ ( frontsegP @ nil @ sk1 )
    | ~ ( segmentP @ sk2 @ nil ) ),
    inference(pattern_uni,[status(thm)],[1005:[]]) ).

thf(1028,plain,
    ( ~ ( segmentP @ sk2 @ nil )
    | ( ( frontsegP @ nil @ sk1 )
     != ( frontsegP @ nil @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[592,1006]) ).

thf(1030,plain,
    ( ~ ( segmentP @ sk2 @ nil )
    | ( nil != nil )
    | ( sk1 != nil ) ),
    inference(simp,[status(thm)],[1028]) ).

thf(1032,plain,
    ( ~ ( segmentP @ sk2 @ nil )
    | ( sk1 != nil ) ),
    inference(simp,[status(thm)],[1030]) ).

thf(1106,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( sk1 != nil )
      | ( ( segmentP @ A @ nil )
       != ( segmentP @ sk2 @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[243,1032]) ).

thf(1107,plain,
    ( ~ ( ssList @ sk2 )
    | ( sk1 != nil ) ),
    inference(pattern_uni,[status(thm)],[1106:[bind(A,$thf( sk2 ))]]) ).

thf(1126,plain,
    ( ~ $true
    | ( sk1 != nil ) ),
    inference(rewrite,[status(thm)],[1107,105]) ).

thf(1127,plain,
    sk1 != nil,
    inference(simp,[status(thm)],[1126]) ).

thf(645,plain,
    ! [A: $i] :
      ( ~ ( neq @ A @ A )
      | ( ( ssItem @ sk5 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[609,213]) ).

thf(646,plain,
    ~ ( neq @ sk5 @ sk5 ),
    inference(pattern_uni,[status(thm)],[645:[bind(A,$thf( sk5 ))]]) ).

thf(798,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ~ ( neq @ nil @ sk5 )
      | ( A != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[128,646]) ).

thf(799,plain,
    ( ~ ( ssList @ sk5 )
    | ~ ( frontsegP @ nil @ sk5 )
    | ~ ( neq @ nil @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[798:[bind(A,$thf( sk5 ))]]) ).

thf(26427,plain,
    ( ~ ( ssList @ sk5 )
    | ~ ( neq @ nil @ sk5 )
    | ( ( frontsegP @ nil @ sk5 )
     != ( frontsegP @ nil @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[592,799]) ).

thf(26454,plain,
    ( ~ ( ssList @ sk5 )
    | ~ ( neq @ nil @ sk5 )
    | ( nil != nil )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[26427]) ).

thf(26488,plain,
    ( ~ ( ssList @ sk5 )
    | ~ ( neq @ nil @ sk5 )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[26454]) ).

thf(27014,plain,
    ( ~ ( neq @ nil @ sk5 )
    | ( sk5 != nil )
    | ( ( ssList @ sk5 )
     != ( ssList @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[334,26488]) ).

thf(27095,plain,
    ( ~ ( neq @ nil @ sk5 )
    | ( sk5 != nil )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[27014]) ).

thf(27111,plain,
    ( ~ ( neq @ nil @ sk5 )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[27095]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil != A )
       => ( ssList @ ( tl @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).

thf(288,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil != A )
       => ( ssList @ ( tl @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(10304,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ~ ( memberP @ nil @ A )
      | ( ( ssItem @ ( sk12 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10110,232]) ).

thf(10305,plain,
    ( ( strictorderP @ sk2 )
    | ~ ( memberP @ nil @ ( sk12 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[10304:[bind(A,$thf( sk12 @ sk2 ))]]) ).

thf(173,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( app @ ( app @ ( sk13 @ A ) @ ( cons @ ( sk11 @ A ) @ ( sk14 @ A ) ) ) @ ( cons @ ( sk12 @ A ) @ ( sk15 @ A ) ) )
        = A )
      | ( strictorderP @ A ) ),
    inference(cnf,[status(esa)],[172]) ).

thf(184,plain,
    ! [A: $i] :
      ( ( ( app @ ( app @ ( sk13 @ A ) @ ( cons @ ( sk11 @ A ) @ ( sk14 @ A ) ) ) @ ( cons @ ( sk12 @ A ) @ ( sk15 @ A ) ) )
        = A )
      | ~ ( ssList @ A )
      | ( strictorderP @ A ) ),
    inference(lifteq,[status(thm)],[173]) ).

thf(218,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( lt @ A @ A ) ),
    inference(cnf,[status(esa)],[217]) ).

thf(29329,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ~ ( lt @ A @ A )
      | ( ( ssItem @ ( sk17 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29135,218]) ).

thf(29330,plain,
    ( ( strictorderedP @ sk2 )
    | ~ ( lt @ ( sk17 @ sk2 ) @ ( sk17 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[29329:[bind(A,$thf( sk17 @ sk2 ))]]) ).

thf(180,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssList @ ( sk15 @ A ) )
      | ( strictorderP @ A ) ),
    inference(cnf,[status(esa)],[172]) ).

thf(9537,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk15 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,180]) ).

thf(9538,plain,
    ( ( ssList @ ( sk15 @ sk2 ) )
    | ( strictorderP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[9537:[bind(A,$thf( sk2 ))]]) ).

thf(9804,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk15 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9538,292]) ).

thf(9805,plain,
    ( ( strictorderP @ sk2 )
    | ( rearsegP @ ( sk15 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[9804:[bind(A,$thf( sk15 @ sk2 ))]]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( frontsegP @ A @ nil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).

thf(360,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( frontsegP @ A @ nil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(361,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( frontsegP @ A @ nil ) ),
    inference(cnf,[status(esa)],[360]) ).

thf(7385,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk13 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7151,361]) ).

thf(7386,plain,
    ( ( strictorderP @ sk2 )
    | ( frontsegP @ ( sk13 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[7385:[bind(A,$thf( sk13 @ sk2 ))]]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).

thf(389,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(4110,plain,
    ! [A: $i] :
      ( ( ssItem @ ( sk6 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,164]) ).

thf(4111,plain,
    ( ( ssItem @ ( sk6 @ sk2 ) )
    | ( cyclefreeP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[4110:[bind(A,$thf( sk2 ))]]) ).

thf(4223,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk6 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4111,124]) ).

thf(4224,plain,
    ( ( cyclefreeP @ sk2 )
    | ( strictorderedP @ ( cons @ ( sk6 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[4223:[bind(A,$thf( sk6 @ sk2 ))]]) ).

thf(8555,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk14 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,177]) ).

thf(8556,plain,
    ( ( ssList @ ( sk14 @ sk2 ) )
    | ( strictorderP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[8555:[bind(A,$thf( sk2 ))]]) ).

thf(8805,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk14 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8556,292]) ).

thf(8806,plain,
    ( ( strictorderP @ sk2 )
    | ( rearsegP @ ( sk14 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[8805:[bind(A,$thf( sk14 @ sk2 ))]]) ).

thf(9505,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk15 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,180]) ).

thf(9506,plain,
    ( ( ssList @ ( sk15 @ sk1 ) )
    | ( strictorderP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[9505:[bind(A,$thf( sk1 ))]]) ).

thf(12045,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk15 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9506,187]) ).

thf(12046,plain,
    ( ( strictorderP @ sk1 )
    | ( ( app @ ( sk15 @ sk1 ) @ nil )
      = ( sk15 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[12045:[bind(A,$thf( sk15 @ sk1 ))]]) ).

thf(29291,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk17 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29135,124]) ).

thf(29292,plain,
    ( ( strictorderedP @ sk2 )
    | ( strictorderedP @ ( cons @ ( sk17 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[29291:[bind(A,$thf( sk17 @ sk2 ))]]) ).

thf(13819,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk9 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3161,194]) ).

thf(13820,plain,
    ( ( cyclefreeP @ sk2 )
    | ( segmentP @ ( sk9 @ sk2 ) @ ( sk9 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[13819:[bind(A,$thf( sk9 @ sk2 ))]]) ).

thf(12002,plain,
    ! [A: $i] :
      ( ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,187]) ).

thf(12003,plain,
    ( ( app @ sk1 @ nil )
    = sk1 ),
    inference(pattern_uni,[status(thm)],[12002:[bind(A,$thf( sk1 ))]]) ).

thf(25274,plain,
    ! [A: $i] :
      ( ( ( app @ nil @ A )
        = A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,216]) ).

thf(25275,plain,
    ( ( app @ nil @ sk2 )
    = sk2 ),
    inference(pattern_uni,[status(thm)],[25274:[bind(A,$thf( sk2 ))]]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( segmentP @ A @ B )
                  & ( segmentP @ B @ C ) )
               => ( segmentP @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).

thf(188,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( segmentP @ A @ B )
                  & ( segmentP @ B @ C ) )
               => ( segmentP @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(189,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ~ ( segmentP @ A @ B )
      | ~ ( segmentP @ B @ C )
      | ( segmentP @ A @ C ) ),
    inference(cnf,[status(esa)],[188]) ).

thf(225,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ssList @ ( sk20 @ A ) )
      | ( strictorderedP @ A ) ),
    inference(cnf,[status(esa)],[219]) ).

thf(30719,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk20 @ A ) )
      | ( strictorderedP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,225]) ).

thf(30720,plain,
    ( ( ssList @ ( sk20 @ sk2 ) )
    | ( strictorderedP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[30719:[bind(A,$thf( sk2 ))]]) ).

thf(31106,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk20 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[30720,194]) ).

thf(31107,plain,
    ( ( strictorderedP @ sk2 )
    | ( segmentP @ ( sk20 @ sk2 ) @ ( sk20 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[31106:[bind(A,$thf( sk20 @ sk2 ))]]) ).

thf(3311,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk9 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3161,361]) ).

thf(3312,plain,
    ( ( cyclefreeP @ sk2 )
    | ( frontsegP @ ( sk9 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[3311:[bind(A,$thf( sk9 @ sk2 ))]]) ).

thf(7272,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk13 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7119,361]) ).

thf(7273,plain,
    ( ( strictorderP @ sk1 )
    | ( frontsegP @ ( sk13 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[7272:[bind(A,$thf( sk13 @ sk1 ))]]) ).

thf(4582,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk8 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4469,361]) ).

thf(4583,plain,
    ( ( cyclefreeP @ sk1 )
    | ( frontsegP @ ( sk8 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[4582:[bind(A,$thf( sk8 @ sk1 ))]]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( totalorderedP @ ( cons @ A @ B ) )
          <=> ( ( nil = B )
              | ( ( nil != B )
                & ( totalorderedP @ B )
                & ( leq @ A @ ( hd @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax67) ).

thf(321,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( totalorderedP @ ( cons @ A @ B ) )
             => ( ( nil = B )
                | ( ( nil != B )
                  & ( totalorderedP @ B )
                  & ( leq @ A @ ( hd @ B ) ) ) ) )
            & ( ( ( nil = B )
                | ( ( nil != B )
                  & ( totalorderedP @ B )
                  & ( leq @ A @ ( hd @ B ) ) ) )
             => ( totalorderedP @ ( cons @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( nil
           != ( cons @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

thf(485,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( nil
           != ( cons @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(9679,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk15 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9506,243]) ).

thf(9680,plain,
    ( ( strictorderP @ sk1 )
    | ( segmentP @ ( sk15 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[9679:[bind(A,$thf( sk15 @ sk1 ))]]) ).

thf(209,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ( A = B )
      | ( neq @ A @ B ) ),
    inference(cnf,[status(esa)],[208]) ).

thf(211,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ( neq @ A @ B ) ),
    inference(lifteq,[status(thm)],[209]) ).

thf(29259,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk17 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29135,196]) ).

thf(29260,plain,
    ( ( strictorderedP @ sk2 )
    | ( totalorderedP @ ( cons @ ( sk17 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[29259:[bind(A,$thf( sk17 @ sk2 ))]]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( ( lt @ A @ B )
                  & ( lt @ B @ C ) )
               => ( lt @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).

thf(121,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( ( lt @ A @ B )
                  & ( lt @ B @ C ) )
               => ( lt @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(13817,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk13 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7151,194]) ).

thf(13818,plain,
    ( ( strictorderP @ sk2 )
    | ( segmentP @ ( sk13 @ sk2 ) @ ( sk13 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[13817:[bind(A,$thf( sk13 @ sk2 ))]]) ).

thf(7734,plain,
    ! [A: $i] :
      ( ( ssItem @ ( sk11 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,175]) ).

thf(7735,plain,
    ( ( ssItem @ ( sk11 @ sk2 ) )
    | ( strictorderP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[7734:[bind(A,$thf( sk2 ))]]) ).

thf(8049,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk11 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7735,294]) ).

thf(8050,plain,
    ( ( strictorderP @ sk2 )
    | ( equalelemsP @ ( cons @ ( sk11 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[8049:[bind(A,$thf( sk11 @ sk2 ))]]) ).

thf(29939,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk18 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29628,194]) ).

thf(29940,plain,
    ( ( strictorderedP @ sk2 )
    | ( segmentP @ ( sk18 @ sk2 ) @ ( sk18 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[29939:[bind(A,$thf( sk18 @ sk2 ))]]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil != A )
       => ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).

thf(397,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil != A )
       => ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(221,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( lt @ ( sk16 @ A ) @ ( sk17 @ A ) )
      | ( strictorderedP @ A ) ),
    inference(cnf,[status(esa)],[219]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( rearsegP @ A @ B )
                  & ( rearsegP @ B @ C ) )
               => ( rearsegP @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).

thf(453,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( rearsegP @ A @ B )
                  & ( rearsegP @ B @ C ) )
               => ( rearsegP @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( gt @ A @ B )
           => ~ ( gt @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94) ).

thf(131,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( gt @ A @ B )
           => ~ ( gt @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(132,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( gt @ A @ B )
      | ~ ( gt @ B @ A ) ),
    inference(cnf,[status(esa)],[131]) ).

thf(67,axiom,
    strictorderP @ nil,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).

thf(396,plain,
    strictorderP @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(72,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( leq @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).

thf(411,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( leq @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( nil != A )
           => ( ( hd @ ( app @ A @ B ) )
              = ( hd @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85) ).

thf(428,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( nil != A )
           => ( ( hd @ ( app @ A @ B ) )
              = ( hd @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( geq @ A @ B )
          <=> ( leq @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).

thf(507,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( ( geq @ A @ B )
             => ( leq @ B @ A ) )
            & ( ( leq @ B @ A )
             => ( geq @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( ( geq @ A @ B )
              & ( geq @ B @ A ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).

thf(312,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( ( geq @ A @ B )
              & ( geq @ B @ A ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(26742,plain,
    ! [A: $i] :
      ( ~ ( lt @ A @ A )
      | ( ( ssItem @ sk39 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[377,218]) ).

thf(26743,plain,
    ~ ( lt @ sk39 @ sk39 ),
    inference(pattern_uni,[status(thm)],[26742:[bind(A,$thf( sk39 ))]]) ).

thf(2001,plain,
    ! [A: $i] :
      ( ( frontsegP @ A @ nil )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,361]) ).

thf(2002,plain,
    frontsegP @ sk2 @ nil,
    inference(pattern_uni,[status(thm)],[2001:[bind(A,$thf( sk2 ))]]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( gt @ A @ B )
          <=> ( lt @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).

thf(205,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( ( gt @ A @ B )
             => ( lt @ B @ A ) )
            & ( ( lt @ B @ A )
             => ( gt @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(206,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( lt @ B @ A )
      | ( gt @ A @ B ) ),
    inference(cnf,[status(esa)],[205]) ).

thf(2433,plain,
    ! [A: $i] :
      ( ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ sk5 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[609,294]) ).

thf(2434,plain,
    equalelemsP @ ( cons @ sk5 @ nil ),
    inference(pattern_uni,[status(thm)],[2433:[bind(A,$thf( sk5 ))]]) ).

thf(2586,plain,
    equalelemsP @ sk1,
    inference(rewrite,[status(thm)],[2434,700]) ).

thf(7656,plain,
    ! [A: $i] :
      ( ( sk5 != nil )
      | ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ nil )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7637,196]) ).

thf(7657,plain,
    ( ( sk5 != nil )
    | ( totalorderedP @ ( cons @ nil @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[7656:[bind(A,$thf( nil ))]]) ).

thf(378,plain,
    ssItem @ sk38,
    inference(cnf,[status(esa)],[375]) ).

thf(2203,plain,
    ! [A: $i] :
      ( ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ sk38 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[378,196]) ).

thf(2204,plain,
    totalorderedP @ ( cons @ sk38 @ nil ),
    inference(pattern_uni,[status(thm)],[2203:[bind(A,$thf( sk38 ))]]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( ( gt @ A @ B )
                  & ( gt @ B @ C ) )
               => ( gt @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax95) ).

thf(200,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( ( gt @ A @ B )
                  & ( gt @ B @ C ) )
               => ( gt @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(201,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( ssItem @ C )
      | ~ ( gt @ A @ B )
      | ~ ( gt @ B @ C )
      | ( gt @ A @ C ) ),
    inference(cnf,[status(esa)],[200]) ).

thf(26734,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ~ ( lt @ A @ A )
      | ( ( ssItem @ ( sk11 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7717,218]) ).

thf(26735,plain,
    ( ( strictorderP @ sk1 )
    | ~ ( lt @ ( sk11 @ sk1 ) @ ( sk11 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[26734:[bind(A,$thf( sk11 @ sk1 ))]]) ).

thf(713,plain,
    ! [A: $i] :
      ( ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ sk39 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[377,124]) ).

thf(714,plain,
    strictorderedP @ ( cons @ sk39 @ nil ),
    inference(pattern_uni,[status(thm)],[713:[bind(A,$thf( sk39 ))]]) ).

thf(1285,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( segmentP @ nil @ A )
      | ( sk38 != nil )
      | ( A != sk39 ) ),
    inference(paramod_ordered,[status(thm)],[142,379]) ).

thf(1286,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( segmentP @ nil @ sk39 )
    | ( sk38 != nil ) ),
    inference(pattern_uni,[status(thm)],[1285:[bind(A,$thf( sk39 ))]]) ).

thf(3417,plain,
    ( ~ ( segmentP @ nil @ sk39 )
    | ( sk38 != nil )
    | ( ( ssList @ sk39 )
     != ( ssList @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[105,1286]) ).

thf(3450,plain,
    ( ~ ( segmentP @ nil @ sk39 )
    | ( sk38 != nil )
    | ( sk39 != sk2 ) ),
    inference(simp,[status(thm)],[3417]) ).

thf(9681,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk15 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9506,292]) ).

thf(9682,plain,
    ( ( strictorderP @ sk1 )
    | ( rearsegP @ ( sk15 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[9681:[bind(A,$thf( sk15 @ sk1 ))]]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( memberP @ ( cons @ B @ C ) @ A )
              <=> ( ( A = B )
                  | ( memberP @ C @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).

thf(380,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( memberP @ ( cons @ B @ C ) @ A )
                 => ( ( A = B )
                    | ( memberP @ C @ A ) ) )
                & ( ( ( A = B )
                    | ( memberP @ C @ A ) )
                 => ( memberP @ ( cons @ B @ C ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(2492,plain,
    ( ~ ( ssList @ sk39 )
    | ( sk38 != nil )
    | ( ( frontsegP @ nil @ sk39 )
     != ( frontsegP @ nil @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[592,787]) ).

thf(2497,plain,
    ( ~ ( ssList @ sk39 )
    | ( sk38 != nil )
    | ( nil != nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[2492]) ).

thf(2501,plain,
    ( ~ ( ssList @ sk39 )
    | ( sk38 != nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[2497]) ).

thf(2521,plain,
    ( ( sk38 != nil )
    | ( sk39 != nil )
    | ( ( ssList @ sk39 )
     != ( ssList @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[334,2501]) ).

thf(2542,plain,
    ( ( sk38 != nil )
    | ( sk39 != nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[2521]) ).

thf(2550,plain,
    ( ( sk38 != nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[2542]) ).

thf(2704,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( segmentP @ nil @ A )
      | ( sk39 != nil )
      | ( A != sk38 ) ),
    inference(paramod_ordered,[status(thm)],[142,2550]) ).

thf(2705,plain,
    ( ~ ( ssList @ sk38 )
    | ~ ( segmentP @ nil @ sk38 )
    | ( sk39 != nil ) ),
    inference(pattern_uni,[status(thm)],[2704:[bind(A,$thf( sk38 ))]]) ).

thf(161,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( leq @ ( sk6 @ A ) @ ( sk7 @ A ) )
      | ( cyclefreeP @ A ) ),
    inference(cnf,[status(esa)],[157]) ).

thf(3609,plain,
    ! [A: $i] :
      ( ( leq @ ( sk6 @ A ) @ ( sk7 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,161]) ).

thf(3610,plain,
    ( ( leq @ ( sk6 @ sk1 ) @ ( sk7 @ sk1 ) )
    | ( cyclefreeP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[3609:[bind(A,$thf( sk1 ))]]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( app @ C @ B )
                  = ( app @ A @ B ) )
               => ( C = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax79) ).

thf(190,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( app @ C @ B )
                  = ( app @ A @ B ) )
               => ( C = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ( ( app @ C @ B )
       != ( app @ A @ B ) )
      | ( C = A ) ),
    inference(cnf,[status(esa)],[190]) ).

thf(192,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( app @ C @ B )
       != ( app @ A @ B ) )
      | ( C = A )
      | ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C ) ),
    inference(lifteq,[status(thm)],[191]) ).

thf(12057,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk8 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4469,187]) ).

thf(12058,plain,
    ( ( cyclefreeP @ sk1 )
    | ( ( app @ ( sk8 @ sk1 ) @ nil )
      = ( sk8 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[12057:[bind(A,$thf( sk8 @ sk1 ))]]) ).

thf(26758,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ~ ( lt @ A @ A )
      | ( ( ssItem @ ( sk12 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10092,218]) ).

thf(26759,plain,
    ( ( strictorderP @ sk1 )
    | ~ ( lt @ ( sk12 @ sk1 ) @ ( sk12 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[26758:[bind(A,$thf( sk12 @ sk1 ))]]) ).

thf(719,plain,
    ! [A: $i] :
      ( ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ sk5 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[609,124]) ).

thf(720,plain,
    strictorderedP @ ( cons @ sk5 @ nil ),
    inference(pattern_uni,[status(thm)],[719:[bind(A,$thf( sk5 ))]]) ).

thf(729,plain,
    strictorderedP @ sk1,
    inference(rewrite,[status(thm)],[720,700]) ).

thf(29311,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ~ ( neq @ A @ A )
      | ( ( ssItem @ ( sk17 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29135,213]) ).

thf(29312,plain,
    ( ( strictorderedP @ sk2 )
    | ~ ( neq @ ( sk17 @ sk2 ) @ ( sk17 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[29311:[bind(A,$thf( sk17 @ sk2 ))]]) ).

thf(3617,plain,
    ! [A: $i] :
      ( ( leq @ ( sk6 @ A ) @ ( sk7 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,161]) ).

thf(3618,plain,
    ( ( leq @ ( sk6 @ sk2 ) @ ( sk7 @ sk2 ) )
    | ( cyclefreeP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[3617:[bind(A,$thf( sk2 ))]]) ).

thf(1128,plain,
    ~ ( frontsegP @ nil @ sk1 ),
    inference(simplifyReflect,[status(thm)],[805,1127]) ).

thf(1391,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( segmentP @ nil @ A )
      | ( ssItem @ nil )
      | ( A != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[142,609]) ).

thf(1392,plain,
    ( ~ ( ssList @ sk5 )
    | ~ ( segmentP @ nil @ sk5 )
    | ( ssItem @ nil ) ),
    inference(pattern_uni,[status(thm)],[1391:[bind(A,$thf( sk5 ))]]) ).

thf(176,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( lt @ ( sk11 @ A ) @ ( sk12 @ A ) )
      | ( strictorderP @ A ) ),
    inference(cnf,[status(esa)],[172]) ).

thf(8135,plain,
    ! [A: $i] :
      ( ~ ( lt @ ( sk11 @ A ) @ ( sk12 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,176]) ).

thf(8136,plain,
    ( ~ ( lt @ ( sk11 @ sk1 ) @ ( sk12 @ sk1 ) )
    | ( strictorderP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[8135:[bind(A,$thf( sk1 ))]]) ).

thf(84,axiom,
    equalelemsP @ nil,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).

thf(467,plain,
    equalelemsP @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(13777,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk10 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2763,194]) ).

thf(13778,plain,
    ( ( cyclefreeP @ sk2 )
    | ( segmentP @ ( sk10 @ sk2 ) @ ( sk10 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[13777:[bind(A,$thf( sk10 @ sk2 ))]]) ).

thf(7662,plain,
    ! [A: $i] :
      ( ( sk5 != nil )
      | ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ nil )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7637,124]) ).

thf(7663,plain,
    ( ( sk5 != nil )
    | ( strictorderedP @ ( cons @ nil @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[7662:[bind(A,$thf( nil ))]]) ).

thf(223,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( strictorderedP @ A )
      | ~ ( ssItem @ B )
      | ~ ( ssItem @ C )
      | ~ ( ssList @ D )
      | ~ ( ssList @ E )
      | ~ ( ssList @ F )
      | ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
       != A )
      | ( lt @ B @ C ) ),
    inference(cnf,[status(esa)],[219]) ).

thf(228,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
       != A )
      | ~ ( ssList @ A )
      | ~ ( strictorderedP @ A )
      | ~ ( ssItem @ B )
      | ~ ( ssItem @ C )
      | ~ ( ssList @ D )
      | ~ ( ssList @ E )
      | ~ ( ssList @ F )
      | ( lt @ B @ C ) ),
    inference(lifteq,[status(thm)],[223]) ).

thf(229,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
      | ~ ( strictorderedP @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
      | ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( ssList @ C )
      | ~ ( ssList @ D )
      | ~ ( ssList @ E )
      | ( lt @ A @ B ) ),
    inference(simp,[status(thm)],[228]) ).

thf(8057,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ~ ( memberP @ nil @ A )
      | ( ( ssItem @ ( sk11 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7735,232]) ).

thf(8058,plain,
    ( ( strictorderP @ sk2 )
    | ~ ( memberP @ nil @ ( sk11 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[8057:[bind(A,$thf( sk11 @ sk2 ))]]) ).

thf(2708,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ( sk39 != nil )
      | ( A != sk38 ) ),
    inference(paramod_ordered,[status(thm)],[128,2550]) ).

thf(2709,plain,
    ( ~ ( ssList @ sk38 )
    | ~ ( frontsegP @ nil @ sk38 )
    | ( sk39 != nil ) ),
    inference(pattern_uni,[status(thm)],[2708:[bind(A,$thf( sk38 ))]]) ).

thf(5938,plain,
    ( ~ ( frontsegP @ nil @ sk38 )
    | ( sk39 != nil )
    | ( ( ssList @ sk38 )
     != ( ssList @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[105,2709]) ).

thf(5983,plain,
    ( ~ ( frontsegP @ nil @ sk38 )
    | ( sk39 != nil )
    | ( sk38 != sk2 ) ),
    inference(simp,[status(thm)],[5938]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( leq @ A @ B )
           => ( ( A = B )
              | ( lt @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax92) ).

thf(197,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( leq @ A @ B )
           => ( ( A = B )
              | ( lt @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(2746,plain,
    ! [A: $i] :
      ( ( ssList @ ( sk10 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,159]) ).

thf(2747,plain,
    ( ( ssList @ ( sk10 @ sk1 ) )
    | ( cyclefreeP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[2746:[bind(A,$thf( sk1 ))]]) ).

thf(2825,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk10 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2747,243]) ).

thf(2826,plain,
    ( ( cyclefreeP @ sk1 )
    | ( segmentP @ ( sk10 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[2825:[bind(A,$thf( sk10 @ sk1 ))]]) ).

thf(4154,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk6 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4097,196]) ).

thf(4155,plain,
    ( ( cyclefreeP @ sk1 )
    | ( totalorderedP @ ( cons @ ( sk6 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[4154:[bind(A,$thf( sk6 @ sk1 ))]]) ).

thf(79,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( nil != A )
           => ( ( tl @ ( app @ A @ B ) )
              = ( app @ ( tl @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).

thf(435,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( nil != A )
           => ( ( tl @ ( app @ A @ B ) )
              = ( app @ ( tl @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil != A )
       => ( ssItem @ ( hd @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

thf(285,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil != A )
       => ( ssItem @ ( hd @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(8693,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk14 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8524,361]) ).

thf(8694,plain,
    ( ( strictorderP @ sk1 )
    | ( frontsegP @ ( sk14 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[8693:[bind(A,$thf( sk14 @ sk1 ))]]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( app @ ( app @ A @ B ) @ C )
                = ( app @ A @ ( app @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).

thf(154,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( app @ ( app @ A @ B ) @ C )
                = ( app @ A @ ( app @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(155,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ( ( app @ ( app @ A @ B ) @ C )
        = ( app @ A @ ( app @ B @ C ) ) ) ),
    inference(cnf,[status(esa)],[154]) ).

thf(156,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( app @ ( app @ A @ B ) @ C )
        = ( app @ A @ ( app @ B @ C ) ) )
      | ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C ) ),
    inference(lifteq,[status(thm)],[155]) ).

thf(4247,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk6 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4111,294]) ).

thf(4248,plain,
    ( ( cyclefreeP @ sk2 )
    | ( equalelemsP @ ( cons @ ( sk6 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[4247:[bind(A,$thf( sk6 @ sk2 ))]]) ).

thf(13783,plain,
    ! [A: $i] :
      ( ( segmentP @ A @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,194]) ).

thf(13784,plain,
    segmentP @ sk1 @ sk1,
    inference(pattern_uni,[status(thm)],[13783:[bind(A,$thf( sk1 ))]]) ).

thf(2251,plain,
    ( ~ ( segmentP @ sk2 @ sk1 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[109,2250]) ).

thf(2252,plain,
    ~ ( segmentP @ sk2 @ sk1 ),
    inference(simp,[status(thm)],[2251]) ).

thf(13886,plain,
    ( ( segmentP @ sk2 @ sk1 )
   != ( segmentP @ sk1 @ sk1 ) ),
    inference(paramod_ordered,[status(thm)],[13784,2252]) ).

thf(13897,plain,
    ( ( sk2 != sk1 )
    | ( sk1 != sk1 ) ),
    inference(simp,[status(thm)],[13886]) ).

thf(13904,plain,
    sk2 != sk1,
    inference(simp,[status(thm)],[13897]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( memberP @ ( app @ B @ C ) @ A )
              <=> ( ( memberP @ B @ A )
                  | ( memberP @ C @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).

thf(356,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( memberP @ ( app @ B @ C ) @ A )
                 => ( ( memberP @ B @ A )
                    | ( memberP @ C @ A ) ) )
                & ( ( ( memberP @ B @ A )
                    | ( memberP @ C @ A ) )
                 => ( memberP @ ( app @ B @ C ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(158,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( app @ ( app @ ( sk8 @ A ) @ ( cons @ ( sk6 @ A ) @ ( sk9 @ A ) ) ) @ ( cons @ ( sk7 @ A ) @ ( sk10 @ A ) ) )
        = A )
      | ( cyclefreeP @ A ) ),
    inference(cnf,[status(esa)],[157]) ).

thf(169,plain,
    ! [A: $i] :
      ( ( ( app @ ( app @ ( sk8 @ A ) @ ( cons @ ( sk6 @ A ) @ ( sk9 @ A ) ) ) @ ( cons @ ( sk7 @ A ) @ ( sk10 @ A ) ) )
        = A )
      | ~ ( ssList @ A )
      | ( cyclefreeP @ A ) ),
    inference(lifteq,[status(thm)],[158]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( memberP @ A @ B )
          <=> ? [C: $i] :
                ( ( ssList @ C )
                & ? [D: $i] :
                    ( ( ssList @ D )
                    & ( ( app @ C @ ( cons @ B @ D ) )
                      = A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

thf(499,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( ( memberP @ A @ B )
             => ? [C: $i] :
                  ( ( ssList @ C )
                  & ? [D: $i] :
                      ( ( ssList @ D )
                      & ( ( app @ C @ ( cons @ B @ D ) )
                        = A ) ) ) )
            & ( ? [C: $i] :
                  ( ( ssList @ C )
                  & ? [D: $i] :
                      ( ( ssList @ D )
                      & ( ( app @ C @ ( cons @ B @ D ) )
                        = A ) ) )
             => ( memberP @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(8013,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk11 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7735,196]) ).

thf(8014,plain,
    ( ( strictorderP @ sk2 )
    | ( totalorderedP @ ( cons @ ( sk11 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[8013:[bind(A,$thf( sk11 @ sk2 ))]]) ).

thf(8686,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk14 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8524,292]) ).

thf(8687,plain,
    ( ( strictorderP @ sk1 )
    | ( rearsegP @ ( sk14 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[8686:[bind(A,$thf( sk14 @ sk1 ))]]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( ( leq @ A @ B )
              & ( leq @ B @ A ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).

thf(476,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( ( leq @ A @ B )
              & ( leq @ B @ A ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(641,plain,
    ! [A: $i] :
      ( ~ ( neq @ A @ A )
      | ( ( ssItem @ sk38 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[378,213]) ).

thf(642,plain,
    ~ ( neq @ sk38 @ sk38 ),
    inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( sk38 ))]]) ).

thf(178,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( lt @ ( sk12 @ A ) @ ( sk11 @ A ) )
      | ( strictorderP @ A ) ),
    inference(cnf,[status(esa)],[172]) ).

thf(9084,plain,
    ! [A: $i] :
      ( ~ ( lt @ ( sk12 @ A ) @ ( sk11 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,178]) ).

thf(9085,plain,
    ( ~ ( lt @ ( sk12 @ sk1 ) @ ( sk11 @ sk1 ) )
    | ( strictorderP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[9084:[bind(A,$thf( sk1 ))]]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( lt @ A @ B )
          <=> ( ( A != B )
              & ( leq @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93) ).

thf(488,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( ( lt @ A @ B )
             => ( ( A != B )
                & ( leq @ A @ B ) ) )
            & ( ( ( A != B )
                & ( leq @ A @ B ) )
             => ( lt @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(25232,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( ( app @ nil @ A )
        = A )
      | ( ( ssList @ ( sk10 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2763,216]) ).

thf(25233,plain,
    ( ( cyclefreeP @ sk2 )
    | ( ( app @ nil @ ( sk10 @ sk2 ) )
      = ( sk10 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[25232:[bind(A,$thf( sk10 @ sk2 ))]]) ).

thf(5106,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk7 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5004,294]) ).

thf(5107,plain,
    ( ( cyclefreeP @ sk1 )
    | ( equalelemsP @ ( cons @ ( sk7 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[5106:[bind(A,$thf( sk7 @ sk1 ))]]) ).

thf(2829,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk10 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2747,361]) ).

thf(2830,plain,
    ( ( cyclefreeP @ sk1 )
    | ( frontsegP @ ( sk10 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[2829:[bind(A,$thf( sk10 @ sk1 ))]]) ).

thf(1219,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( segmentP @ nil @ A )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[142,1127]) ).

thf(1220,plain,
    ( ~ ( ssList @ sk1 )
    | ~ ( segmentP @ nil @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[1219:[bind(A,$thf( sk1 ))]]) ).

thf(1477,plain,
    ( ~ $true
    | ~ ( segmentP @ nil @ sk1 ) ),
    inference(rewrite,[status(thm)],[1220,106]) ).

thf(1478,plain,
    ~ ( segmentP @ nil @ sk1 ),
    inference(simp,[status(thm)],[1477]) ).

thf(26726,plain,
    ! [A: $i] :
      ( ( sk5 != nil )
      | ~ ( lt @ A @ A )
      | ( ( ssItem @ nil )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7637,218]) ).

thf(26727,plain,
    ( ( sk5 != nil )
    | ~ ( lt @ nil @ nil ) ),
    inference(pattern_uni,[status(thm)],[26726:[bind(A,$thf( nil ))]]) ).

thf(13804,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk15 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9538,194]) ).

thf(13805,plain,
    ( ( strictorderP @ sk2 )
    | ( segmentP @ ( sk15 @ sk2 ) @ ( sk15 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[13804:[bind(A,$thf( sk15 @ sk2 ))]]) ).

thf(4243,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ~ ( neq @ A @ A )
      | ( ( ssItem @ ( sk6 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4111,213]) ).

thf(4244,plain,
    ( ( cyclefreeP @ sk2 )
    | ~ ( neq @ ( sk6 @ sk2 ) @ ( sk6 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[4243:[bind(A,$thf( sk6 @ sk2 ))]]) ).

thf(836,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ~ ( neq @ sk38 @ nil )
      | ( A != sk38 ) ),
    inference(paramod_ordered,[status(thm)],[128,642]) ).

thf(837,plain,
    ( ~ ( ssList @ sk38 )
    | ~ ( frontsegP @ nil @ sk38 )
    | ~ ( neq @ sk38 @ nil ) ),
    inference(pattern_uni,[status(thm)],[836:[bind(A,$thf( sk38 ))]]) ).

thf(12443,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( neq @ nil @ sk39 )
    | ( ( frontsegP @ nil @ sk39 )
     != ( frontsegP @ nil @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[592,777]) ).

thf(12444,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( neq @ nil @ sk39 )
    | ( nil != nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[12443]) ).

thf(12486,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( neq @ nil @ sk39 )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[12444]) ).

thf(13004,plain,
    ( ~ ( neq @ nil @ sk39 )
    | ( sk39 != nil )
    | ( ( ssList @ sk39 )
     != ( ssList @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[334,12486]) ).

thf(13053,plain,
    ( ~ ( neq @ nil @ sk39 )
    | ( sk39 != nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[13004]) ).

thf(13081,plain,
    ( ~ ( neq @ nil @ sk39 )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[13053]) ).

thf(13821,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk8 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4469,194]) ).

thf(13822,plain,
    ( ( cyclefreeP @ sk1 )
    | ( segmentP @ ( sk8 @ sk1 ) @ ( sk8 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[13821:[bind(A,$thf( sk8 @ sk1 ))]]) ).

thf(5021,plain,
    ! [A: $i] :
      ( ( ssItem @ ( sk7 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,166]) ).

thf(5022,plain,
    ( ( ssItem @ ( sk7 @ sk2 ) )
    | ( cyclefreeP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[5021:[bind(A,$thf( sk2 ))]]) ).

thf(5169,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ~ ( memberP @ nil @ A )
      | ( ( ssItem @ ( sk7 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5022,232]) ).

thf(5170,plain,
    ( ( cyclefreeP @ sk2 )
    | ~ ( memberP @ nil @ ( sk7 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[5169:[bind(A,$thf( sk7 @ sk2 ))]]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( frontsegP @ A @ B )
                  & ( frontsegP @ B @ C ) )
               => ( frontsegP @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).

thf(134,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( frontsegP @ A @ B )
                  & ( frontsegP @ B @ C ) )
               => ( frontsegP @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(9688,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk15 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9506,361]) ).

thf(9689,plain,
    ( ( strictorderP @ sk1 )
    | ( frontsegP @ ( sk15 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[9688:[bind(A,$thf( sk15 @ sk1 ))]]) ).

thf(540,plain,
    ! [A: $i] :
      ( ~ ( memberP @ nil @ A )
      | ( ( ssItem @ sk38 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[378,232]) ).

thf(541,plain,
    ~ ( memberP @ nil @ sk38 ),
    inference(pattern_uni,[status(thm)],[540:[bind(A,$thf( sk38 ))]]) ).

thf(538,plain,
    ! [A: $i] :
      ( ~ ( memberP @ nil @ A )
      | ( ( ssItem @ sk39 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[377,232]) ).

thf(539,plain,
    ~ ( memberP @ nil @ sk39 ),
    inference(pattern_uni,[status(thm)],[538:[bind(A,$thf( sk39 ))]]) ).

thf(772,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ~ ( memberP @ nil @ nil )
      | ( A != sk39 ) ),
    inference(paramod_ordered,[status(thm)],[128,539]) ).

thf(773,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( frontsegP @ nil @ sk39 )
    | ~ ( memberP @ nil @ nil ) ),
    inference(pattern_uni,[status(thm)],[772:[bind(A,$thf( sk39 ))]]) ).

thf(1990,plain,
    ! [A: $i] :
      ( ( frontsegP @ A @ nil )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,361]) ).

thf(1991,plain,
    frontsegP @ sk1 @ nil,
    inference(pattern_uni,[status(thm)],[1990:[bind(A,$thf( sk1 ))]]) ).

thf(38,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil != A )
       => ? [B: $i] :
            ( ( ssList @ B )
            & ( ( tl @ A )
              = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).

thf(244,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil != A )
       => ? [B: $i] :
            ( ( ssList @ B )
            & ( ( tl @ A )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(31024,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk20 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[30720,243]) ).

thf(31025,plain,
    ( ( strictorderedP @ sk2 )
    | ( segmentP @ ( sk20 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[31024:[bind(A,$thf( sk20 @ sk2 ))]]) ).

thf(31952,plain,
    ( ~ ( ssList @ sk38 )
    | ~ ( neq @ sk38 @ nil )
    | ( ( frontsegP @ nil @ sk38 )
     != ( frontsegP @ nil @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[592,837]) ).

thf(32000,plain,
    ( ~ ( ssList @ sk38 )
    | ~ ( neq @ sk38 @ nil )
    | ( nil != nil )
    | ( sk38 != nil ) ),
    inference(simp,[status(thm)],[31952]) ).

thf(32001,plain,
    ( ~ ( ssList @ sk38 )
    | ~ ( neq @ sk38 @ nil )
    | ( sk38 != nil ) ),
    inference(simp,[status(thm)],[32000]) ).

thf(32059,plain,
    ( ~ ( neq @ sk38 @ nil )
    | ( sk38 != nil )
    | ( ( ssList @ sk38 )
     != ( ssList @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[334,32001]) ).

thf(32126,plain,
    ( ~ ( neq @ sk38 @ nil )
    | ( sk38 != nil )
    | ( sk38 != nil ) ),
    inference(simp,[status(thm)],[32059]) ).

thf(32173,plain,
    ( ~ ( neq @ sk38 @ nil )
    | ( sk38 != nil ) ),
    inference(simp,[status(thm)],[32126]) ).

thf(3305,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk9 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3161,243]) ).

thf(3306,plain,
    ( ( cyclefreeP @ sk2 )
    | ( segmentP @ ( sk9 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[3305:[bind(A,$thf( sk9 @ sk2 ))]]) ).

thf(2903,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk10 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2763,292]) ).

thf(2904,plain,
    ( ( cyclefreeP @ sk2 )
    | ( rearsegP @ ( sk10 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[2903:[bind(A,$thf( sk10 @ sk2 ))]]) ).

thf(1102,plain,
    ! [A: $i] :
      ( ( segmentP @ A @ nil )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,243]) ).

thf(1103,plain,
    segmentP @ sk1 @ nil,
    inference(pattern_uni,[status(thm)],[1102:[bind(A,$thf( sk1 ))]]) ).

thf(8039,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ~ ( neq @ A @ A )
      | ( ( ssItem @ ( sk11 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7735,213]) ).

thf(8040,plain,
    ( ( strictorderP @ sk2 )
    | ~ ( neq @ ( sk11 @ sk2 ) @ ( sk11 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[8039:[bind(A,$thf( sk11 @ sk2 ))]]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( frontsegP @ A @ B )
              & ( frontsegP @ B @ A ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).

thf(146,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( frontsegP @ A @ B )
              & ( frontsegP @ B @ A ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(147,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( frontsegP @ A @ B )
      | ~ ( frontsegP @ B @ A )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(148,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( frontsegP @ A @ B )
      | ~ ( frontsegP @ B @ A ) ),
    inference(lifteq,[status(thm)],[147]) ).

thf(4576,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk8 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4469,292]) ).

thf(4577,plain,
    ( ( cyclefreeP @ sk1 )
    | ( rearsegP @ ( sk8 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[4576:[bind(A,$thf( sk8 @ sk1 ))]]) ).

thf(7909,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ~ ( neq @ A @ A )
      | ( ( ssItem @ ( sk11 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7717,213]) ).

thf(7910,plain,
    ( ( strictorderP @ sk1 )
    | ~ ( neq @ ( sk11 @ sk1 ) @ ( sk11 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[7909:[bind(A,$thf( sk11 @ sk1 ))]]) ).

thf(163,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( leq @ ( sk7 @ A ) @ ( sk6 @ A ) )
      | ( cyclefreeP @ A ) ),
    inference(cnf,[status(esa)],[157]) ).

thf(3870,plain,
    ! [A: $i] :
      ( ( leq @ ( sk7 @ A ) @ ( sk6 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,163]) ).

thf(3871,plain,
    ( ( leq @ ( sk7 @ sk1 ) @ ( sk6 @ sk1 ) )
    | ( cyclefreeP @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[3870:[bind(A,$thf( sk1 ))]]) ).

thf(5137,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk7 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5022,124]) ).

thf(5138,plain,
    ( ( cyclefreeP @ sk2 )
    | ( strictorderedP @ ( cons @ ( sk7 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[5137:[bind(A,$thf( sk7 @ sk2 ))]]) ).

thf(4255,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ~ ( memberP @ nil @ A )
      | ( ( ssItem @ ( sk6 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4111,232]) ).

thf(4256,plain,
    ( ( cyclefreeP @ sk2 )
    | ~ ( memberP @ nil @ ( sk6 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[4255:[bind(A,$thf( sk6 @ sk2 ))]]) ).

thf(29347,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk17 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29135,294]) ).

thf(29348,plain,
    ( ( strictorderedP @ sk2 )
    | ( equalelemsP @ ( cons @ ( sk17 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[29347:[bind(A,$thf( sk17 @ sk2 ))]]) ).

thf(7919,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk11 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7717,294]) ).

thf(7920,plain,
    ( ( strictorderP @ sk1 )
    | ( equalelemsP @ ( cons @ ( sk11 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[7919:[bind(A,$thf( sk11 @ sk1 ))]]) ).

thf(12051,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk13 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7119,187]) ).

thf(12052,plain,
    ( ( strictorderP @ sk1 )
    | ( ( app @ ( sk13 @ sk1 ) @ nil )
      = ( sk13 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[12051:[bind(A,$thf( sk13 @ sk1 ))]]) ).

thf(28161,plain,
    ! [A: $i] :
      ( ~ ( lt @ ( sk16 @ A ) @ ( sk17 @ A ) )
      | ( strictorderedP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,221]) ).

thf(28162,plain,
    ( ~ ( lt @ ( sk16 @ sk2 ) @ ( sk17 @ sk2 ) )
    | ( strictorderedP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[28161:[bind(A,$thf( sk2 ))]]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( cons @ B @ A )
            = ( app @ ( cons @ B @ nil ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).

thf(149,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( cons @ B @ A )
            = ( app @ ( cons @ B @ nil ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( singletonP @ A )
      <=> ? [B: $i] :
            ( ( ssItem @ B )
            & ( ( cons @ B @ nil )
              = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

thf(402,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( ( singletonP @ A )
         => ? [B: $i] :
              ( ( ssItem @ B )
              & ( ( cons @ B @ nil )
                = A ) ) )
        & ( ? [B: $i] :
              ( ( ssItem @ B )
              & ( ( cons @ B @ nil )
                = A ) )
         => ( singletonP @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(13808,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk15 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9506,194]) ).

thf(13809,plain,
    ( ( strictorderP @ sk1 )
    | ( segmentP @ ( sk15 @ sk1 ) @ ( sk15 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[13808:[bind(A,$thf( sk15 @ sk1 ))]]) ).

thf(28,axiom,
    ~ ( singletonP @ nil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).

thf(203,plain,
    ~ ( singletonP @ nil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(204,plain,
    ~ ( singletonP @ nil ),
    inference(polarity_switch,[status(thm)],[203]) ).

thf(73,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( strictorderP @ ( cons @ A @ nil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).

thf(413,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( strictorderP @ ( cons @ A @ nil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(3233,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk9 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3143,361]) ).

thf(3234,plain,
    ( ( cyclefreeP @ sk1 )
    | ( frontsegP @ ( sk9 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[3233:[bind(A,$thf( sk9 @ sk1 ))]]) ).

thf(26728,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ~ ( lt @ A @ A )
      | ( ( ssItem @ ( sk12 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10110,218]) ).

thf(26729,plain,
    ( ( strictorderP @ sk2 )
    | ~ ( lt @ ( sk12 @ sk2 ) @ ( sk12 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[26728:[bind(A,$thf( sk12 @ sk2 ))]]) ).

thf(10241,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ~ ( memberP @ nil @ A )
      | ( ( ssItem @ ( sk12 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10092,232]) ).

thf(10242,plain,
    ( ( strictorderP @ sk1 )
    | ~ ( memberP @ nil @ ( sk12 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[10241:[bind(A,$thf( sk12 @ sk1 ))]]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( app @ B @ C )
                  = ( app @ B @ A ) )
               => ( C = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax80) ).

thf(391,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ( ( ( app @ B @ C )
                  = ( app @ B @ A ) )
               => ( C = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(29876,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk18 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29628,361]) ).

thf(29877,plain,
    ( ( strictorderedP @ sk2 )
    | ( frontsegP @ ( sk18 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[29876:[bind(A,$thf( sk18 @ sk2 ))]]) ).

thf(95,axiom,
    totalorderP @ nil,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).

thf(498,plain,
    totalorderP @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( nil != B )
              & ( nil != A )
              & ( ( hd @ B )
                = ( hd @ A ) )
              & ( ( tl @ B )
                = ( tl @ A ) ) )
           => ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax77) ).

thf(335,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( nil != B )
              & ( nil != A )
              & ( ( hd @ B )
                = ( hd @ A ) )
              & ( ( tl @ B )
                = ( tl @ A ) ) )
           => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(9802,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk15 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9538,243]) ).

thf(9803,plain,
    ( ( strictorderP @ sk2 )
    | ( segmentP @ ( sk15 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[9802:[bind(A,$thf( sk15 @ sk2 ))]]) ).

thf(7688,plain,
    ! [A: $i] :
      ( ( sk5 != nil )
      | ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ nil )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7637,294]) ).

thf(7689,plain,
    ( ( sk5 != nil )
    | ( equalelemsP @ ( cons @ nil @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[7688:[bind(A,$thf( nil ))]]) ).

thf(5157,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ~ ( neq @ A @ A )
      | ( ( ssItem @ ( sk7 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5022,213]) ).

thf(5158,plain,
    ( ( cyclefreeP @ sk2 )
    | ~ ( neq @ ( sk7 @ sk2 ) @ ( sk7 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[5157:[bind(A,$thf( sk7 @ sk2 ))]]) ).

thf(5102,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ~ ( neq @ A @ A )
      | ( ( ssItem @ ( sk7 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5004,213]) ).

thf(5103,plain,
    ( ( cyclefreeP @ sk1 )
    | ~ ( neq @ ( sk7 @ sk1 ) @ ( sk7 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[5102:[bind(A,$thf( sk7 @ sk1 ))]]) ).

thf(10203,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk12 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10092,124]) ).

thf(10204,plain,
    ( ( strictorderP @ sk1 )
    | ( strictorderedP @ ( cons @ ( sk12 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[10203:[bind(A,$thf( sk12 @ sk1 ))]]) ).

thf(226,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( app @ ( app @ ( sk18 @ A ) @ ( cons @ ( sk16 @ A ) @ ( sk19 @ A ) ) ) @ ( cons @ ( sk17 @ A ) @ ( sk20 @ A ) ) )
        = A )
      | ( strictorderedP @ A ) ),
    inference(cnf,[status(esa)],[219]) ).

thf(230,plain,
    ! [A: $i] :
      ( ( ( app @ ( app @ ( sk18 @ A ) @ ( cons @ ( sk16 @ A ) @ ( sk19 @ A ) ) ) @ ( cons @ ( sk17 @ A ) @ ( sk20 @ A ) ) )
        = A )
      | ~ ( ssList @ A )
      | ( strictorderedP @ A ) ),
    inference(lifteq,[status(thm)],[226]) ).

thf(10296,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk12 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10110,294]) ).

thf(10297,plain,
    ( ( strictorderP @ sk2 )
    | ( equalelemsP @ ( cons @ ( sk12 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[10296:[bind(A,$thf( sk12 @ sk2 ))]]) ).

thf(2905,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk10 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2763,361]) ).

thf(2906,plain,
    ( ( cyclefreeP @ sk2 )
    | ( frontsegP @ ( sk10 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[2905:[bind(A,$thf( sk10 @ sk2 ))]]) ).

thf(7378,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk13 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7151,292]) ).

thf(7379,plain,
    ( ( strictorderP @ sk2 )
    | ( rearsegP @ ( sk13 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[7378:[bind(A,$thf( sk13 @ sk2 ))]]) ).

thf(60,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( duplicatefreeP @ A )
      <=> ! [B: $i] :
            ( ( ssItem @ B )
           => ! [C: $i] :
                ( ( ssItem @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ! [E: $i] :
                        ( ( ssList @ E )
                       => ! [F: $i] :
                            ( ( ssList @ F )
                           => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                = A )
                             => ( B != C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).

thf(362,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( ( duplicatefreeP @ A )
         => ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ( B != C ) ) ) ) ) ) ) )
        & ( ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ( B != C ) ) ) ) ) ) )
         => ( duplicatefreeP @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(27798,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk19 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[27501,194]) ).

thf(27799,plain,
    ( ( strictorderedP @ sk2 )
    | ( segmentP @ ( sk19 @ sk2 ) @ ( sk19 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[27798:[bind(A,$thf( sk19 @ sk2 ))]]) ).

thf(63,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( ( geq @ A @ B )
                  & ( geq @ B @ C ) )
               => ( geq @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax88) ).

thf(387,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( ( geq @ A @ B )
                  & ( geq @ B @ C ) )
               => ( geq @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(27722,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk19 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[27501,292]) ).

thf(27723,plain,
    ( ( strictorderedP @ sk2 )
    | ( rearsegP @ ( sk19 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[27722:[bind(A,$thf( sk19 @ sk2 ))]]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( rearsegP @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).

thf(483,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( rearsegP @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(27737,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk19 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[27501,361]) ).

thf(27738,plain,
    ( ( strictorderedP @ sk2 )
    | ( frontsegP @ ( sk19 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[27737:[bind(A,$thf( sk19 @ sk2 ))]]) ).

thf(26750,plain,
    ! [A: $i] :
      ( ~ ( lt @ A @ A )
      | ( ( ssItem @ sk38 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[378,218]) ).

thf(26751,plain,
    ~ ( lt @ sk38 @ sk38 ),
    inference(pattern_uni,[status(thm)],[26750:[bind(A,$thf( sk38 ))]]) ).

thf(7927,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ~ ( memberP @ nil @ A )
      | ( ( ssItem @ ( sk11 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7717,232]) ).

thf(7928,plain,
    ( ( strictorderP @ sk1 )
    | ~ ( memberP @ nil @ ( sk11 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[7927:[bind(A,$thf( sk11 @ sk1 ))]]) ).

thf(1197,plain,
    ! [A: $i] :
      ( ( rearsegP @ A @ nil )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,292]) ).

thf(1198,plain,
    rearsegP @ sk2 @ nil,
    inference(pattern_uni,[status(thm)],[1197:[bind(A,$thf( sk2 ))]]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( totalorderedP @ A )
      <=> ! [B: $i] :
            ( ( ssItem @ B )
           => ! [C: $i] :
                ( ( ssItem @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ! [E: $i] :
                        ( ( ssList @ E )
                       => ! [F: $i] :
                            ( ( ssList @ F )
                           => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                = A )
                             => ( leq @ B @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).

thf(455,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( ( totalorderedP @ A )
         => ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ( leq @ B @ C ) ) ) ) ) ) ) )
        & ( ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ! [F: $i] :
                              ( ( ssList @ F )
                             => ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
                                  = A )
                               => ( leq @ B @ C ) ) ) ) ) ) )
         => ( totalorderedP @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( ( leq @ A @ B )
                  & ( leq @ B @ C ) )
               => ( leq @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).

thf(394,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( ( leq @ A @ B )
                  & ( leq @ B @ C ) )
               => ( leq @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(135,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ~ ( frontsegP @ A @ B )
      | ~ ( frontsegP @ B @ C )
      | ( frontsegP @ A @ C ) ),
    inference(cnf,[status(esa)],[134]) ).

thf(850,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ~ ( memberP @ nil @ nil )
      | ( A != sk38 ) ),
    inference(paramod_ordered,[status(thm)],[128,541]) ).

thf(851,plain,
    ( ~ ( ssList @ sk38 )
    | ~ ( frontsegP @ nil @ sk38 )
    | ~ ( memberP @ nil @ nil ) ),
    inference(pattern_uni,[status(thm)],[850:[bind(A,$thf( sk38 ))]]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( equalelemsP @ A )
      <=> ! [B: $i] :
            ( ( ssItem @ B )
           => ! [C: $i] :
                ( ( ssItem @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ! [E: $i] :
                        ( ( ssList @ E )
                       => ( ( ( app @ D @ ( cons @ B @ ( cons @ C @ E ) ) )
                            = A )
                         => ( B = C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).

thf(438,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( ( equalelemsP @ A )
         => ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ( ( ( app @ D @ ( cons @ B @ ( cons @ C @ E ) ) )
                              = A )
                           => ( B = C ) ) ) ) ) ) )
        & ( ! [B: $i] :
              ( ( ssItem @ B )
             => ! [C: $i] :
                  ( ( ssItem @ C )
                 => ! [D: $i] :
                      ( ( ssList @ D )
                     => ! [E: $i] :
                          ( ( ssList @ E )
                         => ( ( ( app @ D @ ( cons @ B @ ( cons @ C @ E ) ) )
                              = A )
                           => ( B = C ) ) ) ) ) )
         => ( equalelemsP @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(7883,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk11 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7717,196]) ).

thf(7884,plain,
    ( ( strictorderP @ sk1 )
    | ( totalorderedP @ ( cons @ ( sk11 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[7883:[bind(A,$thf( sk11 @ sk1 ))]]) ).

thf(12059,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk10 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2747,187]) ).

thf(12060,plain,
    ( ( cyclefreeP @ sk1 )
    | ( ( app @ ( sk10 @ sk1 ) @ nil )
      = ( sk10 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[12059:[bind(A,$thf( sk10 @ sk1 ))]]) ).

thf(1176,plain,
    ! [B: $i,A: $i] :
      ( ( ( hd @ sk1 )
        = B )
      | ~ ( ssList @ A )
      | ~ ( ssItem @ B )
      | ( ( cons @ sk5 @ nil )
       != ( cons @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[700,138]) ).

thf(1177,plain,
    ( ( ( hd @ sk1 )
      = sk5 )
    | ~ ( ssList @ nil )
    | ~ ( ssItem @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[1176:[bind(A,$thf( nil )),bind(B,$thf( sk5 ))]]) ).

thf(11506,plain,
    ( ( ( hd @ sk1 )
      = sk5 )
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[1177,609,334]) ).

thf(11507,plain,
    ( ( hd @ sk1 )
    = sk5 ),
    inference(simp,[status(thm)],[11506]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( ( leq @ A @ B )
                  & ( lt @ B @ C ) )
               => ( lt @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax91) ).

thf(431,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( ( leq @ A @ B )
                  & ( lt @ B @ C ) )
               => ( lt @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( cons @ C @ ( app @ B @ A ) )
                = ( app @ ( cons @ C @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).

thf(473,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ( ( cons @ C @ ( app @ B @ A ) )
                = ( app @ ( cons @ C @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(9096,plain,
    ! [A: $i] :
      ( ~ ( lt @ ( sk12 @ A ) @ ( sk11 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,178]) ).

thf(9097,plain,
    ( ~ ( lt @ ( sk12 @ sk2 ) @ ( sk11 @ sk2 ) )
    | ( strictorderP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[9096:[bind(A,$thf( sk2 ))]]) ).

thf(12047,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk14 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8524,187]) ).

thf(12048,plain,
    ( ( strictorderP @ sk1 )
    | ( ( app @ ( sk14 @ sk1 ) @ nil )
      = ( sk14 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[12047:[bind(A,$thf( sk14 @ sk1 ))]]) ).

thf(7678,plain,
    ! [A: $i] :
      ( ( sk5 != nil )
      | ~ ( neq @ A @ A )
      | ( ( ssItem @ nil )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7637,213]) ).

thf(7679,plain,
    ( ( sk5 != nil )
    | ~ ( neq @ nil @ nil ) ),
    inference(pattern_uni,[status(thm)],[7678:[bind(A,$thf( nil ))]]) ).

thf(26732,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ~ ( lt @ A @ A )
      | ( ( ssItem @ ( sk11 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7735,218]) ).

thf(26733,plain,
    ( ( strictorderP @ sk2 )
    | ~ ( lt @ ( sk11 @ sk2 ) @ ( sk11 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[26732:[bind(A,$thf( sk11 @ sk2 ))]]) ).

thf(8019,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk11 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7735,124]) ).

thf(8020,plain,
    ( ( strictorderP @ sk2 )
    | ( strictorderedP @ ( cons @ ( sk11 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[8019:[bind(A,$thf( sk11 @ sk2 ))]]) ).

thf(8803,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk14 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8556,243]) ).

thf(8804,plain,
    ( ( strictorderP @ sk2 )
    | ( segmentP @ ( sk14 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[8803:[bind(A,$thf( sk14 @ sk2 ))]]) ).

thf(12,axiom,
    cyclefreeP @ nil,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).

thf(145,plain,
    cyclefreeP @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(99,plain,
    ( ( memberP @ sk4 @ sk5 )
    | ( nil = sk4 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(116,plain,
    ( ( sk4 = nil )
    | ( memberP @ sk4 @ sk5 ) ),
    inference(lifteq,[status(thm)],[99]) ).

thf(543,plain,
    ( ( sk2 = nil )
    | ( memberP @ sk2 @ sk5 ) ),
    inference(rewrite,[status(thm)],[116,115]) ).

thf(689,plain,
    ( ( memberP @ sk2 @ sk5 )
    | ( sk2 != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[543,601]) ).

thf(690,plain,
    memberP @ sk2 @ sk5,
    inference(pattern_uni,[status(thm)],[689:[]]) ).

thf(11315,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( memberP @ nil @ nil )
    | ( ( frontsegP @ nil @ sk39 )
     != ( frontsegP @ nil @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[592,773]) ).

thf(11337,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( memberP @ nil @ nil )
    | ( nil != nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[11315]) ).

thf(11366,plain,
    ( ~ ( ssList @ sk39 )
    | ~ ( memberP @ nil @ nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[11337]) ).

thf(11384,plain,
    ( ~ ( memberP @ nil @ nil )
    | ( sk39 != nil )
    | ( ( ssList @ sk39 )
     != ( ssList @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[334,11366]) ).

thf(11441,plain,
    ( ~ ( memberP @ nil @ nil )
    | ( sk39 != nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[11384]) ).

thf(11461,plain,
    ( ~ ( memberP @ nil @ nil )
    | ( sk39 != nil ) ),
    inference(simp,[status(thm)],[11441]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ! [D: $i] :
                  ( ( ssItem @ D )
                 => ( ( ( cons @ C @ A )
                      = ( cons @ D @ B ) )
                   => ( ( C = D )
                      & ( B = A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).

thf(295,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssItem @ C )
             => ! [D: $i] :
                  ( ( ssItem @ D )
                 => ( ( ( cons @ C @ A )
                      = ( cons @ D @ B ) )
                   => ( ( C = D )
                      & ( B = A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(12055,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk9 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3161,187]) ).

thf(12056,plain,
    ( ( cyclefreeP @ sk2 )
    | ( ( app @ ( sk9 @ sk2 ) @ nil )
      = ( sk9 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[12055:[bind(A,$thf( sk9 @ sk2 ))]]) ).

thf(26738,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ~ ( lt @ A @ A )
      | ( ( ssItem @ ( sk7 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5022,218]) ).

thf(26739,plain,
    ( ( cyclefreeP @ sk2 )
    | ~ ( lt @ ( sk7 @ sk2 ) @ ( sk7 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[26738:[bind(A,$thf( sk7 @ sk2 ))]]) ).

thf(3227,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk9 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3143,243]) ).

thf(3228,plain,
    ( ( cyclefreeP @ sk1 )
    | ( segmentP @ ( sk9 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[3227:[bind(A,$thf( sk9 @ sk1 ))]]) ).

thf(13812,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk14 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8556,194]) ).

thf(13813,plain,
    ( ( strictorderP @ sk2 )
    | ( segmentP @ ( sk14 @ sk2 ) @ ( sk14 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[13812:[bind(A,$thf( sk14 @ sk2 ))]]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ssList @ ( app @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

thf(409,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ssList @ ( app @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(8812,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk14 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8556,361]) ).

thf(8813,plain,
    ( ( strictorderP @ sk2 )
    | ( frontsegP @ ( sk14 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[8812:[bind(A,$thf( sk14 @ sk2 ))]]) ).

thf(198,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( leq @ A @ B )
      | ( A = B )
      | ( lt @ A @ B ) ),
    inference(cnf,[status(esa)],[197]) ).

thf(199,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( leq @ A @ B )
      | ( lt @ A @ B ) ),
    inference(lifteq,[status(thm)],[198]) ).

thf(7263,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk13 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7119,243]) ).

thf(7264,plain,
    ( ( strictorderP @ sk1 )
    | ( segmentP @ ( sk13 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[7263:[bind(A,$thf( sk13 @ sk1 ))]]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( segmentP @ A @ B )
          <=> ? [C: $i] :
                ( ( ssList @ C )
                & ? [D: $i] :
                    ( ( ssList @ D )
                    & ( ( app @ ( app @ C @ B ) @ D )
                      = A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).

thf(338,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( segmentP @ A @ B )
             => ? [C: $i] :
                  ( ( ssList @ C )
                  & ? [D: $i] :
                      ( ( ssList @ D )
                      & ( ( app @ ( app @ C @ B ) @ D )
                        = A ) ) ) )
            & ( ? [C: $i] :
                  ( ( ssList @ C )
                  & ? [D: $i] :
                      ( ( ssList @ D )
                      & ( ( app @ ( app @ C @ B ) @ D )
                        = A ) ) )
             => ( segmentP @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(25272,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( ( app @ nil @ A )
        = A )
      | ( ( ssList @ ( sk9 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3143,216]) ).

thf(25273,plain,
    ( ( cyclefreeP @ sk1 )
    | ( ( app @ nil @ ( sk9 @ sk1 ) )
      = ( sk9 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[25272:[bind(A,$thf( sk9 @ sk1 ))]]) ).

thf(834,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ~ ( neq @ nil @ sk38 )
      | ( A != sk38 ) ),
    inference(paramod_ordered,[status(thm)],[128,642]) ).

thf(835,plain,
    ( ~ ( ssList @ sk38 )
    | ~ ( frontsegP @ nil @ sk38 )
    | ~ ( neq @ nil @ sk38 ) ),
    inference(pattern_uni,[status(thm)],[834:[bind(A,$thf( sk38 ))]]) ).

thf(30246,plain,
    ( ~ ( ssList @ sk38 )
    | ~ ( neq @ nil @ sk38 )
    | ( ( frontsegP @ nil @ sk38 )
     != ( frontsegP @ nil @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[592,835]) ).

thf(30264,plain,
    ( ~ ( ssList @ sk38 )
    | ~ ( neq @ nil @ sk38 )
    | ( nil != nil )
    | ( sk38 != nil ) ),
    inference(simp,[status(thm)],[30246]) ).

thf(30302,plain,
    ( ~ ( ssList @ sk38 )
    | ~ ( neq @ nil @ sk38 )
    | ( sk38 != nil ) ),
    inference(simp,[status(thm)],[30264]) ).

thf(30349,plain,
    ( ~ ( neq @ nil @ sk38 )
    | ( sk38 != nil )
    | ( ( ssList @ sk38 )
     != ( ssList @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[334,30302]) ).

thf(30436,plain,
    ( ~ ( neq @ nil @ sk38 )
    | ( sk38 != nil )
    | ( sk38 != nil ) ),
    inference(simp,[status(thm)],[30349]) ).

thf(30454,plain,
    ( ~ ( neq @ nil @ sk38 )
    | ( sk38 != nil ) ),
    inference(simp,[status(thm)],[30436]) ).

thf(29859,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk18 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29628,243]) ).

thf(29860,plain,
    ( ( strictorderedP @ sk2 )
    | ( segmentP @ ( sk18 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[29859:[bind(A,$thf( sk18 @ sk2 ))]]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( segmentP @ A @ B )
              & ( segmentP @ B @ A ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).

thf(470,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( segmentP @ A @ B )
              & ( segmentP @ B @ A ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(8147,plain,
    ! [A: $i] :
      ( ~ ( lt @ ( sk11 @ A ) @ ( sk12 @ A ) )
      | ( strictorderP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,176]) ).

thf(8148,plain,
    ( ~ ( lt @ ( sk11 @ sk2 ) @ ( sk12 @ sk2 ) )
    | ( strictorderP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[8147:[bind(A,$thf( sk2 ))]]) ).

thf(2462,plain,
    ( ~ ( frontsegP @ nil @ sk39 )
    | ( sk38 != nil )
    | ( ( ssList @ sk39 )
     != ( ssList @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[105,787]) ).

thf(2500,plain,
    ( ~ ( frontsegP @ nil @ sk39 )
    | ( sk38 != nil )
    | ( sk39 != sk2 ) ),
    inference(simp,[status(thm)],[2462]) ).

thf(26756,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ~ ( lt @ A @ A )
      | ( ( ssItem @ ( sk7 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5004,218]) ).

thf(26757,plain,
    ( ( cyclefreeP @ sk1 )
    | ~ ( lt @ ( sk7 @ sk1 ) @ ( sk7 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[26756:[bind(A,$thf( sk7 @ sk1 ))]]) ).

thf(4670,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk8 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4493,361]) ).

thf(4671,plain,
    ( ( cyclefreeP @ sk2 )
    | ( frontsegP @ ( sk8 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[4670:[bind(A,$thf( sk8 @ sk2 ))]]) ).

thf(26744,plain,
    ! [A: $i] :
      ( ~ ( lt @ A @ A )
      | ( ( ssItem @ sk5 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[609,218]) ).

thf(26745,plain,
    ~ ( lt @ sk5 @ sk5 ),
    inference(pattern_uni,[status(thm)],[26744:[bind(A,$thf( sk5 ))]]) ).

thf(12053,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk13 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7151,187]) ).

thf(12054,plain,
    ( ( strictorderP @ sk2 )
    | ( ( app @ ( sk13 @ sk2 ) @ nil )
      = ( sk13 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[12053:[bind(A,$thf( sk13 @ sk2 ))]]) ).

thf(5082,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk7 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5004,124]) ).

thf(5083,plain,
    ( ( cyclefreeP @ sk1 )
    | ( strictorderedP @ ( cons @ ( sk7 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[5082:[bind(A,$thf( sk7 @ sk1 ))]]) ).

thf(3411,plain,
    ( ~ ( segmentP @ nil @ sk39 )
    | ( sk38 != nil )
    | ( ( ssList @ sk39 )
     != ( ssList @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[106,1286]) ).

thf(3452,plain,
    ( ~ ( segmentP @ nil @ sk39 )
    | ( sk38 != nil )
    | ( sk39 != sk1 ) ),
    inference(simp,[status(thm)],[3411]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( tl @ ( cons @ B @ A ) )
            = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).

thf(450,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ( ( tl @ ( cons @ B @ A ) )
            = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(13796,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk9 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3143,194]) ).

thf(13797,plain,
    ( ( cyclefreeP @ sk1 )
    | ( segmentP @ ( sk9 @ sk1 ) @ ( sk9 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[13796:[bind(A,$thf( sk9 @ sk1 ))]]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( rearsegP @ A @ B )
              & ( rearsegP @ B @ A ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).

thf(495,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( rearsegP @ A @ B )
              & ( rearsegP @ B @ A ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(5114,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ~ ( memberP @ nil @ A )
      | ( ( ssItem @ ( sk7 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5004,232]) ).

thf(5115,plain,
    ( ( cyclefreeP @ sk1 )
    | ~ ( memberP @ nil @ ( sk7 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[5114:[bind(A,$thf( sk7 @ sk1 ))]]) ).

thf(5123,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk7 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5022,196]) ).

thf(5124,plain,
    ( ( cyclefreeP @ sk2 )
    | ( totalorderedP @ ( cons @ ( sk7 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[5123:[bind(A,$thf( sk7 @ sk2 ))]]) ).

thf(10260,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk12 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10110,196]) ).

thf(10261,plain,
    ( ( strictorderP @ sk2 )
    | ( totalorderedP @ ( cons @ ( sk12 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[10260:[bind(A,$thf( sk12 @ sk2 ))]]) ).

thf(2827,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk10 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2747,292]) ).

thf(2828,plain,
    ( ( cyclefreeP @ sk1 )
    | ( rearsegP @ ( sk10 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[2827:[bind(A,$thf( sk10 @ sk1 ))]]) ).

thf(171,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssItem @ B )
      | ( ssList @ ( cons @ B @ A ) ) ),
    inference(cnf,[status(esa)],[170]) ).

thf(12049,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk14 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8556,187]) ).

thf(12050,plain,
    ( ( strictorderP @ sk2 )
    | ( ( app @ ( sk14 @ sk2 ) @ nil )
      = ( sk14 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[12049:[bind(A,$thf( sk14 @ sk2 ))]]) ).

thf(25241,plain,
    ! [A: $i] :
      ( ( ( app @ nil @ A )
        = A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[106,216]) ).

thf(25242,plain,
    ( ( app @ nil @ sk1 )
    = sk1 ),
    inference(pattern_uni,[status(thm)],[25241:[bind(A,$thf( sk1 ))]]) ).

thf(25294,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( ( app @ nil @ A )
        = A )
      | ( ( ssList @ ( sk15 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9538,216]) ).

thf(25295,plain,
    ( ( strictorderP @ sk2 )
    | ( ( app @ nil @ ( sk15 @ sk2 ) )
      = ( sk15 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[25294:[bind(A,$thf( sk15 @ sk2 ))]]) ).

thf(207,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( gt @ A @ B )
      | ( lt @ B @ A ) ),
    inference(cnf,[status(esa)],[205]) ).

thf(2182,plain,
    ! [A: $i] :
      ( ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ sk39 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[377,196]) ).

thf(2183,plain,
    totalorderedP @ ( cons @ sk39 @ nil ),
    inference(pattern_uni,[status(thm)],[2182:[bind(A,$thf( sk39 ))]]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( strictorderedP @ ( cons @ A @ B ) )
          <=> ( ( nil = B )
              | ( ( nil != B )
                & ( strictorderedP @ B )
                & ( lt @ A @ ( hd @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax70) ).

thf(272,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( strictorderedP @ ( cons @ A @ B ) )
             => ( ( nil = B )
                | ( ( nil != B )
                  & ( strictorderedP @ B )
                  & ( lt @ A @ ( hd @ B ) ) ) ) )
            & ( ( ( nil = B )
                | ( ( nil != B )
                  & ( strictorderedP @ B )
                  & ( lt @ A @ ( hd @ B ) ) ) )
             => ( strictorderedP @ ( cons @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(2901,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk10 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2763,243]) ).

thf(2902,plain,
    ( ( cyclefreeP @ sk2 )
    | ( segmentP @ ( sk10 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[2901:[bind(A,$thf( sk10 @ sk2 ))]]) ).

thf(800,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ~ ( neq @ sk5 @ nil )
      | ( A != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[128,646]) ).

thf(801,plain,
    ( ~ ( ssList @ sk5 )
    | ~ ( frontsegP @ nil @ sk5 )
    | ~ ( neq @ sk5 @ nil ) ),
    inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( sk5 ))]]) ).

thf(28709,plain,
    ( ~ ( ssList @ sk5 )
    | ~ ( neq @ sk5 @ nil )
    | ( ( frontsegP @ nil @ sk5 )
     != ( frontsegP @ nil @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[592,801]) ).

thf(28717,plain,
    ( ~ ( ssList @ sk5 )
    | ~ ( neq @ sk5 @ nil )
    | ( nil != nil )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[28709]) ).

thf(28762,plain,
    ( ~ ( ssList @ sk5 )
    | ~ ( neq @ sk5 @ nil )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[28717]) ).

thf(28810,plain,
    ( ~ ( neq @ sk5 @ nil )
    | ( sk5 != nil )
    | ( ( ssList @ sk5 )
     != ( ssList @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[334,28762]) ).

thf(28891,plain,
    ( ~ ( neq @ sk5 @ nil )
    | ( sk5 != nil )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[28810]) ).

thf(28910,plain,
    ( ~ ( neq @ sk5 @ nil )
    | ( sk5 != nil ) ),
    inference(simp,[status(thm)],[28891]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( nil
              = ( app @ A @ B ) )
          <=> ( ( nil = B )
              & ( nil = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).

thf(346,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( nil
                = ( app @ A @ B ) )
             => ( ( nil = B )
                & ( nil = A ) ) )
            & ( ( ( nil = B )
                & ( nil = A ) )
             => ( nil
                = ( app @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(5161,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk7 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5022,294]) ).

thf(5162,plain,
    ( ( cyclefreeP @ sk2 )
    | ( equalelemsP @ ( cons @ ( sk7 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[5161:[bind(A,$thf( sk7 @ sk2 ))]]) ).

thf(7265,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk13 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7119,292]) ).

thf(7266,plain,
    ( ( strictorderP @ sk1 )
    | ( rearsegP @ ( sk13 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[7265:[bind(A,$thf( sk13 @ sk1 ))]]) ).

thf(36,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( frontsegP @ A @ B )
          <=> ? [C: $i] :
                ( ( ssList @ C )
                & ( ( app @ B @ C )
                  = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

thf(235,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( frontsegP @ A @ B )
             => ? [C: $i] :
                  ( ( ssList @ C )
                  & ( ( app @ B @ C )
                    = A ) ) )
            & ( ? [C: $i] :
                  ( ( ssList @ C )
                  & ( ( app @ B @ C )
                    = A ) )
             => ( frontsegP @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( frontsegP @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).

thf(433,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( frontsegP @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(3878,plain,
    ! [A: $i] :
      ( ( leq @ ( sk7 @ A ) @ ( sk6 @ A ) )
      | ( cyclefreeP @ A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,163]) ).

thf(3879,plain,
    ( ( leq @ ( sk7 @ sk2 ) @ ( sk6 @ sk2 ) )
    | ( cyclefreeP @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[3878:[bind(A,$thf( sk2 ))]]) ).

thf(715,plain,
    ! [A: $i] :
      ( ( strictorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ sk38 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[378,124]) ).

thf(716,plain,
    strictorderedP @ ( cons @ sk38 @ nil ),
    inference(pattern_uni,[status(thm)],[715:[bind(A,$thf( sk38 ))]]) ).

thf(1115,plain,
    ! [A: $i] :
      ( ( segmentP @ A @ nil )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,243]) ).

thf(1116,plain,
    segmentP @ sk2 @ nil,
    inference(pattern_uni,[status(thm)],[1115:[bind(A,$thf( sk2 ))]]) ).

thf(150,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssItem @ B )
      | ( ( cons @ B @ A )
        = ( app @ ( cons @ B @ nil ) @ A ) ) ),
    inference(cnf,[status(esa)],[149]) ).

thf(151,plain,
    ! [B: $i,A: $i] :
      ( ( ( app @ ( cons @ B @ nil ) @ A )
        = ( cons @ B @ A ) )
      | ~ ( ssList @ A )
      | ~ ( ssItem @ B ) ),
    inference(lifteq,[status(thm)],[150]) ).

thf(51,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( neq @ A @ B )
          <=> ( A != B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

thf(315,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( neq @ A @ B )
             => ( A != B ) )
            & ( ( A != B )
             => ( neq @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(179,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( strictorderP @ A )
      | ~ ( ssItem @ B )
      | ~ ( ssItem @ C )
      | ~ ( ssList @ D )
      | ~ ( ssList @ E )
      | ~ ( ssList @ F )
      | ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
       != A )
      | ( lt @ B @ C )
      | ( lt @ C @ B ) ),
    inference(cnf,[status(esa)],[172]) ).

thf(182,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
       != A )
      | ~ ( ssList @ A )
      | ~ ( strictorderP @ A )
      | ~ ( ssItem @ B )
      | ~ ( ssItem @ C )
      | ~ ( ssList @ D )
      | ~ ( ssList @ E )
      | ~ ( ssList @ F )
      | ( lt @ B @ C )
      | ( lt @ C @ B ) ),
    inference(lifteq,[status(thm)],[179]) ).

thf(183,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
      | ~ ( strictorderP @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
      | ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( ssList @ C )
      | ~ ( ssList @ D )
      | ~ ( ssList @ E )
      | ( lt @ A @ B )
      | ( lt @ B @ A ) ),
    inference(simp,[status(thm)],[182]) ).

thf(75,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( rearsegP @ nil @ A )
      <=> ( nil = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).

thf(422,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( ( rearsegP @ nil @ A )
         => ( nil = A ) )
        & ( ( nil = A )
         => ( rearsegP @ nil @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(4662,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk8 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4493,243]) ).

thf(4663,plain,
    ( ( cyclefreeP @ sk2 )
    | ( segmentP @ ( sk8 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[4662:[bind(A,$thf( sk8 @ sk2 ))]]) ).

thf(9811,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk15 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9538,361]) ).

thf(9812,plain,
    ( ( strictorderP @ sk2 )
    | ( frontsegP @ ( sk15 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[9811:[bind(A,$thf( sk15 @ sk2 ))]]) ).

thf(48,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil != A )
       => ? [B: $i] :
            ( ( ssItem @ B )
            & ( ( hd @ A )
              = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).

thf(300,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil != A )
       => ? [B: $i] :
            ( ( ssItem @ B )
            & ( ( hd @ A )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(40,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil = A )
        | ? [B: $i] :
            ( ( ssList @ B )
            & ? [C: $i] :
                ( ( ssItem @ C )
                & ( ( cons @ C @ B )
                  = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).

thf(262,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( ( nil = A )
        | ? [B: $i] :
            ( ( ssList @ B )
            & ? [C: $i] :
                ( ( ssItem @ C )
                & ( ( cons @ C @ B )
                  = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(162,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( cyclefreeP @ A )
      | ~ ( ssItem @ B )
      | ~ ( ssItem @ C )
      | ~ ( ssList @ D )
      | ~ ( ssList @ E )
      | ~ ( ssList @ F )
      | ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
       != A )
      | ~ ( leq @ B @ C )
      | ~ ( leq @ C @ B ) ),
    inference(cnf,[status(esa)],[157]) ).

thf(167,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
       != A )
      | ~ ( ssList @ A )
      | ~ ( cyclefreeP @ A )
      | ~ ( ssItem @ B )
      | ~ ( ssItem @ C )
      | ~ ( ssList @ D )
      | ~ ( ssList @ E )
      | ~ ( ssList @ F )
      | ~ ( leq @ B @ C )
      | ~ ( leq @ C @ B ) ),
    inference(lifteq,[status(thm)],[162]) ).

thf(168,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
      | ~ ( cyclefreeP @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
      | ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( ssList @ C )
      | ~ ( ssList @ D )
      | ~ ( ssList @ E )
      | ~ ( leq @ A @ B )
      | ~ ( leq @ B @ A ) ),
    inference(simp,[status(thm)],[167]) ).

thf(4786,plain,
    ( ~ ( segmentP @ nil @ sk38 )
    | ( sk39 != nil )
    | ( ( ssList @ sk38 )
     != ( ssList @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[106,2705]) ).

thf(4841,plain,
    ( ~ ( segmentP @ nil @ sk38 )
    | ( sk39 != nil )
    | ( sk38 != sk1 ) ),
    inference(simp,[status(thm)],[4786]) ).

thf(49,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ! [D: $i] :
                  ( ( ssList @ D )
                 => ( ( frontsegP @ ( cons @ A @ C ) @ ( cons @ B @ D ) )
                  <=> ( ( A = B )
                      & ( frontsegP @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).

thf(305,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ! [B: $i] :
          ( ( ssItem @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ! [D: $i] :
                  ( ( ssList @ D )
                 => ( ( ( frontsegP @ ( cons @ A @ C ) @ ( cons @ B @ D ) )
                     => ( ( A = B )
                        & ( frontsegP @ C @ D ) ) )
                    & ( ( ( A = B )
                        & ( frontsegP @ C @ D ) )
                     => ( frontsegP @ ( cons @ A @ C ) @ ( cons @ B @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(4209,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk6 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4111,196]) ).

thf(4210,plain,
    ( ( cyclefreeP @ sk2 )
    | ( totalorderedP @ ( cons @ ( sk6 @ sk2 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[4209:[bind(A,$thf( sk6 @ sk2 ))]]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( cyclefreeP @ ( cons @ A @ nil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).

thf(400,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( cyclefreeP @ ( cons @ A @ nil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(12021,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk9 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3143,187]) ).

thf(12022,plain,
    ( ( cyclefreeP @ sk1 )
    | ( ( app @ ( sk9 @ sk1 ) @ nil )
      = ( sk9 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[12021:[bind(A,$thf( sk9 @ sk1 ))]]) ).

thf(10223,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ~ ( neq @ A @ A )
      | ( ( ssItem @ ( sk12 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10092,213]) ).

thf(10224,plain,
    ( ( strictorderP @ sk1 )
    | ~ ( neq @ ( sk12 @ sk1 ) @ ( sk12 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[10223:[bind(A,$thf( sk12 @ sk1 ))]]) ).

thf(31026,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( rearsegP @ A @ nil )
      | ( ( ssList @ ( sk20 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[30720,292]) ).

thf(31027,plain,
    ( ( strictorderedP @ sk2 )
    | ( rearsegP @ ( sk20 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[31026:[bind(A,$thf( sk20 @ sk2 ))]]) ).

thf(748,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( frontsegP @ nil @ A )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[128,697]) ).

thf(749,plain,
    ( ~ ( ssList @ sk2 )
    | ~ ( frontsegP @ nil @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[748:[bind(A,$thf( sk2 ))]]) ).

thf(917,plain,
    ( ~ $true
    | ~ ( frontsegP @ nil @ sk2 ) ),
    inference(rewrite,[status(thm)],[749,105]) ).

thf(918,plain,
    ~ ( frontsegP @ nil @ sk2 ),
    inference(simp,[status(thm)],[917]) ).

thf(12023,plain,
    ! [A: $i] :
      ( ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,187]) ).

thf(12024,plain,
    ( ( app @ sk2 @ nil )
    = sk2 ),
    inference(pattern_uni,[status(thm)],[12023:[bind(A,$thf( sk2 ))]]) ).

thf(4192,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ ( sk6 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4097,294]) ).

thf(4193,plain,
    ( ( cyclefreeP @ sk1 )
    | ( equalelemsP @ ( cons @ ( sk6 @ sk1 ) @ nil ) ) ),
    inference(pattern_uni,[status(thm)],[4192:[bind(A,$thf( sk6 @ sk1 ))]]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( rearsegP @ A @ B )
          <=> ? [C: $i] :
                ( ( ssList @ C )
                & ( ( app @ C @ B )
                  = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).

thf(415,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ( ( ( rearsegP @ A @ B )
             => ? [C: $i] :
                  ( ( ssList @ C )
                  & ( ( app @ C @ B )
                    = A ) ) )
            & ( ? [C: $i] :
                  ( ( ssList @ C )
                  & ( ( app @ C @ B )
                    = A ) )
             => ( rearsegP @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(4794,plain,
    ( ~ ( segmentP @ nil @ sk38 )
    | ( sk39 != nil )
    | ( ( ssList @ sk38 )
     != ( ssList @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[105,2705]) ).

thf(4848,plain,
    ( ~ ( segmentP @ nil @ sk38 )
    | ( sk39 != nil )
    | ( sk38 != sk2 ) ),
    inference(simp,[status(thm)],[4794]) ).

thf(26724,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ~ ( lt @ A @ A )
      | ( ( ssItem @ ( sk6 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4097,218]) ).

thf(26725,plain,
    ( ( cyclefreeP @ sk1 )
    | ~ ( lt @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[26724:[bind(A,$thf( sk6 @ sk1 ))]]) ).

thf(12041,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ ( sk15 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9538,187]) ).

thf(12042,plain,
    ( ( strictorderP @ sk2 )
    | ( ( app @ ( sk15 @ sk2 ) @ nil )
      = ( sk15 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[12041:[bind(A,$thf( sk15 @ sk2 ))]]) ).

thf(10286,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk2 )
      | ~ ( neq @ A @ A )
      | ( ( ssItem @ ( sk12 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10110,213]) ).

thf(10287,plain,
    ( ( strictorderP @ sk2 )
    | ~ ( neq @ ( sk12 @ sk2 ) @ ( sk12 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[10286:[bind(A,$thf( sk12 @ sk2 ))]]) ).

thf(347,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ( nil != B )
      | ( nil != A )
      | ( nil
        = ( app @ A @ B ) ) ),
    inference(cnf,[status(esa)],[346]) ).

thf(350,plain,
    ! [B: $i,A: $i] :
      ( ( nil != B )
      | ( nil != A )
      | ( ( app @ A @ B )
        = nil )
      | ~ ( ssList @ A )
      | ~ ( ssList @ B ) ),
    inference(lifteq,[status(thm)],[347]) ).

thf(351,plain,
    ( ( ( app @ nil @ nil )
      = nil )
    | ~ ( ssList @ nil ) ),
    inference(simp,[status(thm)],[350]) ).

thf(981,plain,
    ( ( ( app @ nil @ nil )
      = nil )
    | ~ $true ),
    inference(rewrite,[status(thm)],[351,334]) ).

thf(982,plain,
    ( ( app @ nil @ nil )
    = nil ),
    inference(simp,[status(thm)],[981]) ).

thf(31041,plain,
    ! [A: $i] :
      ( ( strictorderedP @ sk2 )
      | ( frontsegP @ A @ nil )
      | ( ( ssList @ ( sk20 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[30720,361]) ).

thf(31042,plain,
    ( ( strictorderedP @ sk2 )
    | ( frontsegP @ ( sk20 @ sk2 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[31041:[bind(A,$thf( sk20 @ sk2 ))]]) ).

thf(1221,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( segmentP @ nil @ A )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[142,697]) ).

thf(1222,plain,
    ( ~ ( ssList @ sk2 )
    | ~ ( segmentP @ nil @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[1221:[bind(A,$thf( sk2 ))]]) ).

thf(1504,plain,
    ( ~ $true
    | ~ ( segmentP @ nil @ sk2 ) ),
    inference(rewrite,[status(thm)],[1222,105]) ).

thf(1505,plain,
    ~ ( segmentP @ nil @ sk2 ),
    inference(simp,[status(thm)],[1504]) ).

thf(26748,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ~ ( lt @ A @ A )
      | ( ( ssItem @ ( sk6 @ sk2 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4111,218]) ).

thf(26749,plain,
    ( ( cyclefreeP @ sk2 )
    | ~ ( lt @ ( sk6 @ sk2 ) @ ( sk6 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[26748:[bind(A,$thf( sk6 @ sk2 ))]]) ).

thf(13823,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk10 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2747,194]) ).

thf(13824,plain,
    ( ( cyclefreeP @ sk1 )
    | ( segmentP @ ( sk10 @ sk1 ) @ ( sk10 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[13823:[bind(A,$thf( sk10 @ sk1 ))]]) ).

thf(13791,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk2 )
      | ( segmentP @ A @ A )
      | ( ( ssList @ ( sk8 @ sk2 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4493,194]) ).

thf(13792,plain,
    ( ( cyclefreeP @ sk2 )
    | ( segmentP @ ( sk8 @ sk2 ) @ ( sk8 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[13791:[bind(A,$thf( sk8 @ sk2 ))]]) ).

thf(122,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssItem @ B )
      | ~ ( ssItem @ C )
      | ~ ( lt @ A @ B )
      | ~ ( lt @ B @ C )
      | ( lt @ A @ C ) ),
    inference(cnf,[status(esa)],[121]) ).

thf(5929,plain,
    ( ~ ( frontsegP @ nil @ sk38 )
    | ( sk39 != nil )
    | ( ( ssList @ sk38 )
     != ( ssList @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[106,2709]) ).

thf(5986,plain,
    ( ~ ( frontsegP @ nil @ sk38 )
    | ( sk39 != nil )
    | ( sk38 != sk1 ) ),
    inference(simp,[status(thm)],[5929]) ).

thf(57,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( totalorderP @ ( cons @ A @ nil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).

thf(354,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( totalorderP @ ( cons @ A @ nil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(2437,plain,
    ! [A: $i] :
      ( ( equalelemsP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ sk38 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[378,294]) ).

thf(2438,plain,
    equalelemsP @ ( cons @ sk38 @ nil ),
    inference(pattern_uni,[status(thm)],[2437:[bind(A,$thf( sk38 ))]]) ).

thf(424,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( nil != A )
      | ( rearsegP @ nil @ A ) ),
    inference(cnf,[status(esa)],[422]) ).

thf(426,plain,
    ! [A: $i] :
      ( ( nil != A )
      | ~ ( ssList @ A )
      | ( rearsegP @ nil @ A ) ),
    inference(lifteq,[status(thm)],[424]) ).

thf(427,plain,
    ( ~ ( ssList @ nil )
    | ( rearsegP @ nil @ nil ) ),
    inference(simp,[status(thm)],[426]) ).

thf(638,plain,
    ( ~ $true
    | ( rearsegP @ nil @ nil ) ),
    inference(rewrite,[status(thm)],[427,334]) ).

thf(639,plain,
    rearsegP @ nil @ nil,
    inference(simp,[status(thm)],[638]) ).

thf(4188,plain,
    ! [A: $i] :
      ( ( cyclefreeP @ sk1 )
      | ~ ( neq @ A @ A )
      | ( ( ssItem @ ( sk6 @ sk1 ) )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4097,213]) ).

thf(4189,plain,
    ( ( cyclefreeP @ sk1 )
    | ~ ( neq @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[4188:[bind(A,$thf( sk6 @ sk1 ))]]) ).

thf(8684,plain,
    ! [A: $i] :
      ( ( strictorderP @ sk1 )
      | ( segmentP @ A @ nil )
      | ( ( ssList @ ( sk14 @ sk1 ) )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8524,243]) ).

thf(8685,plain,
    ( ( strictorderP @ sk1 )
    | ( segmentP @ ( sk14 @ sk1 ) @ nil ) ),
    inference(pattern_uni,[status(thm)],[8684:[bind(A,$thf( sk14 @ sk1 ))]]) ).

thf(57893,plain,
    $false,
    inference(e,[status(thm)],[29862,4201,31504,7890,4169,2412,249,2499,468,234,11998,777,138,1190,479,10267,481,2250,170,10234,217,7377,3230,5069,120,379,13811,202,115,25260,10198,19213,269,13815,4097,142,797,27721,31729,153,4575,7697,174,185,3308,12009,29356,4665,13800,1127,7637,2763,27111,288,10305,184,29330,9805,7386,389,4224,8806,12046,29292,13820,125,196,12003,25275,157,853,189,10110,31107,3312,152,216,164,7273,4583,321,623,485,106,9680,211,646,29260,121,13818,8050,29940,397,221,293,453,132,396,133,411,243,428,29135,507,312,26743,2002,206,2586,7657,292,233,2204,201,220,26735,714,7735,3450,9682,380,2705,160,3610,192,4493,165,12058,334,26759,729,29312,3618,361,1128,1392,8136,467,13778,7663,229,8058,5983,197,2826,4155,435,285,224,8694,697,156,4248,13904,2709,356,169,499,188,8014,193,8687,476,642,9085,3143,488,124,225,7717,25233,5107,2830,1478,26727,13805,4244,837,13081,13822,779,5170,134,360,205,9689,541,1286,773,128,1991,105,244,31025,32173,3306,30720,2904,1103,166,8040,148,161,4577,7910,375,3871,5138,4256,29348,7920,180,12052,28162,149,176,402,13809,204,5022,413,3234,26729,10242,291,391,29877,498,9538,335,181,9803,159,9506,787,7689,8524,5158,187,219,5103,10204,377,230,98,208,8556,172,10297,2906,7379,362,27799,387,7119,609,27723,594,483,27738,2252,26751,799,213,7928,700,1198,2550,455,394,135,851,438,7884,12060,11507,431,473,9097,12048,7151,7679,123,26733,8020,3161,8804,194,145,690,11461,295,12056,26739,3228,4469,13813,409,8813,2747,199,7264,177,338,25273,30454,29860,470,8148,2500,26757,154,27501,4671,4111,175,26745,12054,5083,13784,3452,450,13797,539,495,5115,218,5124,29628,10261,231,203,2828,114,171,139,12050,25242,25295,207,2183,272,2902,28910,346,378,5162,7266,235,433,3879,716,214,1116,151,315,146,183,422,4663,9812,300,835,262,5004,168,190,4841,305,4210,195,400,12022,10224,31027,242,294,918,801,136,12024,4193,10092,415,4848,26725,12042,644,131,10287,982,178,31042,1505,163,200,26749,13824,13792,122,5986,354,2438,639,4189,222,592,232,8685,227]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SWC342+1 : TPTP v8.2.0. Released v2.4.0.
% 0.09/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n027.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sun May 19 03:42:39 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.99/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.16  % [INFO] 	 Parsing done (216ms). 
% 1.30/1.17  % [INFO] 	 Running in sequential loop mode. 
% 2.21/1.53  % [INFO] 	 eprover registered as external prover. 
% 2.21/1.53  % [INFO] 	 cvc4 registered as external prover. 
% 2.21/1.54  % [INFO] 	 Scanning for conjecture ... 
% 2.38/1.67  % [INFO] 	 Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ... 
% 2.52/1.77  % [INFO] 	 Axiom selection finished. Selected 95 axioms (removed 0 axioms). 
% 2.95/1.90  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 3.15/1.92  % [INFO] 	 Type checking passed. 
% 3.15/1.93  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 149.83/27.59  % External prover 'e' found a proof!
% 149.83/27.59  % [INFO] 	 Killing All external provers ... 
% 149.83/27.59  % Time passed: 27124ms (effective reasoning time: 26411ms)
% 149.83/27.59  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 149.83/27.59  % Axioms used in derivation (95): ax74, ax13, ax37, ax14, ax12, ax79, ax20, ax52, ax67, ax24, ax63, ax56, ax4, ax47, ax41, ax90, ax31, ax28, ax9, ax17, ax6, ax45, ax40, ax85, ax35, ax58, ax69, ax78, ax39, ax89, ax27, ax66, ax8, ax91, ax73, ax51, ax48, ax21, ax88, ax62, ax10, ax55, ax32, ax95, ax16, ax80, ax59, ax1, ax7, ax77, ax38, ax44, ax84, ax92, ax94, ax33, ax26, ax61, ax11, ax50, ax87, ax72, ax65, ax22, ax15, ax81, ax76, ax43, ax83, ax19, ax2, ax70, ax54, ax49, ax46, ax34, ax23, ax86, ax25, ax60, ax71, ax57, ax68, ax30, ax42, ax82, ax18, ax3, ax5, ax36, ax64, ax29, ax75, ax53, ax93
% 149.83/27.59  % No. of inferences in proof: 877
% 149.83/27.59  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 27124 ms resp. 26411 ms w/o parsing
% 150.72/27.94  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 150.72/27.95  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------