TSTP Solution File: ITP076^2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP076^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:22:40 EDT 2024

% Result   : Theorem 124.95s 20.73s
% Output   : Refutation 125.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   41
%            Number of leaves      :   84
% Syntax   : Number of formulae    :  501 ( 232 unt;  50 typ;   0 def)
%            Number of atoms       : 1140 ( 562 equ;   4 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives : 3579 ( 378   ~; 235   |;  81   &;2812   @)
%                                         (   0 <=>;  73  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  262 ( 262   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   53 (  49 usr;  21 con; 0-4 aty)
%            Number of variables   : 1039 ( 195   ^ 731   !; 112   ?;1039   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(hF_Mirabelle_hf_type,type,
    hF_Mirabelle_hf: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(hF_Mir1687042746ollect_type,type,
    hF_Mir1687042746ollect: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(hF_Mirabelle_HUnion_type,type,
    hF_Mirabelle_HUnion: hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(hF_Mir569462966eplace_type,type,
    hF_Mir569462966eplace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).

thf(hF_Mirabelle_RepFun_type,type,
    hF_Mirabelle_RepFun: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf ).

thf(hF_Mirabelle_Replace_type,type,
    hF_Mirabelle_Replace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).

thf(hF_Mirabelle_hfst_type,type,
    hF_Mirabelle_hfst: hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(hF_Mir859708136nction_type,type,
    hF_Mir859708136nction: hF_Mirabelle_hf > $o ).

thf(hF_Mirabelle_hmem_type,type,
    hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).

thf(hF_Mirabelle_hpair_type,type,
    hF_Mirabelle_hpair: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(hF_Mir1093797708lation_type,type,
    hF_Mir1093797708lation: hF_Mirabelle_hf > $o ).

thf(hF_Mir165288108strict_type,type,
    hF_Mir165288108strict: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(hF_Mirabelle_hsnd_type,type,
    hF_Mirabelle_hsnd: hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(hF_Mirabelle_hsplit_type,type,
    hF_Mirabelle_hsplit: 
      !>[TA: $tType] : ( ( hF_Mirabelle_hf > hF_Mirabelle_hf > TA ) > hF_Mirabelle_hf > TA ) ).

thf(hF_Mir796903520_hpair_type,type,
    hF_Mir796903520_hpair: hF_Mirabelle_hf > $o ).

thf(r_type,type,
    r: hF_Mirabelle_hf ).

thf(x_type,type,
    x: hF_Mirabelle_hf ).

thf(sk1_type,type,
    sk1: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk2_type,type,
    sk2: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk3_type,type,
    sk3: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk4_type,type,
    sk4: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk6_type,type,
    sk6: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk7_type,type,
    sk7: hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk8_type,type,
    sk8: ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk9_type,type,
    sk9: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk10_type,type,
    sk10: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk11_type,type,
    sk11: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk12_type,type,
    sk12: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk13_type,type,
    sk13: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk14_type,type,
    sk14: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk15_type,type,
    sk15: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk23_type,type,
    sk23: hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk79_type,type,
    sk79: hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk80_type,type,
    sk80: hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(sk127_type,type,
    sk127: hF_Mirabelle_hf ).

thf(sk128_type,type,
    sk128: hF_Mirabelle_hf ).

thf(sk129_type,type,
    sk129: hF_Mirabelle_hf ).

thf(sk366_type,type,
    sk366: hF_Mirabelle_hf ).

thf(sk367_type,type,
    sk367: hF_Mirabelle_hf ).

thf(sk368_type,type,
    sk368: hF_Mirabelle_hf ).

thf(sk369_type,type,
    sk369: hF_Mirabelle_hf ).

thf(sk370_type,type,
    sk370: hF_Mirabelle_hf ).

thf(sk371_type,type,
    sk371: hF_Mirabelle_hf ).

thf(sk372_type,type,
    sk372: hF_Mirabelle_hf ).

thf(sk373_type,type,
    sk373: hF_Mirabelle_hf ).

thf(sk376_type,type,
    sk376: hF_Mirabelle_hf ).

thf(sk377_type,type,
    sk377: hF_Mirabelle_hf ).

thf(sk378_type,type,
    sk378: hF_Mirabelle_hf ).

thf(sk379_type,type,
    sk379: hF_Mirabelle_hf ).

thf(11,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_Replace @ B @ C ) )
      = ( ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ B )
            & ( C @ D @ A )
            & ! [E: hF_Mirabelle_hf] :
                ( ( C @ D @ E )
               => ( E = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Replace__iff) ).

thf(69,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_Replace @ B @ C ) )
      = ( ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ B )
            & ( C @ D @ A )
            & ! [E: hF_Mirabelle_hf] :
                ( ( C @ D @ E )
               => ( E = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(27,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
      ( ! [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ C @ A )
         => ( ( B @ C @ D )
           => ( ( B @ C @ E )
             => ( E = D ) ) ) )
     => ? [C: hF_Mirabelle_hf] :
        ! [D: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ D @ C )
          = ( ? [E: hF_Mirabelle_hf] :
                ( ( hF_Mirabelle_hmem @ E @ A )
                & ( B @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_replacement) ).

thf(129,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
      ( ! [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ C @ A )
         => ( ( B @ C @ D )
           => ( ( B @ C @ E )
             => ( E = D ) ) ) )
     => ? [C: hF_Mirabelle_hf] :
        ! [D: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ D @ C )
          = ( ? [E: hF_Mirabelle_hf] :
                ( ( hF_Mirabelle_hmem @ E @ A )
                & ( B @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(130,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
      ( ! [C: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ C @ A )
         => ! [D: hF_Mirabelle_hf] :
              ( ( B @ C @ D )
             => ! [E: hF_Mirabelle_hf] :
                  ( ( B @ C @ E )
                 => ( E = D ) ) ) )
     => ? [C: hF_Mirabelle_hf] :
        ! [D: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ D @ C )
          = ( ? [E: hF_Mirabelle_hf] :
                ( ( hF_Mirabelle_hmem @ E @ A )
                & ( B @ E @ D ) ) ) ) ),
    inference(miniscope,[status(thm)],[129]) ).

thf(134,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( sk14 @ B @ A )
       != ( sk13 @ B @ A ) )
      | ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    inference(cnf,[status(esa)],[130]) ).

thf(138,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( sk14 @ B @ A )
       != ( sk13 @ B @ A ) )
      | ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    inference(lifteq,[status(thm)],[134]) ).

thf(19,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
    ? [C: hF_Mirabelle_hf] :
    ! [D: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ D @ C )
      = ( ( hF_Mirabelle_hmem @ D @ A )
        & ( B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_comprehension) ).

thf(101,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
    ? [C: hF_Mirabelle_hf] :
    ! [D: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ D @ C )
      = ( ( hF_Mirabelle_hmem @ D @ A )
        & ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(32,axiom,
    ( hF_Mir859708136nction
    = ( ^ [A: hF_Mirabelle_hf] :
        ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
         => ! [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
             => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_hfunction__def) ).

thf(150,plain,
    ( hF_Mir859708136nction
    = ( ^ [A: hF_Mirabelle_hf] :
        ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
         => ! [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
             => ( C = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(151,plain,
    ( hF_Mir859708136nction
    = ( ^ [A: hF_Mirabelle_hf] :
        ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
         => ! [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
             => ( C = D ) ) ) ) ),
    inference(lifteq,[status(thm)],[150]) ).

thf(190,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir859708136nction @ A )
      = ( ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
           => ! [D: hF_Mirabelle_hf] :
                ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
               => ( C = D ) ) ) ) ),
    inference(func_ext,[status(esa)],[151]) ).

thf(1,conjecture,
    hF_Mir859708136nction @ ( hF_Mir165288108strict @ r @ x ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(2,negated_conjecture,
    ~ ( hF_Mir859708136nction @ ( hF_Mir165288108strict @ r @ x ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(34,plain,
    ~ ( hF_Mir859708136nction @ ( hF_Mir165288108strict @ r @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(2474,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
           => ! [D: hF_Mirabelle_hf] :
                ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
               => ( C = D ) ) )
      | ( ( hF_Mir859708136nction @ A )
       != ( hF_Mir859708136nction @ ( hF_Mir165288108strict @ r @ x ) ) ) ),
    inference(paramod_ordered,[status(thm)],[190,34]) ).

thf(2475,plain,
    ~ ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
        ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ ( hF_Mir165288108strict @ r @ x ) )
       => ! [C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ ( hF_Mir165288108strict @ r @ x ) )
           => ( B = C ) ) ),
    inference(pattern_uni,[status(thm)],[2474:[bind(A,$thf( hF_Mir165288108strict @ r @ x ))]]) ).

thf(2502,plain,
    hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) @ ( hF_Mir165288108strict @ r @ x ),
    inference(cnf,[status(esa)],[2475]) ).

thf(15,axiom,
    ! [A: hF_Mirabelle_hf] :
    ? [B: hF_Mirabelle_hf] :
    ! [C: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ C @ B )
      = ( ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ A )
            & ( hF_Mirabelle_hmem @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_union__of__set) ).

thf(83,plain,
    ! [A: hF_Mirabelle_hf] :
    ? [B: hF_Mirabelle_hf] :
    ! [C: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ C @ B )
      = ( ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ A )
            & ( hF_Mirabelle_hmem @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(84,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ B @ ( sk7 @ A ) )
      = ( ? [C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ C @ A )
            & ( hF_Mirabelle_hmem @ B @ C ) ) ) ),
    inference(cnf,[status(esa)],[83]) ).

thf(85,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ B @ ( sk7 @ A ) )
      = ( ? [C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ C @ A )
            & ( hF_Mirabelle_hmem @ B @ C ) ) ) ),
    inference(lifteq,[status(thm)],[84]) ).

thf(20,axiom,
    ! [A: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_hmem__not__refl) ).

thf(104,plain,
    ! [A: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(105,plain,
    ~ ? [A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ A @ A ),
    inference(miniscope,[status(thm)],[104]) ).

thf(106,plain,
    ! [A: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ A @ A ),
    inference(cnf,[status(esa)],[105]) ).

thf(1555,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ A )
            & ( hF_Mirabelle_hmem @ B @ D ) )
      | ( ( hF_Mirabelle_hmem @ B @ ( sk7 @ A ) )
       != ( hF_Mirabelle_hmem @ C @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[85,106]) ).

thf(1556,plain,
    ! [A: hF_Mirabelle_hf] :
      ~ ? [B: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ B @ A )
          & ( hF_Mirabelle_hmem @ ( sk7 @ A ) @ B ) ),
    inference(pattern_uni,[status(thm)],[1555:[bind(A,$thf( D )),bind(B,$thf( sk7 @ D )),bind(C,$thf( sk7 @ D ))]]) ).

thf(1633,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ B @ A )
      | ~ ( hF_Mirabelle_hmem @ ( sk7 @ A ) @ B ) ),
    inference(cnf,[status(esa)],[1556]) ).

thf(1634,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ B @ A )
      | ~ ( hF_Mirabelle_hmem @ ( sk7 @ A ) @ B ) ),
    inference(simp,[status(thm)],[1633]) ).

thf(2558,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ ( sk7 @ A ) @ B )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mirabelle_hmem @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2502,1634]) ).

thf(2559,plain,
    ~ ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir165288108strict @ r @ x ) ) @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) ),
    inference(pattern_uni,[status(thm)],[2558:[bind(A,$thf( hF_Mir165288108strict @ r @ x )),bind(B,$thf( hF_Mirabelle_hpair @ sk127 @ sk129 ))]]) ).

thf(2503,plain,
    hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir165288108strict @ r @ x ),
    inference(cnf,[status(esa)],[2475]) ).

thf(7,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) )
      = ( ( B @ A )
        & ( hF_Mirabelle_hmem @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_HCollect__iff) ).

thf(58,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) )
      = ( ( B @ A )
        & ( hF_Mirabelle_hmem @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(59,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) )
      = ( ( B @ A )
        & ( hF_Mirabelle_hmem @ A @ C ) ) ),
    inference(cnf,[status(esa)],[58]) ).

thf(60,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) )
      = ( ( B @ A )
        & ( hF_Mirabelle_hmem @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[59]) ).

thf(3398,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( B @ A )
        = ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) ) )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mirabelle_hmem @ A @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[2503,60]) ).

thf(3399,plain,
    ! [A: hF_Mirabelle_hf > $o] :
      ( ( A @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) )
      = ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ A @ ( hF_Mir165288108strict @ r @ x ) ) ) ),
    inference(pattern_uni,[status(thm)],[3398:[bind(A,$thf( hF_Mirabelle_hpair @ sk127 @ sk128 )),bind(B,$thf( B )),bind(C,$thf( hF_Mir165288108strict @ r @ x ))]]) ).

thf(3609,plain,
    ! [A: hF_Mirabelle_hf > $o] :
      ( ( A @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) )
      = ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ A @ ( hF_Mir165288108strict @ r @ x ) ) ) ),
    inference(simp,[status(thm)],[3399]) ).

thf(33,axiom,
    hF_Mir859708136nction @ r,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(152,plain,
    hF_Mir859708136nction @ r,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(4974,plain,
    ! [A: hF_Mirabelle_hf > $o] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ A @ ( hF_Mir165288108strict @ r @ x ) ) )
      | ( ( A @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) )
       != ( hF_Mir859708136nction @ r ) ) ),
    inference(paramod_ordered,[status(thm)],[3609,152]) ).

thf(5189,plain,
    ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
    @ ( hF_Mir1687042746ollect
      @ ^ [A: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ r )
      @ ( hF_Mir165288108strict @ r @ x ) ) ),
    inference(pre_uni,[status(thm)],[4974:[bind(A,$thf( ^ [B: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ r ) ))]]) ).

thf(6074,plain,
    ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
    @ ( hF_Mir1687042746ollect
      @ ^ [A: hF_Mirabelle_hf] : $true
      @ ( hF_Mir165288108strict @ r @ x ) ) ),
    inference(rewrite,[status(thm)],[5189,152]) ).

thf(10,axiom,
    ( hF_Mir796903520_hpair
    = ( ^ [A: hF_Mirabelle_hf] :
        ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( A
          = ( hF_Mirabelle_hpair @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_is__hpair__def) ).

thf(67,plain,
    ( hF_Mir796903520_hpair
    = ( ^ [A: hF_Mirabelle_hf] :
        ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( A
          = ( hF_Mirabelle_hpair @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(68,plain,
    ( hF_Mir796903520_hpair
    = ( ^ [A: hF_Mirabelle_hf] :
        ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( A
          = ( hF_Mirabelle_hpair @ B @ C ) ) ) ),
    inference(lifteq,[status(thm)],[67]) ).

thf(156,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir796903520_hpair @ A )
      = ( ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
            ( A
            = ( hF_Mirabelle_hpair @ B @ C ) ) ) ),
    inference(func_ext,[status(esa)],[68]) ).

thf(525,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir796903520_hpair @ A )
      | ~ ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
            ( A
            = ( hF_Mirabelle_hpair @ B @ C ) ) ),
    inference(bool_ext,[status(thm)],[156]) ).

thf(561,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( A
       != ( hF_Mirabelle_hpair @ B @ C ) )
      | ( hF_Mir796903520_hpair @ A ) ),
    inference(cnf,[status(esa)],[525]) ).

thf(562,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( A
       != ( hF_Mirabelle_hpair @ B @ C ) )
      | ( hF_Mir796903520_hpair @ A ) ),
    inference(lifteq,[status(thm)],[561]) ).

thf(563,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( hF_Mir796903520_hpair @ ( hF_Mirabelle_hpair @ A @ B ) ),
    inference(simp,[status(thm)],[562]) ).

thf(4956,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > $o] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ A @ ( hF_Mir165288108strict @ r @ x ) ) )
      | ( ( A @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) )
       != ( hF_Mir796903520_hpair @ ( hF_Mirabelle_hpair @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3609,563]) ).

thf(5133,plain,
    hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ),
    inference(pre_uni,[status(thm)],[4956:[bind(A,$thf( hF_Mir796903520_hpair )),bind(B,$thf( sk127 )),bind(C,$thf( sk128 ))]]) ).

thf(5021,plain,
    ! [A: hF_Mirabelle_hf > $o] :
      ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ A @ ( hF_Mir165288108strict @ r @ x ) ) )
      | ( ( A @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) )
       != ( hF_Mir859708136nction @ ( hF_Mir165288108strict @ r @ x ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3609,34]) ).

thf(5177,plain,
    ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
      @ ( hF_Mir1687042746ollect
        @ ^ [A: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ ( hF_Mir165288108strict @ r @ x ) )
        @ ( hF_Mir165288108strict @ r @ x ) ) ),
    inference(pre_uni,[status(thm)],[5021:[bind(A,$thf( ^ [B: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ ( hF_Mir165288108strict @ r @ x ) ) ))]]) ).

thf(7367,plain,
    ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
      @ ( hF_Mir1687042746ollect
        @ ^ [A: hF_Mirabelle_hf] : $false
        @ ( hF_Mir165288108strict @ r @ x ) ) ),
    inference(rewrite,[status(thm)],[5177,34]) ).

thf(7397,plain,
    ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ) )
   != ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
      @ ( hF_Mir1687042746ollect
        @ ^ [A: hF_Mirabelle_hf] : $false
        @ ( hF_Mir165288108strict @ r @ x ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5133,7367]) ).

thf(7408,plain,
    ( ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
     != ( hF_Mirabelle_hpair @ sk127 @ sk128 ) )
    | ( ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) )
     != ( hF_Mir1687042746ollect
        @ ^ [A: hF_Mirabelle_hf] : $false
        @ ( hF_Mir165288108strict @ r @ x ) ) ) ),
    inference(simp,[status(thm)],[7397]) ).

thf(7448,plain,
    ( ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) )
   != ( hF_Mir1687042746ollect
      @ ^ [A: hF_Mirabelle_hf] : $false
      @ ( hF_Mir165288108strict @ r @ x ) ) ),
    inference(simp,[status(thm)],[7408]) ).

thf(8256,plain,
    ( ( hF_Mir796903520_hpair
     != ( ^ [A: hF_Mirabelle_hf] : $false ) )
    | ( ( hF_Mir165288108strict @ r @ x )
     != ( hF_Mir165288108strict @ r @ x ) ) ),
    inference(simp,[status(thm)],[7448]) ).

thf(8259,plain,
    ( hF_Mir796903520_hpair
   != ( ^ [A: hF_Mirabelle_hf] : $false ) ),
    inference(simp,[status(thm)],[8256]) ).

thf(8260,plain,
    hF_Mir796903520_hpair @ sk366,
    inference(func_ext,[status(esa)],[8259]) ).

thf(25,axiom,
    ! [TA: $tType,A: hF_Mirabelle_hf > hF_Mirabelle_hf > TA,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ TA @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
      = ( A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_hsplit) ).

thf(124,plain,
    ! [TA: $tType,A: hF_Mirabelle_hf > hF_Mirabelle_hf > TA,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ TA @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
      = ( A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(125,plain,
    ! [TA: $tType,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > hF_Mirabelle_hf > TA] :
      ( ( hF_Mirabelle_hsplit @ TA @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
      = ( A @ B @ C ) ),
    inference(cnf,[status(esa)],[124]) ).

thf(126,plain,
    ! [TA: $tType,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > hF_Mirabelle_hf > TA] :
      ( ( hF_Mirabelle_hsplit @ TA @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
      = ( A @ B @ C ) ),
    inference(lifteq,[status(thm)],[125]) ).

thf(10806,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
      ( ( hF_Mirabelle_hsplit @ $o @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
      | ( ( hF_Mir796903520_hpair @ sk366 )
       != ( A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[8260,126]) ).

thf(12523,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mirabelle_hsplit @ $o
      @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : ( hF_Mir796903520_hpair @ B )
      @ ( hF_Mirabelle_hpair @ sk366 @ A ) ),
    inference(pre_uni,[status(thm)],[10806:[bind(A,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : ( hF_Mir796903520_hpair @ D ) )),bind(B,$thf( sk366 )),bind(C,$thf( C ))]]) ).

thf(13062,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mirabelle_hsplit @ $o
      @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : ( hF_Mir796903520_hpair @ B )
      @ ( hF_Mirabelle_hpair @ sk366 @ A ) ),
    inference(simp,[status(thm)],[12523]) ).

thf(8261,plain,
    ( ( ( ^ [A: hF_Mirabelle_hf] :
          ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
            ( A
            = ( hF_Mirabelle_hpair @ B @ C ) ) )
     != ( ^ [A: hF_Mirabelle_hf] : $false ) )
    | ( hF_Mir796903520_hpair != hF_Mir796903520_hpair ) ),
    inference(paramod_ordered,[status(thm)],[68,8259]) ).

thf(8262,plain,
    ( ( ^ [A: hF_Mirabelle_hf] :
        ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( A
          = ( hF_Mirabelle_hpair @ B @ C ) ) )
   != ( ^ [A: hF_Mirabelle_hf] : $false ) ),
    inference(pattern_uni,[status(thm)],[8261:[]]) ).

thf(9245,plain,
    ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( sk371
      = ( hF_Mirabelle_hpair @ A @ B ) ),
    inference(func_ext,[status(esa)],[8262]) ).

thf(9248,plain,
    ( sk371
    = ( hF_Mirabelle_hpair @ sk372 @ sk373 ) ),
    inference(cnf,[status(esa)],[9245]) ).

thf(9249,plain,
    ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
    = sk371 ),
    inference(lifteq,[status(thm)],[9248]) ).

thf(23,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_hfst__conv) ).

thf(118,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(119,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
      = A ),
    inference(cnf,[status(esa)],[118]) ).

thf(120,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
      = A ),
    inference(lifteq,[status(thm)],[119]) ).

thf(9376,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hfst @ sk371 )
        = A )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,120]) ).

thf(9377,plain,
    ( ( hF_Mirabelle_hfst @ sk371 )
    = sk372 ),
    inference(pattern_uni,[status(thm)],[9376:[bind(A,$thf( sk372 )),bind(B,$thf( sk373 ))]]) ).

thf(8265,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( A
          = ( hF_Mirabelle_hpair @ B @ C ) )
      | ( ( hF_Mir796903520_hpair @ sk366 )
       != ( hF_Mir796903520_hpair @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8260,156]) ).

thf(8266,plain,
    ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( sk366
      = ( hF_Mirabelle_hpair @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[8265:[bind(A,$thf( sk366 ))]]) ).

thf(8284,plain,
    ( sk366
    = ( hF_Mirabelle_hpair @ sk367 @ sk368 ) ),
    inference(cnf,[status(esa)],[8266]) ).

thf(8285,plain,
    ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
    = sk366 ),
    inference(lifteq,[status(thm)],[8284]) ).

thf(8298,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hfst @ sk366 )
        = A )
      | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,120]) ).

thf(8299,plain,
    ( ( hF_Mirabelle_hfst @ sk366 )
    = sk367 ),
    inference(pattern_uni,[status(thm)],[8298:[bind(A,$thf( sk367 )),bind(B,$thf( sk368 ))]]) ).

thf(9592,plain,
    ( ( sk372 = sk367 )
    | ( ( hF_Mirabelle_hfst @ sk371 )
     != ( hF_Mirabelle_hfst @ sk366 ) ) ),
    inference(paramod_ordered,[status(thm)],[9377,8299]) ).

thf(9596,plain,
    ( ( sk372 = sk367 )
    | ( sk371 != sk366 ) ),
    inference(simp,[status(thm)],[9592]) ).

thf(13,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hpair @ A @ B )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_hpair__neq__fst) ).

thf(75,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hpair @ A @ B )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(76,plain,
    ~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
        ( ( hF_Mirabelle_hpair @ A @ B )
        = A ),
    inference(miniscope,[status(thm)],[75]) ).

thf(77,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hpair @ A @ B )
     != A ),
    inference(cnf,[status(esa)],[76]) ).

thf(78,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hpair @ A @ B )
     != A ),
    inference(lifteq,[status(thm)],[77]) ).

thf(9382,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( sk371 != A )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,78]) ).

thf(9383,plain,
    sk372 != sk371,
    inference(pattern_uni,[status(thm)],[9382:[bind(A,$thf( sk372 )),bind(B,$thf( sk373 ))]]) ).

thf(10261,plain,
    ( ( sk371 != sk366 )
    | ( sk371 != sk367 )
    | ( sk372 != sk372 ) ),
    inference(paramod_ordered,[status(thm)],[9596,9383]) ).

thf(10262,plain,
    ( ( sk371 != sk366 )
    | ( sk371 != sk367 ) ),
    inference(pattern_uni,[status(thm)],[10261:[]]) ).

thf(21,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ A @ B )
        = ( hF_Mirabelle_hpair @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_hpair__inject) ).

thf(107,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ A @ B )
        = ( hF_Mirabelle_hpair @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(109,plain,
    ! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ A @ B )
       != ( hF_Mirabelle_hpair @ C @ D ) )
      | ( B = D ) ),
    inference(cnf,[status(esa)],[107]) ).

thf(112,plain,
    ! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ A @ B )
       != ( hF_Mirabelle_hpair @ C @ D ) )
      | ( B = D ) ),
    inference(lifteq,[status(thm)],[109]) ).

thf(113,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( sk11 @ A @ ( hF_Mirabelle_hpair @ A @ B ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(hF_Mirabelle_hpair),[sk11])]) ).

thf(8314,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( sk11 @ A @ sk366 )
        = B )
      | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,113]) ).

thf(8315,plain,
    ( ( sk11 @ sk367 @ sk366 )
    = sk368 ),
    inference(pattern_uni,[status(thm)],[8314:[bind(A,$thf( sk367 )),bind(B,$thf( sk368 ))]]) ).

thf(4,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
      ( ! [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ D @ A )
         => ( ( B @ D @ E )
           => ( ( B @ D @ F )
             => ( F = E ) ) ) )
     => ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_PrimReplace__iff) ).

thf(37,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
      ( ! [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ D @ A )
         => ( ( B @ D @ E )
           => ( ( B @ D @ F )
             => ( F = E ) ) ) )
     => ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(38,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
      ( ! [C: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ C @ A )
         => ! [D: hF_Mirabelle_hf] :
              ( ( B @ C @ D )
             => ! [E: hF_Mirabelle_hf] :
                  ( ( B @ C @ E )
                 => ( E = D ) ) ) )
     => ! [C: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
          = ( ? [D: hF_Mirabelle_hf] :
                ( ( hF_Mirabelle_hmem @ D @ A )
                & ( B @ D @ C ) ) ) ) ),
    inference(miniscope,[status(thm)],[37]) ).

thf(40,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( B @ ( sk1 @ B @ A ) @ ( sk2 @ B @ A ) )
      | ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    inference(cnf,[status(esa)],[38]) ).

thf(44,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) )
      | ( B @ ( sk1 @ B @ A ) @ ( sk2 @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[40]) ).

thf(381,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hmem @ B
          @ ( hF_Mir569462966eplace @ A
            @ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) )
        = ( ? [C: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ C @ A )
              & $false ) ) )
      | $false ),
    inference(prim_subst,[status(thm)],[44:[bind(A,$thf( A )),bind(B,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : $false ))]]) ).

thf(502,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ B
        @ ( hF_Mir569462966eplace @ A
          @ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) ),
    inference(simp,[status(thm)],[381]) ).

thf(2569,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) @ ( hF_Mir165288108strict @ r @ x ) )
     != ( hF_Mirabelle_hmem @ B
        @ ( hF_Mir569462966eplace @ A
          @ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[2502,502]) ).

thf(2600,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ sk127 @ sk129 )
       != B )
      | ( ( hF_Mir165288108strict @ r @ x )
       != ( hF_Mir569462966eplace @ A
          @ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) ) ),
    inference(simp,[status(thm)],[2569]) ).

thf(2659,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir165288108strict @ r @ x )
     != ( hF_Mir569462966eplace @ A
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false ) ),
    inference(simp,[status(thm)],[2600]) ).

thf(29,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ! [C: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ C @ A )
          = ( hF_Mirabelle_hmem @ C @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_hf__equalityI) ).

thf(142,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ! [C: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ C @ A )
          = ( hF_Mirabelle_hmem @ C @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(10360,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
      ( ( hF_Mirabelle_hsplit @ $o @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
      | ( ( hF_Mir859708136nction @ r )
       != ( A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[152,126]) ).

thf(12346,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mirabelle_hsplit @ $o
      @ ^ [B: hF_Mirabelle_hf] : hF_Mir859708136nction
      @ ( hF_Mirabelle_hpair @ A @ r ) ),
    inference(pre_uni,[status(thm)],[10360:[bind(A,$thf( ^ [D: hF_Mirabelle_hf] : hF_Mir859708136nction )),bind(B,$thf( B )),bind(C,$thf( r ))]]) ).

thf(12921,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mirabelle_hsplit @ $o
      @ ^ [B: hF_Mirabelle_hf] : hF_Mir859708136nction
      @ ( hF_Mirabelle_hpair @ A @ r ) ),
    inference(simp,[status(thm)],[12346]) ).

thf(108,plain,
    ! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ A @ B )
       != ( hF_Mirabelle_hpair @ C @ D ) )
      | ( A = C ) ),
    inference(cnf,[status(esa)],[107]) ).

thf(110,plain,
    ! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ A @ B )
       != ( hF_Mirabelle_hpair @ C @ D ) )
      | ( A = C ) ),
    inference(lifteq,[status(thm)],[108]) ).

thf(111,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( sk10 @ A @ ( hF_Mirabelle_hpair @ B @ A ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(hF_Mirabelle_hpair),[sk10])]) ).

thf(8334,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( sk10 @ A @ sk366 )
        = B )
      | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
       != ( hF_Mirabelle_hpair @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,111]) ).

thf(8335,plain,
    ( ( sk10 @ sk368 @ sk366 )
    = sk367 ),
    inference(pattern_uni,[status(thm)],[8334:[bind(A,$thf( sk368 )),bind(B,$thf( sk367 ))]]) ).

thf(9401,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mir796903520_hpair @ sk371 )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,563]) ).

thf(9402,plain,
    hF_Mir796903520_hpair @ sk371,
    inference(pattern_uni,[status(thm)],[9401:[bind(A,$thf( sk372 )),bind(B,$thf( sk373 ))]]) ).

thf(9557,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( A
          = ( hF_Mirabelle_hpair @ B @ C ) )
      | ( ( hF_Mir796903520_hpair @ A )
       != ( hF_Mir796903520_hpair @ sk371 ) ) ),
    inference(paramod_ordered,[status(thm)],[156,9402]) ).

thf(9558,plain,
    ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( sk371
      = ( hF_Mirabelle_hpair @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[9557:[bind(A,$thf( sk371 ))]]) ).

thf(9585,plain,
    ( sk371
    = ( hF_Mirabelle_hpair @ sk378 @ sk379 ) ),
    inference(cnf,[status(esa)],[9558]) ).

thf(9586,plain,
    ( ( hF_Mirabelle_hpair @ sk378 @ sk379 )
    = sk371 ),
    inference(lifteq,[status(thm)],[9585]) ).

thf(9,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_hsnd__conv) ).

thf(64,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(65,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
      = B ),
    inference(cnf,[status(esa)],[64]) ).

thf(66,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
      = B ),
    inference(lifteq,[status(thm)],[65]) ).

thf(9752,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsnd @ sk371 )
        = B )
      | ( ( hF_Mirabelle_hpair @ sk378 @ sk379 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9586,66]) ).

thf(9753,plain,
    ( ( hF_Mirabelle_hsnd @ sk371 )
    = sk379 ),
    inference(pattern_uni,[status(thm)],[9752:[bind(A,$thf( sk378 )),bind(B,$thf( sk379 ))]]) ).

thf(9398,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsnd @ sk371 )
        = B )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,66]) ).

thf(9399,plain,
    ( ( hF_Mirabelle_hsnd @ sk371 )
    = sk373 ),
    inference(pattern_uni,[status(thm)],[9398:[bind(A,$thf( sk372 )),bind(B,$thf( sk373 ))]]) ).

thf(10155,plain,
    sk379 = sk373,
    inference(rewrite,[status(thm)],[9753,9399]) ).

thf(10578,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
        = sk373 )
      | ( ( A @ B @ C )
       != sk379 ) ),
    inference(paramod_ordered,[status(thm)],[126,10155]) ).

thf(12499,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : C
        @ ( hF_Mirabelle_hpair @ A @ sk379 ) )
      = sk373 ),
    inference(pre_uni,[status(thm)],[10578:[bind(A,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : E )),bind(B,$thf( B )),bind(C,$thf( sk379 ))]]) ).

thf(13041,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : C
        @ ( hF_Mirabelle_hpair @ A @ sk379 ) )
      = sk373 ),
    inference(simp,[status(thm)],[12499]) ).

thf(17563,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : C
        @ ( hF_Mirabelle_hpair @ A @ sk373 ) )
      = sk373 ),
    inference(rewrite,[status(thm)],[13041,10155]) ).

thf(17570,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( sk373
        = ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
          @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : C
          @ sk371 ) )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ A @ sk373 ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,17563]) ).

thf(17571,plain,
    ( sk373
    = ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
      @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
      @ sk371 ) ),
    inference(pattern_uni,[status(thm)],[17570:[bind(A,$thf( sk372 ))]]) ).

thf(17688,plain,
    ( ( hF_Mirabelle_hpair @ sk372
      @ ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
        @ sk371 ) )
    = sk371 ),
    inference(rewrite,[status(thm)],[9249,17571]) ).

thf(39,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( sk1 @ B @ A ) @ A )
      | ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    inference(cnf,[status(esa)],[38]) ).

thf(43,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) )
      | ( hF_Mirabelle_hmem @ ( sk1 @ B @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[39]) ).

thf(14,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ B )
     => ( ( hF_Mirabelle_HUnion @ A )
       != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_hmem__Sup__ne) ).

thf(79,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ B )
     => ( ( hF_Mirabelle_HUnion @ A )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(80,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ A @ B )
      | ( ( hF_Mirabelle_HUnion @ A )
       != B ) ),
    inference(cnf,[status(esa)],[79]) ).

thf(81,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_HUnion @ A )
       != B )
      | ~ ( hF_Mirabelle_hmem @ A @ B ) ),
    inference(lifteq,[status(thm)],[80]) ).

thf(82,plain,
    ! [A: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ),
    inference(simp,[status(thm)],[81]) ).

thf(164,plain,
    ! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( sk1 @ B @ A ) @ A )
      | ~ ? [E: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ E @ A )
            & ( B @ E @ C ) )
      | ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
       != ( hF_Mirabelle_hmem @ D @ ( hF_Mirabelle_HUnion @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[43,82]) ).

thf(170,plain,
    ! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( sk1 @ B @ A ) @ A )
      | ~ ? [E: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ E @ A )
            & ( B @ E @ C ) )
      | ( C != D )
      | ( ( hF_Mir569462966eplace @ A @ B )
       != ( hF_Mirabelle_HUnion @ D ) ) ),
    inference(simp,[status(thm)],[164]) ).

thf(184,plain,
    ! [E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mir569462966eplace @ A @ B )
       != ( hF_Mirabelle_HUnion @ D ) )
      | ( C != D )
      | ~ ( hF_Mirabelle_hmem @ E @ A )
      | ~ ( B @ E @ C )
      | ( hF_Mirabelle_hmem @ ( sk1 @ B @ A ) @ A ) ),
    inference(cnf,[status(esa)],[170]) ).

thf(185,plain,
    ! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mir569462966eplace @ A @ B )
       != ( hF_Mirabelle_HUnion @ C ) )
      | ~ ( hF_Mirabelle_hmem @ D @ A )
      | ~ ( B @ D @ C )
      | ( hF_Mirabelle_hmem @ ( sk1 @ B @ A ) @ A ) ),
    inference(simp,[status(thm)],[184]) ).

thf(5,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
      ( ( A = B )
     => ( ! [E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ E @ B )
           => ( ( C @ E @ F )
              = ( D @ E @ F ) ) )
       => ( ( hF_Mirabelle_Replace @ A @ C )
          = ( hF_Mirabelle_Replace @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Replace__cong) ).

thf(47,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
      ( ( A = B )
     => ( ! [E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ E @ B )
           => ( ( C @ E @ F )
              = ( D @ E @ F ) ) )
       => ( ( hF_Mirabelle_Replace @ A @ C )
          = ( hF_Mirabelle_Replace @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(48,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( A = B )
     => ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
          ( ! [E: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ E @ B )
             => ! [F: hF_Mirabelle_hf] :
                  ( ( C @ E @ F )
                  = ( D @ E @ F ) ) )
         => ( ( hF_Mirabelle_Replace @ A @ C )
            = ( hF_Mirabelle_Replace @ B @ D ) ) ) ),
    inference(miniscope,[status(thm)],[47]) ).

thf(49,plain,
    ! [D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( A != B )
      | ( ( C @ ( sk4 @ D @ C @ B @ A ) @ ( sk5 @ D @ C @ B @ A ) )
       != ( D @ ( sk4 @ D @ C @ B @ A ) @ ( sk5 @ D @ C @ B @ A ) ) )
      | ( ( hF_Mirabelle_Replace @ A @ C )
        = ( hF_Mirabelle_Replace @ B @ D ) ) ),
    inference(cnf,[status(esa)],[48]) ).

thf(51,plain,
    ! [D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( A != B )
      | ( ( C @ ( sk4 @ D @ C @ B @ A ) @ ( sk5 @ D @ C @ B @ A ) )
       != ( D @ ( sk4 @ D @ C @ B @ A ) @ ( sk5 @ D @ C @ B @ A ) ) )
      | ( ( hF_Mirabelle_Replace @ A @ C )
        = ( hF_Mirabelle_Replace @ B @ D ) ) ),
    inference(lifteq,[status(thm)],[49]) ).

thf(52,plain,
    ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( B @ ( sk4 @ C @ B @ A @ A ) @ ( sk5 @ C @ B @ A @ A ) )
       != ( C @ ( sk4 @ C @ B @ A @ A ) @ ( sk5 @ C @ B @ A @ A ) ) )
      | ( ( hF_Mirabelle_Replace @ A @ B )
        = ( hF_Mirabelle_Replace @ A @ C ) ) ),
    inference(simp,[status(thm)],[51]) ).

thf(3442,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( B @ A )
        & ( hF_Mirabelle_hmem @ A @ C ) )
      | ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) )
       != ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) @ ( hF_Mir165288108strict @ r @ x ) ) ) ),
    inference(paramod_ordered,[status(thm)],[60,2502]) ).

thf(3474,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( B @ A )
        & ( hF_Mirabelle_hmem @ A @ C ) )
      | ( A
       != ( hF_Mirabelle_hpair @ sk127 @ sk129 ) )
      | ( ( hF_Mir1687042746ollect @ B @ C )
       != ( hF_Mir165288108strict @ r @ x ) ) ),
    inference(simp,[status(thm)],[3442]) ).

thf(3674,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mir1687042746ollect @ B @ C )
       != ( hF_Mir165288108strict @ r @ x ) )
      | ( A
       != ( hF_Mirabelle_hpair @ sk127 @ sk129 ) )
      | ( B @ A ) ),
    inference(cnf,[status(esa)],[3474]) ).

thf(3676,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > $o] :
      ( ( ( hF_Mir1687042746ollect @ A @ B )
       != ( hF_Mir165288108strict @ r @ x ) )
      | ( A @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) ) ),
    inference(simp,[status(thm)],[3674]) ).

thf(4179,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mir1687042746ollect
          @ ^ [B: hF_Mirabelle_hf] : $false
          @ A )
       != ( hF_Mir165288108strict @ r @ x ) )
      | $false ),
    inference(prim_subst,[status(thm)],[3676:[bind(A,$thf( ^ [C: hF_Mirabelle_hf] : $false ))]]) ).

thf(4334,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1687042746ollect
        @ ^ [B: hF_Mirabelle_hf] : $false
        @ A )
     != ( hF_Mir165288108strict @ r @ x ) ),
    inference(simp,[status(thm)],[4179]) ).

thf(26,axiom,
    ( ( (=) @ hF_Mirabelle_hf )
    = ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
        ! [C: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ C @ A )
          = ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_hf__ext) ).

thf(127,plain,
    ( ( (=) @ hF_Mirabelle_hf )
    = ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
        ! [C: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ C @ A )
          = ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(128,plain,
    ( ( (=) @ hF_Mirabelle_hf )
    = ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
        ! [C: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ C @ A )
          = ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
    inference(lifteq,[status(thm)],[127]) ).

thf(157,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( (=) @ hF_Mirabelle_hf @ A )
      = ( ^ [B: hF_Mirabelle_hf] :
          ! [C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ C @ A )
            = ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
    inference(func_ext,[status(esa)],[128]) ).

thf(12345,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mirabelle_hsplit @ $o
      @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ B )
      @ ( hF_Mirabelle_hpair @ r @ A ) ),
    inference(pre_uni,[status(thm)],[10360:[bind(A,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ D ) )),bind(B,$thf( r )),bind(C,$thf( C ))]]) ).

thf(12920,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mirabelle_hsplit @ $o
      @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ B )
      @ ( hF_Mirabelle_hpair @ r @ A ) ),
    inference(simp,[status(thm)],[12345]) ).

thf(8316,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsnd @ sk366 )
        = B )
      | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,66]) ).

thf(8317,plain,
    ( ( hF_Mirabelle_hsnd @ sk366 )
    = sk368 ),
    inference(pattern_uni,[status(thm)],[8316:[bind(A,$thf( sk367 )),bind(B,$thf( sk368 ))]]) ).

thf(9600,plain,
    ( ( sk373 = sk368 )
    | ( ( hF_Mirabelle_hsnd @ sk371 )
     != ( hF_Mirabelle_hsnd @ sk366 ) ) ),
    inference(paramod_ordered,[status(thm)],[9399,8317]) ).

thf(9604,plain,
    ( ( sk373 = sk368 )
    | ( sk371 != sk366 ) ),
    inference(simp,[status(thm)],[9600]) ).

thf(17,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hpair @ A @ B )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_hpair__neq__snd) ).

thf(94,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hpair @ A @ B )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(95,plain,
    ~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
        ( ( hF_Mirabelle_hpair @ A @ B )
        = B ),
    inference(miniscope,[status(thm)],[94]) ).

thf(96,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hpair @ A @ B )
     != B ),
    inference(cnf,[status(esa)],[95]) ).

thf(97,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hpair @ A @ B )
     != B ),
    inference(lifteq,[status(thm)],[96]) ).

thf(9387,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( sk371 != B )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,97]) ).

thf(9388,plain,
    sk373 != sk371,
    inference(pattern_uni,[status(thm)],[9387:[bind(A,$thf( sk372 )),bind(B,$thf( sk373 ))]]) ).

thf(14772,plain,
    ( ( sk371 != sk366 )
    | ( sk371 != sk368 )
    | ( sk373 != sk373 ) ),
    inference(paramod_ordered,[status(thm)],[9604,9388]) ).

thf(14773,plain,
    ( ( sk371 != sk366 )
    | ( sk371 != sk368 ) ),
    inference(pattern_uni,[status(thm)],[14772:[]]) ).

thf(42,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( sk3 @ B @ A )
       != ( sk2 @ B @ A ) )
      | ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    inference(cnf,[status(esa)],[38]) ).

thf(46,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( sk3 @ B @ A )
       != ( sk2 @ B @ A ) )
      | ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    inference(lifteq,[status(thm)],[42]) ).

thf(16,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,D: hF_Mirabelle_hf > hF_Mirabelle_hf] :
      ( ( A = B )
     => ( ! [E: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ E @ B )
           => ( ( C @ E )
              = ( D @ E ) ) )
       => ( ( hF_Mirabelle_RepFun @ A @ C )
          = ( hF_Mirabelle_RepFun @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_RepFun__cong) ).

thf(86,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,D: hF_Mirabelle_hf > hF_Mirabelle_hf] :
      ( ( A = B )
     => ( ! [E: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ E @ B )
           => ( ( C @ E )
              = ( D @ E ) ) )
       => ( ( hF_Mirabelle_RepFun @ A @ C )
          = ( hF_Mirabelle_RepFun @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(87,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( A = B )
     => ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,D: hF_Mirabelle_hf > hF_Mirabelle_hf] :
          ( ! [E: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ E @ B )
             => ( ( C @ E )
                = ( D @ E ) ) )
         => ( ( hF_Mirabelle_RepFun @ A @ C )
            = ( hF_Mirabelle_RepFun @ B @ D ) ) ) ),
    inference(miniscope,[status(thm)],[86]) ).

thf(89,plain,
    ! [D: hF_Mirabelle_hf > hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( A != B )
      | ( hF_Mirabelle_hmem @ ( sk8 @ D @ C @ B @ A ) @ B )
      | ( ( hF_Mirabelle_RepFun @ A @ C )
        = ( hF_Mirabelle_RepFun @ B @ D ) ) ),
    inference(cnf,[status(esa)],[87]) ).

thf(92,plain,
    ! [D: hF_Mirabelle_hf > hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( A != B )
      | ( ( hF_Mirabelle_RepFun @ A @ C )
        = ( hF_Mirabelle_RepFun @ B @ D ) )
      | ( hF_Mirabelle_hmem @ ( sk8 @ D @ C @ B @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[89]) ).

thf(93,plain,
    ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_RepFun @ A @ B )
        = ( hF_Mirabelle_RepFun @ A @ C ) )
      | ( hF_Mirabelle_hmem @ ( sk8 @ C @ B @ A @ A ) @ A ) ),
    inference(simp,[status(thm)],[92]) ).

thf(8267,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( A
          = ( hF_Mirabelle_hpair @ B @ C ) )
      | ( ( hF_Mir796903520_hpair @ A )
       != ( hF_Mir796903520_hpair @ sk366 ) ) ),
    inference(paramod_ordered,[status(thm)],[156,8260]) ).

thf(8268,plain,
    ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( sk366
      = ( hF_Mirabelle_hpair @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[8267:[bind(A,$thf( sk366 ))]]) ).

thf(8286,plain,
    ( sk366
    = ( hF_Mirabelle_hpair @ sk369 @ sk370 ) ),
    inference(cnf,[status(esa)],[8268]) ).

thf(8287,plain,
    ( ( hF_Mirabelle_hpair @ sk369 @ sk370 )
    = sk366 ),
    inference(lifteq,[status(thm)],[8286]) ).

thf(8374,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hfst @ sk366 )
        = A )
      | ( ( hF_Mirabelle_hpair @ sk369 @ sk370 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8287,120]) ).

thf(8375,plain,
    ( ( hF_Mirabelle_hfst @ sk366 )
    = sk369 ),
    inference(pattern_uni,[status(thm)],[8374:[bind(A,$thf( sk369 )),bind(B,$thf( sk370 ))]]) ).

thf(9240,plain,
    sk369 = sk367,
    inference(rewrite,[status(thm)],[8375,8299]) ).

thf(6,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
      = ( ? [C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ C @ B )
            & ( hF_Mirabelle_hmem @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_HUnion__iff) ).

thf(55,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
      = ( ? [C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ C @ B )
            & ( hF_Mirabelle_hmem @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(56,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
      = ( ? [C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ C @ B )
            & ( hF_Mirabelle_hmem @ A @ C ) ) ) ),
    inference(cnf,[status(esa)],[55]) ).

thf(57,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
      = ( ? [C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ C @ B )
            & ( hF_Mirabelle_hmem @ A @ C ) ) ) ),
    inference(lifteq,[status(thm)],[56]) ).

thf(8,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ~ ( ( hF_Mirabelle_hmem @ A @ B )
        & ( hF_Mirabelle_hmem @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_hmem__not__sym) ).

thf(61,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ~ ( ( hF_Mirabelle_hmem @ A @ B )
        & ( hF_Mirabelle_hmem @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(62,plain,
    ~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
        ( ( hF_Mirabelle_hmem @ A @ B )
        & ( hF_Mirabelle_hmem @ B @ A ) ),
    inference(miniscope,[status(thm)],[61]) ).

thf(63,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ A @ B )
      | ~ ( hF_Mirabelle_hmem @ B @ A ) ),
    inference(cnf,[status(esa)],[62]) ).

thf(2714,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ B @ A )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mirabelle_hmem @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2503,63]) ).

thf(2715,plain,
    ~ ( hF_Mirabelle_hmem @ ( hF_Mir165288108strict @ r @ x ) @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(pattern_uni,[status(thm)],[2714:[bind(A,$thf( hF_Mirabelle_hpair @ sk127 @ sk128 )),bind(B,$thf( hF_Mir165288108strict @ r @ x ))]]) ).

thf(8325,plain,
    ( ~ ( hF_Mirabelle_hmem @ ( hF_Mir165288108strict @ r @ x ) @ sk366 )
    | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
     != ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,2715]) ).

thf(8352,plain,
    ( ~ ( hF_Mirabelle_hmem @ ( hF_Mir165288108strict @ r @ x ) @ sk366 )
    | ( sk367 != sk127 )
    | ( sk368 != sk128 ) ),
    inference(simp,[status(thm)],[8325]) ).

thf(17691,plain,
    ( ( hF_Mirabelle_hsnd @ sk371 )
    = ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
      @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
      @ sk371 ) ),
    inference(rewrite,[status(thm)],[9399,17571]) ).

thf(6136,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
        @ ( hF_Mir1687042746ollect
          @ ^ [C: hF_Mirabelle_hf] : $true
          @ ( hF_Mir165288108strict @ r @ x ) ) )
     != ( hF_Mirabelle_hmem @ B
        @ ( hF_Mir569462966eplace @ A
          @ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[6074,502]) ).

thf(6186,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
       != B )
      | ( ( hF_Mir1687042746ollect
          @ ^ [C: hF_Mirabelle_hf] : $true
          @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mir569462966eplace @ A
          @ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) ) ),
    inference(simp,[status(thm)],[6136]) ).

thf(6259,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1687042746ollect
        @ ^ [B: hF_Mirabelle_hf] : $true
        @ ( hF_Mir165288108strict @ r @ x ) )
     != ( hF_Mir569462966eplace @ A
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false ) ),
    inference(simp,[status(thm)],[6186]) ).

thf(1176,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ B )
            & ( hF_Mirabelle_hmem @ A @ D ) )
      | ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
       != ( hF_Mirabelle_hmem @ C @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[57,106]) ).

thf(1177,plain,
    ! [A: hF_Mirabelle_hf] :
      ~ ? [B: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ B @ A )
          & ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ A ) @ B ) ),
    inference(pattern_uni,[status(thm)],[1176:[bind(A,$thf( hF_Mirabelle_HUnion @ D )),bind(B,$thf( D )),bind(C,$thf( hF_Mirabelle_HUnion @ D ))]]) ).

thf(1295,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ B @ A )
      | ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ A ) @ B ) ),
    inference(cnf,[status(esa)],[1177]) ).

thf(1296,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ B @ A )
      | ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ A ) @ B ) ),
    inference(simp,[status(thm)],[1295]) ).

thf(2555,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ A ) @ B )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mirabelle_hmem @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2502,1296]) ).

thf(2556,plain,
    ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mir165288108strict @ r @ x ) ) @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) ),
    inference(pattern_uni,[status(thm)],[2555:[bind(A,$thf( hF_Mir165288108strict @ r @ x )),bind(B,$thf( hF_Mirabelle_hpair @ sk127 @ sk129 ))]]) ).

thf(4146,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > $o] :
      ( ( ( hF_Mir1687042746ollect @ A @ B )
       != ( hF_Mir165288108strict @ r @ x ) )
      | ( ( A @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) )
       != ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mir165288108strict @ r @ x ) ) @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3676,2556]) ).

thf(4260,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1687042746ollect @ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mir165288108strict @ r @ x ) ) ) @ A )
     != ( hF_Mir165288108strict @ r @ x ) ),
    inference(pre_uni,[status(thm)],[4146:[bind(A,$thf( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mir165288108strict @ r @ x ) ) )),bind(B,$thf( B ))]]) ).

thf(4329,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1687042746ollect @ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mir165288108strict @ r @ x ) ) ) @ A )
     != ( hF_Mir165288108strict @ r @ x ) ),
    inference(simp,[status(thm)],[4260]) ).

thf(3396,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( B @ A )
        & ( hF_Mirabelle_hmem @ A @ C ) )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2503,60]) ).

thf(3514,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( B @ A )
        & ( hF_Mirabelle_hmem @ A @ C ) )
      | ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
       != A )
      | ( ( hF_Mir165288108strict @ r @ x )
       != ( hF_Mir1687042746ollect @ B @ C ) ) ),
    inference(simp,[status(thm)],[3396]) ).

thf(3722,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mir165288108strict @ r @ x )
       != ( hF_Mir1687042746ollect @ B @ C ) )
      | ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
       != A )
      | ( B @ A ) ),
    inference(cnf,[status(esa)],[3514]) ).

thf(3724,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > $o] :
      ( ( ( hF_Mir165288108strict @ r @ x )
       != ( hF_Mir1687042746ollect @ A @ B ) )
      | ( A @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ) ),
    inference(simp,[status(thm)],[3722]) ).

thf(3,axiom,
    ( hF_Mir1093797708lation
    = ( ^ [A: hF_Mirabelle_hf] :
        ! [B: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ B @ A )
         => ( hF_Mir796903520_hpair @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_hrelation__def) ).

thf(35,plain,
    ( hF_Mir1093797708lation
    = ( ^ [A: hF_Mirabelle_hf] :
        ! [B: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ B @ A )
         => ( hF_Mir796903520_hpair @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(36,plain,
    ( hF_Mir1093797708lation
    = ( ^ [A: hF_Mirabelle_hf] :
        ! [B: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ B @ A )
         => ( hF_Mir796903520_hpair @ B ) ) ) ),
    inference(lifteq,[status(thm)],[35]) ).

thf(155,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ A )
      = ( ! [B: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ B @ A )
           => ( hF_Mir796903520_hpair @ B ) ) ) ),
    inference(func_ext,[status(esa)],[36]) ).

thf(312,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ A )
      | ~ ! [B: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ B @ A )
           => ( hF_Mir796903520_hpair @ B ) ) ),
    inference(bool_ext,[status(thm)],[155]) ).

thf(324,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( sk23 @ A ) @ A )
      | ( hF_Mir1093797708lation @ A ) ),
    inference(cnf,[status(esa)],[312]) ).

thf(606,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ A )
      | ( ( hF_Mirabelle_hmem @ ( sk23 @ A ) @ A )
       != ( hF_Mirabelle_hmem @ B @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[324,106]) ).

thf(622,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ A )
      | ( ( sk23 @ A )
       != B )
      | ( A != B ) ),
    inference(simp,[status(thm)],[606]) ).

thf(646,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ A )
      | ( ( sk23 @ A )
       != A ) ),
    inference(simp,[status(thm)],[622]) ).

thf(24,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ A @ B )
        = ( hF_Mirabelle_hpair @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_hpair__iff) ).

thf(121,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ A @ B )
        = ( hF_Mirabelle_hpair @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(10694,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
      ( ( hF_Mirabelle_hsplit @ $o @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
      | ( ( A @ B @ C )
       != ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir165288108strict @ r @ x ) ) ) ),
    inference(paramod_ordered,[status(thm)],[126,2503]) ).

thf(11064,plain,
    ( hF_Mirabelle_hsplit @ $o
    @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ B @ A )
    @ ( hF_Mirabelle_hpair @ ( hF_Mir165288108strict @ r @ x ) @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ) ),
    inference(pre_uni,[status(thm)],[10694:[bind(A,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ E @ D ) )),bind(B,$thf( hF_Mir165288108strict @ r @ x )),bind(C,$thf( hF_Mirabelle_hpair @ sk127 @ sk128 ))]]) ).

thf(6092,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
        @ ( hF_Mir1687042746ollect
          @ ^ [B: hF_Mirabelle_hf] : $true
          @ ( hF_Mir165288108strict @ r @ x ) ) )
     != ( hF_Mirabelle_hmem @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[6074,106]) ).

thf(6167,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
       != A )
      | ( ( hF_Mir1687042746ollect
          @ ^ [B: hF_Mirabelle_hf] : $true
          @ ( hF_Mir165288108strict @ r @ x ) )
       != A ) ),
    inference(simp,[status(thm)],[6092]) ).

thf(6227,plain,
    ( ( hF_Mir1687042746ollect
      @ ^ [A: hF_Mirabelle_hf] : $true
      @ ( hF_Mir165288108strict @ r @ x ) )
   != ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(simp,[status(thm)],[6167]) ).

thf(31,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir165288108strict @ B @ C ) )
      = ( ( hF_Mirabelle_hmem @ A @ B )
        & ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
            ( ( A
              = ( hF_Mirabelle_hpair @ D @ E ) )
            & ( hF_Mirabelle_hmem @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_hrestrict__iff) ).

thf(147,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir165288108strict @ B @ C ) )
      = ( ( hF_Mirabelle_hmem @ A @ B )
        & ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
            ( ( A
              = ( hF_Mirabelle_hpair @ D @ E ) )
            & ( hF_Mirabelle_hmem @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(8305,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( sk366 != B )
      | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,97]) ).

thf(8306,plain,
    sk368 != sk366,
    inference(pattern_uni,[status(thm)],[8305:[bind(A,$thf( sk367 )),bind(B,$thf( sk368 ))]]) ).

thf(12,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
    ? [C: hF_Mirabelle_hf] :
    ! [D: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ D @ C )
      = ( ( hF_Mirabelle_hmem @ D @ A )
        | ( hF_Mirabelle_hmem @ D @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_binary__union) ).

thf(72,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
    ? [C: hF_Mirabelle_hf] :
    ! [D: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ D @ C )
      = ( ( hF_Mirabelle_hmem @ D @ A )
        | ( hF_Mirabelle_hmem @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(73,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ C @ ( sk6 @ B @ A ) )
      = ( ( hF_Mirabelle_hmem @ C @ A )
        | ( hF_Mirabelle_hmem @ C @ B ) ) ),
    inference(cnf,[status(esa)],[72]) ).

thf(74,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ C @ ( sk6 @ B @ A ) )
      = ( ( hF_Mirabelle_hmem @ C @ A )
        | ( hF_Mirabelle_hmem @ C @ B ) ) ),
    inference(lifteq,[status(thm)],[73]) ).

thf(2544,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ B @ A )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mirabelle_hmem @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2502,63]) ).

thf(2545,plain,
    ~ ( hF_Mirabelle_hmem @ ( hF_Mir165288108strict @ r @ x ) @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) ),
    inference(pattern_uni,[status(thm)],[2544:[bind(A,$thf( hF_Mirabelle_hpair @ sk127 @ sk129 )),bind(B,$thf( hF_Mir165288108strict @ r @ x ))]]) ).

thf(8327,plain,
    ( ~ ( hF_Mirabelle_hmem @ ( hF_Mir165288108strict @ r @ x ) @ sk366 )
    | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
     != ( hF_Mirabelle_hpair @ sk127 @ sk129 ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,2545]) ).

thf(8347,plain,
    ( ~ ( hF_Mirabelle_hmem @ ( hF_Mir165288108strict @ r @ x ) @ sk366 )
    | ( sk367 != sk127 )
    | ( sk368 != sk129 ) ),
    inference(simp,[status(thm)],[8327]) ).

thf(15718,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ $o
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ B )
        @ sk371 )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ r @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,12920]) ).

thf(15747,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ $o
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ B )
        @ sk371 )
      | ( sk372 != r )
      | ( sk373 != A ) ),
    inference(simp,[status(thm)],[15718]) ).

thf(15766,plain,
    ( ( hF_Mirabelle_hsplit @ $o
      @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ A )
      @ sk371 )
    | ( sk372 != r ) ),
    inference(simp,[status(thm)],[15747]) ).

thf(9418,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( sk10 @ A @ sk371 )
        = B )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,111]) ).

thf(9419,plain,
    ( ( sk10 @ sk373 @ sk371 )
    = sk372 ),
    inference(pattern_uni,[status(thm)],[9418:[bind(A,$thf( sk373 )),bind(B,$thf( sk372 ))]]) ).

thf(17683,plain,
    ( ( sk10
      @ ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
        @ sk371 )
      @ sk371 )
    = sk372 ),
    inference(rewrite,[status(thm)],[9419,17571]) ).

thf(2501,plain,
    sk128 != sk129,
    inference(cnf,[status(esa)],[2475]) ).

thf(2504,plain,
    sk129 != sk128,
    inference(lifteq,[status(thm)],[2501]) ).

thf(10508,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
       != sk128 )
      | ( ( A @ B @ C )
       != sk129 ) ),
    inference(paramod_ordered,[status(thm)],[126,2504]) ).

thf(12479,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : B
        @ ( hF_Mirabelle_hpair @ sk129 @ A ) )
     != sk128 ),
    inference(pre_uni,[status(thm)],[10508:[bind(A,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : D )),bind(B,$thf( sk129 ))]]) ).

thf(13027,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : B
        @ ( hF_Mirabelle_hpair @ sk129 @ A ) )
     != sk128 ),
    inference(simp,[status(thm)],[12479]) ).

thf(17415,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
          @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : B
          @ sk366 )
       != sk128 )
      | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
       != ( hF_Mirabelle_hpair @ sk129 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,13027]) ).

thf(17423,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
          @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : B
          @ sk366 )
       != sk128 )
      | ( sk367 != sk129 )
      | ( sk368 != A ) ),
    inference(simp,[status(thm)],[17415]) ).

thf(17440,plain,
    ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : A
        @ sk366 )
     != sk128 )
    | ( sk367 != sk129 ) ),
    inference(simp,[status(thm)],[17423]) ).

thf(133,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( B @ ( sk12 @ B @ A ) @ ( sk14 @ B @ A ) )
      | ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    inference(cnf,[status(esa)],[130]) ).

thf(137,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) )
      | ( B @ ( sk12 @ B @ A ) @ ( sk14 @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[133]) ).

thf(4170,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > $o] :
      ( ( ( hF_Mir1687042746ollect @ A @ B )
       != ( hF_Mir165288108strict @ r @ x ) )
      | ( ( A @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) )
       != ( hF_Mirabelle_hmem @ ( hF_Mir165288108strict @ r @ x ) @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3676,2545]) ).

thf(4252,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1687042746ollect @ ( hF_Mirabelle_hmem @ ( hF_Mir165288108strict @ r @ x ) ) @ A )
     != ( hF_Mir165288108strict @ r @ x ) ),
    inference(pre_uni,[status(thm)],[4170:[bind(A,$thf( hF_Mirabelle_hmem @ ( hF_Mir165288108strict @ r @ x ) )),bind(B,$thf( B ))]]) ).

thf(4316,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1687042746ollect @ ( hF_Mirabelle_hmem @ ( hF_Mir165288108strict @ r @ x ) ) @ A )
     != ( hF_Mir165288108strict @ r @ x ) ),
    inference(simp,[status(thm)],[4252]) ).

thf(12524,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mirabelle_hsplit @ $o
      @ ^ [B: hF_Mirabelle_hf] : hF_Mir796903520_hpair
      @ ( hF_Mirabelle_hpair @ A @ sk366 ) ),
    inference(pre_uni,[status(thm)],[10806:[bind(A,$thf( ^ [D: hF_Mirabelle_hf] : hF_Mir796903520_hpair )),bind(B,$thf( B )),bind(C,$thf( sk366 ))]]) ).

thf(13063,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mirabelle_hsplit @ $o
      @ ^ [B: hF_Mirabelle_hf] : hF_Mir796903520_hpair
      @ ( hF_Mirabelle_hpair @ A @ sk366 ) ),
    inference(simp,[status(thm)],[12524]) ).

thf(5474,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ) )
     != ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5133,82]) ).

thf(5546,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
       != A )
      | ( ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(simp,[status(thm)],[5474]) ).

thf(5615,plain,
    ( ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) )
   != ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ) ),
    inference(simp,[status(thm)],[5546]) ).

thf(17687,plain,
    ( sk379
    = ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
      @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
      @ sk371 ) ),
    inference(rewrite,[status(thm)],[10155,17571]) ).

thf(2725,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ A ) @ B )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mirabelle_hmem @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2503,1296]) ).

thf(2726,plain,
    ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mir165288108strict @ r @ x ) ) @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(pattern_uni,[status(thm)],[2725:[bind(A,$thf( hF_Mir165288108strict @ r @ x )),bind(B,$thf( hF_Mirabelle_hpair @ sk127 @ sk128 ))]]) ).

thf(9730,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hfst @ sk371 )
        = A )
      | ( ( hF_Mirabelle_hpair @ sk378 @ sk379 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9586,120]) ).

thf(9731,plain,
    ( ( hF_Mirabelle_hfst @ sk371 )
    = sk378 ),
    inference(pattern_uni,[status(thm)],[9730:[bind(A,$thf( sk378 )),bind(B,$thf( sk379 ))]]) ).

thf(10152,plain,
    sk378 = sk372,
    inference(rewrite,[status(thm)],[9731,9377]) ).

thf(2724,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir165288108strict @ r @ x ) )
     != ( hF_Mirabelle_hmem @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[2503,106]) ).

thf(2761,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
       != A )
      | ( ( hF_Mir165288108strict @ r @ x )
       != A ) ),
    inference(simp,[status(thm)],[2724]) ).

thf(2798,plain,
    ( ( hF_Mir165288108strict @ r @ x )
   != ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(simp,[status(thm)],[2761]) ).

thf(4102,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > $o] :
      ( ( ( hF_Mir1687042746ollect @ A @ B )
       != ( hF_Mir165288108strict @ r @ x ) )
      | ( ( A @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) )
       != ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir165288108strict @ r @ x ) ) @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3676,2559]) ).

thf(4251,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1687042746ollect @ ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir165288108strict @ r @ x ) ) ) @ A )
     != ( hF_Mir165288108strict @ r @ x ) ),
    inference(pre_uni,[status(thm)],[4102:[bind(A,$thf( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir165288108strict @ r @ x ) ) )),bind(B,$thf( B ))]]) ).

thf(4315,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1687042746ollect @ ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir165288108strict @ r @ x ) ) ) @ A )
     != ( hF_Mir165288108strict @ r @ x ) ),
    inference(simp,[status(thm)],[4251]) ).

thf(615,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ A )
      | ( ( hF_Mirabelle_hmem @ ( sk23 @ A ) @ A )
       != ( hF_Mirabelle_hmem @ C
          @ ( hF_Mir569462966eplace @ B
            @ ^ [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] : $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[324,502]) ).

thf(616,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mir1093797708lation
      @ ( hF_Mir569462966eplace @ A
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false ) ),
    inference(pattern_uni,[status(thm)],[615:[bind(A,$thf( hF_Mir569462966eplace @ E @ ^ [E: hF_Mirabelle_hf] : ^ [F: hF_Mirabelle_hf] : $false )),bind(B,$thf( E )),bind(C,$thf( sk23 @ ( hF_Mir569462966eplace @ E @ ^ [E: hF_Mirabelle_hf] : ^ [F: hF_Mirabelle_hf] : $false ) ))]]) ).

thf(637,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mir1093797708lation
      @ ( hF_Mir569462966eplace @ A
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false ) ),
    inference(simp,[status(thm)],[616]) ).

thf(1550,plain,
    ! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hmem @ B @ ( sk7 @ A ) )
        = ( hF_Mirabelle_hmem @ C @ ( hF_Mirabelle_HUnion @ D ) ) )
      | ( ( ? [E: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ E @ A )
              & ( hF_Mirabelle_hmem @ B @ E ) ) )
       != ( ? [E: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ E @ D )
              & ( hF_Mirabelle_hmem @ C @ E ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[85,57]) ).

thf(1551,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ B @ ( sk7 @ A ) )
      = ( hF_Mirabelle_hmem @ B @ ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(pattern_uni,[status(thm)],[1550:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).

thf(1746,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ B @ ( hF_Mirabelle_HUnion @ A ) )
      | ( ( hF_Mirabelle_hmem @ B @ ( sk7 @ A ) )
       != ( hF_Mirabelle_hmem @ C @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1551,106]) ).

thf(1747,plain,
    ! [A: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ ( sk7 @ A ) @ ( hF_Mirabelle_HUnion @ A ) ),
    inference(pattern_uni,[status(thm)],[1746:[bind(A,$thf( D )),bind(B,$thf( sk7 @ D )),bind(C,$thf( sk7 @ D ))]]) ).

thf(1791,plain,
    ! [A: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ ( sk7 @ A ) @ ( hF_Mirabelle_HUnion @ A ) ),
    inference(simp,[status(thm)],[1747]) ).

thf(6096,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ A ) @ B )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
          @ ( hF_Mir1687042746ollect
            @ ^ [C: hF_Mirabelle_hf] : $true
            @ ( hF_Mir165288108strict @ r @ x ) ) )
       != ( hF_Mirabelle_hmem @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[6074,1296]) ).

thf(6097,plain,
    ~ ( hF_Mirabelle_hmem
      @ ( hF_Mirabelle_HUnion
        @ ( hF_Mir1687042746ollect
          @ ^ [A: hF_Mirabelle_hf] : $true
          @ ( hF_Mir165288108strict @ r @ x ) ) )
      @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(pattern_uni,[status(thm)],[6096:[bind(A,$thf( hF_Mir1687042746ollect @ ^ [C: hF_Mirabelle_hf] : $true @ ( hF_Mir165288108strict @ r @ x ) )),bind(B,$thf( hF_Mirabelle_hpair @ sk127 @ sk128 ))]]) ).

thf(2554,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) @ ( hF_Mir165288108strict @ r @ x ) )
     != ( hF_Mirabelle_hmem @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[2502,106]) ).

thf(2586,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ sk127 @ sk129 )
       != A )
      | ( ( hF_Mir165288108strict @ r @ x )
       != A ) ),
    inference(simp,[status(thm)],[2554]) ).

thf(2634,plain,
    ( ( hF_Mir165288108strict @ r @ x )
   != ( hF_Mirabelle_hpair @ sk127 @ sk129 ) ),
    inference(simp,[status(thm)],[2586]) ).

thf(215,plain,
    ! [E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mir569462966eplace @ A @ B )
       != ( hF_Mirabelle_HUnion @ C ) )
      | ~ ( hF_Mirabelle_hmem @ D @ A )
      | ~ ( B @ D @ C )
      | ( ( hF_Mirabelle_hmem @ ( sk1 @ B @ A ) @ A )
       != ( hF_Mirabelle_hmem @ E @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[185,106]) ).

thf(259,plain,
    ! [E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mir569462966eplace @ A @ B )
       != ( hF_Mirabelle_HUnion @ C ) )
      | ~ ( hF_Mirabelle_hmem @ D @ A )
      | ~ ( B @ D @ C )
      | ( ( sk1 @ B @ A )
       != E )
      | ( A != E ) ),
    inference(simp,[status(thm)],[215]) ).

thf(266,plain,
    ! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mir569462966eplace @ A @ B )
       != ( hF_Mirabelle_HUnion @ C ) )
      | ~ ( hF_Mirabelle_hmem @ D @ A )
      | ~ ( B @ D @ C )
      | ( ( sk1 @ B @ A )
       != A ) ),
    inference(simp,[status(thm)],[259]) ).

thf(10415,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
       != sk371 )
      | ( ( A @ B @ C )
       != sk373 ) ),
    inference(paramod_ordered,[status(thm)],[126,9388]) ).

thf(12415,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : C
        @ ( hF_Mirabelle_hpair @ A @ sk373 ) )
     != sk371 ),
    inference(pre_uni,[status(thm)],[10415:[bind(A,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : E )),bind(B,$thf( B )),bind(C,$thf( sk373 ))]]) ).

thf(12975,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : C
        @ ( hF_Mirabelle_hpair @ A @ sk373 ) )
     != sk371 ),
    inference(simp,[status(thm)],[12415]) ).

thf(15934,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( sk371
       != ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
          @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : C
          @ sk366 ) )
      | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
       != ( hF_Mirabelle_hpair @ A @ sk373 ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,12975]) ).

thf(15944,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( sk371
       != ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
          @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : C
          @ sk366 ) )
      | ( sk367 != A )
      | ( sk373 != sk368 ) ),
    inference(simp,[status(thm)],[15934]) ).

thf(15961,plain,
    ( ( sk371
     != ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
        @ sk366 ) )
    | ( sk373 != sk368 ) ),
    inference(simp,[status(thm)],[15944]) ).

thf(19227,plain,
    ( ( sk371
     != ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
        @ sk366 ) )
    | ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
        @ sk371 )
     != sk368 ) ),
    inference(rewrite,[status(thm)],[15961,17571]) ).

thf(15803,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ $o
        @ ^ [B: hF_Mirabelle_hf] : hF_Mir859708136nction
        @ sk366 )
      | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
       != ( hF_Mirabelle_hpair @ A @ r ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,12921]) ).

thf(15842,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ $o
        @ ^ [B: hF_Mirabelle_hf] : hF_Mir859708136nction
        @ sk366 )
      | ( sk367 != A )
      | ( sk368 != r ) ),
    inference(simp,[status(thm)],[15803]) ).

thf(15877,plain,
    ( ( hF_Mirabelle_hsplit @ $o
      @ ^ [A: hF_Mirabelle_hf] : hF_Mir859708136nction
      @ sk366 )
    | ( sk368 != r ) ),
    inference(simp,[status(thm)],[15842]) ).

thf(1195,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ? [D: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ D @ B )
          & ( hF_Mirabelle_hmem @ A @ D ) )
      | ( hF_Mir1093797708lation @ C )
      | ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
       != ( hF_Mirabelle_hmem @ ( sk23 @ C ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[57,324]) ).

thf(1196,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ? [B: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ B @ A )
          & ( hF_Mirabelle_hmem @ ( sk23 @ ( hF_Mirabelle_HUnion @ A ) ) @ B ) )
      | ( hF_Mir1093797708lation @ ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(pattern_uni,[status(thm)],[1195:[bind(A,$thf( sk23 @ ( hF_Mirabelle_HUnion @ E ) )),bind(B,$thf( E )),bind(C,$thf( hF_Mirabelle_HUnion @ E ))]]) ).

thf(1334,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ ( hF_Mirabelle_HUnion @ A ) )
      | ( hF_Mirabelle_hmem @ ( sk79 @ A ) @ A ) ),
    inference(cnf,[status(esa)],[1196]) ).

thf(1336,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ ( hF_Mirabelle_HUnion @ A ) )
      | ( hF_Mirabelle_hmem @ ( sk79 @ A ) @ A ) ),
    inference(simp,[status(thm)],[1334]) ).

thf(2061,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ ( hF_Mirabelle_HUnion @ A ) )
      | ( ( hF_Mirabelle_hmem @ ( sk79 @ A ) @ A )
       != ( hF_Mirabelle_hmem @ C
          @ ( hF_Mir569462966eplace @ B
            @ ^ [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] : $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1336,502]) ).

thf(2062,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mir1093797708lation
      @ ( hF_Mirabelle_HUnion
        @ ( hF_Mir569462966eplace @ A
          @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false ) ) ),
    inference(pattern_uni,[status(thm)],[2061:[bind(A,$thf( hF_Mir569462966eplace @ E @ ^ [E: hF_Mirabelle_hf] : ^ [F: hF_Mirabelle_hf] : $false )),bind(B,$thf( E )),bind(C,$thf( sk79 @ ( hF_Mir569462966eplace @ E @ ^ [E: hF_Mirabelle_hf] : ^ [F: hF_Mirabelle_hf] : $false ) ))]]) ).

thf(2089,plain,
    ! [A: hF_Mirabelle_hf] :
      ( hF_Mir1093797708lation
      @ ( hF_Mirabelle_HUnion
        @ ( hF_Mir569462966eplace @ A
          @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false ) ) ),
    inference(simp,[status(thm)],[2062]) ).

thf(2728,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ ( sk7 @ A ) @ B )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mirabelle_hmem @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2503,1634]) ).

thf(2729,plain,
    ~ ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir165288108strict @ r @ x ) ) @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(pattern_uni,[status(thm)],[2728:[bind(A,$thf( hF_Mir165288108strict @ r @ x )),bind(B,$thf( hF_Mirabelle_hpair @ sk127 @ sk128 ))]]) ).

thf(41,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( B @ ( sk1 @ B @ A ) @ ( sk3 @ B @ A ) )
      | ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    inference(cnf,[status(esa)],[38]) ).

thf(45,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) )
      | ( B @ ( sk1 @ B @ A ) @ ( sk3 @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[41]) ).

thf(2548,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) @ ( hF_Mir165288108strict @ r @ x ) )
     != ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2502,82]) ).

thf(2572,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ sk127 @ sk129 )
       != A )
      | ( ( hF_Mir165288108strict @ r @ x )
       != ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(simp,[status(thm)],[2548]) ).

thf(2602,plain,
    ( ( hF_Mir165288108strict @ r @ x )
   != ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk127 @ sk129 ) ) ),
    inference(simp,[status(thm)],[2572]) ).

thf(70,plain,
    ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_Replace @ B @ C ) )
      = ( ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ B )
            & ( C @ D @ A )
            & ! [E: hF_Mirabelle_hf] :
                ( ( C @ D @ E )
               => ( E = A ) ) ) ) ),
    inference(cnf,[status(esa)],[69]) ).

thf(71,plain,
    ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_Replace @ B @ C ) )
      = ( ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ B )
            & ( C @ D @ A )
            & ! [E: hF_Mirabelle_hf] :
                ( ( C @ D @ E )
               => ( E = A ) ) ) ) ),
    inference(lifteq,[status(thm)],[70]) ).

thf(50,plain,
    ! [D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( A != B )
      | ( hF_Mirabelle_hmem @ ( sk4 @ D @ C @ B @ A ) @ B )
      | ( ( hF_Mirabelle_Replace @ A @ C )
        = ( hF_Mirabelle_Replace @ B @ D ) ) ),
    inference(cnf,[status(esa)],[48]) ).

thf(53,plain,
    ! [D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( A != B )
      | ( ( hF_Mirabelle_Replace @ A @ C )
        = ( hF_Mirabelle_Replace @ B @ D ) )
      | ( hF_Mirabelle_hmem @ ( sk4 @ D @ C @ B @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[50]) ).

thf(54,plain,
    ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_Replace @ A @ B )
        = ( hF_Mirabelle_Replace @ A @ C ) )
      | ( hF_Mirabelle_hmem @ ( sk4 @ C @ B @ A @ A ) @ A ) ),
    inference(simp,[status(thm)],[53]) ).

thf(3343,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) )
        = ( hF_Mirabelle_hmem @ A @ C ) )
      | ( ( hF_Mir859708136nction @ r )
       != ( B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[152,60]) ).

thf(3516,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ r @ ( hF_Mir1687042746ollect @ hF_Mir859708136nction @ A ) )
      = ( hF_Mirabelle_hmem @ r @ A ) ),
    inference(pre_uni,[status(thm)],[3343:[bind(A,$thf( r )),bind(B,$thf( hF_Mir859708136nction )),bind(C,$thf( C ))]]) ).

thf(3726,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ r @ ( hF_Mir1687042746ollect @ hF_Mir859708136nction @ A ) )
      = ( hF_Mirabelle_hmem @ r @ A ) ),
    inference(simp,[status(thm)],[3516]) ).

thf(8300,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( sk366 != A )
      | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,78]) ).

thf(8301,plain,
    sk367 != sk366,
    inference(pattern_uni,[status(thm)],[8300:[bind(A,$thf( sk367 )),bind(B,$thf( sk368 ))]]) ).

thf(8392,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsnd @ sk366 )
        = B )
      | ( ( hF_Mirabelle_hpair @ sk369 @ sk370 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8287,66]) ).

thf(8393,plain,
    ( ( hF_Mirabelle_hsnd @ sk366 )
    = sk370 ),
    inference(pattern_uni,[status(thm)],[8392:[bind(A,$thf( sk369 )),bind(B,$thf( sk370 ))]]) ).

thf(9243,plain,
    sk370 = sk368,
    inference(rewrite,[status(thm)],[8393,8317]) ).

thf(10627,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
       != sk366 )
      | ( ( A @ B @ C )
       != sk367 ) ),
    inference(paramod_ordered,[status(thm)],[126,8301]) ).

thf(12557,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : B
        @ ( hF_Mirabelle_hpair @ sk367 @ A ) )
     != sk366 ),
    inference(pre_uni,[status(thm)],[10627:[bind(A,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : D )),bind(B,$thf( sk367 ))]]) ).

thf(13096,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : B
        @ ( hF_Mirabelle_hpair @ sk367 @ A ) )
     != sk366 ),
    inference(simp,[status(thm)],[12557]) ).

thf(20365,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
          @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : B
          @ sk366 )
       != sk366 )
      | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
       != ( hF_Mirabelle_hpair @ sk367 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,13096]) ).

thf(20366,plain,
    ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
      @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : A
      @ sk366 )
   != sk366 ),
    inference(pattern_uni,[status(thm)],[20365:[bind(A,$thf( sk368 ))]]) ).

thf(1722,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ B @ ( hF_Mirabelle_HUnion @ A ) )
      = ( ? [C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ C @ A )
            & ( hF_Mirabelle_hmem @ B @ C ) ) ) ),
    inference(rewrite,[status(thm)],[85,1551]) ).

thf(9555,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( A
          = ( hF_Mirabelle_hpair @ B @ C ) )
      | ( ( hF_Mir796903520_hpair @ sk371 )
       != ( hF_Mir796903520_hpair @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9402,156]) ).

thf(9556,plain,
    ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( sk371
      = ( hF_Mirabelle_hpair @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[9555:[bind(A,$thf( sk371 ))]]) ).

thf(9583,plain,
    ( sk371
    = ( hF_Mirabelle_hpair @ sk376 @ sk377 ) ),
    inference(cnf,[status(esa)],[9556]) ).

thf(9584,plain,
    ( ( hF_Mirabelle_hpair @ sk376 @ sk377 )
    = sk371 ),
    inference(lifteq,[status(thm)],[9583]) ).

thf(9640,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hfst @ sk371 )
        = A )
      | ( ( hF_Mirabelle_hpair @ sk376 @ sk377 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9584,120]) ).

thf(9641,plain,
    ( ( hF_Mirabelle_hfst @ sk371 )
    = sk376 ),
    inference(pattern_uni,[status(thm)],[9640:[bind(A,$thf( sk376 )),bind(B,$thf( sk377 ))]]) ).

thf(9723,plain,
    sk376 = sk372,
    inference(rewrite,[status(thm)],[9641,9377]) ).

thf(18,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
      = ( ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ B )
            & ( A
              = ( C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_RepFun__iff) ).

thf(98,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
      = ( ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ B )
            & ( A
              = ( C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(102,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ C @ ( sk9 @ B @ A ) )
      = ( ( hF_Mirabelle_hmem @ C @ A )
        & ( B @ C ) ) ),
    inference(cnf,[status(esa)],[101]) ).

thf(103,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ C @ ( sk9 @ B @ A ) )
      = ( ( hF_Mirabelle_hmem @ C @ A )
        & ( B @ C ) ) ),
    inference(lifteq,[status(thm)],[102]) ).

thf(323,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mir796903520_hpair @ ( sk23 @ A ) )
      | ( hF_Mir1093797708lation @ A ) ),
    inference(cnf,[status(esa)],[312]) ).

thf(9396,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( sk11 @ A @ sk371 )
        = B )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,113]) ).

thf(9397,plain,
    ( ( sk11 @ sk372 @ sk371 )
    = sk373 ),
    inference(pattern_uni,[status(thm)],[9396:[bind(A,$thf( sk372 )),bind(B,$thf( sk373 ))]]) ).

thf(17682,plain,
    ( ( sk11 @ sk372 @ sk371 )
    = ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
      @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
      @ sk371 ) ),
    inference(rewrite,[status(thm)],[9397,17571]) ).

thf(88,plain,
    ! [D: hF_Mirabelle_hf > hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( A != B )
      | ( ( C @ ( sk8 @ D @ C @ B @ A ) )
       != ( D @ ( sk8 @ D @ C @ B @ A ) ) )
      | ( ( hF_Mirabelle_RepFun @ A @ C )
        = ( hF_Mirabelle_RepFun @ B @ D ) ) ),
    inference(cnf,[status(esa)],[87]) ).

thf(90,plain,
    ! [D: hF_Mirabelle_hf > hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( A != B )
      | ( ( C @ ( sk8 @ D @ C @ B @ A ) )
       != ( D @ ( sk8 @ D @ C @ B @ A ) ) )
      | ( ( hF_Mirabelle_RepFun @ A @ C )
        = ( hF_Mirabelle_RepFun @ B @ D ) ) ),
    inference(lifteq,[status(thm)],[88]) ).

thf(91,plain,
    ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( B @ ( sk8 @ C @ B @ A @ A ) )
       != ( C @ ( sk8 @ C @ B @ A @ A ) ) )
      | ( ( hF_Mirabelle_RepFun @ A @ B )
        = ( hF_Mirabelle_RepFun @ A @ C ) ) ),
    inference(simp,[status(thm)],[90]) ).

thf(5481,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ A ) @ B )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ) )
       != ( hF_Mirabelle_hmem @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5133,1296]) ).

thf(5482,plain,
    ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ) ) @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(pattern_uni,[status(thm)],[5481:[bind(A,$thf( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) )),bind(B,$thf( hF_Mirabelle_hpair @ sk127 @ sk128 ))]]) ).

thf(15932,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
          @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : C
          @ sk371 )
       != sk371 )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ A @ sk373 ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,12975]) ).

thf(15933,plain,
    ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
      @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
      @ sk371 )
   != sk371 ),
    inference(pattern_uni,[status(thm)],[15932:[bind(A,$thf( sk372 ))]]) ).

thf(6099,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ ( sk7 @ A ) @ B )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
          @ ( hF_Mir1687042746ollect
            @ ^ [C: hF_Mirabelle_hf] : $true
            @ ( hF_Mir165288108strict @ r @ x ) ) )
       != ( hF_Mirabelle_hmem @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[6074,1634]) ).

thf(6100,plain,
    ~ ( hF_Mirabelle_hmem
      @ ( sk7
        @ ( hF_Mir1687042746ollect
          @ ^ [A: hF_Mirabelle_hf] : $true
          @ ( hF_Mir165288108strict @ r @ x ) ) )
      @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(pattern_uni,[status(thm)],[6099:[bind(A,$thf( hF_Mir1687042746ollect @ ^ [C: hF_Mirabelle_hf] : $true @ ( hF_Mir165288108strict @ r @ x ) )),bind(B,$thf( hF_Mirabelle_hpair @ sk127 @ sk128 ))]]) ).

thf(131,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( sk12 @ B @ A ) @ A )
      | ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    inference(cnf,[status(esa)],[130]) ).

thf(135,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) )
      | ( hF_Mirabelle_hmem @ ( sk12 @ B @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[131]) ).

thf(1197,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ A )
      | ? [D: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ D @ C )
          & ( hF_Mirabelle_hmem @ B @ D ) )
      | ( ( hF_Mirabelle_hmem @ ( sk23 @ A ) @ A )
       != ( hF_Mirabelle_hmem @ B @ ( hF_Mirabelle_HUnion @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[324,57]) ).

thf(1198,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ ( hF_Mirabelle_HUnion @ A ) )
      | ? [B: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ B @ A )
          & ( hF_Mirabelle_hmem @ ( sk23 @ ( hF_Mirabelle_HUnion @ A ) ) @ B ) ) ),
    inference(pattern_uni,[status(thm)],[1197:[bind(A,$thf( hF_Mirabelle_HUnion @ E )),bind(B,$thf( sk23 @ ( hF_Mirabelle_HUnion @ E ) )),bind(C,$thf( E ))]]) ).

thf(1338,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( sk80 @ A ) @ A )
      | ( hF_Mir1093797708lation @ ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(cnf,[status(esa)],[1198]) ).

thf(1340,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( sk80 @ A ) @ A )
      | ( hF_Mir1093797708lation @ ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(simp,[status(thm)],[1338]) ).

thf(122,plain,
    ! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ A @ B )
        = ( hF_Mirabelle_hpair @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(cnf,[status(esa)],[121]) ).

thf(123,plain,
    ! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ A @ B )
        = ( hF_Mirabelle_hpair @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(lifteq,[status(thm)],[122]) ).

thf(19132,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf] :
      ( ( sk371
        = ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hpair @ B @ C ) ) )
      | ( ( hF_Mirabelle_hpair @ sk372
          @ ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
            @ ^ [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] : E
            @ sk371 ) )
       != ( A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[17688,126]) ).

thf(19182,plain,
    ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
      @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hpair @ B @ A )
      @ ( hF_Mirabelle_hpair
        @ ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
          @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
          @ sk371 )
        @ sk372 ) )
    = sk371 ),
    inference(pre_uni,[status(thm)],[19132:[bind(A,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : ( hF_Mirabelle_hpair @ E @ D ) )),bind(B,$thf( hF_Mirabelle_hsplit @ hF_Mirabelle_hf @ ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : E @ sk371 )),bind(C,$thf( sk372 ))]]) ).

thf(6131,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ B @ A )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
          @ ( hF_Mir1687042746ollect
            @ ^ [C: hF_Mirabelle_hf] : $true
            @ ( hF_Mir165288108strict @ r @ x ) ) )
       != ( hF_Mirabelle_hmem @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[6074,63]) ).

thf(6132,plain,
    ~ ( hF_Mirabelle_hmem
      @ ( hF_Mir1687042746ollect
        @ ^ [A: hF_Mirabelle_hf] : $true
        @ ( hF_Mir165288108strict @ r @ x ) )
      @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(pattern_uni,[status(thm)],[6131:[bind(A,$thf( hF_Mirabelle_hpair @ sk127 @ sk128 )),bind(B,$thf( hF_Mir1687042746ollect @ ^ [C: hF_Mirabelle_hf] : $true @ ( hF_Mir165288108strict @ r @ x ) ))]]) ).

thf(30,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mir1093797708lation @ ( hF_Mir165288108strict @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hrelation__restr) ).

thf(145,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mir1093797708lation @ ( hF_Mir165288108strict @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(5513,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ B @ A )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ) )
       != ( hF_Mirabelle_hmem @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5133,63]) ).

thf(5514,plain,
    ~ ( hF_Mirabelle_hmem @ ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ) @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(pattern_uni,[status(thm)],[5513:[bind(A,$thf( hF_Mirabelle_hpair @ sk127 @ sk128 )),bind(B,$thf( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ))]]) ).

thf(7395,plain,
    ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
      @ ( hF_Mir1687042746ollect
        @ ^ [A: hF_Mirabelle_hf] : $false
        @ ( hF_Mir165288108strict @ r @ x ) ) )
   != ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir165288108strict @ r @ x ) ) ),
    inference(paramod_ordered,[status(thm)],[2503,7367]) ).

thf(7412,plain,
    ( ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
     != ( hF_Mirabelle_hpair @ sk127 @ sk128 ) )
    | ( ( hF_Mir1687042746ollect
        @ ^ [A: hF_Mirabelle_hf] : $false
        @ ( hF_Mir165288108strict @ r @ x ) )
     != ( hF_Mir165288108strict @ r @ x ) ) ),
    inference(simp,[status(thm)],[7395]) ).

thf(7456,plain,
    ( ( hF_Mir1687042746ollect
      @ ^ [A: hF_Mirabelle_hf] : $false
      @ ( hF_Mir165288108strict @ r @ x ) )
   != ( hF_Mir165288108strict @ r @ x ) ),
    inference(simp,[status(thm)],[7412]) ).

thf(153,plain,
    ( ( hF_Mir859708136nction @ ( hF_Mir165288108strict @ r @ x ) )
   != ( hF_Mir859708136nction @ r ) ),
    inference(paramod_ordered,[status(thm)],[152,34]) ).

thf(154,plain,
    ( ( hF_Mir165288108strict @ r @ x )
   != r ),
    inference(simp,[status(thm)],[153]) ).

thf(15719,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ $o
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ B )
        @ sk366 )
      | ( ( hF_Mirabelle_hpair @ sk367 @ sk368 )
       != ( hF_Mirabelle_hpair @ r @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8285,12920]) ).

thf(15738,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ $o
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ B )
        @ sk366 )
      | ( sk367 != r )
      | ( sk368 != A ) ),
    inference(simp,[status(thm)],[15719]) ).

thf(15790,plain,
    ( ( hF_Mirabelle_hsplit @ $o
      @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mir859708136nction @ A )
      @ sk366 )
    | ( sk367 != r ) ),
    inference(simp,[status(thm)],[15738]) ).

thf(9662,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsnd @ sk371 )
        = B )
      | ( ( hF_Mirabelle_hpair @ sk376 @ sk377 )
       != ( hF_Mirabelle_hpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9584,66]) ).

thf(9663,plain,
    ( ( hF_Mirabelle_hsnd @ sk371 )
    = sk377 ),
    inference(pattern_uni,[status(thm)],[9662:[bind(A,$thf( sk376 )),bind(B,$thf( sk377 ))]]) ).

thf(9726,plain,
    sk377 = sk373,
    inference(rewrite,[status(thm)],[9663,9399]) ).

thf(17685,plain,
    ( sk377
    = ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
      @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
      @ sk371 ) ),
    inference(rewrite,[status(thm)],[9726,17571]) ).

thf(5480,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ) )
     != ( hF_Mirabelle_hmem @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[5133,106]) ).

thf(5534,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
       != A )
      | ( ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) )
       != A ) ),
    inference(simp,[status(thm)],[5480]) ).

thf(5596,plain,
    ( ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) )
   != ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(simp,[status(thm)],[5534]) ).

thf(15802,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ $o
        @ ^ [B: hF_Mirabelle_hf] : hF_Mir859708136nction
        @ sk371 )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ A @ r ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,12921]) ).

thf(15824,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ $o
        @ ^ [B: hF_Mirabelle_hf] : hF_Mir859708136nction
        @ sk371 )
      | ( sk372 != A )
      | ( sk373 != r ) ),
    inference(simp,[status(thm)],[15802]) ).

thf(15859,plain,
    ( ( hF_Mirabelle_hsplit @ $o
      @ ^ [A: hF_Mirabelle_hf] : hF_Mir859708136nction
      @ sk371 )
    | ( sk373 != r ) ),
    inference(simp,[status(thm)],[15824]) ).

thf(19392,plain,
    ( ( hF_Mirabelle_hsplit @ $o
      @ ^ [A: hF_Mirabelle_hf] : hF_Mir859708136nction
      @ sk371 )
    | ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : B
        @ sk371 )
     != r ) ),
    inference(rewrite,[status(thm)],[15859,17571]) ).

thf(2718,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir165288108strict @ r @ x ) )
     != ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2503,82]) ).

thf(2748,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
       != A )
      | ( ( hF_Mir165288108strict @ r @ x )
       != ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(simp,[status(thm)],[2718]) ).

thf(2828,plain,
    ( ( hF_Mir165288108strict @ r @ x )
   != ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ) ),
    inference(simp,[status(thm)],[2748]) ).

thf(5484,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ ( sk7 @ A ) @ B )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ) )
       != ( hF_Mirabelle_hmem @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5133,1634]) ).

thf(5485,plain,
    ~ ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ) ) @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(pattern_uni,[status(thm)],[5484:[bind(A,$thf( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) )),bind(B,$thf( hF_Mirabelle_hpair @ sk127 @ sk128 ))]]) ).

thf(158,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( A = B )
      = ( ! [C: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ C @ A )
            = ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
    inference(func_ext,[status(esa)],[128]) ).

thf(28,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf] :
    ? [C: hF_Mirabelle_hf] :
    ! [D: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ D @ C )
      = ( ? [E: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ E @ A )
            & ( D
              = ( B @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_replacement__fun) ).

thf(139,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf] :
    ? [C: hF_Mirabelle_hf] :
    ! [D: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ D @ C )
      = ( ? [E: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ E @ A )
            & ( D
              = ( B @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(22,axiom,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_hmem__ne) ).

thf(114,plain,
    ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(6085,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
        @ ( hF_Mir1687042746ollect
          @ ^ [B: hF_Mirabelle_hf] : $true
          @ ( hF_Mir165288108strict @ r @ x ) ) )
     != ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[6074,82]) ).

thf(6140,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
       != A )
      | ( ( hF_Mir1687042746ollect
          @ ^ [B: hF_Mirabelle_hf] : $true
          @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mirabelle_HUnion @ A ) ) ),
    inference(simp,[status(thm)],[6085]) ).

thf(6277,plain,
    ( ( hF_Mir1687042746ollect
      @ ^ [A: hF_Mirabelle_hf] : $true
      @ ( hF_Mir165288108strict @ r @ x ) )
   != ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ) ),
    inference(simp,[status(thm)],[6140]) ).

thf(5069,plain,
    ! [A: hF_Mirabelle_hf > $o] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ A @ ( hF_Mir165288108strict @ r @ x ) ) )
      | ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir165288108strict @ r @ x ) )
       != ( A @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2503,3609]) ).

thf(5119,plain,
    ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 )
    @ ( hF_Mir1687042746ollect
      @ ^ [A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ A @ ( hF_Mir165288108strict @ r @ x ) )
      @ ( hF_Mir165288108strict @ r @ x ) ) ),
    inference(pre_uni,[status(thm)],[5069:[bind(A,$thf( ^ [B: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ B @ ( hF_Mir165288108strict @ r @ x ) ) ))]]) ).

thf(146,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( hF_Mir1093797708lation @ ( hF_Mir165288108strict @ A @ B ) ),
    inference(cnf,[status(esa)],[145]) ).

thf(12480,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : C
        @ ( hF_Mirabelle_hpair @ A @ sk129 ) )
     != sk128 ),
    inference(pre_uni,[status(thm)],[10508:[bind(A,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : E )),bind(B,$thf( B )),bind(C,$thf( sk129 ))]]) ).

thf(13028,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : C
        @ ( hF_Mirabelle_hpair @ A @ sk129 ) )
     != sk128 ),
    inference(simp,[status(thm)],[12480]) ).

thf(611,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ A )
      | ~ ( hF_Mirabelle_hmem @ C @ B )
      | ( ( hF_Mirabelle_hmem @ ( sk23 @ A ) @ A )
       != ( hF_Mirabelle_hmem @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[324,63]) ).

thf(612,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ A )
      | ~ ( hF_Mirabelle_hmem @ A @ ( sk23 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[611:[bind(A,$thf( D )),bind(B,$thf( sk23 @ D )),bind(C,$thf( D ))]]) ).

thf(635,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1093797708lation @ A )
      | ~ ( hF_Mirabelle_hmem @ A @ ( sk23 @ A ) ) ),
    inference(simp,[status(thm)],[612]) ).

thf(132,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( B @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
      | ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) ) ),
    inference(cnf,[status(esa)],[130]) ).

thf(136,plain,
    ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
        = ( ? [D: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ D @ A )
              & ( B @ D @ C ) ) ) )
      | ( B @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[132]) ).

thf(5974,plain,
    ( ( ( hF_Mir1687042746ollect
        @ ^ [A: hF_Mirabelle_hf] :
          ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
            ( A
            = ( hF_Mirabelle_hpair @ B @ C ) )
        @ ( hF_Mir165288108strict @ r @ x ) )
     != ( hF_Mirabelle_hpair @ sk127 @ sk128 ) )
    | ( hF_Mir796903520_hpair != hF_Mir796903520_hpair ) ),
    inference(paramod_ordered,[status(thm)],[68,5596]) ).

thf(5975,plain,
    ( ( hF_Mir1687042746ollect
      @ ^ [A: hF_Mirabelle_hf] :
        ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
          ( A
          = ( hF_Mirabelle_hpair @ B @ C ) )
      @ ( hF_Mir165288108strict @ r @ x ) )
   != ( hF_Mirabelle_hpair @ sk127 @ sk128 ) ),
    inference(pattern_uni,[status(thm)],[5974:[]]) ).

thf(17414,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
          @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : B
          @ sk371 )
       != sk128 )
      | ( ( hF_Mirabelle_hpair @ sk372 @ sk373 )
       != ( hF_Mirabelle_hpair @ sk129 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9249,13027]) ).

thf(17439,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
          @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : B
          @ sk371 )
       != sk128 )
      | ( sk372 != sk129 )
      | ( sk373 != A ) ),
    inference(simp,[status(thm)],[17414]) ).

thf(17456,plain,
    ( ( ( hF_Mirabelle_hsplit @ hF_Mirabelle_hf
        @ ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : A
        @ sk371 )
     != sk128 )
    | ( sk372 != sk129 ) ),
    inference(simp,[status(thm)],[17439]) ).

thf(5517,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk127 @ sk128 ) @ ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) ) )
     != ( hF_Mirabelle_hmem @ B
        @ ( hF_Mir569462966eplace @ A
          @ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[5133,502]) ).

thf(5527,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hpair @ sk127 @ sk128 )
       != B )
      | ( ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) )
       != ( hF_Mir569462966eplace @ A
          @ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) ) ),
    inference(simp,[status(thm)],[5517]) ).

thf(5581,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mir1687042746ollect @ hF_Mir796903520_hpair @ ( hF_Mir165288108strict @ r @ x ) )
     != ( hF_Mir569462966eplace @ A
        @ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false ) ),
    inference(simp,[status(thm)],[5527]) ).

thf(99,plain,
    ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
      = ( ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ B )
            & ( A
              = ( C @ D ) ) ) ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(100,plain,
    ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
      = ( ? [D: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ D @ B )
            & ( A
              = ( C @ D ) ) ) ) ),
    inference(lifteq,[status(thm)],[99]) ).

thf(21489,plain,
    $false,
    inference(e,[status(thm)],[69,138,101,2559,6074,13062,10262,8315,120,2659,9383,142,12921,8335,17688,185,37,52,110,4334,157,12920,14773,46,93,152,9240,57,78,8352,17691,6259,4329,3724,646,106,121,11064,6227,147,61,8306,17571,74,8347,3676,60,15766,17683,17440,137,97,1296,1634,4316,324,13063,156,5615,17687,2726,10152,2798,124,4315,637,1791,7448,2504,6097,129,2634,128,266,19227,15877,8262,2089,2729,2556,34,45,64,2602,8259,44,3609,118,71,54,3726,8301,86,9243,113,20366,9377,1722,9723,98,103,323,17682,91,66,155,5482,15933,6100,35,135,563,2503,112,1340,123,19182,1551,5133,13027,6132,145,2715,63,5514,150,67,502,127,2545,1336,7456,154,15790,8317,72,17685,5596,43,8299,19392,2828,8260,5485,104,8285,158,139,55,114,75,58,6277,5119,82,151,36,146,190,9596,13096,107,79,13028,635,94,126,136,2502,5975,9402,47,68,17456,5581,111,7367,83,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : ITP076^2 : TPTP v8.2.0. Released v7.5.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.31  % Computer : n017.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit : 300
% 0.12/0.31  % WCLimit  : 300
% 0.12/0.32  % DateTime : Sat May 18 15:47:39 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 0.76/0.78  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.60/1.08  % [INFO] 	 Parsing done (294ms). 
% 1.89/1.09  % [INFO] 	 Running in sequential loop mode. 
% 2.57/1.35  % [INFO] 	 eprover registered as external prover. 
% 2.57/1.35  % [INFO] 	 cvc4 registered as external prover. 
% 2.57/1.35  % [INFO] 	 Scanning for conjecture ... 
% 2.78/1.44  % [INFO] 	 Found a conjecture (or negated_conjecture) and 298 axioms. Running axiom selection ... 
% 3.07/1.50  % [INFO] 	 Axiom selection finished. Selected 31 axioms (removed 267 axioms). 
% 3.20/1.55  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.20/1.56  % [INFO] 	 Type checking passed. 
% 3.20/1.57  % [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 ... 
% 124.95/20.73  % External prover 'e' found a proof!
% 124.95/20.73  % [INFO] 	 Killing All external provers ... 
% 124.95/20.73  % Time passed: 20273ms (effective reasoning time: 19630ms)
% 124.95/20.73  % 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)>
% 124.95/20.73  % Axioms used in derivation (31): fact_19_hfst__conv, fact_30_Replace__cong, fact_27_RepFun__iff, fact_22_is__hpair__def, fact_31_hmem__Sup__ne, fact_25_Replace__iff, fact_13_comprehension, fact_15_hpair__neq__fst, fact_5_hf__equalityI, fact_16_hpair__neq__snd, fact_24_HUnion__iff, fact_2_hrestrict__iff, fact_3_hpair__iff, fact_7_hmem__ne, fact_18_hsplit, fact_29_RepFun__cong, fact_10_hmem__not__sym, fact_17_replacement__fun, fact_20_hsnd__conv, fact_14_hmem__not__refl, fact_12_union__of__set, fact_0_hrelation__restr, fact_26_HCollect__iff, fact_8_replacement, fact_6_hf__ext, fact_11_hpair__inject, fact_1_hfunction__def, conj_0, fact_9_binary__union, fact_23_PrimReplace__iff, fact_21_hrelation__def
% 124.95/20.73  % No. of inferences in proof: 451
% 124.95/20.73  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 20273 ms resp. 19630 ms w/o parsing
% 125.22/20.85  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 125.22/20.85  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------