TSTP Solution File: PHI007^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : PHI007^5 : TPTP v8.2.0. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 02:18:27 EDT 2024

% Result   : Theorem 92.06s 26.95s
% Output   : Refutation 92.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   70
% Syntax   : Number of formulae    :  418 (  92 unt;  60 typ;   0 def)
%            Number of atoms       : 1418 ( 310 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 3884 ( 672   ~; 303   |;   2   &;2594   @)
%                                         (   0 <=>; 313  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  624 ( 624   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   62 (  59 usr;  43 con; 0-3 aty)
%            Number of variables   : 1210 ( 502   ^ 621   !;  87   ?;1210   :)

% Comments : 
%------------------------------------------------------------------------------
thf(qML_mu_type,type,
    qML_mu: $tType ).

thf(qML_i_type,type,
    qML_i: $tType ).

thf(inconsistency_G_type,type,
    inconsistency_G: qML_mu > qML_i > $o ).

thf(incons1905966852QML_mu_type,type,
    incons1905966852QML_mu: qML_mu > qML_i > $o ).

thf(inconsistency_P_type,type,
    inconsistency_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).

thf(incons1389517216QML_mu_type,type,
    incons1389517216QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).

thf(qML_r_type,type,
    qML_r: qML_i > qML_i > $o ).

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

thf(sk3_type,type,
    sk3: qML_mu ).

thf(sk4_type,type,
    sk4: qML_i ).

thf(sk5_type,type,
    sk5: qML_mu ).

thf(sk6_type,type,
    sk6: qML_i ).

thf(sk7_type,type,
    sk7: qML_mu ).

thf(sk8_type,type,
    sk8: qML_i ).

thf(sk9_type,type,
    sk9: qML_mu ).

thf(sk10_type,type,
    sk10: qML_i ).

thf(sk11_type,type,
    sk11: qML_mu > qML_i > $o ).

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

thf(sk13_type,type,
    sk13: qML_mu ).

thf(sk14_type,type,
    sk14: qML_i ).

thf(sk15_type,type,
    sk15: qML_mu ).

thf(sk16_type,type,
    sk16: qML_i ).

thf(sk17_type,type,
    sk17: qML_mu > qML_i > $o ).

thf(sk20_type,type,
    sk20: qML_mu > qML_i > $o ).

thf(sk21_type,type,
    sk21: qML_mu ).

thf(sk22_type,type,
    sk22: qML_i ).

thf(sk23_type,type,
    sk23: qML_mu ).

thf(sk24_type,type,
    sk24: qML_i ).

thf(sk26_type,type,
    sk26: qML_mu ).

thf(sk27_type,type,
    sk27: qML_i ).

thf(sk28_type,type,
    sk28: qML_mu ).

thf(sk29_type,type,
    sk29: qML_i ).

thf(sk30_type,type,
    sk30: qML_mu ).

thf(sk31_type,type,
    sk31: qML_i ).

thf(sk34_type,type,
    sk34: qML_mu ).

thf(sk35_type,type,
    sk35: qML_i ).

thf(sk37_type,type,
    sk37: qML_i ).

thf(sk43_type,type,
    sk43: qML_i ).

thf(sk55_type,type,
    sk55: qML_i ).

thf(sk59_type,type,
    sk59: qML_i ).

thf(sk62_type,type,
    sk62: qML_mu > qML_i > $o ).

thf(sk64_type,type,
    sk64: qML_mu > qML_i > $o ).

thf(sk67_type,type,
    sk67: qML_mu > qML_i > $o ).

thf(sk76_type,type,
    sk76: qML_i ).

thf(sk89_type,type,
    sk89: qML_i ).

thf(sk120_type,type,
    sk120: qML_i ).

thf(sk122_type,type,
    sk122: qML_i ).

thf(sk126_type,type,
    sk126: qML_mu > qML_i > $o ).

thf(sk132_type,type,
    sk132: qML_mu > qML_i > $o ).

thf(sk133_type,type,
    sk133: qML_mu > qML_i > $o ).

thf(sk134_type,type,
    sk134: qML_mu > qML_i > $o ).

thf(sk140_type,type,
    sk140: qML_mu > qML_i > $o ).

thf(sk144_type,type,
    sk144: qML_i ).

thf(sk149_type,type,
    sk149: qML_i ).

thf(sk350_type,type,
    sk350: qML_mu ).

thf(sk351_type,type,
    sk351: qML_i ).

thf(sk352_type,type,
    sk352: qML_mu ).

thf(sk353_type,type,
    sk353: qML_i ).

thf(sk354_type,type,
    sk354: qML_mu ).

thf(sk355_type,type,
    sk355: qML_i ).

thf(9,axiom,
    ( inconsistency_G
    = ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ C @ B )
         => ( C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_G__def) ).

thf(27,plain,
    ( inconsistency_G
    = ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ C @ B )
         => ( C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(28,plain,
    ( inconsistency_G
    = ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ C @ B )
         => ( C @ A @ B ) ) ) ),
    inference(lifteq,[status(thm)],[27]) ).

thf(34,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( inconsistency_G @ A @ B )
      = ( ! [C: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ C @ B )
           => ( C @ A @ B ) ) ) ),
    inference(func_ext,[status(esa)],[28]) ).

thf(10,axiom,
    ( incons1905966852QML_mu
    = ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ C @ A @ B )
         => ! [D: qML_i] :
              ( ( qML_r @ B @ D )
             => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_NE__def) ).

thf(29,plain,
    ( incons1905966852QML_mu
    = ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ C @ A @ B )
         => ! [D: qML_i] :
              ( ( qML_r @ B @ D )
             => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(30,plain,
    ( incons1905966852QML_mu
    = ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ C @ A @ B )
         => ! [D: qML_i] :
              ( ( qML_r @ B @ D )
             => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
    inference(lifteq,[status(thm)],[29]) ).

thf(8,axiom,
    ! [A: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_A5) ).

thf(25,plain,
    ! [A: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(26,plain,
    ! [A: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ A ),
    inference(cnf,[status(esa)],[25]) ).

thf(6,axiom,
    ! [A: qML_i] : ( inconsistency_P @ inconsistency_G @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_A3) ).

thf(21,plain,
    ! [A: qML_i] : ( inconsistency_P @ inconsistency_G @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(22,plain,
    ! [A: qML_i] : ( inconsistency_P @ inconsistency_G @ A ),
    inference(cnf,[status(esa)],[21]) ).

thf(35,plain,
    ! [A: qML_i] :
      ( ( inconsistency_P
        @ ^ [B: qML_mu,C: qML_i] :
          ! [D: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ D @ C )
           => ( D @ B @ C ) )
        @ A )
      | ( inconsistency_G != inconsistency_G ) ),
    inference(paramod_ordered,[status(thm)],[28,22]) ).

thf(36,plain,
    ! [A: qML_i] :
      ( inconsistency_P
      @ ^ [B: qML_mu,C: qML_i] :
        ! [D: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ D @ C )
         => ( D @ B @ C ) )
      @ A ),
    inference(pattern_uni,[status(thm)],[35:[]]) ).

thf(3,axiom,
    ! [A: qML_i,B: qML_mu > qML_i > $o] :
      ( ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( B @ C @ D )
        @ A )
     => ~ ( inconsistency_P @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_A1a) ).

thf(13,plain,
    ! [A: qML_i,B: qML_mu > qML_i > $o] :
      ( ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( B @ C @ D )
        @ A )
     => ~ ( inconsistency_P @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(14,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P
          @ ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D )
          @ A )
      | ~ ( inconsistency_P @ B @ A ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(46,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E )
          @ B )
      | ( ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] :
            ! [F: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ F @ E )
             => ( F @ D @ E ) )
          @ A )
       != ( inconsistency_P @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[36,14]) ).

thf(47,plain,
    ! [A: qML_i] :
      ~ ( inconsistency_P
        @ ^ [B: qML_mu,C: qML_i] :
            ~ ! [D: qML_mu > qML_i > $o] :
                ( ( inconsistency_P @ D @ C )
               => ( D @ B @ C ) )
        @ A ),
    inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : ! [F: qML_mu > qML_i > $o] : ( ( inconsistency_P @ F @ E ) => ( F @ D @ E ) ) ))]]) ).

thf(199,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P @ incons1905966852QML_mu @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ! [E: qML_mu > qML_i > $o] :
                ( ( inconsistency_P @ E @ D )
               => ( E @ C @ D ) )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[26,47]) ).

thf(202,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( incons1905966852QML_mu
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ! [E: qML_mu > qML_i > $o] :
                  ( ( inconsistency_P @ E @ D )
                 => ( E @ C @ D ) ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[199]) ).

thf(205,plain,
    ( incons1905966852QML_mu
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ B )
             => ( C @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[202]) ).

thf(209,plain,
    ( ( ( ^ [A: qML_mu,B: qML_i] :
          ! [C: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ C @ A @ B )
           => ! [D: qML_i] :
                ( ( qML_r @ B @ D )
               => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ! [C: qML_mu > qML_i > $o] :
                ( ( inconsistency_P @ C @ B )
               => ( C @ A @ B ) ) ) )
    | ( incons1905966852QML_mu != incons1905966852QML_mu ) ),
    inference(paramod_ordered,[status(thm)],[30,205]) ).

thf(210,plain,
    ( ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ C @ A @ B )
         => ! [D: qML_i] :
              ( ( qML_r @ B @ D )
             => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ B )
             => ( C @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[209:[]]) ).

thf(406,plain,
    ( ( ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk23 @ sk24 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk24 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ A @ sk24 )
           => ( A @ sk23 @ sk24 ) ) ) ),
    inference(func_ext,[status(esa)],[210]) ).

thf(859,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ( inconsistency_G @ A @ B ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk23 @ sk24 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk24 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ B )
             => ( C @ A @ B ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ sk24 )
             => ( C @ sk23 @ sk24 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[34,406]) ).

thf(860,plain,
    ( ( ~ ( inconsistency_G @ sk23 @ sk24 ) )
   != ( ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk23 @ sk24 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk24 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[859:[bind(A,$thf( sk23 )),bind(B,$thf( sk24 ))]]) ).

thf(872,plain,
    ( ~ ~ ( inconsistency_G @ sk23 @ sk24 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk23 @ sk24 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk24 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) ),
    inference(bool_ext,[status(thm)],[860]) ).

thf(892,plain,
    ( ( qML_r @ sk24 @ sk76 )
    | ( inconsistency_G @ sk23 @ sk24 ) ),
    inference(cnf,[status(esa)],[872]) ).

thf(68,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( incons1905966852QML_mu @ A @ B )
      = ( ! [C: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ C @ A @ B )
           => ! [D: qML_i] :
                ( ( qML_r @ B @ D )
               => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
    inference(func_ext,[status(esa)],[30]) ).

thf(40,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E )
          @ B )
      | ( ( inconsistency_P @ inconsistency_G @ A )
       != ( inconsistency_P @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[22,14]) ).

thf(41,plain,
    ! [A: qML_i] :
      ~ ( inconsistency_P
        @ ^ [B: qML_mu,C: qML_i] :
            ~ ( inconsistency_G @ B @ C )
        @ A ),
    inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( inconsistency_G ))]]) ).

thf(59,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P @ incons1905966852QML_mu @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( inconsistency_G @ C @ D )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[26,41]) ).

thf(62,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( incons1905966852QML_mu
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( inconsistency_G @ C @ D ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[59]) ).

thf(65,plain,
    ( incons1905966852QML_mu
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ( inconsistency_G @ A @ B ) ) ),
    inference(simp,[status(thm)],[62]) ).

thf(78,plain,
    ( ( ( ^ [A: qML_mu,B: qML_i] :
          ! [C: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ C @ A @ B )
           => ! [D: qML_i] :
                ( ( qML_r @ B @ D )
               => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( inconsistency_G @ A @ B ) ) )
    | ( incons1905966852QML_mu != incons1905966852QML_mu ) ),
    inference(paramod_ordered,[status(thm)],[30,65]) ).

thf(79,plain,
    ( ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ C @ A @ B )
         => ! [D: qML_i] :
              ( ( qML_r @ B @ D )
             => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ( inconsistency_G @ A @ B ) ) ),
    inference(pattern_uni,[status(thm)],[78:[]]) ).

thf(402,plain,
    ( ( ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk21 @ sk22 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk22 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) )
   != ( ~ ( inconsistency_G @ sk21 @ sk22 ) ) ),
    inference(func_ext,[status(esa)],[79]) ).

thf(753,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( inconsistency_P @ C @ B )
               => ( C @ A @ B ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk21 @ sk22 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk22 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) )
      | ( ( inconsistency_G @ A @ B )
       != ( inconsistency_G @ sk21 @ sk22 ) ) ),
    inference(paramod_ordered,[status(thm)],[34,402]) ).

thf(754,plain,
    ( ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ A @ sk22 )
           => ( A @ sk21 @ sk22 ) ) )
   != ( ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk21 @ sk22 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk22 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[753:[bind(A,$thf( sk21 )),bind(B,$thf( sk22 ))]]) ).

thf(1205,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( incons1905966852QML_mu @ A @ B )
       != ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( inconsistency_P @ C @ sk22 )
               => ( C @ sk21 @ sk22 ) ) ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk21 @ sk22 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk22 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[68,754]) ).

thf(1206,plain,
    ( ( incons1905966852QML_mu @ sk21 @ sk22 )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ A @ sk22 )
           => ( A @ sk21 @ sk22 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1205:[bind(A,$thf( sk21 )),bind(B,$thf( sk22 ))]]) ).

thf(1449,plain,
    ( ( incons1905966852QML_mu @ sk21 @ sk22 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk22 )
         => ( A @ sk21 @ sk22 ) ) ),
    inference(bool_ext,[status(thm)],[1206]) ).

thf(1469,plain,
    ( ~ ( sk133 @ sk21 @ sk22 )
    | ( incons1905966852QML_mu @ sk21 @ sk22 ) ),
    inference(cnf,[status(esa)],[1449]) ).

thf(208,plain,
    ( ( incons1905966852QML_mu @ sk13 @ sk14 )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ A @ sk14 )
           => ( A @ sk13 @ sk14 ) ) ) ),
    inference(func_ext,[status(esa)],[205]) ).

thf(756,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ( inconsistency_G @ A @ B ) )
       != ( incons1905966852QML_mu @ sk13 @ sk14 ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ B )
             => ( C @ A @ B ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ sk14 )
             => ( C @ sk13 @ sk14 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[34,208]) ).

thf(757,plain,
    ( ( incons1905966852QML_mu @ sk13 @ sk14 )
   != ( ~ ( inconsistency_G @ sk13 @ sk14 ) ) ),
    inference(pattern_uni,[status(thm)],[756:[bind(A,$thf( sk13 )),bind(B,$thf( sk14 ))]]) ).

thf(1189,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ~ ( inconsistency_G @ sk13 @ sk14 ) ) )
      | ( ( incons1905966852QML_mu @ A @ B )
       != ( incons1905966852QML_mu @ sk13 @ sk14 ) ) ),
    inference(paramod_ordered,[status(thm)],[68,757]) ).

thf(1190,plain,
    ( ( ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk13 @ sk14 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk14 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) )
   != ( ~ ( inconsistency_G @ sk13 @ sk14 ) ) ),
    inference(pattern_uni,[status(thm)],[1189:[bind(A,$thf( sk13 )),bind(B,$thf( sk14 ))]]) ).

thf(215,plain,
    ( ( incons1905966852QML_mu @ sk13 @ sk14 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk14 )
         => ( A @ sk13 @ sk14 ) ) ),
    inference(bool_ext,[status(thm)],[208]) ).

thf(220,plain,
    ( ( inconsistency_P @ sk17 @ sk14 )
    | ( incons1905966852QML_mu @ sk13 @ sk14 ) ),
    inference(cnf,[status(esa)],[215]) ).

thf(43,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E )
          @ B )
      | ( ( inconsistency_P @ incons1905966852QML_mu @ A )
       != ( inconsistency_P @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[26,14]) ).

thf(44,plain,
    ! [A: qML_i] :
      ~ ( inconsistency_P
        @ ^ [B: qML_mu,C: qML_i] :
            ~ ( incons1905966852QML_mu @ B @ C )
        @ A ),
    inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( incons1905966852QML_mu ))]]) ).

thf(539,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk13 @ sk14 )
      | ( ( inconsistency_P @ sk17 @ sk14 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[220,44]) ).

thf(543,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk13 @ sk14 )
      | ( sk17
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C ) ) )
      | ( sk14 != A ) ),
    inference(simp,[status(thm)],[539]) ).

thf(555,plain,
    ( ( incons1905966852QML_mu @ sk13 @ sk14 )
    | ( sk17
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[543]) ).

thf(71,plain,
    ! [A: qML_i] :
      ( ( inconsistency_P
        @ ^ [B: qML_mu,C: qML_i] :
          ! [D: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ D @ B @ C )
           => ! [E: qML_i] :
                ( ( qML_r @ C @ E )
               => ? [F: qML_mu] : ( D @ F @ E ) ) )
        @ A )
      | ( incons1905966852QML_mu != incons1905966852QML_mu ) ),
    inference(paramod_ordered,[status(thm)],[30,26]) ).

thf(72,plain,
    ! [A: qML_i] :
      ( inconsistency_P
      @ ^ [B: qML_mu,C: qML_i] :
        ! [D: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ D @ B @ C )
         => ! [E: qML_i] :
              ( ( qML_r @ C @ E )
             => ? [F: qML_mu] : ( D @ F @ E ) ) )
      @ A ),
    inference(pattern_uni,[status(thm)],[71:[]]) ).

thf(475,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E )
          @ B )
      | ( ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] :
            ! [F: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ F @ D @ E )
             => ! [G: qML_i] :
                  ( ( qML_r @ E @ G )
                 => ? [H: qML_mu] : ( F @ H @ G ) ) )
          @ A )
       != ( inconsistency_P @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[72,14]) ).

thf(476,plain,
    ! [A: qML_i] :
      ~ ( inconsistency_P
        @ ^ [B: qML_mu,C: qML_i] :
            ~ ! [D: qML_mu > qML_i > $o] :
                ( ( incons1389517216QML_mu @ D @ B @ C )
               => ! [E: qML_i] :
                    ( ( qML_r @ C @ E )
                   => ? [F: qML_mu] : ( D @ F @ E ) ) )
        @ A ),
    inference(pattern_uni,[status(thm)],[475:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : ! [F: qML_mu > qML_i > $o] : ( ( incons1389517216QML_mu @ F @ D @ E ) => ! [G: qML_i] : ( ( qML_r @ E @ G ) => ? [H: qML_mu] : ( F @ H @ G ) ) ) ))]]) ).

thf(504,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P @ inconsistency_G @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ! [E: qML_mu > qML_i > $o] :
                ( ( incons1389517216QML_mu @ E @ C @ D )
               => ! [F: qML_i] :
                    ( ( qML_r @ D @ F )
                   => ? [G: qML_mu] : ( E @ G @ F ) ) )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[22,476]) ).

thf(510,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_G
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ! [E: qML_mu > qML_i > $o] :
                  ( ( incons1389517216QML_mu @ E @ C @ D )
                 => ! [F: qML_i] :
                      ( ( qML_r @ D @ F )
                     => ? [G: qML_mu] : ( E @ G @ F ) ) ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[504]) ).

thf(520,plain,
    ( inconsistency_G
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
    inference(simp,[status(thm)],[510]) ).

thf(525,plain,
    ( ( inconsistency_G @ sk30 @ sk31 )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ A @ sk30 @ sk31 )
           => ! [B: qML_i] :
                ( ( qML_r @ sk31 @ B )
               => ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
    inference(func_ext,[status(esa)],[520]) ).

thf(1207,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ( incons1905966852QML_mu @ A @ B ) )
       != ( inconsistency_G @ sk30 @ sk31 ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk30 @ sk31 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk31 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[68,525]) ).

thf(1208,plain,
    ( ( ~ ( incons1905966852QML_mu @ sk30 @ sk31 ) )
   != ( inconsistency_G @ sk30 @ sk31 ) ),
    inference(pattern_uni,[status(thm)],[1207:[bind(A,$thf( sk30 )),bind(B,$thf( sk31 ))]]) ).

thf(1280,plain,
    ( ~ ( incons1905966852QML_mu @ sk30 @ sk31 )
    | ( inconsistency_G @ sk30 @ sk31 ) ),
    inference(bool_ext,[status(thm)],[1208]) ).

thf(1295,plain,
    ( ( inconsistency_G @ sk30 @ sk31 )
    | ~ ( incons1905966852QML_mu @ sk30 @ sk31 ) ),
    inference(cnf,[status(esa)],[1280]) ).

thf(82,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
          ! [E: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ E @ D )
           => ( E @ C @ D ) )
        @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( incons1905966852QML_mu @ C @ D )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[36,44]) ).

thf(85,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( ( ^ [C: qML_mu,D: qML_i] :
            ! [E: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ E @ D )
             => ( E @ C @ D ) ) )
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( incons1905966852QML_mu @ C @ D ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[82]) ).

thf(88,plain,
    ( ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ C @ B )
         => ( C @ A @ B ) ) )
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ( incons1905966852QML_mu @ A @ B ) ) ),
    inference(simp,[status(thm)],[85]) ).

thf(11,axiom,
    ( incons1389517216QML_mu
    = ( ^ [A: qML_mu > qML_i > $o,B: qML_mu,C: qML_i] :
        ! [D: qML_mu > qML_i > $o] :
          ( ( D @ B @ C )
         => ! [E: qML_i] :
              ( ( qML_r @ C @ E )
             => ! [F: qML_mu] :
                  ( ( A @ F @ E )
                 => ( D @ F @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_ess__def) ).

thf(31,plain,
    ( incons1389517216QML_mu
    = ( ^ [A: qML_mu > qML_i > $o,B: qML_mu,C: qML_i] :
        ! [D: qML_mu > qML_i > $o] :
          ( ( D @ B @ C )
         => ! [E: qML_i] :
              ( ( qML_r @ C @ E )
             => ! [F: qML_mu] :
                  ( ( A @ F @ E )
                 => ( D @ F @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(32,plain,
    ( incons1389517216QML_mu
    = ( ^ [A: qML_mu > qML_i > $o,B: qML_mu,C: qML_i] :
        ! [D: qML_mu > qML_i > $o] :
          ( ( D @ B @ C )
         => ! [E: qML_i] :
              ( ( qML_r @ C @ E )
             => ! [F: qML_mu] :
                  ( ( A @ F @ E )
                 => ( D @ F @ E ) ) ) ) ) ),
    inference(lifteq,[status(thm)],[31]) ).

thf(122,plain,
    ! [A: qML_mu > qML_i > $o] :
      ( ( incons1389517216QML_mu @ A )
      = ( ^ [B: qML_mu,C: qML_i] :
          ! [D: qML_mu > qML_i > $o] :
            ( ( D @ B @ C )
           => ! [E: qML_i] :
                ( ( qML_r @ C @ E )
               => ! [F: qML_mu] :
                    ( ( A @ F @ E )
                   => ( D @ F @ E ) ) ) ) ) ),
    inference(func_ext,[status(esa)],[32]) ).

thf(60,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
          ! [E: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ E @ D )
           => ( E @ C @ D ) )
        @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( inconsistency_G @ C @ D )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[36,41]) ).

thf(63,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( ( ^ [C: qML_mu,D: qML_i] :
            ! [E: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ E @ D )
             => ( E @ C @ D ) ) )
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( inconsistency_G @ C @ D ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[60]) ).

thf(66,plain,
    ( ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ C @ B )
         => ( C @ A @ B ) ) )
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ( inconsistency_G @ A @ B ) ) ),
    inference(simp,[status(thm)],[63]) ).

thf(969,plain,
    ! [A: qML_mu > qML_i > $o] :
      ( ( ( incons1389517216QML_mu @ A )
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C ) ) )
      | ( ( ^ [B: qML_mu,C: qML_i] :
            ! [D: qML_mu > qML_i > $o] :
              ( ( D @ B @ C )
             => ! [E: qML_i] :
                  ( ( qML_r @ C @ E )
                 => ! [F: qML_mu] :
                      ( ( A @ F @ E )
                     => ( D @ F @ E ) ) ) ) )
       != ( ^ [B: qML_mu,C: qML_i] :
            ! [D: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ D @ C )
             => ( D @ B @ C ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[122,66]) ).

thf(977,plain,
    ! [A: qML_mu > qML_i > $o] :
      ( ( ( incons1389517216QML_mu @ A )
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C ) ) )
      | ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
              ( ( D @ B @ C )
             => ! [E: qML_i] :
                  ( ( qML_r @ C @ E )
                 => ! [F: qML_mu] :
                      ( ( A @ F @ E )
                     => ( D @ F @ E ) ) ) ) )
       != ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ D @ C )
             => ( D @ B @ C ) ) ) ) ),
    inference(simp,[status(thm)],[969]) ).

thf(81,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P @ inconsistency_G @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( incons1905966852QML_mu @ C @ D )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[22,44]) ).

thf(84,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_G
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( incons1905966852QML_mu @ C @ D ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[81]) ).

thf(87,plain,
    ( inconsistency_G
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ( incons1905966852QML_mu @ A @ B ) ) ),
    inference(simp,[status(thm)],[84]) ).

thf(102,plain,
    ( ( inconsistency_G @ sk5 @ sk6 )
   != ( ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ) ),
    inference(func_ext,[status(esa)],[87]) ).

thf(118,plain,
    ( ~ ( inconsistency_G @ sk5 @ sk6 )
    | ~ ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ),
    inference(bool_ext,[status(thm)],[102]) ).

thf(120,plain,
    ( ( incons1905966852QML_mu @ sk5 @ sk6 )
    | ~ ( inconsistency_G @ sk5 @ sk6 ) ),
    inference(cnf,[status(esa)],[118]) ).

thf(478,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
          ! [E: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ E @ C @ D )
           => ! [F: qML_i] :
                ( ( qML_r @ D @ F )
               => ? [G: qML_mu] : ( E @ G @ F ) ) )
        @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( incons1905966852QML_mu @ C @ D )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[72,44]) ).

thf(485,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( ( ^ [C: qML_mu,D: qML_i] :
            ! [E: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ E @ C @ D )
             => ! [F: qML_i] :
                  ( ( qML_r @ D @ F )
                 => ? [G: qML_mu] : ( E @ G @ F ) ) ) )
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( incons1905966852QML_mu @ C @ D ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[478]) ).

thf(492,plain,
    ( ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ C @ A @ B )
         => ! [D: qML_i] :
              ( ( qML_r @ B @ D )
             => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ( incons1905966852QML_mu @ A @ B ) ) ),
    inference(simp,[status(thm)],[485]) ).

thf(496,plain,
    ( ( ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk26 @ sk27 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk27 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) )
   != ( ~ ( incons1905966852QML_mu @ sk26 @ sk27 ) ) ),
    inference(func_ext,[status(esa)],[492]) ).

thf(643,plain,
    ( ~ ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk26 @ sk27 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk27 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) )
    | ~ ~ ( incons1905966852QML_mu @ sk26 @ sk27 ) ),
    inference(bool_ext,[status(thm)],[496]) ).

thf(655,plain,
    ( ( incons1905966852QML_mu @ sk26 @ sk27 )
    | ( qML_r @ sk27 @ sk43 ) ),
    inference(cnf,[status(esa)],[643]) ).

thf(507,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
          ! [E: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ E @ D )
           => ( E @ C @ D ) )
        @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ! [E: qML_mu > qML_i > $o] :
                ( ( incons1389517216QML_mu @ E @ C @ D )
               => ! [F: qML_i] :
                    ( ( qML_r @ D @ F )
                   => ? [G: qML_mu] : ( E @ G @ F ) ) )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[36,476]) ).

thf(511,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( ( ^ [C: qML_mu,D: qML_i] :
            ! [E: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ E @ D )
             => ( E @ C @ D ) ) )
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ! [E: qML_mu > qML_i > $o] :
                  ( ( incons1389517216QML_mu @ E @ C @ D )
                 => ! [F: qML_i] :
                      ( ( qML_r @ D @ F )
                     => ? [G: qML_mu] : ( E @ G @ F ) ) ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[507]) ).

thf(521,plain,
    ( ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ C @ B )
         => ( C @ A @ B ) ) )
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
    inference(simp,[status(thm)],[511]) ).

thf(619,plain,
    ( ( ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk35 )
         => ( A @ sk34 @ sk35 ) ) )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ A @ sk34 @ sk35 )
           => ! [B: qML_i] :
                ( ( qML_r @ sk35 @ B )
               => ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
    inference(func_ext,[status(esa)],[521]) ).

thf(1172,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ( incons1905966852QML_mu @ A @ B ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ sk35 )
             => ( C @ sk34 @ sk35 ) ) ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk34 @ sk35 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk35 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[68,619]) ).

thf(1173,plain,
    ( ( ~ ( incons1905966852QML_mu @ sk34 @ sk35 ) )
   != ( ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk35 )
         => ( A @ sk34 @ sk35 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1172:[bind(A,$thf( sk34 )),bind(B,$thf( sk35 ))]]) ).

thf(39,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_P @ C @ B )
      | ( ( inconsistency_P @ inconsistency_G @ A )
       != ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E )
          @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[22,14]) ).

thf(51,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_P @ C @ B )
      | ( inconsistency_G
       != ( ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[39]) ).

thf(56,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ( inconsistency_G
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) ) ),
    inference(simp,[status(thm)],[51]) ).

thf(746,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ B )
             => ( C @ A @ B ) ) )
       != ( ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ) )
      | ( ( inconsistency_G @ A @ B )
       != ( inconsistency_G @ sk5 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[34,102]) ).

thf(747,plain,
    ( ( ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk6 )
         => ( A @ sk5 @ sk6 ) ) )
   != ( ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ) ),
    inference(pattern_uni,[status(thm)],[746:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(5,axiom,
    ! [A: qML_i,B: qML_mu > qML_i > $o,C: qML_mu > qML_i > $o] :
      ( ( ( inconsistency_P @ B @ A )
        & ! [D: qML_i] :
            ( ( qML_r @ A @ D )
           => ! [E: qML_mu] :
                ( ( B @ E @ D )
               => ( C @ E @ D ) ) ) )
     => ( inconsistency_P @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_A2) ).

thf(17,plain,
    ! [A: qML_i,B: qML_mu > qML_i > $o,C: qML_mu > qML_i > $o] :
      ( ( ( inconsistency_P @ B @ A )
        & ! [D: qML_i] :
            ( ( qML_r @ A @ D )
           => ! [E: qML_mu] :
                ( ( B @ E @ D )
               => ( C @ E @ D ) ) ) )
     => ( inconsistency_P @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(18,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ~ ( C @ ( sk2 @ C @ B @ A ) @ ( sk1 @ C @ B @ A ) )
      | ( inconsistency_P @ C @ A ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(136,plain,
    ! [D: qML_mu > qML_i > $o,C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_P @ C @ B )
      | ( inconsistency_P @ D @ B )
      | ( ( inconsistency_P @ incons1905966852QML_mu @ A )
       != ( D @ ( sk2 @ D @ C @ B ) @ ( sk1 @ D @ C @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[26,18]) ).

thf(161,plain,
    ! [C: qML_mu > qML_i > qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ( inconsistency_P
        @ ^ [D: qML_mu,E: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ ( C @ D @ E ) )
        @ A ) ),
    inference(pre_uni,[status(thm)],[136:[bind(A,$thf( F @ ( sk2 @ ^ [F: qML_mu] : ^ [G: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ ( F @ F @ G ) ) @ C @ B ) @ ( sk1 @ ^ [F: qML_mu] : ^ [G: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ ( F @ F @ G ) ) @ C @ B ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( ^ [F: qML_mu] : ^ [G: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ ( F @ F @ G ) ) ))]]) ).

thf(164,plain,
    ! [C: qML_mu > qML_i > qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ( inconsistency_P
        @ ^ [D: qML_mu,E: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ ( C @ D @ E ) )
        @ A ) ),
    inference(simp,[status(thm)],[161]) ).

thf(4100,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] : $true
        @ A ) ),
    inference(rewrite,[status(thm)],[164,26]) ).

thf(4138,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ( inconsistency_P
        @ ^ [D: qML_mu,E: qML_i] : $true
        @ B )
      | ( ( inconsistency_P @ inconsistency_G @ A )
       != ( inconsistency_P @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[22,4100]) ).

thf(4139,plain,
    ! [A: qML_i] :
      ( inconsistency_P
      @ ^ [B: qML_mu,C: qML_i] : $true
      @ A ),
    inference(pattern_uni,[status(thm)],[4138:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( inconsistency_G ))]]) ).

thf(42,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_P @ C @ B )
      | ( ( inconsistency_P @ incons1905966852QML_mu @ A )
       != ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E )
          @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[26,14]) ).

thf(49,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_P @ C @ B )
      | ( incons1905966852QML_mu
       != ( ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[42]) ).

thf(54,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ( incons1905966852QML_mu
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) ) ),
    inference(simp,[status(thm)],[49]) ).

thf(4226,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ( incons1905966852QML_mu
       != ( ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E ) ) )
      | ( ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] : $true
          @ A )
       != ( inconsistency_P @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4139,54]) ).

thf(4227,plain,
    ( incons1905966852QML_mu
   != ( ^ [A: qML_mu,B: qML_i] : ~ $true ) ),
    inference(pattern_uni,[status(thm)],[4226:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : $true ))]]) ).

thf(4247,plain,
    ( incons1905966852QML_mu
   != ( ^ [A: qML_mu,B: qML_i] : $false ) ),
    inference(simp,[status(thm)],[4227]) ).

thf(77,plain,
    ( ( incons1905966852QML_mu @ sk3 @ sk4 )
   != ( ~ ( inconsistency_G @ sk3 @ sk4 ) ) ),
    inference(func_ext,[status(esa)],[65]) ).

thf(115,plain,
    ( ( incons1905966852QML_mu @ sk3 @ sk4 )
    | ~ ( inconsistency_G @ sk3 @ sk4 ) ),
    inference(bool_ext,[status(thm)],[77]) ).

thf(117,plain,
    ( ~ ( inconsistency_G @ sk3 @ sk4 )
    | ( incons1905966852QML_mu @ sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[115]) ).

thf(744,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ~ ! [C: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ C @ B )
           => ( C @ A @ B ) )
      | ( incons1905966852QML_mu @ sk3 @ sk4 )
      | ( ( inconsistency_G @ A @ B )
       != ( inconsistency_G @ sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[34,117]) ).

thf(745,plain,
    ( ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk4 )
         => ( A @ sk3 @ sk4 ) )
    | ( incons1905966852QML_mu @ sk3 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[744:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(793,plain,
    ( ( incons1905966852QML_mu @ sk3 @ sk4 )
    | ( inconsistency_P @ sk64 @ sk4 ) ),
    inference(cnf,[status(esa)],[745]) ).

thf(1506,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( incons1905966852QML_mu @ sk3 @ sk4 )
      | ( inconsistency_G
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk64 @ sk4 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[793,56]) ).

thf(1507,plain,
    ( ( incons1905966852QML_mu @ sk3 @ sk4 )
    | ( inconsistency_G
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk64 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1506:[bind(A,$thf( sk4 )),bind(B,$thf( sk64 ))]]) ).

thf(7,axiom,
    ! [A: qML_i,B: qML_mu > qML_i > $o] :
      ( ( inconsistency_P @ B @ A )
     => ! [C: qML_i] :
          ( ( qML_r @ A @ C )
         => ( inconsistency_P @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_A4) ).

thf(23,plain,
    ! [A: qML_i,B: qML_mu > qML_i > $o] :
      ( ( inconsistency_P @ B @ A )
     => ! [C: qML_i] :
          ( ( qML_r @ A @ C )
         => ( inconsistency_P @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(24,plain,
    ! [C: qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ~ ( qML_r @ A @ C )
      | ( inconsistency_P @ B @ C ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(45,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_P @ C @ B )
      | ( ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] :
            ! [F: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ F @ E )
             => ( F @ D @ E ) )
          @ A )
       != ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E )
          @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[36,14]) ).

thf(50,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_P @ C @ B )
      | ( ( ^ [D: qML_mu,E: qML_i] :
            ! [F: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ F @ E )
             => ( F @ D @ E ) ) )
       != ( ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[45]) ).

thf(55,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ( ( ^ [C: qML_mu,D: qML_i] :
            ! [E: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ E @ D )
             => ( E @ C @ D ) ) )
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) ) ),
    inference(simp,[status(thm)],[50]) ).

thf(4232,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ( ( ^ [D: qML_mu,E: qML_i] :
            ! [F: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ F @ E )
             => ( F @ D @ E ) ) )
       != ( ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E ) ) )
      | ( ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] : $true
          @ A )
       != ( inconsistency_P @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4139,55]) ).

thf(4233,plain,
    ( ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ C @ B )
         => ( C @ A @ B ) ) )
   != ( ^ [A: qML_mu,B: qML_i] : ~ $true ) ),
    inference(pattern_uni,[status(thm)],[4232:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : $true ))]]) ).

thf(4249,plain,
    ( ( ^ [A: qML_mu,B: qML_i] :
        ! [C: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ C @ B )
         => ( C @ A @ B ) ) )
   != ( ^ [A: qML_mu,B: qML_i] : $false ) ),
    inference(simp,[status(thm)],[4233]) ).

thf(48,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ( ( inconsistency_P
          @ ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D )
          @ A )
       != ( inconsistency_P @ B @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[14]) ).

thf(52,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ( ( inconsistency_P
          @ ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D )
          @ A )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(simp,[status(thm)],[48]) ).

thf(110,plain,
    ( ( ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk10 )
         => ( A @ sk9 @ sk10 ) ) )
   != ( ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ) ),
    inference(func_ext,[status(esa)],[88]) ).

thf(137,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_G @ sk3 @ sk4 )
      | ~ ( inconsistency_P @ B @ A )
      | ( inconsistency_P @ C @ A )
      | ( ( C @ ( sk2 @ C @ B @ A ) @ ( sk1 @ C @ B @ A ) )
       != ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[117,18]) ).

thf(157,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_G @ sk3 @ sk4 )
      | ~ ( inconsistency_P @ B @ A )
      | ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] : ( incons1905966852QML_mu @ sk3 @ sk4 )
        @ A ) ),
    inference(pre_uni,[status(thm)],[137:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : ( incons1905966852QML_mu @ sk3 @ sk4 ) ))]]) ).

thf(20,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ( qML_r @ A @ ( sk1 @ C @ B @ A ) )
      | ( inconsistency_P @ C @ A ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(990,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( inconsistency_G @ A @ B )
       != ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( incons1389517216QML_mu @ C @ sk34 @ sk35 )
               => ! [D: qML_i] :
                    ( ( qML_r @ sk35 @ D )
                   => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ B )
             => ( C @ A @ B ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ sk35 )
             => ( C @ sk34 @ sk35 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[34,619]) ).

thf(991,plain,
    ( ( inconsistency_G @ sk34 @ sk35 )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ A @ sk34 @ sk35 )
           => ! [B: qML_i] :
                ( ( qML_r @ sk35 @ B )
               => ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[990:[bind(A,$thf( sk34 )),bind(B,$thf( sk35 ))]]) ).

thf(1213,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ( incons1905966852QML_mu @ A @ B ) )
       != ( inconsistency_G @ sk34 @ sk35 ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk34 @ sk35 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk35 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[68,991]) ).

thf(1214,plain,
    ( ( ~ ( incons1905966852QML_mu @ sk34 @ sk35 ) )
   != ( inconsistency_G @ sk34 @ sk35 ) ),
    inference(pattern_uni,[status(thm)],[1213:[bind(A,$thf( sk34 )),bind(B,$thf( sk35 ))]]) ).

thf(1300,plain,
    ( ~ ~ ( incons1905966852QML_mu @ sk34 @ sk35 )
    | ~ ( inconsistency_G @ sk34 @ sk35 ) ),
    inference(bool_ext,[status(thm)],[1214]) ).

thf(1319,plain,
    ( ~ ( inconsistency_G @ sk34 @ sk35 )
    | ( incons1905966852QML_mu @ sk34 @ sk35 ) ),
    inference(cnf,[status(esa)],[1300]) ).

thf(4206,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ( inconsistency_G
       != ( ^ [D: qML_mu,E: qML_i] :
              ~ ( C @ D @ E ) ) )
      | ( ( inconsistency_P
          @ ^ [D: qML_mu,E: qML_i] : $true
          @ A )
       != ( inconsistency_P @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4139,56]) ).

thf(4207,plain,
    ( inconsistency_G
   != ( ^ [A: qML_mu,B: qML_i] : ~ $true ) ),
    inference(pattern_uni,[status(thm)],[4206:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( ^ [D: qML_mu] : ^ [E: qML_i] : $true ))]]) ).

thf(4251,plain,
    ( inconsistency_G
   != ( ^ [A: qML_mu,B: qML_i] : $false ) ),
    inference(simp,[status(thm)],[4207]) ).

thf(4270,plain,
    inconsistency_G @ sk352 @ sk353,
    inference(func_ext,[status(esa)],[4251]) ).

thf(735,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( incons1905966852QML_mu @ sk5 @ sk6 )
      | ~ ! [C: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ C @ B )
           => ( C @ A @ B ) )
      | ( ( inconsistency_G @ A @ B )
       != ( inconsistency_G @ sk5 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[34,120]) ).

thf(736,plain,
    ( ( incons1905966852QML_mu @ sk5 @ sk6 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk6 )
         => ( A @ sk5 @ sk6 ) ) ),
    inference(pattern_uni,[status(thm)],[735:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(781,plain,
    ( ( inconsistency_P @ sk62 @ sk6 )
    | ( incons1905966852QML_mu @ sk5 @ sk6 ) ),
    inference(cnf,[status(esa)],[736]) ).

thf(1378,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk5 @ sk6 )
      | ( ( inconsistency_P @ sk62 @ sk6 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[781,44]) ).

thf(1390,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk5 @ sk6 )
      | ( sk62
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C ) ) )
      | ( sk6 != A ) ),
    inference(simp,[status(thm)],[1378]) ).

thf(1398,plain,
    ( ( incons1905966852QML_mu @ sk5 @ sk6 )
    | ( sk62
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[1390]) ).

thf(4265,plain,
    incons1905966852QML_mu @ sk350 @ sk351,
    inference(func_ext,[status(esa)],[4247]) ).

thf(758,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ B )
             => ( C @ A @ B ) ) )
       != ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( incons1389517216QML_mu @ C @ sk30 @ sk31 )
               => ! [D: qML_i] :
                    ( ( qML_r @ sk31 @ D )
                   => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) )
      | ( ( inconsistency_G @ A @ B )
       != ( inconsistency_G @ sk30 @ sk31 ) ) ),
    inference(paramod_ordered,[status(thm)],[34,525]) ).

thf(759,plain,
    ( ( ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk31 )
         => ( A @ sk30 @ sk31 ) ) )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ A @ sk30 @ sk31 )
           => ! [B: qML_i] :
                ( ( qML_r @ sk31 @ B )
               => ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( sk30 )),bind(B,$thf( sk31 ))]]) ).

thf(1216,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ( incons1905966852QML_mu @ A @ B ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ sk31 )
             => ( C @ sk30 @ sk31 ) ) ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk30 @ sk31 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk31 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[68,759]) ).

thf(1217,plain,
    ( ( ~ ( incons1905966852QML_mu @ sk30 @ sk31 ) )
   != ( ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk31 )
         => ( A @ sk30 @ sk31 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1216:[bind(A,$thf( sk30 )),bind(B,$thf( sk31 ))]]) ).

thf(1471,plain,
    ( ~ ~ ( incons1905966852QML_mu @ sk30 @ sk31 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk31 )
         => ( A @ sk30 @ sk31 ) ) ),
    inference(bool_ext,[status(thm)],[1217]) ).

thf(1494,plain,
    ( ( inconsistency_P @ sk134 @ sk31 )
    | ( incons1905966852QML_mu @ sk30 @ sk31 ) ),
    inference(cnf,[status(esa)],[1471]) ).

thf(105,plain,
    ( ( ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk8 )
         => ( A @ sk7 @ sk8 ) ) )
   != ( ~ ( inconsistency_G @ sk7 @ sk8 ) ) ),
    inference(func_ext,[status(esa)],[66]) ).

thf(184,plain,
    ( ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk8 )
         => ( A @ sk7 @ sk8 ) )
    | ~ ~ ( inconsistency_G @ sk7 @ sk8 ) ),
    inference(bool_ext,[status(thm)],[105]) ).

thf(187,plain,
    ( ( inconsistency_G @ sk7 @ sk8 )
    | ( inconsistency_P @ sk11 @ sk8 ) ),
    inference(cnf,[status(esa)],[184]) ).

thf(1099,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( inconsistency_G @ sk7 @ sk8 )
      | ( inconsistency_G
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk11 @ sk8 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[187,56]) ).

thf(1100,plain,
    ( ( inconsistency_G @ sk7 @ sk8 )
    | ( inconsistency_G
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk11 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1099:[bind(A,$thf( sk8 )),bind(B,$thf( sk11 ))]]) ).

thf(200,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P @ inconsistency_G @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ! [E: qML_mu > qML_i > $o] :
                ( ( inconsistency_P @ E @ D )
               => ( E @ C @ D ) )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[22,47]) ).

thf(203,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_G
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ! [E: qML_mu > qML_i > $o] :
                  ( ( inconsistency_P @ E @ D )
                 => ( E @ C @ D ) ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[200]) ).

thf(206,plain,
    ( inconsistency_G
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ B )
             => ( C @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[203]) ).

thf(211,plain,
    ( ( inconsistency_G @ sk15 @ sk16 )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ A @ sk16 )
           => ( A @ sk15 @ sk16 ) ) ) ),
    inference(func_ext,[status(esa)],[206]) ).

thf(119,plain,
    ( ( inconsistency_G @ sk5 @ sk6 )
    | ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ),
    inference(bool_ext,[status(thm)],[102]) ).

thf(121,plain,
    ( ~ ( incons1905966852QML_mu @ sk5 @ sk6 )
    | ( inconsistency_G @ sk5 @ sk6 ) ),
    inference(cnf,[status(esa)],[119]) ).

thf(1168,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( incons1389517216QML_mu @ C @ A @ B )
               => ! [D: qML_i] :
                    ( ( qML_r @ B @ D )
                   => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ sk10 )
             => ( C @ sk9 @ sk10 ) ) ) )
      | ( ( incons1905966852QML_mu @ A @ B )
       != ( incons1905966852QML_mu @ sk9 @ sk10 ) ) ),
    inference(paramod_ordered,[status(thm)],[68,110]) ).

thf(1169,plain,
    ( ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ A @ sk9 @ sk10 )
           => ! [B: qML_i] :
                ( ( qML_r @ sk10 @ B )
               => ? [C: qML_mu] : ( A @ C @ B ) ) ) )
   != ( ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk10 )
         => ( A @ sk9 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1168:[bind(A,$thf( sk9 )),bind(B,$thf( sk10 ))]]) ).

thf(2861,plain,
    ! [A: qML_mu > qML_i > $o] :
      ( ( ( incons1389517216QML_mu @ A )
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C ) ) )
      | ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( D @ B @ C ) )
       != ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( inconsistency_P @ D @ C ) ) )
      | ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
            ! [E: qML_i] :
              ( ( qML_r @ C @ E )
             => ! [F: qML_mu] :
                  ( ( A @ F @ E )
                 => ( D @ F @ E ) ) ) )
       != ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( D @ B @ C ) ) ) ),
    inference(simp,[status(thm)],[977]) ).

thf(1183,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( incons1389517216QML_mu @ C @ A @ B )
               => ! [D: qML_i] :
                    ( ( qML_r @ B @ D )
                   => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( inconsistency_G @ sk5 @ sk6 ) )
      | ( ( incons1905966852QML_mu @ A @ B )
       != ( incons1905966852QML_mu @ sk5 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[68,102]) ).

thf(1184,plain,
    ( ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ A @ sk5 @ sk6 )
           => ! [B: qML_i] :
                ( ( qML_r @ sk6 @ B )
               => ? [C: qML_mu] : ( A @ C @ B ) ) ) )
   != ( inconsistency_G @ sk5 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[1183:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(1607,plain,
    ( ~ ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk5 @ sk6 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk6 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) )
    | ( inconsistency_G @ sk5 @ sk6 ) ),
    inference(bool_ext,[status(thm)],[1184]) ).

thf(1622,plain,
    ( ( inconsistency_G @ sk5 @ sk6 )
    | ( qML_r @ sk6 @ sk144 ) ),
    inference(cnf,[status(esa)],[1607]) ).

thf(114,plain,
    ( ~ ( incons1905966852QML_mu @ sk3 @ sk4 )
    | ~ ~ ( inconsistency_G @ sk3 @ sk4 ) ),
    inference(bool_ext,[status(thm)],[77]) ).

thf(116,plain,
    ( ( inconsistency_G @ sk3 @ sk4 )
    | ~ ( incons1905966852QML_mu @ sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[114]) ).

thf(189,plain,
    ( ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk10 )
         => ( A @ sk9 @ sk10 ) )
    | ~ ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ),
    inference(bool_ext,[status(thm)],[110]) ).

thf(195,plain,
    ( ( incons1905966852QML_mu @ sk9 @ sk10 )
    | ( inconsistency_P @ sk12 @ sk10 ) ),
    inference(cnf,[status(esa)],[189]) ).

thf(411,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk9 @ sk10 )
      | ( ( inconsistency_P @ sk12 @ sk10 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[195,41]) ).

thf(422,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk9 @ sk10 )
      | ( sk12
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C ) ) )
      | ( sk10 != A ) ),
    inference(simp,[status(thm)],[411]) ).

thf(428,plain,
    ( ( incons1905966852QML_mu @ sk9 @ sk10 )
    | ( sk12
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( inconsistency_G @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[422]) ).

thf(828,plain,
    ( ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk6 )
         => ( A @ sk5 @ sk6 ) )
    | ~ ~ ( incons1905966852QML_mu @ sk5 @ sk6 ) ),
    inference(bool_ext,[status(thm)],[747]) ).

thf(849,plain,
    ( ( incons1905966852QML_mu @ sk5 @ sk6 )
    | ( inconsistency_P @ sk67 @ sk6 ) ),
    inference(cnf,[status(esa)],[828]) ).

thf(69,plain,
    ( ( incons1905966852QML_mu = inconsistency_G )
    | ( ( ^ [A: qML_mu,B: qML_i] :
          ! [C: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ C @ A @ B )
           => ! [D: qML_i] :
                ( ( qML_r @ B @ D )
               => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
     != ( ^ [A: qML_mu,B: qML_i] :
          ! [C: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ C @ B )
           => ( C @ A @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,28]) ).

thf(74,plain,
    ( ( incons1905966852QML_mu = inconsistency_G )
    | ( ( ^ [A: qML_mu,B: qML_i,C: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ C @ A @ B )
           => ! [D: qML_i] :
                ( ( qML_r @ B @ D )
               => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
     != ( ^ [A: qML_mu,B: qML_i,C: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ C @ B )
           => ( C @ A @ B ) ) ) ) ),
    inference(simp,[status(thm)],[69]) ).

thf(738,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( inconsistency_G @ A @ B )
       != ( ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ B )
             => ( C @ A @ B ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ sk10 )
             => ( C @ sk9 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[34,110]) ).

thf(739,plain,
    ( ( inconsistency_G @ sk9 @ sk10 )
   != ( ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ) ),
    inference(pattern_uni,[status(thm)],[738:[bind(A,$thf( sk9 )),bind(B,$thf( sk10 ))]]) ).

thf(798,plain,
    ( ~ ( inconsistency_G @ sk9 @ sk10 )
    | ~ ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ),
    inference(bool_ext,[status(thm)],[739]) ).

thf(815,plain,
    ( ( incons1905966852QML_mu @ sk9 @ sk10 )
    | ~ ( inconsistency_G @ sk9 @ sk10 ) ),
    inference(cnf,[status(esa)],[798]) ).

thf(1559,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( incons1905966852QML_mu @ sk9 @ sk10 )
      | ~ ! [C: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ C @ B )
           => ( C @ A @ B ) )
      | ( ( inconsistency_G @ A @ B )
       != ( inconsistency_G @ sk9 @ sk10 ) ) ),
    inference(paramod_ordered,[status(thm)],[34,815]) ).

thf(1560,plain,
    ( ( incons1905966852QML_mu @ sk9 @ sk10 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk10 )
         => ( A @ sk9 @ sk10 ) ) ),
    inference(pattern_uni,[status(thm)],[1559:[bind(A,$thf( sk9 )),bind(B,$thf( sk10 ))]]) ).

thf(1604,plain,
    ( ~ ( sk140 @ sk9 @ sk10 )
    | ( incons1905966852QML_mu @ sk9 @ sk10 ) ),
    inference(cnf,[status(esa)],[1560]) ).

thf(1198,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( incons1905966852QML_mu @ A @ B )
       != ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( inconsistency_P @ C @ sk24 )
               => ( C @ sk23 @ sk24 ) ) ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk23 @ sk24 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk24 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[68,406]) ).

thf(1199,plain,
    ( ( incons1905966852QML_mu @ sk23 @ sk24 )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ A @ sk24 )
           => ( A @ sk23 @ sk24 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1198:[bind(A,$thf( sk23 )),bind(B,$thf( sk24 ))]]) ).

thf(1470,plain,
    ( ( inconsistency_P @ sk133 @ sk22 )
    | ( incons1905966852QML_mu @ sk21 @ sk22 ) ),
    inference(cnf,[status(esa)],[1449]) ).

thf(1046,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( inconsistency_G @ sk7 @ sk8 )
      | ( incons1905966852QML_mu
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk11 @ sk8 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[187,54]) ).

thf(1047,plain,
    ( ( inconsistency_G @ sk7 @ sk8 )
    | ( incons1905966852QML_mu
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk11 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1046:[bind(A,$thf( sk8 )),bind(B,$thf( sk11 ))]]) ).

thf(1222,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( incons1905966852QML_mu @ A @ B )
       != ( ~ ( inconsistency_G @ sk23 @ sk24 ) ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk23 @ sk24 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk24 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[68,860]) ).

thf(1223,plain,
    ( ( incons1905966852QML_mu @ sk23 @ sk24 )
   != ( ~ ( inconsistency_G @ sk23 @ sk24 ) ) ),
    inference(pattern_uni,[status(thm)],[1222:[bind(A,$thf( sk23 )),bind(B,$thf( sk24 ))]]) ).

thf(817,plain,
    ( ~ ( incons1905966852QML_mu @ sk13 @ sk14 )
    | ~ ~ ( inconsistency_G @ sk13 @ sk14 ) ),
    inference(bool_ext,[status(thm)],[757]) ).

thf(825,plain,
    ( ( inconsistency_G @ sk13 @ sk14 )
    | ~ ( incons1905966852QML_mu @ sk13 @ sk14 ) ),
    inference(cnf,[status(esa)],[817]) ).

thf(419,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk9 @ sk10 )
      | ( ( inconsistency_P @ sk12 @ sk10 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[195,44]) ).

thf(423,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk9 @ sk10 )
      | ( sk12
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C ) ) )
      | ( sk10 != A ) ),
    inference(simp,[status(thm)],[419]) ).

thf(429,plain,
    ( ( incons1905966852QML_mu @ sk9 @ sk10 )
    | ( sk12
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[423]) ).

thf(33,plain,
    ! [A: qML_mu] :
      ( ( inconsistency_G @ A )
      = ( ^ [B: qML_i] :
          ! [C: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ C @ B )
           => ( C @ A @ B ) ) ) ),
    inference(func_ext,[status(esa)],[28]) ).

thf(145,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ( inconsistency_P @ C @ A )
      | ( ( C @ ( sk2 @ C @ B @ A ) @ ( sk1 @ C @ B @ A ) )
       != ( ~ ( inconsistency_P @ C @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[18]) ).

thf(160,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( inconsistency_P @ C @ A )
      | ~ ( inconsistency_P @ B @ A )
      | ( ( C @ ( sk2 @ C @ B @ A ) @ ( sk1 @ C @ B @ A ) )
       != ( ~ ( inconsistency_P @ C @ A ) ) ) ),
    inference(simp,[status(thm)],[145]) ).

thf(1369,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( incons1905966852QML_mu @ sk5 @ sk6 )
      | ( inconsistency_G
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk62 @ sk6 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[781,56]) ).

thf(1370,plain,
    ( ( incons1905966852QML_mu @ sk5 @ sk6 )
    | ( inconsistency_G
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk62 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1369:[bind(A,$thf( sk6 )),bind(B,$thf( sk62 ))]]) ).

thf(4,axiom,
    ! [A: qML_i,B: qML_mu > qML_i > $o] :
      ( ~ ( inconsistency_P @ B @ A )
     => ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( B @ C @ D )
        @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_A1b) ).

thf(15,plain,
    ! [A: qML_i,B: qML_mu > qML_i > $o] :
      ( ~ ( inconsistency_P @ B @ A )
     => ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( B @ C @ D )
        @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(16,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( inconsistency_P @ B @ A )
      | ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( B @ C @ D )
        @ A ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(133,plain,
    ! [E: qML_mu > qML_i > $o,D: qML_mu > qML_i > $o,C: qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( inconsistency_P @ B @ A )
      | ~ ( inconsistency_P @ D @ C )
      | ( inconsistency_P @ E @ C )
      | ( ( inconsistency_P
          @ ^ [F: qML_mu,G: qML_i] :
              ~ ( B @ F @ G )
          @ A )
       != ( E @ ( sk2 @ E @ D @ C ) @ ( sk1 @ E @ D @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[16,18]) ).

thf(162,plain,
    ! [D: qML_mu > qML_i > qML_mu > qML_i > $o,C: qML_mu > qML_i > qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( inconsistency_P
        @ ( D
          @ ( sk2
            @ ^ [E: qML_mu,F: qML_i] :
                ( inconsistency_P
                @ ^ [G: qML_mu,H: qML_i] :
                    ~ ( D @ E @ F @ G @ H )
                @ ( C @ E @ F ) )
            @ B
            @ A )
          @ ( sk1
            @ ^ [E: qML_mu,F: qML_i] :
                ( inconsistency_P
                @ ^ [G: qML_mu,H: qML_i] :
                    ~ ( D @ E @ F @ G @ H )
                @ ( C @ E @ F ) )
            @ B
            @ A ) )
        @ ( C
          @ ( sk2
            @ ^ [E: qML_mu,F: qML_i] :
                ( inconsistency_P
                @ ^ [G: qML_mu,H: qML_i] :
                    ~ ( D @ E @ F @ G @ H )
                @ ( C @ E @ F ) )
            @ B
            @ A )
          @ ( sk1
            @ ^ [E: qML_mu,F: qML_i] :
                ( inconsistency_P
                @ ^ [G: qML_mu,H: qML_i] :
                    ~ ( D @ E @ F @ G @ H )
                @ ( C @ E @ F ) )
            @ B
            @ A ) ) )
      | ~ ( inconsistency_P @ B @ A )
      | ( inconsistency_P
        @ ^ [E: qML_mu,F: qML_i] :
            ( inconsistency_P
            @ ^ [G: qML_mu,H: qML_i] :
                ~ ( D @ E @ F @ G @ H )
            @ ( C @ E @ F ) )
        @ A ) ),
    inference(pre_uni,[status(thm)],[133:[bind(A,$thf( G @ ( sk2 @ ^ [H: qML_mu] : ^ [I: qML_i] : ( inconsistency_P @ ^ [J: qML_mu] : ^ [K: qML_i] : ~ ( H @ H @ I @ J @ K ) @ ( G @ H @ I ) ) @ D @ C ) @ ( sk1 @ ^ [H: qML_mu] : ^ [I: qML_i] : ( inconsistency_P @ ^ [J: qML_mu] : ^ [K: qML_i] : ~ ( H @ H @ I @ J @ K ) @ ( G @ H @ I ) ) @ D @ C ) )),bind(B,$thf( H @ ( sk2 @ ^ [H: qML_mu] : ^ [I: qML_i] : ( inconsistency_P @ ^ [J: qML_mu] : ^ [K: qML_i] : ~ ( H @ H @ I @ J @ K ) @ ( G @ H @ I ) ) @ D @ C ) @ ( sk1 @ ^ [H: qML_mu] : ^ [I: qML_i] : ( inconsistency_P @ ^ [J: qML_mu] : ^ [K: qML_i] : ~ ( H @ H @ I @ J @ K ) @ ( G @ H @ I ) ) @ D @ C ) )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( ^ [H: qML_mu] : ^ [I: qML_i] : ( inconsistency_P @ ^ [J: qML_mu] : ^ [K: qML_i] : ~ ( H @ H @ I @ J @ K ) @ ( G @ H @ I ) ) ))]]) ).

thf(165,plain,
    ! [D: qML_mu > qML_i > qML_mu > qML_i > $o,C: qML_mu > qML_i > qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( inconsistency_P
        @ ( D
          @ ( sk2
            @ ^ [E: qML_mu,F: qML_i] :
                ( inconsistency_P
                @ ^ [G: qML_mu,H: qML_i] :
                    ~ ( D @ E @ F @ G @ H )
                @ ( C @ E @ F ) )
            @ B
            @ A )
          @ ( sk1
            @ ^ [E: qML_mu,F: qML_i] :
                ( inconsistency_P
                @ ^ [G: qML_mu,H: qML_i] :
                    ~ ( D @ E @ F @ G @ H )
                @ ( C @ E @ F ) )
            @ B
            @ A ) )
        @ ( C
          @ ( sk2
            @ ^ [E: qML_mu,F: qML_i] :
                ( inconsistency_P
                @ ^ [G: qML_mu,H: qML_i] :
                    ~ ( D @ E @ F @ G @ H )
                @ ( C @ E @ F ) )
            @ B
            @ A )
          @ ( sk1
            @ ^ [E: qML_mu,F: qML_i] :
                ( inconsistency_P
                @ ^ [G: qML_mu,H: qML_i] :
                    ~ ( D @ E @ F @ G @ H )
                @ ( C @ E @ F ) )
            @ B
            @ A ) ) )
      | ~ ( inconsistency_P @ B @ A )
      | ( inconsistency_P
        @ ^ [E: qML_mu,F: qML_i] :
            ( inconsistency_P
            @ ^ [G: qML_mu,H: qML_i] :
                ~ ( D @ E @ F @ G @ H )
            @ ( C @ E @ F ) )
        @ A ) ),
    inference(simp,[status(thm)],[162]) ).

thf(506,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P @ incons1905966852QML_mu @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ! [E: qML_mu > qML_i > $o] :
                ( ( incons1389517216QML_mu @ E @ C @ D )
               => ! [F: qML_i] :
                    ( ( qML_r @ D @ F )
                   => ? [G: qML_mu] : ( E @ G @ F ) ) )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[26,476]) ).

thf(515,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( incons1905966852QML_mu
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ! [E: qML_mu > qML_i > $o] :
                  ( ( incons1389517216QML_mu @ E @ C @ D )
                 => ! [F: qML_i] :
                      ( ( qML_r @ D @ F )
                     => ? [G: qML_mu] : ( E @ G @ F ) ) ) ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[506]) ).

thf(519,plain,
    ( incons1905966852QML_mu
   != ( ^ [A: qML_mu,B: qML_i] :
          ~ ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
    inference(simp,[status(thm)],[515]) ).

thf(522,plain,
    ( ( incons1905966852QML_mu @ sk28 @ sk29 )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ A @ sk28 @ sk29 )
           => ! [B: qML_i] :
                ( ( qML_r @ sk29 @ B )
               => ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
    inference(func_ext,[status(esa)],[519]) ).

thf(530,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk13 @ sk14 )
      | ( ( inconsistency_P @ sk17 @ sk14 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[220,41]) ).

thf(547,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk13 @ sk14 )
      | ( sk17
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C ) ) )
      | ( sk14 != A ) ),
    inference(simp,[status(thm)],[530]) ).

thf(551,plain,
    ( ( incons1905966852QML_mu @ sk13 @ sk14 )
    | ( sk17
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( inconsistency_G @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[547]) ).

thf(1175,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ~ ! [C: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ C @ A @ B )
           => ! [D: qML_i] :
                ( ( qML_r @ B @ D )
               => ? [E: qML_mu] : ( C @ E @ D ) ) )
      | ( inconsistency_G @ sk5 @ sk6 )
      | ( ( incons1905966852QML_mu @ A @ B )
       != ( incons1905966852QML_mu @ sk5 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[68,121]) ).

thf(1176,plain,
    ( ~ ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk5 @ sk6 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk6 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) )
    | ( inconsistency_G @ sk5 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[1175:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(1259,plain,
    ( ( inconsistency_G @ sk5 @ sk6 )
    | ( qML_r @ sk6 @ sk120 ) ),
    inference(cnf,[status(esa)],[1176]) ).

thf(1493,plain,
    ( ~ ( sk134 @ sk30 @ sk31 )
    | ( incons1905966852QML_mu @ sk30 @ sk31 ) ),
    inference(cnf,[status(esa)],[1471]) ).

thf(124,plain,
    ! [C: qML_i,B: qML_mu,A: qML_mu > qML_i > $o] :
      ( ( incons1389517216QML_mu @ A @ B @ C )
      = ( ! [D: qML_mu > qML_i > $o] :
            ( ( D @ B @ C )
           => ! [E: qML_i] :
                ( ( qML_r @ C @ E )
               => ! [F: qML_mu] :
                    ( ( A @ F @ E )
                   => ( D @ F @ E ) ) ) ) ) ),
    inference(func_ext,[status(esa)],[32]) ).

thf(1003,plain,
    ( ( inconsistency_G @ sk34 @ sk35 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk34 @ sk35 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk35 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) ),
    inference(bool_ext,[status(thm)],[991]) ).

thf(1016,plain,
    ( ( qML_r @ sk35 @ sk89 )
    | ( inconsistency_G @ sk34 @ sk35 ) ),
    inference(cnf,[status(esa)],[1003]) ).

thf(1191,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ~ ( inconsistency_G @ sk3 @ sk4 ) ) )
      | ( ( incons1905966852QML_mu @ A @ B )
       != ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[68,77]) ).

thf(1192,plain,
    ( ( ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk3 @ sk4 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk4 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) )
   != ( ~ ( inconsistency_G @ sk3 @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[1191:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(1322,plain,
    ( ( incons1905966852QML_mu @ sk23 @ sk24 )
    | ~ ( inconsistency_G @ sk23 @ sk24 ) ),
    inference(bool_ext,[status(thm)],[1223]) ).

thf(1333,plain,
    ( ~ ( inconsistency_G @ sk23 @ sk24 )
    | ( incons1905966852QML_mu @ sk23 @ sk24 ) ),
    inference(cnf,[status(esa)],[1322]) ).

thf(230,plain,
    ! [A: qML_i] :
      ( ( inconsistency_G @ sk7 @ sk8 )
      | ( ( inconsistency_P @ sk11 @ sk8 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[187,44]) ).

thf(232,plain,
    ! [A: qML_i] :
      ( ( inconsistency_G @ sk7 @ sk8 )
      | ( sk11
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C ) ) )
      | ( sk8 != A ) ),
    inference(simp,[status(thm)],[230]) ).

thf(237,plain,
    ( ( inconsistency_G @ sk7 @ sk8 )
    | ( sk11
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[232]) ).

thf(392,plain,
    ( ( inconsistency_G @ sk15 @ sk16 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk16 )
         => ( A @ sk15 @ sk16 ) ) ),
    inference(bool_ext,[status(thm)],[211]) ).

thf(398,plain,
    ( ~ ( sk20 @ sk15 @ sk16 )
    | ( inconsistency_G @ sk15 @ sk16 ) ),
    inference(cnf,[status(esa)],[392]) ).

thf(1201,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( inconsistency_P @ C @ sk14 )
               => ( C @ sk13 @ sk14 ) ) ) )
      | ( ( incons1905966852QML_mu @ A @ B )
       != ( incons1905966852QML_mu @ sk13 @ sk14 ) ) ),
    inference(paramod_ordered,[status(thm)],[68,208]) ).

thf(1202,plain,
    ( ( ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk13 @ sk14 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk14 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ A @ sk14 )
           => ( A @ sk13 @ sk14 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1201:[bind(A,$thf( sk13 )),bind(B,$thf( sk14 ))]]) ).

thf(792,plain,
    ( ( incons1905966852QML_mu @ sk3 @ sk4 )
    | ~ ( sk64 @ sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[745]) ).

thf(1651,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( inconsistency_P @ C @ B )
               => ( C @ A @ B ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk3 @ sk4 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk4 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) )
      | ( ( inconsistency_G @ A @ B )
       != ( inconsistency_G @ sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[34,1192]) ).

thf(1652,plain,
    ( ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ A @ sk4 )
           => ( A @ sk3 @ sk4 ) ) )
   != ( ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk3 @ sk4 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk4 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1651:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(1832,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( incons1905966852QML_mu @ A @ B )
       != ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( inconsistency_P @ C @ sk4 )
               => ( C @ sk3 @ sk4 ) ) ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk3 @ sk4 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk4 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[68,1652]) ).

thf(1833,plain,
    ( ( incons1905966852QML_mu @ sk3 @ sk4 )
   != ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( inconsistency_P @ A @ sk4 )
           => ( A @ sk3 @ sk4 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1832:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(818,plain,
    ( ( incons1905966852QML_mu @ sk13 @ sk14 )
    | ~ ( inconsistency_G @ sk13 @ sk14 ) ),
    inference(bool_ext,[status(thm)],[757]) ).

thf(826,plain,
    ( ~ ( inconsistency_G @ sk13 @ sk14 )
    | ( incons1905966852QML_mu @ sk13 @ sk14 ) ),
    inference(cnf,[status(esa)],[818]) ).

thf(1515,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk3 @ sk4 )
      | ( ( inconsistency_P @ sk64 @ sk4 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[793,44]) ).

thf(1527,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk3 @ sk4 )
      | ( sk64
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C ) ) )
      | ( sk4 != A ) ),
    inference(simp,[status(thm)],[1515]) ).

thf(1535,plain,
    ( ( incons1905966852QML_mu @ sk3 @ sk4 )
    | ( sk64
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[1527]) ).

thf(1,conjecture,
    $false,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ $false,
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(12,plain,
    ~ $false,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1321,plain,
    ( ~ ( incons1905966852QML_mu @ sk23 @ sk24 )
    | ~ ~ ( inconsistency_G @ sk23 @ sk24 ) ),
    inference(bool_ext,[status(thm)],[1223]) ).

thf(1332,plain,
    ( ( inconsistency_G @ sk23 @ sk24 )
    | ~ ( incons1905966852QML_mu @ sk23 @ sk24 ) ),
    inference(cnf,[status(esa)],[1321]) ).

thf(219,plain,
    ( ~ ( sk17 @ sk13 @ sk14 )
    | ( incons1905966852QML_mu @ sk13 @ sk14 ) ),
    inference(cnf,[status(esa)],[215]) ).

thf(1042,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( incons1905966852QML_mu @ sk13 @ sk14 )
      | ( incons1905966852QML_mu
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk17 @ sk14 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[220,54]) ).

thf(1043,plain,
    ( ( incons1905966852QML_mu @ sk13 @ sk14 )
    | ( incons1905966852QML_mu
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk17 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1042:[bind(A,$thf( sk14 )),bind(B,$thf( sk17 ))]]) ).

thf(97,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( inconsistency_P @ B @ A )
      | ( ( inconsistency_P
          @ ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D )
          @ A )
       != ( inconsistency_P @ B @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[16]) ).

thf(98,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( inconsistency_P @ B @ A )
      | ( ( inconsistency_P
          @ ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D )
          @ A )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(simp,[status(thm)],[97]) ).

thf(799,plain,
    ( ( inconsistency_G @ sk9 @ sk10 )
    | ~ ( incons1905966852QML_mu @ sk9 @ sk10 ) ),
    inference(bool_ext,[status(thm)],[739]) ).

thf(816,plain,
    ( ~ ( incons1905966852QML_mu @ sk9 @ sk10 )
    | ( inconsistency_G @ sk9 @ sk10 ) ),
    inference(cnf,[status(esa)],[799]) ).

thf(222,plain,
    ! [A: qML_i] :
      ( ( inconsistency_G @ sk7 @ sk8 )
      | ( ( inconsistency_P @ sk11 @ sk8 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[187,41]) ).

thf(235,plain,
    ! [A: qML_i] :
      ( ( inconsistency_G @ sk7 @ sk8 )
      | ( sk11
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C ) ) )
      | ( sk8 != A ) ),
    inference(simp,[status(thm)],[222]) ).

thf(240,plain,
    ( ( inconsistency_G @ sk7 @ sk8 )
    | ( sk11
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( inconsistency_G @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[235]) ).

thf(848,plain,
    ( ( incons1905966852QML_mu @ sk5 @ sk6 )
    | ~ ( sk67 @ sk5 @ sk6 ) ),
    inference(cnf,[status(esa)],[828]) ).

thf(964,plain,
    ! [A: qML_mu > qML_i > $o] :
      ( ( ( incons1389517216QML_mu @ A )
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C ) ) )
      | ( ( ^ [B: qML_mu,C: qML_i] :
            ! [D: qML_mu > qML_i > $o] :
              ( ( D @ B @ C )
             => ! [E: qML_i] :
                  ( ( qML_r @ C @ E )
                 => ! [F: qML_mu] :
                      ( ( A @ F @ E )
                     => ( D @ F @ E ) ) ) ) )
       != ( ^ [B: qML_mu,C: qML_i] :
            ! [D: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ D @ C )
             => ( D @ B @ C ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[122,88]) ).

thf(983,plain,
    ! [A: qML_mu > qML_i > $o] :
      ( ( ( incons1389517216QML_mu @ A )
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C ) ) )
      | ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
              ( ( D @ B @ C )
             => ! [E: qML_i] :
                  ( ( qML_r @ C @ E )
                 => ! [F: qML_mu] :
                      ( ( A @ F @ E )
                     => ( D @ F @ E ) ) ) ) )
       != ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ D @ C )
             => ( D @ B @ C ) ) ) ) ),
    inference(simp,[status(thm)],[964]) ).

thf(129,plain,
    ( ~ ( inconsistency_G @ sk3 @ sk4 )
    | ( inconsistency_G @ sk5 @ sk6 )
    | ( ( incons1905966852QML_mu @ sk5 @ sk6 )
     != ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[117,102]) ).

thf(130,plain,
    ( ( inconsistency_G @ sk5 @ sk6 )
    | ~ ( inconsistency_G @ sk3 @ sk4 )
    | ( sk5 != sk3 )
    | ( sk6 != sk4 ) ),
    inference(simp,[status(thm)],[129]) ).

thf(399,plain,
    ( ( inconsistency_P @ sk20 @ sk16 )
    | ( inconsistency_G @ sk15 @ sk16 ) ),
    inference(cnf,[status(esa)],[392]) ).

thf(1426,plain,
    ( ( incons1905966852QML_mu @ sk23 @ sk24 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk24 )
         => ( A @ sk23 @ sk24 ) ) ),
    inference(bool_ext,[status(thm)],[1199]) ).

thf(1445,plain,
    ( ( inconsistency_P @ sk132 @ sk24 )
    | ( incons1905966852QML_mu @ sk23 @ sk24 ) ),
    inference(cnf,[status(esa)],[1426]) ).

thf(780,plain,
    ( ~ ( sk62 @ sk5 @ sk6 )
    | ( incons1905966852QML_mu @ sk5 @ sk6 ) ),
    inference(cnf,[status(esa)],[736]) ).

thf(1112,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( incons1905966852QML_mu @ sk9 @ sk10 )
      | ( inconsistency_G
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk12 @ sk10 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[195,56]) ).

thf(1113,plain,
    ( ( incons1905966852QML_mu @ sk9 @ sk10 )
    | ( inconsistency_G
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk12 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1112:[bind(A,$thf( sk10 )),bind(B,$thf( sk12 ))]]) ).

thf(1101,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( inconsistency_G @ sk15 @ sk16 )
      | ( inconsistency_G
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk20 @ sk16 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[399,56]) ).

thf(1102,plain,
    ( ( inconsistency_G @ sk15 @ sk16 )
    | ( inconsistency_G
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk20 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1101:[bind(A,$thf( sk16 )),bind(B,$thf( sk20 ))]]) ).

thf(702,plain,
    ! [A: qML_i] :
      ( ( inconsistency_G @ sk15 @ sk16 )
      | ( ( inconsistency_P @ sk20 @ sk16 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[399,41]) ).

thf(714,plain,
    ! [A: qML_i] :
      ( ( inconsistency_G @ sk15 @ sk16 )
      | ( sk20
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C ) ) )
      | ( sk16 != A ) ),
    inference(simp,[status(thm)],[702]) ).

thf(722,plain,
    ( ( inconsistency_G @ sk15 @ sk16 )
    | ( sk20
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( inconsistency_G @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[714]) ).

thf(1165,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( incons1389517216QML_mu @ C @ A @ B )
               => ! [D: qML_i] :
                    ( ( qML_r @ B @ D )
                   => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( inconsistency_P @ C @ sk6 )
             => ( C @ sk5 @ sk6 ) ) ) )
      | ( ( incons1905966852QML_mu @ A @ B )
       != ( incons1905966852QML_mu @ sk5 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[68,747]) ).

thf(1166,plain,
    ( ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ A @ sk5 @ sk6 )
           => ! [B: qML_i] :
                ( ( qML_r @ sk6 @ B )
               => ? [C: qML_mu] : ( A @ C @ B ) ) ) )
   != ( ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk6 )
         => ( A @ sk5 @ sk6 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1165:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(1196,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( incons1905966852QML_mu @ A @ B )
       != ( ~ ( inconsistency_G @ sk21 @ sk22 ) ) )
      | ( ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ A @ B )
             => ! [D: qML_i] :
                  ( ( qML_r @ B @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( ! [C: qML_mu > qML_i > $o] :
              ( ( incons1389517216QML_mu @ C @ sk21 @ sk22 )
             => ! [D: qML_i] :
                  ( ( qML_r @ sk22 @ D )
                 => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[68,402]) ).

thf(1197,plain,
    ( ( incons1905966852QML_mu @ sk21 @ sk22 )
   != ( ~ ( inconsistency_G @ sk21 @ sk22 ) ) ),
    inference(pattern_uni,[status(thm)],[1196:[bind(A,$thf( sk21 )),bind(B,$thf( sk22 ))]]) ).

thf(1267,plain,
    ( ( incons1905966852QML_mu @ sk21 @ sk22 )
    | ~ ( inconsistency_G @ sk21 @ sk22 ) ),
    inference(bool_ext,[status(thm)],[1197]) ).

thf(1277,plain,
    ( ~ ( inconsistency_G @ sk21 @ sk22 )
    | ( incons1905966852QML_mu @ sk21 @ sk22 ) ),
    inference(cnf,[status(esa)],[1267]) ).

thf(123,plain,
    ! [B: qML_mu,A: qML_mu > qML_i > $o] :
      ( ( incons1389517216QML_mu @ A @ B )
      = ( ^ [C: qML_i] :
          ! [D: qML_mu > qML_i > $o] :
            ( ( D @ B @ C )
           => ! [E: qML_i] :
                ( ( qML_r @ C @ E )
               => ! [F: qML_mu] :
                    ( ( A @ F @ E )
                   => ( D @ F @ E ) ) ) ) ) ),
    inference(func_ext,[status(esa)],[32]) ).

thf(194,plain,
    ( ( incons1905966852QML_mu @ sk9 @ sk10 )
    | ~ ( sk12 @ sk9 @ sk10 ) ),
    inference(cnf,[status(esa)],[189]) ).

thf(1048,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( inconsistency_G @ sk15 @ sk16 )
      | ( incons1905966852QML_mu
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk20 @ sk16 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[399,54]) ).

thf(1049,plain,
    ( ( inconsistency_G @ sk15 @ sk16 )
    | ( incons1905966852QML_mu
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk20 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1048:[bind(A,$thf( sk16 )),bind(B,$thf( sk20 ))]]) ).

thf(1366,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk5 @ sk6 )
      | ( ( inconsistency_P @ sk62 @ sk6 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[781,41]) ).

thf(1392,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk5 @ sk6 )
      | ( sk62
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C ) ) )
      | ( sk6 != A ) ),
    inference(simp,[status(thm)],[1366]) ).

thf(1400,plain,
    ( ( incons1905966852QML_mu @ sk5 @ sk6 )
    | ( sk62
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( inconsistency_G @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[1392]) ).

thf(1605,plain,
    ( ( inconsistency_P @ sk140 @ sk10 )
    | ( incons1905966852QML_mu @ sk9 @ sk10 ) ),
    inference(cnf,[status(esa)],[1560]) ).

thf(1367,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( incons1905966852QML_mu @ sk5 @ sk6 )
      | ( incons1905966852QML_mu
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk62 @ sk6 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[781,54]) ).

thf(1368,plain,
    ( ( incons1905966852QML_mu @ sk5 @ sk6 )
    | ( incons1905966852QML_mu
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk62 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1367:[bind(A,$thf( sk6 )),bind(B,$thf( sk62 ))]]) ).

thf(67,plain,
    ! [A: qML_mu] :
      ( ( incons1905966852QML_mu @ A )
      = ( ^ [B: qML_i] :
          ! [C: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ C @ A @ B )
           => ! [D: qML_i] :
                ( ( qML_r @ B @ D )
               => ? [E: qML_mu] : ( C @ E @ D ) ) ) ) ),
    inference(func_ext,[status(esa)],[30]) ).

thf(1177,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( inconsistency_G @ sk3 @ sk4 )
      | ~ ! [C: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ C @ A @ B )
           => ! [D: qML_i] :
                ( ( qML_r @ B @ D )
               => ? [E: qML_mu] : ( C @ E @ D ) ) )
      | ( ( incons1905966852QML_mu @ A @ B )
       != ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[68,116]) ).

thf(1178,plain,
    ( ( inconsistency_G @ sk3 @ sk4 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk3 @ sk4 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk4 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1177:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(1262,plain,
    ( ( qML_r @ sk4 @ sk122 )
    | ( inconsistency_G @ sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[1178]) ).

thf(1334,plain,
    ( ~ ~ ( incons1905966852QML_mu @ sk34 @ sk35 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ A @ sk35 )
         => ( A @ sk34 @ sk35 ) ) ),
    inference(bool_ext,[status(thm)],[1173]) ).

thf(1358,plain,
    ( ( inconsistency_P @ sk126 @ sk35 )
    | ( incons1905966852QML_mu @ sk34 @ sk35 ) ),
    inference(cnf,[status(esa)],[1334]) ).

thf(3233,plain,
    ! [D: qML_mu > qML_i > $o,C: qML_i,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_G @ sk3 @ sk4 )
      | ~ ( inconsistency_P @ B @ A )
      | ( inconsistency_G
       != ( ^ [E: qML_mu,F: qML_i] :
              ~ ( D @ E @ F ) ) )
      | ( ( inconsistency_P
          @ ^ [E: qML_mu,F: qML_i] : ( incons1905966852QML_mu @ sk3 @ sk4 )
          @ A )
       != ( inconsistency_P @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[157,56]) ).

thf(3234,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_G @ sk3 @ sk4 )
      | ~ ( inconsistency_P @ B @ A )
      | ( inconsistency_G
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ) ),
    inference(pattern_uni,[status(thm)],[3233:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( ^ [E: qML_mu] : ^ [F: qML_i] : ( incons1905966852QML_mu @ sk3 @ sk4 ) ))]]) ).

thf(3492,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_i,A: qML_i] :
      ( ~ ( inconsistency_G @ sk3 @ sk4 )
      | ( inconsistency_G
       != ( ^ [D: qML_mu,E: qML_i] :
              ~ ( incons1905966852QML_mu @ sk3 @ sk4 ) ) )
      | ( ( inconsistency_P @ inconsistency_G @ A )
       != ( inconsistency_P @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[22,3234]) ).

thf(3493,plain,
    ( ~ ( inconsistency_G @ sk3 @ sk4 )
    | ( inconsistency_G
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( incons1905966852QML_mu @ sk3 @ sk4 ) ) ) ),
    inference(pattern_uni,[status(thm)],[3492:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( inconsistency_G ))]]) ).

thf(1093,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( incons1905966852QML_mu @ sk13 @ sk14 )
      | ( inconsistency_G
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk17 @ sk14 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[220,56]) ).

thf(1094,plain,
    ( ( incons1905966852QML_mu @ sk13 @ sk14 )
    | ( inconsistency_G
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk17 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1093:[bind(A,$thf( sk14 )),bind(B,$thf( sk17 ))]]) ).

thf(708,plain,
    ! [A: qML_i] :
      ( ( inconsistency_G @ sk15 @ sk16 )
      | ( ( inconsistency_P @ sk20 @ sk16 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[399,44]) ).

thf(718,plain,
    ! [A: qML_i] :
      ( ( inconsistency_G @ sk15 @ sk16 )
      | ( sk20
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C ) ) )
      | ( sk16 != A ) ),
    inference(simp,[status(thm)],[708]) ).

thf(727,plain,
    ( ( inconsistency_G @ sk15 @ sk16 )
    | ( sk20
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( incons1905966852QML_mu @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[718]) ).

thf(1266,plain,
    ( ~ ( incons1905966852QML_mu @ sk21 @ sk22 )
    | ~ ~ ( inconsistency_G @ sk21 @ sk22 ) ),
    inference(bool_ext,[status(thm)],[1197]) ).

thf(1276,plain,
    ( ( inconsistency_G @ sk21 @ sk22 )
    | ~ ( incons1905966852QML_mu @ sk21 @ sk22 ) ),
    inference(cnf,[status(esa)],[1266]) ).

thf(1624,plain,
    ( ~ ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk13 @ sk14 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk14 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) )
    | ~ ~ ( inconsistency_G @ sk13 @ sk14 ) ),
    inference(bool_ext,[status(thm)],[1190]) ).

thf(1646,plain,
    ( ( inconsistency_G @ sk13 @ sk14 )
    | ( qML_r @ sk14 @ sk149 ) ),
    inference(cnf,[status(esa)],[1624]) ).

thf(4224,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] : $true
        @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( inconsistency_G @ C @ D )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[4139,41]) ).

thf(4238,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( ( ^ [C: qML_mu,D: qML_i] :
              ~ ( inconsistency_G @ C @ D ) )
       != ( ^ [C: qML_mu,D: qML_i] : $true ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[4224]) ).

thf(4250,plain,
    ( ( ^ [A: qML_mu,B: qML_i] :
          ~ ( inconsistency_G @ A @ B ) )
   != ( ^ [A: qML_mu,B: qML_i] : $true ) ),
    inference(simp,[status(thm)],[4238]) ).

thf(186,plain,
    ( ( inconsistency_G @ sk7 @ sk8 )
    | ~ ( sk11 @ sk7 @ sk8 ) ),
    inference(cnf,[status(esa)],[184]) ).

thf(624,plain,
    ( ~ ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk21 @ sk22 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk22 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) )
    | ~ ~ ( inconsistency_G @ sk21 @ sk22 ) ),
    inference(bool_ext,[status(thm)],[402]) ).

thf(632,plain,
    ( ( inconsistency_G @ sk21 @ sk22 )
    | ( qML_r @ sk22 @ sk37 ) ),
    inference(cnf,[status(esa)],[624]) ).

thf(4225,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] : $true
        @ A )
     != ( inconsistency_P
        @ ^ [C: qML_mu,D: qML_i] :
            ~ ( incons1905966852QML_mu @ C @ D )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[4139,44]) ).

thf(4246,plain,
    ! [B: qML_i,A: qML_i] :
      ( ( ( ^ [C: qML_mu,D: qML_i] :
              ~ ( incons1905966852QML_mu @ C @ D ) )
       != ( ^ [C: qML_mu,D: qML_i] : $true ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[4225]) ).

thf(4261,plain,
    ( ( ^ [A: qML_mu,B: qML_i] :
          ~ ( incons1905966852QML_mu @ A @ B ) )
   != ( ^ [A: qML_mu,B: qML_i] : $true ) ),
    inference(simp,[status(thm)],[4246]) ).

thf(1061,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( incons1905966852QML_mu @ sk9 @ sk10 )
      | ( incons1905966852QML_mu
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk12 @ sk10 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[195,54]) ).

thf(1062,plain,
    ( ( incons1905966852QML_mu @ sk9 @ sk10 )
    | ( incons1905966852QML_mu
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk12 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1061:[bind(A,$thf( sk10 )),bind(B,$thf( sk12 ))]]) ).

thf(1211,plain,
    ! [B: qML_i,A: qML_mu] :
      ( ( ( ~ ! [C: qML_mu > qML_i > $o] :
                ( ( incons1389517216QML_mu @ C @ A @ B )
               => ! [D: qML_i] :
                    ( ( qML_r @ B @ D )
                   => ? [E: qML_mu] : ( C @ E @ D ) ) ) )
       != ( inconsistency_G @ sk9 @ sk10 ) )
      | ( ( incons1905966852QML_mu @ A @ B )
       != ( incons1905966852QML_mu @ sk9 @ sk10 ) ) ),
    inference(paramod_ordered,[status(thm)],[68,739]) ).

thf(1212,plain,
    ( ( ~ ! [A: qML_mu > qML_i > $o] :
            ( ( incons1389517216QML_mu @ A @ sk9 @ sk10 )
           => ! [B: qML_i] :
                ( ( qML_r @ sk10 @ B )
               => ? [C: qML_mu] : ( A @ C @ B ) ) ) )
   != ( inconsistency_G @ sk9 @ sk10 ) ),
    inference(pattern_uni,[status(thm)],[1211:[bind(A,$thf( sk9 )),bind(B,$thf( sk10 ))]]) ).

thf(669,plain,
    ( ( incons1905966852QML_mu @ sk28 @ sk29 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk28 @ sk29 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk29 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) ),
    inference(bool_ext,[status(thm)],[522]) ).

thf(684,plain,
    ( ( qML_r @ sk29 @ sk55 )
    | ( incons1905966852QML_mu @ sk28 @ sk29 ) ),
    inference(cnf,[status(esa)],[669]) ).

thf(1444,plain,
    ( ~ ( sk132 @ sk23 @ sk24 )
    | ( incons1905966852QML_mu @ sk23 @ sk24 ) ),
    inference(cnf,[status(esa)],[1426]) ).

thf(19,plain,
    ! [C: qML_mu > qML_i > $o,B: qML_mu > qML_i > $o,A: qML_i] :
      ( ~ ( inconsistency_P @ B @ A )
      | ( B @ ( sk2 @ C @ B @ A ) @ ( sk1 @ C @ B @ A ) )
      | ( inconsistency_P @ C @ A ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(687,plain,
    ( ( inconsistency_G @ sk30 @ sk31 )
    | ~ ! [A: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ A @ sk30 @ sk31 )
         => ! [B: qML_i] :
              ( ( qML_r @ sk31 @ B )
             => ? [C: qML_mu] : ( A @ C @ B ) ) ) ),
    inference(bool_ext,[status(thm)],[525]) ).

thf(696,plain,
    ( ( qML_r @ sk31 @ sk59 )
    | ( inconsistency_G @ sk30 @ sk31 ) ),
    inference(cnf,[status(esa)],[687]) ).

thf(3177,plain,
    ! [A: qML_mu > qML_i > $o] :
      ( ( ( incons1389517216QML_mu @ A )
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( incons1905966852QML_mu @ B @ C ) ) )
      | ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( D @ B @ C ) )
       != ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( inconsistency_P @ D @ C ) ) )
      | ( ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] :
            ! [E: qML_i] :
              ( ( qML_r @ C @ E )
             => ! [F: qML_mu] :
                  ( ( A @ F @ E )
                 => ( D @ F @ E ) ) ) )
       != ( ^ [B: qML_mu,C: qML_i,D: qML_mu > qML_i > $o] : ( D @ B @ C ) ) ) ),
    inference(simp,[status(thm)],[983]) ).

thf(1503,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk3 @ sk4 )
      | ( ( inconsistency_P @ sk64 @ sk4 )
       != ( inconsistency_P
          @ ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C )
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[793,41]) ).

thf(1529,plain,
    ! [A: qML_i] :
      ( ( incons1905966852QML_mu @ sk3 @ sk4 )
      | ( sk64
       != ( ^ [B: qML_mu,C: qML_i] :
              ~ ( inconsistency_G @ B @ C ) ) )
      | ( sk4 != A ) ),
    inference(simp,[status(thm)],[1503]) ).

thf(1537,plain,
    ( ( incons1905966852QML_mu @ sk3 @ sk4 )
    | ( sk64
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( inconsistency_G @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[1529]) ).

thf(1357,plain,
    ( ~ ( sk126 @ sk34 @ sk35 )
    | ( incons1905966852QML_mu @ sk34 @ sk35 ) ),
    inference(cnf,[status(esa)],[1334]) ).

thf(1279,plain,
    ( ~ ~ ( incons1905966852QML_mu @ sk30 @ sk31 )
    | ~ ( inconsistency_G @ sk30 @ sk31 ) ),
    inference(bool_ext,[status(thm)],[1208]) ).

thf(1299,plain,
    ( ~ ( inconsistency_G @ sk30 @ sk31 )
    | ( incons1905966852QML_mu @ sk30 @ sk31 ) ),
    inference(cnf,[status(esa)],[1279]) ).

thf(1504,plain,
    ! [B: qML_mu > qML_i > $o,A: qML_i] :
      ( ( incons1905966852QML_mu @ sk3 @ sk4 )
      | ( incons1905966852QML_mu
       != ( ^ [C: qML_mu,D: qML_i] :
              ~ ( B @ C @ D ) ) )
      | ( ( inconsistency_P @ sk64 @ sk4 )
       != ( inconsistency_P @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[793,54]) ).

thf(1505,plain,
    ( ( incons1905966852QML_mu @ sk3 @ sk4 )
    | ( incons1905966852QML_mu
     != ( ^ [A: qML_mu,B: qML_i] :
            ~ ( sk64 @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1504:[bind(A,$thf( sk4 )),bind(B,$thf( sk64 ))]]) ).

thf(1301,plain,
    ( ~ ( incons1905966852QML_mu @ sk34 @ sk35 )
    | ( inconsistency_G @ sk34 @ sk35 ) ),
    inference(bool_ext,[status(thm)],[1214]) ).

thf(1320,plain,
    ( ( inconsistency_G @ sk34 @ sk35 )
    | ~ ( incons1905966852QML_mu @ sk34 @ sk35 ) ),
    inference(cnf,[status(esa)],[1301]) ).

thf(4273,plain,
    ~ ~ ( inconsistency_G @ sk354 @ sk355 ),
    inference(func_ext,[status(esa)],[4250]) ).

thf(4274,plain,
    inconsistency_G @ sk354 @ sk355,
    inference(cnf,[status(esa)],[4273]) ).

thf(5374,plain,
    $false,
    inference(e,[status(thm)],[892,1469,1190,555,1295,88,977,120,655,1173,56,747,4247,1507,24,25,4249,52,14,110,619,157,20,1319,4270,1398,4265,1494,1100,29,492,211,121,1169,2861,1622,116,428,849,74,206,1604,1206,117,793,1199,1470,220,102,1047,1223,825,28,429,33,1217,160,21,1370,165,815,65,522,757,551,519,1259,1493,124,77,476,1214,1016,1192,13,41,1333,237,105,205,398,1202,792,17,32,34,1833,402,22,44,1652,826,1535,27,4251,12,54,1332,187,406,219,4139,1043,98,208,816,240,848,520,66,521,983,130,399,1445,780,1113,1102,722,1166,1208,1277,123,754,194,1049,525,18,1400,1605,739,1368,67,16,1262,31,1358,3493,1094,991,727,72,87,759,1276,1646,4250,186,55,632,781,23,4261,1062,26,1212,684,1444,36,30,19,210,195,1197,696,79,3177,860,1537,1357,47,15,68,1299,1505,1320,1184,496,122,4274]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : PHI007^5 : TPTP v8.2.0. Released v6.4.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sat May 18 14:42:53 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.95/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.19/0.97  % [INFO] 	 Parsing done (112ms). 
% 1.19/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.69/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.69/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.86/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ... 
% 1.94/1.27  % [INFO] 	 Axiom selection finished. Selected 9 axioms (removed 0 axioms). 
% 1.94/1.30  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.94/1.30  % [INFO] 	 Type checking passed. 
% 1.94/1.31  % [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 ... 
% 92.06/26.95  % External prover 'e' found a proof!
% 92.06/26.95  % [INFO] 	 Killing All external provers ... 
% 92.06/26.95  % Time passed: 26427ms (effective reasoning time: 25967ms)
% 92.06/26.95  % 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)>
% 92.06/26.95  % Axioms used in derivation (9): fact_7_NE__def, fact_8_ess__def, fact_1_A1b, fact_4_A4, fact_2_A2, fact_0_A1a, fact_6_G__def, fact_3_A3, fact_5_A5
% 92.06/26.95  % No. of inferences in proof: 358
% 92.06/26.95  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 26427 ms resp. 25967 ms w/o parsing
% 92.06/27.07  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 92.06/27.07  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------