Leo-III---1.8.0.UNS-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : LCL096-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 07:50:48 AM UTC 2026

% Result   : Unsatisfiable 144.11s 54.99s
% Output   : Refutation 146.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   60
%            Number of leaves      :    5
% Syntax   : Number of formulae    : 1114 ( 437 unt;   0 typ;   0 def)
%            Number of atoms       : 3191 (1055 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 25508 (1564   ~;1057   |;   0   &;22887   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   : 5016 (   0   ^;5016   !;   0   ?;5016   :)

% Comments : 
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
    is_a_theorem: $i > $o ).

thf(equivalent_decl,type,
    equivalent: $i > $i > $i ).

thf(a_decl,type,
    a: $i ).

thf(b_decl,type,
    b: $i ).

thf(c_decl,type,
    c: $i ).

thf(3,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_2) ).

thf(10,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_4) ).

thf(12,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ is_a_theorem )
      | ~ ( A @ is_a_theorem )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).

thf(8,plain,
    ! [B: $i,A: $i] :
      ( ( B @ is_a_theorem )
      | ~ ( A @ is_a_theorem )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ( B @ is_a_theorem )
      | ~ ( A @ is_a_theorem )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(32,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( F @ equivalent ) @ is_a_theorem ) )
      | ( G @ is_a_theorem )
      | ~ ( F @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[12,9]) ).

thf(33,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( F @ equivalent ) @ is_a_theorem ) )
      | ( G @ is_a_theorem )
      | ~ ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[32]) ).

thf(34,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( R )),bind(B,$thf( V )),bind(C,$thf( Q )),bind(D,$thf( U )),bind(E,$thf( W )),bind(F,$thf( U @ ( Q @ ( V @ ( R @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( U @ ( W @ ( V @ equivalent ) @ equivalent ) @ ( Q @ ( W @ ( R @ equivalent ) @ equivalent ) @ equivalent ) ))]]) ).

thf(47,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[34]) ).

thf(357,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[10,47]) ).

thf(358,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[357]) ).

thf(359,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[358:[bind(A,$thf( N )),bind(B,$thf( P )),bind(C,$thf( Q )),bind(D,$thf( D )),bind(E,$thf( D )),bind(F,$thf( Q @ ( N @ equivalent ) @ ( P @ ( N @ equivalent ) @ equivalent ) )),bind(G,$thf( D )),bind(H,$thf( Q @ ( P @ equivalent ) )),bind(I,$thf( I ))]]) ).

thf(416,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[359]) ).

thf(26,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[10,9]) ).

thf(27,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[26]) ).

thf(28,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( O )),bind(B,$thf( Q )),bind(C,$thf( R )),bind(D,$thf( H )),bind(E,$thf( H @ ( R @ ( Q @ equivalent ) @ ( R @ ( O @ equivalent ) @ ( Q @ ( O @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( H ))]]) ).

thf(51,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[28]) ).

thf(467,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[416,51]) ).

thf(468,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[467]) ).

thf(469,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[468:[bind(A,$thf( ZG @ ( ZI @ ( ZH @ equivalent ) @ equivalent ) )),bind(B,$thf( ZG @ ( ZE @ ( ZH @ equivalent ) @ equivalent ) )),bind(C,$thf( ZH )),bind(D,$thf( ZE )),bind(E,$thf( ZI )),bind(F,$thf( ZG @ ( ZI @ ( ZH @ equivalent ) @ equivalent ) @ ( ZG @ ( ZE @ ( ZH @ equivalent ) @ equivalent ) @ ( ZI @ ( ZE @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( ZE @ ( ZH @ equivalent ) )),bind(H,$thf( ZI @ ( ZH @ equivalent ) )),bind(I,$thf( ZG ))]]) ).

thf(495,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[469]) ).

thf(68,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[12,51]) ).

thf(69,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[68]) ).

thf(70,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( T )),bind(B,$thf( Z )),bind(C,$thf( ZA @ ( T @ equivalent ) )),bind(D,$thf( ZA @ ( Z @ equivalent ) )),bind(E,$thf( Y )),bind(F,$thf( ZA @ ( Z @ equivalent ) @ ( Y @ ( Z @ equivalent ) @ equivalent ) @ ( ZA @ ( T @ equivalent ) @ ( Y @ ( T @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( T )),bind(H,$thf( Z )),bind(I,$thf( ZA ))]]) ).

thf(75,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[70]) ).

thf(116,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[75,9]) ).

thf(117,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[116]) ).

thf(118,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[117:[bind(A,$thf( K )),bind(B,$thf( P )),bind(C,$thf( Q )),bind(D,$thf( R )),bind(E,$thf( R @ ( K @ equivalent ) @ ( P @ ( K @ equivalent ) @ equivalent ) )),bind(F,$thf( R @ ( Q @ equivalent ) @ ( P @ ( Q @ equivalent ) @ equivalent ) ))]]) ).

thf(124,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[118]) ).

thf(512,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[495,124]) ).

thf(513,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[512]) ).

thf(514,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[513:[bind(A,$thf( M )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( J )),bind(E,$thf( J @ ( M @ equivalent ) )),bind(F,$thf( L @ ( M @ ( M @ equivalent ) @ equivalent ) )),bind(G,$thf( G )),bind(H,$thf( L ))]]) ).

thf(528,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[514]) ).

thf(541,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[528,51]) ).

thf(542,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[541]) ).

thf(543,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[542:[bind(A,$thf( Q @ ( X @ equivalent ) @ ( W @ ( W @ equivalent ) @ ( X @ equivalent ) @ equivalent ) )),bind(B,$thf( Q )),bind(C,$thf( W )),bind(D,$thf( Q @ ( Q @ ( X @ equivalent ) @ ( W @ ( W @ equivalent ) @ ( X @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( X )),bind(F,$thf( W @ ( W @ equivalent ) )),bind(G,$thf( Q ))]]) ).

thf(575,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[543]) ).

thf(35,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( G @ is_a_theorem )
      | ~ $true
      | ~ ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[12,9]) ).

thf(36,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( G @ is_a_theorem )
      | ~ ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[35]) ).

thf(37,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( B @ ( F @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( B @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( T )),bind(B,$thf( X )),bind(C,$thf( S )),bind(D,$thf( W )),bind(E,$thf( Y )),bind(F,$thf( W @ ( Y @ ( X @ equivalent ) @ equivalent ) @ ( S @ ( Y @ ( T @ equivalent ) @ equivalent ) @ equivalent ) @ ( W @ ( S @ ( X @ ( T @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( G ))]]) ).

thf(48,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( B @ ( F @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( B @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[37]) ).

thf(700,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[575,48]) ).

thf(701,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[700]) ).

thf(702,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[701:[bind(A,$thf( ZA @ ( ZA @ equivalent ) @ ( Y @ ( Y @ equivalent ) @ equivalent ) )),bind(B,$thf( ZA )),bind(C,$thf( K @ ( Y @ ( L @ equivalent ) @ equivalent ) )),bind(D,$thf( ZA @ ( ZA @ equivalent ) @ ( Y @ ( Y @ equivalent ) @ equivalent ) )),bind(E,$thf( K )),bind(F,$thf( L )),bind(G,$thf( ZA @ ( ZA @ equivalent ) )),bind(H,$thf( Y )),bind(I,$thf( Y ))]]) ).

thf(715,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[702]) ).

thf(727,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( E @ equivalent ) @ ( D @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[715,124]) ).

thf(728,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( E @ equivalent ) @ ( D @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[727]) ).

thf(729,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[728:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( B ))]]) ).

thf(750,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[729]) ).

thf(780,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( C @ ( F @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( G @ ( F @ equivalent ) @ equivalent ) @ ( C @ ( G @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[750,47]) ).

thf(781,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( C @ ( F @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( G @ ( F @ equivalent ) @ equivalent ) @ ( C @ ( G @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[780]) ).

thf(782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[781:[bind(A,$thf( K )),bind(B,$thf( M @ ( L @ equivalent ) )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( K @ ( M @ ( L @ equivalent ) @ equivalent ) )),bind(F,$thf( M )),bind(G,$thf( G ))]]) ).

thf(790,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[782]) ).

thf(44,plain,
    ! [B: $i,A: $i] :
      ( ~ $true
      | ( ( B @ ( A @ equivalent ) @ is_a_theorem )
       != ( A @ is_a_theorem ) )
      | ( B @ is_a_theorem )
      | ~ ( A @ is_a_theorem ) ),
    inference(eqfactor_ordered,[status(thm)],[9]) ).

thf(45,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ is_a_theorem )
       != ( A @ is_a_theorem ) )
      | ~ ( A @ is_a_theorem )
      | ( B @ is_a_theorem ) ),
    inference(simp,[status(thm)],[44]) ).

thf(138,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ is_a_theorem ) )
      | ~ ( E @ is_a_theorem )
      | ~ ( E @ is_a_theorem )
      | ( F @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[124,45]) ).

thf(139,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ is_a_theorem ) )
      | ~ ( E @ is_a_theorem )
      | ( F @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[138]) ).

thf(140,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ equivalent ) @ is_a_theorem )
      | ( D @ ( C @ equivalent ) @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( J )),bind(E,$thf( H @ ( I @ equivalent ) )),bind(F,$thf( J @ ( I @ equivalent ) ))]]) ).

thf(169,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ equivalent ) @ is_a_theorem )
      | ( D @ ( C @ equivalent ) @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[140]) ).

thf(1,negated_conjecture,
    ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_1) ).

thf(6,plain,
    ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(7,plain,
    ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(7712,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( B @ ( C @ equivalent ) @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[169,7]) ).

thf(7713,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( B @ ( C @ equivalent ) @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[7712]) ).

thf(7714,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( c @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[7713:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )),bind(D,$thf( c ))]]) ).

thf(8472,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( G @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[47,7714]) ).

thf(8473,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( G @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8472]) ).

thf(8474,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( c @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[8473:[bind(A,$thf( A )),bind(B,$thf( D )),bind(C,$thf( c )),bind(D,$thf( D )),bind(E,$thf( I )),bind(F,$thf( I @ ( D @ equivalent ) )),bind(G,$thf( A ))]]) ).

thf(8605,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( c @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8474]) ).

thf(10640,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[790,8605]) ).

thf(10641,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[10640]) ).

thf(10642,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( B @ ( a @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[10641:[bind(A,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) )),bind(B,$thf( c )),bind(C,$thf( a )),bind(D,$thf( V )),bind(E,$thf( c @ ( V @ ( a @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( V @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(10822,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( B @ ( a @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[10642]) ).

thf(149,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[75,124]) ).

thf(150,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[149]) ).

thf(151,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( M )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( J @ ( M @ equivalent ) )),bind(F,$thf( N @ ( M @ equivalent ) )),bind(G,$thf( G )),bind(H,$thf( N @ ( M @ equivalent ) ))]]) ).

thf(166,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[151]) ).

thf(177,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[166,51]) ).

thf(178,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[177]) ).

thf(179,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( W @ ( T @ equivalent ) @ ( V @ ( T @ equivalent ) @ equivalent ) )),bind(B,$thf( V )),bind(C,$thf( W )),bind(D,$thf( W @ ( V @ equivalent ) @ ( W @ ( T @ equivalent ) @ ( V @ ( T @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( T )),bind(F,$thf( V )),bind(G,$thf( W ))]]) ).

thf(193,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[179]) ).

thf(604,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[193,48]) ).

thf(605,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[604]) ).

thf(606,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[605:[bind(A,$thf( K @ ( W @ ( L @ equivalent ) @ equivalent ) )),bind(B,$thf( U )),bind(C,$thf( U @ ( W @ ( W @ equivalent ) @ equivalent ) )),bind(D,$thf( U @ ( W @ ( W @ equivalent ) @ equivalent ) @ ( U @ equivalent ) )),bind(E,$thf( K )),bind(F,$thf( L )),bind(G,$thf( U )),bind(H,$thf( W )),bind(I,$thf( W ))]]) ).

thf(638,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[606]) ).

thf(4,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_3) ).

thf(11,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(38,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( F @ equivalent ) @ is_a_theorem ) )
      | ( G @ is_a_theorem )
      | ~ ( F @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[11,9]) ).

thf(39,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( F @ equivalent ) @ is_a_theorem ) )
      | ( G @ is_a_theorem )
      | ~ ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[38]) ).

thf(40,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( R )),bind(B,$thf( V )),bind(C,$thf( W )),bind(D,$thf( U )),bind(E,$thf( I )),bind(F,$thf( I @ ( U @ ( W @ ( V @ equivalent ) @ equivalent ) @ ( U @ ( W @ ( R @ equivalent ) @ ( V @ ( R @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( I ))]]) ).

thf(49,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[40]) ).

thf(874,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( F @ ( H @ ( E @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[528,49]) ).

thf(875,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( F @ ( H @ ( E @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[874]) ).

thf(876,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[875:[bind(A,$thf( R @ ( Z @ ( Y @ equivalent ) @ ( Z @ ( Y @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( R )),bind(C,$thf( Z )),bind(D,$thf( R @ ( R @ ( Z @ ( Y @ equivalent ) @ ( Z @ ( Y @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( Y )),bind(F,$thf( R )),bind(G,$thf( Z )),bind(H,$thf( Z ))]]) ).

thf(894,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[876]) ).

thf(929,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[894,51]) ).

thf(930,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[929]) ).

thf(931,plain,
    ! [A: $i] : ( A @ ( A @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[930:[bind(A,$thf( K @ ( K @ equivalent ) )),bind(B,$thf( B )),bind(C,$thf( K )),bind(D,$thf( K @ ( K @ equivalent ) )),bind(E,$thf( B )),bind(F,$thf( K )),bind(G,$thf( K ))]]) ).

thf(938,plain,
    ! [A: $i] : ( A @ ( A @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[931]) ).

thf(8281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( C @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[938,7714]) ).

thf(8282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( C @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8281]) ).

thf(8283,plain,
    ! [A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8282:[bind(A,$thf( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )),bind(B,$thf( B )),bind(C,$thf( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ))]]) ).

thf(8619,plain,
    ! [A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8283]) ).

thf(8884,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( C @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[638,8619]) ).

thf(8885,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
     != ( c @ ( C @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8884]) ).

thf(9077,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
     != ( c @ ( C @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[8885]) ).

thf(689,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( F @ equivalent ) @ ( E @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[575,124]) ).

thf(690,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( F @ equivalent ) @ ( E @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[689]) ).

thf(691,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[690:[bind(A,$thf( O @ ( S @ ( S @ equivalent ) @ ( P @ equivalent ) @ equivalent ) )),bind(B,$thf( S )),bind(C,$thf( P )),bind(D,$thf( S @ ( S @ equivalent ) @ ( P @ equivalent ) )),bind(E,$thf( O @ ( S @ ( S @ equivalent ) @ ( P @ equivalent ) @ equivalent ) @ ( P @ equivalent ) )),bind(F,$thf( F )),bind(G,$thf( O ))]]) ).

thf(710,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[691]) ).

thf(1440,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[710,48]) ).

thf(1441,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1440]) ).

thf(1442,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1441:[bind(A,$thf( ZB @ ( ZF @ ( ZF @ ( ZN @ ( ZN @ equivalent ) @ ( ZK @ equivalent ) @ equivalent ) @ ( ZK @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( ZB )),bind(C,$thf( ZF @ ( ZN @ ( ZN @ equivalent ) @ ( ZK @ equivalent ) @ equivalent ) )),bind(D,$thf( ZN )),bind(E,$thf( ZB @ ( ZB @ ( ZF @ ( ZF @ ( ZN @ ( ZN @ equivalent ) @ ( ZK @ equivalent ) @ equivalent ) @ ( ZK @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZF )),bind(G,$thf( ZK )),bind(H,$thf( ZB )),bind(I,$thf( ZF @ ( ZN @ ( ZN @ equivalent ) @ ( ZK @ equivalent ) @ equivalent ) )),bind(J,$thf( ZN @ ( ZN @ equivalent ) ))]]) ).

thf(1453,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1442]) ).

thf(119,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ $true
      | ~ ( F @ ( E @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[75,9]) ).

thf(120,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ ( F @ ( E @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[119]) ).

thf(121,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( M )),bind(B,$thf( R )),bind(C,$thf( S )),bind(D,$thf( T )),bind(E,$thf( T @ ( S @ equivalent ) @ ( R @ ( S @ equivalent ) @ equivalent ) @ ( T @ ( M @ equivalent ) @ ( R @ ( M @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(125,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[121]) ).

thf(3100,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1453,125]) ).

thf(3101,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3100]) ).

thf(3102,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3101:[bind(A,$thf( ZS @ ( ZR @ equivalent ) @ ( ZS @ ( ZP @ equivalent ) @ ( ZO @ ( ZO @ equivalent ) @ ( ZP @ equivalent ) @ equivalent ) @ ( ZR @ equivalent ) @ equivalent ) )),bind(B,$thf( ZS @ ( ZP @ equivalent ) )),bind(C,$thf( ZP )),bind(D,$thf( ZO )),bind(E,$thf( ZS @ ( ZR @ equivalent ) @ ( ZS @ ( ZP @ equivalent ) @ ( ZO @ ( ZO @ equivalent ) @ ( ZP @ equivalent ) @ equivalent ) @ ( ZR @ equivalent ) @ equivalent ) )),bind(F,$thf( ZP )),bind(G,$thf( ZS @ ( ZP @ equivalent ) @ ( ZO @ ( ZO @ equivalent ) @ ( ZP @ equivalent ) @ equivalent ) )),bind(H,$thf( ZR )),bind(I,$thf( ZS ))]]) ).

thf(3152,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3102]) ).

thf(3408,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3152,48]) ).

thf(3409,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3408]) ).

thf(3410,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3409:[bind(A,$thf( ZD )),bind(B,$thf( R @ ( ZB @ equivalent ) )),bind(C,$thf( V @ ( ZD @ ( ZD @ equivalent ) @ ( ZB @ ( ZB @ equivalent ) @ equivalent ) @ equivalent ) )),bind(D,$thf( V )),bind(E,$thf( V @ ( V @ ( ZD @ ( ZD @ equivalent ) @ ( ZB @ ( ZB @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZD @ ( ZD @ equivalent ) )),bind(G,$thf( ZB )),bind(H,$thf( V )),bind(I,$thf( ZB )),bind(J,$thf( R ))]]) ).

thf(3428,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3410]) ).

thf(3452,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( F @ equivalent ) @ ( E @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3428,124]) ).

thf(3453,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( F @ equivalent ) @ ( E @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3452]) ).

thf(3454,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3453:[bind(A,$thf( O @ ( U @ ( U @ equivalent ) @ ( S @ ( S @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( S )),bind(C,$thf( U )),bind(D,$thf( U @ ( U @ equivalent ) @ ( S @ ( S @ equivalent ) @ equivalent ) )),bind(E,$thf( O @ ( U @ ( U @ equivalent ) @ ( S @ ( S @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( F )),bind(G,$thf( O ))]]) ).

thf(3494,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3454]) ).

thf(4736,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3494,51]) ).

thf(4737,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[4736]) ).

thf(4738,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[4737:[bind(A,$thf( V @ ( ZG @ equivalent ) @ ( ZF @ ( ZF @ equivalent ) @ ( ZD @ ( ZD @ equivalent ) @ equivalent ) @ ( ZG @ equivalent ) @ equivalent ) )),bind(B,$thf( V )),bind(C,$thf( ZD )),bind(D,$thf( ZF )),bind(E,$thf( V @ ( V @ ( ZG @ equivalent ) @ ( ZF @ ( ZF @ equivalent ) @ ( ZD @ ( ZD @ equivalent ) @ equivalent ) @ ( ZG @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZG )),bind(G,$thf( ZF @ ( ZF @ equivalent ) @ ( ZD @ ( ZD @ equivalent ) @ equivalent ) )),bind(H,$thf( V ))]]) ).

thf(4746,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[4738]) ).

thf(4951,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4746,48]) ).

thf(4952,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[4951]) ).

thf(4953,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[4952:[bind(A,$thf( ZN @ ( ZN @ equivalent ) @ ( ZL @ ( ZL @ equivalent ) @ equivalent ) @ ( ZH @ ( ZH @ equivalent ) @ equivalent ) )),bind(B,$thf( ZL )),bind(C,$thf( ZN )),bind(D,$thf( L @ ( ZH @ ( M @ equivalent ) @ equivalent ) )),bind(E,$thf( ZN @ ( ZN @ equivalent ) @ ( ZL @ ( ZL @ equivalent ) @ equivalent ) @ ( ZH @ ( ZH @ equivalent ) @ equivalent ) )),bind(F,$thf( L )),bind(G,$thf( M )),bind(H,$thf( ZN @ ( ZN @ equivalent ) @ ( ZL @ ( ZL @ equivalent ) @ equivalent ) )),bind(I,$thf( ZH )),bind(J,$thf( ZH ))]]) ).

thf(4978,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[4953]) ).

thf(152,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[124,51]) ).

thf(153,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[152]) ).

thf(154,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( B @ ( A @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( A )),bind(B,$thf( X @ ( V @ equivalent ) )),bind(C,$thf( X @ ( W @ equivalent ) @ ( V @ ( W @ equivalent ) @ equivalent ) )),bind(D,$thf( R )),bind(E,$thf( R @ ( X @ ( W @ equivalent ) @ ( V @ ( W @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( W )),bind(G,$thf( V )),bind(H,$thf( X ))]]) ).

thf(168,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( B @ ( A @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[154]) ).

thf(7026,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4978,168]) ).

thf(7027,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[7026]) ).

thf(7028,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[7027:[bind(A,$thf( B @ ( B @ equivalent ) )),bind(B,$thf( B )),bind(C,$thf( L )),bind(D,$thf( B @ ( B @ equivalent ) )),bind(E,$thf( L @ ( L @ equivalent ) )),bind(F,$thf( B )),bind(G,$thf( G )),bind(H,$thf( B ))]]) ).

thf(7235,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[7028]) ).

thf(7408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[7235,7]) ).

thf(7409,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[7408]) ).

thf(7439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[7409]) ).

thf(22861,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) )
       != c )
      | ( ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[7439]) ).

thf(921,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( F @ ( H @ ( E @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[894,49]) ).

thf(922,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( F @ ( H @ ( E @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[921]) ).

thf(923,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[922:[bind(A,$thf( ZL @ ( ZK @ equivalent ) @ ( ZJ @ ( ZK @ equivalent ) @ equivalent ) @ ( ZL @ ( ZJ @ equivalent ) @ equivalent ) )),bind(B,$thf( ZJ @ ( ZK @ equivalent ) )),bind(C,$thf( ZL @ ( ZK @ equivalent ) )),bind(D,$thf( ZL @ ( ZK @ equivalent ) @ ( ZJ @ ( ZK @ equivalent ) @ equivalent ) @ ( ZL @ ( ZJ @ equivalent ) @ equivalent ) )),bind(E,$thf( ZK )),bind(F,$thf( ZL @ ( ZK @ equivalent ) @ ( ZJ @ ( ZK @ equivalent ) @ equivalent ) )),bind(G,$thf( ZJ )),bind(H,$thf( ZL ))]]) ).

thf(943,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[923]) ).

thf(10519,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[943,8605]) ).

thf(10520,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[10519]) ).

thf(10521,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[10520:[bind(A,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )),bind(B,$thf( V )),bind(C,$thf( c )),bind(D,$thf( c @ ( V @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( V @ equivalent ) @ equivalent ) )),bind(E,$thf( E ))]]) ).

thf(10812,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[10521]) ).

thf(8445,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[790,7714]) ).

thf(8446,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8445]) ).

thf(8447,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( B @ ( a @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8446:[bind(A,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) )),bind(B,$thf( c )),bind(C,$thf( a )),bind(D,$thf( V )),bind(E,$thf( E )),bind(F,$thf( c @ ( V @ ( a @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( V @ equivalent ) @ equivalent ) ))]]) ).

thf(8639,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( B @ ( a @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8447]) ).

thf(3465,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3428,7]) ).

thf(3466,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3465]) ).

thf(3480,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[3466]) ).

thf(3562,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != c )
      | ( ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[3480]) ).

thf(3563,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[3562]) ).

thf(3565,plain,
    ! [B: $i,A: $i] :
      ( ( c != c )
      | ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[3563]) ).

thf(3566,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ),
    inference(simp,[status(thm)],[3565]) ).

thf(8997,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( F @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( B @ ( A @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[168,8619]) ).

thf(8998,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( F @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( B @ ( A @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8997]) ).

thf(8999,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( c @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8998:[bind(A,$thf( A )),bind(B,$thf( c @ ( R @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) )),bind(C,$thf( R )),bind(D,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )),bind(E,$thf( c )),bind(F,$thf( R @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ))]]) ).

thf(9091,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( c @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8999]) ).

thf(129,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[10,124]) ).

thf(130,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[129]) ).

thf(131,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ equivalent ) @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( ZA )),bind(B,$thf( ZC )),bind(C,$thf( ZD )),bind(D,$thf( T @ ( ZD @ ( ZC @ equivalent ) @ ( ZD @ ( ZA @ equivalent ) @ ( ZC @ ( ZA @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( ZD @ ( ZC @ equivalent ) @ ( ZD @ ( ZA @ equivalent ) @ ( ZC @ ( ZA @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( T @ ( ZD @ ( ZC @ equivalent ) @ ( ZD @ ( ZA @ equivalent ) @ ( ZC @ ( ZA @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( G )),bind(H,$thf( T ))]]) ).

thf(163,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ equivalent ) @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[131]) ).

thf(325,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[163,51]) ).

thf(326,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[325]) ).

thf(327,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( E @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( ZA @ ( ZP @ equivalent ) @ ( ZO @ ( ZN @ equivalent ) @ ( ZO @ ( ZL @ equivalent ) @ ( ZN @ ( ZL @ equivalent ) @ equivalent ) @ equivalent ) @ ( ZP @ equivalent ) @ equivalent ) )),bind(B,$thf( ZA )),bind(C,$thf( ZL )),bind(D,$thf( ZN )),bind(E,$thf( ZO )),bind(F,$thf( ZA @ ( ZA @ ( ZP @ equivalent ) @ ( ZO @ ( ZN @ equivalent ) @ ( ZO @ ( ZL @ equivalent ) @ ( ZN @ ( ZL @ equivalent ) @ equivalent ) @ equivalent ) @ ( ZP @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( ZP )),bind(H,$thf( ZO @ ( ZN @ equivalent ) @ ( ZO @ ( ZL @ equivalent ) @ ( ZN @ ( ZL @ equivalent ) @ equivalent ) @ equivalent ) )),bind(I,$thf( ZA ))]]) ).

thf(352,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( E @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[327]) ).

thf(615,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[528,48]) ).

thf(616,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[615]) ).

thf(617,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[616:[bind(A,$thf( ZI @ ( ZK @ ( ZF @ equivalent ) @ ( ZJ @ ( ZF @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( ZI @ ( ZK @ ( ZJ @ equivalent ) @ equivalent ) )),bind(C,$thf( ZK @ ( ZF @ equivalent ) )),bind(D,$thf( ZI @ ( ZK @ ( ZJ @ equivalent ) @ equivalent ) @ ( ZI @ ( ZK @ ( ZF @ equivalent ) @ ( ZJ @ ( ZF @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( ZK @ ( ZF @ equivalent ) )),bind(F,$thf( ZF )),bind(G,$thf( ZI )),bind(H,$thf( ZJ )),bind(I,$thf( ZK ))]]) ).

thf(629,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[617]) ).

thf(4719,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ ( I @ ( F @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3494,49]) ).

thf(4720,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ ( I @ ( F @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[4719]) ).

thf(4721,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[4720:[bind(A,$thf( W @ ( ZI @ ( ZI @ equivalent ) @ ( ZF @ equivalent ) @ ( ZE @ ( ZE @ equivalent ) @ ( ZF @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( W )),bind(C,$thf( ZE )),bind(D,$thf( ZI )),bind(E,$thf( W @ ( W @ ( ZI @ ( ZI @ equivalent ) @ ( ZF @ equivalent ) @ ( ZE @ ( ZE @ equivalent ) @ ( ZF @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZF )),bind(G,$thf( W )),bind(H,$thf( ZE @ ( ZE @ equivalent ) )),bind(I,$thf( ZI @ ( ZI @ equivalent ) ))]]) ).

thf(4754,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[4721]) ).

thf(5077,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ ( I @ ( F @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4754,49]) ).

thf(5078,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ ( I @ ( F @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[5077]) ).

thf(5079,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[5078:[bind(A,$thf( ZK @ ( ZK @ equivalent ) @ ( ZI @ ( ZH @ equivalent ) @ equivalent ) @ ( ZH @ ( ZI @ equivalent ) @ equivalent ) )),bind(B,$thf( ZH )),bind(C,$thf( ZI @ ( ZH @ equivalent ) )),bind(D,$thf( ZK )),bind(E,$thf( ZK @ ( ZK @ equivalent ) @ ( ZI @ ( ZH @ equivalent ) @ equivalent ) @ ( ZH @ ( ZI @ equivalent ) @ equivalent ) )),bind(F,$thf( ZH )),bind(G,$thf( ZK @ ( ZK @ equivalent ) @ ( ZI @ ( ZH @ equivalent ) @ equivalent ) )),bind(H,$thf( ZI )),bind(I,$thf( ZH ))]]) ).

thf(5116,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[5079]) ).

thf(141,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[12,124]) ).

thf(142,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[141]) ).

thf(143,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[142:[bind(A,$thf( L )),bind(B,$thf( Q )),bind(C,$thf( K )),bind(D,$thf( O )),bind(E,$thf( Q )),bind(F,$thf( K @ ( Q @ ( L @ equivalent ) @ equivalent ) )),bind(G,$thf( O )),bind(H,$thf( H )),bind(I,$thf( O @ ( Q @ ( Q @ equivalent ) @ equivalent ) ))]]) ).

thf(171,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[143]) ).

thf(208,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[171,9]) ).

thf(209,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[208]) ).

thf(210,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( K @ ( H @ equivalent ) )),bind(E,$thf( K @ ( M @ ( M @ equivalent ) @ equivalent ) @ ( H @ equivalent ) ))]]) ).

thf(221,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[210]) ).

thf(11330,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[7235,221]) ).

thf(11331,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11330]) ).

thf(11332,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11331:[bind(A,$thf( L )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( L @ ( K @ equivalent ) @ ( L @ ( K @ equivalent ) @ equivalent ) )),bind(E,$thf( N @ ( N @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11688,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11332]) ).

thf(740,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( C @ ( F @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( G @ ( F @ equivalent ) @ equivalent ) @ ( C @ ( G @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[715,47]) ).

thf(741,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( C @ ( F @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( G @ ( F @ equivalent ) @ equivalent ) @ ( C @ ( G @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[740]) ).

thf(742,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[741:[bind(A,$thf( K @ ( J @ equivalent ) )),bind(B,$thf( M )),bind(C,$thf( K @ ( J @ equivalent ) )),bind(D,$thf( J )),bind(E,$thf( M @ ( M @ equivalent ) )),bind(F,$thf( K )),bind(G,$thf( G ))]]) ).

thf(749,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[742]) ).

thf(1490,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[749,48]) ).

thf(1491,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1490]) ).

thf(1492,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1491:[bind(A,$thf( V )),bind(B,$thf( L @ ( Z @ ( M @ equivalent ) @ equivalent ) )),bind(C,$thf( V @ ( Z @ ( Z @ equivalent ) @ equivalent ) )),bind(D,$thf( ZB )),bind(E,$thf( ZB @ ( ZB @ equivalent ) @ ( V @ ( V @ ( Z @ ( Z @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( L )),bind(G,$thf( M )),bind(H,$thf( V )),bind(I,$thf( Z )),bind(J,$thf( Z ))]]) ).

thf(1509,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1492]) ).

thf(1596,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( D @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( D @ ( H @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1509,47]) ).

thf(1597,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( D @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( D @ ( H @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1596]) ).

thf(1598,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1597:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( A )),bind(E,$thf( J @ ( J @ equivalent ) )),bind(F,$thf( L @ ( L @ equivalent ) )),bind(G,$thf( A )),bind(H,$thf( H ))]]) ).

thf(1611,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1598]) ).

thf(183,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true
      | ~ ( E @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[166,9]) ).

thf(184,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ ( E @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[183]) ).

thf(185,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( L )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( O @ ( N @ equivalent ) @ ( L @ equivalent ) @ ( O @ ( N @ equivalent ) @ ( L @ equivalent ) @ equivalent ) )),bind(E,$thf( E ))]]) ).

thf(194,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[185]) ).

thf(9469,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1611,194]) ).

thf(9470,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9469]) ).

thf(9471,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[9470:[bind(A,$thf( ZD @ ( ZC @ equivalent ) @ ( Z @ ( Z @ equivalent ) @ equivalent ) )),bind(B,$thf( ZD @ ( ZC @ equivalent ) )),bind(C,$thf( Z )),bind(D,$thf( ZF )),bind(E,$thf( ZF @ ( ZF @ equivalent ) @ ( ZD @ ( ZC @ equivalent ) @ ( ZD @ ( ZC @ equivalent ) @ ( Z @ ( Z @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( Z @ ( Z @ equivalent ) )),bind(G,$thf( ZC )),bind(H,$thf( ZD ))]]) ).

thf(9621,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[9471]) ).

thf(562,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[528,7]) ).

thf(563,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[562]) ).

thf(567,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[563]) ).

thf(1215,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[567]) ).

thf(1403,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) )
       != c )
      | ( A
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1215]) ).

thf(1404,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[1403]) ).

thf(1405,plain,
    ! [B: $i,A: $i] :
      ( ( c != c )
      | ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( A @ ( B @ ( B @ equivalent ) @ equivalent ) ) )
      | ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(eqfactor_ordered,[status(thm)],[1404]) ).

thf(1406,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( A @ ( B @ ( B @ equivalent ) @ equivalent ) ) )
      | ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[1405]) ).

thf(1102,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[943,51]) ).

thf(1103,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1102]) ).

thf(1104,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1103:[bind(A,$thf( ZC @ ( X @ equivalent ) @ ( ZB @ ( X @ equivalent ) @ equivalent ) )),bind(B,$thf( Z )),bind(C,$thf( ZC @ ( ZB @ equivalent ) )),bind(D,$thf( ZC @ ( ZB @ equivalent ) @ ( Z @ equivalent ) @ ( ZC @ ( X @ equivalent ) @ ( ZB @ ( X @ equivalent ) @ equivalent ) @ ( Z @ equivalent ) @ equivalent ) )),bind(E,$thf( X )),bind(F,$thf( ZB )),bind(G,$thf( ZC ))]]) ).

thf(1114,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1104]) ).

thf(1775,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1114,51]) ).

thf(1776,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1775]) ).

thf(1777,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1776:[bind(A,$thf( ZC )),bind(B,$thf( ZF @ ( ZC @ equivalent ) @ ( ZA @ equivalent ) @ ( ZE @ ( ZC @ equivalent ) @ ( ZA @ equivalent ) @ equivalent ) )),bind(C,$thf( ZE )),bind(D,$thf( ZF )),bind(E,$thf( ZF @ ( ZE @ equivalent ) @ ( ZF @ ( ZC @ equivalent ) @ ( ZA @ equivalent ) @ ( ZE @ ( ZC @ equivalent ) @ ( ZA @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZA )),bind(G,$thf( ZE @ ( ZC @ equivalent ) )),bind(H,$thf( ZF @ ( ZC @ equivalent ) ))]]) ).

thf(1788,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1777]) ).

thf(205,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[171,51]) ).

thf(206,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[205]) ).

thf(207,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( ZC @ ( V @ equivalent ) @ ( ZB @ ( V @ equivalent ) @ equivalent ) )),bind(B,$thf( ZC @ ( ZB @ equivalent ) )),bind(C,$thf( ZA )),bind(D,$thf( ZC @ ( ZB @ equivalent ) @ ( ZA @ ( ZA @ equivalent ) @ equivalent ) @ ( ZC @ ( V @ equivalent ) @ ( ZB @ ( V @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( V )),bind(F,$thf( ZB )),bind(G,$thf( ZC ))]]) ).

thf(226,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[207]) ).

thf(363,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[226,47]) ).

thf(364,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[363]) ).

thf(365,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[364:[bind(A,$thf( J )),bind(B,$thf( O )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( Q @ ( J @ equivalent ) )),bind(F,$thf( J )),bind(G,$thf( Q @ ( P @ equivalent ) @ ( O @ ( O @ equivalent ) @ equivalent ) )),bind(H,$thf( P )),bind(I,$thf( I ))]]) ).

thf(420,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[365]) ).

thf(3033,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( J @ ( I @ equivalent ) @ ( H @ ( I @ equivalent ) @ equivalent ) @ ( J @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[420,125]) ).

thf(3034,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( J @ ( I @ equivalent ) @ ( H @ ( I @ equivalent ) @ equivalent ) @ ( J @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3033]) ).

thf(3035,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3034:[bind(A,$thf( ZD @ ( ZC @ equivalent ) )),bind(B,$thf( L @ ( ZC @ equivalent ) )),bind(C,$thf( Z )),bind(D,$thf( ZA )),bind(E,$thf( ZD @ ( ZC @ equivalent ) )),bind(F,$thf( ZD @ ( ZC @ equivalent ) @ ( ZA @ equivalent ) @ ( Z @ ( Z @ equivalent ) @ equivalent ) @ ( ZD @ ( ZC @ equivalent ) @ ( ZA @ equivalent ) @ equivalent ) )),bind(G,$thf( ZC )),bind(H,$thf( L )),bind(I,$thf( ZC )),bind(J,$thf( ZD ))]]) ).

thf(3175,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3035]) ).

thf(3567,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[3566]) ).

thf(3690,plain,
    ! [B: $i,A: $i] :
      ( ( B != a )
      | ( B
       != ( b @ ( b @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[3567]) ).

thf(3691,plain,
    ! [A: $i] :
      ( ( ( b @ ( b @ equivalent ) )
       != a )
      | ( ( A @ ( A @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[3690]) ).

thf(3692,plain,
    ! [A: $i] :
      ( ( a != a )
      | ( ( b @ ( b @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != a ) ),
    inference(eqfactor_ordered,[status(thm)],[3691]) ).

thf(3693,plain,
    ( ( b @ ( b @ equivalent ) )
   != a ),
    inference(pattern_uni,[status(thm)],[3692:[bind(A,$thf( b ))]]) ).

thf(144,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[124,7]) ).

thf(145,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[144]) ).

thf(161,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[145]) ).

thf(3759,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) )
       != c )
      | ( ( B @ ( C @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[161]) ).

thf(5467,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) )
       != c )
      | ( B != c )
      | ( C
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3759]) ).

thf(5753,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ ( B @ ( A @ equivalent ) @ ( c @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[5467]) ).

thf(6006,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( F @ equivalent ) @ ( c @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( G @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[47,5753]) ).

thf(6007,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( F @ equivalent ) @ ( c @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( G @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6006]) ).

thf(6008,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ ( A @ ( c @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[6007:[bind(A,$thf( c )),bind(B,$thf( D )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I )),bind(F,$thf( I @ ( D @ equivalent ) )),bind(G,$thf( C ))]]) ).

thf(6079,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ ( A @ ( c @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6008]) ).

thf(6694,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( G @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( F @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[416,6079]) ).

thf(6695,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( G @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( F @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[6694]) ).

thf(6696,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(pattern_uni,[status(thm)],[6695:[bind(A,$thf( c )),bind(B,$thf( ZE @ ( ZD @ equivalent ) @ ( ZC @ ( ZD @ equivalent ) @ equivalent ) )),bind(C,$thf( ZD )),bind(D,$thf( ZC )),bind(E,$thf( ZE )),bind(F,$thf( c @ ( ZE @ ( ZD @ equivalent ) @ ( ZC @ ( ZD @ equivalent ) @ equivalent ) @ ( ZE @ ( ZC @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( ZE @ ( ZD @ equivalent ) @ ( ZC @ ( ZD @ equivalent ) @ equivalent ) ))]]) ).

thf(6894,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[6696]) ).

thf(1587,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1509,7]) ).

thf(1588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1587]) ).

thf(1601,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[1588]) ).

thf(2569,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) )
       != c )
      | ( ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1601]) ).

thf(2570,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) )
       != c )
      | ( A != c )
      | ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[2569]) ).

thf(2571,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) )
       != c )
      | ( ( c @ ( A @ ( A @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[2570]) ).

thf(2573,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) )
       != c )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[2571]) ).

thf(2574,plain,
    ! [B: $i,A: $i] :
      ( ( c != c )
      | ( ( B @ ( B @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != a ) ),
    inference(eqfactor_ordered,[status(thm)],[2573]) ).

thf(2575,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[2574]) ).

thf(14534,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ ( c @ ( E @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[221,9091]) ).

thf(14535,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ ( c @ ( E @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[14534]) ).

thf(14536,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[14535:[bind(A,$thf( c @ ( O @ equivalent ) @ ( K @ ( K @ equivalent ) @ equivalent ) )),bind(B,$thf( c @ ( O @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) )),bind(C,$thf( K )),bind(D,$thf( K @ ( K @ equivalent ) )),bind(E,$thf( O ))]]) ).

thf(14757,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[14536]) ).

thf(18711,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( G @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( G @ equivalent ) @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[47,14757]) ).

thf(18712,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( G @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( G @ equivalent ) @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[18711]) ).

thf(18713,plain,
    ! [A: $i] :
      ~ ( c @ ( c @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[18712:[bind(A,$thf( c @ ( E @ equivalent ) )),bind(B,$thf( E )),bind(C,$thf( c )),bind(D,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )),bind(E,$thf( E )),bind(F,$thf( E )),bind(G,$thf( E ))]]) ).

thf(18801,plain,
    ! [A: $i] :
      ~ ( c @ ( c @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[18713]) ).

thf(18874,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[938,18801]) ).

thf(18875,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[18874]) ).

thf(19044,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) )
     != ( c @ ( c @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[18875]) ).

thf(5807,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5116,7]) ).

thf(5808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[5807]) ).

thf(5834,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[5808]) ).

thf(20466,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
       != c )
      | ( ( A @ ( B @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[5834]) ).

thf(20468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
       != c )
      | ( A != c )
      | ( B
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[20466]) ).

thf(20469,plain,
    ! [A: $i] :
      ( ( A @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[20468]) ).

thf(703,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( D @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( D @ ( H @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[575,47]) ).

thf(704,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( D @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( D @ ( H @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[703]) ).

thf(705,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[704:[bind(A,$thf( L )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L @ ( K @ equivalent ) )),bind(E,$thf( K )),bind(F,$thf( L )),bind(G,$thf( J @ ( J @ equivalent ) )),bind(H,$thf( H ))]]) ).

thf(709,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[705]) ).

thf(1328,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[709,48]) ).

thf(1329,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1328]) ).

thf(1330,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1329:[bind(A,$thf( Z )),bind(B,$thf( X )),bind(C,$thf( L @ ( ZB @ ( M @ equivalent ) @ equivalent ) )),bind(D,$thf( Z @ ( ZB @ ( ZB @ equivalent ) @ equivalent ) )),bind(E,$thf( Z @ ( ZB @ ( ZB @ equivalent ) @ equivalent ) @ ( Z @ ( X @ ( X @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( L )),bind(G,$thf( M )),bind(H,$thf( Z )),bind(I,$thf( ZB )),bind(J,$thf( ZB ))]]) ).

thf(1346,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1330]) ).

thf(1387,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( D @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( D @ ( H @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1346,47]) ).

thf(1388,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( D @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( D @ ( H @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1387]) ).

thf(1389,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1388:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( J )),bind(E,$thf( A )),bind(F,$thf( J @ ( L @ ( L @ equivalent ) @ equivalent ) )),bind(G,$thf( A )),bind(H,$thf( H ))]]) ).

thf(1396,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1389]) ).

thf(8333,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[1396,7714]) ).

thf(8334,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8333]) ).

thf(8335,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8334:[bind(A,$thf( a )),bind(B,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) )),bind(C,$thf( c )),bind(D,$thf( V )),bind(E,$thf( E )),bind(F,$thf( c @ ( V @ ( V @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ))]]) ).

thf(8622,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8335]) ).

thf(924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[894,7]) ).

thf(925,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[924]) ).

thf(935,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[925]) ).

thf(1731,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != c )
      | ( ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[935]) ).

thf(1732,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[1731]) ).

thf(1734,plain,
    ! [B: $i,A: $i] :
      ( ( c != c )
      | ( ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1732]) ).

thf(1735,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
     != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ),
    inference(simp,[status(thm)],[1734]) ).

thf(11324,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( C @ equivalent ) @ is_a_theorem ) )
      | ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[715,221]) ).

thf(11325,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( C @ equivalent ) @ is_a_theorem ) )
      | ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11324]) ).

thf(11326,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11325:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( G @ ( G @ equivalent ) )),bind(D,$thf( I @ ( I @ equivalent ) )),bind(E,$thf( E ))]]) ).

thf(11684,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11326]) ).

thf(8467,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[528,7714]) ).

thf(8468,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8467]) ).

thf(8469,plain,
    ! [A: $i] :
      ~ ( c @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8468:[bind(A,$thf( A )),bind(B,$thf( c )),bind(C,$thf( I )),bind(D,$thf( A )),bind(E,$thf( c @ ( I @ ( I @ equivalent ) @ equivalent ) ))]]) ).

thf(8603,plain,
    ! [A: $i] :
      ~ ( c @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8469]) ).

thf(8697,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[938,8603]) ).

thf(8698,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) @ is_a_theorem )
     != ( c @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8697]) ).

thf(8848,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) )
     != ( c @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[8698]) ).

thf(26832,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != ( c @ ( C @ equivalent ) ) )
      | ( A
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[9077]) ).

thf(26833,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( B @ equivalent ) ) ),
    inference(simp,[status(thm)],[26832]) ).

thf(698,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[575,7]) ).

thf(699,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[698]) ).

thf(707,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[699]) ).

thf(1612,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != c )
      | ( ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[707]) ).

thf(1613,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) )
     != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[1612]) ).

thf(203,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[171,7]) ).

thf(204,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[203]) ).

thf(220,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[204]) ).

thf(320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[220]) ).

thf(4730,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3494,48]) ).

thf(4731,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[4730]) ).

thf(4732,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[4731:[bind(A,$thf( ZH @ ( ZF @ ( ZF @ equivalent ) @ ( ZI @ ( ZJ @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( ZH @ ( ZJ @ ( ZI @ equivalent ) @ equivalent ) )),bind(C,$thf( ZJ )),bind(D,$thf( ZF )),bind(E,$thf( ZH @ ( ZJ @ ( ZI @ equivalent ) @ equivalent ) @ ( ZH @ ( ZF @ ( ZF @ equivalent ) @ ( ZI @ ( ZJ @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZF @ ( ZF @ equivalent ) )),bind(G,$thf( ZJ )),bind(H,$thf( ZH )),bind(I,$thf( ZI )),bind(J,$thf( ZJ ))]]) ).

thf(4760,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[4732]) ).

thf(13,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[10,7]) ).

thf(14,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[13]) ).

thf(15,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[14]) ).

thf(22,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D != c )
      | ( ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[15]) ).

thf(23,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[22]) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c != c )
      | ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[23]) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ),
    inference(simp,[status(thm)],[24]) ).

thf(46,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) )
       != A )
      | ~ ( A @ is_a_theorem )
      | ( B @ is_a_theorem ) ),
    inference(simp,[status(thm)],[44]) ).

thf(248,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( ( E @ ( D @ equivalent ) )
       != D )
      | ~ $true
      | ( E @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[166,46]) ).

thf(249,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( ( E @ ( D @ equivalent ) )
       != D )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[248]) ).

thf(250,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[249:[bind(A,$thf( L )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( O @ ( N @ equivalent ) @ ( L @ equivalent ) @ ( O @ ( N @ equivalent ) @ ( L @ equivalent ) @ equivalent ) )),bind(E,$thf( E ))]]) ).

thf(257,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[250]) ).

thf(9012,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( F @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[47,8619]) ).

thf(9013,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( F @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9012]) ).

thf(9014,plain,
    ! [A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[9013:[bind(A,$thf( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )),bind(B,$thf( D )),bind(C,$thf( c )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( H @ ( D @ equivalent ) ))]]) ).

thf(9092,plain,
    ! [A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[9014]) ).

thf(9106,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[715,9092]) ).

thf(9107,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9106]) ).

thf(9283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[9107]) ).

thf(31276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[9283]) ).

thf(9383,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[710,194]) ).

thf(9384,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9383]) ).

thf(9385,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[9384:[bind(A,$thf( R @ ( Z @ ( Z @ equivalent ) @ ( W @ equivalent ) @ equivalent ) @ ( W @ equivalent ) )),bind(B,$thf( R )),bind(C,$thf( W )),bind(D,$thf( Z )),bind(E,$thf( R @ ( R @ ( Z @ ( Z @ equivalent ) @ ( W @ equivalent ) @ equivalent ) @ ( W @ equivalent ) @ equivalent ) )),bind(F,$thf( W )),bind(G,$thf( Z @ ( Z @ equivalent ) @ ( W @ equivalent ) )),bind(H,$thf( R ))]]) ).

thf(9578,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[9385]) ).

thf(11548,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[9578,221]) ).

thf(11549,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11548]) ).

thf(11550,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11549:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( J @ ( N @ ( N @ equivalent ) @ ( K @ equivalent ) @ equivalent ) @ ( K @ equivalent ) )),bind(E,$thf( J )),bind(F,$thf( F ))]]) ).

thf(11667,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11550]) ).

thf(8878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( C @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[715,8619]) ).

thf(8879,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( C @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8878]) ).

thf(9040,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( C @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[8879]) ).

thf(26552,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) )
       != ( c @ ( C @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[9040]) ).

thf(211,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true
      | ~ ( E @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[171,9]) ).

thf(212,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ ( E @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[211]) ).

thf(213,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[212:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( M @ ( O @ ( O @ equivalent ) @ equivalent ) @ ( J @ equivalent ) @ ( M @ ( J @ equivalent ) @ equivalent ) )),bind(E,$thf( E ))]]) ).

thf(222,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[213]) ).

thf(12765,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( G @ ( H @ ( H @ equivalent ) @ equivalent ) @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[710,222]) ).

thf(12766,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( G @ ( H @ ( H @ equivalent ) @ equivalent ) @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[12765]) ).

thf(12767,plain,
    ! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[12766:[bind(A,$thf( N @ ( R @ ( R @ equivalent ) @ equivalent ) )),bind(B,$thf( N )),bind(C,$thf( R @ ( R @ equivalent ) )),bind(D,$thf( R )),bind(E,$thf( N @ ( N @ ( R @ ( R @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( R @ ( R @ equivalent ) )),bind(G,$thf( N )),bind(H,$thf( R @ ( R @ equivalent ) ))]]) ).

thf(12991,plain,
    ! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[12767]) ).

thf(13115,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( C @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ ( G @ ( F @ equivalent ) @ ( E @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[12991,168]) ).

thf(13116,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( C @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ ( G @ ( F @ equivalent ) @ ( E @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[13115]) ).

thf(13117,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ ( A @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[13116:[bind(A,$thf( K @ ( M @ ( M @ equivalent ) @ equivalent ) )),bind(B,$thf( M )),bind(C,$thf( M @ ( M @ equivalent ) )),bind(D,$thf( K )),bind(E,$thf( M @ ( M @ equivalent ) )),bind(F,$thf( F )),bind(G,$thf( K ))]]) ).

thf(13170,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ ( A @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[13117]) ).

thf(1769,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1114,48]) ).

thf(1770,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1769]) ).

thf(1771,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1770:[bind(A,$thf( R @ ( Z @ equivalent ) )),bind(B,$thf( ZB @ ( ZA @ ( Z @ ( Z @ equivalent ) @ equivalent ) @ equivalent ) )),bind(C,$thf( ZA )),bind(D,$thf( ZB )),bind(E,$thf( ZB @ ( ZA @ equivalent ) @ ( ZB @ ( ZA @ ( Z @ ( Z @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZA )),bind(G,$thf( Z )),bind(H,$thf( ZB )),bind(I,$thf( Z )),bind(J,$thf( R ))]]) ).

thf(1785,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1771]) ).

thf(1819,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1785,7]) ).

thf(1820,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1819]) ).

thf(1832,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[1820]) ).

thf(8652,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[715,8603]) ).

thf(8653,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8652]) ).

thf(8858,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[8653]) ).

thf(24608,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) )
       != ( c @ ( C @ ( C @ equivalent ) @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[8858]) ).

thf(29,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ $true
      | ~ ( F @ ( E @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[10,9]) ).

thf(30,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ ( F @ ( E @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[29]) ).

thf(31,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( B @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( Q )),bind(B,$thf( S )),bind(C,$thf( T )),bind(D,$thf( H )),bind(E,$thf( H @ ( H @ ( T @ ( S @ equivalent ) @ ( T @ ( Q @ equivalent ) @ ( S @ ( Q @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(52,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( B @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[31]) ).

thf(8483,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3494,7714]) ).

thf(8484,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8483]) ).

thf(8485,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8484:[bind(A,$thf( A )),bind(B,$thf( c )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( A )),bind(F,$thf( c @ ( N @ ( N @ equivalent ) @ ( L @ ( L @ equivalent ) @ equivalent ) @ equivalent ) ))]]) ).

thf(8610,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8485]) ).

thf(272,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( F @ equivalent ) @ ( E @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[193,124]) ).

thf(273,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( F @ equivalent ) @ ( E @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[272]) ).

thf(284,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( G @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) ) )
      | ( G @ ( F @ equivalent ) @ ( E @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[273]) ).

thf(3070,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[226,125]) ).

thf(3071,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3070]) ).

thf(3072,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3071:[bind(A,$thf( K @ ( X @ equivalent ) )),bind(B,$thf( S )),bind(C,$thf( Y @ ( X @ equivalent ) )),bind(D,$thf( Y @ ( X @ equivalent ) )),bind(E,$thf( Y @ ( X @ equivalent ) @ ( Y @ ( X @ equivalent ) @ equivalent ) @ ( S @ ( S @ equivalent ) @ equivalent ) )),bind(F,$thf( X )),bind(G,$thf( K )),bind(H,$thf( X )),bind(I,$thf( Y ))]]) ).

thf(3146,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3072]) ).

thf(3214,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3146,7]) ).

thf(3215,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3214]) ).

thf(3232,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[3215]) ).

thf(3312,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[3232]) ).

thf(175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[166,7]) ).

thf(176,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[175]) ).

thf(192,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[176]) ).

thf(197,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) )
       != c )
      | ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[192]) ).

thf(198,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ equivalent ) )
       != c )
      | ( ( C @ ( B @ equivalent ) )
       != c )
      | ( A
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[197]) ).

thf(199,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[198]) ).

thf(227,plain,
    ! [B: $i,A: $i] :
      ( ( c != c )
      | ( ( B @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( B @ ( A @ equivalent ) ) )
      | ( ( B @ ( A @ equivalent ) )
       != c ) ),
    inference(eqfactor_ordered,[status(thm)],[199]) ).

thf(228,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( B @ ( A @ equivalent ) ) )
      | ( ( B @ ( A @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[227]) ).

thf(8156,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[5116,7714]) ).

thf(8157,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8156]) ).

thf(8158,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8157:[bind(A,$thf( c )),bind(B,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )),bind(C,$thf( W )),bind(D,$thf( D )),bind(E,$thf( W @ ( W @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) ))]]) ).

thf(8632,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8158]) ).

thf(16,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[11,7]) ).

thf(17,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[16]) ).

thf(18,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[17]) ).

thf(56,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E != c )
      | ( ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[18]) ).

thf(57,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[56]) ).

thf(292,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) )
       != E )
      | ~ $true
      | ( F @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[226,46]) ).

thf(293,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) )
       != E )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[292]) ).

thf(294,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( M )),bind(B,$thf( R )),bind(C,$thf( S )),bind(D,$thf( T )),bind(E,$thf( T @ ( S @ equivalent ) @ ( R @ ( R @ equivalent ) @ equivalent ) @ ( T @ ( M @ equivalent ) @ ( S @ ( M @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(316,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[294]) ).

thf(11631,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[575,221]) ).

thf(11632,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11631]) ).

thf(11633,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11632:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N @ ( M @ equivalent ) @ ( L @ ( L @ equivalent ) @ ( M @ equivalent ) @ equivalent ) )),bind(E,$thf( N )),bind(F,$thf( F ))]]) ).

thf(11716,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11633]) ).

thf(146,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[11,124]) ).

thf(147,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[146]) ).

thf(148,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( ZH )),bind(B,$thf( ZL )),bind(C,$thf( ZM )),bind(D,$thf( ZK )),bind(E,$thf( Y @ ( ZK @ ( ZM @ ( ZL @ equivalent ) @ equivalent ) @ ( ZK @ ( ZM @ ( ZH @ equivalent ) @ ( ZL @ ( ZH @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZK @ ( ZM @ ( ZL @ equivalent ) @ equivalent ) @ ( ZK @ ( ZM @ ( ZH @ equivalent ) @ ( ZL @ ( ZH @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( Y @ ( ZK @ ( ZM @ ( ZL @ equivalent ) @ equivalent ) @ ( ZK @ ( ZM @ ( ZH @ equivalent ) @ ( ZL @ ( ZH @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(H,$thf( H )),bind(I,$thf( Y ))]]) ).

thf(164,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[148]) ).

thf(2903,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( K @ ( J @ equivalent ) @ equivalent ) @ ( G @ ( K @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ ( I @ ( G @ ( J @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[420,48]) ).

thf(2904,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( K @ ( J @ equivalent ) @ equivalent ) @ ( G @ ( K @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ ( I @ ( G @ ( J @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[2903]) ).

thf(2905,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[2904:[bind(A,$thf( ZE )),bind(B,$thf( M @ ( ZG @ ( N @ equivalent ) @ equivalent ) )),bind(C,$thf( ZA )),bind(D,$thf( ZB )),bind(E,$thf( ZE @ ( ZG @ ( ZG @ equivalent ) @ equivalent ) )),bind(F,$thf( ZE @ ( ZG @ ( ZG @ equivalent ) @ equivalent ) @ ( ZB @ equivalent ) @ ( ZA @ ( ZA @ equivalent ) @ equivalent ) @ ( ZE @ ( ZB @ equivalent ) @ equivalent ) )),bind(G,$thf( M )),bind(H,$thf( N )),bind(I,$thf( ZE )),bind(J,$thf( ZG )),bind(K,$thf( ZG ))]]) ).

thf(2928,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[2905]) ).

thf(3330,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2928,124]) ).

thf(3331,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3330]) ).

thf(3332,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3331:[bind(A,$thf( N )),bind(B,$thf( N @ ( N @ equivalent ) )),bind(C,$thf( P )),bind(D,$thf( R )),bind(E,$thf( N @ ( N @ equivalent ) )),bind(F,$thf( P )),bind(G,$thf( G )),bind(H,$thf( P @ ( R @ ( R @ equivalent ) @ equivalent ) @ ( N @ ( N @ equivalent ) @ equivalent ) ))]]) ).

thf(3362,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3332]) ).

thf(6824,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3362,6079]) ).

thf(6825,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[6824]) ).

thf(6826,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(pattern_uni,[status(thm)],[6825:[bind(A,$thf( L @ ( L @ equivalent ) )),bind(B,$thf( P )),bind(C,$thf( c )),bind(D,$thf( T )),bind(E,$thf( c @ ( T @ ( T @ equivalent ) @ equivalent ) @ ( P @ ( P @ equivalent ) @ equivalent ) @ ( L @ ( L @ equivalent ) @ equivalent ) )),bind(F,$thf( L ))]]) ).

thf(6895,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[6826]) ).

thf(11312,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5116,221]) ).

thf(11313,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11312]) ).

thf(11314,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11313:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( K @ ( L @ equivalent ) )),bind(E,$thf( N @ ( N @ equivalent ) @ ( L @ ( K @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11676,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11314]) ).

thf(346,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[163,7]) ).

thf(347,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ equivalent ) @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[346]) ).

thf(348,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ equivalent ) @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[347]) ).

thf(9335,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( E @ equivalent ) @ ( G @ ( F @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5116,194]) ).

thf(9336,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( E @ equivalent ) @ ( G @ ( F @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9335]) ).

thf(9337,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[9336:[bind(A,$thf( ZA @ ( Z @ equivalent ) @ ( X @ equivalent ) )),bind(B,$thf( ZA @ ( Z @ equivalent ) @ ( X @ equivalent ) )),bind(C,$thf( ZC )),bind(D,$thf( ZC @ ( ZC @ equivalent ) @ ( ZA @ ( Z @ equivalent ) @ ( X @ equivalent ) @ ( ZA @ ( Z @ equivalent ) @ ( X @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( X )),bind(F,$thf( Z )),bind(G,$thf( ZA ))]]) ).

thf(9616,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[9337]) ).

thf(1094,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[943,7]) ).

thf(1095,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1094]) ).

thf(1108,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[1095]) ).

thf(1796,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) )
       != c )
      | ( ( C @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1108]) ).

thf(112,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[75,7]) ).

thf(113,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[112]) ).

thf(123,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[113]) ).

thf(128,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) )
       != c )
      | ( ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[123]) ).

thf(3564,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) )
       != c )
      | ( ( D @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[128]) ).

thf(3750,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c != c )
      | ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) )
       != ( D @ ( A @ equivalent ) ) )
      | ( ( D @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[3564]) ).

thf(3752,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) )
       != ( D @ ( A @ equivalent ) ) )
      | ( ( D @ ( A @ equivalent ) )
       != c )
      | ( B
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( A != a ) ),
    inference(simp,[status(thm)],[3750]) ).

thf(3756,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
       != ( B @ ( a @ equivalent ) ) )
      | ( ( B @ ( a @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[3752]) ).

thf(9112,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[638,9092]) ).

thf(9113,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9112]) ).

thf(9272,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[9113]) ).

thf(8188,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[638,7714]) ).

thf(8189,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8188]) ).

thf(8190,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8189:[bind(A,$thf( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )),bind(B,$thf( P )),bind(C,$thf( C )),bind(D,$thf( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( P @ ( P @ equivalent ) @ equivalent ) ))]]) ).

thf(8638,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8190]) ).

thf(13616,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( E @ ( E @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[221,8638]) ).

thf(13617,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( E @ ( E @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[13616]) ).

thf(13618,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[13617:[bind(A,$thf( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( K @ ( K @ equivalent ) @ equivalent ) @ ( U @ ( U @ equivalent ) @ equivalent ) )),bind(B,$thf( c )),bind(C,$thf( U )),bind(D,$thf( U @ ( U @ equivalent ) )),bind(E,$thf( K ))]]) ).

thf(13838,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[13618]) ).

thf(19,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[12,7]) ).

thf(20,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[19]) ).

thf(21,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[20]) ).

thf(61,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != c )
      | ( ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[21]) ).

thf(310,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[226,7]) ).

thf(311,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[310]) ).

thf(312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[311]) ).

thf(71,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[11,51]) ).

thf(72,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[71]) ).

thf(74,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( F @ ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[72]) ).

thf(307,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ is_a_theorem ) )
      | ~ ( E @ is_a_theorem )
      | ~ ( E @ is_a_theorem )
      | ( F @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[226,45]) ).

thf(308,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ is_a_theorem ) )
      | ~ ( E @ is_a_theorem )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[307]) ).

thf(309,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( K )),bind(B,$thf( P )),bind(C,$thf( Q )),bind(D,$thf( R )),bind(E,$thf( R @ ( K @ equivalent ) @ ( Q @ ( K @ equivalent ) @ equivalent ) )),bind(F,$thf( R @ ( Q @ equivalent ) @ ( P @ ( P @ equivalent ) @ equivalent ) ))]]) ).

thf(315,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[309]) ).

thf(27939,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ( F @ ( E @ equivalent ) @ ( D @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[715,315]) ).

thf(27940,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( E @ equivalent ) @ ( D @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[27939]) ).

thf(27941,plain,
    ! [B: $i,A: $i] : ( A @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[27940:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( B ))]]) ).

thf(28476,plain,
    ! [B: $i,A: $i] : ( A @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[27941]) ).

thf(28690,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[28476,7]) ).

thf(28691,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[28690]) ).

thf(28772,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[28691]) ).

thf(6969,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[710,168]) ).

thf(6970,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6969]) ).

thf(6971,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[6970:[bind(A,$thf( A )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( O )),bind(E,$thf( A )),bind(F,$thf( K )),bind(G,$thf( L )),bind(H,$thf( H )),bind(I,$thf( K @ ( O @ ( O @ equivalent ) @ ( L @ equivalent ) @ equivalent ) ))]]) ).

thf(7217,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[6971]) ).

thf(1736,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( ( B @ ( A @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[1735]) ).

thf(9320,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c @ ( B @ ( B @ equivalent ) @ equivalent ) ) )
      | ( A
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[8848]) ).

thf(9321,plain,
    ! [A: $i] :
      ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != ( c @ ( A @ ( A @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[9320]) ).

thf(9322,plain,
    ! [A: $i] :
      ( ( c != c )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[9321]) ).

thf(9323,plain,
    ! [A: $i] :
      ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
     != ( A @ ( A @ equivalent ) ) ),
    inference(simp,[status(thm)],[9322]) ).

thf(58,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c != c )
      | ( ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[57]) ).

thf(59,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ),
    inference(simp,[status(thm)],[58]) ).

thf(60,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[59]) ).

thf(9472,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( E @ equivalent ) @ ( G @ ( F @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1785,194]) ).

thf(9473,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( E @ equivalent ) @ ( G @ ( F @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9472]) ).

thf(9474,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[9473:[bind(A,$thf( Y )),bind(B,$thf( ZA @ ( Z @ equivalent ) )),bind(C,$thf( ZA @ ( Z @ equivalent ) @ ( Y @ ( Y @ equivalent ) @ equivalent ) )),bind(D,$thf( ZA @ ( Z @ equivalent ) @ ( Y @ ( Y @ equivalent ) @ equivalent ) @ ( ZA @ ( Z @ equivalent ) @ equivalent ) )),bind(E,$thf( Y @ ( Y @ equivalent ) )),bind(F,$thf( Z )),bind(G,$thf( ZA ))]]) ).

thf(9555,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[9474]) ).

thf(10502,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[9555,8605]) ).

thf(10503,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[10502]) ).

thf(10504,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[10503:[bind(A,$thf( O )),bind(B,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )),bind(C,$thf( c )),bind(D,$thf( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( O @ ( O @ equivalent ) @ equivalent ) )),bind(E,$thf( E ))]]) ).

thf(10811,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[10504]) ).

thf(1376,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1346,7]) ).

thf(1377,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1376]) ).

thf(1390,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[1377]) ).

thf(1898,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) )
       != c )
      | ( ( B @ ( A @ ( A @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1390]) ).

thf(1899,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) )
       != c )
      | ( B != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1898]) ).

thf(1900,plain,
    ! [B: $i,A: $i] :
      ( ( ( c @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1899]) ).

thf(13204,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( E @ ( E @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[221,8632]) ).

thf(13205,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( E @ ( E @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[13204]) ).

thf(13206,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[13205:[bind(A,$thf( S @ ( S @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) @ ( U @ ( U @ equivalent ) @ equivalent ) )),bind(B,$thf( c )),bind(C,$thf( U )),bind(D,$thf( U @ ( U @ equivalent ) )),bind(E,$thf( S ))]]) ).

thf(13423,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[13206]) ).

thf(12484,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( c @ ( E @ ( E @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[221,8622]) ).

thf(12485,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( c @ ( E @ ( E @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[12484]) ).

thf(12486,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[12485:[bind(A,$thf( c @ ( S @ ( S @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( U @ ( U @ equivalent ) @ equivalent ) )),bind(B,$thf( c )),bind(C,$thf( U )),bind(D,$thf( U @ ( U @ equivalent ) )),bind(E,$thf( S ))]]) ).

thf(12700,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[12486]) ).

thf(132,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[124,124]) ).

thf(133,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[132]) ).

thf(134,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ equivalent ) @ ( B @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( C )),bind(F,$thf( B )),bind(G,$thf( G )),bind(H,$thf( D ))]]) ).

thf(165,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ equivalent ) @ ( B @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[134]) ).

thf(6704,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ equivalent ) @ ( B @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true
      | ~ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[165,6079]) ).

thf(6705,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ equivalent ) @ ( B @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6704]) ).

thf(6706,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ ( B @ ( A @ equivalent ) @ ( c @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[6705:[bind(A,$thf( A )),bind(B,$thf( c )),bind(C,$thf( J )),bind(D,$thf( L @ ( L @ equivalent ) )),bind(E,$thf( J @ ( L @ ( L @ equivalent ) @ equivalent ) )),bind(F,$thf( L ))]]) ).

thf(6897,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ ( B @ ( A @ equivalent ) @ ( c @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6706]) ).

thf(236,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) )
       != E )
      | ~ $true
      | ( F @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[124,46]) ).

thf(237,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) )
       != E )
      | ( F @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[236]) ).

thf(238,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) ) )
      | ( B @ is_a_theorem )
      | ~ ( E @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( L @ ( K @ equivalent ) @ ( J @ ( K @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(260,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) ) )
      | ( B @ is_a_theorem )
      | ~ ( E @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[238]) ).

thf(334,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( G @ is_a_theorem )
      | ~ $true
      | ~ ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[163,9]) ).

thf(335,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( G @ is_a_theorem )
      | ~ ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[334]) ).

thf(336,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( F @ ( E @ equivalent ) @ ( F @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[335:[bind(A,$thf( X )),bind(B,$thf( Y )),bind(C,$thf( T )),bind(D,$thf( V )),bind(E,$thf( W )),bind(F,$thf( Y @ ( X @ equivalent ) @ ( Y @ ( W @ ( V @ equivalent ) @ ( W @ ( T @ equivalent ) @ ( V @ ( T @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( X @ equivalent ) @ equivalent ) )),bind(G,$thf( G ))]]) ).

thf(349,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( F @ ( E @ equivalent ) @ ( F @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[336]) ).

thf(13028,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( C @ equivalent ) @ is_a_theorem ) )
      | ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[12991,221]) ).

thf(13029,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( C @ equivalent ) @ is_a_theorem ) )
      | ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[13028]) ).

thf(13030,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[13029:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( G @ ( I @ ( I @ equivalent ) @ equivalent ) )),bind(D,$thf( G )),bind(E,$thf( E ))]]) ).

thf(13158,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[13030]) ).

thf(1483,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[749,124]) ).

thf(1484,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1483]) ).

thf(1485,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1484:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( J @ ( L @ equivalent ) )),bind(F,$thf( L @ ( L @ equivalent ) )),bind(G,$thf( G )),bind(H,$thf( N @ ( N @ equivalent ) ))]]) ).

thf(1508,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1485]) ).

thf(1546,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1508,51]) ).

thf(1547,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1546]) ).

thf(1548,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1547:[bind(A,$thf( U @ ( T @ equivalent ) @ ( U @ ( T @ equivalent ) @ equivalent ) )),bind(B,$thf( U )),bind(C,$thf( W )),bind(D,$thf( W @ ( W @ equivalent ) @ ( U @ ( T @ equivalent ) @ ( U @ ( T @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( T )),bind(F,$thf( U )),bind(G,$thf( U ))]]) ).

thf(1557,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1548]) ).

thf(1643,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1557,7]) ).

thf(1644,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1643]) ).

thf(1656,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[1644]) ).

thf(2873,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1656]) ).

thf(62,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D != a )
      | ( ( C @ ( B @ equivalent ) )
       != ( b @ ( b @ equivalent ) ) )
      | ( ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[60]) ).

thf(63,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) )
       != ( b @ ( b @ equivalent ) ) )
      | ( ( a @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[62]) ).

thf(64,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C != b )
      | ( B != b )
      | ( ( a @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[63]) ).

thf(65,plain,
    ! [A: $i] :
      ( ( a @ ( b @ ( A @ equivalent ) @ ( b @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
     != a ),
    inference(simp,[status(thm)],[64]) ).

thf(4693,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3494,125]) ).

thf(4694,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[4693]) ).

thf(4695,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[4694:[bind(A,$thf( ZI @ ( ZF @ equivalent ) @ ( ZE @ ( ZE @ equivalent ) @ ( ZF @ equivalent ) @ equivalent ) )),bind(B,$thf( ZI @ ( ZK @ ( ZK @ equivalent ) @ equivalent ) )),bind(C,$thf( ZK )),bind(D,$thf( ZE )),bind(E,$thf( ZI @ ( ZK @ ( ZK @ equivalent ) @ equivalent ) @ ( ZI @ ( ZF @ equivalent ) @ ( ZE @ ( ZE @ equivalent ) @ ( ZF @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZF )),bind(G,$thf( ZE @ ( ZE @ equivalent ) )),bind(H,$thf( ZK @ ( ZK @ equivalent ) )),bind(I,$thf( ZI ))]]) ).

thf(4757,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[4695]) ).

thf(323,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
       != c )
      | ( B != c )
      | ( A
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[320]) ).

thf(324,plain,
    ! [A: $i] :
      ( ( c @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[323]) ).

thf(9344,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3175,194]) ).

thf(9345,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9344]) ).

thf(9346,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[9345:[bind(A,$thf( R )),bind(B,$thf( ZB @ ( ZA @ equivalent ) @ ( Y @ equivalent ) )),bind(C,$thf( Y )),bind(D,$thf( ZB @ ( ZA @ equivalent ) )),bind(E,$thf( ZB @ ( ZA @ equivalent ) @ ( Y @ equivalent ) @ ( ZB @ ( ZA @ equivalent ) @ ( Y @ equivalent ) @ equivalent ) @ ( R @ ( R @ equivalent ) @ equivalent ) )),bind(F,$thf( Y )),bind(G,$thf( ZA )),bind(H,$thf( ZB ))]]) ).

thf(9554,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[9346]) ).

thf(1829,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( D @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( D @ ( H @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1785,47]) ).

thf(1830,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( D @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( D @ ( H @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1829]) ).

thf(1831,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1830:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( L )),bind(E,$thf( J @ ( J @ equivalent ) )),bind(F,$thf( L @ ( K @ equivalent ) )),bind(G,$thf( K )),bind(H,$thf( H ))]]) ).

thf(1837,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1831]) ).

thf(1225,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( F @ ( F @ ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[629,52]) ).

thf(1226,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( F @ ( F @ ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1225]) ).

thf(1227,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1226:[bind(A,$thf( ZU @ ( ZT @ equivalent ) @ ( ZS @ ( ZT @ equivalent ) @ equivalent ) )),bind(B,$thf( ZO @ ( ZU @ ( ZT @ equivalent ) @ ( ZS @ ( ZT @ equivalent ) @ equivalent ) @ equivalent ) )),bind(C,$thf( ZU @ ( ZS @ equivalent ) )),bind(D,$thf( ZO )),bind(E,$thf( ZO @ ( ZU @ ( ZT @ equivalent ) @ ( ZS @ ( ZT @ equivalent ) @ equivalent ) @ equivalent ) @ ( ZO @ ( ZU @ ( ZS @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZO @ ( ZU @ ( ZT @ equivalent ) @ ( ZS @ ( ZT @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( ZT )),bind(H,$thf( ZS )),bind(I,$thf( ZU ))]]) ).

thf(1291,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1227]) ).

thf(1373,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( F @ ( H @ ( E @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1346,49]) ).

thf(1374,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( F @ ( H @ ( E @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1373]) ).

thf(1375,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1374:[bind(A,$thf( ZR @ ( ZQ @ equivalent ) @ ( ZP @ ( ZQ @ equivalent ) @ equivalent ) )),bind(B,$thf( ZR @ ( ZQ @ equivalent ) @ ( ZP @ ( ZQ @ equivalent ) @ equivalent ) @ ( ZR @ ( ZP @ equivalent ) @ equivalent ) )),bind(C,$thf( ZH )),bind(D,$thf( ZR @ ( ZQ @ equivalent ) @ ( ZP @ ( ZQ @ equivalent ) @ equivalent ) @ ( ZR @ ( ZP @ equivalent ) @ equivalent ) @ ( ZH @ ( ZH @ equivalent ) @ equivalent ) )),bind(E,$thf( ZQ )),bind(F,$thf( ZR @ ( ZQ @ equivalent ) @ ( ZP @ ( ZQ @ equivalent ) @ equivalent ) )),bind(G,$thf( ZP )),bind(H,$thf( ZR ))]]) ).

thf(1402,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1375]) ).

thf(6927,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[709,168]) ).

thf(6928,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6927]) ).

thf(6929,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( B @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[6928:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( M @ ( M @ equivalent ) )),bind(D,$thf( D )),bind(E,$thf( K @ ( M @ ( M @ equivalent ) @ equivalent ) )),bind(F,$thf( D )),bind(G,$thf( M @ ( M @ equivalent ) )),bind(H,$thf( H )),bind(I,$thf( D ))]]) ).

thf(7205,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( B @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[6929]) ).

thf(1538,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1508,7]) ).

thf(1539,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1538]) ).

thf(1552,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[1539]) ).

thf(2153,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( B @ equivalent ) @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1552]) ).

thf(2154,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( B @ equivalent ) )
       != c )
      | ( A
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[2153]) ).

thf(2155,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[2154]) ).

thf(2356,plain,
    ! [B: $i,A: $i] :
      ( ( c != c )
      | ( ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != c ) ),
    inference(eqfactor_ordered,[status(thm)],[2155]) ).

thf(2358,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) )
       != A )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != A )
      | ( ( A @ ( A @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[2356]) ).

thf(2359,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[2358]) ).

thf(8925,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( B @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[938,8619]) ).

thf(8926,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) @ is_a_theorem )
     != ( c @ ( B @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8925]) ).

thf(9066,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) )
     != ( c @ ( B @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[8926]) ).

thf(9327,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c @ ( B @ equivalent ) ) )
      | ( A
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[9066]) ).

thf(9328,plain,
    ! [A: $i] :
      ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
     != ( c @ ( A @ equivalent ) ) ),
    inference(simp,[status(thm)],[9327]) ).

thf(53,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[25]) ).

thf(280,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[193,7]) ).

thf(281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[280]) ).

thf(282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[281]) ).

thf(356,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) )
       != c )
      | ( ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[282]) ).

thf(27948,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ( H @ ( G @ equivalent ) @ ( F @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[709,315]) ).

thf(27949,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[27948]) ).

thf(27950,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[27949:[bind(A,$thf( J )),bind(B,$thf( N )),bind(C,$thf( N @ ( N @ equivalent ) )),bind(D,$thf( L )),bind(E,$thf( J @ ( N @ ( N @ equivalent ) @ equivalent ) )),bind(F,$thf( F )),bind(G,$thf( L @ ( N @ ( N @ equivalent ) @ equivalent ) )),bind(H,$thf( L ))]]) ).

thf(28480,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[27950]) ).

thf(775,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[750,7]) ).

thf(776,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[775]) ).

thf(783,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[776]) ).

thf(245,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) )
       != E )
      | ~ $true
      | ( F @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[75,46]) ).

thf(246,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) )
       != E )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[245]) ).

thf(247,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[246:[bind(A,$thf( M )),bind(B,$thf( R )),bind(C,$thf( S )),bind(D,$thf( T )),bind(E,$thf( T @ ( S @ equivalent ) @ ( R @ ( S @ equivalent ) @ equivalent ) @ ( T @ ( M @ equivalent ) @ ( R @ ( M @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(256,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[247]) ).

thf(76,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != c )
      | ( D != c )
      | ( ( C @ ( B @ ( A @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[61]) ).

thf(77,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( D @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != c )
      | ( ( C @ ( B @ ( A @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[76]) ).

thf(8462,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[575,7714]) ).

thf(8463,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8462]) ).

thf(8464,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8463:[bind(A,$thf( c @ ( Q @ ( Q @ equivalent ) @ ( N @ equivalent ) @ equivalent ) )),bind(B,$thf( Q )),bind(C,$thf( N )),bind(D,$thf( Q @ ( Q @ equivalent ) @ ( N @ equivalent ) )),bind(E,$thf( c @ ( Q @ ( Q @ equivalent ) @ ( N @ equivalent ) @ equivalent ) @ ( N @ equivalent ) ))]]) ).

thf(8602,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8464]) ).

thf(10260,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( G @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ ( F @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[47,8602]) ).

thf(10261,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( G @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ ( F @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[10260]) ).

thf(10262,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( A @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[10261:[bind(A,$thf( c )),bind(B,$thf( a )),bind(C,$thf( c @ ( ZC @ ( ZC @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( V @ equivalent ) @ equivalent ) @ equivalent ) )),bind(D,$thf( V )),bind(E,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) )),bind(F,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( V @ equivalent ) )),bind(G,$thf( ZC ))]]) ).

thf(10342,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( A @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[10262]) ).

thf(26554,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != c )
      | ( B != C )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[26552]) ).

thf(26585,plain,
    ! [A: $i] :
      ( ( A @ ( A @ equivalent ) )
     != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( c @ equivalent ) ) ),
    inference(simp,[status(thm)],[26554]) ).

thf(3010,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[709,125]) ).

thf(3011,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3010]) ).

thf(3012,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3011:[bind(A,$thf( Y @ ( X @ equivalent ) )),bind(B,$thf( U )),bind(C,$thf( K @ ( X @ equivalent ) )),bind(D,$thf( Y @ ( X @ equivalent ) )),bind(E,$thf( Y @ ( X @ equivalent ) @ ( Y @ ( X @ equivalent ) @ ( U @ ( U @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( X )),bind(G,$thf( K )),bind(H,$thf( X )),bind(I,$thf( Y ))]]) ).

thf(3168,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3012]) ).

thf(3278,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3168,7]) ).

thf(3279,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3278]) ).

thf(3294,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[3279]) ).

thf(7314,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[7205,7]) ).

thf(7315,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[7314]) ).

thf(7352,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[7315]) ).

thf(22617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != c )
      | ( ( A @ ( B @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[7352]) ).

thf(22618,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[22617]) ).

thf(24851,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c @ ( C @ ( C @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) )
      | ( ( B @ ( B @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[24608]) ).

thf(24865,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c != c )
      | ( ( C @ ( C @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
      | ( B != A )
      | ( B != A )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[24851]) ).

thf(24868,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[24865]) ).

thf(25774,plain,
    ! [B: $i,A: $i] :
      ( ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
      | ( ( B @ ( B @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[24868]) ).

thf(25777,plain,
    ! [B: $i,A: $i] :
      ( ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
      | ( B != A )
      | ( B != A )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[25774]) ).

thf(25794,plain,
    ! [A: $i] :
      ( ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[25777]) ).

thf(8200,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3152,7714]) ).

thf(8201,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8200]) ).

thf(8202,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8201:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( C )),bind(D,$thf( c )),bind(E,$thf( C )),bind(F,$thf( c @ ( M @ equivalent ) @ ( L @ ( L @ equivalent ) @ ( M @ equivalent ) @ equivalent ) ))]]) ).

thf(8599,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8202]) ).

thf(1446,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[710,51]) ).

thf(1447,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1446]) ).

thf(1448,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1447:[bind(A,$thf( V @ ( ZH @ ( ZH @ equivalent ) @ ( ZE @ equivalent ) @ equivalent ) @ ( ZA @ equivalent ) @ ( ZE @ ( ZA @ equivalent ) @ equivalent ) )),bind(B,$thf( V )),bind(C,$thf( ZE )),bind(D,$thf( ZH )),bind(E,$thf( V @ ( V @ ( ZH @ ( ZH @ equivalent ) @ ( ZE @ equivalent ) @ equivalent ) @ ( ZA @ equivalent ) @ ( ZE @ ( ZA @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZA )),bind(G,$thf( ZE )),bind(H,$thf( V @ ( ZH @ ( ZH @ equivalent ) @ ( ZE @ equivalent ) @ equivalent ) ))]]) ).

thf(1456,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1448]) ).

thf(25781,plain,
    ! [B: $i,A: $i] :
      ( ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) )
       != c )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != a )
      | ( B != A )
      | ( B != A )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[25774]) ).

thf(25797,plain,
    ! [A: $i] :
      ( ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) )
       != c )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != a )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[25781]) ).

thf(2874,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) )
       != c )
      | ( ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1832]) ).

thf(3243,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) )
       != c )
      | ( C != c )
      | ( ( B @ ( A @ ( A @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[2874]) ).

thf(3244,plain,
    ! [B: $i,A: $i] :
      ( ( ( c @ ( B @ equivalent ) )
       != c )
      | ( ( B @ ( A @ ( A @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[3243]) ).

thf(3246,plain,
    ! [B: $i,A: $i] :
      ( ( ( c @ ( B @ equivalent ) )
       != c )
      | ( B
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[3244]) ).

thf(3247,plain,
    ! [A: $i] :
      ( ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[3246]) ).

thf(9541,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3494,194]) ).

thf(9542,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9541]) ).

thf(9543,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[9542:[bind(A,$thf( ZH @ ( ZG @ equivalent ) @ ( ZD @ ( ZD @ equivalent ) @ ( ZB @ ( ZB @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( ZH @ ( ZG @ equivalent ) )),bind(C,$thf( ZB )),bind(D,$thf( ZD )),bind(E,$thf( ZH @ ( ZG @ equivalent ) @ ( ZH @ ( ZG @ equivalent ) @ ( ZD @ ( ZD @ equivalent ) @ ( ZB @ ( ZB @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZD @ ( ZD @ equivalent ) @ ( ZB @ ( ZB @ equivalent ) @ equivalent ) )),bind(G,$thf( ZG )),bind(H,$thf( ZH ))]]) ).

thf(9598,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[9543]) ).

thf(589,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[226,48]) ).

thf(590,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( F @ ( J @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ ( H @ ( F @ ( I @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[589]) ).

thf(591,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[590:[bind(A,$thf( L @ ( ZB @ ( M @ equivalent ) @ equivalent ) )),bind(B,$thf( V )),bind(C,$thf( Z )),bind(D,$thf( Z @ ( ZB @ ( ZB @ equivalent ) @ equivalent ) )),bind(E,$thf( Z @ ( ZB @ ( ZB @ equivalent ) @ equivalent ) @ ( Z @ equivalent ) @ ( V @ ( V @ equivalent ) @ equivalent ) )),bind(F,$thf( L )),bind(G,$thf( M )),bind(H,$thf( Z )),bind(I,$thf( ZB )),bind(J,$thf( ZB ))]]) ).

thf(632,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[591]) ).

thf(815,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[632,7]) ).

thf(816,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[815]) ).

thf(824,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[816]) ).

thf(1720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[824]) ).

thf(24161,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[11667,7714]) ).

thf(24162,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[24161]) ).

thf(24163,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[24162:[bind(A,$thf( N )),bind(B,$thf( c )),bind(C,$thf( N @ ( N @ equivalent ) )),bind(D,$thf( L )),bind(E,$thf( N @ ( N @ equivalent ) )),bind(F,$thf( c @ ( L @ ( L @ equivalent ) @ ( N @ ( N @ equivalent ) @ equivalent ) @ equivalent ) ))]]) ).

thf(24298,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[24163]) ).

thf(3749,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) )
       != c )
      | ( ( D @ ( A @ equivalent ) )
       != c )
      | ( B
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( A != a ) ),
    inference(simp,[status(thm)],[3564]) ).

thf(3755,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
       != c )
      | ( ( B @ ( a @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[3749]) ).

thf(93,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( ( G @ ( F @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ~ $true
      | ( G @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[11,45]) ).

thf(94,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( ( G @ ( F @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( G @ is_a_theorem ) ),
    inference(simp,[status(thm)],[93]) ).

thf(95,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( B @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( T )),bind(B,$thf( X )),bind(C,$thf( Y )),bind(D,$thf( W )),bind(E,$thf( I )),bind(F,$thf( I @ ( I @ ( W @ ( Y @ ( X @ equivalent ) @ equivalent ) @ ( W @ ( Y @ ( T @ equivalent ) @ ( X @ ( T @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( G ))]]) ).

thf(105,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( B @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[95]) ).

thf(10357,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[5116,8605]) ).

thf(10358,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[10357]) ).

thf(10359,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[10358:[bind(A,$thf( c )),bind(B,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )),bind(C,$thf( W )),bind(D,$thf( W @ ( W @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) )),bind(E,$thf( E ))]]) ).

thf(10819,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( c @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[10359]) ).

thf(5937,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( c @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( F @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2928,5753]) ).

thf(5938,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( c @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( F @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[5937]) ).

thf(5939,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(pattern_uni,[status(thm)],[5938:[bind(A,$thf( L )),bind(B,$thf( L @ ( L @ equivalent ) )),bind(C,$thf( c )),bind(D,$thf( P )),bind(E,$thf( L @ ( L @ equivalent ) )),bind(F,$thf( c @ ( P @ ( P @ equivalent ) @ equivalent ) @ ( L @ ( L @ equivalent ) @ equivalent ) ))]]) ).

thf(6070,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[5939]) ).

thf(5051,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4754,125]) ).

thf(5052,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[5051]) ).

thf(5053,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[5052:[bind(A,$thf( ZG @ ( ZG @ equivalent ) @ ( ZD @ equivalent ) @ ( ZC @ ( ZC @ equivalent ) @ ( ZD @ equivalent ) @ equivalent ) )),bind(B,$thf( ZC )),bind(C,$thf( C )),bind(D,$thf( ZG )),bind(E,$thf( ZG @ ( ZG @ equivalent ) @ ( ZD @ equivalent ) @ ( ZC @ ( ZC @ equivalent ) @ ( ZD @ equivalent ) @ equivalent ) )),bind(F,$thf( C )),bind(G,$thf( ZC @ ( ZC @ equivalent ) )),bind(H,$thf( ZD )),bind(I,$thf( ZG @ ( ZG @ equivalent ) ))]]) ).

thf(5119,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[5053]) ).

thf(6614,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5119,7]) ).

thf(6615,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6614]) ).

thf(6647,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[6615]) ).

thf(6816,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[790,6079]) ).

thf(6817,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[6816]) ).

thf(6818,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(pattern_uni,[status(thm)],[6817:[bind(A,$thf( M )),bind(B,$thf( c )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( c @ ( N @ ( M @ equivalent ) @ equivalent ) @ ( M @ ( N @ equivalent ) @ equivalent ) )),bind(F,$thf( M ))]]) ).

thf(6891,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[6818]) ).

thf(8227,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[1291,7714]) ).

thf(8228,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8227]) ).

thf(8229,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( a @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8228:[bind(A,$thf( c )),bind(B,$thf( a )),bind(C,$thf( Q )),bind(D,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) )),bind(E,$thf( E )),bind(F,$thf( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( Q @ equivalent ) @ ( a @ ( Q @ equivalent ) @ equivalent ) @ equivalent ) ))]]) ).

thf(8609,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( a @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8229]) ).

thf(22622,plain,
    ! [B: $i,A: $i] :
      ( ( ( c @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( B @ equivalent ) @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[22618]) ).

thf(1614,plain,
    ! [B: $i,A: $i] :
      ( ( ( c @ ( B @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) @ ( B @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1613]) ).

thf(1615,plain,
    ! [B: $i,A: $i] :
      ( ( ( c @ ( B @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( B != a ) ),
    inference(simp,[status(thm)],[1614]) ).

thf(1616,plain,
    ! [A: $i] :
      ( ( ( c @ ( a @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1615]) ).

thf(5822,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5116,51]) ).

thf(5823,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[5822]) ).

thf(5824,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[5823:[bind(A,$thf( ZA @ ( Y @ equivalent ) )),bind(B,$thf( ZA @ ( Z @ equivalent ) @ ( Y @ ( Z @ equivalent ) @ equivalent ) )),bind(C,$thf( ZC )),bind(D,$thf( ZC @ ( ZC @ equivalent ) @ ( ZA @ ( Z @ equivalent ) @ ( Y @ ( Z @ equivalent ) @ equivalent ) @ ( ZA @ ( Y @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( Z )),bind(F,$thf( Y )),bind(G,$thf( ZA ))]]) ).

thf(5840,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[5824]) ).

thf(66,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[10,51]) ).

thf(67,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[66]) ).

thf(73,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[67]) ).

thf(3475,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( D @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( D @ ( H @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3428,47]) ).

thf(3476,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( D @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( D @ ( H @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3475]) ).

thf(3477,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3476:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( A )),bind(E,$thf( J @ ( J @ equivalent ) )),bind(F,$thf( A )),bind(G,$thf( L @ ( L @ equivalent ) )),bind(H,$thf( H ))]]) ).

thf(3491,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3477]) ).

thf(4135,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( D @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3491,125]) ).

thf(4136,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( D @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[4135]) ).

thf(4137,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[4136:[bind(A,$thf( ZE @ ( ZD @ equivalent ) @ ( ZC @ ( ZD @ equivalent ) @ equivalent ) )),bind(B,$thf( ZE @ ( ZC @ equivalent ) )),bind(C,$thf( ZC )),bind(D,$thf( W )),bind(E,$thf( ZE @ ( ZD @ equivalent ) @ ( ZC @ ( ZD @ equivalent ) @ equivalent ) @ ( ZE @ ( ZC @ equivalent ) @ ( W @ ( W @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZC )),bind(G,$thf( ZC )),bind(H,$thf( ZD )),bind(I,$thf( ZE ))]]) ).

thf(4184,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[4137]) ).

thf(2931,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[2873]) ).

thf(2933,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c != c )
      | ( ( C @ ( C @ equivalent ) )
       != ( B @ ( A @ equivalent ) ) )
      | ( ( B @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[2931]) ).

thf(2934,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(pattern_uni,[status(thm)],[2933:[bind(A,$thf( C )),bind(B,$thf( C ))]]) ).

thf(2936,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[2934]) ).

thf(1726,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( D @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != c )
      | ( C
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( ( B @ ( A @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[77]) ).

thf(1727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[1726]) ).

thf(6950,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[894,168]) ).

thf(6951,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6950]) ).

thf(6952,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( B @ ( A @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[6951:[bind(A,$thf( P @ ( V @ ( U @ equivalent ) @ ( V @ ( U @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( U )),bind(C,$thf( V )),bind(D,$thf( V @ ( U @ equivalent ) @ ( V @ ( U @ equivalent ) @ equivalent ) )),bind(E,$thf( P )),bind(F,$thf( V @ ( U @ equivalent ) @ ( V @ ( U @ equivalent ) @ equivalent ) )),bind(G,$thf( G )),bind(H,$thf( P ))]]) ).

thf(7212,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( B @ ( A @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[6952]) ).

thf(11595,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1508,221]) ).

thf(11596,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11595]) ).

thf(11597,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11596:[bind(A,$thf( K )),bind(B,$thf( J )),bind(C,$thf( N )),bind(D,$thf( J @ ( J @ equivalent ) @ ( K @ equivalent ) )),bind(E,$thf( N @ ( N @ equivalent ) @ ( K @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11693,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11597]) ).

thf(277,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ~ ( D @ is_a_theorem )
      | ~ ( D @ is_a_theorem )
      | ( E @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[193,45]) ).

thf(278,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ~ ( D @ is_a_theorem )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[277]) ).

thf(279,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ( C @ ( B @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[278:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( M @ ( J @ equivalent ) @ ( L @ ( J @ equivalent ) @ equivalent ) )),bind(E,$thf( M @ ( L @ equivalent ) ))]]) ).

thf(286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ( C @ ( B @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[279]) ).

thf(24916,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[11667,286]) ).

thf(24917,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[24916]) ).

thf(24918,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[24917:[bind(A,$thf( O )),bind(B,$thf( I )),bind(C,$thf( O @ ( O @ equivalent ) )),bind(D,$thf( M )),bind(E,$thf( O @ ( O @ equivalent ) )),bind(F,$thf( I @ ( M @ ( M @ equivalent ) @ ( O @ ( O @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( I ))]]) ).

thf(25224,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[24918]) ).

thf(13077,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[12991,7]) ).

thf(13078,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[13077]) ).

thf(13135,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[13078]) ).

thf(3818,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( E @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[938,161]) ).

thf(3819,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( E @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[3818]) ).

thf(3820,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(pattern_uni,[status(thm)],[3819:[bind(A,$thf( G @ ( F @ equivalent ) )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( G ))]]) ).

thf(4000,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[3820]) ).

thf(1764,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ ( I @ ( F @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1114,49]) ).

thf(1765,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ ( I @ ( F @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1764]) ).

thf(1766,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1765:[bind(A,$thf( ZD )),bind(B,$thf( ZG @ ( ZD @ equivalent ) @ ( ZF @ ( ZB @ equivalent ) @ ( ZD @ ( ZB @ equivalent ) @ equivalent ) @ equivalent ) )),bind(C,$thf( ZF )),bind(D,$thf( ZG )),bind(E,$thf( ZG @ ( ZF @ equivalent ) @ ( ZG @ ( ZD @ equivalent ) @ ( ZF @ ( ZB @ equivalent ) @ ( ZD @ ( ZB @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZB )),bind(G,$thf( ZG @ ( ZD @ equivalent ) )),bind(H,$thf( ZD )),bind(I,$thf( ZF ))]]) ).

thf(1784,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1766]) ).

thf(5010,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4978,7]) ).

thf(5011,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[5010]) ).

thf(5029,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[5011]) ).

thf(5121,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[5029]) ).

thf(8658,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[638,8603]) ).

thf(8659,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
     != ( c @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8658]) ).

thf(8809,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
     != ( c @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[8659]) ).

thf(736,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[715,7]) ).

thf(737,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[736]) ).

thf(743,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[737]) ).

thf(535,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) )
       != c )
      | ( ( C @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[356]) ).

thf(536,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) )
       != c )
      | ( ( C @ ( A @ equivalent ) )
       != c )
      | ( B
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( A != a ) ),
    inference(simp,[status(thm)],[535]) ).

thf(539,plain,
    ! [A: $i] :
      ( ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ equivalent ) )
       != c )
      | ( ( A @ ( a @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[536]) ).

thf(576,plain,
    ! [A: $i] :
      ( ( c != c )
      | ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( A @ ( a @ equivalent ) ) )
      | ( ( A @ ( a @ equivalent ) )
       != c ) ),
    inference(eqfactor_ordered,[status(thm)],[539]) ).

thf(577,plain,
    ! [A: $i] :
      ( ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( A @ ( a @ equivalent ) ) )
      | ( ( A @ ( a @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[576]) ).

thf(251,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( ( E @ ( D @ equivalent ) )
       != D )
      | ~ $true
      | ( E @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[171,46]) ).

thf(252,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( ( E @ ( D @ equivalent ) )
       != D )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[251]) ).

thf(253,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[252:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( M @ ( O @ ( O @ equivalent ) @ equivalent ) @ ( J @ equivalent ) @ ( M @ ( J @ equivalent ) @ equivalent ) )),bind(E,$thf( E ))]]) ).

thf(259,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[253]) ).

thf(27636,plain,
    ! [A: $i] :
      ( ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) )
      | ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[25794]) ).

thf(27644,plain,
    ! [A: $i] :
      ( ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[27636]) ).

thf(29086,plain,
    ! [A: $i] :
      ( ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[27644]) ).

thf(29089,plain,
    ! [A: $i] :
      ( ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) )
       != c )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != a )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[29086]) ).

thf(3754,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) )
       != D )
      | ( ( B @ ( C @ equivalent ) )
       != A )
      | ( ( D @ ( A @ equivalent ) )
       != c )
      | ( B
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) ) )
      | ( A != a ) ),
    inference(simp,[status(thm)],[3750]) ).

thf(3758,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) )
       != B )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
       != a )
      | ( ( B @ ( a @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[3754]) ).

thf(26557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c @ ( C @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) )
      | ( ( B @ ( B @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ equivalent ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[26552]) ).

thf(26560,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c @ ( C @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) )
      | ( B
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) )
      | ( B != C )
      | ( A
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) )
      | ( A != C ) ),
    inference(simp,[status(thm)],[26557]) ).

thf(26572,plain,
    ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) )
   != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[26560]) ).

thf(6707,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1837,6079]) ).

thf(6708,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[6707]) ).

thf(6709,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(pattern_uni,[status(thm)],[6708:[bind(A,$thf( P @ ( P @ equivalent ) )),bind(B,$thf( P )),bind(C,$thf( Q )),bind(D,$thf( c )),bind(E,$thf( c @ ( Q @ equivalent ) @ ( P @ ( P @ equivalent ) @ ( Q @ equivalent ) @ equivalent ) )),bind(F,$thf( P @ ( P @ equivalent ) ))]]) ).

thf(6898,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[6709]) ).

thf(290,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[226,51]) ).

thf(291,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[290]) ).

thf(313,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[291]) ).

thf(11533,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1509,221]) ).

thf(11534,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11533]) ).

thf(11535,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11534:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( H @ ( H @ ( L @ ( L @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( N @ ( N @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11662,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11535]) ).

thf(20915,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) @ ( B @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[6647]) ).

thf(537,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c != c )
      | ( ( C @ ( B @ equivalent ) )
       != ( C @ ( A @ equivalent ) ) )
      | ( ( C @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[535]) ).

thf(538,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( B ))]]) ).

thf(540,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[538]) ).

thf(11560,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1785,221]) ).

thf(11561,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11560]) ).

thf(11562,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11561:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ ( L @ ( L @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( N @ ( M @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11671,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11562]) ).

thf(3467,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3428,48]) ).

thf(3468,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3467]) ).

thf(3469,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3468:[bind(A,$thf( ZQ @ ( ZQ @ equivalent ) @ ( ZO @ ( ZN @ equivalent ) @ equivalent ) @ ( ZN @ ( ZJ @ equivalent ) @ ( ZO @ ( ZJ @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( ZN @ ( ZJ @ equivalent ) )),bind(C,$thf( ZQ )),bind(D,$thf( ZQ @ ( ZQ @ equivalent ) @ ( ZO @ ( ZN @ equivalent ) @ equivalent ) @ ( ZN @ ( ZJ @ equivalent ) @ ( ZO @ ( ZJ @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( ZN @ ( ZJ @ equivalent ) )),bind(F,$thf( ZJ )),bind(G,$thf( ZQ @ ( ZQ @ equivalent ) )),bind(H,$thf( ZN )),bind(I,$thf( ZO ))]]) ).

thf(3487,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3469]) ).

thf(2116,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1402,124]) ).

thf(2117,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[2116]) ).

thf(2118,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[2117:[bind(A,$thf( P @ ( N @ equivalent ) )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( P @ ( N @ equivalent ) )),bind(F,$thf( P @ ( N @ equivalent ) )),bind(G,$thf( G )),bind(H,$thf( P @ ( O @ equivalent ) @ ( N @ ( O @ equivalent ) @ equivalent ) ))]]) ).

thf(2148,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[2118]) ).

thf(968,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[938,7]) ).

thf(969,plain,
    ! [A: $i] :
      ( ( A @ ( A @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[968]) ).

thf(979,plain,
    ! [A: $i] :
      ( ( A @ ( A @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[969]) ).

thf(1407,plain,
    ! [B: $i,A: $i] :
      ( ( A != A )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != ( B @ ( B @ equivalent ) ) )
      | ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[1405]) ).

thf(1408,plain,
    ! [B: $i,A: $i] :
      ( ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != ( B @ ( B @ equivalent ) ) )
      | ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[1407]) ).

thf(229,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) )
       != B )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != A )
      | ( ( B @ ( A @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[227]) ).

thf(230,plain,
    ! [A: $i] :
      ( ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != A )
      | ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[229]) ).

thf(298,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ $true
      | ~ ( F @ ( E @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[226,9]) ).

thf(299,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ ( F @ ( E @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[298]) ).

thf(300,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[299:[bind(A,$thf( M )),bind(B,$thf( R )),bind(C,$thf( S )),bind(D,$thf( T )),bind(E,$thf( T @ ( S @ equivalent ) @ ( R @ ( R @ equivalent ) @ equivalent ) @ ( T @ ( M @ equivalent ) @ ( S @ ( M @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(318,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[300]) ).

thf(11634,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[528,221]) ).

thf(11635,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11634]) ).

thf(11636,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11635:[bind(A,$thf( M )),bind(B,$thf( N )),bind(C,$thf( L )),bind(D,$thf( N @ ( L @ ( L @ equivalent ) @ equivalent ) @ ( M @ equivalent ) )),bind(E,$thf( N @ ( M @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11718,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11636]) ).

thf(4201,plain,
    ! [B: $i,A: $i] :
      ( ( B != a )
      | ( ( B @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) ) )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
       != a )
      | ( ( B @ ( a @ equivalent ) )
       != c ) ),
    inference(eqfactor_ordered,[status(thm)],[3758]) ).

thf(4203,plain,
    ! [A: $i] :
      ( ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
       != ( a @ ( A @ equivalent ) ) )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
       != a )
      | ( ( a @ ( a @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[4201]) ).

thf(22863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) )
       != c )
      | ( ( A @ ( B @ equivalent ) )
       != c )
      | ( ( A @ ( B @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[22861]) ).

thf(580,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( K @ ( J @ equivalent ) @ equivalent ) @ ( G @ ( K @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ ( I @ ( G @ ( J @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[352,48]) ).

thf(581,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( I @ ( K @ ( J @ equivalent ) @ equivalent ) @ ( G @ ( K @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ ( I @ ( G @ ( J @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[580]) ).

thf(582,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[581:[bind(A,$thf( ZZA @ ( ZZ @ equivalent ) @ ( ZZA @ ( ZX @ equivalent ) @ ( ZZ @ ( ZX @ equivalent ) @ equivalent ) @ equivalent ) @ ( ZQ @ ( ZQ @ equivalent ) @ equivalent ) )),bind(B,$thf( ZX )),bind(C,$thf( ZZ )),bind(D,$thf( ZZA )),bind(E,$thf( M @ ( ZQ @ ( N @ equivalent ) @ equivalent ) )),bind(F,$thf( ZZA @ ( ZZ @ equivalent ) @ ( ZZA @ ( ZX @ equivalent ) @ ( ZZ @ ( ZX @ equivalent ) @ equivalent ) @ equivalent ) @ ( ZQ @ ( ZQ @ equivalent ) @ equivalent ) )),bind(G,$thf( M )),bind(H,$thf( N )),bind(I,$thf( ZZA @ ( ZZ @ equivalent ) @ ( ZZA @ ( ZX @ equivalent ) @ ( ZZ @ ( ZX @ equivalent ) @ equivalent ) @ equivalent ) )),bind(J,$thf( ZQ )),bind(K,$thf( ZQ ))]]) ).

thf(626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[582]) ).

thf(660,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[638,7]) ).

thf(661,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[660]) ).

thf(668,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[661]) ).

thf(8323,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[943,7714]) ).

thf(8324,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[8323]) ).

thf(8325,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[8324:[bind(A,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )),bind(B,$thf( V )),bind(C,$thf( c )),bind(D,$thf( D )),bind(E,$thf( c @ ( V @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( V @ equivalent ) @ equivalent ) ))]]) ).

thf(8620,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( A @ equivalent ) @ ( c @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[8325]) ).

thf(23619,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != ( c @ ( C @ ( C @ equivalent ) @ equivalent ) ) )
      | ( A
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[8809]) ).

thf(23620,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != ( c @ ( B @ ( B @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[23619]) ).

thf(3392,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3152,124]) ).

thf(3393,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( H @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3392]) ).

thf(3394,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3393:[bind(A,$thf( N )),bind(B,$thf( O )),bind(C,$thf( C )),bind(D,$thf( P )),bind(E,$thf( C )),bind(F,$thf( P @ ( O @ equivalent ) @ ( N @ ( N @ equivalent ) @ ( O @ equivalent ) @ equivalent ) )),bind(G,$thf( G )),bind(H,$thf( P ))]]) ).

thf(3423,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3394]) ).

thf(214,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( ( E @ ( D @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ~ $true
      | ( E @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[171,45]) ).

thf(215,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( ( E @ ( D @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[214]) ).

thf(216,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( M @ ( O @ ( O @ equivalent ) @ equivalent ) @ ( J @ equivalent ) @ ( M @ ( J @ equivalent ) @ equivalent ) )),bind(E,$thf( E ))]]) ).

thf(223,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[216]) ).

thf(10139,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ equivalent ) @ ( B @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( F @ ( F @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[165,8602]) ).

thf(10140,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ equivalent ) @ ( B @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( F @ ( F @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[10139]) ).

thf(10141,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( c @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[10140:[bind(A,$thf( A )),bind(B,$thf( c )),bind(C,$thf( c @ ( ZD @ ( ZD @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) )),bind(D,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )),bind(E,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )),bind(F,$thf( ZD ))]]) ).

thf(10343,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( c @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[10141]) ).

thf(15222,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( E @ ( E @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ ( c @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[221,10343]) ).

thf(15223,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( E @ ( E @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ ( c @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[15222]) ).

thf(15224,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[15223:[bind(A,$thf( c @ ( I @ ( I @ equivalent ) @ equivalent ) )),bind(B,$thf( c @ ( U @ ( U @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) )),bind(C,$thf( I )),bind(D,$thf( I @ ( I @ equivalent ) )),bind(E,$thf( U ))]]) ).

thf(15447,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[15224]) ).

thf(19224,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( G @ ( G @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[47,15447]) ).

thf(19225,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( c @ ( G @ ( G @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[19224]) ).

thf(19226,plain,
    ! [A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[19225:[bind(A,$thf( c )),bind(B,$thf( O @ ( O @ equivalent ) )),bind(C,$thf( c )),bind(D,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )),bind(E,$thf( O @ ( O @ equivalent ) )),bind(F,$thf( O @ ( O @ equivalent ) )),bind(G,$thf( O ))]]) ).

thf(19316,plain,
    ! [A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[19226]) ).

thf(19389,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[938,19316]) ).

thf(19390,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[19389]) ).

thf(19516,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[19390]) ).

thf(7173,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3494,168]) ).

thf(7174,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[7173]) ).

thf(7175,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( B @ equivalent ) @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[7174:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( M )),bind(D,$thf( O )),bind(E,$thf( A )),bind(F,$thf( B )),bind(G,$thf( O @ ( O @ equivalent ) @ ( M @ ( M @ equivalent ) @ equivalent ) )),bind(H,$thf( H )),bind(I,$thf( B ))]]) ).

thf(7200,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( B @ equivalent ) @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[7175]) ).

thf(135,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ~ $true
      | ( F @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[124,45]) ).

thf(136,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[135]) ).

thf(137,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( B @ is_a_theorem )
      | ~ ( E @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[136:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( L @ ( K @ equivalent ) @ ( J @ ( K @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(167,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( B @ is_a_theorem )
      | ~ ( E @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[137]) ).

thf(3403,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ ( I @ ( F @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3152,49]) ).

thf(3404,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ ( I @ ( F @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3403]) ).

thf(3405,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3404:[bind(A,$thf( ZG )),bind(B,$thf( ZH )),bind(C,$thf( W @ ( ZH @ equivalent ) @ ( ZG @ ( ZG @ equivalent ) @ ( ZD @ equivalent ) @ ( ZH @ ( ZD @ equivalent ) @ equivalent ) @ equivalent ) )),bind(D,$thf( W )),bind(E,$thf( W @ ( W @ ( ZH @ equivalent ) @ ( ZG @ ( ZG @ equivalent ) @ ( ZD @ equivalent ) @ ( ZH @ ( ZD @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZD )),bind(G,$thf( W @ ( ZH @ equivalent ) )),bind(H,$thf( ZH )),bind(I,$thf( ZG @ ( ZG @ equivalent ) ))]]) ).

thf(3427,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3405]) ).

thf(158,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ $true
      | ~ ( F @ ( E @ equivalent ) @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[124,9]) ).

thf(159,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( F @ is_a_theorem )
      | ~ ( F @ ( E @ equivalent ) @ is_a_theorem )
      | ~ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[158]) ).

thf(160,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ is_a_theorem )
      | ~ ( B @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( E @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( L @ ( K @ equivalent ) @ ( J @ ( K @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(162,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ is_a_theorem )
      | ~ ( B @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ ( E @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[160]) ).

thf(10422,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[1291,8605]) ).

thf(10423,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[10422]) ).

thf(10424,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( a @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[10423:[bind(A,$thf( c )),bind(B,$thf( a )),bind(C,$thf( Q )),bind(D,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) )),bind(E,$thf( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( Q @ equivalent ) @ ( a @ ( Q @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(10829,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( a @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[10424]) ).

thf(242,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( ( G @ ( F @ equivalent ) )
       != F )
      | ~ $true
      | ( G @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[11,46]) ).

thf(243,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( ( G @ ( F @ equivalent ) )
       != F )
      | ( G @ is_a_theorem ) ),
    inference(simp,[status(thm)],[242]) ).

thf(244,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( B @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( T )),bind(B,$thf( X )),bind(C,$thf( Y )),bind(D,$thf( W )),bind(E,$thf( I )),bind(F,$thf( I @ ( I @ ( W @ ( Y @ ( X @ equivalent ) @ equivalent ) @ ( W @ ( Y @ ( T @ equivalent ) @ ( X @ ( T @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( G ))]]) ).

thf(255,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( B @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[244]) ).

thf(10529,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( c @ ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[1396,8605]) ).

thf(10530,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( c @ ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[10529]) ).

thf(10531,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[10530:[bind(A,$thf( a )),bind(B,$thf( a @ ( b @ ( b @ equivalent ) @ equivalent ) )),bind(C,$thf( c )),bind(D,$thf( V )),bind(E,$thf( c @ ( V @ ( V @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(10814,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[10531]) ).

thf(11420,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[193,221]) ).

thf(11421,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11420]) ).

thf(11422,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11421:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( N @ ( K @ equivalent ) @ ( M @ ( K @ equivalent ) @ equivalent ) )),bind(E,$thf( N @ ( M @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11738,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11422]) ).

thf(3376,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) )
       != c )
      | ( ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[3294]) ).

thf(6947,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3152,168]) ).

thf(6948,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( I @ ( G @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( F @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6947]) ).

thf(6949,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[6948:[bind(A,$thf( M )),bind(B,$thf( N )),bind(C,$thf( C )),bind(D,$thf( O )),bind(E,$thf( C )),bind(F,$thf( O )),bind(G,$thf( M @ ( M @ equivalent ) @ ( N @ equivalent ) )),bind(H,$thf( H )),bind(I,$thf( O @ ( N @ equivalent ) ))]]) ).

thf(7211,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[6949]) ).

thf(6738,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( D @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3491,6079]) ).

thf(6739,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( D @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[6738]) ).

thf(6740,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(pattern_uni,[status(thm)],[6739:[bind(A,$thf( c )),bind(B,$thf( R @ ( R @ equivalent ) )),bind(C,$thf( R )),bind(D,$thf( P )),bind(E,$thf( c @ ( R @ ( R @ equivalent ) @ ( P @ ( P @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( R @ ( R @ equivalent ) ))]]) ).

thf(6902,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[6740]) ).

thf(11598,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[632,221]) ).

thf(11599,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11598]) ).

thf(11600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11599:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( H @ ( H @ equivalent ) )),bind(E,$thf( L @ ( N @ ( N @ equivalent ) @ equivalent ) @ ( L @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11600]) ).

thf(41,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( G @ is_a_theorem )
      | ~ $true
      | ~ ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[11,9]) ).

thf(42,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( G @ is_a_theorem )
      | ~ ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[41]) ).

thf(43,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( B @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( T )),bind(B,$thf( X )),bind(C,$thf( Y )),bind(D,$thf( W )),bind(E,$thf( I )),bind(F,$thf( I @ ( I @ ( W @ ( Y @ ( X @ equivalent ) @ equivalent ) @ ( W @ ( Y @ ( T @ equivalent ) @ ( X @ ( T @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( G ))]]) ).

thf(50,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ is_a_theorem )
      | ~ ( A @ ( B @ ( B @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( C @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[43]) ).

thf(1216,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( B @ ( C @ ( C @ ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( B @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[938,52]) ).

thf(1217,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( B @ ( C @ ( C @ ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( B @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1216]) ).

thf(1218,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1217:[bind(A,$thf( V @ ( V @ ( ZH @ ( ZG @ equivalent ) @ ( ZH @ ( ZE @ equivalent ) @ ( ZG @ ( ZE @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( V @ ( V @ ( ZH @ ( ZG @ equivalent ) @ ( ZH @ ( ZE @ equivalent ) @ ( ZG @ ( ZE @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(C,$thf( V )),bind(D,$thf( ZE )),bind(E,$thf( ZG )),bind(F,$thf( ZH ))]]) ).

thf(1285,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1218]) ).

thf(11530,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3146,221]) ).

thf(11531,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11530]) ).

thf(11532,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11531:[bind(A,$thf( H )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( H @ ( H @ equivalent ) )),bind(E,$thf( N @ ( M @ equivalent ) @ ( N @ ( M @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11661,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11532]) ).

thf(1700,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[790,51]) ).

thf(1701,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1700]) ).

thf(1702,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1701:[bind(A,$thf( ZB @ ( Y @ equivalent ) )),bind(B,$thf( ZB @ ( ZA @ equivalent ) )),bind(C,$thf( ZA @ ( Y @ equivalent ) )),bind(D,$thf( X )),bind(E,$thf( ZB @ ( ZA @ equivalent ) @ ( X @ ( ZA @ ( Y @ equivalent ) @ equivalent ) @ equivalent ) @ ( ZB @ ( Y @ equivalent ) @ ( X @ equivalent ) @ equivalent ) )),bind(F,$thf( Y )),bind(G,$thf( ZA )),bind(H,$thf( ZB ))]]) ).

thf(1710,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1702]) ).

thf(2393,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( A @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1710,51]) ).

thf(2394,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( A @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[2393]) ).

thf(2395,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[2394:[bind(A,$thf( ZB @ ( Y @ equivalent ) @ ( X @ ( Y @ equivalent ) @ equivalent ) )),bind(B,$thf( X )),bind(C,$thf( ZA )),bind(D,$thf( ZB )),bind(E,$thf( ZB @ ( ZA @ equivalent ) @ ( ZB @ ( Y @ equivalent ) @ ( X @ ( Y @ equivalent ) @ equivalent ) @ ( ZA @ ( X @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( Y )),bind(G,$thf( X )),bind(H,$thf( ZB ))]]) ).

thf(2411,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[2395]) ).

thf(2357,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( A @ ( A @ equivalent ) ) )
      | ( ( A @ ( A @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[2356]) ).

thf(9151,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[938,9092]) ).

thf(9152,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) @ is_a_theorem )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9151]) ).

thf(9257,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ equivalent ) )
     != ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) ) ),
    inference(simp,[status(thm)],[9152]) ).

thf(4200,plain,
    ! [B: $i,A: $i] :
      ( ( B != c )
      | ( ( B @ ( A @ equivalent ) )
       != ( B @ ( a @ equivalent ) ) )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
       != a )
      | ( ( B @ ( a @ equivalent ) )
       != c ) ),
    inference(eqfactor_ordered,[status(thm)],[3758]) ).

thf(4202,plain,
    ( ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
     != a )
    | ( ( c @ ( a @ equivalent ) )
     != c ) ),
    inference(pattern_uni,[status(thm)],[4200:[bind(A,$thf( a )),bind(B,$thf( c ))]]) ).

thf(304,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ~ $true
      | ( F @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[226,45]) ).

thf(305,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[304]) ).

thf(306,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( M )),bind(B,$thf( R )),bind(C,$thf( S )),bind(D,$thf( T )),bind(E,$thf( T @ ( S @ equivalent ) @ ( R @ ( R @ equivalent ) @ equivalent ) @ ( T @ ( M @ equivalent ) @ ( S @ ( M @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(314,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[306]) ).

thf(9418,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( D @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3491,194]) ).

thf(9419,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( D @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9418]) ).

thf(9420,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[9419:[bind(A,$thf( ZF @ ( ZE @ equivalent ) @ ( ZD @ ( ZD @ equivalent ) @ equivalent ) )),bind(B,$thf( ZF @ ( ZE @ equivalent ) )),bind(C,$thf( ZD )),bind(D,$thf( X )),bind(E,$thf( ZF @ ( ZE @ equivalent ) @ ( ZD @ ( ZD @ equivalent ) @ equivalent ) @ ( ZF @ ( ZE @ equivalent ) @ ( X @ ( X @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZD @ ( ZD @ equivalent ) )),bind(G,$thf( ZE )),bind(H,$thf( ZF ))]]) ).

thf(9601,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[9420]) ).

thf(6992,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3428,168]) ).

thf(6993,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( H @ ( G @ equivalent ) @ ( F @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6992]) ).

thf(6994,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( B @ ( A @ equivalent ) @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[6993:[bind(A,$thf( P @ ( V @ ( V @ equivalent ) @ ( T @ ( T @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( T )),bind(C,$thf( V )),bind(D,$thf( V @ ( V @ equivalent ) @ ( T @ ( T @ equivalent ) @ equivalent ) )),bind(E,$thf( P )),bind(F,$thf( V @ ( V @ equivalent ) @ ( T @ ( T @ equivalent ) @ equivalent ) )),bind(G,$thf( G )),bind(H,$thf( P ))]]) ).

thf(7224,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( B @ ( A @ equivalent ) @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[6994]) ).

thf(991,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[743]) ).

thf(19787,plain,
    ! [B: $i,A: $i] :
      ( ( A != c )
      | ( A
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[19516]) ).

thf(19788,plain,
    ! [A: $i] :
      ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[19787]) ).

thf(1848,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) )
       != c )
      | ( C != c )
      | ( A
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1796]) ).

thf(1849,plain,
    ! [A: $i] :
      ( ( c @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[1848]) ).

thf(6712,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1291,6079]) ).

thf(6713,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( c @ ( F @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( E @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[6712]) ).

thf(6714,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(pattern_uni,[status(thm)],[6713:[bind(A,$thf( c )),bind(B,$thf( N )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( c @ ( N @ ( M @ equivalent ) @ ( N @ ( M @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( N ))]]) ).

thf(6899,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( B @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[6714]) ).

thf(1821,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1785,48]) ).

thf(1822,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( E @ ( I @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ ( G @ ( E @ ( H @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1821]) ).

thf(1823,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( D @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1822:[bind(A,$thf( ZL @ ( ZH @ equivalent ) )),bind(B,$thf( ZK )),bind(C,$thf( ZK @ ( ZM @ ( ZL @ equivalent ) @ equivalent ) @ ( ZL @ ( ZH @ equivalent ) @ ( ZM @ ( ZH @ equivalent ) @ equivalent ) @ equivalent ) )),bind(D,$thf( ZK @ ( ZM @ ( ZL @ equivalent ) @ equivalent ) @ ( ZL @ ( ZH @ equivalent ) @ ( ZM @ ( ZH @ equivalent ) @ equivalent ) @ equivalent ) @ ( ZK @ equivalent ) )),bind(E,$thf( ZL @ ( ZH @ equivalent ) )),bind(F,$thf( ZH )),bind(G,$thf( ZK )),bind(H,$thf( ZL )),bind(I,$thf( ZM ))]]) ).

thf(1844,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( D @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1823]) ).

thf(5974,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( D @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( c @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( F @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1844,5753]) ).

thf(5975,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( D @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ is_a_theorem )
       != ( F @ ( E @ equivalent ) @ ( c @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( F @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[5974]) ).

thf(5976,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(pattern_uni,[status(thm)],[5975:[bind(A,$thf( Y )),bind(B,$thf( c @ ( Z @ ( Y @ equivalent ) @ ( X @ ( Y @ equivalent ) @ equivalent ) @ equivalent ) )),bind(C,$thf( Z )),bind(D,$thf( X )),bind(E,$thf( Z @ ( Y @ equivalent ) @ ( X @ ( Y @ equivalent ) @ equivalent ) )),bind(F,$thf( c @ ( Z @ ( Y @ equivalent ) @ ( X @ ( Y @ equivalent ) @ equivalent ) @ equivalent ) @ ( X @ ( Z @ equivalent ) @ equivalent ) ))]]) ).

thf(6073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( A @ ( C @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[5976]) ).

thf(2888,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[420,124]) ).

thf(2889,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( I @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[2888]) ).

thf(2890,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[2889:[bind(A,$thf( K )),bind(B,$thf( R )),bind(C,$thf( Q )),bind(D,$thf( R )),bind(E,$thf( S )),bind(F,$thf( K @ ( R @ equivalent ) )),bind(G,$thf( S @ ( R @ equivalent ) )),bind(H,$thf( H )),bind(I,$thf( S @ ( R @ equivalent ) @ ( Q @ ( Q @ equivalent ) @ equivalent ) ))]]) ).

thf(2924,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[2890]) ).

thf(1535,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( F @ ( H @ ( E @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1508,49]) ).

thf(1536,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( F @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( F @ ( H @ ( E @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[1535]) ).

thf(1537,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[1536:[bind(A,$thf( ZF @ ( ZE @ equivalent ) @ ( ZF @ ( ZC @ equivalent ) @ ( ZE @ ( ZC @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( ZF @ ( ZE @ equivalent ) )),bind(C,$thf( ZH )),bind(D,$thf( ZH @ ( ZH @ equivalent ) @ ( ZF @ ( ZE @ equivalent ) @ ( ZF @ ( ZC @ equivalent ) @ ( ZE @ ( ZC @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( ZC )),bind(F,$thf( ZF @ ( ZE @ equivalent ) )),bind(G,$thf( ZE )),bind(H,$thf( ZF ))]]) ).

thf(1553,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[1537]) ).

thf(11575,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3168,221]) ).

thf(11576,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11575]) ).

thf(11577,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11576:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ equivalent ) @ ( J @ ( J @ equivalent ) @ equivalent ) )),bind(E,$thf( N @ ( M @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11681,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11577]) ).

thf(4006,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( A @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[4000]) ).

thf(12089,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( c @ ( E @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[221,8620]) ).

thf(12090,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( c @ ( E @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[12089]) ).

thf(12091,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[12090:[bind(A,$thf( c @ ( R @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( R @ equivalent ) @ equivalent ) @ ( U @ ( U @ equivalent ) @ equivalent ) )),bind(B,$thf( c )),bind(C,$thf( U )),bind(D,$thf( U @ ( U @ equivalent ) )),bind(E,$thf( R ))]]) ).

thf(12302,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( A @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[12091]) ).

thf(6743,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( G @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( F @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[12,6079]) ).

thf(6744,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( G @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( F @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[6743]) ).

thf(6745,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(pattern_uni,[status(thm)],[6744:[bind(A,$thf( R )),bind(B,$thf( V )),bind(C,$thf( V @ ( R @ equivalent ) )),bind(D,$thf( c )),bind(E,$thf( W )),bind(F,$thf( c @ ( W @ ( V @ equivalent ) @ equivalent ) @ ( V @ ( R @ equivalent ) @ ( W @ ( R @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( V @ ( R @ equivalent ) ))]]) ).

thf(6903,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[6745]) ).

thf(11440,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ ( a @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[221,8609]) ).

thf(11441,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ ( a @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11440]) ).

thf(11442,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( a @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11441:[bind(A,$thf( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( N @ equivalent ) @ ( a @ ( N @ equivalent ) @ equivalent ) @ equivalent ) @ ( U @ ( U @ equivalent ) @ equivalent ) )),bind(B,$thf( c )),bind(C,$thf( U )),bind(D,$thf( U @ ( U @ equivalent ) )),bind(E,$thf( N ))]]) ).

thf(11745,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( a @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11442]) ).

thf(233,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) )
       != E )
      | ~ $true
      | ( F @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[10,46]) ).

thf(234,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) )
       != E )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[233]) ).

thf(235,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( B @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[234:[bind(A,$thf( Q )),bind(B,$thf( S )),bind(C,$thf( T )),bind(D,$thf( H )),bind(E,$thf( H @ ( H @ ( T @ ( S @ equivalent ) @ ( T @ ( Q @ equivalent ) @ ( S @ ( Q @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(258,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( B @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[235]) ).

thf(9496,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1453,194]) ).

thf(9497,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ ( H @ ( G @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[9496]) ).

thf(9498,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[9497:[bind(A,$thf( ZT @ ( ZS @ equivalent ) @ ( ZT @ ( ZS @ equivalent ) @ ( ZP @ ( ZP @ equivalent ) @ ( ZM @ equivalent ) @ equivalent ) @ ( ZM @ equivalent ) @ equivalent ) )),bind(B,$thf( ZT @ ( ZS @ equivalent ) )),bind(C,$thf( ZM )),bind(D,$thf( ZP )),bind(E,$thf( ZT @ ( ZS @ equivalent ) @ ( ZT @ ( ZS @ equivalent ) @ ( ZP @ ( ZP @ equivalent ) @ ( ZM @ equivalent ) @ equivalent ) @ ( ZM @ equivalent ) @ equivalent ) )),bind(F,$thf( ZT @ ( ZS @ equivalent ) @ ( ZP @ ( ZP @ equivalent ) @ ( ZM @ equivalent ) @ equivalent ) @ ( ZM @ equivalent ) )),bind(G,$thf( ZS )),bind(H,$thf( ZT ))]]) ).

thf(9569,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[9498]) ).

thf(25137,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[9569,286]) ).

thf(25138,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[25137]) ).

thf(25139,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[25138:[bind(A,$thf( N )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( O )),bind(E,$thf( N )),bind(F,$thf( O @ ( N @ equivalent ) @ ( M @ ( M @ equivalent ) @ ( N @ equivalent ) @ equivalent ) )),bind(G,$thf( O ))]]) ).

thf(25205,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[25139]) ).

thf(54,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C != a )
      | ( B
       != ( b @ ( b @ equivalent ) ) )
      | ( ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[53]) ).

thf(55,plain,
    ! [A: $i] :
      ( ( a @ ( A @ equivalent ) @ ( b @ ( b @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
     != a ),
    inference(simp,[status(thm)],[54]) ).

thf(11470,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4978,221]) ).

thf(11471,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11470]) ).

thf(11472,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11471:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( H @ ( H @ equivalent ) )),bind(E,$thf( N @ ( N @ equivalent ) @ ( L @ ( L @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11755,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11472]) ).

thf(263,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( ( E @ ( D @ equivalent ) )
       != D )
      | ~ $true
      | ( E @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[193,46]) ).

thf(264,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ is_a_theorem ) )
      | ( ( E @ ( D @ equivalent ) )
       != D )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[263]) ).

thf(265,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( L )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( O @ ( N @ equivalent ) @ ( O @ ( L @ equivalent ) @ ( N @ ( L @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( E ))]]) ).

thf(287,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[265]) ).

thf(832,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != c )
      | ( A
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[668]) ).

thf(833,plain,
    ! [A: $i] :
      ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[832]) ).

thf(11423,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3428,221]) ).

thf(11424,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11423]) ).

thf(11425,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11424:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( H @ ( N @ ( N @ equivalent ) @ ( L @ ( L @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( H )),bind(F,$thf( F ))]]) ).

thf(11739,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( D @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11425]) ).

thf(28833,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ equivalent ) )
       != c )
      | ( ( B @ ( B @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[28772]) ).

thf(11625,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1346,221]) ).

thf(11626,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11625]) ).

thf(11627,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11626:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( L @ ( J @ ( J @ equivalent ) @ equivalent ) )),bind(E,$thf( L @ ( N @ ( N @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(11712,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( C @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11627]) ).

thf(11345,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( D @ ( C @ equivalent ) @ is_a_theorem ) )
      | ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[638,221]) ).

thf(11346,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( D @ ( C @ equivalent ) @ is_a_theorem ) )
      | ( D @ ( E @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11345]) ).

thf(11347,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11346:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( G )),bind(D,$thf( G @ ( I @ ( I @ equivalent ) @ equivalent ) )),bind(E,$thf( E ))]]) ).

thf(11695,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11347]) ).

thf(1722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) )
       != c )
      | ( A != c )
      | ( A
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[1720]) ).

thf(1723,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
       != c )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[1722]) ).

thf(1724,plain,
    ! [B: $i,A: $i] :
      ( ( c != c )
      | ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
      | ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
       != c ) ),
    inference(eqfactor_ordered,[status(thm)],[1723]) ).

thf(1725,plain,
    ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
   != c ),
    inference(pattern_uni,[status(thm)],[1724:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).

thf(14276,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( c @ ( E @ ( a @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[221,8639]) ).

thf(14277,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
       != ( c @ ( D @ equivalent ) @ ( c @ ( E @ ( a @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[14276]) ).

thf(14278,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( A @ ( a @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[14277:[bind(A,$thf( c @ ( S @ ( a @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( S @ equivalent ) @ equivalent ) @ ( U @ ( U @ equivalent ) @ equivalent ) )),bind(B,$thf( c )),bind(C,$thf( U )),bind(D,$thf( U @ ( U @ equivalent ) )),bind(E,$thf( S ))]]) ).

thf(14499,plain,
    ! [B: $i,A: $i] :
      ~ ( c @ ( c @ ( A @ ( a @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[14278]) ).

thf(3557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) )
       != c )
      | ( ( C @ ( B @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[3376]) ).

thf(3558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) )
       != c )
      | ( ( A @ ( A @ equivalent ) )
       != ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[3557]) ).

thf(6678,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( E @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( D @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5116,6079]) ).

thf(6679,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( A @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( E @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( D @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[6678]) ).

thf(6680,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( c @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(pattern_uni,[status(thm)],[6679:[bind(A,$thf( c )),bind(B,$thf( M @ ( M @ equivalent ) )),bind(C,$thf( O )),bind(D,$thf( O @ ( O @ equivalent ) @ ( M @ ( M @ equivalent ) @ ( c @ equivalent ) @ equivalent ) )),bind(E,$thf( M ))]]) ).

thf(6889,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( c @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[6680]) ).

thf(261,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[193,51]) ).

thf(262,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[261]) ).

thf(283,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( D @ is_a_theorem ) ),
    inference(simp,[status(thm)],[262]) ).

thf(1741,plain,
    ! [B: $i,A: $i] :
      ( ( B != a )
      | ( A
       != ( b @ ( b @ equivalent ) ) )
      | ( ( B @ ( A @ equivalent ) )
       != a ) ),
    inference(simp,[status(thm)],[1736]) ).

thf(1742,plain,
    ( ( a @ ( b @ ( b @ equivalent ) @ equivalent ) )
   != a ),
    inference(simp,[status(thm)],[1741]) ).

thf(11363,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[894,221]) ).

thf(11364,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( D @ equivalent ) @ is_a_theorem ) )
      | ( E @ ( F @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[11363]) ).

thf(11365,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[11364:[bind(A,$thf( H )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( H @ ( N @ ( M @ equivalent ) @ ( N @ ( M @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( H )),bind(F,$thf( F ))]]) ).

thf(11707,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( D @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[11365]) ).

thf(1120,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ equivalent ) )
       != c )
      | ( ( A @ ( B @ equivalent ) )
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[783]) ).

thf(239,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( ( G @ ( F @ equivalent ) )
       != F )
      | ~ $true
      | ( G @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[12,46]) ).

thf(240,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ is_a_theorem ) )
      | ( ( G @ ( F @ equivalent ) )
       != F )
      | ( G @ is_a_theorem ) ),
    inference(simp,[status(thm)],[239]) ).

thf(241,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( B @ ( F @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( B @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( B @ ( F @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( B @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( T )),bind(B,$thf( X )),bind(C,$thf( S )),bind(D,$thf( W )),bind(E,$thf( Y )),bind(F,$thf( W @ ( Y @ ( X @ equivalent ) @ equivalent ) @ ( S @ ( Y @ ( T @ equivalent ) @ equivalent ) @ equivalent ) @ ( W @ ( S @ ( X @ ( T @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( G ))]]) ).

thf(254,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( B @ ( F @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( B @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( B @ ( F @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( B @ ( E @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[241]) ).

thf(25905,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ~ $true
      | ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[11676,286]) ).

thf(25906,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( G @ ( E @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( G @ ( F @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[25905]) ).

thf(25907,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[25906:[bind(A,$thf( O )),bind(B,$thf( L )),bind(C,$thf( O @ ( O @ equivalent ) )),bind(D,$thf( Q )),bind(E,$thf( O @ ( O @ equivalent ) )),bind(F,$thf( L )),bind(G,$thf( Q @ ( Q @ equivalent ) @ ( O @ ( O @ equivalent ) @ ( L @ equivalent ) @ equivalent ) ))]]) ).

thf(26035,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[25907]) ).

thf(114,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[75,51]) ).

thf(115,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[114]) ).

thf(122,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[115]) ).

thf(30577,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ equivalent ) @ equivalent ) )
       != c )
      | ( A
       != ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( C @ ( C @ equivalent ) @ equivalent ) ) ) ),
    inference(simp,[status(thm)],[9272]) ).

thf(30578,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ ( A @ ( A @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[30577]) ).

thf(3414,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3152,51]) ).

thf(3415,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( A @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( E @ is_a_theorem ) ),
    inference(simp,[status(thm)],[3414]) ).

thf(3416,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ equivalent ) @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(pattern_uni,[status(thm)],[3415:[bind(A,$thf( ZD )),bind(B,$thf( ZG )),bind(C,$thf( V @ ( ZG @ equivalent ) @ ( ZE @ equivalent ) @ ( ZD @ ( ZD @ equivalent ) @ ( ZG @ equivalent ) @ ( ZE @ equivalent ) @ equivalent ) )),bind(D,$thf( V )),bind(E,$thf( V @ ( V @ ( ZG @ equivalent ) @ ( ZE @ equivalent ) @ ( ZD @ ( ZD @ equivalent ) @ ( ZG @ equivalent ) @ ( ZE @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZE )),bind(G,$thf( ZD @ ( ZD @ equivalent ) @ ( ZG @ equivalent ) )),bind(H,$thf( V @ ( ZG @ equivalent ) ))]]) ).

thf(3432,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( A @ ( D @ equivalent ) @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ ( D @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
    inference(simp,[status(thm)],[3416]) ).

thf(6831,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( G @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( F @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[47,6079]) ).

thf(6832,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( D @ equivalent ) @ equivalent ) @ ( A @ ( E @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( F @ ( c @ ( G @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( F @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ ( C @ ( A @ ( D @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6831]) ).

thf(6833,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ ( A @ ( c @ ( B @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[6832:[bind(A,$thf( c )),bind(B,$thf( K )),bind(C,$thf( I )),bind(D,$thf( J )),bind(E,$thf( K )),bind(F,$thf( I @ ( K @ ( J @ equivalent ) @ equivalent ) )),bind(G,$thf( K ))]]) ).

thf(6896,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ ( A @ ( c @ ( B @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
    inference(simp,[status(thm)],[6833]) ).

thf(21221,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( E @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3428,6896]) ).

thf(21222,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( C @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( D @ ( c @ ( E @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(simp,[status(thm)],[21221]) ).

thf(21223,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( A @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(pattern_uni,[status(thm)],[21222:[bind(A,$thf( c )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( c )),bind(E,$thf( J @ ( J @ equivalent ) )),bind(F,$thf( H @ ( H @ equivalent ) ))]]) ).

thf(21446,plain,
    ! [B: $i,A: $i] :
      ( ( c @ ( A @ ( A @ equivalent ) @ ( B @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
     != c ),
    inference(simp,[status(thm)],[21223]) ).

thf(81,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ~ $true
      | ( F @ is_a_theorem ) ),
    inference(paramod_ordered,[status(thm)],[10,45]) ).

thf(82,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( ( F @ ( E @ equivalent ) @ is_a_theorem )
       != ( E @ is_a_theorem ) )
      | ( F @ is_a_theorem ) ),
    inference(simp,[status(thm)],[81]) ).

thf(83,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( B @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( A @ is_a_theorem ) ),
    inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( Q )),bind(B,$thf( S )),bind(C,$thf( T )),bind(D,$thf( H )),bind(E,$thf( H @ ( H @ ( T @ ( S @ equivalent ) @ ( T @ ( Q @ equivalent ) @ ( S @ ( Q @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).

thf(100,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
       != ( B @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
      | ( A @ is_a_theorem ) ),
    inference(simp,[status(thm)],[83]) ).

thf(231,plain,
    ! [A: $i] :
      ( ( A != c )
      | ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) )
      | ( ( A @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
       != c ) ),
    inference(eqfactor_ordered,[status(thm)],[230]) ).

thf(232,plain,
    ( ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
   != c ),
    inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( c ))]]) ).

thf(32057,plain,
    $false,
    inference(e,[status(thm)],[10822,9077,22861,10812,8639,3566,9091,352,629,5116,11688,9621,1406,10,1788,3175,715,3693,6894,2575,19044,20469,8622,1735,11684,8848,26833,709,7235,1613,1601,320,4760,25,8603,257,31276,11667,18801,26552,125,13170,1832,24608,2571,52,8610,638,46,284,416,3312,228,8632,57,316,11716,164,9283,6895,11676,348,3152,5834,9616,221,1796,3756,9272,13838,1215,61,312,74,6,3567,28772,7217,220,1736,9323,60,10811,7439,1900,894,13423,12700,192,21,165,6079,6897,260,349,13158,2873,197,65,4757,4746,1656,324,9554,1837,12991,1291,710,1402,7205,2359,9328,9,8619,53,356,169,28480,783,420,256,124,77,193,10342,3428,26585,3294,22618,25794,1114,8599,1456,2153,1552,25797,3247,14757,9598,1720,28476,24298,3755,128,105,938,3563,10819,6070,6647,6891,8609,22622,1616,5840,1732,73,4184,2936,1727,9040,824,20466,45,161,7212,11693,25224,3491,13135,4000,7714,1784,5121,286,8809,743,577,259,29089,3758,26572,59,6898,12,313,11662,49,20915,540,11671,4978,3487,9555,2573,2148,979,1408,230,567,7,318,11718,4203,1557,535,22863,626,943,668,2928,8620,8605,2874,23620,3480,1396,3759,3423,223,2931,19516,7200,226,167,3427,19316,162,3146,1509,10829,123,194,15447,255,749,10814,11738,48,3376,63,18,7211,707,6902,282,11694,1611,9578,4754,50,2569,199,8858,5753,1785,1285,11661,3564,10343,2411,2357,9257,4202,314,9601,7224,991,19788,1404,1898,1849,6899,6073,11,8602,3168,2924,1553,1844,11681,495,4006,1390,1453,1108,12302,539,9092,6903,11745,1508,258,25205,55,632,171,23,8,75,24868,9569,8638,11755,27644,5119,9321,1614,287,833,168,11739,28833,51,11712,790,11695,315,1725,2155,14499,3232,3558,1710,6889,1346,283,1742,3244,3362,11707,528,47,15,163,9066,3494,1120,7352,575,254,5029,26035,122,30578,935,3432,21446,222,100,232,6896]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL096-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39  % Computer : n026.cluster.edu
% 0.13/0.39  % Model    : x86_64 x86_64
% 0.13/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39  % Memory   : 8046.5625MB
% 0.13/0.39  % OS       : Linux 6.8.0-71-generic
% 0.13/0.39  % CPULimit : 300
% 0.13/0.39  % WCLimit  : 300
% 0.13/0.39  % DateTime : Fri Sep 25 21:53:25 UTC 2026
% 0.13/0.40  % CPUTime  : 
% 0.13/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/1.00  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.24/1.18  % [INFO] 	 Parsing done (183ms). 
% 1.38/1.20  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.40  % [INFO] 	 eprover registered as external prover. 
% 1.71/1.41  % [INFO] 	 Scanning for conjecture ... 
% 1.71/1.45  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 1.71/1.46  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.71/1.47  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.71/1.47  % [INFO] 	 Type checking passed. 
% 1.71/1.48  % [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 ... 
% 144.11/54.98  % External prover 'e' found a proof!
% 144.11/54.98  % [INFO] 	 Killing All external provers ... 
% 144.11/54.98  % Time passed: 54431ms (effective reasoning time: 53776ms)
% 144.11/54.99  % Axioms used in derivation (4): lg_2, lg_4, condensed_detachment, lg_3
% 144.11/54.99  % No. of inferences in proof: 1114
% 144.11/54.99  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 54431 ms resp. 53776 ms w/o parsing
% 146.77/55.68  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 146.77/55.69  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------