%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GRP488-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 16 22:27:46 EDT 2022

% Result   : Unsatisfiable 0.18s 0.54s
% Output   : Proof 0.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   63
%            Number of leaves      :   84
% Syntax   : Number of formulae    :  623 ( 544 unt;   5 typ;   0 def)
%            Number of atoms       :  700 ( 695 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  147 (  69   ~;  65   |;   0   &)
%                                         (  13 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :   25 (   3 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  241 ( 234   !;   0   ?; 241   :)

% Comments : 
%------------------------------------------------------------------------------
tff(a2_type,type,
    a2: $i ).

tff(multiply_type,type,
    multiply: ( $i * $i ) > $i ).

tff(identity_type,type,
    identity: $i ).

tff(double_divide_type,type,
    double_divide: ( $i * $i ) > $i ).

tff(inverse_type,type,
    inverse: $i > $i ).

tff(1,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
      <=> ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
  <=> ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
  <=> ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

tff(5,plain,
    ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)) = a2 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)) = a2,
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(11,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(unit_resolution,[status(thm)],[10,7]) ).

tff(12,plain,
    ^ [A: $i] :
      refl(
        ( ( inverse(A) = double_divide(A,identity) )
      <=> ( inverse(A) = double_divide(A,identity) ) )),
    inference(bind,[status(th)],]) ).

tff(13,plain,
    ( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
  <=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
    inference(quant_intro,[status(thm)],[12]) ).

tff(14,plain,
    ( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
  <=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).

tff(16,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(skolemize,[status(sab)],[16]) ).

tff(18,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(modus_ponens,[status(thm)],[17,13]) ).

tff(19,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(20,plain,
    inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[19,18]) ).

tff(21,plain,
    double_divide(double_divide(a2,identity),identity) = inverse(double_divide(a2,identity)),
    inference(symmetry,[status(thm)],[20]) ).

tff(22,plain,
    ^ [A: $i] :
      refl(
        ( ( identity = double_divide(A,inverse(A)) )
      <=> ( identity = double_divide(A,inverse(A)) ) )),
    inference(bind,[status(th)],]) ).

tff(23,plain,
    ( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
  <=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
    inference(quant_intro,[status(thm)],[22]) ).

tff(24,plain,
    ( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
  <=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,axiom,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).

tff(26,plain,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    inference(modus_ponens,[status(thm)],[25,24]) ).

tff(27,plain,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    inference(skolemize,[status(sab)],[26]) ).

tff(28,plain,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    inference(modus_ponens,[status(thm)],[27,23]) ).

tff(29,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(30,plain,
    identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[29,28]) ).

tff(31,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = identity,
    inference(symmetry,[status(thm)],[30]) ).

tff(32,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(a2,identity),identity),
    inference(monotonicity,[status(thm)],[31]) ).

tff(33,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(double_divide(a2,identity)),
    inference(transitivity,[status(thm)],[32,21]) ).

tff(34,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(monotonicity,[status(thm)],[33]) ).

tff(35,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(symmetry,[status(thm)],[34]) ).

tff(36,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),a2),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(37,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),a2),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[36,7]) ).

tff(38,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)) = double_divide(a2,identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(39,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)) = double_divide(a2,identity),
    inference(unit_resolution,[status(thm)],[38,7]) ).

tff(40,plain,
    double_divide(a2,identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)),
    inference(symmetry,[status(thm)],[39]) ).

tff(41,plain,
    double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(a2,identity),
    inference(monotonicity,[status(thm)],[31]) ).

tff(42,plain,
    double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)),
    inference(transitivity,[status(thm)],[41,40]) ).

tff(43,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),
    inference(monotonicity,[status(thm)],[42]) ).

tff(44,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),
    inference(monotonicity,[status(thm)],[43]) ).

tff(45,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),a2) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),
    inference(monotonicity,[status(thm)],[44]) ).

tff(46,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),a2),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity),
    inference(monotonicity,[status(thm)],[45]) ).

tff(47,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),a2),identity),
    inference(symmetry,[status(thm)],[46]) ).

tff(48,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),a2),identity)),
    inference(monotonicity,[status(thm)],[47]) ).

tff(49,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(50,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity),
    inference(unit_resolution,[status(thm)],[49,7]) ).

tff(51,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(52,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),
    inference(unit_resolution,[status(thm)],[51,7]) ).

tff(53,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)),
    inference(symmetry,[status(thm)],[52]) ).

tff(54,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[53,48,37]) ).

tff(55,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)),
    inference(monotonicity,[status(thm)],[54,50]) ).

tff(56,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[55,48,37,35]) ).

tff(57,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[56]) ).

tff(58,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
    inference(symmetry,[status(thm)],[57]) ).

tff(59,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(60,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[59,7]) ).

tff(61,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = inverse(double_divide(a2,identity)),
    inference(transitivity,[status(thm)],[60,21]) ).

tff(62,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(monotonicity,[status(thm)],[61]) ).

tff(63,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[62,35]) ).

tff(64,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[63]) ).

tff(65,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
    inference(transitivity,[status(thm)],[64,58]) ).

tff(66,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[65]) ).

tff(67,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[66]) ).

tff(68,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(symmetry,[status(thm)],[67]) ).

tff(69,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(70,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[69,7]) ).

tff(71,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = inverse(double_divide(a2,identity)),
    inference(transitivity,[status(thm)],[70,21]) ).

tff(72,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(monotonicity,[status(thm)],[71]) ).

tff(73,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[72,35]) ).

tff(74,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[73]) ).

tff(75,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
    inference(transitivity,[status(thm)],[74,58]) ).

tff(76,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[75]) ).

tff(77,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[76]) ).

tff(78,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(transitivity,[status(thm)],[77,68]) ).

tff(79,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(monotonicity,[status(thm)],[78]) ).

tff(80,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[79]) ).

tff(81,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(82,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity),
    inference(unit_resolution,[status(thm)],[81,7]) ).

tff(83,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[82]) ).

tff(84,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
    inference(transitivity,[status(thm)],[34,31]) ).

tff(85,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(monotonicity,[status(thm)],[30,84]) ).

tff(86,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),
    inference(monotonicity,[status(thm)],[85,40]) ).

tff(87,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),
    inference(symmetry,[status(thm)],[86]) ).

tff(88,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)) = double_divide(a2,identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(89,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)) = double_divide(a2,identity),
    inference(unit_resolution,[status(thm)],[88,7]) ).

tff(90,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(monotonicity,[status(thm)],[21]) ).

tff(91,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
    inference(symmetry,[status(thm)],[90]) ).

tff(92,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(93,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[92,7]) ).

tff(94,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
    inference(transitivity,[status(thm)],[93,91]) ).

tff(95,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[94]) ).

tff(96,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[95]) ).

tff(97,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),
    inference(symmetry,[status(thm)],[96]) ).

tff(98,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(a2,inverse(a2)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(99,plain,
    identity = double_divide(a2,inverse(a2)),
    inference(unit_resolution,[status(thm)],[98,28]) ).

tff(100,plain,
    double_divide(a2,inverse(a2)) = identity,
    inference(symmetry,[status(thm)],[99]) ).

tff(101,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(a2) = double_divide(a2,identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(102,plain,
    inverse(a2) = double_divide(a2,identity),
    inference(unit_resolution,[status(thm)],[101,18]) ).

tff(103,plain,
    double_divide(a2,identity) = inverse(a2),
    inference(symmetry,[status(thm)],[102]) ).

tff(104,plain,
    double_divide(a2,double_divide(a2,identity)) = double_divide(a2,inverse(a2)),
    inference(monotonicity,[status(thm)],[103]) ).

tff(105,plain,
    double_divide(a2,double_divide(a2,identity)) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
    inference(transitivity,[status(thm)],[104,100,30,91]) ).

tff(106,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(a2,identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[105]) ).

tff(107,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(a2,identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[106]) ).

tff(108,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(a2,identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),
    inference(transitivity,[status(thm)],[107,97]) ).

tff(109,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(a2,identity)))),a2) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),a2),
    inference(monotonicity,[status(thm)],[108]) ).

tff(110,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),a2),identity),
    inference(monotonicity,[status(thm)],[109]) ).

tff(111,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),a2),identity)),
    inference(monotonicity,[status(thm)],[110]) ).

tff(112,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),a2),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)),
    inference(symmetry,[status(thm)],[111]) ).

tff(113,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),a2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(114,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),a2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(unit_resolution,[status(thm)],[113,7]) ).

tff(115,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),a2),identity)),
    inference(symmetry,[status(thm)],[114]) ).

tff(116,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)),
    inference(transitivity,[status(thm)],[115,112,89,40]) ).

tff(117,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(118,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(unit_resolution,[status(thm)],[117,7]) ).

tff(119,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(120,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[119,7]) ).

tff(121,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
    inference(transitivity,[status(thm)],[120,91]) ).

tff(122,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[121]) ).

tff(123,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[122]) ).

tff(124,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),
    inference(symmetry,[status(thm)],[123]) ).

tff(125,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = identity,
    inference(transitivity,[status(thm)],[90,31]) ).

tff(126,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(a2,identity),identity),
    inference(monotonicity,[status(thm)],[125]) ).

tff(127,plain,
    double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(symmetry,[status(thm)],[126]) ).

tff(128,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)) = identity,
    inference(transitivity,[status(thm)],[48,37,31]) ).

tff(129,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity))) = double_divide(double_divide(a2,identity),identity),
    inference(monotonicity,[status(thm)],[128]) ).

tff(130,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[129,127]) ).

tff(131,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[130]) ).

tff(132,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),
    inference(symmetry,[status(thm)],[131]) ).

tff(133,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(monotonicity,[status(thm)],[132,30]) ).

tff(134,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[133,125]) ).

tff(135,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(symmetry,[status(thm)],[134]) ).

tff(136,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(137,plain,
    identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(unit_resolution,[status(thm)],[136,28]) ).

tff(138,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
    inference(symmetry,[status(thm)],[137]) ).

tff(139,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(140,plain,
    inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(unit_resolution,[status(thm)],[139,18]) ).

tff(141,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(symmetry,[status(thm)],[140]) ).

tff(142,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[141]) ).

tff(143,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = identity,
    inference(transitivity,[status(thm)],[142,138]) ).

tff(144,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[133,143]) ).

tff(145,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[144,135]) ).

tff(146,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[145]) ).

tff(147,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),
    inference(transitivity,[status(thm)],[146,124]) ).

tff(148,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(monotonicity,[status(thm)],[147]) ).

tff(149,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[148]) ).

tff(150,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(monotonicity,[status(thm)],[149]) ).

tff(151,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[150]) ).

tff(152,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(153,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity),
    inference(unit_resolution,[status(thm)],[152,7]) ).

tff(154,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[153]) ).

tff(155,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(156,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity),
    inference(unit_resolution,[status(thm)],[155,7]) ).

tff(157,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(158,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[157,7]) ).

tff(159,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(160,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[159,7]) ).

tff(161,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
    inference(transitivity,[status(thm)],[160,91]) ).

tff(162,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[161]) ).

tff(163,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[162]) ).

tff(164,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),
    inference(symmetry,[status(thm)],[163]) ).

tff(165,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),
    inference(monotonicity,[status(thm)],[31]) ).

tff(166,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
    inference(transitivity,[status(thm)],[165,53,48,37,91]) ).

tff(167,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[166]) ).

tff(168,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[167]) ).

tff(169,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),
    inference(transitivity,[status(thm)],[168,164]) ).

tff(170,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[169]) ).

tff(171,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[170]) ).

tff(172,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(symmetry,[status(thm)],[171]) ).

tff(173,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(monotonicity,[status(thm)],[172]) ).

tff(174,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(175,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity),
    inference(unit_resolution,[status(thm)],[174,7]) ).

tff(176,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[175]) ).

tff(177,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(178,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity),
    inference(unit_resolution,[status(thm)],[177,7]) ).

tff(179,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = identity,
    inference(transitivity,[status(thm)],[178,176,173,158,31]) ).

tff(180,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[48,37,35]) ).

tff(181,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) = identity,
    inference(transitivity,[status(thm)],[53,48,37,31]) ).

tff(182,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[181,180]) ).

tff(183,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity))) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[182,85,141]) ).

tff(184,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[30,183]) ).

tff(185,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))) = identity,
    inference(transitivity,[status(thm)],[184,138]) ).

tff(186,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[185,35]) ).

tff(187,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(symmetry,[status(thm)],[186]) ).

tff(188,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(symmetry,[status(thm)],[85]) ).

tff(189,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[188,187]) ).

tff(190,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[189,125]) ).

tff(191,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(symmetry,[status(thm)],[190]) ).

tff(192,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = identity,
    inference(transitivity,[status(thm)],[120,31]) ).

tff(193,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[189,192]) ).

tff(194,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[193,191]) ).

tff(195,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[194]) ).

tff(196,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),
    inference(symmetry,[status(thm)],[195]) ).

tff(197,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(monotonicity,[status(thm)],[196,30]) ).

tff(198,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[197,179]) ).

tff(199,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(monotonicity,[status(thm)],[30,198]) ).

tff(200,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[178]) ).

tff(201,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[173]) ).

tff(202,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[158]) ).

tff(203,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(a2,identity),
    inference(transitivity,[status(thm)],[115,112,89]) ).

tff(204,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(monotonicity,[status(thm)],[203,21]) ).

tff(205,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(transitivity,[status(thm)],[204,202,201,175,200]) ).

tff(206,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))),
    inference(monotonicity,[status(thm)],[205]) ).

tff(207,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),
    inference(monotonicity,[status(thm)],[206]) ).

tff(208,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(transitivity,[status(thm)],[207,199,156,154,151,118]) ).

tff(209,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),
    inference(monotonicity,[status(thm)],[208,116]) ).

tff(210,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),
    inference(transitivity,[status(thm)],[209,87]) ).

tff(211,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity),
    inference(monotonicity,[status(thm)],[210]) ).

tff(212,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),identity),
    inference(symmetry,[status(thm)],[211]) ).

tff(213,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),a2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(214,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),a2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity),
    inference(unit_resolution,[status(thm)],[213,7]) ).

tff(215,plain,
    double_divide(a2,double_divide(a2,identity)) = identity,
    inference(transitivity,[status(thm)],[104,100]) ).

tff(216,plain,
    double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity))) = double_divide(double_divide(a2,identity),identity),
    inference(monotonicity,[status(thm)],[215]) ).

tff(217,plain,
    double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[216,127]) ).

tff(218,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[217]) ).

tff(219,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),
    inference(symmetry,[status(thm)],[218]) ).

tff(220,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(221,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[220,7]) ).

tff(222,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)) = identity,
    inference(transitivity,[status(thm)],[221,31]) ).

tff(223,plain,
    double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity))) = double_divide(double_divide(a2,identity),identity),
    inference(monotonicity,[status(thm)],[222]) ).

tff(224,plain,
    double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[223,127]) ).

tff(225,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[224]) ).

tff(226,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[225,219]) ).

tff(227,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),a2) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),
    inference(monotonicity,[status(thm)],[226]) ).

tff(228,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),a2),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),
    inference(monotonicity,[status(thm)],[227]) ).

tff(229,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),a2),identity)) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)),
    inference(monotonicity,[status(thm)],[228]) ).

tff(230,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),a2),identity)),
    inference(symmetry,[status(thm)],[229]) ).

tff(231,plain,
    double_divide(a2,identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),identity),
    inference(transitivity,[status(thm)],[40,230,214,212]) ).

tff(232,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),identity)),
    inference(monotonicity,[status(thm)],[231]) ).

tff(233,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),
    inference(symmetry,[status(thm)],[232]) ).

tff(234,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),identity)) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(235,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),identity)) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[234,7]) ).

tff(236,plain,
    double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),identity)),
    inference(symmetry,[status(thm)],[235]) ).

tff(237,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(238,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[237,7]) ).

tff(239,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(240,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity),
    inference(unit_resolution,[status(thm)],[239,7]) ).

tff(241,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(242,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[241,7]) ).

tff(243,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[31,35]) ).

tff(244,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[243,85,141]) ).

tff(245,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[54,244]) ).

tff(246,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[245,138,30,35]) ).

tff(247,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[246]) ).

tff(248,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[247,187]) ).

tff(249,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[248,31]) ).

tff(250,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(symmetry,[status(thm)],[249]) ).

tff(251,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[189]) ).

tff(252,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[251,250]) ).

tff(253,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[252,179]) ).

tff(254,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))),
    inference(symmetry,[status(thm)],[253]) ).

tff(255,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(256,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[255,7]) ).

tff(257,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = identity,
    inference(transitivity,[status(thm)],[256,31]) ).

tff(258,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[252,257]) ).

tff(259,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))),
    inference(transitivity,[status(thm)],[258,254]) ).

tff(260,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),
    inference(monotonicity,[status(thm)],[259]) ).

tff(261,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),
    inference(symmetry,[status(thm)],[260]) ).

tff(262,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = identity,
    inference(transitivity,[status(thm)],[165,53,48,37,31]) ).

tff(263,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[252,262]) ).

tff(264,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))),
    inference(transitivity,[status(thm)],[263,254]) ).

tff(265,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),
    inference(monotonicity,[status(thm)],[264]) ).

tff(266,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),
    inference(transitivity,[status(thm)],[265,261]) ).

tff(267,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[266]) ).

tff(268,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[267]) ).

tff(269,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(symmetry,[status(thm)],[268]) ).

tff(270,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(monotonicity,[status(thm)],[269]) ).

tff(271,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(272,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[271,7]) ).

tff(273,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = identity,
    inference(transitivity,[status(thm)],[272,31]) ).

tff(274,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[252,273]) ).

tff(275,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))),
    inference(transitivity,[status(thm)],[274,254]) ).

tff(276,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),
    inference(monotonicity,[status(thm)],[275]) ).

tff(277,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),
    inference(transitivity,[status(thm)],[276,261]) ).

tff(278,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[277]) ).

tff(279,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[278]) ).

tff(280,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(monotonicity,[status(thm)],[279]) ).

tff(281,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(282,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(unit_resolution,[status(thm)],[281,7]) ).

tff(283,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[282]) ).

tff(284,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = inverse(double_divide(a2,identity)),
    inference(transitivity,[status(thm)],[238,21]) ).

tff(285,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(monotonicity,[status(thm)],[284]) ).

tff(286,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[285,35]) ).

tff(287,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[286]) ).

tff(288,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[287,187]) ).

tff(289,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[288,31]) ).

tff(290,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[289,250]) ).

tff(291,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[290]) ).

tff(292,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = identity,
    inference(transitivity,[status(thm)],[291,283,280,270,242,31]) ).

tff(293,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(a2,identity),
    inference(monotonicity,[status(thm)],[292]) ).

tff(294,plain,
    double_divide(a2,identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[293]) ).

tff(295,plain,
    double_divide(a2,identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity),
    inference(transitivity,[status(thm)],[294,240]) ).

tff(296,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[90,35]) ).

tff(297,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[181,296]) ).

tff(298,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[297,85,141]) ).

tff(299,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[30,298]) ).

tff(300,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[299,138,30]) ).

tff(301,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)),
    inference(monotonicity,[status(thm)],[300,295]) ).

tff(302,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),
    inference(transitivity,[status(thm)],[301,238,236,233]) ).

tff(303,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity),
    inference(monotonicity,[status(thm)],[302]) ).

tff(304,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity),
    inference(symmetry,[status(thm)],[303]) ).

tff(305,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(306,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[305,7]) ).

tff(307,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(308,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[307,7]) ).

tff(309,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
    inference(transitivity,[status(thm)],[308,91]) ).

tff(310,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[309]) ).

tff(311,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[310]) ).

tff(312,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),
    inference(transitivity,[status(thm)],[311,164]) ).

tff(313,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[312]) ).

tff(314,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[313]) ).

tff(315,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(monotonicity,[status(thm)],[314]) ).

tff(316,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(317,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),
    inference(unit_resolution,[status(thm)],[316,7]) ).

tff(318,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[317]) ).

tff(319,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[318,315,173,158]) ).

tff(320,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[319,244]) ).

tff(321,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[320,138,30,35]) ).

tff(322,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[321]) ).

tff(323,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[322,187]) ).

tff(324,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[323,31]) ).

tff(325,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[324,250]) ).

tff(326,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[325]) ).

tff(327,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(symmetry,[status(thm)],[326]) ).

tff(328,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[156,154,151,118,141]) ).

tff(329,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[319,328]) ).

tff(330,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[329,138,30,35]) ).

tff(331,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[330]) ).

tff(332,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[331,187]) ).

tff(333,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[332,31]) ).

tff(334,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[333,250]) ).

tff(335,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[334]) ).

tff(336,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(transitivity,[status(thm)],[335,327]) ).

tff(337,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(monotonicity,[status(thm)],[336]) ).

tff(338,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(339,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(unit_resolution,[status(thm)],[338,7]) ).

tff(340,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[339]) ).

tff(341,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[199,156,154,151,118,188,187]) ).

tff(342,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[341,31]) ).

tff(343,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[342,250]) ).

tff(344,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[343]) ).

tff(345,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(symmetry,[status(thm)],[344]) ).

tff(346,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[280]) ).

tff(347,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[270]) ).

tff(348,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[242]) ).

tff(349,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(transitivity,[status(thm)],[348,347,346,282,345]) ).

tff(350,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(monotonicity,[status(thm)],[195,349]) ).

tff(351,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(symmetry,[status(thm)],[350]) ).

tff(352,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(353,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(unit_resolution,[status(thm)],[352,7]) ).

tff(354,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[353]) ).

tff(355,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(356,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(unit_resolution,[status(thm)],[355,7]) ).

tff(357,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[252,143]) ).

tff(358,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))),
    inference(transitivity,[status(thm)],[357,254]) ).

tff(359,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),
    inference(monotonicity,[status(thm)],[358]) ).

tff(360,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(monotonicity,[status(thm)],[359]) ).

tff(361,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[360]) ).

tff(362,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(symmetry,[status(thm)],[361]) ).

tff(363,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(monotonicity,[status(thm)],[362]) ).

tff(364,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[363]) ).

tff(365,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(366,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(unit_resolution,[status(thm)],[365,7]) ).

tff(367,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[366]) ).

tff(368,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[186,85,367,364,356,354,351]) ).

tff(369,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[368]) ).

tff(370,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = identity,
    inference(transitivity,[status(thm)],[369,340,337,306,31]) ).

tff(371,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),
    inference(monotonicity,[status(thm)],[370]) ).

tff(372,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[50]) ).

tff(373,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(374,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity),
    inference(unit_resolution,[status(thm)],[373,7]) ).

tff(375,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
    inference(transitivity,[status(thm)],[48,37,91]) ).

tff(376,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[375]) ).

tff(377,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[376]) ).

tff(378,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),
    inference(transitivity,[status(thm)],[377,124]) ).

tff(379,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(monotonicity,[status(thm)],[378]) ).

tff(380,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[379]) ).

tff(381,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(symmetry,[status(thm)],[380]) ).

tff(382,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(monotonicity,[status(thm)],[381]) ).

tff(383,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[118]) ).

tff(384,plain,
    identity = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[30,35]) ).

tff(385,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(386,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[385,7]) ).

tff(387,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
    inference(transitivity,[status(thm)],[386,91]) ).

tff(388,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[387]) ).

tff(389,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[388]) ).

tff(390,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),
    inference(transitivity,[status(thm)],[389,164]) ).

tff(391,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[390]) ).

tff(392,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[391]) ).

tff(393,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(monotonicity,[status(thm)],[392]) ).

tff(394,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(395,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(unit_resolution,[status(thm)],[394,7]) ).

tff(396,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[395]) ).

tff(397,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)) = a2 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(398,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)) = a2,
    inference(unit_resolution,[status(thm)],[397,7]) ).

tff(399,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),
    inference(monotonicity,[status(thm)],[219]) ).

tff(400,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[165,53,48,37,35]) ).

tff(401,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[181,400]) ).

tff(402,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[401,85,141]) ).

tff(403,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[30,402]) ).

tff(404,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(symmetry,[status(thm)],[403]) ).

tff(405,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(transitivity,[status(thm)],[53,48,37,31,137,404]) ).

tff(406,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[405,399]) ).

tff(407,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2)),
    inference(symmetry,[status(thm)],[406]) ).

tff(408,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(transitivity,[status(thm)],[57,85,383,150,382,374,372,371,53,48,37,31,137,404]) ).

tff(409,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[408]) ).

tff(410,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
    inference(transitivity,[status(thm)],[188,58]) ).

tff(411,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[410,399]) ).

tff(412,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2)),
    inference(transitivity,[status(thm)],[411,409,407]) ).

tff(413,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),
    inference(monotonicity,[status(thm)],[412]) ).

tff(414,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),
    inference(monotonicity,[status(thm)],[413]) ).

tff(415,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity),
    inference(monotonicity,[status(thm)],[414]) ).

tff(416,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity),
    inference(symmetry,[status(thm)],[415]) ).

tff(417,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)),
    inference(monotonicity,[status(thm)],[416]) ).

tff(418,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)) = a2,
    inference(transitivity,[status(thm)],[417,398]) ).

tff(419,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[31]) ).

tff(420,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(monotonicity,[status(thm)],[319,419]) ).

tff(421,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(symmetry,[status(thm)],[420]) ).

tff(422,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(423,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),
    inference(unit_resolution,[status(thm)],[422,7]) ).

tff(424,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[423]) ).

tff(425,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(426,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),
    inference(unit_resolution,[status(thm)],[425,7]) ).

tff(427,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),identity),
    inference(monotonicity,[status(thm)],[262]) ).

tff(428,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[427,127]) ).

tff(429,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[428]) ).

tff(430,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(symmetry,[status(thm)],[429]) ).

tff(431,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[430]) ).

tff(432,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[431]) ).

tff(433,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
      <=> ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) )),
    inference(bind,[status(th)],]) ).

tff(434,plain,
    ( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
  <=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
    inference(quant_intro,[status(thm)],[433]) ).

tff(435,plain,
    ( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
  <=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(436,axiom,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).

tff(437,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(modus_ponens,[status(thm)],[436,435]) ).

tff(438,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(skolemize,[status(sab)],[437]) ).

tff(439,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(modus_ponens,[status(thm)],[438,434]) ).

tff(440,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(441,plain,
    multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(unit_resolution,[status(thm)],[440,439]) ).

tff(442,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(symmetry,[status(thm)],[299]) ).

tff(443,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(transitivity,[status(thm)],[53,48,37,31,137,442]) ).

tff(444,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),
    inference(monotonicity,[status(thm)],[443,41]) ).

tff(445,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[444,301,238,127]) ).

tff(446,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[445]) ).

tff(447,plain,
    multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),
    inference(monotonicity,[status(thm)],[446]) ).

tff(448,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(449,plain,
    multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(unit_resolution,[status(thm)],[448,439]) ).

tff(450,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = multiply(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),
    inference(symmetry,[status(thm)],[449]) ).

tff(451,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(symmetry,[status(thm)],[444]) ).

tff(452,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)) = double_divide(a2,identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(453,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)) = double_divide(a2,identity),
    inference(unit_resolution,[status(thm)],[452,7]) ).

tff(454,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),
    inference(monotonicity,[status(thm)],[443,453]) ).

tff(455,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[454,451]) ).

tff(456,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[455]) ).

tff(457,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),
    inference(symmetry,[status(thm)],[456]) ).

tff(458,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[457]) ).

tff(459,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(symmetry,[status(thm)],[458]) ).

tff(460,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[459]) ).

tff(461,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(transitivity,[status(thm)],[460,450,447,441,432,115,112,89,294,240,304,83,80,11]) ).

tff(462,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(monotonicity,[status(thm)],[461]) ).

tff(463,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[462]) ).

tff(464,plain,
    double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[70]) ).

tff(465,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[126,464,463,426,424,421]) ).

tff(466,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[465]) ).

tff(467,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(symmetry,[status(thm)],[466]) ).

tff(468,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(469,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity),
    inference(unit_resolution,[status(thm)],[468,7]) ).

tff(470,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),a2),identity)),
    inference(symmetry,[status(thm)],[214]) ).

tff(471,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity),
    inference(monotonicity,[status(thm)],[87]) ).

tff(472,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity) = double_divide(a2,identity),
    inference(transitivity,[status(thm)],[471,470,229,39]) ).

tff(473,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(a2,identity),identity),
    inference(monotonicity,[status(thm)],[472,125]) ).

tff(474,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[473,127]) ).

tff(475,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[474]) ).

tff(476,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[375]) ).

tff(477,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[476]) ).

tff(478,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),
    inference(transitivity,[status(thm)],[477,475,132]) ).

tff(479,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(monotonicity,[status(thm)],[478]) ).

tff(480,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[479]) ).

tff(481,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(symmetry,[status(thm)],[480]) ).

tff(482,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(monotonicity,[status(thm)],[481]) ).

tff(483,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity),
    inference(transitivity,[status(thm)],[482,469]) ).

tff(484,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)),
    inference(monotonicity,[status(thm)],[54,483]) ).

tff(485,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[484,48,37,35]) ).

tff(486,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[485]) ).

tff(487,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
    inference(symmetry,[status(thm)],[486]) ).

tff(488,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(489,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[488,7]) ).

tff(490,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),
    inference(monotonicity,[status(thm)],[475]) ).

tff(491,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity),
    inference(monotonicity,[status(thm)],[490]) ).

tff(492,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity),
    inference(symmetry,[status(thm)],[491]) ).

tff(493,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)),
    inference(monotonicity,[status(thm)],[492]) ).

tff(494,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = inverse(double_divide(a2,identity)),
    inference(transitivity,[status(thm)],[493,489,21]) ).

tff(495,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(monotonicity,[status(thm)],[494]) ).

tff(496,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[495,35]) ).

tff(497,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[496]) ).

tff(498,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
    inference(transitivity,[status(thm)],[497,487]) ).

tff(499,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),
    inference(monotonicity,[status(thm)],[498]) ).

tff(500,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),
    inference(symmetry,[status(thm)],[499]) ).

tff(501,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[253,283,280,270,242,35]) ).

tff(502,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[501]) ).

tff(503,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(504,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[503,7]) ).

tff(505,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[166]) ).

tff(506,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[505]) ).

tff(507,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(transitivity,[status(thm)],[506,475,430]) ).

tff(508,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[507]) ).

tff(509,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[508]) ).

tff(510,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(symmetry,[status(thm)],[509]) ).

tff(511,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(monotonicity,[status(thm)],[510]) ).

tff(512,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = identity,
    inference(transitivity,[status(thm)],[511,504,31]) ).

tff(513,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[252,512]) ).

tff(514,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity))),
    inference(transitivity,[status(thm)],[513,254]) ).

tff(515,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(a2,identity)),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),
    inference(monotonicity,[status(thm)],[514]) ).

tff(516,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),
    inference(transitivity,[status(thm)],[515,502,487]) ).

tff(517,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),
    inference(monotonicity,[status(thm)],[516]) ).

tff(518,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),
    inference(transitivity,[status(thm)],[517,500]) ).

tff(519,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity),
    inference(monotonicity,[status(thm)],[518]) ).

tff(520,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity),
    inference(symmetry,[status(thm)],[519]) ).

tff(521,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(522,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity),
    inference(unit_resolution,[status(thm)],[521,7]) ).

tff(523,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),a2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(524,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),a2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(unit_resolution,[status(thm)],[523,7]) ).

tff(525,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(526,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[525,7]) ).

tff(527,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)) = inverse(double_divide(a2,identity)),
    inference(transitivity,[status(thm)],[526,21]) ).

tff(528,plain,
    double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(monotonicity,[status(thm)],[527]) ).

tff(529,plain,
    double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[528,35]) ).

tff(530,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[529]) ).

tff(531,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),
    inference(symmetry,[status(thm)],[530]) ).

tff(532,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(533,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity),
    inference(unit_resolution,[status(thm)],[532,7]) ).

tff(534,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)),
    inference(monotonicity,[status(thm)],[54,533]) ).

tff(535,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[534,48,37,35]) ).

tff(536,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[535]) ).

tff(537,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),
    inference(transitivity,[status(thm)],[536,531]) ).

tff(538,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),a2) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),
    inference(monotonicity,[status(thm)],[537]) ).

tff(539,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),a2),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity),
    inference(monotonicity,[status(thm)],[538]) ).

tff(540,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),a2),identity),
    inference(symmetry,[status(thm)],[539]) ).

tff(541,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),a2),identity)),
    inference(monotonicity,[status(thm)],[540]) ).

tff(542,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[541,524,135]) ).

tff(543,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity) = identity,
    inference(transitivity,[status(thm)],[318,315,173,158,31]) ).

tff(544,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[543,542]) ).

tff(545,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity))),
    inference(symmetry,[status(thm)],[544]) ).

tff(546,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(547,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(unit_resolution,[status(thm)],[546,7]) ).

tff(548,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity),
    inference(monotonicity,[status(thm)],[500]) ).

tff(549,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity),
    inference(symmetry,[status(thm)],[548]) ).

tff(550,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)),
    inference(monotonicity,[status(thm)],[549]) ).

tff(551,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[550,547,135]) ).

tff(552,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[543,551]) ).

tff(553,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity))),
    inference(transitivity,[status(thm)],[552,545]) ).

tff(554,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity)))),
    inference(monotonicity,[status(thm)],[553]) ).

tff(555,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[554]) ).

tff(556,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[555]) ).

tff(557,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(monotonicity,[status(thm)],[556]) ).

tff(558,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[557]) ).

tff(559,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(560,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity),
    inference(unit_resolution,[status(thm)],[559,7]) ).

tff(561,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)),
    inference(symmetry,[status(thm)],[560]) ).

tff(562,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),
    inference(transitivity,[status(thm)],[188,531]) ).

tff(563,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),a2) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),
    inference(monotonicity,[status(thm)],[562]) ).

tff(564,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),a2),
    inference(symmetry,[status(thm)],[563]) ).

tff(565,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),a2),identity),
    inference(monotonicity,[status(thm)],[564]) ).

tff(566,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),a2),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(a2,identity)),identity)))),a2),identity),
    inference(symmetry,[status(thm)],[565]) ).

tff(567,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),a2),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(568,plain,
    multiply(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),a2),identity),
    inference(unit_resolution,[status(thm)],[567,439]) ).

tff(569,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[383,150,382,374,372,371,53,48,37]) ).

tff(570,plain,
    multiply(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = multiply(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(monotonicity,[status(thm)],[569]) ).

tff(571,plain,
    multiply(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = multiply(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),
    inference(symmetry,[status(thm)],[570]) ).

tff(572,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(573,plain,
    multiply(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2),identity),
    inference(unit_resolution,[status(thm)],[572,439]) ).

tff(574,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2),identity) = multiply(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(symmetry,[status(thm)],[573]) ).

tff(575,plain,
    double_divide(a2,double_divide(a2,identity)) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[104,100,30,35]) ).

tff(576,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[181,575]) ).

tff(577,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity))) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[576,85,141]) ).

tff(578,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[30,577]) ).

tff(579,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),
    inference(symmetry,[status(thm)],[578]) ).

tff(580,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[31,137,579]) ).

tff(581,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),
    inference(monotonicity,[status(thm)],[580]) ).

tff(582,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),
    inference(monotonicity,[status(thm)],[581]) ).

tff(583,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2),identity),
    inference(symmetry,[status(thm)],[582]) ).

tff(584,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity),
    inference(transitivity,[status(thm)],[420,423,583,574,571,568,566,561,558,522,520]) ).

tff(585,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[382]) ).

tff(586,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[374]) ).

tff(587,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[371]) ).

tff(588,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),a2),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),identity)),
    inference(symmetry,[status(thm)],[48]) ).

tff(589,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),a2),identity)),
    inference(symmetry,[status(thm)],[37]) ).

tff(590,plain,
    identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(transitivity,[status(thm)],[30,589,588,52,587,50,586,585,151,118]) ).

tff(591,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)),
    inference(monotonicity,[status(thm)],[590,584]) ).

tff(592,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),a2)),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(symmetry,[status(thm)],[591]) ).

tff(593,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(594,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(unit_resolution,[status(thm)],[593,7]) ).

tff(595,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity)))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)))),identity)),
    inference(symmetry,[status(thm)],[594]) ).

tff(596,plain,
    double_divide(a2,identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),identity),double_divide(a2,double_divide(a2,identity)))),a2),identity)),
    inference(symmetry,[status(thm)],[89]) ).

tff(597,plain,
    double_divide(a2,identity) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[596,111,114,595,592,467,219]) ).

tff(598,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),
    inference(monotonicity,[status(thm)],[597,418]) ).

tff(599,plain,
    identity = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(transitivity,[status(thm)],[137,404]) ).

tff(600,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),
    inference(monotonicity,[status(thm)],[599,598]) ).

tff(601,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2)),identity),
    inference(monotonicity,[status(thm)],[600,31]) ).

tff(602,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = identity,
    inference(transitivity,[status(thm)],[601,396,393,173,158,31]) ).

tff(603,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[602,384]) ).

tff(604,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = identity,
    inference(transitivity,[status(thm)],[603,85,383,150,382,374,372,371,53,48,37,31]) ).

tff(605,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(a2,identity),
    inference(monotonicity,[status(thm)],[604]) ).

tff(606,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
    | ( double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(607,plain,
    double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity),
    inference(unit_resolution,[status(thm)],[606,7]) ).

tff(608,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(symmetry,[status(thm)],[607]) ).

tff(609,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(transitivity,[status(thm)],[608,605,294,240,304,83,80,11]) ).

tff(610,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(monotonicity,[status(thm)],[609]) ).

tff(611,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity)))),a2),identity),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),a2))),double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),identity)),
    inference(symmetry,[status(thm)],[610]) ).

tff(612,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(identity,a2) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(613,plain,
    multiply(identity,a2) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[612,439]) ).

tff(614,plain,
    multiply(identity,a2) = a2,
    inference(transitivity,[status(thm)],[613,464,611,9]) ).

tff(615,plain,
    ( ( multiply(identity,a2) != a2 )
  <=> ( multiply(identity,a2) != a2 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(616,axiom,
    multiply(identity,a2) != a2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).

tff(617,plain,
    multiply(identity,a2) != a2,
    inference(modus_ponens,[status(thm)],[616,615]) ).

tff(618,plain,
    $false,
    inference(unit_resolution,[status(thm)],[617,614]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GRP488-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Aug 31 17:16:15 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33  Usage: tptp [options] [-file:]file
% 0.12/0.33    -h, -?       prints this message.
% 0.12/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.33    -m, -model   generate model.
% 0.12/0.33    -p, -proof   generate proof.
% 0.12/0.33    -c, -core    generate unsat core of named formulas.
% 0.12/0.33    -st, -statistics display statistics.
% 0.12/0.33    -t:timeout   set timeout (in second).
% 0.12/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33    -<param>:<value> configuration parameter and value.
% 0.12/0.33    -o:<output-file> file to place output in.
% 0.18/0.54  % SZS status Unsatisfiable
% 0.18/0.54  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------