Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : GRP492-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n001.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 : Sat Jun 21 05:07:55 AM UTC 2025

% Result   : Unsatisfiable 19.65s 19.83s
% Output   : Proof 19.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   41
%            Number of leaves      :  166
% Syntax   : Number of formulae    : 1049 ( 888 unt;   0 typ;   0 def)
%            Number of atoms       : 1218 (1213 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  321 ( 156   ~; 152   |;   0   &)
%                                         (  13 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :   18 (   3 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  460 ( 453   !;   0   ?; 460   :)

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

tff(c3_type,type,
    c3: $i ).

tff(b3_type,type,
    b3: $i ).

tff(a3_type,type,
    a3: $i ).

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

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

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

tff(1,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(2,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)],[1]) ).

tff(3,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(4,axiom,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).

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

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

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

tff(8,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(a3,multiply(b3,c3)) = double_divide(double_divide(multiply(b3,c3),a3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(9,plain,
    multiply(a3,multiply(b3,c3)) = double_divide(double_divide(multiply(b3,c3),a3),identity),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    double_divide(double_divide(multiply(b3,c3),a3),identity) = multiply(a3,multiply(b3,c3)),
    inference(symmetry,[status(thm)],[9]) ).

tff(11,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(( ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
      <=> ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C ) )),
    inference(bind,[status(th)],[]) ).

tff(12,plain,
    ( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
  <=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,plain,
    ( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
  <=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(14,axiom,
    ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

tff(15,plain,
    ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C ),
    inference(modus_ponens,[status(thm)],[14,13]) ).

tff(16,plain,
    ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C ),
    inference(skolemize,[status(sab)],[15]) ).

tff(17,plain,
    ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3))))) = double_divide(double_divide(multiply(b3,c3),a3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(19,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3))))) = double_divide(double_divide(multiply(b3,c3),a3),identity),
    inference(unit_resolution,[status(thm)],[18,17]) ).

tff(20,plain,
    ^ [A: $i] :
      refl(( ( identity = double_divide(A,inverse(A)) )
      <=> ( identity = double_divide(A,inverse(A)) ) )),
    inference(bind,[status(th)],[]) ).

tff(21,plain,
    ( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
  <=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
    inference(quant_intro,[status(thm)],[20]) ).

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

tff(23,axiom,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).

tff(24,plain,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    inference(modus_ponens,[status(thm)],[23,22]) ).

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

tff(26,plain,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    inference(modus_ponens,[status(thm)],[25,21]) ).

tff(27,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(28,plain,
    identity = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
    inference(unit_resolution,[status(thm)],[27,26]) ).

tff(29,plain,
    double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) = identity,
    inference(symmetry,[status(thm)],[28]) ).

tff(30,plain,
    double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(identity,c3),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(31,plain,
    double_divide(double_divide(identity,c3),identity) = double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[30]) ).

tff(32,plain,
    double_divide(double_divide(double_divide(identity,c3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[31,29]) ).

tff(33,plain,
    double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(identity,c3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[32]) ).

tff(34,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,c3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(35,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,c3),
    inference(unit_resolution,[status(thm)],[34,17]) ).

tff(36,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(identity,c3),identity),
    inference(monotonicity,[status(thm)],[35]) ).

tff(37,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(38,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),
    inference(unit_resolution,[status(thm)],[37,7]) ).

tff(39,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(40,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[39,17]) ).

tff(41,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[40]) ).

tff(42,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3))))))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),
    inference(monotonicity,[status(thm)],[41,40]) ).

tff(43,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(monotonicity,[status(thm)],[42]) ).

tff(44,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))))),
    inference(symmetry,[status(thm)],[43]) ).

tff(45,plain,
    ^ [A: $i] :
      refl(( ( inverse(A) = double_divide(A,identity) )
      <=> ( inverse(A) = double_divide(A,identity) ) )),
    inference(bind,[status(th)],[]) ).

tff(46,plain,
    ( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
  <=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
    inference(quant_intro,[status(thm)],[45]) ).

tff(47,plain,
    ( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
  <=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(48,axiom,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).

tff(49,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(modus_ponens,[status(thm)],[48,47]) ).

tff(50,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(skolemize,[status(sab)],[49]) ).

tff(51,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(modus_ponens,[status(thm)],[50,46]) ).

tff(52,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(53,plain,
    inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),identity),
    inference(unit_resolution,[status(thm)],[52,51]) ).

tff(54,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),identity) = inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[53]) ).

tff(55,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(56,plain,
    double_divide(identity,identity) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),identity),
    inference(symmetry,[status(thm)],[55]) ).

tff(57,plain,
    double_divide(identity,identity) = inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[56,54]) ).

tff(58,plain,
    double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[28,57]) ).

tff(59,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[58]) ).

tff(60,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(61,plain,
    identity = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(unit_resolution,[status(thm)],[60,26]) ).

tff(62,plain,
    identity = double_divide(identity,double_divide(identity,identity)),
    inference(transitivity,[status(thm)],[61,59]) ).

tff(63,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3))))))))),
    inference(monotonicity,[status(thm)],[62,44]) ).

tff(64,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3))))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
    inference(symmetry,[status(thm)],[63]) ).

tff(65,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3))))))))) = double_divide(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(66,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3))))))))) = double_divide(identity,identity),
    inference(unit_resolution,[status(thm)],[65,17]) ).

tff(67,plain,
    double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(c3,multiply(a3,b3))))))))),
    inference(symmetry,[status(thm)],[66]) ).

tff(68,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))))) = double_divide(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(69,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))))) = double_divide(identity,identity),
    inference(unit_resolution,[status(thm)],[68,17]) ).

tff(70,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))) = double_divide(double_divide(b3,a3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(71,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))) = double_divide(double_divide(b3,a3),identity),
    inference(unit_resolution,[status(thm)],[70,17]) ).

tff(72,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))),identity) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(monotonicity,[status(thm)],[71]) ).

tff(73,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),
    inference(monotonicity,[status(thm)],[72,71]) ).

tff(74,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),
    inference(monotonicity,[status(thm)],[73]) ).

tff(75,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = identity,
    inference(symmetry,[status(thm)],[61]) ).

tff(76,plain,
    double_divide(identity,double_divide(identity,identity)) = identity,
    inference(transitivity,[status(thm)],[58,75]) ).

tff(77,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(monotonicity,[status(thm)],[76,74]) ).

tff(78,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))))),
    inference(symmetry,[status(thm)],[77]) ).

tff(79,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(80,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(unit_resolution,[status(thm)],[79,17]) ).

tff(81,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(82,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(unit_resolution,[status(thm)],[81,17]) ).

tff(83,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),
    inference(monotonicity,[status(thm)],[82]) ).

tff(84,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
    inference(monotonicity,[status(thm)],[83,82]) ).

tff(85,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))),
    inference(monotonicity,[status(thm)],[84]) ).

tff(86,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(identity,identity),
    inference(transitivity,[status(thm)],[78,69]) ).

tff(87,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))) = double_divide(identity,double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[86]) ).

tff(88,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))) = identity,
    inference(transitivity,[status(thm)],[87,58,75]) ).

tff(89,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))))),
    inference(monotonicity,[status(thm)],[88,85]) ).

tff(90,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[89]) ).

tff(91,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[29,29]) ).

tff(92,plain,
    double_divide(identity,identity) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[91]) ).

tff(93,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))) = identity ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(94,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))) = identity,
    inference(unit_resolution,[status(thm)],[93,17]) ).

tff(95,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(96,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),
    inference(unit_resolution,[status(thm)],[95,17]) ).

tff(97,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),
    inference(monotonicity,[status(thm)],[96]) ).

tff(98,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(monotonicity,[status(thm)],[97,96]) ).

tff(99,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),
    inference(monotonicity,[status(thm)],[98]) ).

tff(100,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))),
    inference(symmetry,[status(thm)],[99]) ).

tff(101,plain,
    double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))))),
    inference(symmetry,[status(thm)],[69]) ).

tff(102,plain,
    double_divide(identity,identity) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(transitivity,[status(thm)],[101,77]) ).

tff(103,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(monotonicity,[status(thm)],[102,100]) ).

tff(104,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),
    inference(symmetry,[status(thm)],[103]) ).

tff(105,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(106,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),
    inference(unit_resolution,[status(thm)],[105,17]) ).

tff(107,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[106]) ).

tff(108,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(109,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),
    inference(unit_resolution,[status(thm)],[108,17]) ).

tff(110,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(111,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),
    inference(unit_resolution,[status(thm)],[110,17]) ).

tff(112,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(113,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(unit_resolution,[status(thm)],[112,17]) ).

tff(114,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),
    inference(monotonicity,[status(thm)],[113]) ).

tff(115,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(monotonicity,[status(thm)],[114,113]) ).

tff(116,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
    inference(monotonicity,[status(thm)],[115]) ).

tff(117,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))),
    inference(symmetry,[status(thm)],[116]) ).

tff(118,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(119,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(unit_resolution,[status(thm)],[118,17]) ).

tff(120,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),
    inference(monotonicity,[status(thm)],[119]) ).

tff(121,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(monotonicity,[status(thm)],[120,119]) ).

tff(122,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
    inference(monotonicity,[status(thm)],[121]) ).

tff(123,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))),
    inference(transitivity,[status(thm)],[122,117]) ).

tff(124,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(transitivity,[status(thm)],[63,66,101,77]) ).

tff(125,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(monotonicity,[status(thm)],[124,123]) ).

tff(126,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(127,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(unit_resolution,[status(thm)],[126,17]) ).

tff(128,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[127]) ).

tff(129,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(130,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[129,17]) ).

tff(131,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[130]) ).

tff(132,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),
    inference(monotonicity,[status(thm)],[131,130]) ).

tff(133,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(monotonicity,[status(thm)],[132]) ).

tff(134,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = identity,
    inference(transitivity,[status(thm)],[133,128,125,111,107,104,94]) ).

tff(135,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[78,69,92]) ).

tff(136,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[135,134]) ).

tff(137,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[136]) ).

tff(138,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(139,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(unit_resolution,[status(thm)],[138,7]) ).

tff(140,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[125]) ).

tff(141,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[111]) ).

tff(142,plain,
    identity = double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),
    inference(symmetry,[status(thm)],[94]) ).

tff(143,plain,
    double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(transitivity,[status(thm)],[29,142,103,106,141,140,127]) ).

tff(144,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
    inference(monotonicity,[status(thm)],[143]) ).

tff(145,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[144]) ).

tff(146,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(147,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(unit_resolution,[status(thm)],[146,7]) ).

tff(148,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
    inference(symmetry,[status(thm)],[147]) ).

tff(149,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(150,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[149]) ).

tff(151,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[150,29]) ).

tff(152,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = identity,
    inference(transitivity,[status(thm)],[151,148,145,139,137,109,107,104,94]) ).

tff(153,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = identity,
    inference(transitivity,[status(thm)],[148,145,139,137,109,107,104,94]) ).

tff(154,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[153,152]) ).

tff(155,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[151]) ).

tff(156,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[139]) ).

tff(157,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[109]) ).

tff(158,plain,
    identity = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(transitivity,[status(thm)],[142,103,106,157,136,156,144,147]) ).

tff(159,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[158,155]) ).

tff(160,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))) = identity,
    inference(transitivity,[status(thm)],[128,125,111,107,104,94]) ).

tff(161,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[150,160]) ).

tff(162,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity)),
    inference(monotonicity,[status(thm)],[161]) ).

tff(163,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[162,159,154,92]) ).

tff(164,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[158,163]) ).

tff(165,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))))),
    inference(symmetry,[status(thm)],[164]) ).

tff(166,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[153,91]) ).

tff(167,plain,
    double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(symmetry,[status(thm)],[166]) ).

tff(168,plain,
    double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
    inference(transitivity,[status(thm)],[29,61,59,167,165,90,80,78,69,67,64]) ).

tff(169,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[94]) ).

tff(170,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[169,92]) ).

tff(171,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[170,94]) ).

tff(172,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))),
    inference(symmetry,[status(thm)],[171]) ).

tff(173,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))) = identity ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(174,plain,
    double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))) = identity,
    inference(unit_resolution,[status(thm)],[173,17]) ).

tff(175,plain,
    double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[174]) ).

tff(176,plain,
    double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[175,92]) ).

tff(177,plain,
    double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[176,174]) ).

tff(178,plain,
    double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))),
    inference(transitivity,[status(thm)],[177,172]) ).

tff(179,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),
    inference(monotonicity,[status(thm)],[178]) ).

tff(180,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))))),
    inference(symmetry,[status(thm)],[179]) ).

tff(181,plain,
    double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))))),
    inference(monotonicity,[status(thm)],[180]) ).

tff(182,plain,
    double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))))) = double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),
    inference(symmetry,[status(thm)],[181]) ).

tff(183,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))))) = double_divide(identity,c3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(184,plain,
    double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))))) = double_divide(identity,c3),
    inference(unit_resolution,[status(thm)],[183,17]) ).

tff(185,plain,
    double_divide(identity,c3) = double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))))),
    inference(symmetry,[status(thm)],[184]) ).

tff(186,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))) = c3 ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(187,plain,
    double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))) = c3,
    inference(unit_resolution,[status(thm)],[186,17]) ).

tff(188,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(189,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(unit_resolution,[status(thm)],[188,17]) ).

tff(190,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),
    inference(monotonicity,[status(thm)],[189]) ).

tff(191,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(monotonicity,[status(thm)],[190,189]) ).

tff(192,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
    inference(monotonicity,[status(thm)],[191]) ).

tff(193,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))),
    inference(transitivity,[status(thm)],[192,117]) ).

tff(194,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(195,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(unit_resolution,[status(thm)],[194,17]) ).

tff(196,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(a3,b3) = double_divide(double_divide(b3,a3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(197,plain,
    multiply(a3,b3) = double_divide(double_divide(b3,a3),identity),
    inference(unit_resolution,[status(thm)],[196,7]) ).

tff(198,plain,
    double_divide(double_divide(b3,a3),identity) = multiply(a3,b3),
    inference(symmetry,[status(thm)],[197]) ).

tff(199,plain,
    double_divide(c3,double_divide(double_divide(b3,a3),identity)) = double_divide(c3,multiply(a3,b3)),
    inference(monotonicity,[status(thm)],[198]) ).

tff(200,plain,
    double_divide(c3,multiply(a3,b3)) = double_divide(c3,double_divide(double_divide(b3,a3),identity)),
    inference(symmetry,[status(thm)],[199]) ).

tff(201,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(c3,multiply(a3,b3)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(202,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(c3,multiply(a3,b3)),
    inference(unit_resolution,[status(thm)],[201,17]) ).

tff(203,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(c3,double_divide(double_divide(b3,a3),identity)),
    inference(transitivity,[status(thm)],[202,200]) ).

tff(204,plain,
    double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(monotonicity,[status(thm)],[199]) ).

tff(205,plain,
    double_divide(double_divide(c3,multiply(a3,b3)),identity) = double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
    inference(symmetry,[status(thm)],[204]) ).

tff(206,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(monotonicity,[status(thm)],[202]) ).

tff(207,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
    inference(transitivity,[status(thm)],[206,205]) ).

tff(208,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),
    inference(monotonicity,[status(thm)],[207,203]) ).

tff(209,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),
    inference(monotonicity,[status(thm)],[208]) ).

tff(210,plain,
    double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))),
    inference(symmetry,[status(thm)],[209]) ).

tff(211,plain,
    double_divide(identity,double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),
    inference(symmetry,[status(thm)],[87]) ).

tff(212,plain,
    identity = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),
    inference(transitivity,[status(thm)],[61,59,211]) ).

tff(213,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(monotonicity,[status(thm)],[212,210]) ).

tff(214,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(transitivity,[status(thm)],[213,195]) ).

tff(215,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(monotonicity,[status(thm)],[214,193]) ).

tff(216,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(217,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),
    inference(unit_resolution,[status(thm)],[216,17]) ).

tff(218,plain,
    double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[217]) ).

tff(219,plain,
    double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))) = identity,
    inference(transitivity,[status(thm)],[218,215,111,107,104,94]) ).

tff(220,plain,
    double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))) = double_divide(double_divide(identity,c3),identity),
    inference(monotonicity,[status(thm)],[219]) ).

tff(221,plain,
    double_divide(double_divide(identity,c3),identity) = double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))),
    inference(symmetry,[status(thm)],[220]) ).

tff(222,plain,
    double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = c3,
    inference(transitivity,[status(thm)],[30,221,187]) ).

tff(223,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,c3),
    inference(monotonicity,[status(thm)],[153,222]) ).

tff(224,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),
    inference(transitivity,[status(thm)],[223,185,182]) ).

tff(225,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(226,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(identity,identity),
    inference(unit_resolution,[status(thm)],[225,17]) ).

tff(227,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[226,92]) ).

tff(228,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[227]) ).

tff(229,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),
    inference(symmetry,[status(thm)],[228]) ).

tff(230,plain,
    identity = double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),
    inference(transitivity,[status(thm)],[142,103,106,157,136,229]) ).

tff(231,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))),
    inference(monotonicity,[status(thm)],[230,224]) ).

tff(232,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(symmetry,[status(thm)],[231]) ).

tff(233,plain,
    double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(identity,c3),
    inference(transitivity,[status(thm)],[181,184]) ).

tff(234,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity) = identity,
    inference(transitivity,[status(thm)],[228,137,109,107,104,94]) ).

tff(235,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))) = double_divide(identity,double_divide(identity,c3)),
    inference(monotonicity,[status(thm)],[234,233]) ).

tff(236,plain,
    double_divide(identity,double_divide(identity,c3)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))),
    inference(symmetry,[status(thm)],[235]) ).

tff(237,plain,
    double_divide(identity,double_divide(identity,c3)) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(transitivity,[status(thm)],[236,232]) ).

tff(238,plain,
    multiply(double_divide(identity,double_divide(identity,c3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))),
    inference(monotonicity,[status(thm)],[237,168]) ).

tff(239,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(identity,c3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,c3))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(240,plain,
    multiply(double_divide(identity,double_divide(identity,c3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,c3))),identity),
    inference(unit_resolution,[status(thm)],[239,7]) ).

tff(241,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,c3))),identity) = multiply(double_divide(identity,double_divide(identity,c3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[240]) ).

tff(242,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(243,plain,
    double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[242,17]) ).

tff(244,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[243]) ).

tff(245,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),
    inference(monotonicity,[status(thm)],[244,243]) ).

tff(246,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(monotonicity,[status(thm)],[245]) ).

tff(247,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = identity,
    inference(transitivity,[status(thm)],[246,128,125,111,107,104,94]) ).

tff(248,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,c3))) = double_divide(identity,double_divide(identity,double_divide(identity,c3))),
    inference(monotonicity,[status(thm)],[29]) ).

tff(249,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,c3))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,c3))),
    inference(symmetry,[status(thm)],[248]) ).

tff(250,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,c3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,c3))),identity),
    inference(monotonicity,[status(thm)],[249,247]) ).

tff(251,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,c3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,c3)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(252,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,c3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,c3)),
    inference(unit_resolution,[status(thm)],[251,17]) ).

tff(253,plain,
    double_divide(identity,double_divide(identity,c3)) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,c3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[252]) ).

tff(254,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,c3)) = double_divide(identity,double_divide(identity,c3)),
    inference(monotonicity,[status(thm)],[29]) ).

tff(255,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,c3)) = double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[254,253,250,241,238,38,36,31]) ).

tff(256,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,c3)),identity) = double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[255]) ).

tff(257,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(258,plain,
    double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[257,17]) ).

tff(259,plain,
    double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[258]) ).

tff(260,plain,
    double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),
    inference(monotonicity,[status(thm)],[259,258]) ).

tff(261,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(monotonicity,[status(thm)],[260]) ).

tff(262,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = identity,
    inference(transitivity,[status(thm)],[261,128,125,111,107,104,94]) ).

tff(263,plain,
    double_divide(identity,double_divide(identity,c3)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,c3)),
    inference(symmetry,[status(thm)],[254]) ).

tff(264,plain,
    double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,c3)),identity),
    inference(monotonicity,[status(thm)],[263,262]) ).

tff(265,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,c3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(266,plain,
    double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,c3),
    inference(unit_resolution,[status(thm)],[265,17]) ).

tff(267,plain,
    double_divide(identity,c3) = double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[266]) ).

tff(268,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))))) = double_divide(identity,c3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(269,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))))) = double_divide(identity,c3),
    inference(unit_resolution,[status(thm)],[268,17]) ).

tff(270,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))) = identity ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(271,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))) = identity,
    inference(unit_resolution,[status(thm)],[270,17]) ).

tff(272,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)) = double_divide(identity,double_divide(identity,b3)),
    inference(monotonicity,[status(thm)],[29]) ).

tff(273,plain,
    double_divide(identity,double_divide(identity,b3)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)),
    inference(symmetry,[status(thm)],[272]) ).

tff(274,plain,
    double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)),identity),
    inference(monotonicity,[status(thm)],[273,29]) ).

tff(275,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)),identity) = double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[274]) ).

tff(276,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,b3)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(277,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,b3)),
    inference(unit_resolution,[status(thm)],[276,17]) ).

tff(278,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))) = double_divide(identity,b3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(279,plain,
    double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))) = double_divide(identity,b3),
    inference(unit_resolution,[status(thm)],[278,17]) ).

tff(280,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))),identity) = double_divide(double_divide(identity,b3),identity),
    inference(monotonicity,[status(thm)],[279]) ).

tff(281,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)),
    inference(monotonicity,[status(thm)],[280,279]) ).

tff(282,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3))),
    inference(monotonicity,[status(thm)],[281]) ).

tff(283,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))))),
    inference(symmetry,[status(thm)],[282]) ).

tff(284,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))))))),
    inference(monotonicity,[status(thm)],[283]) ).

tff(285,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)),
    inference(transitivity,[status(thm)],[284,277,273]) ).

tff(286,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)),identity),
    inference(monotonicity,[status(thm)],[285]) ).

tff(287,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))),identity) = double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[286,275]) ).

tff(288,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[287,271]) ).

tff(289,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3))))),
    inference(symmetry,[status(thm)],[288]) ).

tff(290,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))))) = double_divide(identity,double_divide(identity,b3)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(291,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))))) = double_divide(identity,double_divide(identity,b3)),
    inference(unit_resolution,[status(thm)],[290,17]) ).

tff(292,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3))))))) = double_divide(identity,b3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(293,plain,
    double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3))))))) = double_divide(identity,b3),
    inference(unit_resolution,[status(thm)],[292,17]) ).

tff(294,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))) = double_divide(double_divide(c3,b3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(295,plain,
    double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))) = double_divide(double_divide(c3,b3),identity),
    inference(unit_resolution,[status(thm)],[294,17]) ).

tff(296,plain,
    double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),identity) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
    inference(monotonicity,[status(thm)],[295]) ).

tff(297,plain,
    double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3))))) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),
    inference(monotonicity,[status(thm)],[296,295]) ).

tff(298,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),
    inference(monotonicity,[status(thm)],[297]) ).

tff(299,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))))),
    inference(symmetry,[status(thm)],[298]) ).

tff(300,plain,
    double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3))))))),
    inference(monotonicity,[status(thm)],[299]) ).

tff(301,plain,
    double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(identity,b3),
    inference(transitivity,[status(thm)],[300,293]) ).

tff(302,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(c3,b3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(303,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(c3,b3),
    inference(unit_resolution,[status(thm)],[302,17]) ).

tff(304,plain,
    double_divide(c3,b3) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),
    inference(symmetry,[status(thm)],[303]) ).

tff(305,plain,
    double_divide(double_divide(c3,b3),identity) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),
    inference(monotonicity,[status(thm)],[304]) ).

tff(306,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity) = double_divide(double_divide(c3,b3),identity),
    inference(symmetry,[status(thm)],[305]) ).

tff(307,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))) = double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)),
    inference(monotonicity,[status(thm)],[306,301]) ).

tff(308,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))),
    inference(monotonicity,[status(thm)],[307]) ).

tff(309,plain,
    double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))))),
    inference(symmetry,[status(thm)],[308]) ).

tff(310,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))))),
    inference(monotonicity,[status(thm)],[309]) ).

tff(311,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)),
    inference(transitivity,[status(thm)],[310,291,273]) ).

tff(312,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)),identity),
    inference(monotonicity,[status(thm)],[311]) ).

tff(313,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity) = double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[312,275]) ).

tff(314,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[313,174]) ).

tff(315,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3))))),
    inference(transitivity,[status(thm)],[314,289]) ).

tff(316,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))))),
    inference(monotonicity,[status(thm)],[315]) ).

tff(317,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))))),
    inference(symmetry,[status(thm)],[316]) ).

tff(318,plain,
    double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(identity,b3),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(319,plain,
    double_divide(double_divide(identity,b3),identity) = double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[318]) ).

tff(320,plain,
    double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3))))))) = double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),
    inference(symmetry,[status(thm)],[300]) ).

tff(321,plain,
    double_divide(identity,b3) = double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3)))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(double_divide(c3,b3),identity),a3))))))),
    inference(symmetry,[status(thm)],[293]) ).

tff(322,plain,
    double_divide(identity,b3) = double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),
    inference(transitivity,[status(thm)],[321,320]) ).

tff(323,plain,
    double_divide(double_divide(identity,b3),identity) = double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),
    inference(monotonicity,[status(thm)],[322]) ).

tff(324,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity) = double_divide(double_divide(identity,b3),identity),
    inference(symmetry,[status(thm)],[323]) ).

tff(325,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(identity,b3))) = double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(326,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(identity,b3))) = double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),
    inference(unit_resolution,[status(thm)],[325,7]) ).

tff(327,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(328,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(unit_resolution,[status(thm)],[327,17]) ).

tff(329,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),
    inference(monotonicity,[status(thm)],[328]) ).

tff(330,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(monotonicity,[status(thm)],[329,328]) ).

tff(331,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),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(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))),
    inference(transitivity,[status(thm)],[331,117]) ).

tff(333,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)))))))) = double_divide(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(334,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)))))))) = double_divide(identity,identity),
    inference(unit_resolution,[status(thm)],[333,17]) ).

tff(335,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))) = double_divide(double_divide(c3,b3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(336,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))) = double_divide(double_divide(c3,b3),identity),
    inference(unit_resolution,[status(thm)],[335,17]) ).

tff(337,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))),identity) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
    inference(monotonicity,[status(thm)],[336]) ).

tff(338,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)))))) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),
    inference(monotonicity,[status(thm)],[337,336]) ).

tff(339,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),
    inference(monotonicity,[status(thm)],[338]) ).

tff(340,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))))),
    inference(symmetry,[status(thm)],[339]) ).

tff(341,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)))))))),
    inference(monotonicity,[status(thm)],[62,340]) ).

tff(342,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(transitivity,[status(thm)],[341,334,101,77]) ).

tff(343,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(monotonicity,[status(thm)],[342,332]) ).

tff(344,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(345,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),
    inference(unit_resolution,[status(thm)],[344,17]) ).

tff(346,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[345]) ).

tff(347,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
    inference(transitivity,[status(thm)],[346,343,111,107,104,94,28]) ).

tff(348,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(identity,b3))) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))),
    inference(monotonicity,[status(thm)],[347]) ).

tff(349,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(identity,b3))),
    inference(symmetry,[status(thm)],[348]) ).

tff(350,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))) = double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(351,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))) = double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(unit_resolution,[status(thm)],[350,7]) ).

tff(352,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))),
    inference(symmetry,[status(thm)],[351]) ).

tff(353,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3))))) = double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[288,352,349,326,324,319]) ).

tff(354,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[158,353]) ).

tff(355,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,b3),identity),double_divide(identity,b3)))))),
    inference(symmetry,[status(thm)],[354]) ).

tff(356,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))) = b3 ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(357,plain,
    double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))) = b3,
    inference(unit_resolution,[status(thm)],[356,17]) ).

tff(358,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(359,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(unit_resolution,[status(thm)],[358,17]) ).

tff(360,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),
    inference(monotonicity,[status(thm)],[359]) ).

tff(361,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(monotonicity,[status(thm)],[360,359]) ).

tff(362,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
    inference(monotonicity,[status(thm)],[361]) ).

tff(363,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))),
    inference(transitivity,[status(thm)],[362,117]) ).

tff(364,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(365,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(unit_resolution,[status(thm)],[364,17]) ).

tff(366,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(b3,a3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(367,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(b3,a3),
    inference(unit_resolution,[status(thm)],[366,17]) ).

tff(368,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(b3,a3),identity),
    inference(monotonicity,[status(thm)],[367]) ).

tff(369,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),
    inference(monotonicity,[status(thm)],[368,367]) ).

tff(370,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),
    inference(monotonicity,[status(thm)],[369]) ).

tff(371,plain,
    double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))),
    inference(symmetry,[status(thm)],[370]) ).

tff(372,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(monotonicity,[status(thm)],[212,371]) ).

tff(373,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(transitivity,[status(thm)],[372,365]) ).

tff(374,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(monotonicity,[status(thm)],[373,363]) ).

tff(375,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(376,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),
    inference(unit_resolution,[status(thm)],[375,17]) ).

tff(377,plain,
    double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[376]) ).

tff(378,plain,
    double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))) = identity,
    inference(transitivity,[status(thm)],[377,374,111,107,104,94]) ).

tff(379,plain,
    double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))) = double_divide(double_divide(identity,b3),identity),
    inference(monotonicity,[status(thm)],[378]) ).

tff(380,plain,
    double_divide(double_divide(identity,b3),identity) = double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[379]) ).

tff(381,plain,
    double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = b3,
    inference(transitivity,[status(thm)],[318,380,357]) ).

tff(382,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,b3),
    inference(monotonicity,[status(thm)],[153,381]) ).

tff(383,plain,
    double_divide(identity,b3) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(symmetry,[status(thm)],[382]) ).

tff(384,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,b3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(385,plain,
    double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,b3),
    inference(unit_resolution,[status(thm)],[384,17]) ).

tff(386,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(387,plain,
    double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[386,17]) ).

tff(388,plain,
    double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[387]) ).

tff(389,plain,
    double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),
    inference(monotonicity,[status(thm)],[388,387]) ).

tff(390,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(monotonicity,[status(thm)],[389]) ).

tff(391,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = identity,
    inference(transitivity,[status(thm)],[390,128,125,111,107,104,94]) ).

tff(392,plain,
    double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)),identity),
    inference(monotonicity,[status(thm)],[273,391]) ).

tff(393,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)),identity) = double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[392]) ).

tff(394,plain,
    double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))))),
    inference(transitivity,[status(thm)],[274,393,385,383,355,317]) ).

tff(395,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity))))))) = double_divide(identity,double_divide(c3,b3)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(396,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity))))))) = double_divide(identity,double_divide(c3,b3)),
    inference(unit_resolution,[status(thm)],[395,17]) ).

tff(397,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(b3,a3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(398,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(b3,a3),
    inference(unit_resolution,[status(thm)],[397,17]) ).

tff(399,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity) = double_divide(double_divide(b3,a3),identity),
    inference(monotonicity,[status(thm)],[398]) ).

tff(400,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity))))) = double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),
    inference(monotonicity,[status(thm)],[399,398]) ).

tff(401,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),
    inference(monotonicity,[status(thm)],[400]) ).

tff(402,plain,
    double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),
    inference(symmetry,[status(thm)],[401]) ).

tff(403,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),identity))))))),
    inference(monotonicity,[status(thm)],[402]) ).

tff(404,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))) = double_divide(identity,double_divide(c3,b3)),
    inference(transitivity,[status(thm)],[403,396]) ).

tff(405,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity) = double_divide(double_divide(identity,double_divide(c3,b3)),identity),
    inference(monotonicity,[status(thm)],[404]) ).

tff(406,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))),
    inference(monotonicity,[status(thm)],[405,404]) ).

tff(407,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))),
    inference(monotonicity,[status(thm)],[406]) ).

tff(408,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))),
    inference(symmetry,[status(thm)],[407]) ).

tff(409,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))),
    inference(monotonicity,[status(thm)],[408]) ).

tff(410,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),
    inference(symmetry,[status(thm)],[409]) ).

tff(411,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))) = double_divide(identity,double_divide(identity,double_divide(c3,b3))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(412,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))) = double_divide(identity,double_divide(identity,double_divide(c3,b3))),
    inference(unit_resolution,[status(thm)],[411,17]) ).

tff(413,plain,
    double_divide(identity,double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))),
    inference(symmetry,[status(thm)],[412]) ).

tff(414,plain,
    double_divide(identity,double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),
    inference(transitivity,[status(thm)],[413,410]) ).

tff(415,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))) = identity ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(416,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))) = identity,
    inference(unit_resolution,[status(thm)],[415,17]) ).

tff(417,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[416]) ).

tff(418,plain,
    double_divide(identity,identity) = double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),
    inference(symmetry,[status(thm)],[417]) ).

tff(419,plain,
    identity = double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),
    inference(transitivity,[status(thm)],[61,59,167,165,90,80,78,69,418]) ).

tff(420,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))))),
    inference(monotonicity,[status(thm)],[419,414]) ).

tff(421,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),
    inference(symmetry,[status(thm)],[420]) ).

tff(422,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(double_divide(b3,a3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(423,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(double_divide(b3,a3),identity),
    inference(unit_resolution,[status(thm)],[422,17]) ).

tff(424,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(monotonicity,[status(thm)],[423]) ).

tff(425,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),
    inference(monotonicity,[status(thm)],[424,423]) ).

tff(426,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),
    inference(monotonicity,[status(thm)],[425]) ).

tff(427,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))))),
    inference(symmetry,[status(thm)],[426]) ).

tff(428,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))),
    inference(monotonicity,[status(thm)],[427]) ).

tff(429,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(symmetry,[status(thm)],[428]) ).

tff(430,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))) = double_divide(identity,double_divide(c3,b3)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(431,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))) = double_divide(identity,double_divide(c3,b3)),
    inference(unit_resolution,[status(thm)],[430,17]) ).

tff(432,plain,
    double_divide(identity,double_divide(c3,b3)) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))),
    inference(symmetry,[status(thm)],[431]) ).

tff(433,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(434,plain,
    identity = double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))),
    inference(unit_resolution,[status(thm)],[433,26]) ).

tff(435,plain,
    double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))) = identity,
    inference(symmetry,[status(thm)],[434]) ).

tff(436,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(c3,b3)) = double_divide(double_divide(c3,b3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(437,plain,
    inverse(double_divide(c3,b3)) = double_divide(double_divide(c3,b3),identity),
    inference(unit_resolution,[status(thm)],[436,51]) ).

tff(438,plain,
    double_divide(double_divide(c3,b3),identity) = inverse(double_divide(c3,b3)),
    inference(symmetry,[status(thm)],[437]) ).

tff(439,plain,
    double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(c3,b3),inverse(double_divide(c3,b3))),
    inference(monotonicity,[status(thm)],[438]) ).

tff(440,plain,
    double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)) = identity,
    inference(transitivity,[status(thm)],[439,435]) ).

tff(441,plain,
    double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[440]) ).

tff(442,plain,
    double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[441,92]) ).

tff(443,plain,
    double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[442,440]) ).

tff(444,plain,
    double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))),
    inference(transitivity,[status(thm)],[443,172]) ).

tff(445,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),
    inference(monotonicity,[status(thm)],[444]) ).

tff(446,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))),
    inference(symmetry,[status(thm)],[445]) ).

tff(447,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))))),
    inference(monotonicity,[status(thm)],[446]) ).

tff(448,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))))) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),
    inference(symmetry,[status(thm)],[447]) ).

tff(449,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))))) = double_divide(c3,b3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(450,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))))) = double_divide(c3,b3),
    inference(unit_resolution,[status(thm)],[449,17]) ).

tff(451,plain,
    double_divide(c3,b3) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))))),
    inference(symmetry,[status(thm)],[450]) ).

tff(452,plain,
    double_divide(c3,b3) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),
    inference(transitivity,[status(thm)],[451,448]) ).

tff(453,plain,
    double_divide(identity,double_divide(c3,b3)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))),
    inference(monotonicity,[status(thm)],[230,452]) ).

tff(454,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))) = double_divide(identity,double_divide(c3,b3)),
    inference(symmetry,[status(thm)],[453]) ).

tff(455,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(transitivity,[status(thm)],[454,432,429]) ).

tff(456,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))))),
    inference(symmetry,[status(thm)],[74]) ).

tff(457,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))))))),
    inference(monotonicity,[status(thm)],[456]) ).

tff(458,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[457,69,92]) ).

tff(459,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[458]) ).

tff(460,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),
    inference(symmetry,[status(thm)],[459]) ).

tff(461,plain,
    identity = double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),
    inference(transitivity,[status(thm)],[142,103,106,157,136,460]) ).

tff(462,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),
    inference(monotonicity,[status(thm)],[461,455]) ).

tff(463,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))))),
    inference(symmetry,[status(thm)],[462]) ).

tff(464,plain,
    double_divide(identity,double_divide(c3,b3)) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(transitivity,[status(thm)],[432,429]) ).

tff(465,plain,
    double_divide(identity,double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),
    inference(monotonicity,[status(thm)],[461,464]) ).

tff(466,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))))),
    inference(transitivity,[status(thm)],[409,412,465,463]) ).

tff(467,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,identity))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[76]) ).

tff(468,plain,
    double_divide(identity,identity) = double_divide(identity,double_divide(identity,double_divide(identity,identity))),
    inference(symmetry,[status(thm)],[467]) ).

tff(469,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity) = double_divide(identity,double_divide(identity,double_divide(identity,identity))),
    inference(transitivity,[status(thm)],[417,468]) ).

tff(470,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))))),
    inference(monotonicity,[status(thm)],[469,466]) ).

tff(471,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))))) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))))),
    inference(symmetry,[status(thm)],[470]) ).

tff(472,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))))) = double_divide(identity,double_divide(c3,b3)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(473,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))))) = double_divide(identity,double_divide(c3,b3)),
    inference(unit_resolution,[status(thm)],[472,17]) ).

tff(474,plain,
    double_divide(identity,double_divide(c3,b3)) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))))),
    inference(symmetry,[status(thm)],[473]) ).

tff(475,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(c3,b3)),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(476,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),identity) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[475]) ).

tff(477,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[343]) ).

tff(478,plain,
    identity = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),
    inference(transitivity,[status(thm)],[142,103,106,141,477,345]) ).

tff(479,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),identity) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),
    inference(monotonicity,[status(thm)],[478]) ).

tff(480,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(identity,double_divide(c3,b3)),identity),
    inference(symmetry,[status(thm)],[479]) ).

tff(481,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[447,450,304,480,476]) ).

tff(482,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(transitivity,[status(thm)],[228,156,144,147]) ).

tff(483,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[482,481]) ).

tff(484,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))),
    inference(symmetry,[status(thm)],[483]) ).

tff(485,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))) = identity ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(486,plain,
    double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))) = identity,
    inference(unit_resolution,[status(thm)],[485,17]) ).

tff(487,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[486]) ).

tff(488,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[487,92]) ).

tff(489,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[488,486]) ).

tff(490,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))))) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))),
    inference(transitivity,[status(thm)],[489,172]) ).

tff(491,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),
    inference(monotonicity,[status(thm)],[490]) ).

tff(492,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))))),
    inference(symmetry,[status(thm)],[491]) ).

tff(493,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))))))),
    inference(monotonicity,[status(thm)],[492]) ).

tff(494,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),
    inference(symmetry,[status(thm)],[493]) ).

tff(495,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(496,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
    inference(unit_resolution,[status(thm)],[495,17]) ).

tff(497,plain,
    double_divide(identity,double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3))))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)),identity),double_divide(identity,double_divide(c3,b3)))))))),
    inference(symmetry,[status(thm)],[496]) ).

tff(498,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity))))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(499,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity))))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
    inference(unit_resolution,[status(thm)],[498,17]) ).

tff(500,plain,
    double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(c3,b3),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(501,plain,
    double_divide(double_divide(c3,b3),identity) = double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[500]) ).

tff(502,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))) = double_divide(double_divide(c3,b3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(503,plain,
    double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))) = double_divide(double_divide(c3,b3),identity),
    inference(unit_resolution,[status(thm)],[502,17]) ).

tff(504,plain,
    double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))) = double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[503,501]) ).

tff(505,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))))))) = double_divide(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(506,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))))))) = double_divide(identity,identity),
    inference(unit_resolution,[status(thm)],[505,17]) ).

tff(507,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))) = double_divide(double_divide(double_divide(c3,b3),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(508,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
    inference(unit_resolution,[status(thm)],[507,17]) ).

tff(509,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),
    inference(monotonicity,[status(thm)],[508]) ).

tff(510,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))))) = double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)),
    inference(monotonicity,[status(thm)],[509,508]) ).

tff(511,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity))),
    inference(monotonicity,[status(thm)],[510]) ).

tff(512,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))))),
    inference(symmetry,[status(thm)],[511]) ).

tff(513,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))))))),
    inference(monotonicity,[status(thm)],[512]) ).

tff(514,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[513,506,92]) ).

tff(515,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[514]) ).

tff(516,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[515,504]) ).

tff(517,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(monotonicity,[status(thm)],[516]) ).

tff(518,plain,
    double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(519,plain,
    double_divide(identity,identity) = double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[518]) ).

tff(520,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,identity))) = double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[467,519]) ).

tff(521,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity))))))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(monotonicity,[status(thm)],[520,517]) ).

tff(522,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity))))))),
    inference(symmetry,[status(thm)],[521]) ).

tff(523,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(c3,b3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(524,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(c3,b3),
    inference(unit_resolution,[status(thm)],[523,17]) ).

tff(525,plain,
    double_divide(c3,b3) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(symmetry,[status(thm)],[524]) ).

tff(526,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),
    inference(transitivity,[status(thm)],[475,479,303,525,522,499,497,494]) ).

tff(527,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),
    inference(transitivity,[status(thm)],[148,145,139,229]) ).

tff(528,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))),
    inference(monotonicity,[status(thm)],[527,526]) ).

tff(529,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(symmetry,[status(thm)],[528]) ).

tff(530,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
    inference(transitivity,[status(thm)],[493,496]) ).

tff(531,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),
    inference(monotonicity,[status(thm)],[234,530]) ).

tff(532,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))))),
    inference(symmetry,[status(thm)],[531]) ).

tff(533,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(534,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),
    inference(unit_resolution,[status(thm)],[533,17]) ).

tff(535,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(536,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[535,17]) ).

tff(537,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[536]) ).

tff(538,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),
    inference(monotonicity,[status(thm)],[537,536]) ).

tff(539,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(monotonicity,[status(thm)],[538]) ).

tff(540,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = identity,
    inference(transitivity,[status(thm)],[539,128,125,111,107,104,94]) ).

tff(541,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),
    inference(monotonicity,[status(thm)],[29]) ).

tff(542,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),
    inference(symmetry,[status(thm)],[541]) ).

tff(543,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),identity),
    inference(monotonicity,[status(thm)],[542,540]) ).

tff(544,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[543]) ).

tff(545,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(546,plain,
    multiply(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),identity),
    inference(unit_resolution,[status(thm)],[545,7]) ).

tff(547,plain,
    double_divide(identity,double_divide(double_divide(c3,b3),identity)) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),double_divide(double_divide(double_divide(c3,b3),identity),identity))))))),
    inference(symmetry,[status(thm)],[499]) ).

tff(548,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
    inference(monotonicity,[status(thm)],[153,500]) ).

tff(549,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[548,547,521,524,304,480,476]) ).

tff(550,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[158,549]) ).

tff(551,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(symmetry,[status(thm)],[550]) ).

tff(552,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(transitivity,[status(thm)],[532,529,551]) ).

tff(553,plain,
    multiply(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))),
    inference(monotonicity,[status(thm)],[552,168]) ).

tff(554,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = multiply(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[553]) ).

tff(555,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(556,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),
    inference(unit_resolution,[status(thm)],[555,7]) ).

tff(557,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))),
    inference(symmetry,[status(thm)],[556]) ).

tff(558,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(c3,b3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(559,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(c3,b3),
    inference(unit_resolution,[status(thm)],[558,17]) ).

tff(560,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(c3,b3),identity),
    inference(monotonicity,[status(thm)],[559]) ).

tff(561,plain,
    double_divide(double_divide(c3,b3),identity) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),
    inference(symmetry,[status(thm)],[560]) ).

tff(562,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(563,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),
    inference(unit_resolution,[status(thm)],[562,7]) ).

tff(564,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(c3,b3))) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))),
    inference(monotonicity,[status(thm)],[347]) ).

tff(565,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(c3,b3))),
    inference(symmetry,[status(thm)],[564]) ).

tff(566,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(567,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(unit_resolution,[status(thm)],[566,7]) ).

tff(568,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,b3))),
    inference(symmetry,[status(thm)],[567]) ).

tff(569,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),
    inference(transitivity,[status(thm)],[568,565,563,306,561,557,554,546,544,534,532,529,484,454,474,471,421]) ).

tff(570,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,b3))),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3)))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),double_divide(identity,b3))))))),
    inference(monotonicity,[status(thm)],[569,394]) ).

tff(571,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,b3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(572,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,b3),
    inference(unit_resolution,[status(thm)],[571,17]) ).

tff(573,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(identity,b3),identity),
    inference(monotonicity,[status(thm)],[572]) ).

tff(574,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(575,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),
    inference(unit_resolution,[status(thm)],[574,7]) ).

tff(576,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),
    inference(transitivity,[status(thm)],[382,321,320]) ).

tff(577,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),identity),double_divide(double_divide(double_divide(c3,b3),identity),double_divide(c3,b3)))))))),
    inference(monotonicity,[status(thm)],[340]) ).

tff(578,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[577,334,92]) ).

tff(579,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[578]) ).

tff(580,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),
    inference(symmetry,[status(thm)],[579]) ).

tff(581,plain,
    identity = double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),
    inference(transitivity,[status(thm)],[142,103,106,157,136,580]) ).

tff(582,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))),
    inference(monotonicity,[status(thm)],[581,576]) ).

tff(583,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(symmetry,[status(thm)],[582]) ).

tff(584,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity) = identity,
    inference(transitivity,[status(thm)],[579,137,109,107,104,94]) ).

tff(585,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))) = double_divide(identity,double_divide(identity,b3)),
    inference(monotonicity,[status(thm)],[584,301]) ).

tff(586,plain,
    double_divide(identity,double_divide(identity,b3)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))))),
    inference(symmetry,[status(thm)],[585]) ).

tff(587,plain,
    double_divide(identity,double_divide(identity,b3)) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(transitivity,[status(thm)],[586,583]) ).

tff(588,plain,
    multiply(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))),
    inference(monotonicity,[status(thm)],[587,168]) ).

tff(589,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(590,plain,
    multiply(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))),identity),
    inference(unit_resolution,[status(thm)],[589,7]) ).

tff(591,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))),identity) = multiply(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[590]) ).

tff(592,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(593,plain,
    double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[592,17]) ).

tff(594,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[593]) ).

tff(595,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),
    inference(monotonicity,[status(thm)],[594,593]) ).

tff(596,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(monotonicity,[status(thm)],[595]) ).

tff(597,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = identity,
    inference(transitivity,[status(thm)],[596,128,125,111,107,104,94]) ).

tff(598,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))) = double_divide(identity,double_divide(identity,double_divide(identity,b3))),
    inference(monotonicity,[status(thm)],[29]) ).

tff(599,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,b3))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))),
    inference(symmetry,[status(thm)],[598]) ).

tff(600,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))),identity),
    inference(monotonicity,[status(thm)],[599,597]) ).

tff(601,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,b3)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(602,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,b3)),
    inference(unit_resolution,[status(thm)],[601,17]) ).

tff(603,plain,
    double_divide(identity,double_divide(identity,b3)) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[602]) ).

tff(604,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)) = double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[272,603,600,591,588,575,573,319]) ).

tff(605,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)),identity) = double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[604]) ).

tff(606,plain,
    double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,b3)),identity),
    inference(symmetry,[status(thm)],[605]) ).

tff(607,plain,
    double_divide(double_divide(double_divide(identity,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[319,29]) ).

tff(608,plain,
    double_divide(double_divide(double_divide(identity,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[607,606,275]) ).

tff(609,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[608]) ).

tff(610,plain,
    double_divide(double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(identity,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[607]) ).

tff(611,plain,
    double_divide(identity,b3) = double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[385]) ).

tff(612,plain,
    double_divide(identity,double_divide(identity,b3)) = double_divide(double_divide(identity,b3),identity),
    inference(transitivity,[status(thm)],[603,600,591,588,575,573]) ).

tff(613,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(identity,b3),identity)),
    inference(monotonicity,[status(thm)],[612]) ).

tff(614,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(identity,b3),identity)) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,b3))),
    inference(symmetry,[status(thm)],[613]) ).

tff(615,plain,
    double_divide(double_divide(identity,b3),identity) = b3,
    inference(transitivity,[status(thm)],[380,357]) ).

tff(616,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(identity,b3),identity)) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),b3),
    inference(monotonicity,[status(thm)],[615]) ).

tff(617,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),b3) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(identity,b3),identity)),
    inference(symmetry,[status(thm)],[616]) ).

tff(618,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),b3) = double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(619,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),b3) = double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(unit_resolution,[status(thm)],[618,7]) ).

tff(620,plain,
    double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),b3),
    inference(symmetry,[status(thm)],[619]) ).

tff(621,plain,
    b3 = double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[357]) ).

tff(622,plain,
    double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[621,29]) ).

tff(623,plain,
    double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity) = double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[622]) ).

tff(624,plain,
    double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[623,29]) ).

tff(625,plain,
    double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[624,620,617,614,349,326,324,319]) ).

tff(626,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[625]) ).

tff(627,plain,
    double_divide(double_divide(b3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[624]) ).

tff(628,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(identity,b3))),
    inference(symmetry,[status(thm)],[326]) ).

tff(629,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)))) = b3 ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(630,plain,
    double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)))) = b3,
    inference(unit_resolution,[status(thm)],[629,17]) ).

tff(631,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(632,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),
    inference(unit_resolution,[status(thm)],[631,17]) ).

tff(633,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(634,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[633,17]) ).

tff(635,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[634]) ).

tff(636,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),
    inference(monotonicity,[status(thm)],[635,634]) ).

tff(637,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(monotonicity,[status(thm)],[636]) ).

tff(638,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))),
    inference(symmetry,[status(thm)],[637]) ).

tff(639,plain,
    identity = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))),
    inference(transitivity,[status(thm)],[142,103,106,141,140,127,638]) ).

tff(640,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)))),
    inference(monotonicity,[status(thm)],[29]) ).

tff(641,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)))),identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(monotonicity,[status(thm)],[640,639]) ).

tff(642,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(643,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)))),identity),
    inference(unit_resolution,[status(thm)],[642,7]) ).

tff(644,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(b3,c3) = double_divide(double_divide(c3,b3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(645,plain,
    multiply(b3,c3) = double_divide(double_divide(c3,b3),identity),
    inference(unit_resolution,[status(thm)],[644,7]) ).

tff(646,plain,
    double_divide(double_divide(c3,b3),identity) = multiply(b3,c3),
    inference(symmetry,[status(thm)],[645]) ).

tff(647,plain,
    double_divide(double_divide(double_divide(c3,b3),identity),a3) = double_divide(multiply(b3,c3),a3),
    inference(monotonicity,[status(thm)],[646]) ).

tff(648,plain,
    double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) = double_divide(double_divide(multiply(b3,c3),a3),identity),
    inference(monotonicity,[status(thm)],[647]) ).

tff(649,plain,
    double_divide(double_divide(multiply(b3,c3),a3),identity) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),
    inference(symmetry,[status(thm)],[648]) ).

tff(650,plain,
    double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)) = double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)),
    inference(monotonicity,[status(thm)],[649]) ).

tff(651,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3))))))))) = double_divide(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(652,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3))))))))) = double_divide(identity,identity),
    inference(unit_resolution,[status(thm)],[651,17]) ).

tff(653,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(654,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[653]) ).

tff(655,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(656,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),
    inference(unit_resolution,[status(thm)],[655,17]) ).

tff(657,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))),
    inference(monotonicity,[status(thm)],[519]) ).

tff(658,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[657,656,654]) ).

tff(659,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[658]) ).

tff(660,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[659,658]) ).

tff(661,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(monotonicity,[status(thm)],[660]) ).

tff(662,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))))),
    inference(symmetry,[status(thm)],[661]) ).

tff(663,plain,
    double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))) = double_divide(identity,double_divide(identity,identity)),
    inference(transitivity,[status(thm)],[377,374,111,107,104,94,61,59]) ).

tff(664,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(identity,double_divide(b3,a3))))))))),
    inference(monotonicity,[status(thm)],[663,662]) ).

tff(665,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(666,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),
    inference(unit_resolution,[status(thm)],[665,17]) ).

tff(667,plain,
    double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(symmetry,[status(thm)],[666]) ).

tff(668,plain,
    double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[667,664,652,92]) ).

tff(669,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[668]) ).

tff(670,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity) = identity,
    inference(transitivity,[status(thm)],[669,137,109,107,104,94]) ).

tff(671,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),
    inference(monotonicity,[status(thm)],[670,650]) ).

tff(672,plain,
    multiply(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(monotonicity,[status(thm)],[671]) ).

tff(673,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(674,plain,
    multiply(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),identity),
    inference(unit_resolution,[status(thm)],[673,7]) ).

tff(675,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[674]) ).

tff(676,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),
    inference(monotonicity,[status(thm)],[29]) ).

tff(677,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[676]) ).

tff(678,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[677,29]) ).

tff(679,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3))),
    inference(transitivity,[status(thm)],[678,675,672,643,641,632]) ).

tff(680,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),inverse(double_divide(double_divide(double_divide(c3,b3),identity),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(681,plain,
    identity = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),inverse(double_divide(double_divide(double_divide(c3,b3),identity),identity))),
    inference(unit_resolution,[status(thm)],[680,26]) ).

tff(682,plain,
    double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),inverse(double_divide(double_divide(double_divide(c3,b3),identity),identity))) = identity,
    inference(symmetry,[status(thm)],[681]) ).

tff(683,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(double_divide(c3,b3),identity),identity)) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(684,plain,
    inverse(double_divide(double_divide(double_divide(c3,b3),identity),identity)) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),
    inference(unit_resolution,[status(thm)],[683,51]) ).

tff(685,plain,
    double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity) = inverse(double_divide(double_divide(double_divide(c3,b3),identity),identity)),
    inference(symmetry,[status(thm)],[684]) ).

tff(686,plain,
    double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(687,plain,
    double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = inverse(double_divide(double_divide(double_divide(c3,b3),identity),identity)),
    inference(transitivity,[status(thm)],[686,685]) ).

tff(688,plain,
    double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
    inference(monotonicity,[status(thm)],[500]) ).

tff(689,plain,
    double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),inverse(double_divide(double_divide(double_divide(c3,b3),identity),identity))),
    inference(monotonicity,[status(thm)],[688,687]) ).

tff(690,plain,
    double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = identity,
    inference(transitivity,[status(thm)],[689,682]) ).

tff(691,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[690]) ).

tff(692,plain,
    double_divide(identity,identity) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(symmetry,[status(thm)],[691]) ).

tff(693,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(transitivity,[status(thm)],[171,156,144,147]) ).

tff(694,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity)),
    inference(monotonicity,[status(thm)],[693]) ).

tff(695,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(transitivity,[status(thm)],[445,694,159,154,692]) ).

tff(696,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))))) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(monotonicity,[status(thm)],[695]) ).

tff(697,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(c3,b3),double_divide(double_divide(c3,b3),identity))))),
    inference(symmetry,[status(thm)],[696]) ).

tff(698,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(c3,b3),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(699,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(c3,b3),identity),identity),
    inference(unit_resolution,[status(thm)],[698,17]) ).

tff(700,plain,
    double_divide(double_divide(double_divide(c3,b3),identity),identity) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(symmetry,[status(thm)],[699]) ).

tff(701,plain,
    double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(identity,double_divide(double_divide(c3,b3),identity)),
    inference(transitivity,[status(thm)],[688,700,697,450,525,522,499]) ).

tff(702,plain,
    double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),double_divide(b3,a3)))),
    inference(monotonicity,[status(thm)],[701,679]) ).

tff(703,plain,
    double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[702,630,621,379,323,628,348,613,616,619,627]) ).

tff(704,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[158,703]) ).

tff(705,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(double_divide(double_divide(identity,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[704,626,382,611,392,605,610]) ).

tff(706,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity)))),identity) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),identity),identity),double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(c3,b3))),
    inference(symmetry,[status(thm)],[563]) ).

tff(707,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),identity) = multiply(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[546]) ).

tff(708,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(c3,b3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[534]) ).

tff(709,plain,
    double_divide(identity,double_divide(c3,b3)) = double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(transitivity,[status(thm)],[453,483,528,531,708,543,707,553,556,560,305,706,564,567]) ).

tff(710,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,b3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[709,705]) ).

tff(711,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(712,plain,
    double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),
    inference(unit_resolution,[status(thm)],[711,17]) ).

tff(713,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(c3,b3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,b3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(symmetry,[status(thm)],[712]) ).

tff(714,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3)))) = double_divide(double_divide(double_divide(identity,c3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[713,710,609,570,269,267,264,256,33]) ).

tff(715,plain,
    double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(b3,a3),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(716,plain,
    double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(monotonicity,[status(thm)],[715]) ).

tff(717,plain,
    double_divide(double_divide(double_divide(b3,a3),identity),identity) = double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(symmetry,[status(thm)],[716]) ).

tff(718,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(719,plain,
    double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(unit_resolution,[status(thm)],[718,17]) ).

tff(720,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),inverse(double_divide(double_divide(double_divide(b3,a3),identity),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(721,plain,
    identity = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),inverse(double_divide(double_divide(double_divide(b3,a3),identity),identity))),
    inference(unit_resolution,[status(thm)],[720,26]) ).

tff(722,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),inverse(double_divide(double_divide(double_divide(b3,a3),identity),identity))) = identity,
    inference(symmetry,[status(thm)],[721]) ).

tff(723,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(double_divide(b3,a3),identity),identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(724,plain,
    inverse(double_divide(double_divide(double_divide(b3,a3),identity),identity)) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),
    inference(unit_resolution,[status(thm)],[723,51]) ).

tff(725,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity) = inverse(double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(symmetry,[status(thm)],[724]) ).

tff(726,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(727,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = inverse(double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(transitivity,[status(thm)],[726,725]) ).

tff(728,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),inverse(double_divide(double_divide(double_divide(b3,a3),identity),identity))),
    inference(monotonicity,[status(thm)],[716,727]) ).

tff(729,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = identity,
    inference(transitivity,[status(thm)],[728,722]) ).

tff(730,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[729]) ).

tff(731,plain,
    double_divide(identity,identity) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(symmetry,[status(thm)],[730]) ).

tff(732,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(733,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(unit_resolution,[status(thm)],[732,17]) ).

tff(734,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),
    inference(monotonicity,[status(thm)],[733]) ).

tff(735,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
    inference(monotonicity,[status(thm)],[734,733]) ).

tff(736,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))),
    inference(monotonicity,[status(thm)],[735]) ).

tff(737,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(transitivity,[status(thm)],[736,162,159,154,731]) ).

tff(738,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(b3,a3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(739,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(b3,a3),
    inference(unit_resolution,[status(thm)],[738,17]) ).

tff(740,plain,
    double_divide(double_divide(b3,a3),identity) = double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[715]) ).

tff(741,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(double_divide(b3,a3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(742,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(double_divide(b3,a3),identity),
    inference(unit_resolution,[status(thm)],[741,17]) ).

tff(743,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[742,740]) ).

tff(744,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity)))))))) = double_divide(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(745,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity)))))))) = double_divide(identity,identity),
    inference(unit_resolution,[status(thm)],[744,17]) ).

tff(746,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(747,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(unit_resolution,[status(thm)],[746,17]) ).

tff(748,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),
    inference(monotonicity,[status(thm)],[747]) ).

tff(749,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity)))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(monotonicity,[status(thm)],[748,747]) ).

tff(750,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
    inference(monotonicity,[status(thm)],[749]) ).

tff(751,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity))))))),
    inference(symmetry,[status(thm)],[750]) ).

tff(752,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(c3,b3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(c3,b3),identity)))))))),
    inference(monotonicity,[status(thm)],[751]) ).

tff(753,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[752,745,92]) ).

tff(754,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[753]) ).

tff(755,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[754,743]) ).

tff(756,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(monotonicity,[status(thm)],[755]) ).

tff(757,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))))),
    inference(symmetry,[status(thm)],[756]) ).

tff(758,plain,
    double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(identity,double_divide(identity,double_divide(identity,identity))),
    inference(transitivity,[status(thm)],[518,468]) ).

tff(759,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))),
    inference(monotonicity,[status(thm)],[758,757]) ).

tff(760,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(symmetry,[status(thm)],[759]) ).

tff(761,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))) = double_divide(identity,double_divide(double_divide(b3,a3),identity)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(762,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))) = double_divide(identity,double_divide(double_divide(b3,a3),identity)),
    inference(unit_resolution,[status(thm)],[761,17]) ).

tff(763,plain,
    double_divide(identity,double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))),
    inference(symmetry,[status(thm)],[762]) ).

tff(764,plain,
    double_divide(identity,double_divide(double_divide(b3,a3),identity)) = double_divide(b3,a3),
    inference(transitivity,[status(thm)],[763,760,739]) ).

tff(765,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(b3,a3),identity))) = double_divide(identity,double_divide(b3,a3)),
    inference(monotonicity,[status(thm)],[764]) ).

tff(766,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(monotonicity,[status(thm)],[765,737]) ).

tff(767,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(b3,a3),identity)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(768,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(b3,a3),identity)),
    inference(unit_resolution,[status(thm)],[767,17]) ).

tff(769,plain,
    double_divide(identity,double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[768]) ).

tff(770,plain,
    double_divide(identity,double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(transitivity,[status(thm)],[769,766,719,717]) ).

tff(771,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,c3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[770,714]) ).

tff(772,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,c3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(b3,a3)),identity),double_divide(double_divide(double_divide(multiply(b3,c3),a3),identity),double_divide(b3,a3))))),
    inference(symmetry,[status(thm)],[771]) ).

tff(773,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(774,plain,
    double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(unit_resolution,[status(thm)],[773,17]) ).

tff(775,plain,
    double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),
    inference(monotonicity,[status(thm)],[774]) ).

tff(776,plain,
    double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(monotonicity,[status(thm)],[775,774]) ).

tff(777,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))),
    inference(monotonicity,[status(thm)],[776]) ).

tff(778,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))),
    inference(symmetry,[status(thm)],[777]) ).

tff(779,plain,
    double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),
    inference(monotonicity,[status(thm)],[778]) ).

tff(780,plain,
    double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))) = double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),
    inference(symmetry,[status(thm)],[779]) ).

tff(781,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))) = double_divide(identity,c3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(782,plain,
    double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))) = double_divide(identity,c3),
    inference(unit_resolution,[status(thm)],[781,17]) ).

tff(783,plain,
    double_divide(identity,c3) = double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),
    inference(symmetry,[status(thm)],[782]) ).

tff(784,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,c3)),identity) = double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[264]) ).

tff(785,plain,
    double_divide(double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,c3)),identity),
    inference(symmetry,[status(thm)],[256]) ).

tff(786,plain,
    double_divide(double_divide(double_divide(identity,c3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),
    inference(transitivity,[status(thm)],[32,785,784,266,783,780]) ).

tff(787,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(monotonicity,[status(thm)],[742]) ).

tff(788,plain,
    double_divide(double_divide(double_divide(b3,a3),identity),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),
    inference(symmetry,[status(thm)],[787]) ).

tff(789,plain,
    double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),
    inference(transitivity,[status(thm)],[716,788]) ).

tff(790,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,c3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))),
    inference(monotonicity,[status(thm)],[789,786]) ).

tff(791,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,c3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(symmetry,[status(thm)],[790]) ).

tff(792,plain,
    c3 = double_divide(double_divide(identity,c3),double_divide(identity,double_divide(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))),
    inference(symmetry,[status(thm)],[187]) ).

tff(793,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))) = c3 ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(794,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))) = c3,
    inference(unit_resolution,[status(thm)],[793,17]) ).

tff(795,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(double_divide(b3,a3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(796,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(double_divide(b3,a3),identity),
    inference(unit_resolution,[status(thm)],[795,17]) ).

tff(797,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(monotonicity,[status(thm)],[796]) ).

tff(798,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),
    inference(monotonicity,[status(thm)],[797,796]) ).

tff(799,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),
    inference(monotonicity,[status(thm)],[798]) ).

tff(800,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))))),
    inference(symmetry,[status(thm)],[799]) ).

tff(801,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))),
    inference(monotonicity,[status(thm)],[800]) ).

tff(802,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(symmetry,[status(thm)],[801]) ).

tff(803,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))) = double_divide(identity,double_divide(c3,multiply(a3,b3))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(804,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))) = double_divide(identity,double_divide(c3,multiply(a3,b3))),
    inference(unit_resolution,[status(thm)],[803,17]) ).

tff(805,plain,
    double_divide(identity,double_divide(c3,multiply(a3,b3))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))))),
    inference(symmetry,[status(thm)],[804]) ).

tff(806,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(c3,multiply(a3,b3)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(807,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(c3,multiply(a3,b3)),
    inference(unit_resolution,[status(thm)],[806,17]) ).

tff(808,plain,
    identity = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(transitivity,[status(thm)],[142,103,106,141,140,127]) ).

tff(809,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
    inference(monotonicity,[status(thm)],[808]) ).

tff(810,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity) = double_divide(c3,multiply(a3,b3)),
    inference(transitivity,[status(thm)],[809,807]) ).

tff(811,plain,
    double_divide(identity,double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity)) = double_divide(identity,double_divide(c3,multiply(a3,b3))),
    inference(monotonicity,[status(thm)],[810]) ).

tff(812,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(813,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity)),
    inference(monotonicity,[status(thm)],[153,812]) ).

tff(814,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[812]) ).

tff(815,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),
    inference(symmetry,[status(thm)],[809]) ).

tff(816,plain,
    double_divide(c3,multiply(a3,b3)) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
    inference(symmetry,[status(thm)],[807]) ).

tff(817,plain,
    double_divide(c3,double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[199,816,815,814]) ).

tff(818,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(819,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(identity,identity),
    inference(unit_resolution,[status(thm)],[818,17]) ).

tff(820,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(821,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[820]) ).

tff(822,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(823,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),
    inference(unit_resolution,[status(thm)],[822,17]) ).

tff(824,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),
    inference(monotonicity,[status(thm)],[519]) ).

tff(825,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[824,823,821]) ).

tff(826,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(b3,a3)) = double_divide(double_divide(b3,a3),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(827,plain,
    inverse(double_divide(b3,a3)) = double_divide(double_divide(b3,a3),identity),
    inference(unit_resolution,[status(thm)],[826,51]) ).

tff(828,plain,
    double_divide(double_divide(b3,a3),identity) = inverse(double_divide(b3,a3)),
    inference(symmetry,[status(thm)],[827]) ).

tff(829,plain,
    double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
    inference(monotonicity,[status(thm)],[828]) ).

tff(830,plain,
    double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)) = identity,
    inference(transitivity,[status(thm)],[829,29]) ).

tff(831,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[821,830]) ).

tff(832,plain,
    double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) = double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),
    inference(symmetry,[status(thm)],[829]) ).

tff(833,plain,
    identity = double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),
    inference(transitivity,[status(thm)],[28,832]) ).

tff(834,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),
    inference(transitivity,[status(thm)],[824,823]) ).

tff(835,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))),
    inference(monotonicity,[status(thm)],[834,833]) ).

tff(836,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(transitivity,[status(thm)],[835,831]) ).

tff(837,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[836,825]) ).

tff(838,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(monotonicity,[status(thm)],[837]) ).

tff(839,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),
    inference(symmetry,[status(thm)],[838]) ).

tff(840,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) = double_divide(identity,double_divide(identity,identity)),
    inference(transitivity,[status(thm)],[107,104,94,61,59]) ).

tff(841,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),
    inference(monotonicity,[status(thm)],[840,839]) ).

tff(842,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(843,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),
    inference(unit_resolution,[status(thm)],[842,17]) ).

tff(844,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(symmetry,[status(thm)],[843]) ).

tff(845,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[844,841,819,92]) ).

tff(846,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[845]) ).

tff(847,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(transitivity,[status(thm)],[846,156,144,147]) ).

tff(848,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[847,817]) ).

tff(849,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(transitivity,[status(thm)],[848,813,811,805,802]) ).

tff(850,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),
    inference(monotonicity,[status(thm)],[461,849]) ).

tff(851,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),
    inference(symmetry,[status(thm)],[850]) ).

tff(852,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(identity,double_divide(c3,multiply(a3,b3))),
    inference(transitivity,[status(thm)],[801,804]) ).

tff(853,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity) = identity,
    inference(transitivity,[status(thm)],[459,137,109,107,104,94]) ).

tff(854,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))) = double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),
    inference(monotonicity,[status(thm)],[853,852]) ).

tff(855,plain,
    double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))),
    inference(symmetry,[status(thm)],[854]) ).

tff(856,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(857,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),
    inference(unit_resolution,[status(thm)],[856,17]) ).

tff(858,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(c3,multiply(a3,b3)),inverse(double_divide(c3,multiply(a3,b3)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(859,plain,
    identity = double_divide(double_divide(c3,multiply(a3,b3)),inverse(double_divide(c3,multiply(a3,b3)))),
    inference(unit_resolution,[status(thm)],[858,26]) ).

tff(860,plain,
    double_divide(double_divide(c3,multiply(a3,b3)),inverse(double_divide(c3,multiply(a3,b3)))) = identity,
    inference(symmetry,[status(thm)],[859]) ).

tff(861,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(c3,multiply(a3,b3))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(862,plain,
    inverse(double_divide(c3,multiply(a3,b3))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[861,51]) ).

tff(863,plain,
    double_divide(double_divide(c3,multiply(a3,b3)),identity) = inverse(double_divide(c3,multiply(a3,b3))),
    inference(symmetry,[status(thm)],[862]) ).

tff(864,plain,
    double_divide(double_divide(c3,multiply(a3,b3)),identity) = double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),identity),
    inference(monotonicity,[status(thm)],[816]) ).

tff(865,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),identity) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(symmetry,[status(thm)],[864]) ).

tff(866,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(867,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),identity),
    inference(unit_resolution,[status(thm)],[866,7]) ).

tff(868,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
    inference(transitivity,[status(thm)],[128,125,111,107,104,94,28]) ).

tff(869,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,multiply(a3,b3)))),
    inference(monotonicity,[status(thm)],[868]) ).

tff(870,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(c3,multiply(a3,b3)))),
    inference(symmetry,[status(thm)],[869]) ).

tff(871,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(872,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,multiply(a3,b3)))) = double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(unit_resolution,[status(thm)],[871,7]) ).

tff(873,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(c3,multiply(a3,b3)))),
    inference(symmetry,[status(thm)],[872]) ).

tff(874,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[814,29]) ).

tff(875,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = inverse(double_divide(c3,multiply(a3,b3))),
    inference(transitivity,[status(thm)],[874,873,870,867,865,863]) ).

tff(876,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity))))))) = double_divide(identity,double_divide(c3,multiply(a3,b3))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(877,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity))))))) = double_divide(identity,double_divide(c3,multiply(a3,b3))),
    inference(unit_resolution,[status(thm)],[876,17]) ).

tff(878,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(879,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[878,17]) ).

tff(880,plain,
    double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[879]) ).

tff(881,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity))))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),
    inference(monotonicity,[status(thm)],[880,879]) ).

tff(882,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(monotonicity,[status(thm)],[881]) ).

tff(883,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))))),
    inference(symmetry,[status(thm)],[882]) ).

tff(884,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity))))))),
    inference(monotonicity,[status(thm)],[883]) ).

tff(885,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(identity,double_divide(c3,multiply(a3,b3))),
    inference(transitivity,[status(thm)],[884,877]) ).

tff(886,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),identity) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),
    inference(monotonicity,[status(thm)],[885]) ).

tff(887,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(888,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),identity),
    inference(unit_resolution,[status(thm)],[887,7]) ).

tff(889,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),
    inference(monotonicity,[status(thm)],[143]) ).

tff(890,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(891,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(unit_resolution,[status(thm)],[890,7]) ).

tff(892,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),
    inference(symmetry,[status(thm)],[891]) ).

tff(893,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(c3,multiply(a3,b3)),
    inference(transitivity,[status(thm)],[892,889,888,886,809,807]) ).

tff(894,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(c3,multiply(a3,b3)),inverse(double_divide(c3,multiply(a3,b3)))),
    inference(monotonicity,[status(thm)],[893,875]) ).

tff(895,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[894,860,142,103,106,157,136,156,144,147,155]) ).

tff(896,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[158,895]) ).

tff(897,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(symmetry,[status(thm)],[896]) ).

tff(898,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(899,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(unit_resolution,[status(thm)],[898,17]) ).

tff(900,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),
    inference(monotonicity,[status(thm)],[899]) ).

tff(901,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)))),
    inference(monotonicity,[status(thm)],[900,899]) ).

tff(902,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))))),
    inference(monotonicity,[status(thm)],[901]) ).

tff(903,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(transitivity,[status(thm)],[902,162,159,897]) ).

tff(904,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(monotonicity,[status(thm)],[903]) ).

tff(905,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[904]) ).

tff(906,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(907,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),
    inference(unit_resolution,[status(thm)],[906,17]) ).

tff(908,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(c3,multiply(a3,b3)))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(symmetry,[status(thm)],[907]) ).

tff(909,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = double_divide(c3,multiply(a3,b3)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(910,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = double_divide(c3,multiply(a3,b3)),
    inference(unit_resolution,[status(thm)],[909,17]) ).

tff(911,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),inverse(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(912,plain,
    identity = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),inverse(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity))),
    inference(unit_resolution,[status(thm)],[911,26]) ).

tff(913,plain,
    double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),inverse(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity))) = identity,
    inference(symmetry,[status(thm)],[912]) ).

tff(914,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(915,plain,
    inverse(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),identity),
    inference(unit_resolution,[status(thm)],[914,51]) ).

tff(916,plain,
    double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),identity) = inverse(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)),
    inference(symmetry,[status(thm)],[915]) ).

tff(917,plain,
    double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(918,plain,
    double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = inverse(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)),
    inference(transitivity,[status(thm)],[917,916]) ).

tff(919,plain,
    double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(920,plain,
    double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[919]) ).

tff(921,plain,
    double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),inverse(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity))),
    inference(monotonicity,[status(thm)],[920,918]) ).

tff(922,plain,
    double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = identity,
    inference(transitivity,[status(thm)],[921,913]) ).

tff(923,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[922]) ).

tff(924,plain,
    double_divide(identity,identity) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(symmetry,[status(thm)],[923]) ).

tff(925,plain,
    double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)) = double_divide(double_divide(c3,multiply(a3,b3)),inverse(double_divide(c3,multiply(a3,b3)))),
    inference(monotonicity,[status(thm)],[863]) ).

tff(926,plain,
    double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)) = identity,
    inference(transitivity,[status(thm)],[925,860]) ).

tff(927,plain,
    double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[926]) ).

tff(928,plain,
    double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),identity) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[927,92]) ).

tff(929,plain,
    double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[928,926]) ).

tff(930,plain,
    double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity))) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))),
    inference(transitivity,[status(thm)],[929,172]) ).

tff(931,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),
    inference(monotonicity,[status(thm)],[930]) ).

tff(932,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),
    inference(transitivity,[status(thm)],[931,694,159,154,924]) ).

tff(933,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity))))) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(monotonicity,[status(thm)],[932]) ).

tff(934,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity)),identity),double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(c3,multiply(a3,b3)),identity))))),
    inference(symmetry,[status(thm)],[933]) ).

tff(935,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(936,plain,
    double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(unit_resolution,[status(thm)],[935,17]) ).

tff(937,plain,
    double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity) = double_divide(double_divide(identity,double_divide(c3,multiply(a3,b3))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(symmetry,[status(thm)],[936]) ).

tff(938,plain,
    double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(939,plain,
    double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity)))),
    inference(transitivity,[status(thm)],[938,937,934,910,816,815,908,905,857,855,851]) ).

tff(940,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(941,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(unit_resolution,[status(thm)],[940,17]) ).

tff(942,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(943,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[942,17]) ).

tff(944,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),
    inference(monotonicity,[status(thm)],[943]) ).

tff(945,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))) = double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity)),
    inference(monotonicity,[status(thm)],[944,943]) ).

tff(946,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),
    inference(monotonicity,[status(thm)],[945]) ).

tff(947,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))))) = identity,
    inference(transitivity,[status(thm)],[946,128,125,111,107,104,94]) ).

tff(948,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))),
    inference(monotonicity,[status(thm)],[29]) ).

tff(949,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))),
    inference(symmetry,[status(thm)],[948]) ).

tff(950,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))),identity),
    inference(monotonicity,[status(thm)],[949,947]) ).

tff(951,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))),identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[950]) ).

tff(952,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(953,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity))),identity),
    inference(unit_resolution,[status(thm)],[952,7]) ).

tff(954,plain,
    double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))) = double_divide(identity,identity),
    inference(transitivity,[status(thm)],[29,61,59,167,165,90,80,78,69]) ).

tff(955,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))),
    inference(monotonicity,[status(thm)],[832]) ).

tff(956,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[955]) ).

tff(957,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[158,956]) ).

tff(958,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),
    inference(symmetry,[status(thm)],[957]) ).

tff(959,plain,
    double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(monotonicity,[status(thm)],[29]) ).

tff(960,plain,
    double_divide(double_divide(double_divide(b3,a3),identity),identity) = double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[959]) ).

tff(961,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(identity,double_divide(b3,a3)) = double_divide(double_divide(double_divide(b3,a3),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(962,plain,
    multiply(identity,double_divide(b3,a3)) = double_divide(double_divide(double_divide(b3,a3),identity),identity),
    inference(unit_resolution,[status(thm)],[961,7]) ).

tff(963,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(b3,a3),identity))) = multiply(identity,double_divide(b3,a3)),
    inference(monotonicity,[status(thm)],[29,764]) ).

tff(964,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(965,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(unit_resolution,[status(thm)],[964,7]) ).

tff(966,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(double_divide(b3,a3),identity))),
    inference(symmetry,[status(thm)],[965]) ).

tff(967,plain,
    double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)) = double_divide(identity,double_divide(double_divide(b3,a3),identity)),
    inference(monotonicity,[status(thm)],[29]) ).

tff(968,plain,
    double_divide(identity,double_divide(double_divide(b3,a3),identity)) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),
    inference(symmetry,[status(thm)],[967]) ).

tff(969,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),
    inference(monotonicity,[status(thm)],[968,29]) ).

tff(970,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[969]) ).

tff(971,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[970,830]) ).

tff(972,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[955,971,966,963,962,960]) ).

tff(973,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[972]) ).

tff(974,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(symmetry,[status(thm)],[973]) ).

tff(975,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(monotonicity,[status(thm)],[153,959]) ).

tff(976,plain,
    double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(symmetry,[status(thm)],[975]) ).

tff(977,plain,
    double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),
    inference(transitivity,[status(thm)],[976,974,958]) ).

tff(978,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[977,954]) ).

tff(979,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)) = multiply(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[978]) ).

tff(980,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(981,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))),identity),
    inference(unit_resolution,[status(thm)],[980,7]) ).

tff(982,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))),identity) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[981]) ).

tff(983,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))) = double_divide(b3,a3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(984,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))) = double_divide(b3,a3),
    inference(unit_resolution,[status(thm)],[983,17]) ).

tff(985,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))),
    inference(monotonicity,[status(thm)],[519]) ).

tff(986,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))) = double_divide(b3,a3),
    inference(transitivity,[status(thm)],[985,984]) ).

tff(987,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))),identity) = double_divide(double_divide(b3,a3),identity),
    inference(monotonicity,[status(thm)],[986]) ).

tff(988,plain,
    double_divide(double_divide(b3,a3),identity) = double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))),identity),
    inference(symmetry,[status(thm)],[987]) ).

tff(989,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(b3,a3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(990,plain,
    double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))) = double_divide(b3,a3),
    inference(unit_resolution,[status(thm)],[989,17]) ).

tff(991,plain,
    double_divide(b3,a3) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),
    inference(symmetry,[status(thm)],[990]) ).

tff(992,plain,
    double_divide(double_divide(b3,a3),identity) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),
    inference(monotonicity,[status(thm)],[991]) ).

tff(993,plain,
    double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity) = double_divide(double_divide(b3,a3),identity),
    inference(symmetry,[status(thm)],[992]) ).

tff(994,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(995,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity),
    inference(unit_resolution,[status(thm)],[994,7]) ).

tff(996,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),
    inference(transitivity,[status(thm)],[107,104,94,28]) ).

tff(997,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(b3,a3))) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),
    inference(monotonicity,[status(thm)],[996]) ).

tff(998,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(b3,a3))),
    inference(symmetry,[status(thm)],[997]) ).

tff(999,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(1000,plain,
    multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(unit_resolution,[status(thm)],[999,7]) ).

tff(1001,plain,
    double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = multiply(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(identity,double_divide(b3,a3))),
    inference(symmetry,[status(thm)],[1000]) ).

tff(1002,plain,
    double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity) = double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),
    inference(transitivity,[status(thm)],[1001,998,995,993,988,982,979,953,951,941]) ).

tff(1003,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(b3,a3),identity),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)),identity),double_divide(c3,double_divide(double_divide(b3,a3),identity))))),
    inference(monotonicity,[status(thm)],[1002,939]) ).

tff(1004,plain,
    double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity) = double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(symmetry,[status(thm)],[938]) ).

tff(1005,plain,
    double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))),identity) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(b3,a3))),
    inference(symmetry,[status(thm)],[995]) ).

tff(1006,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))) = double_divide(b3,a3) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(1007,plain,
    double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))) = double_divide(b3,a3),
    inference(unit_resolution,[status(thm)],[1006,17]) ).

tff(1008,plain,
    double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[830]) ).

tff(1009,plain,
    double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),identity) = double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[1008,92]) ).

tff(1010,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(monotonicity,[status(thm)],[1009,830]) ).

tff(1011,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))),
    inference(transitivity,[status(thm)],[1010,172]) ).

tff(1012,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),
    inference(monotonicity,[status(thm)],[1011]) ).

tff(1013,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)))),
    inference(symmetry,[status(thm)],[1012]) ).

tff(1014,plain,
    double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),identity))))),
    inference(monotonicity,[status(thm)],[1013]) ).

tff(1015,plain,
    double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))) = double_divide(b3,a3),
    inference(transitivity,[status(thm)],[1014,1007]) ).

tff(1016,plain,
    double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity) = double_divide(double_divide(b3,a3),identity),
    inference(monotonicity,[status(thm)],[1015]) ).

tff(1017,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(1018,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))))))))),identity),
    inference(unit_resolution,[status(thm)],[1017,7]) ).

tff(1019,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity)) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),
    inference(symmetry,[status(thm)],[694]) ).

tff(1020,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity)),
    inference(symmetry,[status(thm)],[159]) ).

tff(1021,plain,
    double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(symmetry,[status(thm)],[154]) ).

tff(1022,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),
    inference(transitivity,[status(thm)],[730,1021,1020,1019]) ).

tff(1023,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(b3,a3))) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),identity)))))))),double_divide(identity,double_divide(b3,a3))),
    inference(monotonicity,[status(thm)],[1022]) ).

tff(1024,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(1025,plain,
    multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(b3,a3))) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),
    inference(unit_resolution,[status(thm)],[1024,7]) ).

tff(1026,plain,
    double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity) = multiply(double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))),double_divide(identity,double_divide(b3,a3))),
    inference(symmetry,[status(thm)],[1025]) ).

tff(1027,plain,
    double_divide(double_divide(double_divide(b3,a3),identity),identity) = double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),
    inference(symmetry,[status(thm)],[719]) ).

tff(1028,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),
    inference(monotonicity,[status(thm)],[1027]) ).

tff(1029,plain,
    double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity) = double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),
    inference(transitivity,[status(thm)],[1028,1026,1023,1018,1016,992,1005,997,1000]) ).

tff(1030,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[1029,1004]) ).

tff(1031,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)) = double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),
    inference(transitivity,[status(thm)],[1030,1003,794,792,220,31]) ).

tff(1032,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(monotonicity,[status(thm)],[158,1031]) ).

tff(1033,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity))),
    inference(symmetry,[status(thm)],[1032]) ).

tff(1034,plain,
    double_divide(identity,c3) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,c3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))),
    inference(symmetry,[status(thm)],[223]) ).

tff(1035,plain,
    double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity))),
    inference(transitivity,[status(thm)],[779,782,1034,1033]) ).

tff(1036,plain,
    double_divide(double_divide(identity,double_divide(b3,a3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(b3,a3),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(b3,a3),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity),double_divide(double_divide(c3,multiply(a3,b3)),identity))),double_divide(double_divide(b3,a3),inverse(double_divide(b3,a3)))))))))),
    inference(symmetry,[status(thm)],[766]) ).

tff(1037,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity) = double_divide(identity,double_divide(double_divide(b3,a3),identity)),
    inference(transitivity,[status(thm)],[787,1027,1036,768]) ).

tff(1038,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))),
    inference(monotonicity,[status(thm)],[1037,1035]) ).

tff(1039,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity)))),identity),double_divide(double_divide(identity,double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(b3,a3),identity),identity))))),
    inference(symmetry,[status(thm)],[1038]) ).

tff(1040,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(1041,plain,
    double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[1040,17]) ).

tff(1042,plain,
    double_divide(double_divide(c3,multiply(a3,b3)),identity) = double_divide(double_divide(identity,double_divide(double_divide(b3,a3),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),identity),identity),identity),double_divide(double_divide(double_divide(c3,multiply(a3,b3)),identity),identity)))),
    inference(symmetry,[status(thm)],[1041]) ).

tff(1043,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(multiply(a3,b3),c3) = double_divide(double_divide(c3,multiply(a3,b3)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(1044,plain,
    multiply(multiply(a3,b3),c3) = double_divide(double_divide(c3,multiply(a3,b3)),identity),
    inference(unit_resolution,[status(thm)],[1043,7]) ).

tff(1045,plain,
    multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
    inference(transitivity,[status(thm)],[1044,1042,1039,791,772,19,10]) ).

tff(1046,plain,
    ( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
  <=> ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(1047,axiom,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).

tff(1048,plain,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    inference(modus_ponens,[status(thm)],[1047,1046]) ).

tff(1049,plain,
    $false,
    inference(unit_resolution,[status(thm)],[1048,1045]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GRP492-1 : TPTP v9.0.0. Released v2.6.0.
% 0.12/0.13  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n001.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Thu Jun 19 16:15:33 EDT 2025
% 0.12/0.35  % CPUTime    : 
% 19.65/19.83  % SZS status Unsatisfiable
% 19.65/19.83  % SZS output start Proof
% See solution above
% 19.95/20.19  % E exiting
%------------------------------------------------------------------------------