%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GRP491-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 16 22:27:48 EDT 2022

% Result   : Unsatisfiable 0.50s 0.62s
% Output   : Proof 0.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   40
%            Number of leaves      :   40
% Syntax   : Number of formulae    :  175 ( 140 unt;   5 typ;   0 def)
%            Number of atoms       :  208 ( 203 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   59 (  25   ~;  21   |;   0   &)
%                                         (  13 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :   16 (   3 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  101 (  94   !;   0   ?; 101   :)

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

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

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

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

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

tff(1,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( double_divide(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(2,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)],[1]) ).

tff(3,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(4,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(5,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)],[4,3]) ).

tff(6,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)],[5]) ).

tff(7,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)],[6,2]) ).

tff(8,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,a2),double_divide(identity,double_divide(double_divide(double_divide(a2,double_divide(a2,identity)),identity),double_divide(a2,double_divide(a2,identity))))) = a2 ) ),
    inference(quant_inst,[status(thm)],]) ).

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

tff(10,plain,
    ^ [A: $i] :
      refl(
        ( ( identity = double_divide(A,inverse(A)) )
      <=> ( identity = double_divide(A,inverse(A)) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
  <=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

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

tff(13,axiom,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).

tff(14,plain,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    inference(modus_ponens,[status(thm)],[13,12]) ).

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

tff(16,plain,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    inference(modus_ponens,[status(thm)],[15,11]) ).

tff(17,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(18,plain,
    identity = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))),
    inference(unit_resolution,[status(thm)],[17,16]) ).

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

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

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

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

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

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

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

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

tff(27,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(28,plain,
    inverse(double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
    inference(unit_resolution,[status(thm)],[27,26]) ).

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

tff(30,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(31,plain,
    identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[30,16]) ).

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

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

tff(34,plain,
    double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(double_divide(double_divide(a2,identity),identity)),
    inference(transitivity,[status(thm)],[33,29]) ).

tff(35,plain,
    double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(a2,identity),
    inference(monotonicity,[status(thm)],[32]) ).

tff(36,plain,
    double_divide(double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(a2,identity),identity),
    inference(monotonicity,[status(thm)],[35]) ).

tff(37,plain,
    double_divide(double_divide(double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[36,34]) ).

tff(38,plain,
    double_divide(double_divide(double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
    inference(transitivity,[status(thm)],[37,19]) ).

tff(39,plain,
    double_divide(identity,double_divide(double_divide(double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(monotonicity,[status(thm)],[31,38]) ).

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

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

tff(42,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(unit_resolution,[status(thm)],[41,7]) ).

tff(43,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(double_divide(a2,identity),identity),a2)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(44,plain,
    inverse(double_divide(double_divide(double_divide(a2,identity),identity),a2)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),
    inference(unit_resolution,[status(thm)],[43,26]) ).

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

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

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

tff(48,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),inverse(double_divide(double_divide(double_divide(a2,identity),identity),a2))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(49,plain,
    identity = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),inverse(double_divide(double_divide(double_divide(a2,identity),identity),a2))),
    inference(unit_resolution,[status(thm)],[48,16]) ).

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

tff(51,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[50,7]) ).

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

tff(53,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),
    inference(unit_resolution,[status(thm)],[52,7]) ).

tff(54,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(monotonicity,[status(thm)],[31,32]) ).

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

tff(56,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),
    inference(monotonicity,[status(thm)],[55]) ).

tff(57,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),
    inference(transitivity,[status(thm)],[56,51,32,49,47]) ).

tff(58,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),inverse(double_divide(double_divide(double_divide(a2,identity),identity),a2))) = identity,
    inference(symmetry,[status(thm)],[49]) ).

tff(59,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[46,58,31]) ).

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

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

tff(62,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[56,51]) ).

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

tff(64,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),
    inference(transitivity,[status(thm)],[63,61]) ).

tff(65,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))),
    inference(monotonicity,[status(thm)],[64,57]) ).

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

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

tff(68,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(69,plain,
    identity = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))),
    inference(unit_resolution,[status(thm)],[68,16]) ).

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

tff(71,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),
    inference(transitivity,[status(thm)],[70,49,47]) ).

tff(72,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[70,31]) ).

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

tff(74,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),
    inference(transitivity,[status(thm)],[73,61]) ).

tff(75,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))),
    inference(monotonicity,[status(thm)],[74,71]) ).

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

tff(77,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))))),
    inference(transitivity,[status(thm)],[76,67]) ).

tff(78,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(79,plain,
    inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(unit_resolution,[status(thm)],[78,26]) ).

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

tff(81,plain,
    double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[31,80]) ).

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

tff(83,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))))),
    inference(symmetry,[status(thm)],[76]) ).

tff(84,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))))))),
    inference(monotonicity,[status(thm)],[83]) ).

tff(85,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),
    inference(transitivity,[status(thm)],[84,53]) ).

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

tff(87,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[86,7]) ).

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

tff(89,plain,
    identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(unit_resolution,[status(thm)],[88,16]) ).

tff(90,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
    inference(symmetry,[status(thm)],[89]) ).

tff(91,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[80]) ).

tff(92,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),
    inference(transitivity,[status(thm)],[91,90,49,47]) ).

tff(93,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[91,90,31]) ).

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

tff(95,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),
    inference(transitivity,[status(thm)],[94,61]) ).

tff(96,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))),
    inference(monotonicity,[status(thm)],[95,92]) ).

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

tff(98,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),
    inference(symmetry,[status(thm)],[97]) ).

tff(99,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))))),
    inference(monotonicity,[status(thm)],[55,98]) ).

tff(100,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[99,87]) ).

tff(101,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(monotonicity,[status(thm)],[100]) ).

tff(102,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))),identity) = double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[101,55]) ).

tff(103,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),
    inference(monotonicity,[status(thm)],[102,85]) ).

tff(104,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)))))) = identity,
    inference(transitivity,[status(thm)],[103,51,32]) ).

tff(105,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(monotonicity,[status(thm)],[31,104]) ).

tff(106,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))))) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[105,80]) ).

tff(107,plain,
    double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[81,90,31]) ).

tff(108,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)))))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[107,106]) ).

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

tff(110,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))))),identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),
    inference(unit_resolution,[status(thm)],[109,7]) ).

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

tff(112,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),
    inference(transitivity,[status(thm)],[111,108,82]) ).

tff(113,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),inverse(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))))),
    inference(monotonicity,[status(thm)],[112,77]) ).

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

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

tff(116,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(unit_resolution,[status(thm)],[115,7]) ).

tff(117,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))))))),
    inference(symmetry,[status(thm)],[116]) ).

tff(118,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))))),
    inference(transitivity,[status(thm)],[117,114,53]) ).

tff(119,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity),double_divide(double_divide(a2,identity),a2)))))),
    inference(monotonicity,[status(thm)],[55,118]) ).

tff(120,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),
    inference(transitivity,[status(thm)],[119,51,32,49,47]) ).

tff(121,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))),
    inference(monotonicity,[status(thm)],[95,120]) ).

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

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

tff(124,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)))),
    inference(transitivity,[status(thm)],[97,123]) ).

tff(125,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))))),
    inference(monotonicity,[status(thm)],[124]) ).

tff(126,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))))),
    inference(symmetry,[status(thm)],[87]) ).

tff(127,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),inverse(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(128,plain,
    identity = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),inverse(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(unit_resolution,[status(thm)],[127,16]) ).

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

tff(130,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(131,plain,
    inverse(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),
    inference(unit_resolution,[status(thm)],[130,26]) ).

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

tff(133,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)) = identity,
    inference(transitivity,[status(thm)],[46,58]) ).

tff(134,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),
    inference(monotonicity,[status(thm)],[60,133]) ).

tff(135,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))) = inverse(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),
    inference(transitivity,[status(thm)],[134,132]) ).

tff(136,plain,
    identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(transitivity,[status(thm)],[31,126,125,42]) ).

tff(137,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),inverse(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(monotonicity,[status(thm)],[136,135]) ).

tff(138,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(a2,inverse(a2)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(139,plain,
    identity = double_divide(a2,inverse(a2)),
    inference(unit_resolution,[status(thm)],[138,16]) ).

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

tff(141,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(a2) = double_divide(a2,identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(142,plain,
    inverse(a2) = double_divide(a2,identity),
    inference(unit_resolution,[status(thm)],[141,26]) ).

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

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

tff(145,plain,
    double_divide(a2,double_divide(a2,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),
    inference(transitivity,[status(thm)],[144,140,49,47]) ).

tff(146,plain,
    double_divide(a2,double_divide(a2,identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[144,140,31]) ).

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

tff(148,plain,
    double_divide(double_divide(a2,double_divide(a2,identity)),identity) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),
    inference(transitivity,[status(thm)],[147,61]) ).

tff(149,plain,
    double_divide(double_divide(double_divide(a2,double_divide(a2,identity)),identity),double_divide(a2,double_divide(a2,identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),a2),identity))),
    inference(monotonicity,[status(thm)],[148,145]) ).

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

tff(151,plain,
    double_divide(identity,double_divide(double_divide(double_divide(a2,double_divide(a2,identity)),identity),double_divide(a2,double_divide(a2,identity)))) = double_divide(identity,double_divide(double_divide(double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(transitivity,[status(thm)],[150,137,129,31,126,125,42,40]) ).

tff(152,plain,
    double_divide(double_divide(identity,a2),double_divide(identity,double_divide(double_divide(double_divide(a2,double_divide(a2,identity)),identity),double_divide(a2,double_divide(a2,identity))))) = double_divide(double_divide(identity,a2),double_divide(identity,double_divide(double_divide(double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),
    inference(monotonicity,[status(thm)],[151]) ).

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

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

tff(155,plain,
    double_divide(double_divide(identity,a2),double_divide(identity,double_divide(double_divide(double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[154,7]) ).

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

tff(157,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(158,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)],[157]) ).

tff(159,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(160,axiom,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).

tff(161,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(modus_ponens,[status(thm)],[160,159]) ).

tff(162,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(skolemize,[status(sab)],[161]) ).

tff(163,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(modus_ponens,[status(thm)],[162,158]) ).

tff(164,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(identity,a2) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(165,plain,
    multiply(identity,a2) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[164,163]) ).

tff(166,plain,
    multiply(identity,a2) = a2,
    inference(transitivity,[status(thm)],[165,156,153,9]) ).

tff(167,plain,
    ( ( multiply(identity,a2) != a2 )
  <=> ( multiply(identity,a2) != a2 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(168,axiom,
    multiply(identity,a2) != a2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).

tff(169,plain,
    multiply(identity,a2) != a2,
    inference(modus_ponens,[status(thm)],[168,167]) ).

tff(170,plain,
    $false,
    inference(unit_resolution,[status(thm)],[169,166]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP491-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34  % Computer : n007.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Wed Aug 31 17:00:17 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34  Usage: tptp [options] [-file:]file
% 0.14/0.34    -h, -?       prints this message.
% 0.14/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.34    -m, -model   generate model.
% 0.14/0.34    -p, -proof   generate proof.
% 0.14/0.34    -c, -core    generate unsat core of named formulas.
% 0.14/0.34    -st, -statistics display statistics.
% 0.14/0.34    -t:timeout   set timeout (in second).
% 0.14/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34    -<param>:<value> configuration parameter and value.
% 0.14/0.34    -o:<output-file> file to place output in.
% 0.50/0.62  % SZS status Unsatisfiable
% 0.50/0.62  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------