Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : GRP574-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:08:06 AM UTC 2025

% Result   : Unsatisfiable 0.20s 0.54s
% Output   : Proof 0.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   44
% Syntax   : Number of formulae    :  260 ( 221 unt;   0 typ;   0 def)
%            Number of atoms       :  307 ( 302 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   77 (  34   ~;  30   |;   0   &)
%                                         (  13 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :   14 (   2 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  132 ( 125   !;   0   ?; 132   :)

% 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(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
      <=> ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B ) )),
    inference(bind,[status(th)],[]) ).

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

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

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

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

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

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

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

tff(9,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,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(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

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

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

tff(20,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(21,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[20,7]) ).

tff(22,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(23,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)],[22,16]) ).

tff(24,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)],[23]) ).

tff(25,plain,
    ^ [A: $i] :
      refl(( ( inverse(A) = double_divide(A,identity) )
      <=> ( inverse(A) = double_divide(A,identity) ) )),
    inference(bind,[status(th)],[]) ).

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

tff(27,plain,
    ( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
  <=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(28,axiom,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).

tff(29,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(modus_ponens,[status(thm)],[28,27]) ).

tff(30,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(skolemize,[status(sab)],[29]) ).

tff(31,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(modus_ponens,[status(thm)],[30,26]) ).

tff(32,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(33,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)],[32,31]) ).

tff(34,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)],[33]) ).

tff(35,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(36,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[35,7]) ).

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

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

tff(39,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[38,36]) ).

tff(40,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(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)],[39,34]) ).

tff(41,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = identity,
    inference(transitivity,[status(thm)],[40,24]) ).

tff(42,plain,
    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),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,41]) ).

tff(43,plain,
    double_divide(identity,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),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(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)],[42]) ).

tff(44,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[19]) ).

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

tff(46,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[37,45,34]) ).

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

tff(48,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))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[47,24,18]) ).

tff(49,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))),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)],[48,34]) ).

tff(50,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))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = identity,
    inference(transitivity,[status(thm)],[49,24]) ).

tff(51,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,50]) ).

tff(52,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),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),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(transitivity,[status(thm)],[51,43]) ).

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

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

tff(55,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(double_divide(double_divide(a2,identity),identity),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))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(56,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),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))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[55,7]) ).

tff(57,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)) = double_divide(a2,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(58,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)) = double_divide(a2,identity),
    inference(unit_resolution,[status(thm)],[57,7]) ).

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

tff(60,plain,
    inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[59,31]) ).

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

tff(62,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(a2,identity),identity),
    inference(monotonicity,[status(thm)],[19]) ).

tff(63,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(double_divide(a2,identity)),
    inference(transitivity,[status(thm)],[62,61]) ).

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

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

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

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

tff(68,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))),double_divide(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),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[67,44]) ).

tff(69,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))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(a2,identity),
    inference(transitivity,[status(thm)],[68,58]) ).

tff(70,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(a2,inverse(a2)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(71,plain,
    identity = double_divide(a2,inverse(a2)),
    inference(unit_resolution,[status(thm)],[70,16]) ).

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

tff(73,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(a2) = double_divide(a2,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(74,plain,
    inverse(a2) = double_divide(a2,identity),
    inference(unit_resolution,[status(thm)],[73,31]) ).

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

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

tff(77,plain,
    double_divide(a2,double_divide(a2,identity)) = identity,
    inference(transitivity,[status(thm)],[76,72]) ).

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

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

tff(80,plain,
    double_divide(double_divide(double_divide(a2,identity),identity),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))),double_divide(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),double_divide(a2,double_divide(a2,identity))),double_divide(a2,identity)),
    inference(monotonicity,[status(thm)],[79,69]) ).

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

tff(82,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( 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),double_divide(a2,double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity))),double_divide(a2,identity)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(83,plain,
    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),double_divide(a2,double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity))),double_divide(a2,identity)),
    inference(unit_resolution,[status(thm)],[82,7]) ).

tff(84,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),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))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[81,37]) ).

tff(85,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[84,56]) ).

tff(86,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),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)],[85,34]) ).

tff(87,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(a2,double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = identity,
    inference(transitivity,[status(thm)],[86,24]) ).

tff(88,plain,
    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),double_divide(a2,double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,87]) ).

tff(89,plain,
    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),double_divide(a2,double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),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),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(transitivity,[status(thm)],[88,43]) ).

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

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

tff(92,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(monotonicity,[status(thm)],[61]) ).

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

tff(94,plain,
    identity = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
    inference(transitivity,[status(thm)],[18,93]) ).

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

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

tff(97,plain,
    double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(transitivity,[status(thm)],[96,43]) ).

tff(98,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = 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),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[97,37]) ).

tff(99,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(a2,identity),identity),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))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(transitivity,[status(thm)],[98,91,83,81]) ).

tff(100,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(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),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))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[99,44]) ).

tff(101,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = identity,
    inference(transitivity,[status(thm)],[100,56,19]) ).

tff(102,plain,
    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),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,101]) ).

tff(103,plain,
    double_divide(identity,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),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(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)],[102]) ).

tff(104,plain,
    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),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(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))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(transitivity,[status(thm)],[42,103]) ).

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

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

tff(107,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( 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),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(108,plain,
    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),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
    inference(unit_resolution,[status(thm)],[107,7]) ).

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

tff(110,plain,
    double_divide(identity,identity) = identity,
    inference(transitivity,[status(thm)],[95,109,106,54,21,19]) ).

tff(111,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = identity,
    inference(transitivity,[status(thm)],[92,19]) ).

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

tff(113,plain,
    double_divide(double_divide(a2,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(monotonicity,[status(thm)],[112,61]) ).

tff(114,plain,
    double_divide(double_divide(a2,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity)) = identity,
    inference(transitivity,[status(thm)],[113,19]) ).

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

tff(116,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
    inference(monotonicity,[status(thm)],[115,110]) ).

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

tff(118,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(119,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
    inference(unit_resolution,[status(thm)],[118,7]) ).

tff(120,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(121,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[120,7]) ).

tff(122,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(123,plain,
    identity = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity))),
    inference(unit_resolution,[status(thm)],[122,16]) ).

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

tff(125,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

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

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

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

tff(129,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)) = identity,
    inference(transitivity,[status(thm)],[128,124]) ).

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

tff(131,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity))),
    inference(monotonicity,[status(thm)],[130,127]) ).

tff(132,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity)) = identity,
    inference(transitivity,[status(thm)],[131,124]) ).

tff(133,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
    inference(monotonicity,[status(thm)],[19]) ).

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

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

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

tff(137,plain,
    double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[96,45,34]) ).

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

tff(139,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = identity,
    inference(transitivity,[status(thm)],[138,24]) ).

tff(140,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[134,139]) ).

tff(141,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),
    inference(transitivity,[status(thm)],[140,136]) ).

tff(142,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[141,44]) ).

tff(143,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(a2,identity),identity),
    inference(transitivity,[status(thm)],[142,121]) ).

tff(144,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,111]) ).

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

tff(146,plain,
    double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[96,145]) ).

tff(147,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity)),
    inference(monotonicity,[status(thm)],[146,143]) ).

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

tff(149,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(150,plain,
    double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[149,7]) ).

tff(151,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(152,plain,
    identity = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))),
    inference(unit_resolution,[status(thm)],[151,16]) ).

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

tff(154,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(155,plain,
    inverse(double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
    inference(unit_resolution,[status(thm)],[154,31]) ).

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

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

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

tff(159,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[37]) ).

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

tff(161,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity))),double_divide(identity,identity)) = a2 ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(162,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity))),double_divide(identity,identity)) = a2,
    inference(unit_resolution,[status(thm)],[161,7]) ).

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

tff(164,plain,
    double_divide(double_divide(double_divide(a2,identity),identity),identity) = double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),
    inference(symmetry,[status(thm)],[115]) ).

tff(165,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[164,37]) ).

tff(166,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[165,9,163,160]) ).

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

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

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

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

tff(171,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( 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),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(172,plain,
    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),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[171,7]) ).

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

tff(174,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity))) = inverse(double_divide(double_divide(a2,identity),identity)),
    inference(transitivity,[status(thm)],[173,170,158,156]) ).

tff(175,plain,
    double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),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)],[174]) ).

tff(176,plain,
    double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[175,153,18]) ).

tff(177,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),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)],[176,34]) ).

tff(178,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = identity,
    inference(transitivity,[status(thm)],[177,24]) ).

tff(179,plain,
    double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(a2,identity),
    inference(monotonicity,[status(thm)],[19]) ).

tff(180,plain,
    double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(a2),
    inference(transitivity,[status(thm)],[179,75]) ).

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

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

tff(183,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[19,71,182]) ).

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

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

tff(186,plain,
    double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),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),inverse(double_divide(a2,identity))),double_divide(a2,identity)),identity),
    inference(monotonicity,[status(thm)],[185,178]) ).

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

tff(188,plain,
    double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity)),identity),
    inference(monotonicity,[status(thm)],[185,139]) ).

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

tff(190,plain,
    double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[189,44]) ).

tff(191,plain,
    double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(a2,identity),identity),
    inference(transitivity,[status(thm)],[190,150]) ).

tff(192,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity)),
    inference(monotonicity,[status(thm)],[146,191]) ).

tff(193,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(transitivity,[status(thm)],[192,148]) ).

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

tff(195,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(196,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),
    inference(unit_resolution,[status(thm)],[195,7]) ).

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

tff(198,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(a2,double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(199,plain,
    double_divide(double_divide(a2,double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),
    inference(unit_resolution,[status(thm)],[198,7]) ).

tff(200,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(201,plain,
    double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[200,7]) ).

tff(202,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(203,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
    inference(unit_resolution,[status(thm)],[202,7]) ).

tff(204,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( 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),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(205,plain,
    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),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),
    inference(unit_resolution,[status(thm)],[204,7]) ).

tff(206,plain,
    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),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[37]) ).

tff(207,plain,
    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),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[206,205]) ).

tff(208,plain,
    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),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[207,44]) ).

tff(209,plain,
    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),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
    inference(transitivity,[status(thm)],[208,203]) ).

tff(210,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)],[19]) ).

tff(211,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)],[210,156]) ).

tff(212,plain,
    double_divide(double_divide(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)],[211]) ).

tff(213,plain,
    double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(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)],[212]) ).

tff(214,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(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)],[19,152,213]) ).

tff(215,plain,
    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),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(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),identity)),
    inference(monotonicity,[status(thm)],[214,209]) ).

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

tff(217,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity))) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
    inference(transitivity,[status(thm)],[173,170,158]) ).

tff(218,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))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),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),identity)),
    inference(monotonicity,[status(thm)],[214,217]) ).

tff(219,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))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(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),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(transitivity,[status(thm)],[218,216]) ).

tff(220,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))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),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),inverse(double_divide(a2,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),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[219,44]) ).

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

tff(222,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B )
    | ( 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),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,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),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(223,plain,
    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),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,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),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(unit_resolution,[status(thm)],[222,7]) ).

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

tff(225,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[37]) ).

tff(226,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),
    inference(transitivity,[status(thm)],[225,203,164]) ).

tff(227,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[226,44]) ).

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

tff(229,plain,
    a2 = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[9]) ).

tff(230,plain,
    a2 = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),
    inference(transitivity,[status(thm)],[229,228]) ).

tff(231,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2) = 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),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(monotonicity,[status(thm)],[230]) ).

tff(232,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2) = 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))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)),
    inference(transitivity,[status(thm)],[231,224,221]) ).

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

tff(234,plain,
    double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[233,44]) ).

tff(235,plain,
    double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = identity,
    inference(transitivity,[status(thm)],[234,201,19]) ).

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

tff(237,plain,
    double_divide(a2,identity) = double_divide(a2,double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(symmetry,[status(thm)],[236]) ).

tff(238,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[37]) ).

tff(239,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(a2,double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
    inference(transitivity,[status(thm)],[238,58,237]) ).

tff(240,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),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(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,double_divide(double_divide(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),a2)),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(identity,identity)),
    inference(monotonicity,[status(thm)],[239,44]) ).

tff(241,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),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))),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,identity)),
    inference(symmetry,[status(thm)],[21]) ).

tff(242,plain,
    identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(transitivity,[status(thm)],[18,241,53,105,108,96,45]) ).

tff(243,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(symmetry,[status(thm)],[238]) ).

tff(244,plain,
    double_divide(a2,identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[58]) ).

tff(245,plain,
    double_divide(a2,identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(transitivity,[status(thm)],[244,243]) ).

tff(246,plain,
    double_divide(double_divide(a2,identity),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),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(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)],[245,242]) ).

tff(247,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(248,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)],[247]) ).

tff(249,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(250,axiom,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).

tff(251,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(modus_ponens,[status(thm)],[250,249]) ).

tff(252,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(skolemize,[status(sab)],[251]) ).

tff(253,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(modus_ponens,[status(thm)],[252,248]) ).

tff(254,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(255,plain,
    multiply(identity,a2) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[254,253]) ).

tff(256,plain,
    multiply(identity,a2) = a2,
    inference(transitivity,[status(thm)],[255,246,240,199,197,194,119,117,9]) ).

tff(257,plain,
    ( ( multiply(identity,a2) != a2 )
  <=> ( multiply(identity,a2) != a2 ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(258,axiom,
    multiply(identity,a2) != a2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).

tff(259,plain,
    multiply(identity,a2) != a2,
    inference(modus_ponens,[status(thm)],[258,257]) ).

tff(260,plain,
    $false,
    inference(unit_resolution,[status(thm)],[259,256]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP574-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.12  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Jun 19 16:19:24 EDT 2025
% 0.13/0.34  % CPUTime    : 
% 0.20/0.54  % SZS status Unsatisfiable
% 0.20/0.54  % SZS output start Proof
% See solution above
% 0.44/0.61  % E exiting
%------------------------------------------------------------------------------